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https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book	Series ISSN: 1939-5221 Series ISSN: 1939-5221 Series ISSN: 1939-5221 SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING Series Editor: Steven F. Barrett, University of Wyoming Series Editor: Steven F. Barrett, University of Wyoming Series Editor: Steven F. Barrett, University of Wyoming Fundamentals of Engineering Fundamentals of Engineering Fundamentals of Engineering Economics and Decision Analysis Economics and Decision Analysis Economics and Decision Analysis David L. Whitman, University of Wyoming David L. Whitman, University of Wyoming David L. Whitman, University of Wyoming Ronald E. Terry, Brigham Young University Ronald E. Terry, Brigham Young University Ronald E. Terry, Brigham Young University The authors cover two general topics: basic engineering economics and risk analysis in this text. Within The authors cover two general topics: basic engineering economics and risk analysis in this text. Within The authors cover two general topics: basic engineering economics and risk analysis in this text. Within the topic of engineering economics are discussions on the time value of money and interest relationships. the topic of engineering economics are discussions on the time value of money and interest relationships. the topic of engineering economics are discussions on the time value of money and interest relationships. These interest relationships are used to deﬁne certain project criteria that are used by engineers and These interest relationships are used to deﬁne certain project criteria that are used by engineers and These interest relationships are used to deﬁne certain project criteria that are used by engineers and project managers to select the best economic choice among several alternatives. Projects examined will project managers to select the best economic choice among several alternatives. Projects examined will project managers to select the best economic choice among several alternatives. Projects examined will include both income-and service-producing investments. The effects of escalation, inﬂation, and taxes include both income-and service-producing investments. The effects of escalation, inﬂation, and taxes include both income-and service-producing investments. The effects of escalation, inﬂation, and taxes on the economic analysis of alternatives are discussed. Risk analysis incorporates the concepts of probability on the economic analysis of alternatives are discussed. Risk analysis incorporates the concepts of probability on the economic analysis of alternatives are discussed. Risk analysis incorporates the concepts of probability and statistics in the evaluation of alternatives. This allows management to determine the probability of and statistics in the evaluation of alternatives. This allows management to determine the probability of and statistics in the evaluation of alternatives. This allows management to determine the probability of success or failure of the project. Two types of sensitivity analyses are presented.The ﬁrst is referred to as success or failure of the project. Two types of sensitivity analyses are presented.The ﬁrst is referred to as success or failure of the project. Two types of sensitivity analyses are presented.The ﬁrst is referred to as the range approach while the second uses probabilistic concepts to determine a measure of the risk the range approach while the second uses probabilistic concepts to determine a measure of the risk the range approach while the second uses probabilistic concepts to determine a measure of the risk involved. The authors have designed the text to assist individuals to prepare to successfully complete the involved. The authors have designed the text to assist individuals to prepare to successfully complete the involved. The authors have designed the text to assist individuals to prepare to successfully complete the economics portions of the Fundamentals of Engineering Exam. economics portions of the Fundamentals of Engineering Exam. economics portions of the Fundamentals of Engineering Exam. About SYNTHESIs About SYNTHESIs About SYNTHESIs This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development provide concise, original presentations of important research and development provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com visit www.morganclaypool.com visit www.morganclaypool.com Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers & & & ISBN: 978-1-60845-864-6 ISBN: 978-1-60845-864-6 ISBN: 978-1-60845-864-6 90000 90000 90000 w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m 9 78 1 608 458646 9 78 1 608 458646 9 78 1 608 458646 W W W H H H I I I T T T M M M A A A N N N • • • T E R R Y T E R R Y T E R R Y F F F U U U N N N D D D A A A M M M E E E N N N T T T A A A L L L S S S O O O F F F E E E N N N G G G I I I N N N E E E E E E R R R I I I N N N G G G E E E C C C O O O N N N O O O M M M I I I C C C S S S A A A N N N D D D D D D E E E C C C I I I S S S I I I O O O N N N A A A N N N A A A L L L Y Y Y S S S I I I S S S M M M o o o r r r g g g a a a n n n & & & C C C l l l a a a y y y p p p o o o o o o l l l CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers & & & Fundamentals of Fundamentals of Fundamentals of Engineering Economics Engineering Economics Engineering Economics and Decision Analysis and Decision Analysis and Decision Analysis David Whitman David Whitman David Whitman Ronald E. Terry Ronald E. Terry Ronald E. Terry SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING Steven F. Barrett, Series Editor Steven F. Barrett, Series Editor Steven F. Barrett, Series Editor Fundamentals of Engineering Economics and Decision Analysis Synthesis Lectures on Engineering Editor Steven S. Barrett, University of Wyoming Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 iii Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2012 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry www.morganclaypool.com ISBN: 9781608458646 paperback ISBN: 9781608458653 ebook DOI 10.2200/S00410ED1V01Y201203ENG018 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #18 Series Editor: Steven S. Barrett, University of Wyoming Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X Fundamentals of Engineering Economics and Decision Analysis David L. Whitman University of Wyoming Ronald E. Terry Brigham Young University SYNTHESIS LECTURES ON ENGINEERING #18 CM& Morgan & cLaypool publishers ABSTRACT The authors cover two general topics: basic engineering economics and risk analysis in this text. Within the topic of engineering economics are discussions on the time value of money and interest relationships. These interest relationships are used to deﬁne certain project criteria that are used by engineers and project managers to select the best economic choice among several alternatives. Projects examined will include both income- and service-producing investments. The effects of escalation, inﬂation, and taxes on the economic analysis of alternatives are discussed. Risk analysis incorporates the concepts of probability and statistics in the evaluation of alternatives. This allows management to determine the probability of success or failure of the project. Two types of sensitivity analyses are presented.The ﬁrst is referred to as the range approach while the second uses probabilistic concepts to determine a measure of the risk involved. The authors have designed the text to assist individuals to prepare to successfully complete the economics portions of the Fundamentals of Engineering Exam. KEYWORDS engineering economics, time value of money, net present value, internal rate of return, cash ﬂow analysis, probability, statistics, risk analysis vii To our parents, wives, children, and grandchildren with much love and gratitude for everything. Contents ix 1 2 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Engineering Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Basic Engineering Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Fundamentals of Engineering Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Interest and the Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 2.2 2.3 2.4 2.5 2.6 Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Sources of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Interest Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.2 Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.3 Nominal, Effective, and Continuous Interest Rates . . . . . . . . . . . . . . . . . . . . 5 Cash Flow Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Interest Formulas for Discrete Compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5.1 Single Payments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.2 Uniform Series (Annuities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5.3 Uniform Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.4 The use of Financial Functions in Excel® . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.5 Example Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Interest Formulas for Continuous Compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6.1 Continuous Compounding for Discrete Payments . . . . . . . . . . . . . . . . . . . . 19 2.6.2 Continuous Compounding for Continuous Payments . . . . . . . . . . . . . . . . . 19 2.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Project Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Alternate Uses of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 x 4 5 3.3 Minimum Acceptable Rate of Return (MARR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 3.5 3.6 3.7 3.8 3.9 Equivalence Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Net Present Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5.1 Analysis of a Single Investment Opportunity . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5.2 Do Nothing Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.3 Analysis of Multiple Investment Opportunities . . . . . . . . . . . . . . . . . . . . . . 30 Rate of Return Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.1 Internal Rate of Return (IRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.2 Spreadsheet Formula for IRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.6.3 External Rate of Return (ERR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.6.4 Spreadsheet Formula for ERR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 The Reinvestment Question in Rate of Return Calculations . . . . . . . . . . . . . . . . . . 37 3.7.1 Perception #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.7.2 Perception #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.7.3 Final Comments on ERR and IRR Relationships . . . . . . . . . . . . . . . . . . . . 41 Acceleration Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Payout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Service Producing Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1 4.2 4.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Equal Life Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.1 Equivalence Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.2 Rate of Return Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Unequal Life Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.1 Least Common Multiple Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.2 Common Study Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Income Producing Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1 5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Investment in a Single Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3 Mutually Exclusive Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.1 Equivalence Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.2 Rate of Return Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.3.3 Using Excel® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.4 5.5 5.6 5.7 Unequal Life Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Independent and Contingent Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.1 Independent Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.2 Contingent Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.3 Limited Investment Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Ranking Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 xi 6 Determination of Project Cash Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.1 6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Escalation and Inﬂation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.3.1 Straight-Line Depreciation (SL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.3.2 Declining-Balance Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.3 Sum-of-the-Years-Digits (SYD) Depreciation . . . . . . . . . . . . . . . . . . . . . . . 97 6.3.4 Modiﬁed Accelerated Cost Recovery System (MACRS) . . . . . . . . . . . . . 102 6.4 Cash Flow Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.1 Capital Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.2 Gross Revenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.3 Operating Expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.4 Before-Tax Proﬁt Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.5 Before-Tax Cash Flow Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.6 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.4.7 Taxable Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.4.8 State and Federal Income Tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.4.9 Net Proﬁt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4.10 Cash Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7 Financial Leverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.1 7.2 7.3 7.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Financial Leverage and Associated Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Adjustment to Cash Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3.1 Leverage and Mutually Exclusive Projects . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.3.2 Excel® Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 xii 8 Basic Statistics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.1 8.2 8.3 8.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2.1 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2.2 Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 8.2.3 Frequency Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8.2.4 Relative Frequency Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.3.1 Classical Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.3.2 Relative Frequency Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.3.3 Subjective Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.3.4 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 9 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.1 9.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.1.1 Range Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.1.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A Compound Interest Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 xiii Preface Those individuals working on the development of an income-generating project, either for personal use or company use, are frequently called upon to determine if the endeavor will prove proﬁtable if fully developed. By proﬁtable, we simply mean that the project will provide a desirable rate of return on investment through the generation of revenue that offsets any capital and/or operating costs. The intent of this book is to provide individuals with the tools to evaluate projects to determine proﬁtability.The subject has been called: Engineering Economics or Project Evaluation or Economic Evaluation or Decision Analysis. Whatever one chooses to call it, the reader who studies this material and becomes proﬁcient in its content, will be able to analyze project cash ﬂows and make a decision as to the proﬁtability of the project. The authors, mainly because of their engineering backgrounds, have chosen to refer to the subject matter as engineering economics. In addition to income-generating projects, this book will also assist those individuals who are analyzing two or more ways of doing a service-producing project. A service-producing project is one, that instead of generating income for the investor, provides a service at a cost to the investor. An example could be the renting versus purchasing of a vehicle to provide a needed service for a company. The authors cover two general topics: basic engineering economics and risk analysis in the text. Chapters 2-6 contain content relative to basic engineering economics and Chapters 7-9 present material on risk analysis. Within the topic of engineering economics are discussions on the time value of money and interest relationships. These interest relationships are used to deﬁne certain project criteria that are used by engineers and project managers to select the best economic choice among several alterna- tives. Projects examined will include both income and service producing investments. The effects of escalation, inﬂation, and taxes on the economic analysis of alternatives are discussed. There is always risk involved in undertaking a project. Risk analysis incorporates the concepts of probability and statistics in the evaluation of alternatives. This allows management to determine the probability of success or failure of the project. Two types of sensitivity analyses are presented. The ﬁrst is referred to as the range approach while the second uses probabilistic concepts to determine a measure of the risk involved. The authors have designed the text to assist individuals to prepare to successfully complete the economics portions of the Fundamentals of Engineering Exam. xiv PREFACE The authors wish to thank Joel Claypool and his associates at Morgan & Claypool for their encouragement and excellent work on the preparation and production of this text. David L. Whitman and Ronald E. Terry May 2012 C H A P T E R 1 Introduction 1 1.1 ENGINEERING ECONOMICS Nearly all projects that are proposed to be undertaken by any engineering ﬁrm will be, at some point, subjected to close economic scrutiny. The results of this analysis will be a basis (perhaps one of many) for deciding whether or not to proceed with the project. The major emphasis of this text, therefore, is to provide the engineer with the tools necessary to make the aforementioned economic decision. There are two general topics which are included in this textbook: basic engineering economics and risk analysis. A very brief overview of each of these topics is presented in the following paragraphs. 1.1.1 BASIC ENGINEERING ECONOMICS Within this topic are discussions on the time value of money and interest relationships. These interest relationships are used to deﬁne certain project criteria that are used by engineers and project managers to select the best economic choice among several alternatives. Projects examined will include traditional projects that generate a proﬁt for the company and service producing projects which do not provide income, but do provide a needed service. The effects of escalation, inﬂation, and taxes on the economic analysis of alternatives will be discussed. 1.1.2 RISK ANALYSIS There is always risk involved in undertaking a project. Management is interested in the quantiﬁcation of that risk. Risk analysis incorporates the concepts of probability and statistics in the evaluation of alternatives. This allows management to determine the probability of success or failure of the project. While there are a variety of ways to incorporate risk analysis into the evaluation of a project, the authors will present two methods that utilize what is known as sensitivity analysis. That is, deter- mining the sensitivity of the economic viability of a project as the costs and/or incomes vary about estimated values. The ﬁrst is referred to as the range approach, while the second uses probabilistic concepts to determine a measure of the risk involved. 1.2 DECISION ANALYSIS As described above, the overall objective of any economic analysis is to provide a basis for making a sound decision regarding any particular project. For example, suppose that an engineer is given the assignment to implement a project for which there are multiple alternative methods that will achieve the goals of the project. The question is: which alternative should be chosen? The reader 2 1. INTRODUCTION should recognize that there is always a choice among two or more alternatives. However, if only one technical alternative is found, then that alternative must be compared with the “do nothing” case. The “do nothing” case represents the situation where a company keeps its money invested in other alternatives which earn some minimum rate of return. The minimum rate of return will be referred to as the minimum acceptable rate of return (MARR) and will be discussed in detail in Chapter 2. Thus, there are always at least two alternatives in any economic decision. This textbook will provide the engineer with the necessary tools to determine the “best” economic choice among the alternatives. However, one must realize that ﬁnal decisions are not only made on the results of the economic evaluations. Other general areas of consideration could be classiﬁed as ﬁnancial and intangible issues. The “best” economic choice will be made through the proper use of the time value of money formulas that will be presented. Financial aspects have to do with the obtaining of funds required to initiate the project. There are several sources which may be considered, i.e., internal company funds, lending institutions, the issuing of bonds, or the issuing of new stock. The intangible area of a project is the most difﬁcult to analyze. Included in the intangible aspects are environmental, social, and political impacts. These are the most difﬁcult to quantify. The focus of this textbook will be on the economic aspects of a project and very little time will be devoted to the areas of ﬁnancial and intangible aspects. However, they are alluded to from time to time in order to remind the engineer of their importance and the obligation to consider them in the ﬁnal decision. 1.3 FUNDAMENTALS OF ENGINEERING EXAM It is envisioned that information found in this textbook will prepare students to successfully complete the economics portions of the Fundamentals of Engineering Exam. The speciﬁcations for this exam can be found at http://www.ncees.org/Exams/FE_exam.php. C H A P T E R 2 3 Interest and the Time Value of Money 2.1 TIME VALUE OF MONEY When an individual or a company desires to invest an amount of capital in a long-term project, the effect of time on the value of that capital needs to be considered. The effect of time on the value of money can be illustrated by the following examples. Consider a sum of $1000 that an individual has accumulated. If the $1000 were buried in a can under a tree for some future need, the individual, one year later, would still have $1000. However, if the $1000 were placed in an insured savings account earning 3% interest for one year, the amount would have grown to $1030. Obviously, the length of time and the different investment opportunities (represented by different interest rates) lead to varying amounts of money that the $1000 can yield at some future date. A second example deals with the same $1000 and its purchasing power as a function of time. Suppose an individual has a choice of purchasing 1000 items now at a price of $1.00 per item or waiting until a future date to make the purchase. If, over the course of one year, the price increased to $1.03 per item, the $1000 will only be able to purchase 970 items. Thus, the value, in terms of purchasing power, has decreased with time. The longer the life of the project, the more important will be the considerations of the time value of money. Other factors that affect the outcome of investment projects are inﬂation, taxes, and risk. These will be discussed later in the text. 2.2 SOURCES OF CAPITAL There are, in general, two sources of capital needed to make an investment. Capital can be obtained either from the investor’s own funds or from a lender. Wherever capital is obtained, there is a cost associated with the use of the funds. If they are obtained from a lender, the cost of capital is the interest rate at which the funds are loaned to the investor. This interest rate reﬂects the current state of the economy as a whole, the bank’s administrative costs, and, perhaps, the risk associated with the particular loan as viewed by the lender. If the investor chooses to use his own funds for the required capital, then the cost is called the opportunity cost of capital. The opportunity cost reﬂects the income that could be generated from other opportunities the investor might have for his funds. This opportunity cost is often referred to as the minimum acceptable rate of return 4 2. INTEREST AND THE TIME VALUE OF MONEY (MARR). This minimum acceptable rate of return could be the interest rate obtained by placing the funds in a certiﬁcate of deposit or savings account at a bank or it could be the rate of return on another investment opportunity.The MARR is an important concept in the evaluation of investment opportunities and will be discussed in Chapter 3. For now, the MARR will just be treated as an interest rate, i. 2.3 2.3.1 INTEREST CONCEPTS SIMPLE INTEREST The amount of interest earned by an investment (for example, a single principal deposit in a savings account) is called simple interest when the interest is found by Equation 2.1: I = P in (2.1) where, I = total interest, dollars P = amount of principal, dollars i = interest rate per interest period, fraction n = number of interest periods. Consider the following example. Individual A agrees to loan individual B $1000 for a time period of 3 years. B agrees to pay A the $1000 at the end of the 3 years, plus an amount of interest determined by applying a simple interest rate of 10% per year. The total interest charge will be: I = (1000)(0.10)(3) = $300 Therefore, at the end of 3 years, B will pay a total of $1300 to A which would represent the $1000 initially borrowed plus $300 interest for the use of A’s money. 2.3.2 COMPOUND INTEREST Simple interest concepts are used infrequently in today’s business dealings, but they do provide the basis for compounded interest rate concepts that are utilized. Compounded interest is computed by applying the interest rate to the remaining unpaid principal plus any accumulated interest. One could consider it as “the interest earns interest.” Referring back to the example presented above, the total interest that B will pay A over 3 years would be calculated as the following: Iyr 1 = (1000)(0.1) = $100, which would result in a balance at the end of year 1 of $1100 Iyr 2 = (1100)(0.1) = $110, which would result in a balance at the end of year 2 of $1210 Iyr 3 = (1210)(0.1) = $121, which would result in a balance at the end of year 3 of $1331 Therefore, at the end of 3 years, B will pay a total of $1331 to A which is $31 higher than for the simple interest case. This difference results from compounding the interest. One should note that the difference between these two methods will become larger as the interest rate and number of interest periods increase. 2.3. INTEREST CONCEPTS 5 2.3.3 NOMINAL, EFFECTIVE, AND CONTINUOUS INTEREST RATES The length of the interest period can and does vary from application to application. Common interest rate periods are annually, semi-annually, quarterly, monthly, daily, and in the limiting case, continuously. The amount of interest that is earned or charged to a principal will increase as the compounding period becomes smaller. Usually, a lending institution will quote a nominal annual percentage rate. However, payments on the loan are made more often than annually. For example, consider a loan that is quoted at 10% nominal with semi-annual compounding (and, thus, semi-annual payments). The 10% annual interest compounded semi-annually means that every one-half year, 5% interest is earned or charged to the principal. This leads to the concept of effective yearly interest rate. The effective yearly interest rate can be found by computing the value that the principal has grown to at the end of year one, F , subtracting the original principal, and then dividing by the principal: F = 1000 + 1000(.05) + (1000 + 1000(.05))(.05) = 1000(1.05)2 Therefore, the effective rate is: ie = (1000(1.05)2 − 1000)/1000 = 0.1025 or 10.25% per year In general, the effective rate can be found by: (cid:2) ie = (cid:3) m − 1 1 + i m where, m = number of interest periods per year i = yearly nominal interest rate, fraction ie = yearly effective interest rate, fraction. In the limiting case of continuous compounding, the effective rate is given by: ie = ei − 1 (2.2) (2.3) Table 2.1 lists the effective rates for various compounding time periods for a 10% nominal rate. As can be observed in Table 2.1, the difference between the effective rates generated by the various compounding periods is relatively small. The differences can become insigniﬁcant when considering the many uncertainties associated with analyzing most economic investments. One should be careful with the term Annual Percentage Rate (APR) when dealing with lending institutions. The APR is a yearly percentage rate that expresses the total ﬁnance charge on a loan over its entire term. The APR includes the nominal interest rate, fees, points, and mortgage insurance, and is therefore a more complete measure of a loan’s cost than the interest rate alone. The loan’s nominal interest rate, not its APR, is used to calculate the monthly principal and interest payment. 6 2. INTEREST AND THE TIME VALUE OF MONEY Table 2.1: Example of effective interest rates for compounding time periods 2.4 CASH FLOW DIAGRAMS The construction of a cash ﬂow diagram, sometimes referred to as a time line, will greatly aid in the analysis of an investment opportunity. The cash ﬂow diagram is a way of accounting for all cash incomes and outﬂows at their appropriate position in time. That is, in general terms, the cash ﬂow for any particular period is the income received during that period minus the expenses incurred during that same period. A good analogy to a cash ﬂow diagram is one’s checkbook. Deposits and checks are written at speciﬁc points in time. These transactions could be consolidated on a monthly basis to show the net cash ﬂow in or out of the checkbook each month. Usually, once the cash ﬂow diagram is constructed properly, the economic analysis becomes relatively easy to complete. There are several ways of constructing a cash ﬂow diagram and the following method is utilized by the authors. A horizontal line is drawn which represents the length of time (life) of the investment opportunity (project). The interest periods are then marked off and labeled above the line. At the extreme left of the time line is time zero (or, as will be deﬁned in the next section, the Present). Time zero represents the time when the ﬁrst cash ﬂow is made for this project. Time zero is, therefore, deﬁned by each project and not by a speciﬁc calendar date. Time zero can also be interpreted as the beginning of time period 1. All cash ﬂows are then placed beneath the time line, corresponding to the position in time (or interest periods) in which they occurred. Negative cash ﬂows (expenses exceeding revenues) are given a minus sign. In the time line illustrated below, CF1, CF2, etc., represent the cash ﬂows occurring at the end of interest period 1, 2, etc. The authors often use a break in the time line for brevity. When dealing with investments in engineering projects, the normal approach is to assume that all investments for a particular year are made at the beginning of the year, while all revenues and operating expenses occur at the end of the year. This will lead to a conservative evaluation of the project using the techniques presented in Chapter 3. 0 1 2 3 CF0 CF1 CF2 CF3 … … 2.4. CASH FLOW DIAGRAMS 7 n-2 n-1 n CFn-2 CFn-1 CFn Example 2.1 Consider the example of a 3-year auto loan from the view of the lender. The lender provides $20,000 to the client (a negative cash ﬂow for the lender) at month 0 at an interest rate of 0.5% per month. In exchange, the lender receives $608 per month from the client over the next 36 months. The resulting cash ﬂow diagram would be: 0 1 2 3 … 34 35 36 -20,000 608 608 608 ... 608 608 608 Before equations can be developed that relate the time value of money, it is necessary to deﬁne a set of notations that will be used throughout the text. P = Present sum of money. The present (time zero) is deﬁned as any point from which the analyst wishes to measure time. F = Future sum of money. The future is deﬁned as any point n that is greater than time zero. A = Annuity. This is a uniform set of equal payments that occur at the end of each interest period from one to n. G = Uniform gradient. This is a series of payments that uniformly increase or decrease over the life of the project. i = Compound interest rate per period. n = Total number of compounding periods in the cash ﬂow diagram. The cash ﬂow diagrams that follow should help to deﬁne these sums of money. 8 2. INTEREST AND THE TIME VALUE OF MONEY Present, P : 0 1 2 3 … n-2 n-1 n P Future, F : 0 1 2 3 … n-2 n-1 n Annuity, A: 0 1 2 3 … n-2 n-1 n F A Gradient, G: 0 1 A 2 A 3 … … A A n-2 n-1 A n G 2G … (n-3)G (n-2)G (n-1)G 2.5 INTEREST FORMULAS FOR DISCRETE COMPOUNDING The following section contains the derivation and sample calculations for nine interest formulas used in most economic calculations. These formulas demonstrate the “equivalency” between the various 2.5. INTEREST FORMULAS FOR DISCRETE COMPOUNDING 9 sums of money described above at speciﬁc values of the interest rate, i, and the number of periods, n. For example, in the example of the 3-year car loan, the $608 monthly payment is “equivalent” to the $20,000 initial loan at an interest rate of 0.5% per month. These formulas are based on discrete compounding, i.e., the interest is compounded at the end of each ﬁnite interest period. Formulas used with continuous compounding will be presented later. SINGLE PAYMENTS 2.5.1 The ﬁrst formula to be derived allows the calculation of the equivalent future amount F , of a present sum, P . Suppose P is placed in a bank account that earns i% interest per period. It will grow to a future amount, F , at the end of n interest periods according to: F = P (1 + i)n (2.4) The derivation of Equation 2.4 is given by: The factor (1 + i)n is frequently called the Single Payment Compound Amount Factor and is symbolized in this text by (F /P )i,n. If one is given the amount of P , one uses the (F /P )i,n factor to ﬁnd the equivalent value of F . That is, F = P (F /P )i,n (2.5) Similarly, if a future amount, F , is known and it is desired to calculate the equivalent present amount, P , then Equation 2.4 can be arranged as: P = F (1 + i) −n (2.6) The factor (1 + i)−n is frequently called the Single Payment Present Worth Factor and is symbolized in this text by (P /F )i,n. If one is given the amount of F , one uses the (P /F )i,n factor to ﬁnd the equivalent value of P . That is, P = F (P /F )i,n (2.7) 10 2. INTEREST AND THE TIME VALUE OF MONEY 2.5.2 UNIFORM SERIES (ANNUITIES) It is often necessary to know the amount of a uniform series payment, A, which would be equivalent to a present sum, P , or a future sum, F . In the following formulas that relate P , F , and A, it is imperative that the reader understands that: 1) P occurs one interest period before the ﬁrst value of A; 2) A occurs at the end of each interest period; and 3) F occurs at the same time as the last A (at time n). These relationships were illustrated in the previous cash ﬂow diagrams that originally deﬁned each of them. The value of a future sum, F , of a series of uniform payments, each of value A, can be found by summing the future worth of each individual payment. That is, treat each A as a distinct present value (but with a different time zero) and use (F /P )i,n to calculate its contribution to the total F : F = A(1 + i)n−1 + A(1 + i)n−2 + A(1 + i)n−3 + . . . + A(1 + i)1 + A (2.8) Multiplying both sides of Equation 2.8 by (1 + i) yields F (1 + i) = A(1 + i)n + A(1 + i)n−1 + A(1 + i)n−2 + . . . + A(1 + i)2 + A(1 + i) (2.9) Subtracting Equation 2.8 from 2.9 yields F (1 + i) − F = A(1 + i)n − A Solving for F in terms of A results in: F = A{[(1 + i)n − 1]/i} (2.10) The term in the {} brackets is called the Uniform Series Compound Amount Factor and is symbolized by (F /A)i,n. If one is given the amount of A, one uses the (F /A)i,n factor to ﬁnd the equivalent value of F . That is, Rearranging Equation 2.10 and solving for A yields F = A(F /A)i,n A = F {i/[(1 + i)n − 1]} (2.11) (2.12) The term in the { } brackets is called the Sinking Fund Factor and is symbolized by (A/F )i,n. If one is given the amount of F , one uses the (A/F )i,n factor to ﬁnd the equivalent value of A. That is, A = F (A/F )i,n (2.13) Substitution of Equation 2.10 into Equation 2.6 yields Equation 2.14 which contains the Uniform Series Present Worth Factor, (P /A)i,n in the {} brackets: P = A{[(1 + i)n − 1]/[i(1 + i)n]} (2.14) (2.15) (2.16) (2.17) 2.5. INTEREST FORMULAS FOR DISCRETE COMPOUNDING 11 If one is given the amount of A, one uses the (P /A)i,n factor to ﬁnd the equivalent value of P . That is, P = A(P /A)i,n Rearranging Equation 2.14 and solving for A yields A = P {[i(1 + i)n]/[(1 + i)n − 1]} The term in the { } brackets is called the Capital Recovery Factor and is symbolized by (A/P )i,n. If one is given the amount of P , one uses the (A/P )i,n factor to ﬁnd the equivalent value of A. That is, A = P (A/P )i,n 2.5.3 UNIFORM GRADIENT In some applications, a series of cash ﬂows will be generated from a project analysis which uniformly increase or decrease from an initial value. The cash ﬂow diagram is repeated here for clarity. 0 1 2 3 G 2G … … n-2 n-1 n (n-3)G (n-2)G (n-1)G Without derivation, Equations 2.18, 2.20, and 2.22 can be developed that relate the gradient, G, to an equivalent annuity, an equivalent present sum, and an equivalent future sum: A = G{1/i − n/[(1 + i)n − 1]} (2.18) The term in the { } brackets is symbolized by (A/G)i,n. If one is given the amount of G, one uses the (A/G)i,n factor to ﬁnd the equivalent value of A. That is, A = G(A/G)i,n P = G{[(1 + i)n − 1]/[i2(1 + i)n] − n/[i(1 + i)n]} (2.19) (2.20) The term in the { } brackets is symbolized by (P /G)i,n. If one is given the amount of G, one uses the (P /G)i,n factor to ﬁnd the equivalent value of P . That is, P = G(P /G)i,n F = G{[(1 + i)n − 1]/i2 − n/i} (2.21) (2.22) The term in the { } brackets is symbolized by (F /G)i,n. If one is given the amount of G, one uses the (F /G)i,n factor to ﬁnd the equivalent value of F . That is, F = G(F /G)i,n (2.23) 12 2. INTEREST AND THE TIME VALUE OF MONEY The equations for the nine factors are given in Table 2.2 and numerical values are tabulated in Appendix A for various values of interest rate, i, and number of periods, n so that the user can look them up rather than use the actual formulas. Rather than memorizing which factor is needed for a speciﬁc equivalency, think about the formulas in terms of “units conversion.” That is, if the input to a system has units of X and the output of that system has units of Y, the system provides a units conversion of (Y/X). Thus, if one is given A (input) and wants to ﬁnd G (output), the correct formula to use would be (G/A). Knowing the value of the interest rate and the number of periods, one can look up or compute the value of the formula. Table 2.2: Formulas for discrete compounding Factor Name Converts Single Payment Compound Amount to F given P Symbol (F / P) i,n Single Payment Present Worth to P given F (P / F) i,n Uniform Series Compound Amount to F given A (F / A) i,n Uniform Series Sinking Fund Uniform Series Present Worth to A given F (A / F) i,n to P given A (P / A) i,n Capital Recovery to A given P (A/ P) i,n Uniform Gradient Present Worth Uniform Gradient Future Value Uniform Gradient Uniform Series to P given G (P/ G) i,n to F given G (F / G) i,n to A given G (A / G)i,n Formula (1 + i) n (1 + i) -n -1n (1 + i) i i (1 + i) -1n (1 + i) i (1 + i) -1n n n i (1 + i) (1 + i) -1n (1 + i) 2 i (1 + i) -1n n - n (1 + i) i n -1n (1 + i) 2 i - n i 1 - i n (1 + i) -1n 2.5. INTEREST FORMULAS FOR DISCRETE COMPOUNDING 13 2.5.4 THE USE OF FINANCIAL FUNCTIONS IN EXCEL® Many cash ﬂow situations can be simulated by using a spreadsheet such as Microsoft Excel®. This will become more evident in future chapters, but this chapter presents the following useful ﬁnancial functions: Future Value: =FV(rate, nper, pmt, pv, type) Present Value: =PV(rate, nper, pmt, fv, type) Annuity: =PMT(rate, nper, pv, fv, type) Unfortunately, Excel® does not have a built-in function for gradient-type cash ﬂows. That can, however, be overcome with functions that will be presented in later chapters. In each of these functions, the variables are as follows: (cid:129) rate is the interest rate (as a fraction) per period (cid:129) nper is the number of interest bearing periods (cid:129) pmt is an annuity (A) sum of money (cid:129) pv is a present (P ) value sum of money (occurs at time = 0) (cid:129) fv is a future (F ) value sum of money (occurs at time = nper) (cid:129) type is 0 for end of period cash ﬂows and 1 for beginning of period cash ﬂows It should also be noted that in order to use these functions as equivalents for (P /A), (P /F ), etc., the values of pmt, pv, and fv need to be input as negative numbers. An example of a simple Excel® spreadsheet that computes the six functions given above is shown for 10% annual interest rate for 10 years. The actual formulas are shown as well. Recall that one needs to set “type” equal to zero to designate that the cash ﬂows occur at the end of each period. An explanation of the values in the various Excel formulas may be necessary. For example, in the formula that computes F/A (cell B7), the values are as follows: “B1” is the interest rate as a fraction, “B2” is for 10 periods, “B3” is for an annual annuity payment of $1 per year, “0” represents the fact that there is no present value payment, and “B6” deﬁnes that the various payments are at the end of the period. Since the formula ﬁnds the future value of a $1 annuity, we have effectively computed (F/A). Some additional Excel® ﬁnancial functions that might be of some interest at this point are: 14 2. INTEREST AND THE TIME VALUE OF MONEY A B A B rate 1 nper 2 pmt(A) 3 pv (P) 4 fv (F) 5 type 6 F/A 7 F/P 8 P/A 9 10 P/F 11 A/P 12 A/F 0.1 10 -1 -1 -1 0 15.937 2.5937 6.1446 0.38554 0.16275 0.062745 rate 1 nper 2 pmt(A) 3 pv(P) 4 fv(F) 5 type 6 F/A 7 F/P 8 P/A 9 10 P/F 11 A/P 12 A/F 0.1 10 -1 -1 -1 0 =FV(B1,B2,B3,0,B6) =FV(B1,B2,0,B4,B6) =PV(B1,B2,B3,0,B6) =PV(B1,B2,0,B5,B6) =PMT(B1,B2,B4,0,B6) =PMT(B1,B2,0,B5,B6) Effective Interest Rate: =EFFECT(normal_rate, npery) Number of periods: =NPER(rate, pmt, pv, fv, type) The new variables are deﬁned as follows: (cid:129) normal_rate = the nominal annual interest rate (as a fraction) (cid:129) npery = the number of compounding periods per year The effective interest table for 10% nominal interest rate can be created in Excel® as follows (note that in the case of continuous compounding, npery=1,000,000 is close enough to give the answer to the desired number of signiﬁcant digits). One can compare Table 2.3 with Table 2.1 to see consistency between the calculations in Excel® and those performed with the speciﬁc formula for ieff . The NPER function is useful for determining how many compounding periods are necessary to achieve a desired result. For example, one might want to determine how many years it will take for an original investment to double in value if the interest rate is varied from 1% per year to 25% per year. This is shown in Table 2.4. The explanation of the values in the NPER formulas in Table 2.4 is as follows: “A3/100” represents the interest rate as a fraction, “0” is for no annuity payment, “-1” is for a present value amount of $1, “2” is for a future value of $2, and “0” deﬁnes the amounts as end of year payments. One can also note that the product of the interest rate (as a percentage) and the # of periods to double the value of the investment varies from 70 to 75. This is commonly known as the “Rule of 2.5. INTEREST FORMULAS FOR DISCRETE COMPOUNDING 15 Table 2.3: Using Excel® to compute effective interest rates for a nominal 10% interest rate. Table 2.4: Using Excel to compute the number of years needed to double the value of an initial investment. 72.” If one takes 72 and divides by the interest rate (as a percentage), the resultant value is a close approximation of how long it will take for an investment to double. 2.5.5 EXAMPLE PROBLEMS At this point, it would be beneﬁcial to examine some of the practical applications of these formulas. Example 2.2 If $10,000 is invested in a fund earning 15% compounded annually, what will it grow to in 10 years? Solution: F = P (F /P )i,n = 10, 000(F /P )15,10 = 10, 000(4.0456) = $40, 456 16 2. INTEREST AND THE TIME VALUE OF MONEY Example 2.3 It is desired to accumulate $5,000 at the end of a 15-year period. What amount needs to be invested if the annual interest rate is 10% compounded semi-annually? Assume the given interest rate is a nominal rate and that the principal is compounded at 5% per period. Solution: P = F (P /F )i,n = 5, 000(P /F )5,30 = 5000(0.23138) = $1, 157 Example 2.4 What interest rate, compounded annually, will make a uniform series investment (at the end of each year) of $1,000 equivalent to a future sum of $7,442? The investment period is 5 years. Solution: F = A(F /A)i,n ⇒ 7, 442 = 1, 000(F /A)i,5 ⇒ (F /A)i,5 = 7.442 Searching the various interest tables in Appendix A for n = 5 yields i = 20% Example 2.5 An individual wishes to have $6,000 available after 8 years. If the interest rate is 7% com- pounded annually, what uniform amount must be deposited at the end of each year? Solution: A = F (A/F )i,n = 6, 000(A/F )7,8 = 6, 000(0.09747) = $585 Example 2.6 An individual wishes to place an amount of money in a savings account and, at the end of one month and for every month thereafter for 30 months, draw out $1,000. What amount must be placed in the account if the interest rate is 12% (nominal rate) compounded monthly? Solution: i(monthly) = 0.12/12 = 0.01(1%) P = A(P /A)i,n = 1, 000(P /A)1,30 = 1, 000(25.808) = $25, 808 Example 2.7 A principal of $50,000 is to be borrowed at an interest rate of 15% compounded monthly for 30 years. What will be the monthly payment to repay the loan? Solution: i (monthly) = 0.15/12 = 0.0125(1.25%). Since Appendix A does not contain a table for that interest rate, one must use the formulas. A = P (A/P )i,n = 50, 000(A/P )1.25,360 = 50, 000{[(0.0125)(1 + 0.0125)360]/[(1 + 0.0125)360 − 1]} = 50, 000(0.012644) = $632 2.5. INTEREST FORMULAS FOR DISCRETE COMPOUNDING 17 Example 2.8 An individual deposits $1,000 at the end of each year into an investment account that earns 8% per year compounded monthly. What is the balance in his account after 10 years? Solution: Since the time frame of the deposits (annually) does not match the time frame of the interest rate (monthly), one must convert to an effective annual interest rate before computing the correct formulas. (cid:2) 1 + i m (cid:3) m (cid:2) (cid:3) 12 ie = F = A(F /A)i,n = 1, 000(F /A)8.30,10 = 1, 000{[(1 + 0.0830)10 − 1]/0.0830} − 1 = 0.0830 − 1 = 1 + 0.08 12 = 1, 000(14.694) = $14, 694 Example 2.9 Calculate the future worth of the following 6-year cash diagram if the interest rate is 10% compounded annually. 0 1 2 3 4 5 6 1000 1200 1400 1600 1800 2000 There are a number of ways to solve this economic problem, which is the case for most cash ﬂow evaluations. One technique might be shorter in terms of the number of formulas to look up or calculate, but all will result in the same answer. Solution 1: Note that this series of cash ﬂows can be broken into an annuity of $1,000 per year and a gradient of $200 per year. One can compute the future value of each of these contributions separately and then add to get the ﬁnal result. FAnnuity FGradient = A(F /A)i,n = 1, 000(F /A)10,6 = 1, 000(7.7156) = $7, 715.60 = G(F /G)i,n = 200(F /G)10,6 = 200(17.156) = $3, 431.22 F = 7, 715.60 + 3, 431.22 = $11, 147 18 2. INTEREST AND THE TIME VALUE OF MONEY Solution 2: Convert the gradient to an equivalent annuity, add this value to the $1,000 annuity and then convert to the future. AGradient ATotal = G(A/G)i,n = 200(A/G)10,6 = 200(2.2236) = $444.72 = 1, 000 + 444.72 = $1, 444.72 F = A(F /A)i,n = 1, 444.72(F /A)10,6 = 1, 444.72(7.7156) = $11, 147 Solution 3: Treat each cash ﬂow as an individual, single payment, ﬁnd the future value of each individual payment and then add to get the total future value. FCF 1 = P (F /P )i,n = 1, 000(F /P )10,5 = 1, 000(1.6105) = $1, 610.50 FCF 2 = P (F /P )i,n = 1, 200(F /P )10,4 = 1, 200(1.4641) = $1, 756.92 FCF 3 = P (F /P )i,n = 1, 400(F /P )10,3 = 1, 400(1.3310) = $1, 863.40 FCF 4 = P (F /P )i,n = 1, 600(F /P )10,2 = 1, 600(1.2100) = $1, 936.00 FCF 5 = P (F /P )i,n = 1, 800(F /P )10,1 = 1, 800(1.1000) = $1, 980.00 FCF 6 = P (F /P )i,n = 2, 000(F /P )10,0 = 2, 000(1.0000) = $2, 000.00 F = 1.610.50 + 1, 756.92 + 1, 863.40 + 1, 936.00 + 1, 980.00 + 2, 000.00 = $11, 147 Example 2.10 Calculate the present worth of the following 10-year cash ﬂow diagram if the annual interest rate is 20% compounded annually. 0 1 2 3 … 8 9 10 2000 1900 1800 … 1300 1200 1100 Solution: Again, there are a variety of methods to solve this problem. One technique is to recognize that the cash ﬂow is made up of an annuity of $2,000 and a gradient of −$100. ATotal = 2, 000 − 100(A/G)20,10 = 2, 000 − 100(3.0739) = $1, 692.61 P = A(P /A)i,n = 1, 692.61(P /A)20,10 = 1, 692.61(4.1925) = $7, 096 2.6. INTEREST FORMULAS FOR CONTINUOUS COMPOUNDING 19 2.6 INTEREST FORMULAS FOR CONTINUOUS COMPOUNDING In the last section, the assumption was made that money was received or dispersed and interest rates were compounded at the end of each discrete compounding period. In some projects (consider a banking institution for example), money is received and dispersed on a nearly continuous basis. If the evaluator wishes to consider the effect of continuous cash ﬂow and/or continuous compounding of interest, one needs to utilize a slightly different set of formulas that relate P , F , and A. 2.6.1 CONTINUOUS COMPOUNDING FOR DISCRETE PAYMENTS The following formulas apply to the situation where payments (or withdrawals) to an account are made at discrete points in time, while the account accumulates interest on a continuous basis: (P /F )i,n = e−in (P /A)i,n = (ein − 1)/[ein(ei − 1)] (F /A)i,n = (ein − 1)/[(ei − 1)] (2.24) (2.25) (2.26) 2.6.2 CONTINUOUS COMPOUNDING FOR CONTINUOUS PAYMENTS The other application of continuous compounding is the case where the deposits or withdrawals to an account are being made on a nearly continuous basis. One example of this situation would be a credit card company that receives charges and payments on millions of cards throughout each day. For this case, the following deﬁnitions need to be made: ¯P , ¯F , ¯A = the total amount of funds received over one period (present sum, future sum, or annuity, respectively). The following ﬁgures demonstrate these deﬁnitions: 20 2. INTEREST AND THE TIME VALUE OF MONEY The appropriate formulas are: (P / ¯F )i,n = [i(1 + i)−n]/[ln(1 + i)] (F / ¯P )i,n = [i(1 + i)n−1]/[ln(1 + i)] (F / ¯A)i,n = (ein − 1)/i (P / ¯A)i,n = (ein − 1)/[i(ein)] (2.27) (2.28) (2.29) (2.30) where, i is the nominal interest rate per period. 2.7 PROBLEMS 2.1. Given a nominal rate of 20%, what is the effective annual interest rate if the interest is compounded under each of the following scenarios: (a) Quarterly (b) Monthly (c) Daily (d) Continuously 2.2. What is the percentage difference between the effective rates determined by annual and continuous compounding for nominal interest rates of: (a) 10% (b) 20% (c) 30% 2.3. A company has decided to invest in a project to make a product. The initial investment cost will be $1,000,000 to be spread over the ﬁrst two years with $700,000 in the ﬁrst year and $300,000 in the second. The plan calls for producing products at the following rates: 5,000 units in year 2; 10,000 in year 3; 30,000 in year 4; 30,000 in year 5; $10,000 in year 6; and $5,000 in year 7. Products will be sold for $50 each throughout the life of the project and cash operating expenses will be $60,000 per year for years 2 through 7. Construct a cash ﬂow diagram for the project. 2.7. PROBLEMS 21 2.4. Example 2.1 presented a cash ﬂow diagram for an automobile loan as seen through the eyes of the lender. Construct the corresponding cash ﬂow diagram as seen through the eyes of the borrower. 2.5. A $1,000 investment has grown to $2,476 in 8 years. What interest rate (compounded annually) has it earned? 2.6. What present sum is equivalent to a future sum of $25,000 (after 5 years) at an interest rate of 8% compounded annually? 2.7. If $200 is placed at the end of each year for 10 years in an account earning 7% interest compounded annually, what amount will be accumulated at the end of 10 years? 2.8. What uniform series would be equivalent to a future sum of $10,000 if the series extends for 10 years and earns 12% interest compounded semi-annually? 2.9. An annual deposit of $1,000 is placed in an account at the beginning of each year for 5 years. What is the present value of that series if interest is 12% compounded annually? What is the future value at the end of the 5th year? 2.10. What will be the future value, 10 years from the ﬁrst payment, of the series of deposits in problem 2.9? 2.11. What monthly car payments for the next 30 months are required to amortize a loan of $4,000 if interest is 12% compounded monthly? 2.12. Payments of $1,000 are to be made at the end of each year for the next 3 years. What is the present worth of the three payments if interest is 12% compounded monthly? What series of monthly payments would be equivalent to the $1,000 year payments? 2.13. An individual agrees to lease a building to a ﬁrm with yearly payments shown on the cash ﬂow diagram below.What is the future worth of the payments if interest is 15% compounded annually? 0 1 2 3 4 5 6 7 8 9 10 3000 3000 3000 3000 3300 3600 3900 4200 4500 4800 2.14. An engineer wishes to buy a house but can only afford monthly payments of $1500. 30- year loans are available at 5.75% interest compounded monthly. If the engineer can make a $20,000 down payment, what is the price of the most expensive house that the engineer can afford to purchase? 22 2. INTEREST AND THE TIME VALUE OF MONEY 2.15. A young woman placed $200.00 in a savings account paying monthly interest. After one year, her balance has grown to $214.00. What was the effective annual interest rate? What was the nominal annual interest rate? 2.16. Find the value of cash ﬂow X that will make the two cash ﬂows equivalent. Interest is 10% compounded annually. Time on the diagram is given in years. 0 1 2 3 4 5 6 100 120 140 160 0 1 2 X X X 2.17. It takes a full $10,000 to put on a Festival of Laughingly Absurd Walks (FLAW) each year. Immediately before this year’s FLAW, the sponsoring committee ﬁnds that it has $40,000 in an account paying 15% interest compounded annually. After this year, how many more FLAWs can be sponsored without raising more money? 2.18. If $10,000 is borrowed at 12% interest compounded monthly, what would the monthly payments be if the loan is for 5 years? What would the annual payment be if the loan is for 5 years? Assume all payments occur at the end of a given period. 2.19. Calculate the value of the following cash ﬂow diagram at the end of year 4. Interest is 10% per year compounded annually. 0 1 2 3 4 5 6 7 8 9 10 1000 500 500 750 1000 800 600 400 2000 2.20. Calculate the future worth 5 years from now of a present sum of $2,000 if: 2.7. PROBLEMS 23 (a) Annual interest is 10% compounded annually (b) Annual interest is 10% compounded quarterly (c) Annual interest is 10% compounded continuously 2.21. Calculate the present value of 10 uniform $2,000 payments if: (a) Annual interest is 10% compounded continuously and payments are received at the end of each year (b) Annual interest is 10% compounded continuously and payments are received contin- uously over the year 2.22. A gas station sells $125,000 worth of gasoline over the course of a year. If this revenue is collected and deposited continuously into an account that earns 8% interest, compounded annually, how much money would the station have in its account at the end of the year? 2.23. Develop an Excel® spreadsheet that computes the six functions — (P /A), (P /F ), (F /A), (F /P ), (A/P ), (A/F ) — for a ﬁxed interest rate and the number of periods ranging from 1 to 100. 2.24. Use the Excel® NPER function to determine how long it will take for an investment to triple in value at interest rates of 1%, 5%, 10%, 15%, 20%, and 25%. Can you determine an approximate “Rule” for how to quickly calculate how long it takes for an investment to triple in value? C H A P T E R 3 25 Project Evaluation Methods INTRODUCTION 3.1 In order to make informed decisions on one or more potential investments, methods must be devel- oped that provide a numerical evaluation of a project. Both equivalence and rate of return methods will be developed in this chapter. Consider the following cash ﬂow diagrams that contain income generating streams. 1 2 3 … 18 19 20 A: 0 1,000,000 B: 0 1 2 3 … 18 19 20 100,000 100,000 100,000 … 100,000 100,000 100,000 Since there are no cash ﬂows for A after period 0, the present value of cash ﬂow A is simply $1,000,000. For B, since the $100,000 occurs at the end of each period for 20 periods, multiplying the $100,000 by (P /A)i,20 will yield a present value for the interest rate used in the formula. For example, if the interest rate is 12% per year, the present value would be $746,944. If the question “which cash ﬂow represents the largest present value?” is asked, the answer is obviously cash ﬂow A. Now consider a different question. Suppose you have just won a lottery and you have a choice of receiving $1,000,000 now or receiving $100,000 at the end of each year for 20 years. If interest is expected to be constant at 12% for the next 20 years as in the previous paragraph, which set of payments would you prefer? Since this question is represented by the cash ﬂow diagrams shown above and the interest rate of 12%, the choice can be made by analyzing the present values of the two cash ﬂow diagrams. Since cash ﬂow A yields a larger present value than cash ﬂow B at an interest rate of 12%, the proper choice would be to accept option A. 26 3. PROJECT EVALUATION METHODS However, what if the interest rate is expected to be 0% over the 20 year period? What would the best choice be under that scenario? If interest is 0%, then money is worth the same no matter when it occurs. At 0% interest, the present value of cash ﬂow B becomes $2,000,000 and cash ﬂow B becomes the correct choice. The discussion in the previous two paragraphs infer that at some interest rate between 0% and 12%, the two cash ﬂow diagrams are equivalent. A trial and error solution yields this interest rate to be about 7.75%. This discussion has just introduced two of the more popular techniques (equivalence methods and rate of return methods) used to evaluate the ﬁnancial value of projects and help the evaluator choose between multiple projects. These will be discussed in more detail later in this chapter. 3.2 ALTERNATE USES OF CAPITAL Investment analysis or project evaluation involves making a decision between alternative uses of capital. A cash ﬂow diagram is constructed for each alternative according to the speciﬁc parameters of that alternative and evaluated using the concepts of time value of money that were discussed in Chapter 2. The results of the evaluations are then compared and a decision is made as to which alternative is the best option. Several evaluation methods can be used in analyzing investment opportunities. Two general types of calculations that will be introduced here are: (1) equivalence methods which involve the determination of an equivalent present, annual, or future worth of a cash ﬂow diagram given a speciﬁc interest rate; and (2) rate of return methods which involve the determination of an interest rate produced by the cash ﬂow diagram. 3.3 MINIMUM ACCEPTABLE RATE OF RETURN (MARR) When using either the equivalence method or the rate of return method for comparing alternatives, a minimum acceptable rate of return, MARR, needs to be deﬁned. The value of MARR is set as the lower limit for investment which is acceptable to an individual or a company. The MARR may vary from individual to individual, company to company, and even within the structure of a speciﬁc company. The lower bound for the MARR is generally set at the cost of capital, which reﬂects the expense of obtaining funds for a given project. How much higher the MARR is above the cost of capital depends on a particular company’s or individual’s position and the particular project. For example, an individual who borrows money at 5% interest rate in order to invest in a proﬁt-generating project would have an MARR of at least 5%, but would probably want to set the MARR at, say, 10% in order to generate a net increase in his/her personal worth based on the estimated proﬁtability of the project. Similarly, if individuals are using their own funds to invest, their cost of capital would be the interest rate that their money is currently earning in a savings account, certiﬁcate of deposit, or other investments. A company’s MARR is usually set by the portfolio of projects in which the company can invest. That is, what is the minimum interest that a company can earn by investing its money in what it would consider to be a “guaranteed” success? For engineers performing economic evaluations for their companies, the MARR will be provided by upper management so that they will not have to make that determination. 3.4. EQUIVALENCE METHODS 27 3.4 EQUIVALENCE METHODS In the equivalence methods to determine either the acceptability of a single project or to choose the “best” project, the MARR is used as the interest rate in present, future, or annuity calculations. A net present value, NPV (sometimes called the net present worth), net future value, NFV, or net annual value, NAV, is calculated by one of the following equations: (cid:4) N P V = N F V = N AV = Present Value of Cash Flows with Future Value of Cash Flows with (cid:4) (cid:4) Annuity Value of Cash Flows with i = MARR i = MARR i = MARR (3.1) (3.2) (3.3) Since N P V , N F V , and N AV are related by the interest formulas developed in Chapter 2, any one of the three calculations will yield the same conclusion (in terms of economic viability of the project) as the other two. Because of this fact, most analysts concentrate on the NP V method, as do the authors of this text. 3.5 NET PRESENT VALUE 3.5.1 ANALYSIS OF A SINGLE INVESTMENT OPPORTUNITY For a single investment opportunity, the NP V would be calculated using the MARR as the interest rate. A positive value for N P V indicates that the project which is represented by the cash ﬂow diagram earns an actual interest rate greater than the MARR, a negative value for NP V indicates that it earns an actual interest rate less than the MARR, and an NP V value of zero indicates that it earns the MARR. Since the MARR represents the decision point for determining the viability of a project for a particular investor, a positive NP V would indicate that the project is an acceptable one. Example 3.1 Consider the project represented by the following cash ﬂow diagram. The project requires an initial investment of $1,000 that returns positive cash ﬂows as shown. The MARR is 10%. 0 1 2 3 4 5 -1000 500 600 700 800 900 28 3. PROJECT EVALUATION METHODS N P V = −1000 + 500(P /A)10,5 + 100(P /G)10,5 = −1000 + 500(3.7908) + 100(6.8618) = $1582 Since the N P V is greater than zero, this project would be an acceptable one to the investor. An alternative method to calculate the NP V is to treat each individual cash ﬂow as a future value at various values of n. While this technique might require more formulas than recognizing annuities and gradients in the cash ﬂow diagram, it will always yield a correct value for NP V : N P V = − 1000 + 500(P /F )10,1 + 600(P /F )10,2 + 700(P /F )10,3 + 800(P /F )10,4 + 900(P /F )10,5 N P V = $1582 In Excel®, one can use the NP V function to make the same calculation. However, some caution is necessary. The function is: = NP V (rate, value1, value2, …). where, rate = interest rate per period (as a fraction). value1, value2, ... = cash ﬂows that occur at the end of period 1, end of period 2, etc. One can see that the NPV function does not include the investment period 0. Therefore, in order to calculate the N P V of the entire cash ﬂow diagram, one needs to include the initial investment. For example, the complete Excel formula to compute the NP V of a series of cash ﬂows would be as shown in Figure 3.1: = CF0 + NP V (rate, value1, value2,…) One can see that the results from Excel match the NP V calculations from the other two methods. Example 3.2 Consider the project represented by the following cash ﬂow diagram. The project requires an initial investment of $1,000 that returns positive cash ﬂows as shown. The MARR is 10%. 0 1 2 3 4 5 -1000 150 200 250 300 350 A MARR = B 10% A B 1 MARR = 0.1 3.5. NET PRESENT VALUE 29 Year 0 1 2 3 4 5 CF -1000 500 600 700 800 900 NPV = 1582 3 4 5 6 7 8 9 10 11 Year 0 1 2 3 4 5 CF -1000 500 600 700 800 900 NPV = =B4+NPV(B1,B5:B9) 1 3 4 5 6 7 8 9 10 11 Figure 3.1: Demonstration of the use of the NP V function in Excel®. N P V = −1000 + 150(P /A)10,5 + 50(P /G)10,5 = −1000 + 150(3.7908) + 50(6.8618) = −$88 Since the N P V is negative, the project will not earn the MARR and, therefore, is not accept- able to this investor. Now a question arises: What does the investor do with the $1000? Since the time-line represents the only ‘new’ investment opportunity available to the investor and the NP V analysis suggests that it is not acceptable, the investor will choose to do nothing with the $1000. The concept of the “do nothing” project will be deﬁned in the next section. 3.5.2 DO NOTHING PROJECT Example 3.2 indicates that there is always a choice to “do nothing” with investment funds. That is, even if a project, like the one described in Example 3.2, is the only new investment available and the ﬁnancial analysis indicates that it is unacceptable, an investor can always choose to keep the proposed funds, $1000 in the case of Example 3.2, where they currently are and “do nothing” with those funds. The “do nothing” project does not mean that the investment funds are going to be buried in a can in the backyard where they earn nothing. The “do nothing” project means that the funds are already invested in a project that is earning the MARR. As mentioned before, for individuals, this could mean leaving their funds in their savings accounts. By deﬁnition, the NP V of the “do 30 3. PROJECT EVALUATION METHODS nothing” project is zero.Thus, when a single investment opportunity is being evaluated, one is always comparing it against a second opportunity which is to leave the money in the “do nothing” project. 3.5.3 ANALYSIS OF MULTIPLE INVESTMENT OPPORTUNITIES For the purpose of this initial discussion of investing in multiple projects, assume that all of the prospective projects to be evaluated require the same initial investment, that the investor only has enough funds to invest in one of the projects, and that the decision will be based solely on NP V analysis. These assumptions will be removed in subsequent chapters and discussed further. In addi- tion, if at least one of the proposed projects has a positive NP V , then the “do nothing” project need not be considered. Example 3.3 Consider the following two investment opportunities. The investor’s MARR is 10% and the investor only has enough funds to invest in one of the projects. Which one should be chosen? Project A: 0 1 2 3 4 5 -800 215 215 215 215 215 Project B: 0 1 2 3 4 5 -800 100 100 100 100 900 N P V for Project A = −800 + 215(P /A)10,5 = $15.0 N P V for Project B = −800 + 100(P /A)10,5 + 800(P /F )10,5 = $75.8 Both projects show positive values of NP V . Therefore, both would be acceptable as long as the investor had at least $800 to invest. In addition, the “do nothing” alternative does not need to be considered. If the investor only has enough funds to invest in one of the projects, the NP V values indicate that Project B is the best economic choice. 3.6. RATE OF RETURN METHODS 31 3.6 RATE OF RETURN METHODS The second general type of project evaluation technique involves the determination of an unknown interest rate for a given cash ﬂow diagram. This interest rate is usually referred to as a rate of return. There are several rates of return that can be calculated. Two will be presented in this chapter. The ﬁrst is called the Internal Rate of Return (IRR) which is also known as the Discounted Cash Flow Rate of Return (DCFROR). The second is the External Rate of Return (ERR) which is also known as the Growth Rate of Return. The I RR is the rate of return earned by a particular individual’s or company’s investment.The ERR represents the overall growth of invested dollars for an individual or a company. The differences will become apparent in the following discussion and example problems. INTERNAL RATE OF RETURN (IRR) 3.6.1 The I RR is deﬁned as the interest rate which discounts a series of cash ﬂows to an NP V value of zero: (cid:4) N P V = 0 = Present Value of Cash Flows with the interest rate equal to I RR (3.4) The equation can also be written as: N P V = 0 = n(cid:4) j =0 CFj (P /F )I RR,j = n(cid:4) j =0 CFj (1 + I RR)j (3.5) where, CFj = cash ﬂow for period j j = period of cash ﬂow n = total number of periods It should be noted that one cannot normally solve explicitly for the I RR from Equation 3.5. Therefore, a trial and error solution is usually required. Graphically, the relationship between N P V , interest rate, and I RR is demonstrated in Figure 3.2. Once the I RR is calculated, it is then compared with the MARR. If the I RR is greater than the MARR, the project is considered to be acceptable to the investor. 32 3. PROJECT EVALUATION METHODS NPV vs Interest Rate $ , V P N 600 500 400 300 200 100 0 -100 -200 -300 IRR = 0.125 0 0.05 0.1 0.15 0.2 0.25 Interest Rate, fra(cid:272)(cid:415)on Figure 3.2: General form of net present value as a function of interest rate. (Note, for this example, when NP V = 0, the interest rate, or I RR, is 0.125.) Example 3.4 Consider the two investment opportunities examined in Example 3.3. The investor’s MARR is 10% and the investor only has enough funds to invest in one of the projects. What are the I RRs for each project? Project A: 0 1 2 3 4 5 -800 215 215 215 215 215 Project B: 0 1 2 3 4 5 3.6. RATE OF RETURN METHODS 33 -800 100 100 100 100 900 As noted, the calculation of I RR usually involves a trial and error approach. While the NP V versus interest rate curve is not a straight line, it is generally accurate enough to bracket the I RR solution within 5% and then linearly interpolate for the answer. Project A: N P V for Project A = −800 + 215(P /A)i,5 Interpolating for I RR: I RR = 10.0 + (cid:5) (cid:6) 15.0−0 15.0−(−79.3) (15.0 − 10.0) = 10.8% Project B: N P V for Project B = −800 + 100(P /A)i,5 + 800(P /F )i,5 Interest rate, % N P V 100.0 75.8 -67.0 (cid:6) 0.0 10.0 15.0 (cid:5) Interpolating for I RR: I RR = 10.0 + (15.0 − 10.0) = 12.6%. It should be noted that Figure 3.2 was generated with the cash ﬂows from Project B. Thus, the “true” answer for I RR is 12.5% compared to the interpolated value of 12.6%. 75.8−0 75.8−(−67.0) In this example, the I RRs of both projects are greater than the investor’s MARR, so both projects are acceptable. It would appear that since the I RR of Project B is greater than the I RR of Project A, then Project B is the best alternative. This is, indeed, the proper interpretation – but only because the initial investment values for both projects were the same. One must be very careful in ranking projects by I RR values as will be shown in Chapter 5. SPREADSHEET FORMULA FOR IRR 3.6.2 Excel® has a built-in function to calculate Internal Rate of Return. 34 3. PROJECT EVALUATION METHODS The function is: where, = I RR(values, guess) values = cash ﬂows that occur for the project guess = initial estimate of the IRR (as a fraction) This function automatically takes care of the year 0 cash ﬂow without having to include it as a separate term such as was necessary in the NP V calculation with Excel®. One can see that the cash ﬂows in Figure 3.3 are the same as Project B in the previous example. A MARR = B 10% A B 1 MARR = 0.1 Year 0 1 2 3 4 5 CF -800 100 100 100 100 900 NPV = IRR = 75.8 12.5% 3 4 5 6 7 8 9 10 11 12 Year 0 1 2 3 4 5 CF -800 100 100 100 100 900 NPV = IRR = =B4+NPV(B1,B5:B9) =IRR(B4:B9,0.1) 1 3 4 5 6 7 8 9 10 11 12 Figure 3.3: Demonstration of the use of the NP V and I RR functions in Excel®. As in Figure 3.2, Excel provides the “true” value for I RR without the need for a trial and error solution and without interpolating. 3.6.3 EXTERNAL RATE OF RETURN (ERR) The External Rate of Return (ERR) or Growth Rate of Return is found by determining the interest rate that will satisfy the following equation. ⎡ ⎤ (cid:7) (cid:7) n(cid:4) (cid:7) (cid:7) (cid:7) (cid:7) j =0 (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) Cj (P /F )MARR,j n(cid:4) ⎣ = j =0 Ij (F /P )MARR,n−j ⎦ (P /F )ERR,n (3.6) where, Cj = negative cash ﬂow at period j Ij = positive cash ﬂow at period j n = life of project 3.6. RATE OF RETURN METHODS 35 The equation states that positive cash ﬂows (Ij s) derived from the project are reinvested at the MARR to generate a future value, which is called FI , at the end of the project life. All negative cash ﬂows (investments) are brought back in time at the MARR to generate a present value, which is called PC, at year zero. The interest rate which will then discount FI to a value equal to the value of PC is determined to be the ERR. Another way of looking at the external rate of return is to set up a second project which is called the reinvestment project. The negative cash ﬂows for the reinvestment project are the positive cash ﬂows from the original project. A future value of the cash ﬂows of the reinvestment project is determined using the MARR as the interest rate (FI ). The original project and reinvestment project are then added together to give a third project. The positive cash ﬂows from the original project and the costs from the reinvestment project should have netted out to zero. The remaining cash ﬂows for the third project will be the negative cash ﬂow at year zero, any other negative cash ﬂows from the original project at the year of occurrence, and the future value determined for the second project. All negative cash ﬂows are brought back to time zero at the MARR to generate a present value (PC). The ERR is then determined by ﬁnding the interest rate which will bring the future value to a year zero value equal to the present value of the negative cash ﬂows. The ERR method has a calculation advantage over the I RR method in that the ERR can be solved for directly without a trial and error procedure. The steps in the calculation procedure are: Cj (P /F )MARR,j (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) n(cid:4) (cid:7) (cid:7) (cid:7) (cid:7) j =0 n(cid:4) Ij (F /P )MARR,n−j PC = FI = j =0 ERR = (FI /PC)1/n − 1 (3.7) (3.8) (3.9) Example 3.5 Consider the two investment opportunities examined in Example 3.4. The investor’s MARR is 10% and the investor only has enough funds to invest in one of the projects. What are the ERRs for the projects? Project A: 0 1 2 3 4 5 -800 215 215 215 215 215 36 3. PROJECT EVALUATION METHODS Project B: 0 1 2 3 4 5 -800 100 100 100 100 900 Project A: PC = \| − 800\| = 800 FI = 215(F /A)10,5 = 1312.6 ERR = (1312.6/800)1/5 − 1 = 0.104 = 10.4% Project B: PC = \| − 800\| = 800 FI = 100(F /A)10,5 + 800 = 1410.5 ERR = (1410.5/800)1/5 − 1 = 0.120 = 12.0% In this example, the ERRs of both projects are greater than the investor’s MARR, so both projects are acceptable. It would appear that since the ERR of Project B is greater than the ERR of Project A, then Project B is the best alternative. This is, indeed, the proper interpretation – but only because the initial investment values for both projects were the same. Again, one must be very careful in ranking projects by ERR values as will be shown in Chapter 5. One additional observation can be made about the relationship between MARR, I RR, and ERR. The ERR will always lie between the MARR and the I RR. Thus, MARR ≤ ERR ≤ I RR or MARR ≥ ERR ≥ I RR Example 3.6 Consider the investment opportunity below. The investor’s MARR is 10%. What are the N P V , I RR, and ERR values for the project? Project A: 0 1 2 3 4 5 -1000 500 500 -200 500 500 3.7. THE REINVESTMENT QUESTION IN RATE OF RETURN CALCULATIONS 37 N P V = − 1000 + 500(P /F )10,1 + 500(P /F )10,2 − 200(P /F )10,3 + 500(P /F )10,4 + 500(P /F )10,5 N P V =$369.4 NPV: IRR: Interest rate, % 10.0 20.0 30.0 25.0 N P V 369.4 90.2 -100.8 -13.8 (cid:5) Interpolating between 20% and 25%: I RR = 20.0 + 90.2−0 90.2−(−13.8) (cid:6) (25.0 − 20.0) = 24.3% ERR: PC = \| − 1000 − 200(P /F )10,3\| = $1150.3 FI = 500(F /P )10,4 + 500(F /P )10,3 + 500(F /P )10,1 + 500 = $2447.6 ERR = (2447.6/1150.3)1/5 − 1 = 0.163 = 16.3% All three economic indicators show that this project is an acceptable one. SPREADSHEET FORMULA FOR ERR 3.6.4 Excel® has a built-in function that can be used to calculate the External Rate of Return. The function is: = MI RR(values, ﬁnance_rate, reinvestment_rate) where, values = cash ﬂows that occur for the project ﬁnance_rate = interest rate for discounting the negative cash ﬂows to year 0 (as a fraction) reinvestment_rate = interest rate for reinvesting the positive cash ﬂows to year n (as a fraction) One needs to set both the ﬁnance_rate and the reinvestment_rate to MARR. As with I RR, this function automatically takes care of the year 0 cash ﬂow without having to include it as a separate term. Figure 3.4 demonstrates this formula (along with NPV and IRR) for the cash ﬂows given in Example 3.6. 3.7 THE REINVESTMENT QUESTION IN RATE OF RETURN CALCULATIONS The virtues of the I RR calculation have been argued for years by evaluators. When the I RR method was ﬁrst introduced, it was met with a great deal of enthusiasm and is still one of the most popular 38 3. PROJECT EVALUATION METHODS A MARR = B 10% A B 1 MARR = 0.1 Year 0 1 2 3 4 5 CF -1000 500 500 -200 500 500 NPV = IRR = ERR = 369.5 24.3% 16.3% 3 4 5 6 7 8 9 10 11 12 13 Year 0 1 2 3 4 5 CF -1000 500 500 -200 500 500 NPV = IRR = ERR = =B4+NPV(B1,B5:B9) =IRR(B4:B9,0.1) =MIRR(B4:B9,B1,B1) 1 3 4 5 6 7 8 9 10 11 12 13 Figure 3.4: Demonstration of the use of the NP V , I RR, and MI RR(ERR) functions in Excel®. evaluation methods used. Surveys have indicated that a vast majority of the companies polled use I RR either by itself or in conjunction with other methods when evaluating projects. However, in spite of the popularity of the I RR method, many evaluators still question its meaning and validity. The basic question has to do with whether or not a reinvestment of incomes is implied in the calculation procedure. That is, one argument is that in order for the original project investment to “earn” the I RR, the positive cash ﬂows generated by the project must be reinvested in another project that “earns” the same I RR. The other argument is that reinvestment is not necessary to “earn” the I RR. In fact, both arguments may be true depending on the evaluator’s perception of what is meant by the phrase “earning the IRR.” To begin the discussion of the reinvestment question, consider Example 3.7. 3.7. THE REINVESTMENT QUESTION IN RATE OF RETURN CALCULATIONS 39 Example 3.7 An investment of $5000 will yield $1931.45 at the end of each year for 4 years. What is the value of the project’s I RR? If the MARR is 15%, what is the project’s ERR? 0 1 2 3 4 -5000 1931.45 1931.45 1931.45 1931.45 I RR : NP V = −5000 + 1931.45(P /A)i,4 (P /A)I RR,4 = 2.5887 For NP V = 0, Examining the interest tables in Appendix A, one can determine that the I RR is 20.0%. ERR : PC = \| − 5000\| = $5000 FI = 1931.45(F /A)15,4 = $9644 ERR = (9644/5000)1/4 − 1 = 0.178 = 17.8% By deﬁnition, the calculation of ERR requires that the incomes be reinvested at the MARR of 15%. If the MARR had been higher, say 18%, the value of the ERR would have been higher. If the MARR were 20%, one can show that the ERR is now equal to 20% (same as the I RR). Thus, if the interest rate used for the reinvestment of incomes and for ﬁnding the present value of the costs (negative cash ﬂows) is the I RR, then the values of MARR, I RR, and ERR will be identical. While not shown here, this can be demonstrated, mathematically, for any set of cash ﬂows. Now, let’s expand on this example in order to determine the effect of different perceptions of an investment “earning” a particular interest rate. 3.7.1 PERCEPTION #1 The ﬁrst perception of an investment “earning” a particular interest rate parallels the concept of investing money in a savings account for a speciﬁed period of time. In this perception, “earning” means that an initial investment will yield a future value given by (F /P )i,n. Using the values from this example, a $5000 investment earning 20% (the I RR) for 4 years should result in a future sum of: F = 5000(F /P )20,4 = $10, 368 However, if the individual cash ﬂows of $1931.45 (recall that these cash ﬂows yielded an I RR of 20%) were buried in a can under a tree (thus earning no interest), the total future accumulated 40 3. PROJECT EVALUATION METHODS amount would be: F = (4)(1931.45) = $7, 725.80 Since the four individual cash ﬂows yield a future sum signiﬁcantly less than $10,368, the initial investment has not “earned” a 20% interest rate according to this perception of “earning.” In fact, the actual rate of return would be: i = (7725.80/5000)1/4 − 1 = 0.115 = 11.5%, not 20%! However, if the individual cash ﬂows were reinvested in an account that earned 20% interest, the future sum accumulated in that account would be: F = 1931.45(F /A)20,4 = $10, 368 and the “earned” interest rate would indeed be 20%. Thus, in this perception, in order to “earn” the I RR (20%) interest rate on the entire initial investment ($5,000), any cash ﬂows received before the end of the project must be reinvested in another project that has the same I RR. 3.7.2 PERCEPTION #2 The second perception more closely parallels the concept of making a loan to a project and having that loan be paid back at some interest rate. In this perception, interest is “earned” only on the portion of the total loan that is still unpaid. The unpaid portion of the loan is also known as the unamortized portion. Again, consider the cash ﬂows in Example 3.7. During the ﬁrst year, interest is earned on the entire $5000 investment (or loan). The required interest amount at the calculated I RR of 20% would be: I1 = 5000(0.20) = $1000 This means that $931.45 can be used to “payback” a portion of the original investment, leaving an unamortized amount of $4,068.55. The required interest amount in the second year would then be: I2 = 4068.55(0.20) = $813.71 The reminder of that year’s cash ﬂow, $1,117.74, would be used to further reduce the unamortized portion of the investment to $2,950.81. Table 3.1 summarizes this sequence for the entire project life. Note that the total interest “earned” is the same as would have been “earned” under perception #1 if the cash ﬂows were not reinvested. However, banking institutions agree that this repayment scheme has indeed “earned” 20% on the original loan of $5,000. In the opinion of the authors, the ﬁnal conclusion is that the question of whether reinvestment of the cash ﬂows at the I RR must occur or not is really more of an issue of perceiving what is meant by “earning a return.” Banking institutions readily “invest” in projects via loans to companies or Table 3.1: Amortization table for a loan 3.8. ACCELERATION PROJECTS 41 individuals and receive the I RR as deﬁned in perception #2 without automatic reinvestment at that same rate. However, an individual or company that is expecting to generate a future sum of money based on earning the I RR on the original investment for the entire life of the project must depend on reinvestment of the cash ﬂows at that speciﬁc I RR in order to actually have the desired future sum. It should be noted that, independent of the reinvestment question, I RR analysis still results in a powerful economic evaluation tool. 3.7.3 FINAL COMMENTS ON ERR AND IRR RELATIONSHIPS The ERR is a measure of the growth of the investment dollars. The I RR does not have the same meaning since it is a measure of the project proﬁtability only. If a company wants a true measure of its growth based on a speciﬁc investment, then ERR analysis should be used. Both the I RR and ERR are valid investment analysis techniques and, if applied correctly, will yield the same conclusion regarding the viability of an investment to the company or individual. It will be shown in the next section that the ERR method has some advantages in particular analysis situations. 3.8 ACCELERATION PROJECTS When a series of cash ﬂows changes from a positive value to a negative value (or negative to positive) more than once, the cash ﬂows may generate multiple positive real solutions to the I RR equation.The number of solutions is governed by Descartes’ rule. The rule states that if the terms of a polynomial with real coefﬁcients are ordered by descending variable exponent, then the number of positive roots of the polynomial is equal to the number of sign differences between consecutive nonzero 42 3. PROJECT EVALUATION METHODS coefﬁcients. Since the I RR equation can be rearranged to form a polynomial of order n, this rule will apply since the coefﬁcients will be related to the cash ﬂows. A series of cash ﬂows with more than one sign change is called an acceleration project.This type of project is created when a second capital investment must occur after one or more years of positive incomes. For example, consider a manufacturing facility that will require signiﬁcant upgrading after several years. The multiple values of I RR rates calculated when there are multiple sign changes are difﬁcult to interpret as to which might be the correct return on investment. Since the ERR equation does not form a polynomial, it always has a unique answer and, therefore, should be the rate of return technique of choice in acceleration projects. A modiﬁed I RR calculation can be made by ﬁnding the present value of all of the negative cash ﬂows by discounting to year 0 at the MARR and then using the normal I RR equation. It should be noted that the investor can always use the equivalence methods (NP V speciﬁcally) in this situation without difﬁculty. In Example 3.6, a cash ﬂow was presented that had sign changes between the 2nd and 3rd year and the 3rd and 4th year. In this case, the analyst should be aware that multiple positive values of I RR might exist. For that speciﬁc example, the nth order polynomial that is created by the NP V = 0 equation is developed as follows: − 1000 + 500(P /F )I RR,1 + 500(P /F )I RR,2 − 200(P /F )I RR,3 + 500(P /F )I RR,4 + 500(P /F )I RR,5 = 0 − 1000 + 500 (1 + I RR) + 500 (1 + I RR)2 − 200 (1 + I RR)3 + 500 (1 + I RR)4 + 500 (1 + I RR)5 = 0 I RR5 + 4.5 I RR3 + 7.5 I RR3 + 5.7 I RR2 + 1.4 I RR − 0.8 = 0 Since the 5th order polynomial only has one sign change, there is only one positive value of I RR for the cash ﬂows in Example 3.6. Example 3.8 will demonstrate a situation where more than one positive value exists. Example 3.8 Given the following cash ﬂow diagram, plot the NP V versus interest rate and determine the two positive values of I RR that would be predicted by Descartes’ rule. Assume an MARR of 5%. 3.8. ACCELERATION PROJECTS 43 Solution: From the plot of NP V versus interest rate and the Excel® spreadsheet, it can be seen that there are two values for I RR: 9.1% and 57.2%. One can use Excel® to ﬁnd both rates of return by adjusting the initial guess. An initial guess of 10% will yield the 9.1% value and an initial guess of 50% will yield the 57.2% value. This creates an unfortunate situation in that one must have an idea of the value of the larger root in order to have Excel® compute it. The 6th order polynomial that could be developed is: I RR6 + 5.1 I RR5 + 9.3 I RR4 + 5.4 I RR3 − 2.7 I RR2 − 3.1 I RR + 0.3 = 0 One can see that there are two sign changes in the list of terms and, therefore, two positive values for I RR. As mentioned before, the multiple values of IRR cause difﬁculties in interpretation. With a total investment (without time value of money) of $320 and the total of the positive incomes (without time value of money) of $290, one would be hard pressed to accept that this project “earns” 9.1%, let alone 57.2%! Comparing 9.1% to the MARR of 5% would seem to indicate that this project is acceptable. 44 3. PROJECT EVALUATION METHODS Let’s examine the ERR, NP V , and modiﬁed I RR for this project: ERR : N P V : PC FI ERR = \| − 100 − 90(P /F )5,4 − 80(P /F )5,5 − 50(P /F )5,6\| = $274.0 = 90(F /P )5,5 + 120(F /P )5,4 + 80(F /P )5,3 = $353.3 = (353.3/274.0)1/6 − 1 = 0.043 = 4.3% . The table or the ﬁgure show that the NP V at an interest rate of 5% (the investor’s MARR) is -$10.4. The modiﬁed I RR would be calculated by replacing the negative cash ﬂows with PC calculated above to create a new set of cash ﬂows as follows: 0 1 2 3 4 5 6 -274 90 120 80 0 0 0 Using the trial and error solution technique or Excel®, the modiﬁed I RR is 2.9%. Thus, the ERR, the modiﬁed I RR, and the NPV indicate that this project is not an acceptable project for the investor. In summary, acceleration projects have the potential to add another level of complexity to the calculation of I RR in that multiple positive rates may exist. The authors strongly suggest that evaluators utilize N P V or ERR calculations to determine the economic viability of acceleration projects. 3.9 PAYOUT A supplementary evaluation technique that is frequently used is payout period or simply payout. Payout may be calculated with or without discounting although it is usually calculated without considering the time value of money. Payout refers to the time that it takes for a project to return its initial investment. Thus, it’s a quick measure of how long the investment is at risk. Although this time may be a very useful piece of information to compute for a particular project, payout analysis is limited in its use as an evaluation criterion. It does not serve as a useful screening criterion since it ignores any cash ﬂows occurring past the payout period. Therefore, it must be used in conjunction with one of the evaluation techniques that have already been presented. Example 3.9 Given the following cash ﬂow diagram, compute the undiscounted payout time and the discounted payout time if MARR is 15%. 0 1 2 3 4 3.9. PAYOUT 45 -100 60 60 60 60 Undiscounted Payout: Year Cash Flow 0 1 2 (cid:1086) 100 60 60 Cumula(cid:415)ve Cash Flow (cid:1086) 100 (cid:1086) 40 20 Interpolate between years 1 and 2 to ﬁnd when the cumulative cash ﬂow equals zero: Payout = 1 + (cid:3) (cid:2) −40 − 0 −40 − (20) (2 − 1) = 1.67 years Discounted Payout: Year Cash Flow Discounted Cash Flow 0 1 2 3 (cid:1086) 100 60 60 60 100 60(P /F ) 15.1 = 52.2 60(P /F ) 15.2 = 45.4 60(P /F ) 15.3 = 39.4 Cumula(cid:415)ve Discounted Cash Flow (cid:1086) 100 (cid:1086) 47.8 (cid:1086) 2.4 37.0 Interpolate between years 2 and 3 to ﬁnd when the cumulative cash ﬂow equals zero: Payout = 2 + (cid:3) (cid:2) −2.4 − 0 −2.4 − (37.0) (3 − 2) = 2.06 years Discounted payout measures the time for the project to return the initial investment and a 15% rate of return on that initial investment. 46 3. PROJECT EVALUATION METHODS 3.10 PROBLEMS 3.1. Calculate the present value and annual value of the following cash ﬂow diagram. MARR is 15%. 0 1 2 3 4 5 6 7 -2500 500 650 800 800 800 800 800 3.2. Calculate the I RR and ERR for the cash ﬂow diagram given in Problem 3.1. 3.3. An individual is considering the purchase of a property that he believes he can resell for $25,000 at the end of 10 years. The property will generate positive cash ﬂows of $1,500 per year for the 10 years. What is the maximum that the individual should pay for the property if his MARR is 12%? 3.4. An investment of $10,000 will yield $33,000 at the end of 5 years with no other cash ﬂows. What is the I RR of this investment? 3.5. Calculate the I RR for the following cash ﬂow diagram. 0 1 2 3 4 5 -2000 -500 1000 1000 1000 1000 3.6. A company invests $30,650 in a project which yields an income (positive cash ﬂow) of $10,000 in the ﬁrst year, $9,000 in the second, $8,000 in the third, … etc … and $1,000 in the tenth, along with an extra $10,000 income at the end of year 10. The company’s MARR is 10%. Determine the I RR and ERR of this project. 3.7. Determine the N P V , ERR, and modiﬁed I RR for the following cash ﬂow diagram. Use an MARR of 15%. 3.10. PROBLEMS 47 0 1 2 3 -50 100 100 -100 3.8. Determine the N P V , NAV , modiﬁed I RR, and ERR for the following cash ﬂow diagram if the MARR is 10%. 0 1 2 3 4 -75 50 50 -30 200 3.9. You are a project engineer and you have to make a choice between two contractors to perform some rebuilding work on a manufacturing facility. One contractor proposes that he will do the work for $1,300,000 payable immediately. The other contractor proposes that he will perform the same job for $1,400,000 payable in eight equal quarterly payments, starting 3 months after the job begins. A nominal rate of 14% should be used as the MARR. What equivalent annual interest rate is the second contractor offering? Which contractor’s offer would you accept? Repeat the analysis with the NP V technique. 3.10. John Q. Customer has received his bill for the next 6 months premium on his auto insurance. The bill allows him two methods to pay his premium of $189.00. He can either pay the entire amount now, or he can pay $99.00 now, which includes half of the premium plus a $4.50 prepaid “service charge” and $94.50 in two months, the other half of the premium. The insurance company is, implicitly, offering John a “loan.” What is the effective annual interest rate of the loan? Would you take the “loan?” Why or why not? 48 3. PROJECT EVALUATION METHODS 3.11. A project is expected to cost $2,000,000 and have the following net revenues: Year Net Revenue 1,000,000 800,000 600,000 400,000 200,000 100,000 1 2 3 4 5 6 Calculate the undiscounted and discounted payout periods. The MARR is 15%. 3.12. Engineer A retires at the age of 65 with a retirement account worth $500,000. At what interest rate would this amount need to be invested in order to withdraw $50,000 at the end of each of the next 15 years? 3.13. Develop an Excel® spreadsheet to compute NP V , NAV , NF V , I RR, and ERR for the cash ﬂow diagram given in Problem 3.1. 3.14. Develop an Excel® spreadsheet to solve Problem 3.3 for MARR values of 5%, 10%, 12%, 15% and 20%. 3.15. Develop an Excel® spreadsheet to solve Problem 3.4 for initial investments of $5000, $10000 and $15000. 3.16. Develop an Excel® spreadsheet to solve Problem 3.5 for initial investments of $2000, $1500, and $1000. 3.17. Develop an Excel® spreadsheet to solve Problem 3.6. 3.18. Develop an Excel® spreadsheet to solve Problem 3.7. 3.19. Develop an Excel® spreadsheet to solve Problem 3.8. 3.20. Develop an Excel® spreadsheet to solve Problem 3.9. 3.21. Develop an Excel® spreadsheet to solve Problem 3.10. 3.22. Develop an Excel® spreadsheet to solve Problem 3.11 for MARR values of 5%, 10%, and 15%. 3.23. Develop an Excel® spreadsheet to solve Problem 3.12. C H A P T E R 4 49 Service Producing Investments 4.1 INTRODUCTION There are, in general, two types of investments—one which produces income and one which produces a service. A service producing investment is one that results in a cash ﬂow diagram that normally contains no positive cash ﬂows with the exception of a possible salvage value of the service. Salvage value is the estimated value of an asset at the end of its useful life. It is assumed that the asset can be sold (as scrap metal for example) for this value as a positive cash ﬂow to the project. The authors use the symbol L to represent the positive cash ﬂow due to salvage value. An example of a service producing investment would be the consideration of either purchasing a new vehicle for a ﬁeld ofﬁce or leasing the vehicle. The vehicle provides a necessary service for the personnel in the ﬁeld ofﬁce but does not directly produce any income for the company. Generally, a leased vehicle would not have any salvage value since it is just returned to the leasing agency at the end of the lease period, while a purchased vehicle would have some salvage value since it could be sold to another owner. This chapter will discuss evaluation techniques for service producing investments for equal and unequal life alternatives. 4.2 EQUAL LIFE ALTERNATIVES Consider the following situation. An investment needs to be made by a company for a particular service that is necessary for the company to conduct its business. Two or more alternatives have been identiﬁed that provide the same service over the same time period. These alternatives are known as equal life alternatives and they lend themselves to straight forward application of the evaluation methods that were presented in Chapter 3. 4.2.1 EQUIVALENCE TECHNIQUES The equivalence techniques, primarily NPV, are valid methods to choose the correct alternative. However, since service producing investments deal primarily with costs, NPV is replaced with Net Present Cost (NPC) which is the absolute value of the NPV. When the evaluator calculates NPC, the simplest approach is to change the signs of all of the project’s cash ﬂows as will be demonstrated in Example 4.1. The alternative with the lowest NPC would be the best economic choice. Similarly, Net Annual Value (NAV) is replaced with Net Annual Cost (NAC). 50 4. SERVICE PRODUCING INVESTMENTS Example 4.1 Two alternatives are being considered which provide the same service and which have the same useful life of ﬁve years. Alternative A has an initial capital investment of $12,000, annual operating costs of $3,500, and a salvage value of $5,000. Alternative B has an initial capital investment of $20,000, annual operating costs of $1,500, and a salvage value of $10,000. If the company’s MARR is 15%, which alternative would be the best economic choice? Use NPC and NAC analysis. Alternative A: 0 1 2 3 4 5 -12000 -3500 -3500 -3500 -3500 -3500 L = 5000 Alternative B: 0 1 2 3 4 5 -20000 -1500 -1500 -1500 -1500 -1500 L = 10000 NPC: NAC: N P CA = 12000 + 3500(P /A)15,5 − 5000(P /F )15,5 = $21, 250 N P CB = 20000 + 1500(P /A)15,5 − 10000(P /F )15,5 = $20, 060 N ACA = 12000(A/P )15,5 + 3500 − 5000(A/F )15,5 = $6, 340 N ACB = 20000(A/P )15,5 + 1500 − 10000(A/F )15,5 = $5, 980 Both NPC and NAC analysis indicate that Alternative B is the best economic choice since it has the lowest cost under these conditions. 4.2.2 RATE OF RETURN METHODS Rate of return methods need to be altered since there are generally no positive cash ﬂows in a service producing investment except, perhaps, a salvage value. Under that scenario, the deﬁnitions of IRR and ERR don’t make any sense and, in fact, generally do not result in positive values. 4.2. EQUAL LIFE ALTERNATIVES 51 When comparing two service producing investment alternatives, an incremental project rate of return (either IRR or ERR) is determined and compared to the MARR. The cash ﬂows for the incremental project are found by taking the cash ﬂows from the investment with the larger initial capital cost and subtracting the cash ﬂows from the investment with the lower initial capital cost. It should be fairly obvious that if the alternative with the larger initial capital cost doesn’t have lower annual costs than the alternative with the lower initial capital cost, it will never be the economic choice. Therefore, one would expect the incremental project cash ﬂow diagram to be represented by a negative initial investment, followed by positive cash ﬂows that represent the savings generated by choosing the alternative with the larger initial capital cost over the alternative with the lower initial capital cost. Thus, another name for this incremental project is the “savings project.” The rate of return (either IRR or ERR) can now be calculated for the savings project. If the rate of return is larger than the MARR, this indicates that the savings project is an acceptable project which thereby insinuates that the correct economic choice would be the alternative with the larger initial capital cost. The net savings that occur by choosing the alternative with the larger initial capital cost more than offset its additional initial capital cost. If the IRR or ERR is less than the MARR, the savings project is not an acceptable project and, therefore, the alternative with the lower initial capital cost will be the economic choice. If there are more than two alternatives, all of the alternatives should ﬁrst be listed in descending order of initial capital cost and the various pairings of alternatives would be evaluated using one of the techniques above. For example, if there were three alternatives (A, B, C) in order of initial capital costs (with A having the highest and C having the lowest), one would ﬁrst compare A to B. If A is the better choice, one would then compare A to C to determine the best overall choice. However, if B were the better choice, the next comparison would be B to C to determine the best overall choice. Example 4.2 Compare Alternatives A and B given in Example 4.1 and determine the best economic choice using IRR and ERR techniques. Recall that the MARR is 15%. Since Alternative B has the highest initial capital cost, the savings project would be created by subtracting the cash ﬂows of Alternative A from those of Alternative B: Savings Project, B-A: 0 1 2 3 4 5 -8000 2000 2000 2000 2000 2000 L = 5000 The N P V of this project is given by: N P VB−A = −8000 + 2000(P /A)i,5 + 5000(P /F )i,5 52 4. SERVICE PRODUCING INVESTMENTS Interest Rate, % 15 20 N P V 1190.1 -9.4 Interpolation yields an I RR = 20%. Since I RR > MARR, B is the best economic choice. ERR : PC = \| − 8000\| = 8000 FI = 2000(F /A)15,5 + 5000 = 18485 ERR = (18485/8000)1/5 − 1 = 0.182 = 18.2% Again, the ERR would indicate that Alternative B is the best economic choice. Example 4.3 Given the 3 alternatives below that provide the same service over a 4 year period, develop an Excel® spreadsheet that uses IRR analysis to determine which alternative is the best economic choice. MARR is 10%. Alternative A: 0 1 2 3 4 -1000 -300 -350 -400 -450 L = 200 Alternative B: 0 1 2 3 4 -800 -320 -380 -440 -500 L = 100 Alternative C: 0 1 2 3 4 4.2. EQUAL LIFE ALTERNATIVES 53 -700 -340 -410 -480 -550 L = 50 Spreadsheet and Results: Incremental IRR calculations for Example 4.3: A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 The N P V and I RR functions are the same as presented in Chapter 3. The spreadsheet shows the comparisons between all three projects. Since the initial investment of Alternative A is greater than the initial investment of Alternative B and the initial investment of Alternative B is greater than the initial investment of Alternative C, the alternatives are already correctly ordered by size of initial investment. NPC analysis shows that Alternative B has the lowest net present cost and, therefore, should be the alternative of choice. The analysis of the incremental I RR calculations would be completed as follows: 1. Compare the ﬁrst two alternatives. 2. Since the I RR of Incremental Project A-B (5.7%) is less than the MARR (10%), Alternative B is a better choice than Alternative A. 54 4. SERVICE PRODUCING INVESTMENTS 3. Now compare Alternative B with Alternative C. 4. Since the I RR of Incremental Project B-C (23.5%) is greater than the MARR (10%), Alter- native B is a better choice than Alternative C. Therefore, Alternative B is the best economic choice (same as determined from the NPC method). Note that since Alternative B was a better choice than Alternative A, one never utilizes the incremen- tal IRR that is calculated for the Incremental Project A-C. However, it is a necessary portion of the Excel® spreadsheet since one does not know, ahead of time, which Alternatives will be eliminated during the analysis of the results. 4.3 UNEQUAL LIFE ALTERNATIVES The analysis of service producing investments that have alternatives which provide the same service but have unequal project lives cannot be completed without modiﬁcations to the alternatives. A common evaluation life for each alternative must be found before a proper economic decision can be made. This is because the deﬁnition of two alternatives providing the same service includes the assumption that they provide this service for the same length of time. For example, one cannot compare an alternative to purchase a vehicle, keep it for 5 years, and then sell it for its salvage value to a three-year lease option for the same vehicle. Both options are providing the service of a vehicle, but the service is provided for different lengths of time. There are, in general, two methods employed by evaluators to ﬁnd common evaluation lives in these situations. The ﬁrst method requires the determination of a least common multiple of service lives for the alternatives being considered. The second method involves the determination of a common study period which will be either the life of the shortest or longest alternative. In both methods, cost assumptions must be made that will impact the ﬁnal analysis. 4.3.1 LEAST COMMON MULTIPLE METHOD The least common multiple method of ﬁnding a common service life utilizes the same principles that are involved in determining the common denominator when adding or subtracting fractions. Consider the example of two alternatives having useful lives of 3 and 4 years. The least common multiple in this case would be 12 since there is not a smaller number which is divisible by 3 and 4 without leaving partial years as a remainder. The alternative having a useful life of 3 years would be repeated 4 times on a time line to reach the least common multiple of 12 years. The other alternative would be repeated 3 times. A couple of disadvantages of this method should immediately come to mind. First, costs do not stay constant over time, so one would need to predict the future cost of each alternative. Cost escalation will be discussed in Chapter 6, but even this approach requires a number of assumptions. Secondly, one or more of the alternatives may be rendered obsolete by the development of new technology before the end of the time period that corresponds to the least common multiple is reached. 4.3. UNEQUAL LIFE ALTERNATIVES 55 4.3.2 COMMON STUDY PERIOD The common study period method of ﬁnding a common service life utilizes either the life of the shortest alternative or the life of the longest alternative as the common study period. To determine which of these to use, the length of the common study period should be, if possible, the length of time that the service is actually required. If the life of the shortest alternative is used, the extra years of the longer life alternative are neglected and a new salvage value is assigned at the end of the common study period. The new salvage value will typically be larger than the original salvage value since it should reﬂect the value of the extra years that are neglected. If the life of the longest alternative is used, the shorter project needs to be extended via one of two methods. The project can be extended by either estimating the cost involved to repair the service to get additional years of service from it or by purchasing a new unit of service. Both of these require some assumptions with regard to future cost. Example 4.4 The cash ﬂows shown below represent two alternatives which can provide the same service. Assume that the MARR is 15%. Use both methods described above to determine which alternative is the best economic choice. (Numbers are in $1,000.) Alternative A: 0 1 2 3 9 10 -150 -3 -3 -3 …… -3 -3 L = 10 Alternative B: 0 1 2 3 4 5 -50 -18 -18 -18 -18 -18 L = 8 56 4. SERVICE PRODUCING INVESTMENTS Least Common Multiple Technique: The least common multiple of 5 and 10 is 10. Therefore, one needs to extend Alternative B from 5 to 10 years. It will be assumed that there is no escalation in the costs for Alternative B for the second 5 year period. In Chapter 6, we will consider this same problem with cost escalation. Therefore, Alternative B extended to 10 years would be: Alternative B (extended to 10 years): 0 1 2 3 5 6 9 10 -50 -18 -18 -18…… -18 L = 8 -50 -18 …… -18 -18 L = 8 N P C Analysis: N P CA = 150 + 3(P /A)15,10 − 10(P /F )15,10 = $162.6 N P Cextended B = 50 + 18(P /A)15,10 + 42(P /F )15,5 − 8(P /F )15,10 = $159.2 N P C analysis indicates that Alternative B is the best economic choice under the assumptions that were made (e.g., no increase in costs for the second 5 years). If costs increase or if technology makes Alternative B obsolete, then this analysis will be inaccurate and one may need to consider other non-economic factors in making this decision. Common Study Period Technique: Let’s shorten Alternate A to 5 years by neglecting the costs in the ﬁnal 5 years and by increasing the salvage value that could be received at year 5 to $80,000. Alternative A (shortened to 5 years): 0 1 2 3 4 5 -150 -3 -3 -3 -3 -3 L = 80 N P C Analysis: N P Cshortened A = 150 + 3(P /A)15,5 − 80(P /F )15,5 = $120.3 NP CB = 50 + 18(P /A)15,5 − 8(P /F )15,5 = $106.4 N P C analysis indicates that Alternative B is the best economic choice under these set of assumptions (e.g., the new estimated salvage value for Alternative A and the assumption that one can actually “sell” Alternative A for salvage at the end of 5 years). 4.4. PROBLEMS 57 4.4 PROBLEMS 4.1. A mining company is in need of four trucks. Suppliers will offer the options of purchasing or leasing the trucks. The purchase price is $200,000. Maintenance, insurance, and general operating costs (payable at the end of each year) will be $30,000 in year 1, $40,000 in year 2, and $50,000 in year 3 with an expected salvage value of $70,000 at the end of year 3. The lease price is $80,000 per year for the 3 years (payable at the beginning of each year). The lease covers maintenance costs, but insurance and general operating costs will be $25,000 per year (payable at the end of each year). If the company’s MARR is 20%, determine the best economic choice. 4.2. A natural gas producing company is considering two engine systems for use in driving a small compressor. System A can be purchased for $120,000 and is expected to have a life of 4 years. Annual diesel fuel consumption is estimated to be 60 gallons per day of use. System B can be purchased for $150,000 and is expected to have a life of 4 years. Annual propane fuel consumption is estimated to be 40 gallons per day of use. Both engines have salvage values equal to 15% of initial cost and both will accomplish the needed requirements. Estimates of fuel costs for each system and expected days of use each year are as follows: Assume that MARR is 8% and that all other costs besides fuel will be the same for both systems. Which system is the best economic choice? 58 4. SERVICE PRODUCING INVESTMENTS 4.3. Use ERR analysis to determine which alternative would be the best economical choice. Verify your decision with NPC analysis. Assume the MARR equals 10%. Alternative A: 0 1 2 3 4 -500 -25 -25 -25 -25 L = 100 Alternative B: 0 1 2 3 4 -300 -50 -50 -50 -50 L = 25 Alternative C: 0 1 2 3 4 -250 -75 -60 -45 -30 L = 10 Alternative D: 0 1 2 3 4 -450 -35 -35 -35 -35 L = 100 4.4. Consider the two service producing projects described below. They will provide the same service but they do not have equal lives. Use NPC, IRR, and ERR analyses to determine which alternative should be chosen. For the least common multiple method, assume no increases in future costs for either project. For the common study period method, assume that the salvage value for Alternative B will increase to $4,000 at the end of year 3. The MARR is 10%. 4.4. PROBLEMS 59 Alternative A: 0 1 2 3 -15000 -1000 -1000 -1000 L = 0 Alternative B: 0 1 2 3 4 -10000 -3000 -3000 -3000 -3000 L = 2000 4.5. Use Excel® to solve Problem 4.1 for values of MARR of 10%, 15%, 20%, and 25%. 4.6. Use Excel® to solve Problem 4.2 for values of MARR of 5%, 8%, and 12%. 4.7. Use Excel® to determine what initial cost of Alternative A in Problem 4.2 would make the two systems equal at an MARR of 8%. 4.8. Use Excel® to solve Problem 4.3. 4.9. Use Excel® to solve Problem 4.4. C H A P T E R 5 61 Income Producing Investments 5.1 INTRODUCTION In the previous chapter, investments were considered that only provided a service of some kind for the investor. In this chapter, investments that generate income (or proﬁt) are discussed. The evaluation techniques to be used will be identical to those introduced in Chapter 3. However, one additional concept needs to be introduced when an investor is faced with making decisions between multiple alternatives. This concept is the fact that income producing investment situations can be classiﬁed as being either mutually exclusive, independent, or contingent as deﬁned in later sections of this chapter. 5.2 INVESTMENT IN A SINGLE PROJECT If an investor is being offered the opportunity to invest in a single project (that is, without considering any other alternatives other than the “do nothing” alternative), he needs to consider the following two economic issues: (cid:129) Does he have enough money to invest in this project? (cid:129) Is the project proﬁtable enough? If one does not consider the option of the investor borrowing money from a lending institution, the answer to the ﬁrst question should be a clear “yes” or “no.” If the answer is “no,” then the investor cannot invest in the project. Chapter 7 will cover ﬁnancial leverage which will allow for the borrowing of money. If the answer to the ﬁrst question is “yes,” then project proﬁtability needs to be considered in order to answer the second question. Utilizing the analysis techniques presented in Chapter 3, this would mean one of the following: (cid:129) The N P V of the project, calculated at the investor’s MARR, is greater than zero. (Similarly, N AV or N F V would be greater than zero.) (cid:129) The I RR of the project is greater than the investor’s MARR. (cid:129) The ERR of the project is greater than the investor’s MARR. Of these three options, the authors strongly suggest the NPV method. This will become clearer as this chapter proceeds. 62 5. INCOME PRODUCING INVESTMENTS Example 5.1 An investor with MARR of 15% has been presented with the opportunity to invest in the following income producing project. Assume that he has $20,000 to invest. Should he invest in this project based on economic considerations? 0 1 2 3 9 10 -20000 7500 7500 7500 …… 7500 7500 L = 10000 Using the NPV, IRR, and ERR techniques described in Chapter 3: N P V : I RR : ERR : N P V = −20000 + 7500(P /A)15,10 + 10000(P /F )15,10 = $20, 115 N P V = −20000 + 7500(P /A)I RR,10 + 10000(P /F )I RR,10 = 0 Trial and error solution yields PC = \| − 20000\| = $20, 000 FI = 7500(F /A)15,10 + 10000 = $162, 300 ERR = (162300/20000)1/10 − 1 = 0.233 = 23.3% I RR = 36.7% Since N P V > 0, I RR > MARR, and ERR > MARR, this project would be acceptable to the investor. 5.3 MUTUALLY EXCLUSIVE ALTERNATIVES When considering two or more alternatives in an economic analysis situation in which only one alternative may be chosen, the alternatives are said to be mutually exclusive. Examples of mutually exclusive alternatives would include the choice between two or more ways to develop a physical property location (for example, build a gas station or a laundromat, but not both) or the choice between two or more projects when faced with limited investment capital. To evaluate choices in mutually exclusive situations, it is necessary to ﬁrst determine if each alternative is economically acceptable using the same questions as listed above. Any alternatives that are not acceptable will be discarded. The remaining alternatives can then be ranked by a couple of methods and the project at the top of the ranking is the best economic choice. 5.3.1 EQUIVALENCE TECHNIQUES Equivalence techniques are those that use NPV, NAV, or NFV calculations. As explained earlier, for a given project, if one of these values is greater than zero then the others will be also. Recall that values greater than zero indicate that the alternative is an acceptable one. Obviously, if the value is zero, the project earns exactly the MARR. Thus, the evaluation approach, using NP V as the calculation choice, is as follows: 5.3. MUTUALLY EXCLUSIVE ALTERNATIVES 63 1. Calculate the N P V for each alternative. 2. Eliminate any alternative with NP V < 0. 3. If all alternatives have NP V < 0, then the investor’s decision should be the “do nothing” alternative. 4. If one or more alternatives have NP V ≥ 0, the alternative with the largest positive NP V is the best economic choice. Example 5.2 In addition to the alternative given in Example 5.1, consider the situation where an investor with an MARR of 15% has the choice between that alternative and the two additional ones given below. Assume that the investor has $80,000 to invest. Also assume that the three alternatives are mutually exclusive projects. This may occur because they represent alternatives in which only one can actually be “built” or may occur because the investor only has $80,000 to invest so he only has enough capital to invest in one. Let’s call the project in Example 5.1 Alternative A. Thus, new alternatives are Alternative B and Alternative C. Alternative B: 0 1 2 3 9 10 -80000 20000 20000 20000 …… 20000 20000 L = 25000 Alternative C: 0 1 2 3 9 10 -70000 17500 17500 17500 …… 17500 17500 L = 21875 64 5. INCOME PRODUCING INVESTMENTS Using the NPV technique described in Chapter 3: N P V : N P VB = −80000 + 20000(P /A)15,10 + 25000(P /F )15,10 = $26, 560 N P VC = −70000 + 17500(P /A)15,10 + 21875(P /F )15,10 = $23, 240 Since N P VA, N P VB , and NP VC are all greater than zero, all three alternatives would be acceptable to the investor. However, since these are mutually exclusive alternatives, Alternative B is the overall best economic choice because its NP V is the largest. One might think that the evaluator should directly compare any two projects (such as A and B in the previous example) by using incremental NPV analysis. The following calculations will demonstrate that this approach is not necessary because the NPV of an incremental project such as B-A is governed by the following relationship: NP V B−A = NP V B − NP V A From Example 5.1, N P V A = $20, 115 and from Example 5.2, NP V B = $26, 560. Using the relationship above, N P V B−A should be $6,445. The following cash ﬂow diagram represents the incremental project B-A: Alternative B-A: 0 1 2 3 9 10 -60000 12500 12500 12500 …… 12500 12500 L = 15000 NPV: N P V B−A = −60000 + 12500 (P A)15,10 Note that the NPV of the incremental project, B-A, is, indeed, numerically equal to the + 15000 (P = $6, 445 F )15,10 (cid:12) (cid:12) difference between the NPV values of alternative B and A (B minus A). 5.3.2 RATE OF RETURN TECHNIQUES One can use both the internal rate of return (IRR) and external rate of return (ERR) methods to ﬁnd the best alternative from a list of mutually exclusive alternatives. However, unlike NP V , it will be shown that the alternative with the highest I RR or ERR is not necessarily the best economic choice. One must be very careful not to simply rank the projects by I RR or ERR. The process to determine the best alternative using I RR or ERR is as follows: 1. Calculate the I RR or ERR for each alternative. 2. Eliminate any alternative with I RR or ERR < MARR. 5.3. MUTUALLY EXCLUSIVE ALTERNATIVES 65 3. If all alternatives have I RR or ERR < MARR, then the investor’s decision should be the “do nothing” alternative. 4. If one or more alternatives have I RR or ERR ≥ MARR, then those alternatives should be rank ordered from the one with the highest initial investment to the one with the lowest initial investment. 5. A comparison is made between the alternatives with the two largest initial investments. Create an incremental project cash ﬂow diagram by subtracting the cash ﬂows of the lower initial investment from those of the higher initial investment. 6. Calculate the I RR or ERR of the incremental project. If this I RR or ERR is ≥ MARR, then the alternative with the larger initial investment is the better economic choice. Similarly, if this I RR or ERR is < MARR, then the alternative with the lower initial investment is the better economic choice. Keep the best alternative and discard the other one. 7. If additional alternatives are still available, return to step 5 and compare the alternative that was kept from step 6 with the one with the next lower initial investment. 8. If no additional alternatives remain, the best economic choice is the alternative that was kept from step 6. Example 5.3 Consider the three alternatives A, B, and C introduced in the earlier example problems. Use IRR and ERR analysis to determine the best economic choice. The MARR is 15%. Alternative A: 0 1 2 3 9 10 -20000 7500 7500 7500 …… 7500 7500 L = 10000 I RR : N P V = 0 = −20000 + 7500(P /A)I RR,10 + 10000(P /F )I RR,10 Trial and error solution yields I RR = 36.7% 66 5. INCOME PRODUCING INVESTMENTS ERR : PC = \| − 20000\| = $20, 000 FI = 7500(F /A)15,10 + 10000 = $162, 300 ERR = (162300/20000)1/10 − 1 = 0.233 = 23.3% Alternative B: 0 1 2 3 9 10 -80000 20000 20000 20000 …… 20000 20000 L = 25000 I RR : N P V = 0 = −80000 + 20000(P /A)I RR,10 + 25000(P /F )I RR,10 Trial and error solution yields I RR = 22.7% ERR : PC = \| − 80000\| = $80, 000 FI = 20000(F /A)15,10 + 25000 = $431, 100 ERR = (431100/80000)1/10 − 1 = 0.183 = 18.3% Alternative C: 0 1 2 3 9 10 -70000 17500 17500 17500 …… 17500 17500 L = 21875 I RR : N P V = 0 = −70000 + 17500(P /A)I RR,10 + 21875(P /F )I RR,10 Trial and error solution yields I RR = 22.7% 5.3. MUTUALLY EXCLUSIVE ALTERNATIVES 67 ERR : PC = \| − 70000\| = $70, 000 FI = 17500(F /A)15,10 + 21875 = $377, 200 ERR = (377200/70000)1/10 − 1 = 0.183 = 18.3% As one can see, all three alternatives have I RR and ERR ≥ MARR. Therefore, all three alternatives are acceptable. Putting them in ranked order by initial investment yields: Alterna ve B C A Ini al Investment $80,000 $70,000 $20,000 ERR I RR 22.7% 18.3% 22.7% 18.3% 36.7% 23.3% At this point, one cannot simply choose the alternative with the highest I RR or ERR as the best overall economic choice. First, compare Alternative B to Alternative C: Alternative B-C: 0 1 2 3 9 10 -10000 2500 2500 2500 …… 2500 2500 L = 3125 Using the techniques described in Chapter 3: I RR : N P V = 0 = −10000 + 2500(P /A)I RR,10 + 3125(P /F )I RR,10 Trial and error solution yields I RR = 22.7% ERR : PC = \| − 10000\| = $10, 000 FI = 2500(F /A)15,10 + 3125 = $53, 900 ERR = (53900/10000)1/10 − 1 = 0.183 = 18.3% Since both the I RR and ERR are greater than the MARR, this indicates that Alternative B is better than Alternative C. Eliminate Alternative C from further consideration and compare Alternative B to the next alternative. 68 5. INCOME PRODUCING INVESTMENTS Comparing Alternative B to Alternative A: Alternative B-A: 0 1 2 3 9 10 -60000 12500 12500 12500 …… 12500 12500 L = 15000 Using the techniques described in Chapter 3: I RR : N P V = 0 = −60000 + 12500(P /A)I RR,10 + 15000(P /F )I RR,10 Trial and error solution yields I RR = 17.6% ERR : PC = \| − 60000\| = $60, 000 FI = 12500(F /A)15,10 + 15000 = $268, 800 ERR = (268800/60000)1/10 − 1 = 0.162 = 16.2% Since both the I RR and ERR are greater than the MARR, this indicates that Alternative B is better than Alternative A. Since the list of mutually exclusive alternatives has been exhausted, Alternative B is the best overall economic choice. In summary, one cannot use the values of the I RR and ERR from individual alternatives to determine the best economic choice. If one were to do that, the results shown in the table for this example would indicate that Alternative A is the best economic choice since it has the largest values of I RR and ERR. However, both NP V and incremental rate of return analyses clearly show that Alternative B is the best economic choice. Example 5.4 To further reinforce the fact that one should not rank investments through the use of rate of return, consider the following example. You are an investor with only $10 in your pocket. Two friends offer you the following opportunities: Friend #1 needs $1 from you, but will give you $2 back at the end of the day. Friend #2 needs all $10 of your money, but will give you $12 back at the end of the day. Which opportunity is better for you from an economic point of view? Examine this using NPV and incremental IRR approaches. Since the time frame is short (1 day), your daily MARR can be considered to be very close to 0%. Friend #1 Alternative: 5.3. MUTUALLY EXCLUSIVE ALTERNATIVES 69 1 2 1 12 0 -1 N P V : N P V = −1 + 2(P /F )0,1 = $1 N P V = −1 + 2(P /F )I RR,1 = 0 I RR: Trial and error solution yields I RR = 100% Friend #2 Alternative: 0 -10 N P V : N P V = −10 + 12(P /F )0,1 = $2 I RR: Trial and error solution yields I RR = 20% N P V = −10 + 12(P /F )I RR,1 = 0 NPV analysis indicates that Friend#2 Alternative is the best economic choice, but IRR analysis appears to indicate that Friend#1 Alternative is the best. Friend #1 is offering a 100% rate of return and Friend #2 is offering a 20% rate of return. One might think that Friend #1’s offer is the best. However, at the end of the day, you only have $11 in your pocket if you invest with Friend #1, but $12 if you invest with Friend #2. It is clear, therefore, that you should invest with Friend #2 even though that friend is offering a lower rate of return. The reason that the higher rate of return option is not the best option in this case is that the other $9 in your pocket is earning 0% rate of return. Combining 0% rate of return on $9 and 100% rate of return on $1 ends up yielding a 10% overall rate of return if you invest with Friend #1. 70 5. INCOME PRODUCING INVESTMENTS Incremental Alternative of Friend#2 – Friend#1: 0 -9 1 10 N P V = −9 + 10(P /F )I RR,1 = 0 I RR: Trial and error solution yields I RR = 11.1% Since the incremental I RR is greater than your MARR, this indicates that Friend #2 Alter- native is, indeed, the best economic choice. This example also introduces the notion of risk in an investment. Obviously, the mathematical analysis has shown that loaning Friend #2 is the better investment. But, it requires you, the lender, to ‘give up’ all of your money. If there was a chance that neither friend could come through with their repayment, then it might be better to keep the $9 in your pocket and invest in Friend #1. In the event that neither friend could provide their repayment, at least you would still have $9 left of your money. The concept of risk in investments will be discussed much more in Chapter 9. 5.3.3 USING EXCEL® As shown in the previous chapters, Excel® can be used to choose the best alternative among a group of mutually exclusive alternatives. Since Excel® offers the ability to quickly calculate incremental rates of return, there is no need to manually choose the pairs of alternatives to be evaluated. However, this requires that one needs to evaluate each possible pair of alternatives (starting with all alterna- tives ordered from highest to lowest initial investment) and then analyze the results table rather than analyze speciﬁc pairs one at a time. For example, for Alternatives A, B, and C presented in Examples 5.1 through 5.3, an Excel® spreadsheet might look like what is shown in Table 5.1. Recall that within the original alternatives, Alternative B had the largest initial investment, C had the next highest initial investment, and A had the lowest initial investment. Thus, the pairs of interest are B-C, B-A, and C-A. One would use Table 5.1 as follows: If using NPV analysis: 1. Note that the values of NP V given in cells B17, C17, and D17 are all positive. This indicates that all three alternatives are acceptable. 2. Note that Cell C17 contains the largest value of NP V . This would indicate that Alter- native B is the best economic choice. 5.3. MUTUALLY EXCLUSIVE ALTERNATIVES 71 T a b l e 5 . 1 : E x c e l ® s o l u t i o n o f E x a m p l e s 5 . 1 t h r o u g h 5 . 3 72 5. INCOME PRODUCING INVESTMENTS If using IRR or ERR analysis (we will use IRR for this analysis): 1. Note that the values of I RR given in cells B18, C18, and D18 are all greater than the MARR. This indicates that all three alternatives are acceptable. 2. Examine cell F18, which is the result of comparing the ﬁrst pair of projects: B and C. Since this value (22.7%) is larger than the MARR, this would indicate that Alternative B is better than Alternative C. Alternative C is thus removed from further consideration and the next viable pair would be B-A. 3. Examine cell G18, which is the result of comparing projects B and A. Since this value (17.6%) is larger than the MARR, this would indicate that Alternative B is better than Alternative A. 4. Since all necessary pairs have been examined, Alternative B is the best economic choice. 5. While column H is required to calculate the NP V , I RR, and ERR of the C-A pair, it is not utilized in this example since Alternative C was removed from consideration after its comparison against Alternative B. However, when developing this spreadsheet, one does not know the result of the incremental analyses and, thus, all possible pairs must be included. In addition, depending on the value of MARR, column H might be utilized in other scenarios. 5.4 UNEQUAL LIFE ALTERNATIVES Recall in Chapter 4 that if one was comparing service producing investments that have unequal lives, one must choose one of two methods to force the projects to the same length of time. This is because, to be comparable, the service must be offered for the same length of time. In income producing investments, creating a common life is not required for NPV analysis. However, for NAV, NFV, IRR, or ERR analysis, one must make the lives the same. Usually the life of the longest alternative is used as the common evaluation life. If should be noted, however, that to extend an income producing investment, one does not extend the positive cash ﬂows. Instead, zero cash ﬂows are used to extend the life of the project. This is the case because one is assuming that the cash ﬂows from the income producing investment have already been estimated out to the full life of the project and the project will be shut down at that time. When conducting incremental rate of return analyses on unequal life alternatives, the evaluator may ﬁnd that the incremental project has multiple changes in sign of the yearly cash ﬂows. This was described in Chapter 3 as an acceleration project. Since the alternating signs may yield multiple I RR values, either the modiﬁed IRR or ERR technique will need to be applied in the analysis. Example 5.5 Use NPV, NAV, NFV, IRR, and ERR analyses to evaluate the unequal life alternatives below. MARR is 12%. 5.4. UNEQUAL LIFE ALTERNATIVES 73 0 1 2 3 4 -200 100 100 100 100 Alternative A: Alternative B: 0 1 2 3 4 5 6 -300 90 90 90 90 90 90 NPV analysis: N P VA = −200 + 100(P /A)12,4 = $103.7 N P VB = −300 + 90(P /A)12,6 = $70.0 Alternative A is the best economic choice based on NPV analysis. NAV, NFV, IRR, and ERR Analyses: From the NPV analysis above, both alternatives are acceptable. Now, perform the incremental analysis for NAV, NFV, IRR and ERR. Use six years as the common evaluation life by extending Alternative A for two additional years with zero cash ﬂows: Alternative A extended to six years: 0 1 2 3 4 5 -200 100 100 100 100 0 6 0 74 5. INCOME PRODUCING INVESTMENTS The incremental project is then: Alternative B-A: 0 1 2 3 4 5 6 -100 -10 -10 -10 -10 90 90 N AV : N AVB−A = −100(A/P )12,6 − 10(P /A)12,4(A/P )12,6 + 90(F /A)12,2(A/F )12,6 = $ − 8.20 Since the incremental NAV is less than zero, Alternative A is the best economic choice. N F V : N F VB−A = − 100(F /P )12,6 − 10(P /A)12,4(F /P )12,6 + 90(F /A)12,2 = $ − 66.5 Since the incremental NF V is less than zero, Alternative A is the best economic choice. I RR: N P VB−A = 0 = −100 − 10(P /A)I RR,4 + 90(P /A)I RR,2(P /F )I RR,4 Trial and error solution yields I RRB−A = 5.4% Since I RRB−A is less than the MARR, Alternative A is the best economic choice. ERR: PCB−A FIB−A =\| − 100 − 10(P /A)12,4\| = $130.4 =90(F /A)12,2 = $190.8 ERRB−A =(190.8/130.4)1/6 − 1 = 0.0655 = 6.55% Since ERRB−A is less than the MARR, Alternative A is the best economic choice. In summary, each of the analysis techniques of NPV, NAV, NFV, incremental IRR, and incremental ERR, indicate that Alternative A is the best economic choice. However, of these ﬁve options, the authors strongly suggest the NPV method because it usually involves the least amount of calculations and never requires the use of incremental analyses. 5.5. INDEPENDENT AND CONTINGENT INVESTMENTS 75 5.5 5.5.1 INDEPENDENT AND CONTINGENT INVESTMENTS INDEPENDENT INVESTMENTS Consider the case when an investor is faced with the choice of investing in one or more projects (rather than just one from a list of mutually exclusive alternatives) depending upon how much investment capital is available. These alternatives are said to be independent alternatives. The ﬁnal decision of which projects to invest in will be based on maximizing the NP V for the given investment dollars. This could mean that several combinations of projects will need to be evaluated. 5.5.2 CONTINGENT INVESTMENTS A contingent project is a project that is conditional on the choice of one or more other projects. For example, in the discipline of petroleum engineering, consider that the regional ofﬁce of a large oil company must make a decision to invest in one of the following projects for a particular producing ﬁeld: a series of well workovers to increase production from the existing wells; a polymer ﬂood to capture more oil from the ﬁeld; or drilling a number of new wells within the ﬁeld to expedite the oil recovery from the ﬁeld. Unfortunately, prior to investing in a full-scale polymer ﬂood, the regional ofﬁce must also invest in a pilot polymer ﬂood that will, most likely, not be an economic success by itself. However, if the pilot is technically successful, then the full-scale polymer ﬂood could be considered. Therefore, the full-scale polymer ﬂood would be considered a contingent project because it could not be implemented without also choosing to invest in the pilot ﬂood. Example 5.6 Projects A, B, and C are being considered as investments. List the combinations that will need to be considered under each of the following scenarios: (a) The projects are mutually exclusive (b) The projects are independent (c) Projects A and B are mutually exclusive, but project C is contingent on project B. (a) If the projects are already mutually exclusive, then the investor can only invest in one project. Therefore, the list of combinations would be: Mutually Exclusive Alterna(cid:415)ve Projects Included C A B Possible Combina(cid:415)ons 1 2 3 4 0 1 0 0 0 0 1 0 0 0 0 1 None A B C 76 5. INCOME PRODUCING INVESTMENTS (b) If the projects are independent, then the investor can invest in any or all projects. Therefore, the list of combinations would be: Mutually Exclusive Alterna(cid:415)ve Projects Included C A B Possible Combina(cid:415)ons 1 2 3 4 5 6 7 8 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 None A B C A,B A,C B,C A,B,C (c) For the contingencies given, the list of combinations would be: Mutually Exclusive Alterna(cid:415)ve Projects Included C A B Possible Combina(cid:415)ons 1 2 3 4 0 1 0 0 0 0 1 1 0 0 0 1 None A B B,C Of the list from (b) in this example, the following combinations are missing for the following reasons: 1. C only – Since C is contingent on project B, it cannot stand by itself 2. A,B – Since A and B are mutually exclusive, they cannot be combined together 3. A,C – Since C is contingent on project B and project B is not in this combination, A and C cannot be combined 4. A,B,C – Since A and B are mutually exclusive, they cannot be combined together 5.5. INDEPENDENT AND CONTINGENT INVESTMENTS 77 5.5.3 LIMITED INVESTMENT CAPITAL When investment capital is unlimited and more than one project may be chosen, the analysis simply requires the determination of which project(s) will earn more than the MARR. This can be done with any of the analysis techniques discussed previously. Once the list of acceptable alternatives has been generated, the economic choice is to invest in all of them. When investment capital is limited, the analysis approach is a bit more complicated. The basic approach is to determine all possible combinations of projects in which the total investment is within the capital constraints and then to analyze each of the combinations as being mutually exclusive. The combination with the highest NPV will represent the set of projects in which one should invest. Example 5.7 The cash ﬂow diagrams of six projects, A through F, are shown below. For these projects, determine what combination of projects is the best economic choice using NPV analysis and a MARR of 10%. Projects B, C, and E are mutually exclusive. Projects A and D are mutually exclusive but both are contingent on the acceptance of C. Project F is contingent on the acceptance of either B or E. Consider two separate scenarios: (a) Assume unlimited capital (b) Assume limited capital of $30,000 A: B: C: 0 1 2 3 -5000 2500 2500 2500 0 1 2 3 -30000 13500 13500 13500 0 1 2 3 -15000 10000 10000 10000 78 5. INCOME PRODUCING INVESTMENTS 0 1 2 3 -10000 6000 6000 6000 0 1 2 3 -20000 10000 10000 10000 0 1 2 3 D: E: F: -15000 11000 11000 11000 It can be shown that the individual projects have the following NP V s: Project A B C D E F N P V $1,220 $3,570 $9,870 $4,920 $4,870 $12,360 The table of mutually exclusive alternatives would be: 5.6. RANKING ALTERNATIVES 79 yllautuM Exclusive Alterna ve 1 2 3 4 5 6 7 8 Projects D C 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 B 0 1 0 0 0 0 1 0 E 0 0 0 1 0 0 0 1 Possible Combina ons None B C E A,C C,D B,F E,F F 0 0 0 0 0 0 1 1 A 0 0 0 0 1 0 0 0 tnemtsevnI Capital Needed 0 $30,000 $15,000 $20,000 $20,000 $25,000 $45,000 $35,000 NP V 0 $3,570 $9,870 $4,870 $11,090 $14,790 $14,930 $17,230 (a) There are eight mutually exclusive alternatives that result from the original six individual projects and their interrelationships. When capital is unlimited, the correct economic choice is the alternative that maximizes the NPV. In this case, alternative #8, which consists of investing in projects E and F is the correct economic choice because it has the largest NPV. (b) When capital is limited to $30,000, alternatives #7 and #8 are no longer considered. With those removed, the correct economic choice will be alternative #6 since it will maximize the NPV for those projects whose total investment is less than or equal to $30,000. 5.6 RANKING ALTERNATIVES As mentioned earlier, one can always correctly rank alternatives according to their NP V values. The combination of projects that is within any constraint of investment capital and has the highest N P V will be the alternative of choice. However, one cannot correctly rank alternatives by I RR or ERR values unless one utilizes incremental analyses. To illustrate this further, another example is presented below. Example 5.8 For the six projects listed in Example 5.7, use the IRR and ERR techniques to choose the best mutually exclusive alternative. It can be shown that mutually exclusive alternatives 1 through 8 have the following I RRs and ERRs: 80 5. INCOME PRODUCING INVESTMENTS Alterna(cid:415)ve 1 2 3 4 5 6 7 8 ERR I RR 10.0% 10.0% 16.7% 14.2% 44.6% 30.2% 23.4% 18.3% 39.5% 27.4% 41.3% 28.4% 29.2% 21.7% 36.3% 25.7% Direct ranking by I RR or ERR would indicate that Alternative 3 (project C alone) would be the best economic choice. This is, of course, inconsistent with the previous NPV analysis. To overcome this inconsistency, the evaluator must perform incremental IRR or incremental ERR analyses. For example, the incremental IRR technique is shown below: 1. Order the alternatives from the largest investment to the smallest: Alterna(cid:415)ve 7 8 2 6 4 5 3 1 Capital Investment $45,000 $35,000 $30,000 $25,000 $20,000 $20,000 $15,000 $0 Annual Cash Flow $24,500 $21,000 $13,500 $16,000 $10,000 $12,500 $10,000 $0 2. Calculate the I RR of the incremental project 7-8: 0 1 2 3 -10000 3500 3500 3500 N P V7−8 = 0 = −10000 + 3500(P /A)I RR,3 Trial and error solution yields I RR7−8 = 2.5% Since the incremental I RR is less than the MARR, Alternative #8 is better than Alternative #7. Keep Alternative #8, discard Alternative #7, and compare Alternative #8 with the next one on the list (#2). 5.6. RANKING ALTERNATIVES 81 3. Calculate the I RR of the incremental project 8-2: 0 1 2 3 -5000 7500 7500 7500 N P V8−2 = 0 = −5000 + 7500(P /A)I RR,3 Trial and error solution yields I RR7−8 = 139.0% Since the incremental I RR is greater than the MARR, Alternative #8 is better than Alter- native #2. Keep Alternative #8, discard Alternative #2, and compare Alternative #8 with the next one on the list (#6). 4. Continue in this manner (comparing the best choice with the next one on the list) until one has exhausted all of the alternatives. Alternative #8 will be the last remaining alternative and, thus, will be the best economic choice. This result is now consistent with the one from NPV analysis. A similar method for ERR will yield the same ultimate results of Alternative #8 being the best economic choice. Another way to complete the incremental IRR technique is to compare each alternative with all other alternatives that have a lower capital investment and compute the incremental IRR. This would result in a table of incremental IRRs as given below: Row # Alterna ve with higher capital investment 1 2 3 4 5 6 7 7 8 2 6 4 5 3 IRR7-8 Alterna ve with lower capital investment 8 2.5 2 52.8 139 6 6.1 23.4 471 - 4 33.8 52.8 5.2 601 5 20.7 32.1 4.24- 7.84 3 21.2 29.9 9.51- 3.63 4.32 1 29.2 36.3 6.61 3.14 4.32 5.93 6.44 82 5. INCOME PRODUCING INVESTMENTS The use of this table would be as follows (see the arrows): 1. Start in row 1. Compare incremental alternative 7-8. Since the incremental I RR (2.5%) is less than the MARR (10%), choose Alternative #8. Drop to row 2 (that belongs to Alternative #8). 2. Compare incremental alternative 8-2. Since the incremental I RR (139%) is greater than the MARR (10%), choose Alternative #8. Stay in row 2. 3. Compare incremental alternative 8-6. Since the incremental I RR (23.4%) is greater than the MARR (10%), choose Alternative #8. Stay in row 2. 4. Compare incremental alternative 8-4. Since the incremental I RR (52.8%) is greater than the MARR (10%), choose Alternative #8. Stay in row 2. 5. Compare incremental alternative 8-5. Since the incremental I RR (32.1%) is greater than the MARR (10%), choose Alternative #8. Stay in row 2. 6. Compare incremental alternative 8-3. Since the incremental I RR (29.9%) is greater than the MARR (10%), choose Alternative #8. Stay in row 2. 7. Compare incremental alternative 8-1. Since the incremental I RR (36.3%) is greater than the MARR (10%), choose Alternative #8. Since there are no more alternatives to be compared with Alternative #8, then Alternative #8 is the best economic choice. For the case of limited capital ($30,000), omit Alternatives #7 and #8 from the table. Follow the arrows to show that Alternative #6 is the best economic choice. Alterna ve with higher capital investment 2 6 4 5 3 Alterna ve with lower capital investment 6 -174 4 2.5 106 5 -42.4 48.7 - 3 -15.9 36.3 - 23.4 1 16.6 41.3 23.4 39.5 6.44 In summary, once the incremental I RR table has been created, start with the alternative with the largest initial investment and compare it to the alternative with the second largest initial investment. If the incremental I RR is less than the MARR, drop to the row of the lower initial investment and proceed to compare with the next alternative. If the incremental I RR is greater than the MARR, stay on the same row and proceed to compare with the next alternative. Eventually, one will “exit” from the table on the best economic choice. 5.7. PROBLEMS 83 5.7 PROBLEMS 5.1. Projects A and B below are mutually exclusive alternatives. The cash ﬂow diagrams are given. Determine which project is the best economic choice using NPV, IRR, and ERR analyses. Use a value of 15% for MARR. Project A: 0 1 2 3 9 10 -8000 5000 5000 5000 …… 5000 5000 L = 8000 Project B: 0 1 2 3 9 10 -12000 6000 6000 6000 …… 6000 6000 L = 12000 5.2. Two mutually exclusive, but unequal life, investment projects A and B are shown below. Project A: Project B: 0 1 2 3 4 5 -100 40 40 40 40 140 0 1 2 -120 60 180 84 5. INCOME PRODUCING INVESTMENTS (a) Determine the best economic choice using NPV, IRR, and ERR analyses. Use an MARR of 20%. (b) What value of MARR would reverse the ranking of projects A and B found in part (a)? For Problems 5.3 and 5.4. The following projects are utilized in Problems 5.3 and 5.4. Projects A and B are indepen- dent. Projects C and D are mutually exclusive and both are dependent on the acceptance of B. Project E is dependent on the acceptance of A. B: C: D: - - - - 5.7. PROBLEMS 85 E: - 5.3. For the projects described above, do the following: (a) List all mutually exclusive alternatives. (b) Which alternative should be chosen if the MARR equals 10% and one has unlimited capital? (c) Which alternative should be chosen if the MARR equals 10% and investment capital is limited to $80? 5.4. For the projects described above, do the following: (a) List all mutually exclusive alternatives. (b) Develop the incremental I RR table. (c) Use the table to determine which alternative should be chosen if the MARR equals 10% and one has unlimited capital. (d) Use the table to determine which alternative should be chosen if the MARR equals 10% and investment capital is limited to $80. 5.5. Use NPV and ERR analyses to determine which of the following two mutually exclusive projects is the best economic choice. Use MARR of 15%. Project A: 0 1 2 3 4 -500 200 200 200 200 L = 500 86 5. INCOME PRODUCING INVESTMENTS Project B: 0 1 2 -200 100 100 L = 200 5.6. Suppose you are considering two independent sets of two mutually exclusive projects each plus a ﬁfth project. The ﬁfth project is contingent on two of the ﬁrst four occurring. Make a table that shows all of the mutually exclusive alternatives that are possible and the projects that each alternative contains. 5.7. Projects A through E are being considered by an investor. They all are ten-year projects and the MARR is 10%. Projects A and B are mutually exclusive. Projects C and D are mutually exclusive and contingent on the acceptance of B. Project E is contingent on the acceptance of A. ERR 8% Project A B C D E N P V $5,000 $20,000 $15,000 $10,000 Capital Investment $20,000 $15,000 $30,000 $22,000 $15,000 (a) List all of the possible mutually exclusive alternatives. (b) Which alternative is the best economic choice with unlimited capital? (c) Which alternative is the best economic choice with a capital constraint of $40,000? 5.8. Use Excel® to solve Problem 5.1 for values of MARR of 5%, 15%, 25%, 35%, and 45%. 5.9. Use Excel® to solve Problem 5.2 for values of MARR of 10%, 20%, and 30%. 5.10. Use Excel® to solve Problem 5.3 for values of MARR of 10%, 20%, 25%, and 30%. 5.11. Use Excel® to develop the incremental I RR table for Problem 5.4. Use the table to deter- mine which alternative should be chosen if the MARR equals 10% and one has unlimited capital. 5.12. Use Excel® to solve Problem 5.5 for values of MARR of 5%, 15%, 25%, and 35%. C H A P T E R 6 87 Determination of Project Cash Flow 6.1 INTRODUCTION This chapter contains a discussion of escalation, depreciation, income taxes, and the subsequent generation of cash ﬂows when considering taxes. This chapter is not meant to be a detailed presenta- tion on all of the ramiﬁcations of taxes. Most companies will use tax consultants and/or tax lawyers instead of engineers to handle complicated tax questions. This chapter is meant to provide a basic working knowledge of taxes so that the engineer can develop a stream of before- and after-tax cash ﬂows for a particular project. 6.2 ESCALATION AND INFLATION When considering the effects of escalation on cash ﬂows, it is necessary to deﬁne three types of dollars with which evaluators work. The ﬁrst is what is called today dollars. Today dollars simply refer to the situation where all of the cash ﬂows are calculated without any consideration for changes in prices and costs as a function of time. This, of course, is not consistent with what actually occurs in real life. A second type is escalated or actual dollars. When an evaluator attempts to estimate price and cost changes and subsequently incorporates these changes into the cash ﬂow calculations, then the dollars are said to be escalated. The ﬁnal type is constant dollars. When inﬂation is removed from escalated dollars, then the resulting cash ﬂows are said to be in constant dollars. In order to more fully understand what is meant by these various types of dollars, the terms inﬂation and escalation need to be deﬁned. Inﬂation refers to the general increase of prices with time due to an expanded money supply with no hard assets to support the additional money. By deﬁnition, inﬂation affects prices of all commodities by the same percentage amount. If the money supply decreases, there could be deﬂation or the decrease in prices. There are as many causes of inﬂation as there are people who talk about it. It is not the intent of the authors to discuss these causes. Using the Consumer Price Index (CPI) that is published by the Bureau of Labor Statistics (http://www.bls.gov/data/), the average inﬂation rate for 2000 to 2010 was 2.39% per year. The values of the CP I are shown in Figure 6.1 and Table 6.1 for various time periods. Published values are available back to 1913. One can determine the average inﬂation rate for a given period of time by using the (F /P )i,n formula. Consider the CP I values from two different years, n and m (with n > m). The CP I from 88 6. DETERMINATION OF PROJECT CASH FLOW CPI Since 1960 CPI 250.0 200.0 150.0 100.0 50.0 0.0 1960 1970 1980 Year 1990 2000 2010 Figure 6.1: Consumer price index values for 1960-2010—from http://www.bls.gov/data/. year n will be considered as a future value and the CP I from year m will be considered a present value. Thus: CP In = CP Im(1 + f )n−m which can be solved for the inﬂation rate, f , as (cid:13)(cid:14) f = CP Iyr n/CP Iyr m (cid:15)[1/(n−m)] − 1 (cid:16) ∗ 100 (6.1) For example, the average inﬂation rate between 1980 and 1990 was: (cid:13) (130.7/82.4) [1/10] − 1 (cid:16) ∗ 100 = 4.72% Similarly, the average inﬂation rate between 2009 and 2010 was: (cid:13) (218.056/214.537) [1/1] − 1 (cid:16) ∗ 100 = 1.64% Escalation, on the other hand, refers to the total change in the price of a speciﬁc commodity or service over a period of time. Prices of individual commodities can change due to supply and demand, as well as many other factors. While the inﬂation rate is a single numerical value for all commodities, the escalation rate may be different for each commodity. For example, for 2000 to 2010, the price of food increased an average of 2.69% per year (similar to inﬂation), the price of unleaded gasoline increased an average of 6.32% per year, and the price of computers actually dropped an average of Table 6.1: Consumer price index values for 1980-2010—from http://www.bls.gov/ data/ 6.2. ESCALATION AND INFLATION 89 Year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 CPI 82.4 90.9 96.5 99.6 103.9 107.6 109.6 113.6 118.3 124.0 Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 CPI 130.7 136.2 140.3 144.5 148.2 152.4 156.9 160.5 163.0 166.6 CPI Year 172.2 2000 177.1 2001 179.9 2002 184.0 2003 188.9 2004 195.3 2005 2006 201.6 2007 207.342 215.303 2008 2009 214.537 0102 650.812 Star ng in 2007, the Bureau of Labor Sta s cs began publishing the CPI with three decimal places instead of one 16.4% per year over that same time frame. It should be pointed out that escalation includes the effect of inﬂation. Figure 6.2 shows the price of unleaded gasoline ($/U.S. gallon) from 1976 to 2010. One should notice that the CPI curve in Figure 6.1 is relatively smooth, but the price of any one commodity may ﬂuctuate signiﬁcantly over the same time frame as shown in Figure 6.2. This is due to the fact that the CPI “measures the average change in prices paid for a market basket of goods and services.” (U.S. Department of Labor) The escalated or actual dollar type of analysis referred to above includes both the effect of inﬂation and escalation. This type of analysis attempts to predict the future prices of those elements that are part of the cash ﬂow calculation. One can either let all income and expenses rise at the average inﬂation rate or one can attempt to isolate each commodity and use various escalation rates for each income or expense item. The constant dollar analysis reﬂects the purchasing power of money over the life of the project by factoring out the effect of inﬂation. For example, in constant dollars, the price of unleaded gasoline has increased an average of 3.84% per year and the price of food only increased an average 0.29% per year from 2000 to 2010. This calculation will be shown later in this chapter. The today dollar analysis simply uses the current prices for the commodities that are part of the cash ﬂow calculation for the project and maintains them at this level throughout the life of the project. Thus, there is no consideration of the effects of inﬂation and escalation. The authors believe that one should use either an escalated dollar analysis or a constant dollar analysis when attempting to determine the economic viability of a project. Today dollar analyses 90 6. DETERMINATION OF PROJECT CASH FLOW Price of Unleaded Gasoline $/US gal 3.500 3.000 2.500 2.000 1.500 1.000 0.500 0.000 1970 1980 1990 2000 2010 2020 Year Figure 6.2: Price of unleaded gasoline from 1976 to 2010 (Government Accounting Ofﬁce analysis of Bureau of Labor Statistics (BLS) data). should only be used for projects that have short enough lives that the costs of the commodities that are part of the cash ﬂow calculation do not change substantially. Two rules should be kept clearly in mind when incorporating the effects of inﬂation and escalation. The ﬁrst is that the dollar types, constant or escalated, should never be mixed within a single cash ﬂow diagram. The second is that the MARR that is used in the evaluation must be consistent with the type of dollars used. A rate of return calculated from a set of cash ﬂows that are based on constant dollars should be compared with an MARR that is also based on constant dollars. Similarly, consistency between escalated dollar cash ﬂows and an MARR that is based on escalated dollars is necessary. It should be noted that bank interest rates and investment bond interest rates are based on escalated dollars. Thus, if an investor’s MARR is derived from those types of interest rates, it should also be considered to be an escalated dollar MARR. The relationship between interest rates in escalated and constant dollars can be obtained by comparing the corresponding P /F factors: (P /F )i,n = (P /F )f,n(P /F )ii,n where, i = escalated dollar interest rate, fraction per period f = inﬂation rate, fraction per period ii = constant dollar interest rate, fraction per period If one substitutes the deﬁnition of (P /F ) and does some basic algebra, one can show: 6.2. ESCALATION AND INFLATION 91 ii = (1 + i)/(1 + f ) − 1 (6.2) This equation was utilized earlier to “factor out” the effect of inﬂation from escalation. For example, for the period of 2000-2010, the inﬂation rate was 2.39% per year and the escalation rate for unleaded gasoline was 6.32% per year. Using Equation 6.2, the constant dollar growth of this commodity is: ii = (1 + 0.0632)/(1 + 0.0239) − 1 = 0.0384 = 3.84% Note that just subtracting the inﬂation rate from the escalation rate (a difference of 3.93% in this example) is not the correct way to factor out inﬂation from escalation. The relationships between today dollars, escalated dollars, and constant dollars are shown below: Escalated $ price at the end of the year n = (Today $) ∗ (1 + i)n Constant $ price at the end of the year n = (Escalated $)/(1 + f )n Constant $ price at the end of the year n = (Today $) ∗ ((1 + i)/(1 + f ))n (6.3) (6.4) (6.5) where, i = escalation rate, fraction per year f = inﬂation rate, fraction per year Example 6.1 Cash ﬂow diagrams for projects A and B are shown below. Assume that the cash ﬂows are in escalated dollars and that the escalated dollar MARR is 15%. (a) Calculate the NP V of each project as given and (b) calculate the NP V if one assumes a 5% inﬂation rate. 0 1 2 3 -100 0 55 1 60.5 66.55 2 3 A: B: -100 40 60 80 92 6. DETERMINATION OF PROJECT CASH FLOW (a): N P VA N P VB = −100 + 55(P /F )15,1 + 60.5(P /F )15,2 + 66.55(P /F )15,3 = $37.33 = −100 + 40(P /F )15,1 + 60(P /F )15,2 + 80(P /F )15,3 = $32.75 (b): For part (b), one needs to factor out the effect of inﬂation from the escalated cash ﬂows. In addition, the MARR will have to be adjusted to a constant dollar basis. The cash ﬂows are adjusted by using the (P /F ) factor at 5% for the corresponding number of years. For example, the 55 (year 1 cash ﬂow for Project A) is multiplied by (P /F )5,1 to yield 52.38. When this is done, the cash ﬂows become: 0 1 2 3 -100 52.38 54.88 57.49 0 1 2 3 A: B: -100 38.10 54.42 69.11 The constant dollar MARR will be: ii = (1 + i)/(1 + f ) − 1 = (1 + 0.15)/(1 + 0.05) − 1 = 0.0952 = 9.52% The N P V s then become: N P VA = −100 + 52.38(P /F )9.52,1 + 54.88(P /F )9.52,2 + 57.49(P /F )9.52,3 = $37.34 N P VB = −100 + 38.10(P /F )9.52,1 + 54.42(P /F )9.52,2 + 69.11(P /F )9.52,3 = $32.66 Note that within numerical round off, the NP V s are the same for either escalated or constant dollar analysis. This will always be the case. 6.2. ESCALATION AND INFLATION 93 Example 6.2 A ﬁve-year life project has an initial capital expenditure of $250,000 and annual operating costs beginning at the end of the year 1 of $100,000. At the end of the years 3, 4, and 5 the project receives $500,000 as income. Calculate the I RR for the following cases: (a) Assume the cash ﬂows given are in escalated dollars and the escalated dollar MARR is 25%. (b) Assume the cash ﬂows given are in today dollars and that incomes are escalated at 6% and costs are escalated at 10%. (c) Assume inﬂation is 4% and rework part (b) in terms of constant dollars. (a) (numbers are in $1000): 0 1 2 3 4 5 -250 -100 -100 400 400 400 N P V = 0 = −250 − 100(P /A)I RR,2 + 400(P /A)I RR,3(P /F )I RR,2 Trial and error solution yields I RR = 34.3%. This value would be compared to the escalated MARR of 25% to indicate that it’s an economically acceptable project. (b) (numbers are in $1000): Use Equation 6.3 to convert today dollars to escalated dollars: 94 6. DETERMINATION OF PROJECT CASH FLOW N P V = 0 = −250 − 110(P /F )I RR,1 − 121(P /F )I RR,2 + 463(P /F )I RR,3 + 485(P /F )I RR,4 + 508(P /F )I RR,5 Trial and error solution yields I RR = 39.9%. This value would be compared to the escalated MARR of 25% to indicate that it’s an economically acceptable project. (c) (numbers are in $1000): Use Equation 6.4 to convert the today dollars to constant dollars: Year 0 1 2 3 4 5 Constant $ income 500 (1.06)3 / (1.04)3 = 529 500 (1.06)4 / (1.04)4 = 540 500 (1.06)5 / (1.04)5 = 550 Constant $ costs 250 (1.10)0 / (1.04)0 = -250 - 100 (1.10)1 / (1.04)1 = -106 - 100 (1.10)2 / (1.04)2 = -112 - -100 (1.10)3 / (1.04)3 = -118 -100 (1.10)4 / (1.04)4 = -125 -100 (1.10)5 / (1.04)5 = -132 Constant $ CF -250 -106 -112 411 415 418 N P V = 0 = −250 − 106(P /F )I RR,1 − 112(P /F )I RR,2 + 411(P /F )I RR,3 + 415(P /F )I RR,4 + 418(P /F )I RR,5 Trial and error solution yields I RR = 34.5%. This value would be compared to the constant dollar MARR that is calculated according to Equation 6.1: ii = (1 + 0.25)/(1 + 0.04) − 1 = .202 = 20.2% This value would still indicate that it’s an economically acceptable project. 6.3 DEPRECIATION Certain capital assets of a company lose their value with use and/or with time. A building or an item of equipment are examples of such assets. These assets have an initial value that is equal to the original cost of the asset. However, they may lose value over time due to physical deterioration, development of improved facilities by technological advances, or different demands of their use. The reduction in value is called depreciation. 6.3. DEPRECIATION 95 One also needs to recognize that most governments (including the United States) do not allow companies, for tax purposes, to deduct the entire cost of an asset against their income in the year that the asset is purchased. Since the asset retains at least some portion of its value over its life, companies must prorate the deduction of the original asset cost over the usable life of the asset. Governments will specify particular techniques for this proration. These techniques are called depreciation methods. Therefore, there are two interpretations of a depreciation account for a capital asset. Under the ﬁrst, a company would set aside actual cash in a depreciation account in order to have the necessary funds to replace the asset at the end of its useful life. Under the second, rather than setting aside actual cash in the depreciation account, the company would simply establish depreciation accounts for tax purposes. That is, the depreciation account represents the allowable annual deduction of the asset against the project’s income. The second interpretation represents reality. Thus, the depreciation account that is maintained does not involve real dollars and depreciation expenses are known as “paper” expenses in that they reduce the tax liability of the project but do not represent actual cash expenditures. This chapter contains information on how to handle these paper expenses in the calculation of after-tax cash ﬂows for a project. The most popular depreciation methods used in the United States are straight-line, sum- of-the-years-digits, declining-balance, and the accelerated-cost-recovery-system. All four of these methods will be discussed in this chapter. In addition to the depreciation account, one also maintains a book value account that represents the remaining value of the asset. Book value is simply the initial cost of the asset minus all accumulated depreciation up to a speciﬁc point in time. Depreciation calculations are based on the initial cost of the asset, P , any salvage value of the asset at the end of its useful life, L, and the length of its useful life, N. The quantity P – L represents the total allowable depreciation of the asset if it is held for the entire time period N. 6.3.1 STRAIGHT-LINE DEPRECIATION (SL) When using the straight-line depreciation method, the yearly amount of depreciation is given by Equation 6.6: Dn = (P − L)/N (6.6) where, Dn = depreciation amount in year n, $ n = year of depreciation P = initial cost of the asset, $ L = salvage value of the asset at the end of its useful life, $ N = length of the asset’s useful life, years It should be evident that the depreciation is constant with time when using the straight-line method. 96 6. DETERMINATION OF PROJECT CASH FLOW At the end of any given year, the book value of the asset is given by Equation 6.7: Bn = P − n(P − L)/N (6.7) where, Bn = book value of the asset at the end of year n, $ Excel® has a built-in function called SLN that computes straight-line depreciation: = SLN(Initial_Cost, Salvage, Life) where, Initial_Cost = initial cost of the asset (P ) Salvage = salvage value of the asset (L) Life = asset’s useful life (N) 6.3.2 DECLINING-BALANCE DEPRECIATION Unlike straight-line depreciation, the annual depreciation amount determined using the declining- balance method is not constant with time. The declining-balance method provides for a larger depreciation deduction in the early years of an asset’s life than when using straight-line depreciation. In this method, the depreciation amount is a ﬁxed percentage of the remaining book value of the asset. The equations to calculate the annual depreciation amount and the book value at the end of each year are given in Equations 6.8 and 6.9: Dn = f (1 − f )n−1P Bn = (1 − f )nP (6.8) (6.9) where, f = a ﬁxed percentage as a fraction It should be noted that while the salvage value, L, is not utilized in the equations, one must be careful that the total depreciation does not exceed the amount (P − L). Limits have been placed on the value of f that can be used in the declining-balance method. The value of f cannot exceed 2/N. When the value of 2/N is used, the method is referred to as the double-declining-balance (DDB) method. Excel® has a built-in function called DDB that computes double-declining balance depreci- ation: = DDB(Initial_Cost, Salvage, Life, Period, Factor) 6.3. DEPRECIATION 97 where, Initial_Cost = initial cost of the asset (P ) Salvage = salvage value of the asset (L) Life = asset’s useful life (N) Period = the period of interest Factor = 2 (or omitted) for double-declining balance 6.3.3 SUM-OF-THE-YEARS-DIGITS (SYD) DEPRECIATION This method, like the declining-balance method, provides for an accelerated depreciation deduction in the early years of the useful life of an asset. The equations to calculate the annual depreciation amount and the book value at the end of each year are given in Equations 6.10 and 6.11: Dn = [N − (n − 1)](P − L)/S Bn = P − n(cid:4) Dj j =1 (6.10) (6.11) S = sum of the digits of the useful life of the asset = N(N + 1)/2 where, Excel® has a built-in function called SYD that computes sum-of-the-years-digits deprecia- tion: = SYD(Initial_Cost, Salvage, Life, Period) where, Initial_Cost = initial cost of the asset (P ) Salvage = salvage value of the asset (L) Life = asset’s useful life (N) Period = the period of interest When calculating depreciation amounts for the determination of after-tax cash ﬂows, it is advantageous to use the most accelerated depreciation schedule possible. The sum-of-the-years- digits and the declining-balance methods give larger depreciation amounts in the early years of an asset. The straight-line method may, however, be more advantageous in later years. Example 6.3 A device costs $5000 and has a salvage value of $800 after its useful life of 7 years. Calculate the depreciation deduction that can be taken each year and the book value at the end of each year for the useful life of the asset. Use the following depreciation methods: 98 6. DETERMINATION OF PROJECT CASH FLOW (a) Straight-Line (SL) (b) Double-Declining-Balance (DDB) (c) Sum-of-the-Years-Digits (SYD) (a) For Straight-Line: Dn = (P − L)/N = (5000 − 800)/7 = $600 which remains constant over the 7 years Bn = P − n(P − L)/N = 5000 − 600 n (b) For Double-Declining Balance: f = 2/N = 2/7 = 0.28571 Dn = f (1 − f )n−1P = 0.28571(0.71429)n−15000 = 1428.55(0.71429)n−1 Bn = (1 − f )nP = (0.71429)n5000 = 5000(0.71429)n 0 1 2 3 4 5 6 7 5000 3571 2551 1822 1301 929 800 800 1429 1020 729 521 372 129* 0** D6 would have been calculated as $266, but it was limited to $129 because the book value cannot go below the salvage value. D7 would have been calculated as $190, but it was limited to $0 because the book value had already reached the salvage value at the end of year 6. (c) For Sum-of-the-Years-Digits: S = N (N + 1)/2 = (7)(8)/2 = 28 6.3. DEPRECIATION 99 Dn = [N − (n − 1)](P − L)/S = [7 − (n − 1)](5000 − 800)/28 = 150(8 − n) Bn = P − Dj = 5000 − n(cid:4) j =1 n(cid:4) Dj j =1 The depreciation and book values are shown in Figures 6.3 and 6.4 below to further demon- strate the differences between these three methods. Solution with Excel®: A P = L = N = Year 1 2 3 4 5 6 7 B 5000 800 7 SL $600 $600 $600 $600 $600 $600 $600 C D DDB $1,429 $1,020 $729 $521 $372 $130 $0 SYD $1,050 $900 $750 $600 $450 $300 $150 1 2 3 4 5 6 7 8 9 10 11 12 100 6. DETERMINATION OF PROJECT CASH FLOW , , ) 6 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 7 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 8 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 9 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 0 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 1 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 2 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( D Y S = , , , ) 6 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 7 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 8 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 9 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 0 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 1 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , , ) 2 1 A 3 $ B $ 2 $ B $ 1 $ B $ ( B D D = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , , ) 3 $ B $ 2 $ B $ 1 $ B $ ( N L S = , 1 2 3 4 5 6 7 D D Y S C B D D 0 0 0 5 0 0 8 7 B = P = L = N A L S r a e Y 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1 6.3. DEPRECIATION 101 Deprecia(cid:415)on Values SL DDB SYD D(n) $ 1600 1400 1200 1000 800 600 400 200 0 1 2 3 4 Year 5 6 7 Figure 6.3: Comparison of depreciation values for straight-line, double declining balance, and sum-of- the-years-digits methods. Book Values B(n) $ 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 SL DDB SYD 0 1 2 3 4 5 6 7 Year Figure 6.4: Comparison of book values for straight-line, double declining balance, and sum-of-the- years-digits methods. 102 6. DETERMINATION OF PROJECT CASH FLOW 6.3.4 MODIFIED ACCELERATED COST RECOVERY SYSTEM (MACRS) In 1981, the United States government passed the Economic Recovery Tax Act which made sig- niﬁcant changes in depreciation calculations. The act was further modiﬁed in 1986 which led to the Modiﬁed Accelerated Cost Recovery System (MACRS) for assets that were placed after 1980. MACRS generally simpliﬁed the calculation of depreciation by (a) removing any reference to the salvage value of the asset at the end of its useful life by assuming that L = 0 and (b) using various combinations of the three previously presented depreciation methods to calculate annual deprecia- tion values that are simply percentages of the original asset cost. As in the other methods, the asset’s book value is the original cost minus all accumulated depreciation. That is: Dn = P ∗ Depreciation Rate(depreciable life, n) Bn = P − n(cid:4) Dj j =1 (6.12) (6.13) To determine what depreciation rate to use, one must ﬁrst determine the depreciable life of the asset. The MACRS method created the following classiﬁcations: 3-year property, 5-year property, 7-year property, 10-year property, 15-year property, 20-year property, and 25-year property. IRS publication 946 (http://www.irs.gov/pub/irs-pdf/p946.pdf) deﬁnes the types of assets that ﬁt in each classiﬁcation. Table 6.2 shows a summary of this publication. One should note that any property that doesn’t speciﬁcally ﬁt in another category is automatically classiﬁed as 7-year property. Table 6.3 shows the depreciation rates that are used for various classiﬁcations, assuming a half-year convention (most common assumption). A half-year convention simply recognizes that assets are put into service at various times during any one year. Rather than beginning to depreciate the asset on the actual day that it is put into service, the U.S. government allows a half year of depreciation in the ﬁrst year of use, a full year of depreciation from year two until year N and a half year of depreciation in year N+1. Thus, depreciation for assets that ﬁt in the 7-year depreciation category, are actually spread over a total of 8 years. 6.3. DEPRECIATION 103 Table 6.2: Various classiﬁcations of depreciable property—from http://www.irs.gov/ pub/irs-pdf/p946.pdf Property Classiﬁcation 3-year property 5-year property 7-year property Examples Tractor units for over-the-road use Qualiﬁed rent-to-own property Automobiles, taxis, buses, and trucks Computer and peripheral equipment Ofﬁce machinery Certain geothermal, solar, and wind energy property Ofﬁce furniture and ﬁxtures Agricultural machinery and equipment Any property that does not have a class life and has not been designated by law as being in any other class Any natural gas gathering line placed in service after April 11, 2005 10-year property Vessels, barges, tugs and similar water transportation equipment Qualiﬁed small electric meter and qualiﬁed smart electric grid system placed in service after Oct 3, 2008 15-year property Any municipal wastewater treatment plant Any qualiﬁed restaurant property placed in service before Jan 1, 2012 Electric transmission property used in transmission at 69 or more kilovolts of electricity placed in service after April 11, 2005 Any natural gas distribution line placed in service after April 11, 2005 20-year property Farm buildings Municipal sewers 25-year property Water utility property that is not included as 20-year property 104 6. DETERMINATION OF PROJECT CASH FLOW Table 6.3: Depreciation rates for various property lives—from http://www.irs.gov/pub/ irs-pdf/p946.pdf Although Excel® does not have a built-in function that can be used to directly compute MACRS depreciation, one can use the VDB function if one recognizes that MACRS is deﬁned as DDB depreciation, using 1/2 year convention, and then switching to straight-line depreciation: =VDB(Initial_Cost, Salvage, Life, Start_Period, End_Period, Factor,no_Switch) 6.3. DEPRECIATION 105 where, Initial_Cost = initial cost of the asset (P ) Salvage = salvage value of the asset (L) – set to zero for MACRS Life = asset’s useful life (N) Start_Period to End_Period = the period of interest (which can be fractional time periods). For 1/2 year convention in year 1, use Start_Period = 0 and End_Period = 0.5. For full year convention for years 2 through N, use Start_Period = (n − 1.5) and End_Period = (n − 0.5). For 1/2 year convention in year N + 1, use Start_Period = (N − 0.5) and End_Period =N . Factor = 2 (or omitted for DDB) no_Switch = FALSE (or omitted for automatic switching to straight-line) For example, for 7-year property: 106 6. DETERMINATION OF PROJECT CASH FLOW Example 6.4 Determine the yearly depreciation for the device described in Example 6.3 if it ﬁts in the 7-year life category. Recall that P = $5000. 6.4 CASH FLOW COMPUTATION As described in Chapter 2, cash ﬂow is simply the net change (+ or -) in a company’s or individual’s cash balance relative to a given project. That is, a positive project cash ﬂow for a period would indicate that the company had more cash due to that project at the end of that period than it did at the beginning. A negative project cash ﬂow would indicate just the opposite. The following discussion lists the major considerations in determining cash ﬂow for a project. Cash ﬂows can be calculated as before-tax or after-tax (where the tax is state and federal income tax). It should be noted that the implications of a speciﬁc project on the company’s overall tax situation will ultimately be determined by the company’s accountants and/or tax attorneys. Therefore, most engineering economic analyses will be conducted on before-tax cash ﬂows. However, sometimes it is necessary or informational to evaluate after-tax cash ﬂows. Therefore, both types are covered in this discussion. 6.4.1 CAPITAL INVESTMENT Capital investment is the cash that is expended by the company or the individual necessary to get the project underway. That is, it is money used by the company or individual to purchase ﬁxed assets such as land, machinery, or buildings rather than money used for day-to-day operations. While cash expenditures for ﬁxed assets will generally occur over the length of a speciﬁc time period, it is assumed that, for economic evaluation purposes, it all occurs at the beginning of that time period. Thus, if it takes $500,000 over 6 months to construct a manufacturing facility, one would consider all $500,000 to be spent at the beginning of year 1 (which, recall, is year 0 on the cash ﬂow diagram). Capital investment will include all costs associated with the ﬁxed assets that are being purchased. For example, labor costs, materials, services, etc. that are part of the construction of a manufacturing facility are considered capital investment. 6.4. CASH FLOW COMPUTATION 107 6.4.2 GROSS REVENUE Gross revenue is all revenue that is generated through the sale of a product or service. In most cases, revenue for each product stream can be computed with Equation 6.14: {Gross Revenue} = {#of items sold during a period} ∗ {price per item} (6.14) It should be noted that, for economic evaluation purposes, the period’s gross revenue will be assumed to occur at the end of the particular time period in which it is generated. 6.4.3 OPERATING EXPENSES Operating expenses are all cash outlays that are necessary to produce and sell the product or service. These expenses may include, but are not limited to, items such as labor costs, building rent, utility costs, raw materials, supplies, interest on loans, etc. Operating expenses are normally classiﬁed as either ﬁxed costs or variable costs. Fixed costs represent costs that are independent of the number of units produced (for example building rent), whereas variable costs are proportional to the number of units produced (for example raw materials). Equation 6.15 shows how to compute operating expenses: {Operating Expenses} ={Fixed Costs during a period} + {#of items sold during a period} ∗ {variable cost per item} (6.15) It should be noted that, for economic evaluation purposes, the period’s operating expenses will be assumed to all occur at the end of the particular time period in which it is spent. The assumption that all capital investment will occur at the beginning of each year and that the income and operating expenses will occur at the end of each year is known as end-of-year convention. 6.4.4 BEFORE-TAX PROFIT COMPUTATION For the computation of before-tax proﬁt, one only needs to consider gross revenues and operating expenses: {Before tax Proﬁt} = {Gross Revenue} − {Operating Expenses} (6.16) 6.4.5 BEFORE-TAX CASH FLOW COMPUTATION For the computation of before-tax cash ﬂows, one needs to have information on capital investment, gross revenue, and operating expenses for each time period, n: {Before tax cash ﬂow} = {Gross Revenue} − {Operating Expenses} − {Capital Investment} (6.17) 108 6. DETERMINATION OF PROJECT CASH FLOW Example 6.5 Create the cash ﬂow diagram for the following project. $300,000 is to be expended over 6 months to build a bicycle manufacturing facility. It is assumed that the facility will build 500 bicycles the ﬁrst year and 1000 bicycles in years two through ﬁve.The bicycles will be sold for $500 in the ﬁrst year with an estimated 4% escalation rate in years two through ﬁve. In the ﬁrst year, ﬁxed operating costs will be $20,000 and variable operating costs will be $100 per bicycle. Assume an estimated 3% escalation rate in years two through ﬁve for both operating costs. The table below shows the detailed cash ﬂow calculations for each year that results in the following cash ﬂow diagram ($ in thousands): 0 1 2 3 4 5 -300 180 396.4 413.5 431.3 449.8 Year 0 1 2 3 4 5 Capital Investment 000,003 0 0 0 0 0 Gross Revenue Opera ng Expenses 0 500500 = 250,000 1000500(1.04) = 520,000 1000500(1.04)2 = 540,800 1000500(1.04)3 = 562,400 1000500(1.04)4 = 584,900 0 20,000 + 500100 = 70,000 (20,000 + 1000100)(1.03) = 123,600 (20,000 + 1000100)(1.03)2 = 127,300 (20,000 + 1000100)(1.03)3 = 131,100 (20,000 + 1000100)(1.03)4 = 135,100 Before-tax cash ow 000,003- 180,000 396,400 413,500 431,300 449,800 6.4.6 DEPRECIATION As mentioned above, depreciation costs are “paper expenses” that result from the depreciation of a capital item. That is, there is no actual cash expenditure for this category. The cost does, however, reduce the company’s income tax burden as will be shown. One can pick any of the methods given above to calculate the depreciation expenses. 6.4. CASH FLOW COMPUTATION 109 6.4.7 TAXABLE INCOME Taxable income is the income (or sometimes called gross proﬁt) that is subject to taxation by the United States government: {Taxable Income} = {Gross Revenue} − {Operating Expenses} − {Depreciation} (6.18) 6.4.8 STATE AND FEDERAL INCOME TAX As shown in Table 6.4, U.S. companies compute their U.S. federal income tax (FIT) as a percentage of their taxable income. (United States Code: Title 26, Subtitle A, Chapter 1, Part II, § 11) Even though the FIT rate varies as the taxable income increases, it is common for engineering economic analyses to use a ﬂat tax rate of 35% on all taxable income. In addition, many states in the U.S. have a state income tax of a few percent (0 to 12% with a U.S. average of 6.56%). For engineering economic calculations, it is sufﬁciently accurate to add the state and federal income tax rates together to arrive at an effective tax rate. Table 6.4: United States corporate income tax (FIT) rates—from United States Code: Title 26, Subtitle A, Chapter 1, Part II, § 11. Therefore, {FIT} = {Taxable Income} ∗ {Tax Rate} (6.19) In some circumstances, FIT can be allowed to be a negative value. That is, if the taxable income is negative (a “loss”), multiplying any tax rate by that taxable income would yield a negative value for FIT. This would be the same as the government paying the project for losing money!! However, this computation can be defensible if the project that is being evaluated is only one of many for a large company. Since the company only pays taxes on its total taxable income (that is, from all projects taken together), a loss from one project will reduce the taxes that would be paid by a proﬁtable project. Thus, the project that generates a negative taxable income does indeed yield a negative tax. Allowing negative FIT values is known as a “corporate analysis.” If the project is a “stand alone” project (that is, its proﬁt or loss will not be combined with any other project), then any negative values of FIT must be changed to zero for that year. However, the loss in that year may be carried forward into the future to reduce taxes from a proﬁtable year that occurs later. This is an area where consultation with a corporate tax expert would be necessary. 110 6. DETERMINATION OF PROJECT CASH FLOW 6.4.9 NET PROFIT Net Proﬁt is computed as the taxable income minus the income tax: {Net Proﬁt} = {Taxable Income} − {FIT} = {Taxable Income} ∗ (1 − Tax Rate) (6.20) 6.4.10 CASH FLOW The values deﬁned above can now be combined in order to compute the cash ﬂow (or net cash ﬂow) for a particular period: {Cash Flow} = {Net Proﬁt} + {Depreciation} − {Capital Investment} (6.21) As mentioned before, since depreciation is only a “paper” expense (that is, no actual cash payment is made for depreciation), it must be added back into the cash ﬂow calculation. Depreciation’s only effect, therefore, is to reduce the income tax that is paid. Any capital investment (cash spent on depreciable assets) made during the particular period is subtracted after all other cash ﬂow considerations are taken into account. Example 6.6 Determine the after tax cash ﬂows for the ten years of the following project’s life: Initial capital investment: $1,000,000 Use 7-year MACRS depreciation Total tax rate of 40% Corporate tax analysis Sales Schedule: Year 1 2 3 4 5 6-10 # of units sold 5,000 5,000 7,000 7,000 10,000 10,000 Price per unit $100 $110 $120 $120 $140 $140 Fixed Costs: $200,000 per year Variable Costs: $30 per unit Solution: Year 0 6.4. CASH FLOW COMPUTATION 111 For evaluation purposes, assume that the initial capital investment occurs at the beginning of year 1 (which, by deﬁnition, is year 0). CF0 = −1, 000, 000 Year 1 Gross Revenue = 5,000 100 = $500,000 Operating Costs = 200,000 + 5000 * 30 = $350,000 Depreciation = 0.143 * 1,000,000 = $143,000 Taxable Income = 500,000 - 350,000 - 143,000 = $7,000 FIT = 0.40 * 7,000 = $2,800 CF 1 = 7,000 - 2,800 + 143,000 = $147,200 The remaining nine years are calculated in a similar manner and are shown in the following cash ﬂow table: Gross Revenue 500,000 550,000 840,000 840,000 1,400,000 1,400,000 1,400,000 1,400,000 1,400,000 1,400,000 Year 0 1 2 3 4 5 6 7 8 9 10 Opera ng Costs Deprecia on 350,000 350,000 410,000 410,000 500,000 500,000 500,000 500,000 500,000 500,000 143,000 245,000 175,000 125,000 89,000 89,000 89,000 45,000 0 0 Taxable Income 7,000 -45,000 255,000 305,000 811,000 811,000 811,000 855,000 900,000 900,000 FIT Capital Investment 000,000,1 2,800 -18,000 102,000 122,000 324,000 324,000 324,000 342,000 360,000 360,000 Cash Flow 000,000,1- 147,200 218,000 327,000 308,000 576,000 576,000 576,000 558,000 540,000 540,000 At a value of MARR of 20%, the NP V of this project can be shown to be $518,000 (after tax). One might wish to generate an Excel® spreadsheet to allow additional analysis of this problem if any or all of the given numerical values change. Such a spreadsheet is shown on the next page. From the formulas it can be seen that key numerical values can be easily changed and the remainder of the spreadsheet will change accordingly. The formulas and/or values in each column are shown on the next pages. 112 6. DETERMINATION OF PROJECT CASH FLOW 6.4. CASH FLOW COMPUTATION 113 114 6. DETERMINATION OF PROJECT CASH FLOW 6.5 PROBLEMS 6.1. Using the CP I , compute the average inﬂation rate from 1992 to 2009. 6.5. PROBLEMS 115 6.2. Cash ﬂow diagrams for projects A and B are shown below. Assume that the cash ﬂows are in escalated dollars and that the escalated dollar MARR is 10%. (a) Calculate the N P V of each project as given. (b) Calculate the N P V if one assumes a 5% inﬂation rate. 0 1 2 3 -80 40 0 1 45 2 50 3 -120 100 80 60 6.3. An eight-year life project has an initial capital expenditure of $450,000, annual income of $300,000 beginning at the end of year 1, and annual operating costs of $80,000 beginning at the end of year 1. Calculate the I RR for the following cases: (a) Assume the cash ﬂows given are in escalated dollars and the escalated dollar MARR is 20%. (b) Assume the cash ﬂows given are in today dollars and that incomes are escalated at 7% and costs are escalated at 6%. (c) Assume inﬂation is 4% and rework part (b) in terms of constant dollars. 116 6. DETERMINATION OF PROJECT CASH FLOW 6.4. An investment related to developing a new product is estimated to have the following costs and revenues in today dollars. Do not consider any tax issues. 0 1 2 3 4 5 150,000 Investment: 50,000 Income: Oper Costs: Salvage: 200,000 100,000 200,000 100,000 200,000 100,000 200,000 100,000 0 (a) Evaluate the project’s escalated dollar I RR if both capital costs and operating costs are estimated to escalate at 15% per year from time zero and income is estimated to escalate at 10% per year from time zero. (b) Evaluate the project’s escalated dollar I RR assuming a “washout” of escalation of income and operating costs with a 15% escalation of capital costs per year. “Washout” means any operating cost escalation is offset by the same dollar escalation of revenue (not the same percentage escalation) so that the before-tax proﬁt remains uniform. (c) Compute the constant dollar I RR of case (b) assuming that the rate of inﬂation will be 10% per year. 6.5. Determine the breakeven escalated dollar selling price per unit, X, required in each of years 1 and 2 to achieve a 15% constant dollar project I RR, assuming a 12% per year inﬂation rate. All values are given in today dollars. 0 1 2 Investment: 100,000 Income: Oper Costs: 1000(X) 50,000 1000(X) 50,000 Income escalation = 10% per year from time zero when selling price is $X per unit. Operating Cost escalation = 15% per year from time zero. 1,000 units are to be produced and sold per year. 6.6. Equipment has been purchased for $2,000,000 and put into service with an expected salvage value at the end of 10 years of $200,000. Calculate the annual depreciation using: 6.5. PROBLEMS 117 (a) 10-year straight-line method (b) 10-year double-declining balance method (c) 10-year sum-of-the-years-digits method (d) 10-year MACRS 6.7. Consider a mining and processing project for an oil tar sands project. From the data given below, calculate the after-tax cash ﬂows for a 30-year life of the project and the NP V for an MARR of 15%. (cid:129) Initial capital expenditures totaled $415.5 million and were distributed over four years (10% in year 0, 30% in year 1, 40% in year 2, and 20% in year 3). (cid:129) Beginning in year 4: – 17.666 million tons of ore will be mined per year – Bitumen production rate will be 7.347 million barrels per year – Product yield will be 0.841 barrels of oil per barrel of bitumen – Product selling price will be $80 per barrel – Operating costs: ∗ $10.47 per barrel of bitumen for plant and upgrading costs ∗ $9.02 per ton of ore for mining costs – 10-year straight-line depreciation – 40% tax rate (state and federal) 6.8. The XYZ oil company owns several natural gas wells and is negotiating a 10-year contract to sell the gas from these wells to another company. They are negotiating on the price of the gas in the ﬁrst year, in dollars per thousand cubic feet ($/MCF), including a 4% escalation clause. XYZ expects the wells to produce 33,000 MCF the ﬁrst year and to decline at the rate of 15% every year thereafter. Operating costs are estimated to be $2/MCF and escalate at 3% per year. XYZ has agreed to spend $500,000 now to lay pipelines from each well to the second company’s processing plant. What should the minimum price be the ﬁrst year for this to be acceptable to XYZ? Assume an end-of-year convention and an MARR of 15%. 118 6. DETERMINATION OF PROJECT CASH FLOW 6.9. An investment of $80,000 is projected to generate escalated dollar net revenues (income minus costs) of $10,000 in year 1, $30,000 in year 2, and $40,000 in year 3 with a $40,000 salvage value at the end of year 3. (a) Calculate the escalated dollar I RR for an escalated dollar MARR of 20%. Is this an acceptable investment? (b) Calculate the equivalent constant dollar I RR assuming that inﬂation will be 8% in year 1, 10% in year 2, and 12% in year 3. Is this an acceptable investment? 6.10. The projected cost of the Alaskan oil pipeline was $900 million in 1969 dollars. The ﬁnal cost estimate was nearly $8.5 billion in 1977. What was the average yearly escalation rate for the pipeline? 6.11. Boston’s “Big Dig” is one of the most expensive highway projects in the U.S. The project’s original estimated cost was $2.6 billion in 1982 dollars. The costs in 2005 had risen to over $14.6 billion. (a) What is the value of the $14.6 billion in 1982 dollars? (b) What was the average yearly escalation rate for the project? 6.12. Using Excel® and the CP I values given in Table 6.1, calculate the annual inﬂation rate for each year from 1980 to 2010. 6.13. Use Excel® to solve Problem 6.2 for all 9 combinations of the following: Values of MARR of 5%, 10%, and 15% Inﬂation rates of 2%, 5%, and 7% 6.14. Use Excel® to solve the following problem. An eight-year life project has an initial capital expenditure of $450,000, annual income of $300,000 beginning at the end of year 1, and annual operating costs of $80,000 beginning at the end of year 1. Calculate the I RR for the following cases: (a) Assume the cash ﬂows given are in escalated dollars and the escalated dollar MARR is 10%, 20%, and 30%. (b) Assume the cash ﬂows given are in today dollars and pairs of escalation rates are: a. Incomes are escalated at 7% and costs are escalated at 6% b. Incomes are escalated at 3% and costs are escalated at 5% c. Incomes are escalated at 4% and costs are escalated at 4% (c) Assume inﬂation is 4% and rework all portions of part (b) in terms of constant dollars. 6.5. PROBLEMS 119 6.15. Use Excel® to solve Problem 6.6. Create a line graph that shows the values generated by all four of the methods. 6.16. Use Excel® to solve Problem 6.7. The spreadsheet should allow for the user to easily change any of the numerical values given. 6.17. Use Excel® to solve Problem 6.8. The spreadsheet should allow for the user to easily change any of the numerical values given. C H A P T E R 7 Financial Leverage 121 INTRODUCTION 7.1 Earlier in this text, a brief description of the ﬁnancial aspects involved in economic analyses was presented. It was pointed out that one of the important ﬁnancial aspects had to do with obtaining the funds required to initiate the project. These funds are referred to as the investment capital. As a source for this investment capital, a company could use its own internal funds (what is known as equity funds), borrow funds from an external source (known as debt funds), or use a combination of the two. The ratio of total borrowed funds to the total capital investment is called the ﬁnancial leverage factor. The ratio of borrowed funds to equity funds is called the debt to equity ratio. The degree of ﬁnancial leverage for any given project will affect the economic analysis of the project. FINANCIAL LEVERAGE AND ASSOCIATED RISK 7.2 Under the correct conditions, ﬁnancial leverage will allow an investor (company or individual) to obtain a higher rate of return on its equity capital than it could achieve with no leverage. However, there is often a good deal of added risk associated with leveraged projects. This additional risk is due to the fact that when projects are ﬁnanced with borrowed funds, those funds must be repaid to the lender, independent of the ultimate success or failure of the project. If a leveraged project is only marginally successful during any particular time period, the borrowed funds must be repaid to the lender before any funds are used to pay a return on the equity portion of the investment. 7.3 ADJUSTMENT TO CASH FLOW EQUATIONS Equations 6.14 and 6.15, as well as 6.18 through 6.21, allow the analyst to compute the after-tax cash ﬂows from a project. Some of these equations need to be modiﬁed for the case where the project is leveraged. These modiﬁcations will account for the fact that (a) interest paid on the debt is a pre-tax deduction while (b) the principal paid on the debt is not a pre-tax deduction. Equation 6.18 is modiﬁed as follows: {Taxable Income} ={Gross Revenue} − {Operational Expenses} − {Depreciation} − {Interest paid on debt} Equation 6.21 is modiﬁed as follows: {Cash Flow} ={Net Proﬁt} + {Depreciation} − {Equity Investment} − {Principal paid on debt} (7.1) (7.2) 122 7. FINANCIAL LEVERAGE It should be noted that the investor is allowed to compute depreciation on the total value of each asset in the project independent of the source of funds. Despite the source of funds, the investor owns the full value of the depreciable assets that it procures for the project. Example 7.1 A company is considering a one year investment which will cost $1000.The company’s before- tax MARR is 10%. The $1000 will purchase assets that will be fully depreciated in the one year of operation. There are three possible economic conditions that the company needs to investigate. Details of these conditions are shown below. In addition, the company will consider three different leverage factors: 0.0, 0.4, and 0.7. Interest on any borrowed funds will be 10% over the one year of operation. Use a 40% corporate tax rate and determine the after-tax I RR on the equity funds for each combination of the three economic conditions and the three leverage factors. Note that, for economic condition A, the before-tax IRR on total assets (in this case $1000) is less than the interest rate that will be charged on the loan. For economic condition B, the before-tax I RR on total assets is equal to the interest rate to be charged on the loan and, for economic condition C, the before-tax I RR is greater than the loan interest rate. Revenue – Oper Costs Depreciation Taxable income without leverage I RR on total assets before taxes Economic Conditions C $1200 1000 200 20% B $1100 1000 100 10% A $1050 1000 50 5% Before-tax cash ﬂow diagrams for each economic condition: 0 1 A: 0 1 B: C: 0 1 -1000 1050 -1000 1100 -1000 1200 Table 7.1 shows the cash ﬂows and the computed after-tax I RRs for the 9 different combi- nations. Figure 7.1 shows the after-tax IRR on equity as a function of the leverage factor for the three different economic conditions. 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 123 Table 7.1: Effect of leverage and economic conditions on the after-tax I RR on equity for Example 7.1 124 7. FINANCIAL LEVERAGE Economic Condition A Economic Condition B Economic Condition C Figure 7.1: Effect of leverage factor for various economic conditions for Example 7.1. From the results of Example 7.1, the following observations can be made: 1. Figure 7.1 shows that when the project’s before-tax I RR on assets is less than the interest rate charged on the loan (economic condition A), the after-tax I RR on equity decreases as the leverage factor increases. This makes sense because the project must pay the lender a higher rate of interest than it will be able to pay the owner in rate of return. 2. Figure 7.1 shows that when the project’s before-tax I RR on assets is equal to the interest rate charged on the loan (economic condition B), the after-tax I RR on equity is not affected as the leverage factor increases. This makes sense because the project pays the lender the same rate of interest as it will be able to pay the owner in rate of return. 3. Figure 7.1 shows that when the project’s before-tax I RR on assets is greater than the interest rate charged on the loan (economic condition C), the after-tax I RR on equity increases as the leverage factor increases. This makes sense because the project pays the lender a lower rate of interest than it is able to pay the owner in rate of return. 4. There is more risk to equity capital when projects are leveraged with borrowed money. If the economic conditions are poorer than originally predicted (such as condition A occurring when condition C was predicted when the decision to invest was made), the after-tax I RR on equity will decrease. 5. If enough equity capital exists, companies should not borrow money to fund a project unless the interest rate paid on the debt is less than the before-tax I RR on the project’s total assets. Leverage factors vary from company to company and even within a company from project to project. In general, for most companies other than public utilities (who typically have very high 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 125 leverage factors of 0.6 or greater), leverage factors usually run from 0.3 to 0.5. A highly leveraged project can do very well in a favorable economic climate, but may run into some hard times as economic conditions go from good to bad. Many companies have used this principle to expand rapidly during thriving business conditions. Example 7.2 Consider the following ﬁve-year project with different methods of ﬁnancing. A company has the opportunity to invest in a ﬁve-year project that has an initial capital investment of $100,000. The entire capital investment (total assets) will be depreciated over the ﬁve-year life of the project using straight-line depreciation. Annual incomes and operating costs are expected to be $50,000 and $10,000, respectively. Interest on borrowed money will be 10% compounded annually. Calculate the after-tax IRR on equity for the following cases and assuming a corporate tax rate of 40%. Use an after-tax MARR of 12%. (a) 100% equity. (b) Leverage factor of 0.4. The principal payments will be constant for each of the ﬁve years and the interest paid each year will be based on the outstanding debt balance. (c) Leverage factor of 0.7. The principal payments will be constant for each of the ﬁve years and the interest paid each year will be based on the outstanding debt balance. (d) Leverage factor of 0.4. The principal and interest will be paid with a constant annual payment as calculated according to: P &I payment = Debt ∗ (A/P )10%,5. (e) Leverage factor of 0.4. Interest payments are made each year but the principal is paid back in one lump sum at the end of the project. This is known as yearly interest with a “balloon payment” of the principal at the end. 126 7. FINANCIAL LEVERAGE First, solve for the before-tax I RR on assets. This would be represented by a 0.0 leverage factor and a 0% FIT rate. Therefore, the before-tax I RR on assets for this project is 28.6%. Since the interest rate on borrowed funds is less than this value, leveraging the project should increase the after-tax I RR on equity. (a) This solution will show the effect of the 40% FIT rate compared to the before-tax solution shown previously. 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 127 The 40% FIT tax rate reduces the after-tax I RR on total assets to 18.0%. 128 7. FINANCIAL LEVERAGE (b) This solution will show the effect of a leverage factor of 0.4. 0.4 40000 4000 3200 2400 1600 800 16000 6400 9600 16800 6720 10080 17600 7040 10560 18400 7360 11040 19200 7680 11520 8000 8000 8000 8000 8000 60000 -60000 21600 22080 22560 23040 23520 40000 32000 24000 16000 8000 25.1% 18691 The after-tax I RR on an equity investment of $60,000 has increased to 25.1%. This increase is as expected. Also, the after-tax NP V has increased from a leverage factor of 0.0. (c) This solution will show the effect of a leverage factor of 0.7. 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 129 Increasing the leverage factor to 0.7 further increases the after-tax I RR on equity and the after-tax N P V . 130 7. FINANCIAL LEVERAGE (d) This solution will show the effect of paying constant annual principal and interest payments. Using a more conventional method to repay the debt, the after-tax I RR and after-tax NP V both increase slightly from the ﬁrst repayment method. (e) This solution will show the effect of paying annual interest and then a balloon payment for the principal. 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 131 Modiﬁed I RR using an after-tax MARR of 12%. The balloon repayment method further increases the after-tax I RR and after-tax NP V . From the results of Example 7.2, the following observations can be made: 1. If the results from parts (a), (b), and (c) are compared, it is again found that, under these economic conditions, when the amount of borrowed funds is increased, a higher rate of return is obtained on the equity investment. It should be stressed that this higher rate of return is on a smaller amount of equity dollars compared to ﬁnancing the project with 100% equity funds. 2. It can also be seen that after-tax NP V increases as the leverage factor is increased. NPV analysis would further emphasize that, under the economic conditions of the before-tax I RR on assets being greater than the interest rate paid on the debt, the best option is to maximize 132 7. FINANCIAL LEVERAGE the amount of leverage. By using maximum leverage on each project, a company can invest in more projects and grow more rapidly. 3. Parts (b), (d), and (e) compare three different, but acceptable, methods of repaying the debt portion of the investment. Since the interest on the borrowed money is less than the I RR on assets, it is better to push the repayment of the principal as far forward in time as possible in order to increase I RR on equity and NP V . The balloon payment technique provides the highest I RR and N P V . 7.3.1 LEVERAGE AND MUTUALLY EXCLUSIVE PROJECTS When applying leverage concepts to the evaluation of several projects to determine which one is best, the leverage factor is an important variable. It has been shown in the example problems, that the project I RR on equity is a function of the leverage factor. In order to compare projects, the degree of leverage must be the same on all projects. Many companies have a policy that the comparison of projects is done without considering any leverage for all of the projects. Once a project is chosen, then various methods of ﬁnancing, including different amounts of leverage and repayment techniques, can be investigated as to their effect upon the project. 7.3.2 EXCEL® SPREADSHEET As shown on the next page, the project spreadsheet generated for Example 6.6 can be easily modiﬁed to include the effect of leverage. The only assumptions in the spreadsheet are that the loan will be paid with constant principal payments over the ﬁrst ﬁve years and the interest paid each year will be based on the outstanding debt balance. This could be modiﬁed for other repayment options. 7.3. ADJUSTMENT TO CASH FLOW EQUATIONS 133 134 7. FINANCIAL LEVERAGE PROBLEMS 7.4 7.1. A used piece of heavy equipment is available for purchase at $300,000. A rental company is deciding whether or not to purchase the equipment. The company estimates the equipment will create annual incomes of $110,000 and have annual operating costs of $20,000. The equipment can be depreciated in ﬁve years with straight-line depreciation. Based on the results from part (a) below, should the rental company purchase the equipment if their corporate tax rate is 35%? Consider a ﬁve-year life project and an after-tax MARR of 15%. (a) Determine the return on equity for each of three different leverage factors of 0, 0.4, and 0.7. Assume an interest rate on borrowed funds to be 10% compounded annually. The principal payments will be constant for each of the ﬁve years and the interest paid each year will be based on the outstanding debt balance. (b) Assume two additional economic conditions: (i) annual income increases to $125,000 and (ii) annual income decreases to $95,000. Repeat part (a) for these two economic conditions. Prepare a plot of the I RR on equity versus the leverage factor. 7.2. A corporation’s tax rate is 40%. An outlay of $35,000 is being considered for a new asset. Estimated annual revenues are $30,000 and estimated annual operating costs are $10,000. The useful life of the asset is 5 years and has no salvage value. Use the SYD method of depreciation. A lending institution has offered to loan the corporation 50% of the initial investment cost at an annual interest rate of 12.5%. The principal and interest will be paid with a constant annual payment as calculated according to: P &I payment = Debt ∗ (A/P )12.5%,5. If the corporation’s after-tax MARR is 15%, should it accept the loan? Solve Problem 6.7 using a leverage factor of 0.2. 7.3. 7.4. Use Excel® to solve Problem 6.8 for leverage factors of 0.2 and 0.4. C H A P T E R 8 135 Basic Statistics and Probability 8.1 INTRODUCTION In previous chapters of this text, it was assumed that all of the information needed to make an eco- nomic analysis was known without any uncertainty. In practice, this is a rare situation. Nearly always, an evaluator will need to include a measure of the uncertainty pertaining to one or more variables in the analysis. This uncertainty may, in turn, add signiﬁcant uncertainty about the proﬁtability of an investment. For example, with one set of economic assumptions, the project’s NPV might be greater than zero which would indicate an acceptable investment. However, with a different set of economic assumptions, the project’s NPV might be negative, thereby indicating that the investor should pass on this opportunity. This range of uncertainty about the project’s proﬁtability is one way to deﬁne the “risk” in a project. Having a basic understanding of statistics and probability will allow an evaluator to incorporate various risk factors into the analyses that are to be completed for a project. Some techniques that are available to incorporate uncertainty into project variables, and that apply the ideas of statistics and probability presented in this chapter, will be presented in Chapter 9. 8.2 STATISTICS 8.2.1 MEASURES OF CENTRAL TENDENCY Averages are often used to represent a set of data. Several different types of averages can be calculated. These include the arithmetic mean, the median, the mode, and the geometric mean.These are known as measures of central tendency as they tend to be centrally located within the data. Arithmetic Mean The arithmetic mean of a set of data is calculated with Equation 8.1. The arithmetic mean is also known as the expected value of the data. μ = (cid:17) N(cid:4) (cid:18) xi /N i=1 (8.1) where, xi = the ith value of the data N = total number of data points μ = arithmetic mean 136 8. BASIC STATISTICS AND PROBABILITY Excel® has a built-in function to calculate the arithmetic mean: = AVERAGE(number1, number2,…) where, number1, number2, ... = list of data points Median When a set of data is arranged in order of magnitude, the median of the set is found by taking the middle value (when there is an odd number of values) or the arithmetic mean of the two middle values (when there is an even number of values). Excel® has a built-in function to calculate the median: = MEDIAN(number1, number2,…) Mode The mode is the value which occurs with the greatest frequency. A set of data can have a single mode, several modes, or no modes. Excel® has two built-in functions to calculate the mode: single mode: = MODE.SNGL(number1, number2, …) multiple modes: = MODE.MULT(number1, number2, …) Geometric Mean The geometric mean of a set of data is calculated with Equation 8.2: (cid:19) (cid:20) (cid:20) (cid:21) G = N N(cid:22) xi i=1 (8.2) where, xi = the ith value of the data N = total number of data points N(cid:22) i=1 = (x1)(x2)(x3) . . . (xN −1)(xN ) Excel® has a built-in function to calculate the geometric mean: = GEOMEAN(number1, number2,…) Example 8.1 Consider 100 exam scores from a college-level class as shown below: 8.2. STATISTICS 137 75 76 57 77 54 84 51 94 95 85 67 91 88 38 86 91 77 46 46 87 96 81 94 93 94 67 88 99 48 83 73 87 59 76 60 79 79 85 79 98 78 91 97 35 88 78 46 79 85 74 53 55 81 78 75 73 97 34 87 88 51 88 78 94 86 78 80 85 76 51 47 90 90 88 38 79 90 39 56 57 31 53 83 67 67 39 78 91 48 95 42 74 65 89 99 90 84 82 32 61 (a) Calculate the arithmetic mean: μ = (75 + 67 + 96 + · · · + 95 + 61)/100 = 73.7 (b) Calculate the median: First, order the 100 scores from high to low. Since there is an even number of values, the median is the average of 50th (79) and 51st (78) values, or 78.5. (c) Calculate the mode: Again, order the 100 scores from high to low and ﬁnd the value that occurs most often. In this case, the value of 78 occurs six times. Therefore, the mode is 78. (d) Calculate the geometric mean: √ G = 100 75 ∗ 67 ∗ 96 ∗ · · · ∗ 95 ∗ 61 = 70.9 138 8. BASIC STATISTICS AND PROBABILITY Using Excel®: A B C D E F G H I J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 53 55 81 78 75 73 97 34 87 88 F 53 55 81 78 75 73 97 34 87 88 75 76 57 77 54 84 51 94 95 85 67 91 88 38 86 91 77 46 46 87 96 81 94 93 94 67 88 99 48 83 Average = 73.7 Median = 78.5 78 Geo Mean = 70.9 Mode = A 75 76 57 77 54 84 51 94 95 85 B 67 91 88 38 86 91 77 46 46 87 C 96 81 94 93 94 67 88 99 48 83 73 87 59 76 60 79 79 85 79 98 D 73 87 59 76 60 79 79 85 79 98 78 91 97 35 88 78 46 79 85 74 E 78 91 97 35 88 78 46 79 85 74 Average = =AVERAGE(A1:J10) Median = =MEDIAN(A1:J10) Mode = =MODE.SNGL(A1:J10) Geo Mean = =GEOMEAN(A1:J10) 51 88 78 94 86 78 80 85 76 51 G 51 88 78 94 86 78 80 85 76 51 47 90 90 88 38 79 90 39 56 57 H 47 90 90 88 38 79 90 39 56 57 31 53 83 67 67 39 78 91 48 95 I 31 53 83 67 67 39 78 91 48 95 42 74 65 89 99 90 84 82 32 61 J 42 74 65 89 99 90 84 82 32 61 8.2.2 MEASURES OF DISPERSION It is frequently desired to determine how a set of data is dispersed or spread about its average. Measures of dispersion which will be discussed in this chapter include the range, the mean deviation, the standard deviation, and the variance. 8.2. STATISTICS 139 Range The range of a set of data is simply the difference between the largest and the smallest values of the data. In order to compute the range of a set of data with Excel®, use the MAX and MIN functions: =MAX(number1, number2,…) − MIN(number1, number2,…) Mean Deviation The mean deviation (or average deviation) is the mean of the distances between each value and the mean. It is computed with Equation 8.3: M.D. = (cid:18) \|xi − μ\| /N (cid:17) N(cid:4) i=1 (8.3) where, xi = the ith value of the data μ = the arithmetic mean of the data N = total number of data points Excel® does not have a built-in function to calculate the mean deviation. To use Excel®, do the following: 1. Place the data in a single column (for example, assume 10 data points in cells A1 through A10). 2. Use the formula =AVERAGE(A1:A10) in cell A11 to compute the average of this column of data. This is the mean of the data. 3. In the adjacent column B, use the formula =ABS(A1−$A$11) in cell B1. 4. Copy this formula to cells B2 through B10. 5. Use the formula =AVERAGE(B1:B10) in cell B11 to compute the average of this column of data. This is the mean deviation of the data. Standard Deviation Standard deviation is another measure of the variability of a data set about its mean. Its origins are associated with the normal distribution that is discussed later in this chapter, but it has meaning 140 8. BASIC STATISTICS AND PROBABILITY for any set of data. A small value of standard deviation indicates that the data points are clustered more closely to the mean than a larger value of standard deviation. If the entire population has been sampled (that is, N equals the total possible number of data points in the population), the standard deviation is calculated with Equation 8.4: (cid:19) (cid:20) (cid:20) (cid:21) N(cid:4) σ = (xi − μ)2 /N (8.4) i=1 where, xi = the ith value of the data μ = the arithmetic mean of the data N = total number of data points If one was calculating the standard deviation of 100 exam scores in a particular college-level class with 100 students, then N would be 100 in Equation 8.4. However, if only a subset of the population is being sampled, N should be replaced with N − 1. It can be noted that when N gets larger than about 30, there is very little error introduced by using N instead of N − 1. As an example of a sample, assume that one wanted to measure the mean and standard deviation of the age of the population in a city of 20,000 people. It would be difﬁcult to get the age of all 20,000 people, so a subset of the population is sampled (perhaps 1,000 people). One would use Equation 8.1 to determine the mean age of the population and Equation 8.4 (with N − 1 instead of N) to determine the standard deviation of the population’s age. Excel® has two built-in functions to calculate the standard deviation: =STDEV.P(number1, number2,…) for the entire population or =STDEV.S(number1, number2,…) for a sample of the population. Per Equation 8.4, STDEV.P contains a division by N, whereas STDEV.S contains a division by N − 1. Example 8.2 Consider 100 exam scores from a college-level class as shown below (same as Example 8.1): 75 76 57 77 54 84 51 94 95 85 67 91 88 38 86 91 77 46 46 87 96 81 94 93 94 67 88 99 48 83 73 87 59 76 60 79 79 85 79 98 78 91 97 35 88 78 46 79 85 74 53 55 81 78 75 73 97 34 87 88 51 88 78 94 86 78 80 85 76 51 47 90 90 88 38 79 90 39 56 57 31 53 83 67 67 39 78 91 48 95 42 74 65 89 99 90 84 82 32 61 (a) Calculate the range: 8.2. STATISTICS 141 Order the numbers from high to low. The range is then given by the highest value minus the lowest value. Range = 99-31 = 68. (b) Calculate the mean deviation: M.D. = (\|75 − 73.7\| + \|67 − 73.7\| + \|96 − 73.7\| + · · · + \|95 − 73.7\| + \|61 − 73.7\|) /100 = 15.4 (c) Calculate the standard deviation: (cid:23) σ = (75 − 73.7)2 + (67 − 73.7)2 + · · · + (95 − 73.7)2 + (61 − 73.7)2 100 = 18.5 Using Excel®: A 75 76 57 77 54 84 51 94 95 85 B 67 91 88 38 86 91 77 46 46 87 C 96 81 94 93 94 67 88 99 48 83 D 73 87 59 76 60 79 79 85 79 98 E 78 91 97 35 88 78 46 79 85 74 F 53 55 81 78 75 73 97 34 87 88 G 51 88 78 94 86 78 80 85 76 51 H 47 90 90 88 38 79 90 39 56 57 I 31 53 83 67 67 39 78 91 48 95 J 42 74 65 89 99 90 84 82 32 61 Mode = Average = 73.7 Median = 78.5 78 Geo Mean = 70.9 68 Mean Dev = 15.4 StdDev = 18.5 Range = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 142 8. BASIC STATISTICS AND PROBABILITY A 75 76 57 77 54 84 51 94 95 85 B 67 91 88 38 86 91 77 46 46 87 C 96 81 94 93 94 67 88 99 48 83 D 73 87 59 76 60 79 79 85 79 98 E 78 91 97 35 88 78 46 79 85 74 F 53 55 81 78 75 73 97 34 87 88 G 51 88 78 94 86 78 80 85 76 51 H 47 90 90 88 38 79 90 39 56 57 I 31 53 83 67 67 39 78 91 48 95 J 42 74 65 89 99 90 84 82 32 61 Average = =AVERAGE(A1:J10) Median = =MEDIAN(A1:J10) Mode = =MODE.SNGL(A1:J10) Geo Mean = =GEOMEAN(A1:J10) Range = =MAX(A1:J10)-MIN(A1:J10) 121B= = veD naeM StdDev = )01J:1A(P.VEDTS= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 71 18 *This assumes that the 100 data points are copied to cells A21:A120 and the procedure listed above under Mean Deviation is followed. 8.2.3 FREQUENCY DISTRIBUTIONS The creation of a frequency distribution is another technique to summarize large numbers of raw data. When the raw data are summarized, they begin to take on more meaning and utility. A frequency distribution is made by grouping the raw data into classes and counting the number of items that fall into each class. This number is referred to as the class frequency. A table is then formed which contains a column for the class, a column for the class frequency, and a column for the cumulative class frequency. The resulting table is the frequency distribution. The size and number of classes will depend upon the particular application that is being considered. Typically, frequency distributions contain ﬁve to ten classes, all of equal size. However, some data might lend themselves to classes of unequal size or even classes that might be open ended (normally, the ﬁrst class or the last class or both). The cumulative frequency distribution, Fi, is the summation of the frequency distribution. Example 8.3 Consider 100 exam scores from a college-level class as shown below (same as Example 8.1): 8.2. STATISTICS 143 75 76 57 77 54 84 51 94 95 85 67 91 88 38 86 91 77 46 46 87 96 81 94 93 94 67 88 99 48 83 73 87 59 76 60 79 79 85 79 98 78 91 97 35 88 78 46 79 85 74 53 55 81 78 75 73 97 34 87 88 51 88 78 94 86 78 80 85 76 51 47 90 90 88 38 79 90 39 56 57 31 53 83 67 67 39 78 91 48 95 42 74 65 89 99 90 84 82 32 61 Using ten classes from 0–100, develop the frequency distribution for the data. Solution: Within the frequency distribution, the range of numbers that is used to deﬁne the class is called a class interval. The smaller number is the lower class limit and the larger number is the upper class limit. Note that in Example 8.3, the upper class limit of one class is the same as the lower class limit of the next class. If a value is exactly equal to one of the class limits, one needs to decide in which class it belongs. It doesn’t matter if it is placed in the higher range or the lower range as long as the evaluator remains consistent. In Example 8.3, any value that is equal to a class limit is placed in the lower range (e.g., a value of 90 is placed in the 80-90 class). If this convention is used, then one can deﬁne true class limits for a range. In this case, the true class limits would be 90.5-100.5, 80.5-90.5, 70.5-80.5, etc. Excel® utilizes this convention as well. There are two other terms that need to be deﬁned for frequency distributions. The class size is the difference between the upper true class limit and the lower true class limit. The true class mark 144 8. BASIC STATISTICS AND PROBABILITY is the midpoint of each true class interval or the average between the upper true class limit and the lower true class limit. In Example 8.3, the class size is ten for all ten classes and the true class marks are 95.5, 85.5, 75.5, etc. True Class Limits 0.5-10.5 10.5-20.5 20.5-30.5 30.5-40.5 40.5-50.5 50.5-60.5 60.5-70.5 70.5-80.5 80.5-90.5 90.5-100.5 Total True Class Mark 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 Frequency fi 0 0 0 8 7 12 6 23 27 17 100 Cumula ve Frequency, Fi 0 0 0 8 15 27 33 56 83 100 Frequency distributions are often represented graphically. Graphical representations include histograms, frequency polygons, and relative and cumulative relative frequency diagrams. A histogram consists of a set of rectangles, where a rectangle is drawn for each class interval with the width of each rectangle equal to the class size and the height of the rectangle is the class frequency. The histogram is constructed so that the center of each rectangle lies at its true class mark. Figure 8.1 is the histogram for the data presented in Example 8.3. A frequency polygon can be generated by creating a line graph of the frequency of each class as a function of the true class marks. Figure 8.2 is the frequency polygon for the data presented in Example 8.3. The ﬁrst and last points of the polygon are found on the x-axis at what would be the true class marks associated with class intervals before the ﬁrst actual class interval (located at −4.5) and after the last actual class interval (located at 105.5). 8.2. STATISTICS 145 Histogram 30 25 20 Freq 15 10 5 0 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 Exam Scores Figure 8.1: Histogram for Example 8.3. Frequency Polygon 30 25 20 Freq 15 10 5 0 -4.5 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 105.5 Exam Scores Figure 8.2: Frequency polygon for Example 8.3. 146 8. BASIC STATISTICS AND PROBABILITY 8.2.4 RELATIVE FREQUENCY DISTRIBUTION The relative frequency distribution is constructed by dividing the number of occurrences in each class interval by the total number of points in the data set. The following shows the relative fre- quency distribution for Example 8.3 while Figures 8.3 and 8.4 show the graphical versions of these distributions. True Class Limits True Class Mark 0.5-10.5 10.5-20.5 20.5-30.5 30.5-40.5 40.5-50.5 50.5-60.5 60.5-70.5 70.5-80.5 80.5-90.5 90.5-100.5 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 Rela ve Frequency, fi 0.00 0.00 0.00 0.08 0.07 0.12 0.06 0.23 0.27 0.17 Cumula ve Rela ve Frequency, Fi 0.00 0.00 0.00 0.08 0.15 0.27 0.33 0.56 0.83 1.00 Rela(cid:415)ve Frequency Distribu(cid:415)on 0.3 0.25 0.2 Rel Freq 0.15 0.1 0.05 0 -4.5 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 105.5 Exam Scores Figure 8.3: Relative frequency distribution for Example 8.3. Cumula(cid:415)ve Rela(cid:415)ve Frequency 8.2. STATISTICS 147 Cumul Rela(cid:415)ve Freq 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -4.5 5.5 15.5 25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.5 105.5 Exam Scores Figure 8.4: Cumulative relative frequency for Example 8.3. If the data are presented in frequency distribution form, items such as the mean, mean devi- ation, and standard deviation can be determined from the following equations, respectively. μ(cid:7) = M.D.(cid:7) = M(cid:4) j =1 M(cid:4) fj x(cid:7) j (cid:7) (cid:7) (cid:7)x(cid:7) j (cid:7) (cid:7) (cid:7) − μ(cid:7) fj j =1 (cid:19) (cid:20) (cid:20) (cid:21) M(cid:4) j =1 σ (cid:7) = (cid:5) fj x(cid:7) j − μ(cid:7) (cid:6) 2 (8.5) (8.6) (8.7) where, fj = the relative frequency of the j th class = the true class mark of the j th class x(cid:7) j M = total number of classes μ(cid:7) = the arithmetic mean of the data based on the distribution M.D.(cid:7) = the mean deviation of the data based on the distribution σ (cid:7) = the standard deviation of the data based on the distribution 148 8. BASIC STATISTICS AND PROBABILITY Example 8.4 Calculate the mean, mean deviation, and standard deviation for the data in Example 8.1, using the relative frequency distributions found in Example 8.3: Mean: μ(cid:7) = 0.00 ∗ 5.5 + 0.00 ∗ 15.5 + · · · + 0.27 ∗ 85.5 + 0.17 ∗ 95.5 = 73.3 This value compares favorably to 73.7 computed with all 100 data points. Mean Deviation: M.D.(cid:7) =0.00 ∗ \|5.5 − 73.3\| + 0.00 ∗ \|15.5 − 73.3\| + · · · + 0.27 ∗ \|85.5 − 73.3\| + 0.17 ∗ \|95.5 − 73.3\| =15.1 This value compares favorably to 15.4 computed with all 100 data points. Standard Deviation: (cid:23) σ (cid:7) = 0.00 ∗ (5.5 − 73.3)2 + 0.00 ∗ (15.5 − 73.3)2 + · · · + 0.27 ∗ (85.5 − 73.3)2 + 0.00 ∗ (95.5 − 73.3)2 = 18.3 This value compares favorably to 18.5 computed with all 100 data points. 8.3. PROBABILITY 149 PROBABILITY 8.3 8.3.1 CLASSICAL DEFINITION The classical deﬁnition of probability involves an event occurring from a group or a set of equally likely outcomes. That is, when a fair coin is tossed, the speciﬁc outcome of that event is either a heads or a tails with each outcome equally likely to occur. Suppose that a particular event occurs a certain number of times out of a total possible number of other events. The probability that the desired event will occur is given by Equation 8.8: P (A) = nA/n (8.8) where, P (A) = the probability of event A occuring nA = the number of times event A could occur n = the total number of possible events Example 8.5 Consider the probability of drawing an ace from a fair deck of cards. Since there are four aces in a total of 52 cards and the chances of drawing any speciﬁc card is the same, the probability of drawing an ace would be: P (Ace) = 4/52 = 1/13 = 0.0769 = 7.69% Note that in the above example, the probability of 4/52 is only correct for any given attempt to draw an ace if, when an undesired card is drawn (not an ace), it is returned to the deck before the next card is drawn. This is referred to as sampling with replacement. If the undesired card is not returned to the deck, known as sampling without replacement, the probability changes to 4/51, then 4/50, etc. Example 8.6 Consider the probability of rolling two fair die and getting a total of 8. When rolling two fair die, the possible outcomes are: Die 1 1 1 1 1 1 1 Die 2 1 2 3 4 5 6 Total 2 3 4 5 6 7 Die 1 2 2 2 2 2 2 Die 2 1 2 3 4 5 6 Total 3 4 5 6 7 8 Die 1 3 3 3 3 3 3 Die 2 1 2 3 4 5 6 Total 4 5 6 7 8 9 150 8. BASIC STATISTICS AND PROBABILITY Die 1 4 4 4 4 4 4 Die 2 1 2 3 4 5 6 Total 5 6 7 8 9 10 Die 1 5 5 5 5 5 5 Die 2 1 2 3 4 5 6 Total 6 7 8 9 10 11 Die 1 6 6 6 6 6 6 Die 2 1 2 3 4 5 6 Total 7 8 9 10 11 12 As shown in the table, there are 36 possible outcomes of the dice rolls, ﬁve of which have a value of 8. Therefore, the probability of getting exactly 8 is: P (8) = 5/36 = 0.139 = 13.9% Example 8.7 Consider the ﬂipping of a fair coin (50% probability of a head and 50% probability of a tail). The coin will be ﬂipped three times. What is the probability that 0, 1, 2, and 3 heads occurred in the three ﬂips? First Flip T T T T H H H H Second Flip T T H H T T H H Third Flip T H T H T H T H Total # of Heads 0 1 1 2 1 2 2 3 As shown in the table, there are eight possible outcomes of the three ﬂips. Therefore, P (0Heads) = 1/8 = 0.125 = 12.5% P (1Heads) = 3/8 = 0.375 = 37.5% P (2Heads) = 3/8 = 0.375 = 37.5% P (3Heads) = 1/8 = 0.125 = 12.5% 8.3.2 RELATIVE FREQUENCY DEFINITION 8.3. PROBABILITY 151 The classical deﬁnition of probability uses the concept of equally likely outcomes to aid in the deﬁnition. Since the words “equally likely” themselves imply some notion of probability, the deﬁnition would appear to be a bit circular in nature. To get around this, the concept of relative frequency probability was introduced. If an experiment or trial is going to be repeated a large number of times, the probability that a particular event of the experiment will occur is given by the relative frequency shown in Equation 8.9: P (A) = lim n→∞ (nA/n) (8.9) Example 8.8 Consider the tossing of a coin. One would normally assume that the probability of getting a head on any one toss is 50%. However, consider an experiment where a coin is tossed 100 times and heads occurs 52 times and tails 48 times. For this case, the probability of getting a head would be predicted to be 52%. If the coin is a fair one, as the number of experimental data points gets larger and larger, the probability of getting a head will approach 50%. In most cases throughout engineering, one does not have the luxury of performing an inﬁnite number of experiments in order to determine the true probability of an event occurring. For example, if an engineer is doing failure tests on a particular manufactured component, one can only do a limited number of failure experiments in order to determine the probability of failure. 8.3.3 SUBJECTIVE DEFINITION A third type of probability deﬁnition is known as subjective probability. This type of probability is not determined from theoretical or experimental work, but rather from the experience that an individual or group of individuals has gained during their career in a particular area. This experience is then used to predict the probability of future events. For example, a civil engineer who does road design will gain, over time, a “feeling” or estimation of the probability that a road surface will begin to fail within a certain time range based on weather conditions, quantity of trafﬁc, type of surfacing materials used, etc. In summary, for economic evaluations, it is necessary that probabilities of certain outcomes be assigned. This allows the evaluator to incorporate risk factors into economic analysis situations. The difﬁculty is often in the assigning of the actual probabilities. One or more of the above deﬁnitions may assist the evaluator in this task. 8.3.4 PROBABILITY DISTRIBUTIONS For a given event or set of events, if probability or frequency distributions can be established, the statistical concepts discussed earlier can be applied to calculate means and standard deviations for each event. 152 8. BASIC STATISTICS AND PROBABILITY Two different types of probability distributions, discrete and continuous, will be discussed below. Discrete Distribution A discrete distribution is one which involves an experiment with a ﬁnite number of possibilities. For example, as described earlier, when a fair die is thrown, a 1, 2, 3, 4, 5, or 6 will occur. Thus, the outcome of a throw is a discrete value. Using the classical probability deﬁnition, each possible outcome would have a probability of 1/6. Note that the sum of the probabilities of all possible outcomes will always equal 1.0. Example 8.9 Consider that a certain discrete random variable, x, has a discrete probability distribution as follows: (a) Graph the distribution (b) Find the mean (c) Find the standard deviation (a) Graphically, the distribution is shown in Figure 8.5. Discrete Probability Distribu(cid:415)on 0.3 0.25 0.2 P(x) 0.15 0.1 0.05 0 -3 -1 0 1 2 3 5 8 x Figure 8.5: Probability distribution for the random discrete variable x in Example 8.9. 8.3. PROBABILITY 153 For this distribution, it would be useful to calculate the mean and standard deviation using Equations 8.5 and 8.7: (b) μ(cid:7) = 0.1 ∗ (−3) + 0.2 ∗ (−1) + 0.15 ∗ (0) + 0.25 ∗ (1) + 0.1 ∗ (2) + 0.1 ∗ (3) + 0.05 ∗ (5) + 0.05 ∗ (8) = 0.90 (cid:23) (c) σ (cid:7) = 0.1 ∗ (−3 − 0.9)2 + 0.2 ∗ (−1 − 0.9)2 + 0.15 ∗ (0 − 0.9)2 + 0.25 ∗ (1 − 0.9)2 + 0.1 ∗ (2 − 0.9)2 + 0.1 ∗ (3 − 0.9)2 + 0.05 ∗ (5 − 0.9)2 + 0.05 ∗ (8 − 0.9)2 = 2.51 Solution using Excel®: A B x -3 -1 0 1 2 3 5 8 1 2 3 4 5 6 7 8 9 10 Total = 11 12 Mean = StdDev = 13 P(x) 0.1 0.2 0.15 0.25 0.1 0.1 0.05 0.05 1.00 0.90 2.51 C xP(x) -0.3 -0.2 0 0.25 0.2 0.3 0.25 0.4 D E (x-mu)^2 P(x)(x-mu)^2 1.521 0.722 0.122 0.003 0.121 0.441 0.841 2.521 15.2 3.6 0.8 0.0 1.2 4.4 16.8 50.4 154 8. BASIC STATISTICS AND PROBABILITY A B x -3 -1 0 1 2 3 5 8 1 2 3 4 5 6 7 8 9 10 11 Total = 12 Mean = 13 =SUM(B2:B9) =SUM(C2:C9) StdDev = =SQRT(SUM(E2:E9)) C xP(x) =A2B2 =A3B3 =A4B4 =A5B5 =A6B6 =A7B7 =A8B8 =A9B9 P(x) 0.1 0.2 0.15 0.25 0.1 0.1 0.05 0.05 E D (x-mu)^2 P(x)(x-mu)^2 =B2D2 =B3D3 =B4D4 =B5D5 =B6D6 =B7D7 =B8D8 =B9D9 =(A2-B$12)^2 =(A3-B$12)^2 =(A4-B$12)^2 =(A5-B$12)^2 =(A6-B$12)^2 =(A7-B$12)^2 =(A8-B$12)^2 =(A9-B$12)^2 Binomial Distribution The binomial distribution is a standard discrete distribution that accounts for the case where there are two possible events and the probabilities of each event are not the same. Given a number of independent trials, n, of an experiment that has two possible outcomes (call them success and failure), the probability of a certain number of successes occurring in those n trials is given by Equation 8.10: Pn(x) = Cn x pxqn−x (8.10) where, Pn(x) = the probability of x successes in n trials = the number of combinations of n items taken x at a time = n!/(x!(n − x)!) Cn x p = the probability of a success for any given trial q = the probability of a failure for any given trial = 1 − p In addition to the probability of exactly x successes in n trials, it is also common to determine the probability of less than k successes, greater than k successes, or between l and k successes. Speciﬁcally, 8.3. PROBABILITY 155 Pn(x < k) = k−1(cid:4) Pn(j ) Pn(x > k) = Pn(l < x < k) = j =0 n(cid:4) j =k+1 k−1(cid:4) j =l+1 Pn(j ) Pn(j ) (8.11) (8.12) (8.13) Excel® has a built-in function to compute a binomial distribution: =BINOM.DIST(#_successes, #_trials, prob_of_success, cumulative). where, #_successes = number of successes in n trials (x) #_trials = number of trials (n) prob_of_success = probability of success (p) cumulative = FALSE for probability distribution = TRUE for cumulative probability distribution Example 8.10 The probability that a fuse will be defective when ﬁrst installed is 0.08. If six fuses are selected at random, ﬁnd each of the following: (a) The probability that less than two fuses are defective (b) The probability that four or more fuses are defective (c) The probability that at least one is defective Solution: Deﬁne a success as a fuse that is defective. Therefore, p = 0.08 and q = 0.92. P6(0) = C0 6 (0.08)0(0.92)6 = 6! 0!6! 6 (0.08)1(0.92)5 = 6! 1!5! 6 (0.08)2(0.92)4 = 6! 2!4! = 0.606 P6(1) = C1 = 0.316 P6(2) = C2 = 0.0688 (0.08)0(0.92)6 (0.08)1(0.92)5 (0.08)2(0.92)4 156 8. BASIC STATISTICS AND PROBABILITY P6(3) = C3 = 0.00797 P6(4) = C4 = 0.000520 P6(5) = C5 6 (0.08)3(0.92)3 = 6! 3!3! 6 (0.08)4(0.92)2 = 6! 4!2! 6 (0.08)5(0.92)1 = 6! 5!1! 6 (0.08)6(0.92)0 = 6! 6!0! = 0.0000181 P6(6) = C6 = 0.000000262 (0.08)3(0.92)3 (0.08)4(0.92)2 (0.08)5(0.92)1 (0.08)6(0.92)0 (a) P6(x < 2) = P6(0) + P6(1) = 0.606 + 0.316 = 0.922 (b) P6(x ≥ 4) = P6(4) + P6(5) + P6(6) = 5.20 · 10−4 + 1.81 · 10−5 + 2.62 · 10−7 = 5.38 · 10−4 (c) P6(x > 0) = P6(1) + P6(2) + P6(3) + P6(4) + P6(5) + P6(6) = 0.394 Alternatively, P6(x > 0) = 1 − P6(0) = 1 − 0.606 = 0.394 Using Excel®: In graphical form, the discrete distribution for Example 8.10 can be shown as: 8.3. PROBABILITY 157 P(x) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Binomial Distribu(cid:415)on 6.06E-01 3.16E-01 6.88E-02 7.97E-03 5.20E-04 1.81E-05 2.62E-07 0 1 2 3 4 5 6 # of Successes Continuous Distributions When the value of the event, x, can take on a continuous set of probability values, rather than a set of speciﬁc values, then a probability density function, p(x), exists. While there are a wide variety of continuous distributions possible, the authors have chosen to present three continuous distributions: the uniform distribution, the triangular distribution, and the normal or Gaussian distribution. Figure 8.6 is a representation of a continuous distribution. For continuous probability distributions, the following statements and equations are pertinent: 1. For a given x, p(x) is not the probability of that exact value occurring. Since there are an inﬁnite number of values for x, the probability of any one speciﬁc value of x would be zero. 2. The total area under the curve will equal the value of unity. 3. The mean of the data is calculated with Equation 8.14. μ = (cid:24) ∞ −∞ xp(x)dx (8.14) 158 8. BASIC STATISTICS AND PROBABILITY Con(cid:415)nuous Distribu(cid:415)on 0.25 0.2 0.15 0.1 0.05 p(x) 0 0 2 4 6 10 12 14 16 8 x Figure 8.6: Continuous distribution. 4. The standard deviation of the data is calculated with Equation 8.15: (cid:23)(cid:24) ∞ −∞ σ = x2p(x)dx − μ2 5. The cumulative probability, F (x), is deﬁned with Equation 8.16. F (x) = (cid:24) x −∞ p(x)dx (8.15) (8.16) 6. F (x1) represents the probability that the value of x is less than or equal to x1. 7. The quantity (1 − F (x1)) represents the probability that the value of x is greater than or equal to x1. Uniform or Rectangular Distribution The uniform or rectangular distribution is represented in Figure 8.7. Each value of x has the same probability of occurring. Let a be the minimum value of x and b be the maximum value of x. Since the area under the probability curve must be unity, the height of the uniform distribution will be given by Equation 8.17: h = 1/(b − a) (8.17) 8.3. PROBABILITY 159 Figure 8.7: Uniform or rectangular distribution. The uniform distribution then has the following properties: p(x) = h for a ≤ x ≤ b p(x) = 0 for all other values of x μ = (a + b)/2 √ σ = (b − a)/ 12 F (x) = (x − a)/(b − a) (8.18) (8.19) (8.20) Triangular Distribution The triangular distribution is represented in Figure 8.8. Let a be the minimum value of x, c be the maximum value of x, and b be the mode. P1 and P2 represent the areas from a to b and b to c, respectively. The triangular distribution has the following properties: h = 2/(c − a) P1 = (b − a)/(c − a) P2 = (c − b)/(c − a) (8.21) (8.22) (8.23) 160 8. BASIC STATISTICS AND PROBABILITY h Figure 8.8: Triangular distribution. μ = (a + b + c)/3 σ = (c − a) ∗ (cid:25) (1 − P1P2)/18 F (x) = P1 [(x − a)/(b − a)]2 F (x) = 1 − P2 [(c − x)/(c − b)]2 for a ≤ x ≤ b for b ≤ x ≤ c (8.24) (8.25) (8.26) (8.27) Normal Distribution The Normal or Gaussian distribution is a continuous probability function that takes on the common “bell-shaped curve” as represented in Figure 8.9. The shape of this distribution is calculated with Equation 8.28: p(x) = 1 √ σ 2π (cid:6) 2 (cid:5) x−μ σ − 1 2 e (8.28) where, μ = the mean of the data σ = the standard deviation of the data range of variable x: − ∞ ≤ x ≤ ∞ 8.3. PROBABILITY 161 Figure 8.9: Representation of a unit normal distribution (μ = 0, σ = 1). When μ = 0 and σ = 1, the distribution is called a unit normal distribution and Equation 8.28 simpliﬁes to Equation 8.29: p(x) = 1√ 2π e− x2 2 (8.29) One can convert any set of normally distributed data to a unit normal distribution through the substitution of the variable Z, deﬁned as: Z = (x − μ)/σ (8.30) This allows one to then use Table 8.1 to determine values of p(Z) and F (Z) as deﬁned above. Since the unit normal distribution is symmetrical about Z = 0, one only needs the positive portion of the table. If Z < 0, then use the following equations for p(Z) and F (z): p(−Z) = p(Z) F (−Z) = 1 − F (Z) (8.31) (8.32) Excel® has a built-in function that calculates p(x) and F (x) given x, the mean, and the standard deviation: =NORM.DIST(x,Mean,Std_Dev,Cumulative) where, x = value at which to ﬁnd the value of either of p(x) of F (x) Mean = mean of the distribution Std_Dev = standard deviation of the distribution Cumulative = FALSE for p(x) or =TRUE for F (x). 162 8. BASIC STATISTICS AND PROBABILITY Table 8.1: Values of p(Z) and F (Z) for the unit normal distribution Z 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 p(Z) 0.39894 0.39844 0.39695 0.39448 0.39104 0.38667 0.38139 0.37524 0.36827 0.36053 0.35207 0.34294 0.33322 0.32297 0.31225 0.30114 0.28969 0.27798 0.26609 0.25406 0.24197 0.22988 0.21785 0.20594 0.19419 0.18265 0.17137 0.16038 0.14973 0.13943 0.12952 F(Z) 0.50000 0.51994 0.53983 0.55962 0.57926 0.59871 0.61791 0.63683 0.65542 0.67364 0.69146 0.70884 0.72575 0.74215 0.75804 0.77337 0.78814 0.80234 0.81594 0.82894 0.84134 0.85314 0.86433 0.87493 0.88493 0.89435 0.90320 0.91149 0.91924 0.92647 0.93319 Z 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 p(Z) 0.12001 0.11092 0.10226 0.09405 0.08628 0.07895 0.07206 0.06562 0.05959 0.05399 0.04879 0.04398 0.03955 0.03547 0.03174 0.02833 0.02522 0.02239 0.01984 0.01753 0.01545 0.01358 0.01191 0.01042 0.00909 0.00792 0.00687 0.00595 0.00514 0.00443 F(Z) 0.93943 0.94520 0.95053 0.95543 0.95994 0.96407 0.96784 0.97128 0.97441 0.97725 0.97982 0.98214 0.98422 0.98610 0.98778 0.98928 0.99061 0.99180 0.99286 0.99379 0.99461 0.99534 0.99598 0.99653 0.99702 0.99744 0.99781 0.99813 0.99841 0.99865 There is also a built-in function that calculates x given F (x), the mean, and the standard 8.3. PROBABILITY 163 deviation: =NORM.INV(F(x),Mean,Std_Dev) where, F(x) = value of the cumulative distribution at which to ﬁnd the value of x Example 8.11 An engineer estimates that the selling price of a particular commodity will range from a low of $5.00 per item to a high of $10.00 per item. (a) If the distribution is assumed to be uniform, calculate the mean (or expected) value and the standard deviation for the price of this commodity. Also, calculate the probability that the price will be greater than $9.00. (b) If the distribution is assumed to be triangular with a most likely value (mode) of $7.00 per item, calculate the mean (or expected) value and the standard deviation for the price of this commodity. Also, calculate the probability that the price will be greater than $9.00. Solution (a): The distribution would be: The mean would be: μ = (a + b)/2 = (5 + 10)/2 = 7.50 The standard deviation would be: σ = (b − a)/ The probability of the price being greater than $9.00: √ 12 = (10 − 5)/ √ 12 = 1.443 Prob(> $9) = 1 − F (9) = 1 − {(9 − 5)/(10 − 5)} = 0.20 164 8. BASIC STATISTICS AND PROBABILITY Solution (b): The distribution would be: The mean would be: μ = (a + b + c)/3 = (5 + 7 + 10)/3 = 7.33 The areas would be: P1 = (b − a)/(c − a) = 2/5 = 0.4 and P2 = (c − b)/(c − a) = 3/5 = 0.6 The standard deviation would be: (cid:25) σ = (c − a) ∗ (1 − P1P2)/18 = 5 ∗ (cid:25) (1 − (0.4)(0.6))/18 = 1.03 The probability of the price being greater than $9.00: Prob(> $9) = 1 − F (9) = 1 − 1 − (0.6) [(10 − 9)/(10 − 7)]2 = 0.067 (cid:5) (cid:6) Example 8.12 300 ball bearings are tested for their diameters. The mean diameter was determined to be 0.452 cm and the standard deviation was determined to be 0.010 cm. Assume that the diameters are normally distributed. (a) How many ball bearings would be expected to be smaller than 0.4425 cm? (b) Seventy percent of the ball bearings would be expected to have a diameter greater than what value? The distribution would be: 8.3. PROBABILITY 165 Solution for (a) using the F (Z) table: Z = (x − μ)/σ = (0.4425 − 0.452)/0.010 = −0.95 F (−0.95) = 1 − F (0.95) = 1 − 0.82894 = 0.17106 # of ball bearings less than 0.4425 cm diameter = 0.17106(300) = 51 Solution for (a) using Excel®: A Mean = 1 StdDev = 2 x = 3 4 F(x) = 5 # bearings < x = B 0.452 0.010 0.4425 0.17106 51 1 2 3 4 5 A B = naeM = veDdtS x = 254.0 010.0 0.4425 F(x) = =NORM.DIST(B3,B1,B2,TRUE) =300B4 # bearings < x = Solution for (b) using the F (z) table: One needs the value of Z that produces an F (Z) of 0.30 (for 70% greater than that value). Since 0.30 is less than 0.5, one needs the negative side of the curve. F (−Z) = 1 − F (z) = 1 − .3 = .7. The value of Z for F (0.7) lies between 0.50 and 0.55. Interpolating, Z = 0.524. Therefore, Z for F (Z) of 0.30 is Z = −0.524. Solving for x in Equation 8.30 yields x = Z ∗ σ + μ = −0.524(0.010) + 0.452 = 0.447 cm.Therefore, 70% of the ball bearings will have a diameter greater than 0.447 cm. 166 8. BASIC STATISTICS AND PROBABILITY Solution for (b) using Excel®: A 1 Mean = StdDev = 2 F(x) = 3 x = 4 B 0.452 0.010 0.3 0.44676 1 2 3 4 B A Mean = StdDev = F(x) = 0.452 0.010 0.3 x = =NORM.INV(B3,B1,B2) Combined Distributions In some applications, it will be necessary to work with more than one distribution to describe a particular variable. In order to ﬁnd the mean and standard deviation for the combined distributions, the mean and standard deviation for each separate distribution are ﬁrst determined. Equations 8.33 and 8.34 are then used to calculate the overall average and standard deviation: (cid:4) μc = σc = Aiμi (cid:26) (cid:4) (cid:27) σ 2 i Ai (cid:28) + (μi − μc)2 (8.33) (8.34) where, μc = mean of the combined distributions σc = standard deviation of the combined distributions Ai = probability area associated with each distribution μi = mean of each distribution σi = standard deviation of each distribution (cid:5)(cid:4) (cid:6) Ai = 1 Example 8.13 An oil well has a 25% chance of being a “dry hole” (no oil found) and a 75% chance of ﬁnding an oil reservoir that contains between 10,000 and 60,000 barrels as shown in the distribution below. (a) Calculate the mean and standard deviation of the combined distributions. (b) What is the probability that the reservoir will contain less than 40,000 barrels? (c) What is the probability that the reservoir will contain at least 50,000 barrels? (d) Sketch the cumulative probability distribution, F (x). 8.3. PROBABILITY 167 0.25 p(x) 0 10,000 60,000 barrels Solution for (a): Since the discrete probability at x = 0 is 0.25, the remaining area under the uniform distribu- tion is then 0.75. The mean of the discrete probability distribution is 0 barrels and the mean of the uniform distribution is 35,000 barrels. The mean of the combined distribution: μc = 0.25(0) + 0.75(35, 000) = 26, 250 barrels The standard deviation of the discrete probability distribution is 0 barrels and the standard deviation of the uniform distribution is 14,434 barrels. The standard deviation of the combined distribution is 02 + (0 − 26, 250)2 + 0.75 ∗ 14, 4342 + (35, 000 − 26, 250)2 (cid:28) (cid:27) (cid:28) (cid:29) (cid:27) σc = 0.25 ∗ = 19, 645 barrels Solution for (b): P rob(< 40, 000) = F (40, 000). Recall that F (x) is the area under the probability curve. Therefore, F (40, 000) = 0.25 + 0.75 ∗ [(40, 000 − 10, 000)/(60, 000 − 10, 000)] = 0.70. There is a 70% probability that the reservoir will contain less than 40,000 barrels. Solution for (c): P rob(> 50, 000) = 1 − F (50, 000) = 1 − [0.25 + 0.75 ∗ [(50, 000 − 10, 000)/(60, 000 − 10, 000)]] = 0.15. There is a 15% probability that the reservoir will contain at least 50,000 barrels. 168 8. BASIC STATISTICS AND PROBABILITY Solution for (d): Again, F (x) is the area under the probability distribution. Therefore, for x < 0 for 0 ≤ x ≤ 10, 000 for 10, 000 ≤ x ≤ 60, 000 for x > 60, 000 F (x) = 0 F (x) = 0.25 F (x) = 0.25 + 0.75 [(x − 10, 000)/(60, 000 − 10, 000)] F (x) = 1.0 Cumula(cid:415)ve Probability F(x) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -10000 0 10000 20000 30000 40000 50000 60000 70000 Barrels 8.4 PROBLEMS 8.1. The following values of Young’s Modulus for a rubber compound (in 1000 lb/in 2) have been measured. Determine the following: (a) The frequency distribution using class boundaries of 4-6, 6-8, etc (b) True class boundaries and true class marks (c) The histogram and cumulative frequency diagrams 8 5 12 14 13 10 9 11 6 11 9 8 15 8 5 6 8 11 4 8 10 13 12 6 10 9 8 13 8.2. For the data in Problem 8.1, calculate the mean, median, mode, and standard deviation. Recalculate the mean and standard deviation using the frequency distribution determined in Problem 8.1. 8.4. PROBLEMS 169 8.3. A particular event has two possible outcomes of true and false. There is a 50% probability of getting a true outcome. The event is repeated four times. Construct a table that contains all possible combinations of results and determine the probabilities of getting 0 true outcomes, 1 true outcome, 2 true outcomes, 3 true outcomes, and 4 true outcomes. 8.4. Fifteen castings of a certain type are produced per day in a foundry. The ﬁnished castings are inspected and classiﬁed as defective or non-defective. Records indicate that of the last 500 castings inspected, 16 were defective. Based on this information, ﬁnd the following: (a) The probability of having at no defective castings in a day’s production (b) The probability of having at least two defective castings in a day’s production 8.5. The height of trucks on an interstate highway is approximately normally distributed with mean of 10 ft and standard deviation of 1.5 ft. What is the height of an overpass if the probability that a truck will clear it is 0.999? 8.6. The average life of a certain type of compressor is 10 years with a standard deviation of 1 year. The lives of the compressors follow a normal distribution. The manufacturer replaces, at no cost, all compressors that fail while under the guarantee. If the manufacturer is willing to replace only 3% of all compressors sold, how long of a guarantee should they offer? 8.7. A discrete distribution is given in the table below. Calculate the mean and standard deviation of the distribution. x p(x) 1 0.2 2 0.3 3 0.1 4 0.4 170 8. BASIC STATISTICS AND PROBABILITY 8.8. Determine the mean and standard deviation of the following combined distribution. 8.9. A company is desirous of purchasing a service. The service will cost $10,000 and have a probability of its life that can be described by a triangular distribution with values of a, b, and c equal to 1, 3, and 6 years, respectively. (a) Calculate the mean and the standard deviation of the life of the service (b) What is the probability that the service will last at least 2 years? (c) What is the probability that the service will last at least 5 years? C H A P T E R 9 Sensitivity Analysis 171 9.1 INTRODUCTION A simple way of incorporating the elements of uncertainty into an economic analysis is to use sensitivity analysis. As described earlier, an evaluator will normally need to include a measure of the uncertainty pertaining to one or more variables in the analysis. This uncertainty may, in turn, add signiﬁcant uncertainty about the proﬁtability of an investment. This range of uncertainty about the project’s proﬁtability is one way to deﬁne the risk in a project. Uncertainty in any particular variable can occur for a number of reasons. For example, the method of measuring a parameter may have a certain amount of inaccuracy, the parameter may have to be predicted into the future, or there may be a limited amount of data for a certain parameter. In any case, the best that can be done for a variable with an uncertain value is to choose a reasonable range over which it may vary and, perhaps, the type of distribution that the variable might take on over that range. Two types of sensitivity analysis will be considered in this chapter. The ﬁrst is called the range approach and involves the systematic variation of key variables to determine their overall effect on the proﬁtability of the investment. The second approach uses the concepts of probability and statistics and is referred to as Monte Carlo Simulation (MCS). MCS has also been called probabilistic sensitivity analysis. 9.1.1 RANGE APPROACH When applying the range approach, ranges of variations of key variables, deﬁned by the evaluator, are established. For example, the estimated sales price of a commodity to be sold could be allowed to vary ±10% from a base value during the analysis. The economic analysis is conducted by: (a) choosing an evaluation criteria (normally NPV or IRR); (b) computing the value of this criteria for a base case set of variable values; and (c) repeating the computations by varying each key parameter within the speciﬁed range. There are, in general, two ways of conducting the range approach sensitivity analysis. The ﬁrst is by identifying the most likely, most optimistic, and the most pessimistic cases by varying all of the parameters simultaneously. The most likely case is deﬁned as the case where all variables are at their respective mean values. This method allows the evaluator to determine the minimum and maximum values that could be obtained for the evaluation criteria. It does not, however, allow the evaluator to study the effects of any one variable on the economic analysis. 172 9. SENSITIVITY ANALYSIS The second way is to use the mean values for each key variable and calculate the corresponding value for the evaluation criteria. This is then designated as the base case value. Each key parameter is then varied about its mean value while the other parameters are held constant at their base case values and the evaluation criteria is recalculated. The process is repeated until each parameter has been varied. Typically, each parameter is varied plus or minus 10 to 20% about its mean value. When the calculations have been completed, the results are usually summarized in a “spider plot.” The spider plot, shown schematically in Figure 9.1, is constructed by plotting the evaluation criteria on the vertical axis and the percent variation on the horizontal axis. Quick inspection of the spider plot provides information to the evaluator on which parameter or parameters affect the economic analysis to the greatest degree. The parameter which yields the line with the greatest slope (positive or negative slope) on the spider plot has the most effect on the analysis. As illustrated in the sample plot shown in Figure 9.1, Variable A has the greatest effect on the evaluation criteria. Ev(cid:258)(cid:367)(cid:437)(cid:258)(cid:415)(cid:381)(cid:374) Criteria Variable A Variable B Variable C -X% 0 +X% % vari(cid:258)(cid:415)on from the base case Figure 9.1: Sample spider plot. Example 9.1 A ten-year life project has an initial investment of $87,500, annual operating expenses of $7,500, and annual incomes of $30,000. It is desired to conduct a range approach sensitivity analysis by the two methods described earlier: (a) Determine the most likely, the most optimistic, and the most pessimistic values for the I RR by assuming the values given are the mean values for each parameter and that each parameter has a range of ±20% from the mean value. 9.1. INTRODUCTION 173 (b) Vary each parameter independently by ±20% from the mean values while holding the other two constant at their mean values and develop a spider plot for the calculated I RR values. The cash ﬂow diagram for the most likely (or base case) is as follows: 0 1 2 3 … 8 9 10 -87,500 22,500 22,500 22,500 ---- 22,500 22,500 22,500 Solution for (a): The I RR for the most likely case is computed from the cash ﬂow above to be 22.3%. The most pessimistic case would be the combination of these three variables that would have the most negative inﬂuence on the project’s I RR. This would be a 20% increase in initial investment, a 20% increase in operating expenses, and a 20% decrease in income. The most optimistic case would be the combination of these three variables that would have the most positive inﬂuence on the project’s IRR. This would be a 20% decrease in initial investment, a 20% decrease in operating expenses, and a 20% increase in income. Solution for (b): In this analysis, start with the most likely case from (a) and denote that as the base case. Then vary one parameter at a time by plus and minus 20% and recalculate I RR for each new cash ﬂow diagram. 174 9. SENSITIVITY ANALYSIS Spider Plot Ini(cid:415)al Investment Opera(cid:415)ng Expenses Annual Income IRR 35 30 25 20 15 10 5 0 -25 -15 -5 5 15 25 % (cid:115)(cid:258)(cid:396)(cid:349)(cid:258)(cid:415)on from Base Case From the spider plot, it can be readily seen that the parameter which has the greatest effect on the I RR is the annual income. A larger change in I RR is observed for the same percentage change in the annual income than for initial investment or operating expenses. Changes in the operating expenses have the least effect on the I RR. To minimize the risk that would be created by a ±20% uncertainty in the annual income, it would be beneﬁcial for the evaluator to do additional research into this portion of the cash ﬂow calculation and determine if the range in uncertainty can be reduced. In the example problem, only two values for each variable have been used.To be more complete, several values between −20% and +20% could have been used to generate additional values of I RR. 9.1. INTRODUCTION 175 The primary drawback on the spider plot approach is that it ignores the interactions that occur when more than one variable is allowed to change at a time. Not only does one have to deﬁne many more cases to account for all possible interactions, but it is also difﬁcult to tabulate these results in a meaningful way. Often, the results simply become a tabulated list of I RRs for each case evaluated. For example, consider a problem that has four variables that have uncertain values and that three numerical values for each of the variables are chosen in the range approach. This will result in 81 (3x3x3x3) individual solutions to the problem that must be presented to evaluate the effect of all four variables. It may be very difﬁcult for the evaluator to draw any conclusions from a long tabular list of 81 results. 9.1.2 MONTE CARLO SIMULATION Probabilistic sensitivity analysis or Monte Carlo Simulation (MCS) was introduced in the early 1960s. While it is a very powerful technique, it is often avoided due to the general lack of knowledge among engineers and managers on how it works and the conclusions that can be drawn from it. This section will attempt to explain the technique and its beneﬁts. Consider the example proposed above that contains four variables with uncertain values. Instead of creating a tabular list of 81 evaluator-chosen cases, MCS allows each of the variables to vary between minimum and maximum values according to some prescribed probability distribution and then solves the problem for a large, randomized set of these input variables. The results of the MCS are presented graphically as a cumulative probability distribution of the dependent variable (e.g., I RR, N P V , etc). This probability can then be interpreted using statistical methods to determine the likelihood of a particular solution occurring or not occurring. Distributions that are frequently used are the uniform, triangular, and normal distributions presented in Chapter 8. These are fairly easy to describe mathematically and to input into an Excel® spreadsheet or a computer program. The choice of the particular distribution for a certain variable should be guided by the evaluator’s knowledge of that variable. Within the MCS method, the selection of a value for an independent variable is accomplished by using the fact that the cumulative probability distribution, F (x), will lie between zero and one and will be monotonic in behavior. Thus, the selection of a random number between zero and one will yield a distinct random value for the independent variable between the variable’s minimum and maximum values. A different random number is chosen for each independent variable, resulting in a truly random set of independent variable values. Once the values of all independent variables have been determined, the dependent variable, i.e., an evaluation criteria such as I RR or NP V , can be calculated. This process is then repeated a large number of times and the results of the dependent variable calculations are grouped into class intervals and then the cumulative probability distribution is constructed. The following is a summary of the steps involved in the MCS method: 1. Select the independent variables that contain uncertainty in their values. 176 9. SENSITIVITY ANALYSIS 2. Estimate the minimum and maximum values for each independent variable. 3. Estimate the minimum and maximum values for the dependent variable and set up class intervals in that range such that a probability distribution can be generated. 4. Select a probability distribution that best describes the behavior of each independent variable between its minimum and maximum values. 5. Set up equations which will allow for the calculation of each of the independent variables. This is done by determining expressions for the cumulative probability distributions, F (x), for each independent variable and then solving this expression for the variable, x. 6. Generate a random number for each independent variable. A different random number is determined for each independent variable. Random numbers are available from scientiﬁc calculators, Excel®, or by using Table 9.1. One can enter this table at any random point and then proceed through the table either by rows or columns. Excel® uses the =RAND() function to generate a uniformly distributed random number between zero and one. 7. Use the random numbers to calculate the values for the independent variables using the equations developed in step 5. 8. Calculate the dependent variable (or variables if necessary) for this set of independent variables and increment a counter in the respective class interval. 9. Return to step 6 and repeat steps 6 through 8 a relatively large number of times. A large number of trials might be 100, 1000, or 10,000 depending on the sensitivity of the dependent variable to the independent variables. 10. Construct the cumulative probability distribution for the dependent variable. 9.1. INTRODUCTION 177 T a b l e 9 . 1 : R a n d o m n u m b e r s 178 9. SENSITIVITY ANALYSIS Example 9.2 For the problem described in Example 9.1 and the distributions given below, conduct a Monte Carlo Simulation and summarize the results in a cumulative probability distribution. Complete 10 cases using I RR as the dependent variable. Initial Investment: (cid:47)(cid:374)(cid:349)(cid:415)al Investment 0.00003 0.000025 0.00002 p(x) 0.000015 0.00001 0.000005 0 60000 70000 80000 90000 100000 110000 Dollars Operating Expenses: Oper(cid:258)(cid:415)ng Expenses 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 p(x) 0 5000 6000 7000 8000 9000 10000 Dollars/Year Annual Income: Annual Income 9.1. INTRODUCTION 179 p(x) 0.00009 0.00008 0.00007 0.00006 0.00005 0.00004 0.00003 0.00002 0.00001 0 23000 Solution: 25000 27000 29000 31000 33000 35000 37000 Dollars/Year Develop equations for the independent variables: Let x1 be the value for the initial investment. Since it has a uniform distribution, its cumulative probability (F1) is given by F1 = (x1 − a)/(b − a) = (x1 − 70000)/(105000 − 70000) = (x1 − 70000)/35000 Solving this equation for x1 yields x1 = 35000F1 + 70000 (9.1) Let x2 be the value for the operating expenses. Since it has a triangular distribution, its cumulative probability (F2) is given by P1 = (b − a)/(c − a) = (7500 − 6000)/(9000 − 6000) = 0.5 P2 = 1 − P1 = 0.5 For 6000 ≤ x2 ≤ 7500 or F2 ≤ 0.5 (the value of P1), F2 = P1 [(x2 − a)/(b − a)]2 = 0.5 [(x2 − 6000)/1500]2 Solving this equation for x2 yields x2 = 6000 + 1500 (cid:25) 2F2 (9.2) For 7500 ≤ x2 ≤ 9000 or F2 ≥ 0.5 (the value of P1), F2 = 1 − P2 [(c − x2)/(c − b)]2 = 1 − 0.5 [(9000 − x2)/1500]2 180 9. SENSITIVITY ANALYSIS Solving this equation for x2 yields x2 = 9000 − 1500 (cid:25) 2(1 − F2) (9.3) Let x3 be the value for the annual income. Since it has a uniform distribution, its cumulative probability (F3) is given by F3 = (x3 − a)/(b − a) = (x3 − 24000)/(36000 − 24000) = (x3 − 24000)/12000 Solving this equation for x3 yields First iteration: x3 = 12000F1 + 24000 (9.4) Choose the ﬁrst random number from the table. This will be the value for F1. (F1 = 0.90535). Use this number in Equation 9.1 to determine the value to be used for the initial investment: x1 = 35000(0.90535) + 70000 = 101, 700 Choose the second random number from the table. This will be the value for F2. (F2 = 0.86245). Since F2 ≥ 0.5, use this number in Equation 9.3 to determine the value to be used for the operating expense: x2 = 9000 − 1500 2(1 − 0.86245) = 8, 200 (cid:25) Choose the third random number from the table.This will be the value for F3. (F3 = 0.32775). Use this number in Equation 9.4 to determine the value to be used for the annual income: x3 = 12000(0.32775) + 24000 = 27, 900 These values for initial investment, operating expense, and annual income yield the following cash ﬂow diagram for the project: 0 1 2 3 … 8 9 10 -101,700 19,700 19,700 19,700 ---- 19,700 19,700 19,700 I RR analysis yields a value of 14.3%. This value is tabulated in a list for further processing. Second and successive iterations: Follow the same procedure as listed for the ﬁrst iteration. Three new random numbers are used during each iteration. The results of the ﬁrst ten iterations are shown in the table below. 9.1. INTRODUCTION 181 The cumulative probability distribution for I RR can be developed from information in the following table: 182 9. SENSITIVITY ANALYSIS Interval 10.5-12.5 12.5-14.5 14.5-16.5 16.5-18.5 18.5-20.5 20.5-22.5 22.5-24.5 24.5-26.5 26.5-28.5 28.5-30.5 30.5-32.5 32.5-34.5 Mid-point 11.5 13.5 15.5 17.5 19.5 21.5 23.5 25.5 27.5 29.5 31.5 33.5 Frequency 0 2 1 0 0 4 0 2 0 0 0 1 Prob 0.0 20.0 30.0 0.0 0.0 40.0 0.0 20.0 0.0 0.0 0.0 10.0 CumulProb 0.0 20.0 30.0 30.0 30.0 70.0 70.0 90.0 90.0 90.0 90.0 100.0 Cumu(cid:367)(cid:258)(cid:415)(cid:448)e Probability for IRR Cumul Prob, % 100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 10 15 20 25 30 35 IRR, % With only ten iterations, this graph is too jagged to interpret correctly. The ﬁgure below shows the same analysis after 100 iterations. One can see that the curve is much smoother. If even more iterations are added, the curve will become smoother yet. However, the usefulness of the curve may not increase proportionally to the number of iterations. One should only complete enough iterations to get a reasonably smooth curve. Generally, this takes about 100 iterations, but this may be a function of the actual problem being solved.This number of calculations can be easily completed with Excel®. Cumu(cid:367)(cid:258)(cid:415)(cid:448)e Probability for IRR 9.1. INTRODUCTION 183 F(x), % 100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 10 15 20 25 IRR, % 30 35 40 As discussed in Chapter 8, the use of this graph is as follows. The value of F (x) at any I RR is the probability that the project will attain that I RR or less. For example, there is approximately an 18% probability that the project will earn an I RR value of less than 15%. Thus, if one uses the investor’s MARR, F (x) provides the probability that the project will earn less than that value. The quantity (100 − F (x)) would provide the probability that the project earns greater than that MARR. For example, if the investor’s MARR is 20%, one would enter the horizontal axis at 20% and read a cumulative probability of about 44%. The interpretation would be that there is a 56% probability that the project will yield a 20% I RR or greater. This probability is then a direct measure of risk associated with the project. If an evaluator feels that a 44% probability that the project will not be economically viable is an unacceptable level of risk, then the project should be eliminated from further consideration. However, if, in this example, the investor’s MARR is only 15%, there is only a 18% probability that the project will not be economically viable. This investor would have a more acceptable level of risk. Example 9.3 A particular investment has three uncertain variables of initial cost, future value, and the investment life. The initial cost can be described by a uniform distribution from $100 to $200. The future value can be described by a normal distribution with μ = $300 and σ = $30. The investment life can be described by a discrete probability distribution with 40% probability that n = 5 years, 30% probability that n = 6 years, 20% probability that n = 7 years, and 10% probability that n = 8 years. 184 9. SENSITIVITY ANALYSIS Based on this information, (a) Calculate the minimum rate of return that can be earned, the maximum rate of return that can be earned and the mean rate of return that will be earned. For the normal distribution, assume that the minimum and maximum values of future value will be ±3σ from the mean ($210 and $390, respectively). (b) Complete a Monte Carlo Simulation for this project to determine the probability that the ROR will be at least 15%. Solution for (a): The mean values for the three distributions are: Pmean = (100 + 200)/2 = 150 Fmean = 300 nmean = 0.4 ∗ 5 + 0.3 ∗ 6 + 0.2 ∗ 7 + 0.1 ∗ 8 = 6.0 The rate of return, ROR, can be calculated using the relationship, F = P ∗ (1 + i)n or i = (F /P )1/n − 1 The three cases will be deﬁned as follows: Case Minimum ROR (Most P(cid:286)(cid:400)(cid:400)(cid:349)(cid:373)(cid:349)(cid:400)(cid:415)(cid:272) (cid:18)(cid:258)(cid:400)(cid:286)(cid:895) (cid:68)(cid:286)(cid:258)n ROR (cid:68)(cid:258)(cid:454)(cid:349)mum ROR (Most (cid:75)(cid:393)(cid:415)(cid:373)(cid:349)(cid:400)(cid:415)(cid:272) (cid:18)(cid:258)(cid:400)(cid:286)(cid:895) (cid:47)(cid:374)(cid:349)(cid:415)(cid:258)l Cost, P Future V(cid:258)(cid:367)(cid:437)e, F Life, n ROR $200 $210 $150 $100 $300 $390 8 6 5 0.61% 12.2% 31.3% 9.1. INTRODUCTION 185 Solution for (b): Develop equations for the independent variables: Let x1 be the value for the initial investment. Since it has a uniform distribution, its cumulative probability (F1) is given by F1 = (x1 − a)/(b − a) = (x1 − 100)/(200 − 100) = (x1 − 100)/100 Solving this equation for x1 yields x1 = 100F1 + 100 Let x2 be the value for the future value. Since it has a normal distribution, its cumulative probability (F2) is given by the values in Table 8.1. Once F2(Z) is randomly chosen, the appropriate value of Z is determined from Table 8.1 and then x2 = Z ∗ σ + μ. Let x3 be the value for the project life. Since it has a discrete distribution, its cumulative probability (F3) is given by 5 ≤ x3 < 6 6 ≤ x3 < 7 7 ≤ x3 < 8 x3 ≥ 8 F3 = 0.4 F3 = 0.7 F3 = 0.9 F3 = 1.0 F(x) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Cum(cid:437)(cid:367)(cid:258)(cid:415)ve Probability for Project Life 4 5 6 7 8 9 n, years Thus, once F3 is randomly chosen, the value for x3 will be: F3 ≤ 0.4 0.4 < F3 ≤ 0.7 0.7 < F3 ≤ 0.9 0.9 < F3 ≤ 1.0 x3 = 5 x3 = 6 x3 = 7 x3 = 8 186 9. SENSITIVITY ANALYSIS The dependent variable is ROR which is calculated by using: ROR = (x2/x1)1/x3 − 1. Each iteration can be calculated using the following Excel® spreadsheet: If one tabulates the result in cell B9 into another column of results (for example start in cell A20), the spreadsheet will automatically select three new random numbers and a new result of ROR will be calculated. This result would then be tabulated in cell A21. In order to generate the histogram, this process is repeated manually 100 times (which would result in a column of data from A20 to A119). The results would be as follows: Cumu(cid:367)(cid:258)(cid:415)(cid:448)e Probability for ROR F(x), % 100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 5 10 15 20 25 30 35 ROR, % At ROR of 15%, F (x) is approximately 74%. This means that there is a 74% probability that the ROR will be less than 15% or a 26% probability that the ROR will be at least 15%. 9.2 PROBLEMS 9.1. You are to conduct an extensive sensitivity analysis on the problem described below. The sensitivity analysis will consist of three parts: 9.2. PROBLEMS 187 (a) A range approach where the most optimistic, most likely, and most pessimistic values of the dependent variables NP V and I RR are determined. (b) A range approach where the mean value is determined for each independent variable and then each variable is allowed to vary ±20% about that mean while all other independent variables are held constant. Create spider plots for NP V and I RR using the results. (c) A probabilistic approach using Monte Carlo Simulation. Complete 10 iterations and create cumulative probability curves for NP V and I RR. The project life is 7 years and the MARR is 15%. The initial investment is given by a uniform distribution between $200,000 and $300,000. The annual proﬁt is given by a triangular distribution that has a minimum value of $55,000/year, a mode of $67,500/year, and a maximum value of $85,000/year. The salvage value of the investment is given by a triangular distribution that has a minimum value of $60,000, a mode of $75,000, and a maximum value of $85,000. The cash ﬂow diagram would be: 0 1 2 3 … 6 7 -Invest Pro(cid:302)t Pro(cid:302)t Pro(cid:302)t ---- Pro(cid:302)t Pro(cid:302)t + Salvage 9.2. Complete Problem 9.1 using an Excel® spreadsheet to calculate 100 iterations. Create cumulative probability curves for NP V and I RR. 9.3. The following distributions are given for three independent variables, x1, x2, and x3 and the relationship for the dependent variable, y. Calculate the largest, smallest, and mean values of the dependent variable, y. x1: Uniform distribution between 35 and 50 x2: Triangular distribution between 20 and 40 with a mode of 35 188 9. SENSITIVITY ANALYSIS x3: Discrete distribution with a 50% probability that the value will be 2 and 50% probability that the value will be 4 y = (x1)(x2) + x3 9.4. Using the information given in Problem 9.3, use Monte Carlo Simulation to calculate 10 iterations of the dependent variable and create the cumulative probability diagram for the dependent variable y. 9.5. Complete Problem 9.4 using an Excel® spreadsheet and 100 iterations. 9.6. Complete Problem 9.4 using an Excel® spreadsheet and assuming that independent variable x2 has a normal distribution with a mean of 30 and a standard deviation of 3. Compute 100 iterations and create the cumulative probability diagram for the dependent variable y. A P P E N D I X A 189 Compound Interest Factors 190 APPENDIX A F/P 1.01000 1.02010 1.03030 1.04060 1.05101 1.06152 1.07214 1.08286 1.09369 1.10462 1.11567 1.12683 1.13809 1.14947 1.16097 1.17258 1.18430 1.19615 1.20811 1.22019 1.28243 1.34785 1.41660 1.48886 1.56481 1.64463 1.72852 1.81670 1.90937 2.00676 2.10913 2.21672 2.32979 2.44863 2.57354 2.70481 P/F 0.99010 0.98030 0.97059 0.96098 0.95147 0.94205 0.93272 0.92348 0.91434 0.90529 0.89632 0.88745 0.87866 0.86996 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.77977 0.74192 0.70591 0.67165 0.63905 0.60804 0.57853 0.55045 0.52373 0.49831 0.47413 0.45112 0.42922 0.40839 0.38857 0.36971 i = 1% F/A 1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 10.4622 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190 28.2432 34.7849 41.6603 48.8864 56.4811 64.4632 72.8525 81.6697 90.9366 100.6763 110.9128 121.6715 132.9790 144.8633 157.3538 170.4814 A/F 1.00000 0.49751 0.33002 0.24628 0.19604 0.16255 0.13863 0.12069 0.10674 0.09558 0.08645 0.07885 0.07241 0.06690 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.03541 0.02875 0.02400 0.02046 0.01771 0.01551 0.01373 0.01224 0.01100 0.00993 0.00902 0.00822 0.00752 0.00690 0.00636 0.00587 P/A 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 32.8347 36.0945 39.1961 42.1472 44.9550 47.6266 50.1685 52.5871 54.8882 57.0777 59.1609 61.1430 63.0289 A/G A/P 0.00000 1.01000 0.49751 0.50751 0.99337 0.34002 1.48756 0.25628 1.98010 0.20604 2.47098 0.17255 2.96020 0.14863 3.44777 0.13069 3.93367 0.11674 4.41792 0.10558 4.90052 0.09645 5.38145 0.08885 5.86073 0.08241 6.33836 0.07690 6.81433 0.07212 7.28865 0.06794 7.76131 0.06426 8.23231 0.06098 8.70167 0.05805 0.05542 9.16937 0.04541 11.48312 0.03875 13.75566 0.03400 15.98711 0.03046 18.17761 0.02771 20.32730 0.02551 22.43635 0.02373 24.50495 0.02224 26.53331 0.02100 28.52167 0.01993 30.47026 0.01902 32.37934 0.01822 34.24920 0.01752 36.08013 0.01690 37.87245 0.01636 39.62648 0.01587 41.34257 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 COMPOUND INTEREST FACTORS 191 F/P 1.02000 1.04040 1.06121 1.08243 1.10408 1.12616 1.14869 1.17166 1.19509 1.21899 1.24337 1.26824 1.29361 1.31948 1.34587 1.37279 1.40024 1.42825 1.45681 1.48595 1.64061 1.81136 1.99989 2.20804 2.43785 2.69159 2.97173 3.28103 3.62252 3.99956 4.41584 4.87544 5.38288 5.94313 6.56170 7.24465 P/F 0.98039 0.96117 0.94232 0.92385 0.90573 0.88797 0.87056 0.85349 0.83676 0.82035 0.80426 0.78849 0.77303 0.75788 0.74301 0.72845 0.71416 0.70016 0.68643 0.67297 0.60953 0.55207 0.50003 0.45289 0.41020 0.37153 0.33650 0.30478 0.27605 0.25003 0.22646 0.20511 0.18577 0.16826 0.15240 0.13803 i = 2% F/A 1.0000 2.0200 3.0604 4.1216 5.2040 6.3081 7.4343 8.5830 9.7546 10.9497 12.1687 13.4121 14.6803 15.9739 17.2934 18.6393 20.0121 21.4123 22.8406 24.2974 32.0303 40.5681 49.9945 60.4020 71.8927 84.5794 98.5865 114.0515 131.1262 149.9779 170.7918 193.7720 219.1439 247.1567 278.0850 312.2323 A/F 1.00000 0.49505 0.32675 0.24262 0.19216 0.15853 0.13451 0.11651 0.10252 0.09133 0.08218 0.07456 0.06812 0.06260 0.05783 0.05365 0.04997 0.04670 0.04378 0.04116 0.03122 0.02465 0.02000 0.01656 0.01391 0.01182 0.01014 0.00877 0.00763 0.00667 0.00586 0.00516 0.00456 0.00405 0.00360 0.00320 P/A 0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 19.5235 22.3965 24.9986 27.3555 29.4902 31.4236 33.1748 34.7609 36.1975 37.4986 38.6771 39.7445 40.7113 41.5869 42.3800 43.0984 A/G A/P 0.00000 1.02000 0.49505 0.51505 0.98680 0.34675 1.47525 0.26262 1.96040 0.21216 2.44226 0.17853 2.92082 0.15451 3.39608 0.13651 3.86805 0.12252 4.33674 0.11133 4.80213 0.10218 5.26424 0.09456 5.72307 0.08812 6.17862 0.08260 6.63090 0.07783 7.07990 0.07365 7.52564 0.06997 7.96811 0.06670 8.40732 0.06378 0.06116 8.84328 0.05122 10.97445 0.04465 13.02512 0.04000 14.99613 0.03656 16.88850 0.03391 18.70336 0.03182 20.44198 0.03014 22.10572 0.02877 23.69610 0.02763 25.21471 0.02667 26.66323 0.02586 28.04344 0.02516 29.35718 0.02456 30.60635 0.02405 31.79292 0.02360 32.91889 0.02320 33.98628 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 192 APPENDIX A F/P 1.03000 1.06090 1.09273 1.12551 1.15927 1.19405 1.22987 1.26677 1.30477 1.34392 1.38423 1.42576 1.46853 1.51259 1.55797 1.60471 1.65285 1.70243 1.75351 1.80611 2.09378 2.42726 2.81386 3.26204 3.78160 4.38391 5.08215 5.89160 6.82998 7.91782 9.17893 10.64089 12.33571 14.30047 16.57816 19.21863 P/F 0.97087 0.94260 0.91514 0.88849 0.86261 0.83748 0.81309 0.78941 0.76642 0.74409 0.72242 0.70138 0.68095 0.66112 0.64186 0.62317 0.60502 0.58739 0.57029 0.55368 0.47761 0.41199 0.35538 0.30656 0.26444 0.22811 0.19677 0.16973 0.14641 0.12630 0.10895 0.09398 0.08107 0.06993 0.06032 0.05203 i = 3% F/A 1.0000 2.0300 3.0909 4.1836 5.3091 6.4684 7.6625 8.8923 10.1591 11.4639 12.8078 14.1920 15.6178 17.0863 18.5989 20.1569 21.7616 23.4144 25.1169 26.8704 36.4593 47.5754 60.4621 75.4013 92.7199 112.7969 136.0716 163.0534 194.3328 230.5941 272.6309 321.3630 377.8570 443.3489 519.2720 607.2877 A/F 1.00000 0.49261 0.32353 0.23903 0.18835 0.15460 0.13051 0.11246 0.09843 0.08723 0.07808 0.07046 0.06403 0.05853 0.05377 0.04961 0.04595 0.04271 0.03981 0.03722 0.02743 0.02102 0.01654 0.01326 0.01079 0.00887 0.00735 0.00613 0.00515 0.00434 0.00367 0.00311 0.00265 0.00226 0.00193 0.00165 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 P/A 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 17.4131 19.6004 21.4872 23.1148 24.5187 25.7298 26.7744 27.6756 28.4529 29.1234 29.7018 30.2008 30.6312 31.0024 31.3227 31.5989 A/G A/P 0.00000 1.03000 0.49261 0.52261 0.98030 0.35353 1.46306 0.26903 1.94090 0.21835 2.41383 0.18460 2.88185 0.16051 3.34496 0.14246 3.80318 0.12843 4.25650 0.11723 4.70494 0.10808 5.14850 0.10046 5.58720 0.09403 6.02104 0.08853 6.45004 0.08377 6.87421 0.07961 7.29357 0.07595 7.70812 0.07271 8.11788 0.06981 0.06722 8.52286 0.05743 10.47677 0.05102 12.31407 0.04654 14.03749 0.04326 15.65016 0.04079 17.15557 0.03887 18.55751 0.03735 19.86004 0.03613 21.06742 0.03515 22.18407 0.03434 23.21454 0.03367 24.16342 0.03311 25.03534 0.03265 25.83490 0.03226 26.56665 0.03193 27.23505 0.03165 27.84445 COMPOUND INTEREST FACTORS 193 i = 4% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.04000 1.08160 1.12486 1.16986 1.21665 1.26532 1.31593 1.36857 1.42331 1.48024 1.53945 1.60103 1.66507 1.73168 1.80094 1.87298 1.94790 2.02582 2.10685 2.19112 2.66584 3.24340 3.94609 4.80102 5.84118 7.10668 8.64637 10.51963 12.79874 15.57162 18.94525 23.04980 28.04360 34.11933 41.51139 50.50495 P/F 0.96154 0.92456 0.88900 0.85480 0.82193 0.79031 0.75992 0.73069 0.70259 0.67556 0.64958 0.62460 0.60057 0.57748 0.55526 0.53391 0.51337 0.49363 0.47464 0.45639 0.37512 0.30832 0.25342 0.20829 0.17120 0.14071 0.11566 0.09506 0.07813 0.06422 0.05278 0.04338 0.03566 0.02931 0.02409 0.01980 F/A 1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 10.5828 12.0061 13.4864 15.0258 16.6268 18.2919 20.0236 21.8245 23.6975 25.6454 27.6712 29.7781 41.6459 56.0849 73.6522 95.0255 121.0294 152.6671 191.1592 237.9907 294.9684 364.2905 448.6314 551.2450 676.0901 827.9833 1012.7846 1237.6237 A/F 1.00000 0.49020 0.32035 0.23549 0.18463 0.15076 0.12661 0.10853 0.09449 0.08329 0.07415 0.06655 0.06014 0.05467 0.04994 0.04582 0.04220 0.03899 0.03614 0.03358 0.02401 0.01783 0.01358 0.01052 0.00826 0.00655 0.00523 0.00420 0.00339 0.00275 0.00223 0.00181 0.00148 0.00121 0.00099 0.00081 P/A 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 15.6221 17.2920 18.6646 19.7928 20.7200 21.4822 22.1086 22.6235 23.0467 23.3945 23.6804 23.9154 24.1085 24.2673 24.3978 24.5050 A/G A/P 0.00000 1.04000 0.49020 0.53020 0.97386 0.36035 1.45100 0.27549 1.92161 0.22463 2.38571 0.19076 2.84332 0.16661 3.29443 0.14853 3.73908 0.13449 4.17726 0.12329 4.60901 0.11415 5.03435 0.10655 5.45329 0.10014 5.86586 0.09467 6.27209 0.08994 6.67200 0.08582 7.06563 0.08220 7.45300 0.07899 7.83416 0.07614 8.20912 0.07358 0.06401 9.99252 0.05783 11.62743 0.05358 13.11984 0.05052 14.47651 0.04826 15.70474 0.04655 16.81225 0.04523 17.80704 0.04420 18.69723 0.04339 19.49093 0.04275 20.19614 0.04223 20.82062 0.04181 21.37185 0.04148 21.85693 0.04121 22.28255 0.04099 22.65498 0.04081 22.98000 194 APPENDIX A i = 5% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.05000 1.10250 1.15763 1.21551 1.27628 1.34010 1.40710 1.47746 1.55133 1.62889 1.71034 1.79586 1.88565 1.97993 2.07893 2.18287 2.29202 2.40662 2.52695 2.65330 3.38635 4.32194 5.51602 7.03999 8.98501 11.46740 14.63563 18.67919 23.83990 30.42643 38.83269 49.56144 63.25435 80.73037 103.03468 131.50126 P/F 0.95238 0.90703 0.86384 0.82270 0.78353 0.74622 0.71068 0.67684 0.64461 0.61391 0.58468 0.55684 0.53032 0.50507 0.48102 0.45811 0.43630 0.41552 0.39573 0.37689 0.29530 0.23138 0.18129 0.14205 0.11130 0.08720 0.06833 0.05354 0.04195 0.03287 0.02575 0.02018 0.01581 0.01239 0.00971 0.00760 F/A 1.0000 2.0500 3.1525 4.3101 5.5256 6.8019 8.1420 9.5491 11.0266 12.5779 14.2068 15.9171 17.7130 19.5986 21.5786 23.6575 25.8404 28.1324 30.5390 33.0660 47.7271 66.4388 90.3203 120.7998 159.7002 209.3480 272.7126 353.5837 456.7980 588.5285 756.6537 971.2288 1245.0871 1594.6073 2040.6935 2610.0252 A/F 1.00000 0.48780 0.31721 0.23201 0.18097 0.14702 0.12282 0.10472 0.09069 0.07950 0.07039 0.06283 0.05646 0.05102 0.04634 0.04227 0.03870 0.03555 0.03275 0.03024 0.02095 0.01505 0.01107 0.00828 0.00626 0.00478 0.00367 0.00283 0.00219 0.00170 0.00132 0.00103 0.00080 0.00063 0.00049 0.00038 P/A 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 14.0939 15.3725 16.3742 17.1591 17.7741 18.2559 18.6335 18.9293 19.1611 19.3427 19.4850 19.5965 19.6838 19.7523 19.8059 19.8479 A/G A/P 0.00000 1.05000 0.48780 0.53780 0.96749 0.36721 1.43905 0.28201 1.90252 0.23097 2.35790 0.19702 2.80523 0.17282 3.24451 0.15472 3.67579 0.14069 4.09909 0.12950 4.51444 0.12039 4.92190 0.11283 5.32150 0.10646 5.71329 0.10102 6.09731 0.09634 6.47363 0.09227 6.84229 0.08870 7.20336 0.08555 7.55690 0.08275 7.90297 0.08024 0.07095 9.52377 0.06505 10.96914 0.06107 12.24980 0.05828 13.37747 0.05626 14.36444 0.05478 15.22326 0.05367 15.96645 0.05283 16.60618 0.05219 17.15410 0.05170 17.62119 0.05132 18.01759 0.05103 18.35260 0.05080 18.63463 0.05063 18.87120 0.05049 19.06894 0.05038 19.23372 COMPOUND INTEREST FACTORS 195 i = 6% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.06000 1.12360 1.19102 1.26248 1.33823 1.41852 1.50363 1.59385 1.68948 1.79085 1.89830 2.01220 2.13293 2.26090 2.39656 2.54035 2.69277 2.85434 3.02560 3.20714 4.29187 5.74349 7.68609 10.28572 13.76461 18.42015 24.65032 32.98769 44.14497 59.07593 79.05692 105.79599 141.57890 189.46451 253.54625 339.30208 P/F 0.94340 0.89000 0.83962 0.79209 0.74726 0.70496 0.66506 0.62741 0.59190 0.55839 0.52679 0.49697 0.46884 0.44230 0.41727 0.39365 0.37136 0.35034 0.33051 0.31180 0.23300 0.17411 0.13011 0.09722 0.07265 0.05429 0.04057 0.03031 0.02265 0.01693 0.01265 0.00945 0.00706 0.00528 0.00394 0.00295 F/A 1.0000 2.0600 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 11.4913 13.1808 14.9716 16.8699 18.8821 21.0151 23.2760 25.6725 28.2129 30.9057 33.7600 36.7856 54.8645 79.0582 111.4348 154.7620 212.7435 290.3359 394.1720 533.1282 719.0829 967.9322 1300.9487 1746.5999 2342.9817 3141.0752 4209.1042 5638.3681 A/F 1.00000 0.48544 0.31411 0.22859 0.17740 0.14336 0.11914 0.10104 0.08702 0.07587 0.06679 0.05928 0.05296 0.04758 0.04296 0.03895 0.03544 0.03236 0.02962 0.02718 0.01823 0.01265 0.00897 0.00646 0.00470 0.00344 0.00254 0.00188 0.00139 0.00103 0.00077 0.00057 0.00043 0.00032 0.00024 0.00018 P/A 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 12.7834 13.7648 14.4982 15.0463 15.4558 15.7619 15.9905 16.1614 16.2891 16.3845 16.4558 16.5091 16.5489 16.5787 16.6009 16.6175 A/G A/P 0.00000 1.06000 0.48544 0.54544 0.96118 0.37411 1.42723 0.28859 1.88363 0.23740 2.33040 0.20336 2.76758 0.17914 3.19521 0.16104 3.61333 0.14702 4.02201 0.13587 4.42129 0.12679 4.81126 0.11928 5.19198 0.11296 5.56352 0.10758 5.92598 0.10296 6.27943 0.09895 6.62397 0.09544 6.95970 0.09236 7.28673 0.08962 7.60515 0.08718 0.07823 9.07220 0.07265 10.34221 0.06897 11.43192 0.06646 12.35898 0.06470 13.14129 0.06344 13.79643 0.06254 14.34112 0.06188 14.79095 0.06139 15.16012 0.06103 15.46135 0.06077 15.70583 0.06057 15.90328 0.06043 16.06202 0.06032 16.18912 0.06024 16.29050 0.06018 16.37107 196 APPENDIX A i = 7% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.07000 1.14490 1.22504 1.31080 1.40255 1.50073 1.60578 1.71819 1.83846 1.96715 2.10485 2.25219 2.40985 2.57853 2.75903 2.95216 3.15882 3.37993 3.61653 3.86968 5.42743 7.61226 10.67658 14.97446 21.00245 29.45703 41.31500 57.94643 81.27286 113.98939 159.87602 224.23439 314.50033 441.10298 618.66975 867.71633 P/F 0.93458 0.87344 0.81630 0.76290 0.71299 0.66634 0.62275 0.58201 0.54393 0.50835 0.47509 0.44401 0.41496 0.38782 0.36245 0.33873 0.31657 0.29586 0.27651 0.25842 0.18425 0.13137 0.09366 0.06678 0.04761 0.03395 0.02420 0.01726 0.01230 0.00877 0.00625 0.00446 0.00318 0.00227 0.00162 0.00115 A/F F/A P/A 0.9346 1.0000 1.00000 1.8080 2.0700 0.48309 2.6243 3.2149 0.31105 3.3872 4.4399 0.22523 4.1002 5.7507 0.17389 4.7665 7.1533 0.13980 5.3893 8.6540 0.11555 5.9713 10.2598 0.09747 6.5152 11.9780 0.08349 7.0236 13.8164 0.07238 7.4987 15.7836 0.06336 7.9427 17.8885 0.05590 8.3577 20.1406 0.04965 8.7455 22.5505 0.04434 9.1079 25.1290 0.03979 9.4466 27.8881 0.03586 30.8402 0.03243 9.7632 33.9990 0.02941 10.0591 37.3790 0.02675 10.3356 40.9955 0.02439 10.5940 63.2490 0.01581 11.6536 94.4608 0.01059 12.4090 138.2369 0.00723 12.9477 199.6351 0.00501 13.3317 285.7493 0.00350 13.6055 406.5289 0.00246 13.8007 575.9286 0.00174 13.9399 813.5204 0.00123 14.0392 1146.7552 0.00087 14.1099 1614.1342 0.00062 14.1604 2269.6574 0.00044 14.1964 3189.0627 0.00031 14.2220 4478.5761 0.00022 14.2403 6287.1854 0.00016 14.2533 8823.8535 0.00011 14.2626 12381.6618 0.00008 14.2693 A/G A/P 0.00000 1.07000 0.48309 0.55309 0.95493 0.38105 1.41554 0.29523 1.86495 0.24389 2.30322 0.20980 2.73039 0.18555 3.14654 0.16747 3.55174 0.15349 3.94607 0.14238 4.32963 0.13336 4.70252 0.12590 5.06484 0.11965 5.41673 0.11434 5.75829 0.10979 6.08968 0.10586 6.41102 0.10243 6.72247 0.09941 7.02418 0.09675 7.31631 0.09439 8.63910 0.08581 0.08059 9.74868 0.07723 10.66873 0.07501 11.42335 0.07350 12.03599 0.07246 12.52868 0.07174 12.92146 0.07123 13.23209 0.07087 13.47598 0.07062 13.66619 0.07044 13.81365 0.07031 13.92735 0.07022 14.01458 0.07016 14.08122 0.07011 14.13191 0.07008 14.17034 COMPOUND INTEREST FACTORS 197 i = 8% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.08000 1.16640 1.25971 1.36049 1.46933 1.58687 1.71382 1.85093 1.99900 2.15892 2.33164 2.51817 2.71962 2.93719 3.17217 3.42594 3.70002 3.99602 4.31570 4.66096 6.84848 10.06266 14.78534 21.72452 31.92045 46.90161 68.91386 101.25706 148.77985 218.60641 321.20453 471.95483 693.45649 1018.91509 1497.12055 2199.76126 P/F 0.92593 0.85734 0.79383 0.73503 0.68058 0.63017 0.58349 0.54027 0.50025 0.46319 0.42888 0.39711 0.36770 0.34046 0.31524 0.29189 0.27027 0.25025 0.23171 0.21455 0.14602 0.09938 0.06763 0.04603 0.03133 0.02132 0.01451 0.00988 0.00672 0.00457 0.00311 0.00212 0.00144 0.00098 0.00067 0.00045 F/A A/F P/A 0.9259 1.0000 1.00000 1.7833 2.0800 0.48077 2.5771 3.2464 0.30803 3.3121 4.5061 0.22192 3.9927 5.8666 0.17046 4.6229 7.3359 0.13632 5.2064 8.9228 0.11207 5.7466 10.6366 0.09401 6.2469 12.4876 0.08008 6.7101 14.4866 0.06903 7.1390 16.6455 0.06008 7.5361 18.9771 0.05270 7.9038 21.4953 0.04652 8.2442 24.2149 0.04130 8.5595 27.1521 0.03683 8.8514 30.3243 0.03298 9.1216 33.7502 0.02963 9.3719 37.4502 0.02670 9.6036 41.4463 0.02413 45.7620 0.02185 9.8181 73.1059 0.01368 10.6748 113.2832 0.00883 11.2578 172.3168 0.00580 11.6546 259.0565 0.00386 11.9246 386.5056 0.00259 12.1084 573.7702 0.00174 12.2335 848.9232 0.00118 12.3186 1253.2133 0.00080 12.3766 1847.2481 0.00054 12.4160 2720.0801 0.00037 12.4428 4002.5566 0.00025 12.4611 5886.9354 0.00017 12.4735 8655.7061 0.00012 12.4820 12723.9386 0.00008 12.4877 18701.5069 0.00005 12.4917 27484.5157 0.00004 12.4943 A/G A/P 0.00000 1.08000 0.48077 0.56077 0.94874 0.38803 1.40396 0.30192 1.84647 0.25046 2.27635 0.21632 2.69366 0.19207 3.09852 0.17401 3.49103 0.16008 3.87131 0.14903 4.23950 0.14008 4.59575 0.13270 4.94021 0.12652 5.27305 0.12130 5.59446 0.11683 5.90463 0.11298 6.20375 0.10963 6.49203 0.10670 6.76969 0.10413 7.03695 0.10185 8.22538 0.09368 9.18971 0.08883 9.96107 0.08580 0.08386 10.56992 0.08259 11.04465 0.08174 11.41071 0.08118 11.69015 0.08080 11.90154 0.08054 12.06016 0.08037 12.17832 0.08025 12.26577 0.08017 12.33013 0.08012 12.37725 0.08008 12.41158 0.08005 12.43650 0.08004 12.45452 198 APPENDIX A i = 9% n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 F/P 1.09000 1.18810 1.29503 1.41158 1.53862 1.67710 1.82804 1.99256 2.17189 2.36736 2.58043 2.81266 3.06580 3.34173 3.64248 3.97031 4.32763 4.71712 5.14166 5.60441 8.62308 13.26768 20.41397 31.40942 48.32729 74.35752 114.40826 176.03129 270.84596 416.73009 641.19089 986.55167 1517.93203 2335.52658 3593.49715 5529.04079 P/F 0.91743 0.84168 0.77218 0.70843 0.64993 0.59627 0.54703 0.50187 0.46043 0.42241 0.38753 0.35553 0.32618 0.29925 0.27454 0.25187 0.23107 0.21199 0.19449 0.17843 0.11597 0.07537 0.04899 0.03184 0.02069 0.01345 0.00874 0.00568 0.00369 0.00240 0.00156 0.00101 0.00066 0.00043 0.00028 0.00018 F/A A/F 1.0000 1.00000 2.0900 0.47847 3.2781 0.30505 4.5731 0.21867 5.9847 0.16709 7.5233 0.13292 9.2004 0.10869 11.0285 0.09067 13.0210 0.07680 15.1929 0.06582 17.5603 0.05695 20.1407 0.04965 22.9534 0.04357 26.0192 0.03843 29.3609 0.03406 33.0034 0.03030 36.9737 0.02705 41.3013 0.02421 46.0185 0.02173 51.1601 0.01955 84.7009 0.01181 P/A 0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.8226 136.3075 0.00734 10.2737 215.7108 0.00464 10.5668 337.8824 0.00296 10.7574 525.8587 0.00190 10.8812 815.0836 0.00123 10.9617 1260.0918 0.00079 11.0140 1944.7921 0.00051 11.0480 2998.2885 0.00033 11.0701 4619.2232 0.00022 11.0844 7113.2321 0.00014 11.0938 10950.5741 0.00009 11.0998 16854.8003 0.00006 11.1038 25939.1842 0.00004 11.1064 39916.6350 0.00003 11.1080 61422.6755 0.00002 11.1091 A/G A/P 0.00000 1.09000 0.47847 0.56847 0.94262 0.39505 1.39250 0.30867 1.82820 0.25709 2.24979 0.22292 2.65740 0.19869 3.05117 0.18067 3.43123 0.16680 3.79777 0.15582 4.15096 0.14695 4.49102 0.13965 4.81816 0.13357 5.13262 0.12843 5.43463 0.12406 5.72446 0.12030 6.00238 0.11705 6.26865 0.11421 6.52358 0.11173 6.76745 0.10955 7.83160 0.10181 8.66566 0.09734 9.30829 0.09464 0.09296 9.79573 0.09190 10.16029 0.09123 10.42952 0.09079 10.62614 0.09051 10.76832 0.09033 10.87023 0.09022 10.94273 0.09014 10.99396 0.09009 11.02994 0.09006 11.05508 0.09004 11.07256 0.09003 11.08467 0.09002 11.09302 COMPOUND INTEREST FACTORS 199 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 F/P 1.10000 1.21000 1.33100 1.46410 1.61051 1.77156 1.94872 2.14359 2.35795 2.59374 2.85312 3.13843 3.45227 3.79750 4.17725 4.59497 5.05447 5.55992 6.11591 6.72750 10.8347 17.4494 28.1024 45.2593 72.8905 117.391 189.059 304.482 490.371 789.747 P/F 0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651 0.42410 0.38554 0.35049 0.31863 0.28966 0.26333 0.23939 0.21763 0.19784 0.17986 0.16351 0.14864 0.09230 0.05731 0.03558 0.02209 0.01372 0.00852 0.00529 0.00328 0.00204 0.00127 i = 10% F/A 1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 18.5312 21.3843 24.5227 27.9750 31.7725 35.9497 40.5447 45.5992 51.1591 57.2750 98.3471 164.494 271.024 442.593 718.905 1163.91 1880.59 3034.82 4893.71 7887.47 A/F 1.00000 0.47619 0.30211 0.21547 0.16380 0.12961 0.10541 0.08744 0.07364 0.06275 0.05396 0.04676 0.04078 0.03575 0.03147 0.02782 0.02466 0.02193 0.01955 0.01746 0.01017 0.00608 0.00369 0.00226 0.00139 0.00086 0.00053 0.00033 0.00020 0.00013 P/A 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 9.0770 9.4269 9.6442 9.7791 9.8628 9.9148 9.9471 9.9672 9.9796 9.9873 A/P 1.10000 0.57619 0.40211 0.31547 0.26380 0.22961 0.20541 0.18744 0.17364 0.16275 0.15396 0.14676 0.14078 0.13575 0.13147 0.12782 0.12466 0.12193 0.11955 0.11746 0.11017 0.10608 0.10369 0.10226 0.10139 0.10086 0.10053 0.10033 0.10020 0.10013 A/G 0.00000 0.47619 0.93656 1.38117 1.81013 2.22356 2.62162 3.00448 3.37235 3.72546 4.06405 4.38840 4.69879 4.99553 5.27893 5.54934 5.80710 6.05256 6.28610 6.50808 7.45798 8.17623 8.70860 9.09623 9.37405 9.57041 9.70754 9.80229 9.86718 9.91125 200 APPENDIX A F/P 1.12000 1.25440 1.40493 1.57352 1.76234 1.97382 2.21068 2.47596 2.77308 3.10585 3.47855 3.89598 4.36349 4.88711 5.47357 6.13039 6.86604 7.68997 8.61276 9.64629 17.0001 29.9599 52.7996 93.0510 163.988 289.002 509.321 897.597 1581.87 2787.80 P/F 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197 0.28748 0.25668 0.22917 0.20462 0.18270 0.16312 0.14564 0.13004 0.11611 0.10367 0.05882 0.03338 0.01894 0.01075 0.00610 0.00346 0.00196 0.00111 0.00063 0.00036 i = 12% F/A 1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 42.7533 48.8837 55.7497 63.4397 72.0524 133.334 241.333 431.663 767.091 1358.23 2400.02 4236.01 7471.64 13173.9 23223.3 A/F 1.00000 0.47170 0.29635 0.20923 0.15741 0.12323 0.09912 0.08130 0.06768 0.05698 0.04842 0.04144 0.03568 0.03087 0.02682 0.02339 0.02046 0.01794 0.01576 0.01388 0.00750 0.00414 0.00232 0.00130 0.00074 0.00042 0.00024 0.00013 0.00008 0.00004 P/A 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.8431 8.0552 8.1755 8.2438 8.2825 8.3045 8.3170 8.3240 8.3281 8.3303 A/P 1.12000 0.59170 0.41635 0.32923 0.27741 0.24323 0.21912 0.20130 0.18768 0.17698 0.16842 0.16144 0.15568 0.15087 0.14682 0.14339 0.14046 0.13794 0.13576 0.13388 0.12750 0.12414 0.12232 0.12130 0.12074 0.12042 0.12024 0.12013 0.12008 0.12004 A/G 0.00000 0.47170 0.92461 1.35885 1.77459 2.17205 2.55147 2.91314 3.25742 3.58465 3.89525 4.18965 4.46830 4.73169 4.98030 5.21466 5.43530 5.64274 5.83752 6.02020 6.77084 7.29742 7.65765 7.89879 8.05724 8.15972 8.22513 8.26641 8.29222 8.30821 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 COMPOUND INTEREST FACTORS 201 F/P 1.15000 1.32250 1.52088 1.74901 2.01136 2.31306 2.66002 3.05902 3.51788 4.04556 4.65239 5.35025 6.15279 7.07571 8.13706 9.35762 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.176 267.864 538.769 1083.66 2179.62 4384.00 8817.79 17735.7 P/F 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.21494 0.18691 0.16253 0.14133 0.12289 0.10686 0.09293 0.08081 0.07027 0.06110 0.03038 0.01510 0.00751 0.00373 0.00186 0.00092 0.00046 0.00023 0.00011 0.00006 i = 15% F/A 1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.0668 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.444 212.793 434.745 881.170 1779.09 3585.13 7217.72 14524.1 29220.0 58778.6 118231 A/F 1.00000 0.46512 0.28798 0.20027 0.14832 0.11424 0.09036 0.07285 0.05957 0.04925 0.04107 0.03448 0.02911 0.02469 0.02102 0.01795 0.01537 0.01319 0.01134 0.00976 0.00470 0.00230 0.00113 0.00056 0.00028 0.00014 0.00007 0.00003 0.00002 0.00001 P/A 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 6.6543 6.6605 6.6636 6.6651 6.6659 6.6663 A/P 1.15000 0.61512 0.43798 0.35027 0.29832 0.26424 0.24036 0.22285 0.20957 0.19925 0.19107 0.18448 0.17911 0.17469 0.17102 0.16795 0.16537 0.16319 0.16134 0.15976 0.15470 0.15230 0.15113 0.15056 0.15028 0.15014 0.15007 0.15003 0.15002 0.15001 A/G 0.00000 0.46512 0.90713 1.32626 1.72281 2.09719 2.44985 2.78133 3.09223 3.38320 3.65494 3.90820 4.14376 4.36241 4.56496 4.75225 4.92509 5.08431 5.23073 5.36514 5.88343 6.20663 6.40187 6.51678 6.58299 6.62048 6.64142 6.65298 6.65929 6.66272 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65 70 202 APPENDIX A n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 F/P 1.20000 1.44000 1.72800 2.07360 2.48832 2.98598 3.58318 4.29982 5.15978 6.19174 7.43008 8.91610 10.6993 12.8392 15.4070 18.4884 22.1861 26.6233 31.9480 38.3376 95.3962 237.376 590.668 1469.77 3657.26 9100.44 22644.8 56347.5 P/F 0.83333 0.69444 0.57870 0.48225 0.40188 0.33490 0.27908 0.23257 0.19381 0.16151 0.13459 0.11216 0.09346 0.07789 0.06491 0.05409 0.04507 0.03756 0.03130 0.02608 0.01048 0.00421 0.00169 0.00068 0.00027 0.00011 0.00004 0.00002 i = F/A 1.0000 2.2000 3.6400 5.3680 7.4416 9.9299 12.9159 16.4991 20.7989 25.9587 32.1504 39.5805 48.4966 59.1959 72.0351 87.4421 105.931 128.117 154.740 186.688 471.981 1181.88 2948.34 7343.86 18281.3 45497.2 113219 281733 20% A/F P/A 1.00000 0.8333 0.45455 1.5278 0.27473 2.1065 0.18629 2.5887 0.13438 2.9906 0.10071 3.3255 0.07742 3.6046 0.06061 3.8372 0.04808 4.0310 0.03852 4.1925 0.03110 4.3271 0.02526 4.4392 0.02062 4.5327 0.01689 4.6106 0.01388 4.6755 0.01144 4.7296 0.00944 4.7746 0.00781 4.8122 0.00646 4.8435 0.00536 4.8696 0.00212 4.9476 0.00085 4.9789 0.00034 4.9915 0.00014 4.9966 0.00005 4.9986 0.00002 4.9995 0.00001 4.9998 0.00000 4.9999 A/P 1.20000 0.65455 0.47473 0.38629 0.33438 0.30071 0.27742 0.26061 0.24808 0.23852 0.23110 0.22526 0.22062 0.21689 0.21388 0.21144 0.20944 0.20781 0.20646 0.20536 0.20212 0.20085 0.20034 0.20014 0.20005 0.20002 0.20001 0.20000 A/G 0.00000 0.45455 0.87912 1.27422 1.64051 1.97883 2.29016 2.57562 2.83642 3.07386 3.28929 3.48410 3.65970 3.81749 3.95884 4.08511 4.19759 4.29752 4.38607 4.46435 4.73516 4.87308 4.94064 4.97277 4.98769 4.99451 4.99757 4.99894 COMPOUND INTEREST FACTORS 203 i = 25% F/P 1.25000 1.56250 1.95313 2.44141 3.05176 3.81470 4.76837 5.96046 7.45058 9.31323 11.6415 14.5519 18.1899 22.7374 28.4217 35.5271 44.4089 55.5112 69.3889 86.7362 264.698 807.794 2465.19 7523.16 22958.87 70064.92 213821.2 652530.4 P/F 0.80000 0.64000 0.51200 0.40960 0.32768 0.26214 0.20972 0.16777 0.13422 0.10737 0.08590 0.06872 0.05498 0.04398 0.03518 0.02815 0.02252 0.01801 0.01441 0.01153 0.00378 0.00124 0.00041 0.00013 0.00004 0.00001 0.00000 0.00000 F/A 1.0000 2.2500 3.8125 5.7656 8.2070 11.2588 15.0735 19.8419 25.8023 33.2529 42.5661 54.2077 68.7596 86.9495 109.687 138.109 173.636 218.045 273.556 342.945 1054.79 3227.17 9856.76 30088.7 91831.5 280256 855281 2610118 A/F 1.00000 0.44444 0.26230 0.17344 0.12185 0.08882 0.06634 0.05040 0.03876 0.03007 0.02349 0.01845 0.01454 0.01150 0.00912 0.00724 0.00576 0.00459 0.00366 0.00292 0.00095 0.00031 0.00010 0.00003 0.00001 0.00000 0.00000 0.00000 P/A 0.8000 1.4400 1.9520 2.3616 2.6893 2.9514 3.1611 3.3289 3.4631 3.5705 3.6564 3.7251 3.7801 3.8241 3.8593 3.8874 3.9099 3.9279 3.9424 3.9539 3.9849 3.9950 3.9984 3.9995 3.9998 3.9999 4.0000 4.0000 A/P 1.25000 0.69444 0.51230 0.42344 0.37185 0.33882 0.31634 0.30040 0.28876 0.28007 0.27349 0.26845 0.26454 0.26150 0.25912 0.25724 0.25576 0.25459 0.25366 0.25292 0.25095 0.25031 0.25010 0.25003 0.25001 0.25000 0.25000 0.25000 A/G 0.00000 0.44444 0.85246 1.22493 1.56307 1.86833 2.14243 2.38725 2.60478 2.79710 2.96631 3.11452 3.24374 3.35595 3.45299 3.53660 3.60838 3.66979 3.72218 3.76673 3.90519 3.96282 3.98580 3.99468 3.99804 3.99929 3.99974 3.99991 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 Authors’ Biographies 205 DAVID L. WHITMAN David L. Whitman, P.E., Ph.D. received a B.S. degree (1975) in Electrical Engineering from the University of Wyoming (UW). He also received a Ph.D. degree (1978) in Mineral Engineering from the University of Wyoming. He worked in the synthetic fuels arena prior to becoming a faculty member in Petroleum Engineering at the University of Wyoming in 1981. From 1989 to 2005, he was the Associate Dean of Academics and since 2005 has been a professor of Electrical and Computer Engineering. He received UW’s Ellbogen Outstanding Teacher Award in 1985, UW’s College of Engineering Outstanding Undergraduate Teaching Award in 1990 and 2004 and the ASEE Rocky Mountain Section Outstanding Teaching Award in 2001. He is a Past President of the National Council of Examiners for Engineers and Surveyors (NCEES), chairman of the IEEE-USA Licensure & Registration Committee, and an active member of ASEE. RONALD E. TERRY Ronald E. Terry, Ph.D. received a B.S. in Chemical Engineering from Oregon State University (1971) and a Ph.D. from Brigham Young University (BYU) (1976). He worked for Phillips Petroleum Company after graduate school and began his academic career in 1977 at the University of Kansas in the Chemical and Petroleum Engineering Department. He taught in the Petroleum Engineering Department at the University of Wyoming (1981-1987) and at BYU in the Chemical Engineering Department (1987-2007) and in the Technology and Engineering Education Department (2007- present). He has received teaching awards at the University of Kansas, University of Wyoming, and at Brigham Young University. Early in his career, his scholarship efforts involved researching methods to enhance the pro- duction of oil and gas. After joining BYU, his scholarship centered on pedagogy, student learning, and engineering ethics. He has served as acting department chair, associate dean, and in BYU’s central administration as an Associate in the Ofﬁce of Planning and Assessment for ﬁve years (2003-2008). He is past president of the Rocky Mountain Section of the American Society for Engineering Education.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813065.pdf&bkn=6813064&pdfType=book	SYNTHESIS LECTURES ON ENGINEERING Series Editor: Steven F. Barrett, University of Wyoming Series ISSN: 1939-5221 Crafting Your Research Future A Guide to Successful Master’s and PhD Degrees in Science & Engineering Charles X. Ling Western University, Ontario, Canada Qiang Yang Hong Kong University of Science and Technology, China What is it like to be a researcher or a scientist? For young people, including graduate students and junior faculty members in universities, how can they identify good ideas for research? How do they conduct solid research to verify and realize their new ideas? How can they formulate their ideas and research results into high-quality articles, and publish them in highly competitive journals and conferences? What are effective ways to supervise graduate students so that they can establish themselves quickly in their research careers? In this book, Ling and Yang answer these questions in a step-by-step manner with specific and concrete examples from their first-hand research experience. Critical Acclaim for Crafting Your Research Future “Ling and Yang summarize the practical aspects of the expectations for the modern graduate student. They will all benefit.” —Randy Goebel, University of Alberta “It will be tremendously useful to post-docs and graduate students alike (and perhaps even some junior faculty!).” —Adrian M. Owen, Professor and Canada Excellence Research Chair, Western University “Want to have a successful research career? This is a nice guide and companion!” —Jiawei Han, Abel Bliss Professor, University of Illinois at Urbana-Champaign About Morgan & Claypool Publishers This volume is a printed version of a work that appears in Synthesis, the Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information visit synthesis.morganclaypool.com Mor gan Cl aypool Publishers & ISBN: 978-1-60845-810-3 90000 w w w . m o r g a n c l a y p o o l . c o m 9 781608 458103 Y I N G • L A N G C R A F T I N G Y O U R R E S E A R C H F U T U R E M O R G A N & C L A Y P O O L Critical Acclaim for Crafting Your Research Future “Ling and Yang summarize the practical aspects of the expectations for the modern graduate student. They will all benefit.” — Randy Goebel, Professor of University of Alberta “It will be tremendously useful to post-docs and graduate students alike (and perhaps even some junior faculty!)” — Adrian M. Owen, Professor and Canada Excellence Research Chair, Western University “Want to have a successful research career? This is a nice guide and companion!” — Jiawei Han, Abel Bliss Professor, University of Illinois at Urbana-Champaign Copyright © 2012 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. u Crafting Your Research Fut re A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang www.morganclaypool.com ISBN: 9781608458103 paperback ISBN: 9781608458110 ebook DOI: 10.2200/S00412ED1V01Y201203ENG018 A Publication in the SYnTheSIS LeCTuReS on engIneeRIng Lecture #18 Series Editor: Steven F. Barrett Series ISSN ISSN 1939-5221 print ISSN 1939-523X electronic Crafting Your Research Future A guide to Successful Master’s and Ph.D. Degrees in Science & engineering Charles X. Ling University of Western Ontario, Ontario, Canada Qiang Yang Hong Kong University of Science and Technology, Hong Kong, China SYnTheSIS LeCTuReS on engIneeRIng #18 iv AbStRACt What is it like to be a researcher or a scientist? For young people, including gradu- ate students and junior faculty members in universities, how can they identify good ideas for research? How do they conduct solid research to verify and realize their new ideas? How can they formulate their ideas and research results into high- quality articles, and publish them in highly competitive journals and conferences? What are effective ways to supervise graduate students so that they can establish themselves quickly in their research careers? In this book, Ling and Yang answer these questions in a step-by-step manner with specific and concrete examples from their first-hand research experience. keYwoRdS: Research Methodology, Research Career Guidebook, Guidebook for Graduate Students, Ph.D. and Masters Research, Writing and Publishing Papers, Writing Ph.D. Thesis, Science and Engineering Career. Contents Acknowledgments ......................................................................................ix Preface ......................................................................................................xi 1. basics of Research ..............................................................................1 1.1 What Is Research? ............................................................................ 1 1.2 Who Are Researchers and Who Are Not? ...................................... 2 1.3 What Do Researchers Do? ............................................................... 3 1.4 What Skills and Abilities Are the Most Important for Researchers? ................................................................................ 7 1.5 What Are Some Pros and Cons of Being Researchers? ................. 10 1.6 So, How Do I Become a Researcher? ............................................ 12 1.7 What Are the Differences between a Master’s and Ph.D. Thesis? .......................................................................... 12 1.8 How to Find a Suitable Supervisor for Ph.D. Study ..................... 13 1.9 How Long Does It Take to Get My Ph.D. Degree? ..................... 16 1.10 Three Representative Graduate Students ....................................... 17 2. Goals of Ph.d. Research ..................................................................19 2.1 Goal #1: Be the Best in the Field ................................................... 19 2.2 Goal #2: Be Independent ............................................................... 25 2.3 Three Key Tasks for Getting a Ph.D. (and Master’s) Degree ........ 27 2.4 The Milestones of Getting a Ph.D. Degree ................................... 28 2.5 Distractions to the Goals................................................................ 30 3. Getting Started: Finding New Ideas and organizing Your Plans ....... 33 3.1 Your First Year ................................................................................33 3.2 How to Find Relevant Papers (Literature Search) .........................35 3.3 How to Read Papers .......................................................................37 vi CRAFtING YouR ReSeARCh FutuRe 3.4 Where to Get New Ideas ............................................................... 41 From Ideas to Research and Thesis Topic ..................................... 44 3.5 3.6 How Do I Know If I Am on the Right Track? .............................. 46 3.7 Setting Up a Plan for Ph.D. Thesis Early ...................................... 47 3.8 Learning to Organize Papers and Ideas Well ................................. 49 4. Conducting Solid Research ..............................................................51 4.1 An Overview of a Research Process ............................................... 51 Jim Gray’s Criteria ......................................................................... 54 4.2 4.3 The Research Matrix Method ........................................................ 59 4.4 Carrying Out Your Research .......................................................... 63 4.5 Brand Yourself ................................................................................ 67 4.6 Empirical vs. Theoretical Research ................................................ 69 4.7 Team Work and Multi-Disciplinary Research ............................... 74 5. writing and Publishing Papers .........................................................77 “Publish or Perish” .......................................................................... 78 5.1 5.2 Why Publishing Top-Quality Papers Is Hard ................................ 80 5.3 What Makes a Great Paper? .......................................................... 81 5.4 A Few Untold Truths about Research Papers ................................ 83 5.5 The Roles of You, Your Supervisor, and Proofreader ..................... 85 5.6 Supervisors: How to Improve Your Students’ Writing Most Effectively ....................................................................................... 87 5.7 Where to Submit: Conference or Journals? .................................... 89 5.8 How Are Full-Length Conference Papers Reviewed? ................... 91 5.9 How Are Journal Papers Reviewed? ............................................... 94 6. Misconceptions and tips for Paper writing ......................................99 “It’s So Obvious that Our Paper Is Great” ..................................... 99 6.1 “It Is Your Responsibility to Understand My Paper” ................... 102 6.2 6.3 The 10/30 Test ............................................................................. 103 6.4 Top-Down Refinement of Papers ................................................ 104 6.5 Create a Hierarchy of Subsections and Choose Section Titles Carefully ................................................................ 109 6.6 Tips for Paper Writing ................................................................. 110 6.6.1 Use Certain Words to Signal Readers .............................. 111 6.6.2 Use Simple Sentences, But Not Simpler .......................... 111 CoNteNtS vii 6.6.3 Use a Small Set of Terms Throughout the Paper ............. 112 6.6.4 Use Examples Early and Use Them Throughout the Paper ........................................................................... 113 6.6.5 Use Figures, Diagrams, Charts, Photos, Tables................ 113 6.6.6 Write about Your Motivations and Justifications ............. 114 6.6.7 Pose Potential Questions and Answer Them Yourself ............................................................................. 114 6.6.8 Emphasize and Reiterate Key Points in Your Paper ........ 115 6.6.9 Make Connections Throughout the Paper ....................... 116 6.6.10 Format Papers for Easy Reading ...................................... 116 6.7 Other Misconceptions and Flaws ................................................. 117 6.8 Summary ...................................................................................... 118 7. writing and defending a Ph.d. thesis ...........................................121 7.1 Thesis and Dissertation ................................................................ 121 7.2 Thesis Organization: Top Down or Bottom Up .......................... 122 7.3 Defending Your Thesis ................................................................. 126 8. Life After Ph.d. .............................................................................131 8.1 A Day In the Life of a Typical Professor ..................................... 131 8.2 Applying for Research Grants ...................................................... 135 8.3 Technology Transfer ..................................................................... 144 Summary ................................................................................................ 151 References .............................................................................................. 153 Author biographies ................................................................................. 155 ix Acknowledgments First of all, we thank the thousands of graduate students and researchers who attended our seminars on how to conduct solid research and how to write and publish top-quality papers. To these students: your enthusiasm for research, your questions, and your suggestions helped us tremendously in preparing and finishing this book. It is our wish to motivate and support more young researchers in their path toward a successful research career. From Charles Ling: I wish to dedicate this book to my parents Zongyun Ling and Ruqian Cao. They were both life-long, awarding-winning, high-school teachers. They gave me so much inspiration and guidance throughout my youth, which laid the foundation of my research life from my graduate study to a full research career. This book summarizes over 20 years of experience as a researcher, which represents a direct outcome of my parents’ love, care, and life-long educa- tion for me. I wrote parts of this book on the bedside of my father when he stayed in the hospital for several months in 2011. The book is for you! From Qiang Yang: I dedicate this book to my parents, Professors Haishou Yang and Xiuying Li, who were professors in China’s Peking University and Tsinghua University, respectively, where they worked all their lives until retire- ment. My parents inspired me to pursue a research career in Astrophysics and then Computer Science. Through their own exemplary research careers, they showed me the “garden of research,” which is “full of beautiful flowers waiting to be picked” (to quote from my father). To them: my deepest love and appreciation! Many colleagues, friends, and students read the early drafts of the book, and made many detailed suggestions and comments. Brian Srivastava, a very capable x CRAFtING YouR ReSeARCh FutuRe Ph.D. student at Western, provided detailed and thorough suggestions and com- ments in early draft of the book. Lili Zhao, a research assistant in Hong Kong University of Science and Technology (HKUST), made detailed edits. Luiz Fernando Capretz, Jimmy Huang, Huan Liu, Aijun An, Steve Barrett, Wei Fan, Jenna Butler, Randy Goebel, Eileen Ni, and many others gave us suggestions on various parts of the book. Adrian Owen, Stephen Sims, C.B. Dean and Jiawei Han gave us encouragement after reading parts of the book. Many of our former Ph.D. students, especially Victor Sheng and Weizhu Chen, gave us comments and suggestions. To all: our special gratitude! xi Preface When we were children, we were often asked, “What do you want to be when you grow up?” Our answer, and dream, was: “I want to become a scientist!” Indeed, we have many giants to look up to: from Newton to Einstein, to Nobel Laureates (such as Richard Feynman). However, when we really went through the process of becoming scientists, we found that the road was not all that straightforward; it was full of misconceptions that took many instances of trial and error to find out. True, there are numerous online articles and commentaries, telling young people how to become a successful researcher and scientist, but most are scattered and some are biased. There has not been a central place where one can find advice targeted to answering such questions about the first and most important stepping stone toward becoming a researcher: graduate study. This situation will hopefully be changed with the publishing of this book, “Crafting Your Research Future.” Summarizing more than 20 years of experience in research and practice, we have put together an accessible introductory book for aspiring researchers in science and technology. We strive to make this book accessible to a general audience such that it could be used by readers interested in general areas of science and technology. At the same time, we try to be as specific and concrete as possible, to show you step by step, how research is conducted. We also include several case studies and many specific examples. The book also summarizes over a decade of seminars and talks at over 50 universities and institutes across the world on the topics: how to do research and how to write and publish research papers. In all our talks and seminars, the xii CRAFtING YouR ReSeARCh FutuRe attendance has been overwhelming, with hundreds of students and faculty filling the lecture hall. Questions and answer periods stretched beyond the talk. Each seminar gives us a chance to improve our presentation, and this book is the latest in this effort. Here is a brief overview of the book. Chapter 1 sets the general stage for the book, by discussing what research is, and what researchers are. Chapter 2 discusses the goals of research and lays down the basic steps to- ward a research career. Chapter 3 answers the question of how to get started by looking for a suit- able supervisor, reading relevant literature and getting new ideas. It advocates a principled method with three key steps to guide any research effort. Chapter 4 presents a general methodology on how to evaluate potential directions in order to find one that is high impact, and how to conduct solid and thorough research. It goes into details on the differences between empirical, theo- retical, and multidisciplinary research. Chapter 5 discusses how to write and publish high quality papers in com- petitive journals and conferences. It also provides perspectives from reviewers of journal and conference articles, and provides tips on how to handle reviewers’ comments. Chapter 6 presents a collection of commonly met misconceptions and pit- falls, and offers useful tips on paper writing. Chapter 7 discusses how to plan, organize and write a Ph.D. thesis, and how to defend a Ph.D. thesis. It presents two typical approaches: top down and bottom up. Chapter 8 gives readers a detailed picture on life after Ph.D. by depicting a realistic picture of the life of a professor. This chapter also discusses important issues such as technology transfer. PReFACe xiii Both authors have been university professors for over 20 years, and have su- pervised many Master’s and Ph.D. students. Some of our Ph.D. students are now professors in universities in the US, Canada, China, and other countries. Some are researchers in research institutes and research labs at Google, IBM, and other companies. Some are running start-up companies successfully. We have put a lot of effort into helping our students to choose thesis topics, do solid research, and to publish top-quality papers. Often co-authoring papers with students in our research, we have published over 300 peer-reviewed jour- nal and conference papers. We have also been Associate Editors and Editor in Chief of several top-ranked journals in the computer science field, such as IEEE1 Transactions on Knowledge and Data Engineering and ACM2 Transactions on Intelligent Systems and Technology. A more detailed biography of the authors can be found at the end of the book. 1 IEEE: Institute of Electrical and Electronics Engineers 2 ACM: The Association for Computing Machinery 1 C H A P T ER 1 basics of Research In this chapter, we examine some of the frequently asked questions about the basics of research. If you want to know what researchers and scientists are like, if you are still not sure whether doing research is a suitable career for you, or if you are just a beginner in research, read on. 1.1 whAt IS ReSeARCh? In natural science and engineering, “research” can be loosely defined as making novel and significant contributions to our understanding of the world, based on reproducible observations and verifiable results. There are often large overlaps in scope between research in science and engineering. In science, the emphasis is on discovering new theories, paradigms, approaches, algorithms, simulations, experiments, and so on, while in engineering, the emphasis is to solve real-world problems with new technologies, designs, processes, methods, models, testing, and so on. Novelty and significance are the key ingredients of research in both science and engineering. Something that is “novel,” “new,” “original,” “creative,” “unconventional,” “innovative,” or “ground-breaking,” means that it was unknown previously. In the research arena, it usually means that it was not published previously in academic journals, conference proceedings, books, technical reports, or other accessible venues. Novel work must also be significant or have high impact, be important, useful, seminal, and so on, to qualify as research. A highly significant research will ultimately bring huge benefit to many people in the world. How can novelty and significance be judged? Clearly, if a work, either in the same or in different forms, has been published previously, it is certainly not novel. 2 CRAFtING YouR ReSeARCh FutuRe If the work is only a small derivation or obvious improvement from previous work, it is also not considered novel. “Significance” is harder to judge. A research work is highly significant if it lays the foundation for future work, very significant if it dis- covers new paradigms or methods that can solve new problems, or quite significant if it outperforms previous methods on some important tasks. Often significance can only be assessed in the future; in many conferences and journals, a 10-year “most significant paper award” is given to a paper that made the most significant contributions 10 years ago. One informal measure of the impact of research work is how many other researchers have used this work as the basis to build their own research programs, and how many research papers have cited the work after it was published. Thus, experienced researchers are often called on to review and judge the significance of research papers submitted for publication. Chapter 3 to Chapter 6 will discuss the process of doing research in greater details. 1.2 who ARe ReSeARCheRS ANd who ARe Not? Researchers conduct research as the main part of their professional career. They are also often referred to as scholars or academics. This book is written mainly for researchers-to-be, especially Ph.D. candidates, in natural science and engineering. The book may also be helpful to young researchers in their early careers, such as assistant and associate professors in universities. In many of the sciences, especially natural sciences, researchers are also called scientists. In mathematics, they are known as mathematicians; in computer science, computer scientists; in biology, biologists, and so on. Most researchers work at universities, research institutes, and research labs of large companies. One misconception about researchers and scientists that we want to correct is that typical researchers are old “nerds” or “geeks”: people with either gray hair or no hair, wearing torn clothes, thinking all the time and talking to themselves, and who are incomprehensible and unapproachable. In reality, most researchers and scientists are full of life, fun, versatile, and have many hobbies. A typical example bASICS oF ReSeARCh 3 is Professor Richard Feynman, a physicist and Nobel Laureate who also played music, learned to draw, went to bars, married (three times), acted in a film, trav- eled around the world, wrote many popular science books, and so on. We highly recommend that you read his legendary book: Surely You’re Joking, Mr. Feynman! (published by W.W. Norton). In fact, most researchers and scientists that we know of, including us, are full of color and are “normal” people! Here are some typical examples of non-researchers. Salespersons are not researchers. People who follow routines and instructions, like factory workers and accountants, are not researchers. Teachers and instructors whose main job is teaching in schools, colleges or universities are usually not researchers, unless they develop, test, and experiment on new techniques for education. Engineers solve real-world problems and build things, and if they make novel and significant con- tributions in the process, they are also researchers. Medical doctors and dentists are professionals and usually not researchers, unless they conduct research on new medicines or new treatment. On the one hand, researchers, such as professors, often also do other routine work such as teaching, managing research grants, and so on. On the other hand, many non-researchers also do some research in their work. 1.3 whAt do ReSeARCheRS do? Here is a list of 11 tasks that researchers often do in their day-to-day work. Chapter 8 describes a typical day in the life of a researcher in going about some of these tasks. Task 1. Explore and come up with new ideas (i.e., novelty of re- search). To make sure that the idea is new, researchers must know well the frontier of their research areas by conducting an extensive litera- ture search. Chapter 3 of this book will discuss this in great detail. Task 2. Validate and implement the new ideas to see if they work, and make them work well (i.e., significance of research). Chapter 4 will describe how to do solid research in detail. 4 CRAFtING YouR ReSeARCh FutuRe Task 3. Write up the research outcome in Tasks 1 and 2 as “manu- scripts” or “papers,” and submit them to academic journals, confer- ences, book publishers, or other media outlets. Usually the research manuscript is first peer-reviewed by other researchers in the same field, as they are probably the only qualified people to determine if the work is novel and significant enough to be accepted for publication. To ensure fairness and frankness, reviewers are always anonymous. Often the selection is quite competitive: many top journals and conferences may have an acceptance rate of only 10-20% for full-length papers. That is, the majority of the submissions are rejected. Chapter 5 and Chapter 6 will discuss how to write manuscripts well. Chapter 5 will also share some insights about how papers are reviewed. Task 4. Review papers and manuscripts from other researchers to see if they are novel and significant enough to be accepted for publica- tion. In this role, the researchers become reviewers, as mentioned in Task 3. Task 5. Administrate academic journals and organize academic conferences, especially when one becomes an established researcher. These duties are often time-consuming, and are usually on a volun- tary basis (i.e., no extra income), although in the long run, they help increase the academic and professional visibility of the researcher in his/ her field. Task 6. Attend academic conferences to present papers, to learn the most recent research results, and to exchange research ideas and knowl- edge with other researchers. This is also an important “networking” time with other researchers in the same field. Established researchers may also be invited to give keynote speeches at conferences. Task 7. Apply for research grants from government and other organi- zations to support research, including providing support to graduate bASICS oF ReSeARCh 5 students. As most research work may not have immediate monetary return, usually the government and organizations invest money as grants to support research. The grant application can also be highly competitive. See Chapter 8. Task 8. Supervise graduate students, especially Ph.D. candidates, so they become researchers in the near future. This book is mainly about how to successfully complete both Master’s and Ph.D. study, includ- ing thesis writing and defense. It is also about how to be an effective supervisor. Task 9. Teach graduate and undergraduate courses in universities and colleges. Some of those students will become researchers in the future. Task 10. Perform administrative work for the organizations that re- searchers work in. In the university this includes committee work in the department, faculty, or college, writing reference letters, and so on. Task 11. Commercialize research outcome (also known as Conducting “Technology Transfer”). If particular research work is fundamental, the research outcome is often published in an open forum and the research outcome is published in an open media, often free for other researchers to verify and utilize for further research. However, some research is applicable in the real world, and the results can be com- mercialized. In this case, researchers may also seek to protect their intellectual properties with patents and so on. A small number of researchers even create spin-off start-up companies to commercial- ize their research. We also have a wealth of experience in industrial applications and technology transfer, and we will discuss this topic in Chapter 8 of the book. Many researchers work as professors, with ranks known as assistant, associate, or full professors, in research-oriented universities. Usually they spend a considerable 6 CRAFtING YouR ReSeARCh FutuRe amount of time and effort in Tasks 1, 2, 3, 7, 8 and 9. In terms of research topics and methodologies (Tasks 1 and 2), university professors are quite free in choosing whatever interests them the most, provided that they can produce novel and significant results. They can also freely express their academic views and results in publications (Task 3), provided that the work is peer-reviewed and accepted. Depending on individual researchers, they can also be quite involved in Tasks 5 and 11, and other tasks on the list. Researchers may also work for large companies and various organizations. For example, Microsoft, Google, IBM, GE, DuPont, Pfizer, Boeing, National Institutes of Health (NIH), National Research Council of Canada, and so on all have divisions for research. Researcher’s main duties usually include Tasks 1, 2, 3, and 11. They may also be involved in Tasks 4, 5, and 8; in fact many Ph.D. students conduct research for companies and organizations as interns. In terms of research topics, they are not as free as university professors; they often have to work on research problems that are directly related to the company’s service and products. However, Google has a policy, called Innovation Time Off, where Google engineers can spend 20% of their work time on new projects that the engineers and scientists are interested in doing, but may not be on the company’s current agenda. Ph.D. candidates are researchers-to-be, supervised by university professors. Their main job is Tasks 1–3. Often they also work with their supervisors on many other tasks including Task 8. As senior Ph.Ds, they may help junior Ph.Ds and Master’s students to do research. They need to learn to do these tasks so that when they finish their Ph.D. program, they become independent researchers who can perform Tasks 1–11 reasonably well by themselves. Some disciplines, such as Biology and Physics, have the practice in which one often follows a Ph.D. with a Post Doctoral fellowship, which is a half step between Ph.D. students and pro- fessors. These positions are usually short, but give the researcher an opportunity to learn parts of the process they didn’t see as students, notably managing group budgets and different approaches to management, from their Ph.D. supervisors. bASICS oF ReSeARCh 7 1.4 whAt SkILLS ANd AbILItIeS ARe the MoSt IMPoRtANt FoR ReSeARCheRS? Both of us (the authors) were fascinated by the stories of the famous mathemati- cians and physicists (such as Archimedes, Newton, Euler, Gauss, and Einstein), and dreamed of being scientists when we were young. We can still vividly recall the time when we were middle school students in China. This was the time when the Culture Revolution (during which intellectuals were suppressed1) had just ended, and economic reform was just about to start. One day, a vivid news report entitled “The Goldbach’s Conjecture” (in Chinese), appeared in all major newspapers, ra- dios, and magazines in China. It reported a Chinese mathematician named Chen,2 who proved the “Last Hurdle” to solving the Goldbach’s Conjecture. The report was like “a thunder,” awakening the youth in China as the “spring time for modern science” had arrived in China! The Conjecture, proposed by Goldbach in 1742, can be simply stated as: every even integer greater than 2 can be expressed as the sum of two prime num- bers (one prime plus another prime, or 1+1). Much progress had been made toward the proof of the conjecture since it was proposed. For example, mathematicians before Chen proved that any sufficiently large even integer could be expressed as the sum of two primes, or a prime and the product of 6 primes (1+6). Chen spent more than 10 years in his 50 square-foot apartment and proved the “Last Hurdle” of the Conjecture: every sufficiently large even integer can be expressed as the sum of a prime and the product of two primes (1+2). His proof took over 200 pages. There was only one step to reap the “crown in mathematics” (proving 1+1). One of us (Ling) was so inspired by the report, and intrigued by the appar- ently simple conjecture, that he went to buy several books on number theory by himself (in those years food was still a scarce resource), and spent days passionately reading them and trying to prove 1+1. He knew the proof must be hard, but he believed that he could be very creative, and could think of a novel approach that 1 http://en.wikipedia.org/wiki/Cultural_Revolution 2 Chen Jingrun. http://en.wikipedia.org/wiki/Chen_Jingrun 8 CRAFtING YouR ReSeARCh FutuRe others had not thought of. One day he believed he found an ingenious proof on only two pages, and he rushed to his father announcing his great discovery! His father calmed him down, and asked him to check the proof carefully. You can imagine the outcome. After he entered his undergraduate study in Computer Science, he wrote a computer program to verify the Conjecture for integers with many digits, hop- ing to find a counter example to refute the Conjecture. You can imagine the outcome. The Conjecture of 1+1 remains open today. It has now been verified by computers to even integers of 18 digits long, according to the Wikipedia page on the Conjecture. But he still dreams that someday he can prove it, or refute it. Do you have dreams, passion, curiosity, and creativity? Almost everyone does. These are some of the most important qualities for being researchers. Besides these, we list what you need to succeed on the path of research below. • Passion, focus, enthusiasm, and interests in research. Researchers must be keenly interested and highly passionate about their research, so that they can stay focused and study research problems deeply over weeks, months, or even years. • Curiosity and creativity. Researchers must be highly curious and creative. They often ask many questions, both in research and in daily life, and think “out of the box” for new ideas and solutions that most people have not thought about. They may often think of “plot holes” when they watch movies, and discuss how to make the movies better! • Critical and independent thinking. Researchers must not just fol- low the conventional wisdom and established views. They must think independently and ask critical questions (e.g., what is wrong? How can I make it better?). • Risk taking. Often new ideas do not work, or have been explored and published by others. Researchers must be willing to take risks in exploration. bASICS oF ReSeARCh 9 • high scientific integrity. Researchers must be willing to take risk and fail, and be honest and transparent about failure. They must also be truthful in reporting their research outcome (see Section 5.4). Peter Medawar’s excellent book, Advice to a Young Scientist, should be read by all graduate students. • Quick learning and strong analytical and problem-solving skills. Researchers need to be quick learners for new knowledge and tech- niques needed for research. They must have good analytical and problem-solving skills (which can be learned) to analyze, implement, and test their new ideas (conducting solid research). • diligence. Researchers must stay focused, think deeply, and study new research problems in a great depth. They often work for more than 8 hours a day, and 40 hours a week. They may spend months or even years trying to make some breakthrough in their research. • Good communication skills. As researchers disseminate their results via manuscripts or papers, it is extremely important that they learn to write well. They must be a good “story teller”: knowing their audi- ence (readers) and convincing others quickly to believe in their story (accepting their papers). They must also be able to present their ideas clearly and convincingly in conferences. University professors usually need to teach courses so they must learn to be good instructors, and love teaching classes. What we list above are crucial traits and skills for researchers; other positive per- sonal traits and abilities are also important. You can ask yourself if you are suitable to be a researcher by comparing your personality and strengths with the list above. Note that, however, most of the required abilities and skills can be learned and improved, and one weak ability may be compensated by other stronger ones. For example, if you are not very strong in mathematical theory, you can choose a thesis topic on applied or experimental research. 10 CRAFtING YouR ReSeARCh FutuRe 1.5 whAt ARe SoMe PRoS ANd CoNS oF beING ReSeARCheRS? Here is a list of “Pros” of being researchers. It reflects our personal views. • high career satisfaction. Researchers have more freedom in choosing what interests them the most to work on than many other forms of employment. University professors also have flexible working hours in their university office, and have summer months in which they can focus on research, and travel for conferences and research visits. It is also highly rewarding when researchers make new discoveries and breakthroughs, which benefit people and are recognized by their peers. • Protected research environment. Researchers, especially university professors, have a relatively stable and protected position for research. These positions are usually not much affected by the short-term economic downturns and by the opinions of politicians. To protect academic freedom and give researchers time to produce high-impact results, most universities have a “tenure” system—tenured professors cannot be fired easily when they dissent from prevailing opinion, openly disagree with authorities of any sort, or spend time on unfash- ionable topics’ (Wikipedia), or if their research ‘quantity’ fluctuates due long-term research. Publishing a few high-impact papers is often better than publishing more low-impact ones. • Reasonably good income. Researchers usually have a Ph.D. degree, and their entry salary is often much higher than those with Master’s or Bachelor’s degrees. In addition, researchers’ salary is also quite stable; there is usually no “bonus” or “penalty” if they accomplish a lot or a bit less for Tasks 1–10 in a particular year. This can be regarded as a disincentive, we suppose, as salespersons can earn more money if they sell more products. However, professors can earn an extra income if they hold secondary consulting or business positions, or if they are successful in technology transfer (Task 11). bASICS oF ReSeARCh 11 • Researchers are highly respected by most societies. In 1999 an A&E Biography program selected the 100 most influential persons of the last millennium (from the year 1000 to 2000). Among the top ten most influential persons, five are scientists; they are Galileo (#10), Copernicus (#9), Einstein (#8), Darwin (#4), and Newton (#2). They are highly respected by people. They are also the ultimate role models for young researchers. In addition, we have many other giants to look up to: from Nobel Laureates (such as Richard Feynman), to winners of the Turing Award (the highest distinction in the computer field) and John Fritz Medal (referred to as the highest award in the engineering). Some possible “Cons” of being researchers are: • Researchers often work more than 8 hours a day and 40 hours a week to stay competitive. The amount of work needed for doing Tasks 1 to 11 well can be daunting and intimidating. However, most researchers are highly effective, and they learn to manage time well. In addition, research is a career, not just a “job.” Often researchers are intrigued by research questions, and enjoy thinking about them when they have extra time. They are also thrilled when a breakthrough is made. • Long preparation time. To become a researcher, one usually needs to study at a university for one’s Bachelor’s, Master’s, and Ph.D. degrees. Sometimes they need to take a few years of post-doctoral positions after their Ph.D., before a more stable position is secured. However, Ph.D. candidates and post-doctoral fellows are partially researchers. They usually receive a small to moderate income during that time. • Relatively narrow career choice. Depending on the economy and available funding, in some years the number of job openings for post-doctoral fellows and professors in universities and research- ers in companies can be limited. In addition, the number of Ph.D. students graduating in the last few decades is increasing. Thus, the 12 CRAFtING YouR ReSeARCh FutuRe competition for new positions for professors and researchers can be very high. Also, after you get a Ph.D. degree, you may be “overly qualified” for jobs for Master’s (or Bachelor’s) degrees. However, the economy goes in cycles, and there are many other career choices for researchers, including entrepreneurship (start-ups). When you choose research topics, you must also think carefully what type of jobs (e.g., professors, researchers in companies, etc.) you want to take in the fu- ture. We will discuss how to select research topics in Chapter 3. 1.6 So, how do I beCoMe A ReSeARCheR? Most researchers learn to do research during their Ph.D. study in a reputable uni- versity, supervised by a university professor. To be accepted in a Ph.D. program, you normally need to have Master’s and Bachelor’s degrees in the same or similar areas. If you study for your Master’s and Ph.D. degrees under the same supervisor, usually the combined duration would be shorter than when you work under dif- ferent supervisors. 1.7 whAt ARe the dIFFeReNCeS betweeN A MASteR’S ANd Ph.d. theSIS? First of all, many universities do not require all Master’s students to write a Master’s thesis; often you can get the same Master’s degree by the “course op- tion”—taking a large number of graduate-level courses. But if you want to get a taste of doing research, or if you plan to pursue Ph.D. after your Master’s study, then taking the “thesis option” is advised. As for the differences between Master’s and Ph.D. theses, it is difficult to draw the line precisely. It certainly does not depend on the length of the thesis! Some folk legend says that the shortest Ph.D. thesis is 14 pages long, but the longest is over 1,000 pages. Both Master’s and Ph.D. theses require novel and sig- nificant contributions, but such requirements for a Ph.D. thesis are much higher. Occasionally there is a debate and discussion among thesis examiners if a thesis being examined should really belong to the other category! bASICS oF ReSeARCh 13 One intuitive and approximate way to distinguish between these two types of theses is that the work in a Ph.D. thesis should be publishable or already pub- lished in several top journals and conferences in the field. A Master’s thesis, on the other hand, may only be publishable or already published in 1-2 medium competi- tive journals or conferences in the field. Several typical differences between Master’s and Ph.D. theses and students are outlined below: • A Master’s thesis can apply previous work to a new problem or ap- plication; a Ph.D. thesis normally contains significantly new theory, methods, and applications. • A Master’s thesis can make small, incremental improvements from previous work; a Ph.D. thesis usually presents and studies a new topic in the field, and makes much larger contributions. • A Master’s thesis can be a critical survey of existing works, often with additional comparison of these works theoretically or empirically; a Ph.D. thesis must present some new methods, and compare them with previous works convincingly either by theory or experiments. • A Master’s thesis can report negative results of a seemingly promising approach, and analyze why it does not work; a Ph.D. thesis should contain positive results in addition to analysis of the negative results. • If one graduates with a Master’s degree, he or she may not yet learn to become an independent researcher; his or her job is usually not doing full-time research. A Ph.D. graduate, on the other hand, should be an independent researcher, and can compete for and take a university professor job directly. Again, the distinction is vague, and varies among different fields and disci- plines, universities, and countries. Though this book is written mainly for Ph.D. candidates in Science and Engineering, it applies to Master’s candidates as well with smaller requirements. 14 CRAFtING YouR ReSeARCh FutuRe We will indicate special aspects for Master’s candidates in appropriate places in this book. 1.8 how to FINd A SuItAbLe SuPeRvISoR FoR Ph.d. StudY Different departments and universities have different ways of pairing graduate students with supervisors. Choosing an appropriate supervisor for Ph.D. study is crucial, as you may be “stuck” with him or her for the next 3–5 years. This is also important but less critical for Master’s students as they usually work with their supervisors for 1–2 years. If you and your supervisor do not have a good working relationship in these years, disagreement, tension, and occasionally, hardship and conflict will arise. In general, the following factors should be taken into consideration when choosing your supervisors: • Research areas and interests. The number one most important factor is whether or not your research passion and interests match well with your supervisor or not. Nowadays professors’ profiles, research areas, and publications are usually posted online. We recommend that you go through the department’s website of the school that you are applying to carefully, and spend time studying potential supervisors’ research and publications. You can also write to the potential supervisors, with some intriguing questions about their research, and ask them if they are willing to supervise you. You should mention your research inter- ests and professors you wish to be your supervisors in the application materials. If a professor agrees to supervise you, the chance of being accepted is much higher, given that you satisfy the basic requirements for the university and department that you are applying. Some depart- ments let students choose supervisors one year after they are admitted. This would give you ample time to take courses offered by various professors and talk to them before you choose a supervisor. • Supervisory philosophy and style. This is almost as important as bASICS oF ReSeARCh 15 research areas and interests mentioned above. Two orthogonal dimen- sions can be considered: the amount of pressure and guidance. Some professors are very demanding, which may not be bad for you if you need some pressure to excel, while others are relaxed, so you work at your pace. On the other hand, some professors give their graduate students a lot of guidance, such as what research problems to work on, how to write papers, while others give them a lot of freedom; you may need to figure out a lot of things, including thesis topics, by yourself. Does a potential supervisor’s style of supervision match your personal- ity and working habit? It is important to find this out before settling down with a supervisor. Bring Figure 1.1 to your potential supervisor, and see where he or she stands. • Funding availability. This is also a practical issue to consider. Though the stipend for Ph.D. candidates is usually quite small to live lavishly, you need to be able to live healthily without the need to work eight hours a day in restaurants to make ends meet. Some professors’ fund- FIGuRe 1.1: Two dimensions of the supervisory style: the amount of pressure vs. guidance. 16 CRAFtING YouR ReSeARCh FutuRe ing can last beyond the usual period, e.g., four years in many universi- ties. Some will last only one or two years. Some professors can fund your conference trip if your paper is accepted, while others may not. • Academic and industrial social networks. It is often said that one is in some ways defined by his or her friends. This is very true for gradu- ate studies and even research careers. Remember that when you join a supervisor’s research group, you enter a social network, consisting of all of your supervisor’s former students, advisors, current colleagues, contacts and current and future students. These people will be there to help you succeed. This means that you will be able to talk to them eas- ily about new ideas, references, and job possibilities during and after your Ph.D. study. You might leverage on their social networks as well, thus expanding your views, support, and career opportunities. • track record. It is extremely important for you to do background study to see the academic standing of your potential supervisors in their respective field of research. Today this is easy to do by check- ing on the publications and their citations in search services such as Google Scholar. It also helps to talk to former and current graduate students of the potential supervisors for the issues discussed above. It is also a good idea to read publications of graduate students under supervision of potential supervisors. 1.9 how LoNG doeS It tAke to Get MY Ph.d. deGRee? We often hear students asking: “How long do we need to take before I can gradu- ate with a Ph.D. degree?” Well, to us, the student is asking the wrong question. To begin with, we must make clear what a Ph.D. degree entails (for more details, also see the next chapter: “Goals of Ph.D. Research”). Getting a Ph.D. degree means that you are to learn to view the world in a different way, to be able to identify a new and chal- bASICS oF ReSeARCh 17 lenging problem on your own, and to solve the problem via a new methodology. It also means that you can claim to the world that you are an expert in one impor- tant, albeit narrow field, where others can consider you a leader in this field. One practical criterion is to go to conferences or workshops, where if you find people looking for you because they want to talk to the foremost experts in this field, you know you are ready to graduate, since you have crossed the line to being an expert in your chosen field. Likewise, if you find your work starting to be cited by peers, it is a good sign that you are ready to get your Ph.D. degree, and be called a “Dr”! Thus, the answer to your question (“how long does it take for me to gradu- ate”) is “it depends on you!” Unlike undergraduate study, which usually has a fixed length, Ph.D. study can last from 3 years to 10 years. It all depends on how effectively you accomplish Tasks 1-3 mentioned earlier in this chapter, how you select a suitable Ph.D. topic, and how well you work with your supervisor. This book will provide you with useful guidelines and effective methods of obtaining a Ph.D. in relatively short time. Most of our Ph.D. candidates get their degree in 3 to 5 years. 1.10 thRee RePReSeNtAtIve GRAduAte StudeNtS Throughout this book, we will use three fictitious Ph.D. students as examples. They represent three general types of Ph.D. students, and are based on several past Ph.D. candidates under our supervision. Student A is a Ph.D. candidate whose strength is academic research and whose career dream is a professorship in a university in the US or Canada. He published a good number of papers in competitive conferences and reputable jour- nals, and got his Ph.D. in 4 years. He then became a post-doctoral fellow for two years to deepen his research. He is now a tenure-track assistant professor in a US university. Through the book we will see how he started, how he chose and tried a few different research topics before settling down on his Ph.D. topic, how he did his research, and how he published many papers. 18 CRAFtING YouR ReSeARCh FutuRe Student B is a Ph.D. candidate whose strength is empirical research. He wants to work in a research lab in a company. He has written several conference papers and one journal paper related to the topic of his thesis, but more impor- tantly, he has participated in an international competition, and got into the top-3 in a well-known large-scale experimental contest based on real-world data. Student C is a Ph.D. candidate whose strength is engineering and industrial applications, as well as commercializing his ideas. His research is more applica- tion oriented, and his aim is to build some novel and useful systems in the future and start a venture to commercialize his ideas. He developed a novel experimental system to offer sufficient value over the current state of the art and business. Thus, he has successfully filed a patent and published a few news articles on his technol- ogy. He also published a few conference papers. He builds a startup business after graduation. To cover a whole spectrum of graduate students in our book, we refer to these types of students as Student A, Student B, and Student C, respectively, where they correspond to the three different approaches to Ph.D. study: Student A for an academic and fundamental research type, Student B for an empirical- research type, and Student C for an application and entrepreneurial type. Later in the book, we will use Student A1, Student A2, Student B1, and so on, to describe specific instances of various student types to highlight some specific details. In such cases, Students A1 and A2 are two examples of type-A students. • • • • 19 C H A P T ER 2 Goals of Ph.d. Research Before we describe in detail how to get a Ph.D., we want to first discuss the ul- timate goals of Ph.D. research in this chapter, so that you “begin with the end in mind” for your Ph.D. study. 2.1 GoAL #1: be the beSt IN the FIeLd The number one goal of your Ph.D. study is that, in an important, albeit narrow field (i.e., your thesis topic), your research is the best in the world (in terms of novelty and significance) at the time when you complete your thesis, and you are among the very few best experts in that topic. We can use a very simple figure to illustrate this, as in Figure 2.1. The x-axis represents a certain domain, such as artificial intelligence or water purification. The y-axis is the expertise of knowledge in that domain. A horizontal line in the figure represents the current best knowledge, which is also called the frontier or the state-of-the-art of research. Assume that you will get your Ph.D. in four years. Your yearly research progress is depicted in the figure. Note that this overly simpli- fied diagram is for illustration purpose only. Near the end of your Ph.D. study (say, the third and fourth years), you should produce research that advances the current best knowledge (so that the “best line” will be raised a bit due to your work). The height of your knowledge curve above the “best line” is roughly the novelty of your work; the width is roughly the significance or impact. You should establish yourself in this important (albeit narrow) field. In other words, you should “own” an area. How do you prove that you are ready to establish yourself in your field? A typical way is publishing a 20 CRAFtING YouR ReSeARCh FutuRe FIGuRe 2.1: Progress in four years of Ph.D. study. series of high quality papers in top-ranked conferences and journals in your Ph.D. area (Chapter 5 and Chapter 6), and successfully write up and defend your Ph.D. thesis (often a nerve-racking process; see Chapter 8). Student A1, for example, researched in the area of machine learning, an area in Artificial Intelligence (which is an exciting research area that explores what makes us intelligent and how to make machines intelligent as well). He published over 10 top journals and conference papers, and finished his Ph.D. thesis in 4 years. Student B1 published 5 top-ranked conference and journal papers in 4 years, and finished a system that implements the ideas in these papers. Student C1, on the other hand, finished 3 papers in conferences, but also filed one patent successfully. He graduated with a venture-capital company’s offer to start up a new business. Early in your Ph.D. study (e.g., first year), you can explore various topics that interest you (the several small peaks in Figure 2.1). But soon you should focus (one peak), and try to conduct research in one topic in great depth. Examples of a thesis topic can be cost-sensitive learning with data acquisition (Student A1’s topic, an area of research in machine learning), active-learning and user interface GoALS oF Phd ReSeARCh 21 design for Student B1 (another area of research in computer science), and a new method for harnessing crowdsourcing power (an area of computer and social sciences where computer and human problem solvers work together to tackle a difficult problem, such as language translation) and for Student C1, turn it into a well-formed business model. Chapter 3 and Chapter 4 will discuss this crucial step of selecting Ph.D. topics in more detail. During the four years of your Ph.D. study, you are putting in efforts to literally “push up” your knowledge curves as shown in Figure 2.1. The Area under Curve (AUC), as shown in the figure, is the area between each curve (such as your knowledge curve for year 4) and the x-axis. The value of the AUC roughly represents your effort. This value is cumulative, and should be steadily increasing during the years of your Ph.D. study. If you do not put in sufficiently large effort, it is impossible to advance the frontier of the research. In Chapter 1 we emphasize that researchers must be diligent. You do not need, and often it is impossible to be highly knowledgeable in all topics in a field. However, you do need to be so in areas related to your Ph.D. topics. The shape of the knowledge curves in Figure 2.1 illustrates this. For ex- ample, Student A1’s topic is cost-sensitive learning. He is also very knowledgeable on this topic (a form of supervised learning), but less so on other areas of Artificial Intelligence, such as unsupervised learning. If you are a Master’s student in the thesis option, it usually takes two years for you to finish your thesis. The situation is similar to the first two years in Ph.D. study, with two exceptions: In your first year you often have less chance to explore several topics deeply. You and your supervisor would quickly decide a research topic together, and you would quickly make some novel contributions (your Master’s thesis) in a narrow field in the second year. Figure 2.2 (a) depicts this situation. You may conduct a critical review of several related topics, or write a com- prehensive survey of a recent topic. You provide new insights and draw new rela- tions in one or several broad areas. Figure 2.2 (b) illustrates this situation. See 22 CRAFtING YouR ReSeARCh FutuRe FIGuRe 2.2: Progress in two years of Master’s study. Chapter 1 for more discussions on the differences between Master’s and Ph.D. theses. There are several common situations where Ph.D. candidates do not keep this goal in mind, and may have a hard time, or take many more years to finish their Ph.D. theses. We will discuss them briefly below. In the first situation, they spend most of their Ph.D. study exploring differ- ent topics in the field. They may put in a huge amount of effort over four years (high AUC), but they do not have a focus, and do little in advancing the state- of-the-art in any topics they explore. They essentially accomplish several Master’s theses. But Master’s theses in different topics usually cannot be equal to one Ph.D. thesis. Figure 2.3 depicts this situation. In the second situation, they explore several different topics, and they man- age to make minor contributions and publish a few minor papers in those topics. In this case, they have published on many topics (which may also earn them many Master’s theses), but they do not establish themselves in one. They do not “own” an area, and other researchers do not remember what they have done. Their Ph.D. theses jump between several different topics, and they may have trouble passing the thesis defense. Figure 2.4 depicts this situation. Again, your efforts should have a focus. Instead of publishing three papers on three different topics, it is much better to publish three papers on one topic, GoALS oF Phd ReSeARCh 23 FIGuRe 2.3: What to avoid in a Ph.D. study: cover many areas shallowly. making novel and significant contributions in that area (as in Figure 2.1). By the end of the Ph.D. study, you should “own” an area, so that people will turn to you for advice or for reviewing papers in that area. A few exceptionally strong and productive Ph.D. candidates do manage to advance research in more than one area, but their Ph.D. thesis usually only consists of published papers in one area. A Ph.D. thesis should be coherent, and focus on one (relatively broad) topic. For example, Student A1 in his early research explored the area of co-training, and published papers in a couple of top confer- ences. But then he found that it was not easy to select a Ph.D. thesis topic. After many brainstorm meetings (see Chapter 3), he changed his area to cost-sensitive learning with data acquisition, a less-studied but important new area of cost-sen- sitive learning. He worked very hard, and published several top-rated papers on this new topic in the next 2.5 years, and established himself well in this area. At the end of his four-year Ph.D. study, he successfully defended his Ph.D. thesis on 24 CRAFtING YouR ReSeARCh FutuRe FIGuRe 2.4: What to avoid in a Ph.D. study: publishing in several topics but not well established in any one of the topic areas. cost-sensitive learning with data acquisition. The thesis does not include his early published work on co-training. Of course, when you become a university professor after your Ph.D., you can develop several strong research areas, working with Ph.D. candidates who have different interests. It is usually quite difficult for a Ph.D. candidate to do so in a short amount of time (3–5 years). In the third situation, some Ph.D. candidates are keen to find some research topics that can be advanced with little effort (low AUC). They wish they could just focus on a very narrow problem. Figure 2.5 illustrates this situation. This may only be possible if it is an easy and quick extension of your supervisor’s (or previous Ph.D. candidate’s) work. But in this case, you are not learning to be an independent researcher (see Section 2.2), your contribution is usually minor, and you do not own the area. Thus, for Ph.D. research, the situation in Figure 2.5 is GoALS oF Phd ReSeARCh 25 FIGuRe 2.5: An impossible situation in Ph.D. study. impossible. There is no shortcut in producing highly novel and significant work with little effort, or without knowing related areas. Your supervisor may have a good vision on which research topics and prob- lems are promising to work on as your Ph.D. topic. But your passion, interests, and technical strengths are crucial in Ph.D. topic selection. Chapter 3 and Chapter 4 will explain this in great detail. 2.2 GoAL #2: be INdePeNdeNt The number two goal of your Ph.D. study is to learn to become an independent researcher so that you can do tasks listed in Chapter 1, especially Tasks 1–3 (briefly, find new ideas, do solid research, and publish top papers), well by yourself. This is simply because after you earn your Ph.D. degree, you may be employed in a research-oriented university, and suddenly, you have no research supervisors! You must do everything (Tasks 1–11) by yourself. Being independent also means that 26 CRAFtING YouR ReSeARCh FutuRe FIGuRe 2.6: The “independence curve” for a Ph.D. student. you become an independent thinker—you have your own academic viewpoints and you can back them up with your research. We will use another simple figure to illustrate your learning curve of becom- ing independent. This time the x-axis is the years you spend in the Ph.D. program, and y-axis is the level of independence. It would be good if your independence curve increases linearly with the year, and better if it grows exponentially. See Figure 2.6 for illustration. To be highly independent, you need to develop quickly those skills and abilities crucial for researchers discussed in Chapter 1. For all of the three example Ph.D. candidates we described in Chapter 1, they became independent quickly in 4–5 years of their Ph.D. study. More specifi- cally, in the first two years, we (i.e. supervisors) usually held daily or weekly meetings with them discussing new ideas, methods, and experimental results in detail. We also spent a great effort training them to write well their first papers (see Chapter 5). In the later years, we usually met weekly, or whenever needed, to discuss ideas, approaches, and results at high-level. They can extend and modify the ideas, design and modify experimental settings, and write up the paper drafts, mostly by themselves. They have also learned to review papers and write parts of grant proposals. Some of them have also taught courses, and helped supervise Master’s students. GoALS oF Phd ReSeARCh 27 2.3 thRee keY tASkS FoR GettING A Ph.d. (ANd MASteR’S) deGRee As we discussed in Chapter 1, as a Ph.D. candidate, your key tasks are Tasks 1–3. We will refer to them briefly as: “find new ideas,” “do solid research,” and “publish top papers,” respectively. It is unlikely that you can get a Ph.D. by doing Task 1, then Task 2, and then Task 3 in a sequence only once. Instead, it is an iterative process. There are also often interactions among Tasks 1, 2, and 3. Through several iterations, you broaden and deepen your Ph.D. topic by building up enough re- search results and publishing enough papers. In this case your Ph.D. thesis would simply be a “recompilation” or integration of the published papers (more about this in Chapters 5–7). Figure 2.7 illustrates this process. As mentioned earlier, a good rule of thumb is that you have published a good number of papers in reputable journals and conferences based on your Ph.D. topic. In the following four chapters (Chapters 3–6) we will describe strategies for accomplishing these three key tasks effectively. Chapter 7 will provide you with guidelines on how to write your Ph.D. thesis, and successfully defend it. Note that although your main job as a Ph.D. candidate is Tasks 1–3, often you also work with your supervisor on all other tasks described in Chapter 1. By the end of your Ph.D. study (hopefully within 3–5 years), you should have made FIGuRe 2.7: An iterative process of three key steps in getting your thesis. 28 CRAFtING YouR ReSeARCh FutuRe significant contributions in your Ph.D. thesis, and established yourself as a young, independent, and competent researcher! If you are a Master’s student, however, you usually only need to go through one, or at most two, iterations of Tasks 1–3, after you take the required courses. You should try to publish 1–2 medium competitive conference papers, which should constitute the main body of your Master’s thesis. There is also usually a de- fense process, but the requirement of novelty and significance in Master’s thesis is usually much less than a Ph.D. thesis. Thus, this book is also suitable for Master’s students—the basic processes and strategies are the same. 2.4 the MILeStoNeS oF GettING A Ph.d. deGRee After discussing the three key tasks in getting a Ph.D. degree, we will describe a series of milestones in 4–5 years of your Ph.D. study. They are: • • • • Complete all course credits (one to two years). Pass a written or oral Ph.D. qualifying exam (~2nd Year). Pass a written or oral Ph.D. proposal defense (~3rd–4th year). Pass the final Ph.D. thesis defense (~4th–5th year). A typical graduate school requires a Ph.D. student to complete between five to seven graduate-level courses. For students transferred from other departments and disciplines, they often have to make up some core undergraduate courses that may range from one to three. For example, a Physics student transferring to Computer Science may be required to take Data Structures and Algorithm Design, Theory of Computation, and Operating Systems. All the course works are expected to be finished in roughly one to two years. To prepare yourself for the research, you should try to select the courses that fall within or are closely related to the research area that you are interested in. This is also the time to get your feet wet in the research world. See Section 3.1 for more details. Many universities require Ph.D. students to take an exam known as the Ph.D. qualifying exam. It can be oral, written, or both. The purpose is to make sure that Ph.D. students have sufficient background knowledge to start and con- GoALS oF Phd ReSeARCh 29 duct research. Research life truly starts when you finish the Ph.D. qualifying exam. By this time the student is usually in a celebratory mode, joining parties and sleeping late, mindful that the courses and exam days are finally over, for life! This period in your graduate life may be intoxicating. The problem is that many graduate students may also never wake up from this period. A real challenge for Ph.D. students is that what lies ahead is truly critical, and it is highly advised that the student be prepared for it. The next milestone is the thesis proposal defense. Ph.D. students need to find a thesis topic (see Chapter 3 and Chapter 4), conduct a comprehensive survey of existing works, find a new and exciting problem, and propose solutions to it. In the thesis proposal, the student is asked to lay out the problem to be tackled, all previous approaches in solving the problem, a detailed discussion of their merits and weaknesses, and the student’s particular plan for tackling the problem. The defense is usually oral, in front of a small committee often consisting of faculty members of the same department. Then you must conduct solid research to prove (or disprove) the proposed solutions, often after many revisions along the way. This task turns out to be more difficult and challenging than most people would think, because it is typi- cally loosely structured, and requires methodical and personal organization and perseverance to handle it well. Again refer to Chapter 3 and Chapter 4 on how to find a good research topic, including Gray’s Criteria and the Matrix Method for finding ideas. It is not atypical for a student to try different ideas to see how they pan out, each followed by a conference or journal article. Refer to Chapter 5 and Chapter 6 for paper writing. These activities are basically the iteration of the three key tasks (find new ideas, do solid research, publish top papers) mentioned earlier in this chapter. After you publish a good number of journal and conference papers on the thesis topic, with your supervisor’s approval, you can prepare your Ph.D. thesis and 30 CRAFtING YouR ReSeARCh FutuRe the final defense. Chapter 7 provides a lot of detailed guidelines in writing and defending your thesis successfully. In addition to accomplishing those milestones, Ph.D. students in most uni- versities also need to spend 10–20 hours per week in a teaching assistant (TA) job. 2.5 dIStRACtIoNS to the GoALS Sometimes Ph.D. candidates are distracted during their Ph.D. studies to achieve the two major goals of Ph.D. research effectively. Many Ph.D. students come from countries whose mother tongue is not English, or whose culture is very different from the country they are enrolled in the graduate study. They may have a language barrier, culture shock, homesick- ness, and other circumstances (as we did when we first came to the US to study over 25 years ago). Making friends of various cultural backgrounds and quick learning and adaption are important and helpful in minimizing distractions and focusing on your Ph.D. research quickly. If you are not fluent in spoken English (assuming English is used in lectures and paper writing), preparing the lecture materials before lectures is very effective in helping your learn the English lan- guage and describe things clearly. Chapter 5 will discuss how to write papers well in English, or any other languages. In a typical university, a graduate student often works as a Teaching Assistant (TA) to help fund the study. This is like a “real” job in which graduate students are required to perform 10–20 hours in running tutorials, marking as- signment and exam papers and holding office hours each week for undergraduate courses. TA work is important and should be accomplished well since besides pro- viding funding for your study, it also gives you an opportunity to learn to present yourself well (to students in the class or to individual students). This can be very useful especially if you want to become a professor in the future. This also presents a challenge because now you have to learn to balance different parts of a gradu- ate-student life: teaching and researching, among others. Students should learn to GoALS oF Phd ReSeARCh 31 perform their TA duties effectively, and ensure a sufficient amount of time to be reserved for research. This need to balance one’s life is the same if one has to raise a family, learn how to drive, travel for fun, participate in sports and social activi- ties, and generally, enjoy one’s life. Indeed, you need to have a life, or as people say, “work hard, play hard.” Even with a high demand in research, Ph.D. students (and faculty mem- bers) must find time to do physical exercise to keep themselves fit and healthy. This also improves the efficiency of their brains. In one word, being healthy and staying highly effective in research work and living a good life is the key to achiev- ing the two goals (that is, being the best in your field and being independent) of Ph.D. study successfully in 3–5 years. Some Ph.D. candidates do work hard, and enjoy doing research, to the point that they do not care how long it takes to get a Ph.D.. They enjoy the Ph.D. pro- gram even if it takes more than 8 years. Often the funding from the supervisor and university runs out, and they have to teach many courses to make a living (another distraction). Remember, Ph.D. study is a training process to establish yourself in some area and become a researcher. This can usually be done in 4–5 years, if you follow the guidelines in this book. Then you should defend your Ph.D. thesis, and try to become a full-time researcher, such as university professors, researchers in companies, and be successful. • • • • C H A P T ER 3 33 Getting Started: Finding New Ideas and organizing Your Plans Let us start from the very beginning of the journey: the first year of your Ph.D. study when you will probably take graduate courses, and maybe a comprehensive exam (or Ph.D. qualification exam). We will focus on issues related to your re- search, and show you how to start doing research in the first and second years. 3.1 YouR FIRSt YeAR You should begin your Ph.D. (and Master’s) study by taking several broad, graduate-level courses that are related to your future research, especially courses taught by your supervisor. For example, if your research direction is machine learning, then courses such as Machine Learning, Data Mining, and Statistical Learning are highly relevant. If you are willing to pursue a career as an engineer, then you should probably want to take some fundamental engineering courses, including supporting courses such as statistics and probability, computer software tools such as R or MATLAB, and engineering design courses. In addition, you can read by yourself other broad, graduate-level textbooks and take online video courses (there are many good ones) in the field. This will prepare you to have enough basic knowledge for the research in the field. We use a simple figure to il- lustrate this, as in Figure 3.1. Step A in the figure shows that, after taking courses and reading textbooks, you now have a broad knowledge about the field. While you are taking graduate courses and reading textbooks, you may find certain topics (such as semi-supervised learning, clustering) fascinating and inter- esting. Explore them further by: 34 CRAFtING YouR ReSeARCh FutuRe FIGuRe 3.1: Progress in the first year: taking courses (Step A), and then exploring a few areas (Step B). • • • • • • talking to your supervisors, who may suggest to you certain papers to read, or certain promising directions to explore further; trying to find recent survey papers on these topics; paying attention to invited speeches, special issues of the journals on these topics; trying to go to a conference or two, even low-impact ones that are nearby (and cheap). Talk to researchers, ask them their opinions on the research areas you are interested in, and listen to their paper pre- sentations on what sorts of problems they work on, and how difficult they are. A good paper does not have to win a Nobel Prize to be good. finding recent and high-impact research papers (see Section 3.2) and read them critically and creatively (see Section 3.3). writing a survey or review paper in the topic area you are interested. GettING StARted: New IdeAS ANd oRGANIzING PLANS 35 By the end of your first year, and early in the second year, you should have studied a few potential research topics and areas more deeply. Step B in Fig- ure 3.1 illustrates your knowledge curve with a few peaks (the same as the first- year knowledge curve in Figure 2.1). 3.2 how to FINd ReLevANt PAPeRS (LIteRAtuRe SeARCh) With the Internet, Google Scholar,1 Arnetminer,2 Microsoft’s Academic Search,3 and other search engines for scholarly publications (such as elsevier’s Scirus and CiteseerX 4 ), and publishers’ digital libraries to which many universities subscribe, searching and downloading papers is often a few clicks away (OK, maybe more than a few clicks). The question is: how to find recent and high-impact papers? The process of finding out previous published work is often called literature search. The following are some guidelines: • Usually, highly reputable journals and conferences review and select papers very rigorously. Thus, papers published there are usually more novel and significant. Your supervisor should know well the reputable journals and conferences in the area, and after you work in the area for a while, you will too. • One way to judge the reputation of a journal is to look up its impact factor. The impact factor (IF) of a journal is roughly the average num- ber of citations an average paper published in the journal receives in the preceding two years. For example, if a journal has an impact factor of 10, it means that on ave rage, in the past two years, each paper in the journal received roughly 10 citations from other papers published in journals belonging to a reasonably high-quality pool. This pool of journals, known as the Science Citation Index or SCI, is maintained 1 http://www.scholar.google.com 2 http://www.arnetminer.org/ 3 http://academic.research.microsoft.com/ 4 http://citeseer.ist.psu.edu/ 36 CRAFtING YouR ReSeARCh FutuRe by an organization called the Institute for Scientific Information (ISI). • • Papers published by senior and well-established researchers often have high impact. Use scholarly search engines (mentioned earlier) and search for papers with relevant keywords directly. Those search engines often return a ranked list, combining publication date (novelty), citation counts (impact), and so on together. However, they often do not reveal their ranking algorithms, so you should try different filters, and with several different scholarly search engines. Figure 3.2 shows an example of searching for the topic of “hierarchical classification” in Google Scholar. It returns a ranked list of papers based on an unknown ranking algorithm, but it seems heavily based on citation counts. We can see that the first few papers were published over 10 years ago, with hundreds FIGuRe 3.2: An example of searching for a topic with Google Scholar. GettING StARted: New IdeAS ANd oRGANIzING PLANS 37 of citations (results in Figure 3.2 were obtained on June 9, 2011). But how to find recent papers which often have few or no citations? Google Scholar offers several useful filters, especial the time filter, with “anytime” as default. You can change the time to be “since 2010,” for example, and it returns a ranked list of papers since 2010. After you find some recent and high-impact papers, read them. You can then search again with different keywords used in those papers. For example, “text categorization,” “taxonomy learning,” and “faceted browsing” are different terms for “hierarchical classification.” You can also use the “Cited by” feature of Google Scholar, and find all papers that have cited a paper. Pretty soon you will find tens or hundreds of papers on the topic that you are interested in. How can you read all of these papers, many of which can be quite challeng- ing to read? 3.3 how to ReAd PAPeRS You might ask: who does not know how to read papers? Just read them like reading textbooks! Indeed, most of us read tons of textbooks. Well, there is a fundamental difference between reading well-explained textbooks and reading research papers. You read textbooks mainly for understanding and learning, expecting all details are worked out and “fed” to you, whereas when you read research papers, you are expected to develop your own research ideas and questions to surpass their authors! Another simple way to see the difference is that you read textbooks for receiving existing knowledge, while you read research papers for outputting new knowledge. Clearly, the objectives of these types of reading are entirely different. We often see new Ph.D. (and Master’s) students take two “bad” approaches in reading research papers. The first bad approach is to spend too much time reading the paper very carefully and trying to understand every detail of it, as they read textbooks. Some new Ph.D. students spend days reading one 10-page confer- ence paper, and come to ask us, “how is this done exactly?” We sometimes receive emails asking us implementation details of our published papers. (However, if 38 CRAFtING YouR ReSeARCh FutuRe other researchers are trying to replicate our published work, we will try our best to reply to them.) The right approach is to quickly understand the problems, assumptions, main ideas and the proposed solutions presented in the paper at a high-level. You will then spend more time to analyze the paper critically, find new ideas, and con- duct research to surpass the previous papers. More specifically, you should probably spend 30% (or less) of the time reading and understanding the paper’s main idea and solutions. This amounts to perhaps 1–2 hours to read a 10-page conference paper. How can you read quickly to understand the main idea of a paper, which can be quite technical? Well, the structure of the paper, if well written, should already give you a hint as to which parts are important to read. A research paper usually consists of an abstract and the body of the paper, which is divided into sections with section headings. Each section may have subsections, and then subsubsections, and so on (we will discuss the paper structure more in Chapter 6). A well-written paper should be structured in a top-down fashion; that is, the high-level ideas and solutions should be de- scribed in high-level (sub)sections. Thus, when we read papers, we should focus on high-level (sub)sections, and skim over low-level ones which usually contain technical details. Figure 3.3 illustrates a hypothetical paper and its associated structure. Quite often you only need to read the Abstract and Introduction sections quickly (say 15 minutes) to determine whether the paper addresses your thesis topic. If not, there is no need to read it further. If yes, you would continue to read the main frame- work of the proposed algorithms, main results of experimental comparison, and conclusions. We use red boxes to denote the high-level sections you would read more carefully. The parts marked with the yellow boxes may be quickly skimmed. The parts without the boxes may be omitted in the initial reading. This helps us to read a research paper quickly for the main ideas, problems, and solutions at the high level. GettING StARted: New IdeAS ANd oRGANIzING PLANS 39 FIGuRe 3.3: Structure of the hypothetical paper. We suggest you read the high-level sections (red box) more carefully, skim the lower-level sections (yellow box), and omit technical details (unboxed). Understanding how a paper should be structured and written will also help you learn to write your papers this way in the future. We will focus on how to write powerful and easy-to-follow papers in Chapters 5 and 6. While you spend 30% (or less) of your effort reading and understanding the paper, you should spend 70% (or more) effort thinking creatively and critically: • Critical thinking. What is wrong with the paper? Are the assump- tions reasonable? Is the problem ill-posed? Does the solution have any technical flaws? Student A1 read some papers on co-training (an area in machine learning) when he took our graduate course. He implemented some popular co-training algorithms, and tested them on some real-world datasets. He found that the results were not as good as reported in the published papers. This led us (Student A1 and his supervisor) to 40 CRAFtING YouR ReSeARCh FutuRe question: does co-training really work that well? In what situations does it work well, or not so well? After further research, we wrote and published papers in some top conferences and journals in the field. If he did not challenge the previously established views, there would not be these research outcomes. • Creative thinking. What else can be used to solve the same or broader problem? How can I do it differently, and better? It is extremely important that you form a habit of thinking critically and cre- atively from now on for whatever you read (even newspapers and magazines) or watch (TV or movies). We always think of “plot holes” when we watch movies (critical thinking), and discuss how to make the movies better (creative thinking)! One of the authors (Ling) also works in child education. One fascinating think- ing game he often plays with kids is to read a new story to them or watch a new movie with them. He stops many times during the process and asks kids: what is wrong with the story? How would you continue? How can you make it better? It is crucial to develop a curious, creative, and critical mind, as this is one of the important abilities for doing research (see Chapter 1). Even when you read a paper published 10 years ago, you could still try to think critically and creatively to “discover” new ideas from the paper. Such discov- eries are likely to be re-discoveries (e.g., already published by other researchers). However, if you are used to thinking critically and creatively, when you read recent papers at the frontier of the research in your field, your re-discoveries will likely be true discoveries. Those true discoveries will earn you a Ph.D. degree, and help you establish yourself in the field. We want to emphasize again that in reading research publications, read less, think more. There is ample research in education and psychology showing that if people (and kids) are given too much information or instructions, they become less creative and explorative. After all, for researchers, the purpose of reading published papers is to make new discoveries that go beyond the existing works! GettING StARted: New IdeAS ANd oRGANIzING PLANS 41 Depending on the culture and environment where you grew up and received earlier education, you may already be used to challenging the status quo rather than merely following instructions. If you are not, it may take you some months or even years to change your mentality to be more critical and creative. But if you are aware of it, and try hard, you will improve quickly. There may be one situation where you do need to read carefully the details of a previously published work: when you need to re-implement it. This may sound paradoxical, as our goal is to do novel research, but it does provide food for thought and ready baselines to compare to, especially when starting empirical research. We will discuss this in detail in Section 4.5. The second “bad” approach in reading research papers is side-tracking too far and for too long into some minute details, without seeing the big picture. Often research papers contain some technical information and methods that you are not familiar with. For example, a paper on supervised learning may contain a method that uses quadratic optimization as its subroutine, which you may not know well. It would be a bad approach if you get an 800-page textbook on optimization and read it from cover to cover to “prepare” yourself for that research paper. The right approach is “need-driven learning.” Your undergraduate and Master’s programs should prepare you with enough basic knowledge for doing research. For the missing knowledge, such as the aforementioned quadratic opti- mization in papers you are reading, you sidetrack to learn it quickly, and come back and focus on the main papers you are reading. The key in reading published papers is to know what has been done, and come up with novel ideas. How do you do that? 3.4 wheRe to Get New IdeAS Scientific discovery, at a very high level, can be regarded as a process of com- ing up with some new hypotheses, collecting data and performing experiments, and confirming or refuting the hypotheses. But in reality, the process is far more complex. Hypotheses are like new ideas in research. How to come up with new, 42 CRAFtING YouR ReSeARCh FutuRe interesting, and potentially useful hypotheses? Often the hypotheses need to be modified many times while research is being conducted. How can this be done? How to design experiments to convincingly confirm or refute hypotheses? This section discusses how to find new ideas or hypotheses in research. One risky approach new Ph.D. candidates often use to find new ideas is to read the “future work” section of a paper, or just do the “obvious next thing.” However, these are the ideas that the authors have already thought about, and may have been working on, that they are not really the “future” work per se. Thus, there is a chance that if you worked on these ideas, the authors may always be ahead of you. In addition, your mind will be restricted by the authors — you still have not generated new ideas independently. Earlier, we discussed how you should read less and think more—think critically and creatively. When you are doing that, often you will have questions about the published methods, new ideas and hypotheses about solving the same or different problems, new ways of making assumptions, and so on. You should write down those questions and ideas right away on the margin or the backside of the paper. If you read papers on computers (PDF files), use note-taking software to take notes, or an Adobe PDF Reader equipped with the note-taking function. When you think actively, ideas come and go, and it is crucial to write them down immediately, and study them more deeply later to see if they are indeed new and worth further exploration. In fact, new ideas can come from other unexpected occasions when you keep on thinking about intriguing research questions. Legend says that the an- cient Greek scholar Archimedes had a “Eureka!” moment when he took a public bath and suddenly discovered how to measure the volume of an irregular object (a crown made with gold) by submerging it in the water. He leaped out of a bath, and ran home naked shouting “Eureka!” If you have an “Aha” or “Eureka!” mo- ment when taking a bath, we suggest you also to run to get a pen and paper right away — but remember to always bring pen and paper to the bathroom! Or better GettING StARted: New IdeAS ANd oRGANIzING PLANS 43 yet, bring a laptop or tablet to the bathroom or bathtub, but make sure that it is waterproof ! Sometimes new Ph.D. candidates complain to us that after they read many papers, they find that their “new” ideas have all been discovered! They claim that the more they read, the more difficult the topic seems to be, and the less inter- esting the topic becomes! This can happen in a well-developed, mature research area. In the next section we will point out that you should pay attention to “hot” and recent research topics when you select your Ph.D. topic. Here, we offer you another very important and effective approach to generating new ideas: having a “brainstorm” session with other people. A group brainstorming session is a group session where two or more people actively participate and suggest ideas. These people can be fellow graduate stu- dents, professors, and other researchers, some of whom may even be outside your research area for fresh ideas. It is actually quite important and useful to develop a “team” of people who help each other during your Ph.D. study. In a brainstorming session, often assisted with amply supplied coffee (or a small amount of beer), no ideas should be criticized or judged. New ideas will be drawn and written on a large board, which may help visually stimulate more new ideas. Those ideas can be ex- plored deeply by different graduate students in parallel afterward. Combining “read less, think more” and brainstorming, a very effective ap- proach we often take is to have one person in the group read a just-published paper first. He or she would present only the problem part to the group, and lead the rest to brainstorm: How would I solve it, and do better? What is wrong with the paper? Again, many ideas and solutions may be found, and can be compared with the published paper. Often new research ideas not mentioned in the paper may be generated, and can be explored afterward. A crucial aspect of generating new ideas by you or within a group is to try to generate and treasure bold new ideas. By “bold,” we mean ideas that are radically different from the previous ones, or that refute and overhaul previous work. For 44 CRAFtING YouR ReSeARCh FutuRe example, if you discover that previous work made a wrong or unrealistic assump- tion and you propose a better one, you probably need to propose new algorithms, and solve a different set of problems. Avoid small, incremental improvements, the so-called “salami” ideas which produce “salami” papers (thin and unsubstantial). A small, incremental improvement is, for example, a different way to search for optimal parameters of the same published work, and by doing so you improve the results by, say, 3%. Your new ideas should almost always be application- or prob- lem-driven, not solution driven. This will improve the impact of your research work. For example, Student A1 was initially interested in cost-sensitive learning. After reading many papers on this subject, he wrote a survey on it. Writing a survey paper is an excellent way to start researching in an area. He also extended traditional cost-sensitive learning methods, and published a few papers. However, the work was not bold enough to be a Ph.D. thesis. To help the student, we brain- stormed: what are other forms of costs in cost-sensitive learning that are useful in real-world applications but have not yet been studied? After several brainstorming sessions, we raised new ideas on different data acquisition costs in cost-sensitive learning. After a literature search, we find out that this extensively studied previ- ously. As this is a bold, new idea in the area of cost-sensitive learning, Student A1 explored the idea deeply, checking into previous works that included the support- ing theory, solutions, and application examples. As a consequence of the research, he published several top-rated conference and journal papers, and wrote his Ph.D. thesis on this topic. Since he is one of the first to work on this topic and many people are likely to follow up in this direction, we can say that student A1 “owns” this topic now. 3.5 FRoM IdeAS to ReSeARCh ANd theSIS toPIC A “small” new idea may lead to a conference paper, while several small new ideas on the same topic or one “ground-breaking” new idea can lead to a research and thesis topic. The task of choosing a research and Ph.D. thesis topic is a complex and GettING StARted: New IdeAS ANd oRGANIzING PLANS 45 trial-and-error process. It may also determine your future research direction and career. Section 4.1 provides you with several specific criteria on a good research and thesis topic, proposed by the late computer scientist and Turing Award winner Jim Gray. Here we list some general factors that should be considered carefully: • • Again, your passion and interests in the topic. You must be highly passionate and fascinated in the selected topics. Your technical strengths. Are you theoretical and math oriented? If so you can consider research in theoretical aspects of a field, such as theoretical models. Good at statistics? Consider statistical simulation or optimization, for example. Good at design? Consider a new design and processes. Good at applications? Consider empirical research and killer applications. • how new and how “hot” the topic is. True, one can make novel and significant contributions in virtually any area of science and engi- neering, but it is often quite hard to do so in 4–5 years working on a Ph.D. thesis if a topic has been studied for many decades, and you could spend a huge amount of time just learning and studying previ- ous works. Thus, you should consider recent topics that are or are becoming hot, and in which rapid progress is being made, as your Ph.D. topic. • Your supervisor’s vision and opinions. Your supervisor often has more experience in research and better judgment on new research topics. Sometimes a topic may have been well studied for many years without much breakthrough, even though papers are still being pub- lished on the topic; sometimes a topic can be too hard or too easy. Thus, discussion with your supervisor is often crucial. Note, however, as Ph.D. research would advance the state-of-the-art, no one can be 100% sure if a chosen topic will be adequate for Ph.D. study before actual research is carried out. 46 CRAFtING YouR ReSeARCh FutuRe • Your future career. Do you want to be a professor in universities, or a researcher in companies? For the latter case, you should select em- pirical research where the research project can highlight new ways of applying theories. When selecting a thesis topic and carrying out research to explore the “un- known territory,” is there any way to know “if I am on the right track”? 3.6 how do I kNow IF I AM oN the RIGht tRACk? Many new Ph.D. candidates often feel in the dark if they are selecting a good topic for their Ph.D. thesis, or if they are doing the right thing in their research. An extremely important way to validate your thesis topic is that you complete your first iteration of the three main tasks ( find new ideas, do solid research, publish papers) early in your Ph.D. study. In the later part of the first year, and during the second year of your Ph.D. study, you should start doing research and publishing papers (Tasks 1–3) in re- search topics you are interested in. Start with some small, interesting research problems, and do solid research (see Chapter 4). If you obtain positive and inter- esting results, you can write them up as a conference paper, or a short journal paper (see Chapters 5 and 6), and submit it to a conference or journal. You can start with medium competitive (or local) conferences or journals. As we mentioned earlier, research papers are almost always peer-reviewed by other researchers anonymously. This allows reviewers to write detailed and often critical reviews of your papers. If your paper is accepted, it surely validates your ideas and research topic, and the reviews can help you to further improve your work. If the paper is not accepted, comments from the reviewers will often give you great feedback about your research and the paper. However, it is a bad idea to submit poor and pre mature papers as they can negatively affect your reputation. Here are some other useful ways to validate your Ph.D. topic and research: • • • GettING StARted: New IdeAS ANd oRGANIzING PLANS 47 Discuss your potential topic with your supervisor and other colleagues and Ph.D. students extensively. Discuss your ideas with other researchers who work in the same field via emails. Chat with other researchers in conferences. Keep in mind that people may give less critical feedback than they might in writing reviews of your papers. • Find and read recent Ph.D. theses on similar topics from other uni- versities, and compare the depth and scope of your research work to theirs. To reiterate, it is very important to go through the Tasks 1–3 early in your Ph.D. study. This will not only prepare you for future iterations in your third and fourth year of your Ph.D. study, but also validate your Ph.D. thesis topics. 3.7 SettING uP A PLAN FoR Ph.d. theSIS eARLY After you have gone through Tasks 1–3 once or twice, it is highly desirable to set up a “plan” for your Ph.D. thesis, usually near the end of the second year. The plan looks a lot like a two-level outline of your future Ph.D. thesis, with a list of related research problems to be solved. This is usually possible because you have read many recent papers on this topic critically and creatively, and performed some research already. With the plan, in the next few iterations of your Ph.D. research, you essen- tially pick up some research problems in the plan, do solid research, and publish high-quality papers. Note however, the plan is not carved in stone—you need to remain flexible with the plan. For example, you can skip some research problems if they are too hard or they do not yield enough results. Remember, doing research takes risks in exploring unknown territories. You can also add new, related prob- lems during your research. However, you must have a strong focus—all the research problems you will be solving are within a (broad) thesis topic. In the end, your 48 CRAFtING YouR ReSeARCh FutuRe FIGuRe 3.4: A plan of a sample Ph.D. thesis with a central theme and a list of potential problems to be solved, and how it evolves into the final thesis with publications in [ . . . ]. Some topics are added in later (“new” in the notes), and some were not finished (“unfin- ished” in the notes) in the final Ph.D. thesis. thesis plan and the final Ph.D. thesis outline may have an overlap of 50–80%. This way, it is possible that you can make novel and significant contributions and establish yourself in a certain area (“own” an area) at the end of the four-year Ph.D. study, as seen in Figure 3.1. After Student A1 switched to cost-sensitive learning with data acquisition, we set up a thesis plan together on this new topic. The student worked hard, and published a series of papers in top conferences and journals. This is not surprising as Student A1 has already gone through Tasks 1–3 on earlier research, and can conduct solid research and write papers reasonably well by himself. His final Ph.D. thesis is almost like a simple collection of these relevant papers. See Figure 3.4 for his thesis plan. We put some notes in [ . . . ] in the plan for papers that were later published. Some topics are added in later (“new” in the notes), but some were not finished in his Ph.D. thesis (“unfinished” in the notes). This plan provided a strong focus in his Ph.D. study, yet he was still flexible with the plan. Note that his final Ph.D. thesis does not include his early published work on co-training. A thesis must be a coherent piece of work, usually on one central topic and theme. Ph.D. study usually only takes 3–5 years; this is rather short for making significant contributions in research and for establishing yourself in some area. GettING StARted: New IdeAS ANd oRGANIzING PLANS 49 Having a plan and working systematically (Tasks 1–3 in Chapter 1) according to the plan is crucial to make this happen. 3.8 LeARNING to oRGANIze PAPeRS ANd IdeAS weLL A related but important issue in undertaking the long and arduous task of com- pleting Ph.D. research is the need of a good system to organize the many papers that you have read, notes on ideas you have thought about, and references you have used and cited in your papers. Otherwise it can be hard to find those things during research and when you write your thesis. In the “old” days when we worked on our theses, we created piles of physical papers on different topics, and used text documents to keep track of papers, ideas, and so on. Nowadays most papers are in electronic format, such as PDF, or portable document format, created by Adobe Systems, and there are quite a few “reference management software” that can help you with all of these tasks with ease. Two popular ones are Mendeley5 and Papers.6 Also, you can use ebook software, including iTunes and Kindle to organize PDF files. You can create your own note-taking system, or choose a software package to organize papers, notes, and references, and you need to use it effectively to man- age your research the in several years of your Ph.D. study. • • • • 5 http://www.mendeley.com/ 6 http://www.mekentosj.com/papers/ 51 C H A P T ER 4 Conducting Solid Research In this chapter, we go deeper in describing the process of conducting solid research. We start by giving a high-level overview on the research process (Section 4.1). We then discuss some high-level criteria, called Gray’s Criteria, to judge what research ideas and projects are worthwhile to pursue (Section 4.2). Subsequently, we discuss how to form hypotheses to work on in order to pass the criteria (Section 4.3) and how to confirm or dispel the formulated hypotheses (Section 4.4). We further dis- cuss some other objectives as you go through your research process, such as how to brand yourself (Section 4.5), how to choose between theoretical and empirical research (Section 4.6), and what to expect in team work and multidisciplinary research (Section 4.7). 4.1 AN oveRvIew oF A ReSeARCh PRoCeSS We refer to the steps in which we conduct research as a research process. A re- search process, broadly speaking, consists of the following phases: Step 1: Find a novel and potentially high-impact problem to solve based on the high-level criteria (Section 4.2) on choosing a good problem. Step 2: Find a candidate solution. You then formulate a hypothesis as a (problem, solution) pair. Each hypothesis states that the solution can indeed solve the problem. Step 3: Conduct theoretical or empirical analysis on the hypotheses to confirm or dispel them. You also conduct significance tests to establish the validity of your conclusions on these hypotheses. 52 CRAFtING YouR ReSeARCh FutuRe Step 4: If you are successful in your significance testing, then you are done. Otherwise, you return to Step 2, find another candidate solution to the problem, and repeat the process. Your initial solution to the problem might be a simple one, and there is a good chance that you will fail to solve the problem either because the problem is too hard to solve, or because the solution does not solve the problem. The reason that you often refute your initial solution is that the solution is usually very simple to start with, and other researchers working in the same field may have already thought about the solution to the problem, tried it, and refuted the hypothesis. However, as most published articles only report on “positive” results, you might not be aware of the fact that the solution in fact is not a good fit for the problem, and thought otherwise! In research, we almost always have to revise and “tweak” our initial hypoth- eses to “make them work,” so to speak. Finding the right problems, and forming and revising the most appropriate solutions for these problems, is a highly com- plex and creative process, and thus it is hard to “quantify ” this creative process precisely. We will describe a so-called Research Matrix Method, which inspires us to make systematic associations between problems and solutions. This often leads to new hypotheses and novel ways of solving the same or different problems. See Section 4.3 for detail. How do we confirm that a hypothesis is true? There is a very broad spec- trum of approaches. On one end of the spectrum is a (pure) theoretical approach. It uses mathematics to represent the hypothesis, and logical reasoning and mathematical derivation to prove (or disapprove) it. However, often assumptions need to be made so that proofs can be carried out. One of the most important and classical theoretical work is Euclid’s elements, written in 300 BC. It starts with definitions and some basic assumptions (called axioms or postulates, such as two parallel lines will not intersect if they are extended in any direction), and uses logical reasoning to prove (confirm) hundreds of propositions and theorems, including the Pythagorean Theorem. When a theorem is proved once, it is true CoNduCtING SoLId ReSeARCh 53 forever. There is no need to “run experiments” to verify proven theorems. The key questions to answer are how strong the assumptions are, and how the results can be applied in practice. At the other end of the spectrum is (pure) empirical research. Often such empirical research is closely related to practice, as empirical methods can be easily turned to applications. Thus, do not be afraid to pose some bold hypotheses that represent killer applications —solutions to certain problems that may bring direct benefits to a large number of people. Empirical hypotheses testing can often be stated in a natural language, say English, and can only be confirmed by running experiments on simulated or real data. Experiments can be conducted with people, animals or plants, materials and objects. They can also involve computer simula- tions, and computer programs taking various datasets as inputs. When conducting these experiments, it is crucial that researchers have a sharp eye for interesting and anomalous results. This is another important way to find surprising or new hypotheses during research in addition to the research matrix method we mention in Section 4.3. We often use different materials, datasets, and have different experimental settings in experiments. Do we need to exhaust all possible materials, datasets, or experimental settings, to show our new design and methods are better than previ- ously published results? What if this is impossible? How can we compare with previous design and methods published by other people that we do not have access to? Your decisions on these issues will determine how thorough and rigorous your experiments are to support the validity of the hypothesis. The degree of such empiri- cal evidence with experiments can be quantified, fortunately, by the Significance Tests, which is a subject in statistics. Here the term “significance” does not mean importance or impact, as we have been using in this book. Briefly, a significance test is a statistical procedure to test if a conclusion (e.g., your method is better than previous ones) is likely to happen by chance. See Section 4.4 for more details. In order to pass the test, repeated experiments and head-to-head comparisons usually need to be conducted as part of your research. 54 CRAFtING YouR ReSeARCh FutuRe A more rigorous support can be obtained if you can ask authors of the pub- lished papers to apply their own methods on your materials and data, and your new method is still shown to be better than theirs. This is because the original au- thors can usually apply their own methods better than you could. However, if you only compare your method with those results in some published papers (without reimplementation of these methods on your own), the evidence that supports your hypothesis is considered weak, as the experimental settings can be different, and you might not satisfy the assumptions needed to conduct the significance tests. See Section 4.4 for more details on this. 4.2 JIM GRAY’S CRIteRIA1 Many students think of research as an admirable career, where one can truly make a name in history. Just consider examples in our textbooks: Newton, Galileo, and Einstein, to name a few. However, for a beginning student, research should be both a curious adventure and a serious business to manage. Let’s start with the fun and adventurous part first. One of the authors (Yang) once attended a lecture given by Professor Charles Townes, an American Nobel Prize-winning physicist who made major advances in quantum electronics for lasers and masers. Yang had earlier met Townes when he freshly graduated from Peking University when Townes first visited China on a science mission as President Jimmy Carter’s representative in 1982. In this later seminar, Townes reflected on his joy in his very first discovery, a fish. He said that in his childhood he used to catch fish. One day he got a fish that he could not name according to an encyclopedia. Curious, he wrote a letter to the Smithsonian Institute, a US museum. He was pleasantly surprised when he got a letter in return, noting: “Congratulations, Mr. Townes, you have discovered a new species of fish!” Imagine the joy and excitement this boy experienced when reading these words! 1 Jim Gray was an American computer scientist who was credited for major developments in database theory and a proponent of the fourth paradigm in scientific discovery. CoNduCtING SoLId ReSeARCh 55 Discovery is a childhood joy. As we note in our previous chapters, one enters the research field primarily because innovation and discovery are fun. It is a dream we all have had since childhood. What we want to say in this chapter is that to be prepared for a career in research, we must have more than curiosity; we must have a process in which we can manage our research like managing a business. Just like running business, if we happen to manage it well, it will flourish and prosper. Our impact in the world and our contribution to knowledge will be significant. Otherwise, if we do not manage it well, we will find ourselves frustrated and discouraged. Once we know that we are motivated to do research, our first task is to decide on our objectives and directions in which we will go deeper. This process will definitely be curiosity driven, but should also follow a well-managed process. As noted in previous chapters, finding a good topic takes many activities, ranging from talking to experts in the field to critiquing many papers and works in your field of interest. But if there are several areas that you are more or less equally in- terested in, which one should you choose? How do successful people pick an area to work on? Why are some equally talented people not as successful and impactful as others? In our careers, we have been talking and listening to many “successful” researchers. One of the best-known criteria for high-impact research was sum- marized by the late great computer scientist and Turing Award winner Jim Gray, who was credited with the invention of modern database technology and the fourth paradigm in computer-science research. In his 1999 Turing Award lecture, he stated that good research should • • • • have clear benefit, be simple to state, have no obvious solution, have a criterion where progress and solutions are testable, and where it is possible to break the larger problem down into smaller steps, so that one can see intermediate progress after each step. 56 CRAFtING YouR ReSeARCh FutuRe We will refer to this set of rules as “Gray’s Criteria” hereafter. Take word processing as an example. Suppose a student is very interested in proposing to do research in word-processing technology. This technology has clear benefit, which is very simple to state. However, it is obvious today how to do it, via a variety of word-processing software. Thus, the research is not impactful, unless it is a dramatic improvement on the existing word-processing software. However, suppose that the student has proposed to invent a new word- processing system based on speech input instead. This has clear benefit for a va- riety of people, including the handicapped. It is very simple to state, and it is not yet obvious how to do it accurately since in the speech recognition field today, we are still far from having a robust recognition technology based on voice input. The progress can be testable: by having humans speak to a microphone and producing coherent and accurate text. Finally, the objective can be broken down to smaller steps, including phoneme recognition, sentence recognition, grammatical analysis, and fault tolerant, etc. Thus, this can be considered a good direction to pursue for the student. Going back to our earlier example of Students A, B, and C. Recall that Student A is a type of student mostly interested in fundamental and academic re- search. Earlier we described A1 in detail. Let us use A2 to denote another student of this type. For Student A2 to find a research problem, the question becomes: how do I advance the state-of-the-art in academic research? After reading research papers and proceedings, Student A2 found the topic of “transfer learning” to be a very attractive topic, which studies how knowledge gained by an agent in one domain of expertise can be usefully transformed into knowledge in another, re- lated domain. Transfer learning tries to endow machines with the ability to learn from its experiences that are drawn not only from a single domain of interest, such as examples of categorizing images, but also from other different but related domains of interest, such as reading books. The topic of transfer learning also has its psychological and educational foundations, as it is an integral part of human intelligence. People have the ability to carry out transfer learning, for example, when they learn to plan military and business strategies via their knowledge in CoNduCtING SoLId ReSeARCh 57 playing chess. Student A2 found the topic of transfer learning intriguing enough to con- tinue exploration. In particular, he found the topic of transferring learned models between text and images very interesting, and he started to conduct a thorough survey of existing works in transfer learning, and then applied the Gray’s Criteria to the topic. The topic has clear benefit to many computer science areas, such as data mining and machine learning applications, as these algorithms are a major compo- nent of search engines, social networking applications, and business applications. However, a major bottleneck in these applications is the lack of high quality anno- tated data, because data labeling is a time-consuming task often done by humans. Transfer learning allows one to borrow the knowledge gained from other fields to alleviate the dependency on annotated data in a given domain. In Student A2’s problem context, transferring knowledge gained from text documents to images allows an online social media system to categorize and search for images of interest much faster and more accurately than before. The problem is also simple to state. Try to tell an ordinary computer user that transfer learning allows a search engine to adapt to their personal preferences much better than before, or tell a credit card user that card misuse and fraud de- tection can be made more accurate, and you will know why. In the case of Student A2’s problem, a story of teaching computers to recognize images by reading text sounds very fascinating! While we humans apply transfer learning every day in our lives, it is in fact not that obvious how to do it on a computer. Previous approaches in machine learning and data mining relied on the assumption that the training and testing data are represented similarly. This assumption is no longer valid in Student A2’s problem. To Student A2, progress and solutions in transferring from text to images is clearly testable, as we can use the percentage of correctly categorized images as 58 CRAFtING YouR ReSeARCh FutuRe a measure of success. This measure is a function of the number of text documents fed to the machine for reading, which can be displayed clearly as a chart. Finally, the problem can also be broken down into smaller steps, so that one can see intermediate progress. For example, Student A2 can try to work with an existing translator from text to images. Then he can design algorithms and mod- els to learn the translator from data. Finally, he can consider varying the types of text and images and observe the performance of the resulting transfer-learning system. Now let us turn to another student of type B (empirical research), Student B2, who is interested in large-scale application-oriented problems, with an aim to join research labs in industrial companies after graduation. For Student B2, the transfer-learning problem itself is interesting, but he is interested in seeing large- scale applications at work. To do this, he found an application idea in the area of query classification in search engine design, where the problem is to automatically categorize user queries into categories. For example, when we type in a query “hotel” in a search engine, the system must deduce that the user might be inter- ested in a commercial purchase, thus providing the user with informational results about hotels, as well as advertisements. Making transfer learning work in this search context allows a search engine to quickly adapt to changes in a commercial search and advertising application. This would allow new areas to be quickly de- veloped, and search-query categorization can be readily extended by “transferring” previously annotated query data to new application domains. To demonstrate the innovation, Student B2 plans to build a large-scale data mining system based on transfer learning based on data collected by a search-engine company. To make the data access feasible, he decides to join a commercial search company for one semester as a student intern. For a student of type C (application and entrepreneurship), Student C2, whose aim is to become an entrepreneur, may decide to focus on a more profitable area, online advertising, in order to gain more experience in the area of business intelligence to prepare for his future company. Advertising is a science as much as CoNduCtING SoLId ReSeARCh 59 an art, which touches not only on business as a topic, but also economic theory, game theory, human-computer interaction, artificial intelligence, and data mining. Since carrying out this research involves a multitude of disciplines, the student de- cides to go to various academic as well as business conferences to enlarge his social network. He goes to some more focused and commercial workshops more often, and plays a major role in many functions in conference or workshop organizations such as being a student volunteer. One of the most important aspects of Gray’s Criteria is that the progress should be testable. Today, much research is done by means of system building and empirical testing. In this context, a testable criterion can be further refined to: we must ensure that it is feasible to get credible and a sufficient amount of data. In many student cases under our direct or indirect supervision, we have observed that this is a critical point where many students get stuck: they have invented great ideas, algorithms, and theorems, and implemented systems. The only thing that remained to be resolved is credible verification, and this is where the students often fail: they cannot find credible datasets beyond publicly available toy-ish data, which breaks down the whole process of research. For example, in computer science and engineering, some students conduct research by proposing new algorithms that rely on search-engine log data. However, this data cannot be accessible at university labs. Some of the data are only available via industrial companies such as search-engine companies. In this aspect, students should seek out opportunities to work in collaboration with industrial research labs, where they can take on the position of a research intern, to complete their empirical research. Indeed, this has become one of the most effective ways for students to carry out their research plans. 4.3 the ReSeARCh MAtRIX Method Gray’s last rule says that research should be able to be broken down into smaller steps, so that one can see intermediate progress. This is important, since as we know well in history, new innovations are possible by “standing on the shoulders 60 CRAFtING YouR ReSeARCh FutuRe of the giants.” This applies to great inventions. It also applies to your own research agenda, in which one of these giants may, in fact, be you. One of the most effective methods is the so-called research matrix method, in which one can systematically plot a path to successful research. In Figure 4.1, we see a matrix partitioned via an x-axis, which represents different methods and techniques that we have and a y-axis where we list the potential problems and subproblems we try to solve. Some of the subproblems are related and should be solved in sequence, while others can be solved concurrently. To make the methodology more concrete, let us consider the case of a stu- dent who is interested in machine learning and data mining areas, as we mentioned before. Suppose that the student is interested in making a career in cost-sensitive learning. Cost-sensitive learning concerns how to build a computer-based model that can improve itself over time by considering different costs associated with different types of mistakes made by the model on future examples. This area is particularly important because many practical machine-learning problems are intrinsically cost-sensitive, in that the data is unbalanced. A good starting point is to carry out an extensive survey of this area, as we noted in Chapter 2. Suppose that the student has broken down the cost-sensitive learning area into several sub- FIGuRe 4.1: The research matrix method. CoNduCtING SoLId ReSeARCh 61 problems: cost-sensitive learning when the costs are known, cost-sensitive learning when costs are unknown ahead of time, cost-sensitive learning when the cost is associated with missing data acquisition, and cost-sensitive learning when data comes in stream form. On the method dimension, the y-axis, one can lay out such methods as Bayesian classification, ensemble methods, density-ratio methods, and partition or tree-based methods. Furthermore, one can list out various online learning methods. By examining this matrix, the student can first try to fill in various cells by papers he or she has read before: each citation index such as [3], etc., represents one such paper. The student can optionally put notes in each cell, to denote the strengths and weaknesses of each paper upon reading. The student can find vari- ous surveys and comments on the Internet via search engines, which can get the student quickly into focused areas. These are the areas where there is no existing literature, or few literature pieces, to occupy a cell. Examples in the figure include the column #2, row #4, or cell #(3,3). First, cell #(3,3) offers a perfect opportunity for the student to enter the field, or “get his or her feet wet,” so to speak. The student can try to apply method #3 to subproblem #3 in order to get the necessary practice. Others in the machine- learning field will appreciate the relatively significant impact because this proposed work clearly offers a novel solution for an important subproblem. If this is truly the case, as this is how many of us more senior researchers often started our research career, congratulate yourself—you have entered the door of research. This is where you can taste the sweet fruit of your own discov- ery for the first time. However, more exciting things await you in the matrix, so read on! Example: Student A2 is most interested in pursuing an academic career. He has found a topic in the area of “ transfer learning,” and sets out to find a suit- able topic in this area for his Ph.D. research. After reading the relevant journals, proceedings and articles, Student A2 lists the specific transfer learning related problems as “knowledge transferring in the same feature space,” “knowledge 62 CRAFtING YouR ReSeARCh FutuRe transferring across different feature spaces,” “knowledge transferring with unbal- anced data,” and “knowledge transferring from multiple source domains.” On the method dimension, he lists: “instance-based transfer,” “feature based transfer,” “transferring with ensemble of models,” and “transferring across multiple learn- ing tasks.” From the matrix, he noticed that there has been considerable previous works by other researchers on ”knowledge transferring in the same feature space,” “instance based transfer,” “knowledge transferring across different feature spaces,” “instance based transfer,” etc., but there is relatively little work under ”transferring across different feature spaces,” “transferring across multiple tasks.” After discuss- ing these findings with his supervisor and supervisory committee members, he decides that this is an area to pursue. He then writes a proposal, formulates sev- eral plausible solutions, and sets out to find appropriate data for the experiments. Finally, Student A2 gets several papers published and completes his PH.D. work. In contrast with Student A2, Student C2 is more interested in an industrial and entrepreneurial career. Thus, Student C2 decides on a different topic to pur- sue, but he can still make use of the matrix method. For example, Student C2 finds that the topic of recommendation systems (such as that used by Amazon.com) to be significant and of practical importance. In this area, he finds that the problems can be formulated as a vector “recommendation based on dense matrices,” “recom- mendation based on sparse matrices,” “recommendation with an external ontol- ogy for users and products,” and “evolutionary recommendation with temporal information.” On the solution dimension, he lists “user based recommendation,” “item-based recommendation,” “model-based recommendation.” This gives a ma- trix where Student C2 starts performing a literature search and filling in the cells with references. Student C2 soon finds out that the area of “evolutionary recom- mendation with temporal information,” “model-based recommendation” is both interesting, new and will be of tremendous commercial value if introduced to some well-known commercial online-shopping companies. This idea is confirmed by his committee members, which includes a researcher from a well-known industrial research lab. He sets out to do his research, which can be tested on large-scale data and using well-established evaluation criteria. With this work he applies for a pat- ent and then writes a business plan for a university-based spin-off company. CoNduCtING SoLId ReSeARCh 63 4.4 CARRYING out YouR ReSeARCh Once you have set the research objective and have done the related literature survey, you are ready to conduct your research. A first important step is to state your research objective in one understandable sentence. For example, if your objec- tive is to show that you can design a better search engine than Google, then you might want to be more specific about what you mean by “better,” and formulate your hypothesis more concretely. For example, you might state “my hypothesis is to use social networking information in Web search results toward more accurate ranking results compared to not using such information in Web search.” This hypothesis can be easily understood by even non-computer science people, and can be concretely confirmed or disproved. More concretely, the hypothesis can be further instantiated by the following statement: “my algorithm ABC uses social networking information of masses of users as well as hyperlink information. We expect that ABC gives better Webpage ranking results than Google’s PageRank algorithm2 when the former uses additional social networking knowledge.” It is more advantageous to make your hypothesis more concrete. First, hav- ing a more concrete hypothesis at the outset allows researchers to focus on a few key elements in your work. For example, it allows you to formulate your method- ology and present your ABC algorithm as clearly as possible, so that others can repeat your experiments and confirm your hypothesis. Second, it allows you to decide on the necessary baselines and evaluation metrics in order to confirm or disprove your hypothesis. For example, you may formulate your methodology as one that is based on a theoretical proof that no matter what PageRank algorithm provides in the final result ranking, your ABC algorithm is going to perform at least as well as that by PageRank. In order to show this, you may realize that you need a widely accepted evaluation metric in order to compare the ranking results. 2 http://infolab.stanford.edu/~backrub/google.html 64 CRAFtING YouR ReSeARCh FutuRe For example, you might adopt the “Area Under the ROC Curve’’ (or the AUC measure) as a ranking metric.3 Alternatively, you may wish to use a metric known as Normalized Discounted Cumulative Gain (NDCG4). Whichever metric you might choose to use, you need to follow up with a proof that your ABC algorithm will outperform the PageRank algorithm by a significant margin. If you are more theoretically oriented, you might look for proof methods that can help you show that your hypothesis holds with a series of theorems and corollaries. In many cases, however, the hypothesis can only be answered empirically. If you adopt this path, you’ll need to design the experiments, which involves several key steps. First, you’ll need to identify the datasets and sample the necessary data for your experiments. Often the original dataset is noisy, incomplete, and large, and for this reason they are often called the raw dataset. For example, for showing the superiority of a new search method, one often needs to obtain large quanti- ties of search log data from a real search engine. This raw data is often extremely large and incomplete, but a sample of the data that is properly cleaned can be used to represent the general real world situations that are encountered by a real Web search algorithm. In this case, a section of the data that involves several months that cover the four seasons of a year might suffice. When there are multiple seg- ments of the data that vary in distributions, it is better to sample each part inde- pendently. Furthermore, it is a good idea to apply stratification by partitioning the entire large population into small segments, where the elements of each segment are sampled out randomly. The sampled data is expected to resemble the distribu- tion of the original dataset. Furthermore, when the data have much variance due to unusually high uncertainty, it is a good idea to apply Monte Carlo methods for sampling, where the basic idea is to run repeated computer simulation to generate the data according to the input parameters underlying the data distribution. 3 J. Huang and C.X. Ling. ‘Using AUC and accuracy in evaluating learning algorithms.’ In IEEE Transactions on Knowledge and Data Engineering, volume 17. 2005 4 K. Jarvelin, J. Kekalainen: Cumulated gain-based evaluation of IR techniques. ACM Transactions on Information Systems 20(4), 422–446 (2002). CoNduCtING SoLId ReSeARCh 65 An important aspect of experimental design is to decide the free parameters or independent variables that you must deal with, so that you can decide on their effect on the dependent variable (the search ranking result in our Web-search example). It is important that one of these variables is allowed to vary, while oth- ers (known as control variables) are kept at constant values or randomized. For example, in the search engine design problem, variables include the number of Web pages, the in-degree and out-degree of hyperlinks of each page, the length of each page, and the number of topics discussed in the content of the pages. When all of these parameters are fixed, we have a scenario that represents a snapshot of the real world. When we vary one parameter while holding all others constant, we create a performance comparison chart on which we display both the performance of ABC and PageRank, in order to ascertain the superiority of ABC as a better method. This experiment is often repeated by varying one variable at a time for creating a collection of charted results. Often, even after the experimental metric and comparison baselines are settled, we still have to decide on how to obtain credible subjects on which we ob- tain the results. For example, in the Web search case, we might hire several users to judge the quality of ranking results in response to a search query. Here, we have to decide on a collection of benchmark search queries that other researchers also use in evaluating their algorithms. We must also ensure that the users have a sufficient degree of independence and diversity to ensure the generality of the result. In fact, there is a large amount of literature in psychology on how to choose test subjects to ensure the most credible results. When dealing with models that can be constructed based on the data, it is important that we do not mix the training data used for model building with the data for testing and validating our models and hypothesis. In experimental design, this is known as hold-out tests, in which we hold out a portion of the data purely for evaluating the obtained model. When the data are in short supply, we can also use n-fold cross validation in which we partition the data in n folds, and let each fold take a turn in being the test data with the rest as the training data. This 66 CRAFtING YouR ReSeARCh FutuRe results in n results that can be averaged to produce the final, more reliable result. In doing this, an important issue is to show that the comparison results are con- sistent under different experimental conditions, via statistical measures such as variance and confidence intervals. Finally, once we complete the experiments and produce the results, say in the form of a number of data tables, we must follow up with interpretations and analysis of the results. There are two aspects here. First, we must be able to tell the reader whether the experimental results from competing methods showed significant differences via statistical significance tests. Second, we must explain the significance of the results via what we know from the domain knowledge; in our search example, for example, we need to explain what a certain difference in ranking result would translate to in user experience and search quality. Now we return to the topic of conducting statistical significance tests on your results. The basic idea here is to ensure that the results are not due to random chance. This can be done by setting a significance level at a low value, such as 5%. Then, we can establish that the probability that result is by chance is lower than 5%, and subsequently, we can say that our result is significant; in this case, we can reject the null hypothesis that there is no difference. The significance testing can be done via various significance tests. The stu- dent’s t-test, for example, tells if the means of two sample groups show significant differences. It starts with a null hypothesis that there is really no difference to be detected between the means of the two methods, and set out to show that the null hypothesis can be rejected. The student t-test is used to determine whether there is a difference between two independent sample groups and when the sizes of the groups are reasonably small. Another often-used significance metric is p-value, which is the probability of observing the test statistic value if we assume that the null hypothesis to be true. We often reject the null hypothesis when the test sta- tistic is less than the significance level a. Summarizing, the research process starts with the formulation of one or more hypotheses (often a null hypothesis and alternative hypotheses), and goes CoNduCtING SoLId ReSeARCh 67 through a cycle in which an experimental design is completed together with data selected and sampled, and then the statistical significance of the results ascertained. Finally, domain-related explanations are given so that others can fully appreciate the impact of the findings. In the process, it is important that the experiments are repeatable by others under the same experimental conditions. 4.5 bRANd YouRSeLF Taking the view of the matrix (again, see Figure 4.1), scientific research itself is not very different from what commercial market researchers typically do when launching a product or a company: they have to find out where the market needs truly are. On examination of the matrix again, a more important discovery from the matrix is that an entire area can be “owned” by the young researcher, through which the researcher can truly brand himself or herself as an expert in an area with a significant impact. Let us go horizontal first (see the horizontal arrow in Figure 4.1). This is when you have a good grasp on a significant and high-impact subproblem, perhaps due to your fastidious experimentation and examination of a particular problem at hand, or perhaps because you have gained an important insight by reading many research papers and noticed a lack of attention to a hidden gem. Once you have a good understanding of the nature and complexity of the subproblem, you start asking the questions: “Can method [x] be applied to this problem?” “What impact will be brought forth if I succeed in applying method [x] to this problem?” and, “if method [x] cannot be applied to this problem, what knowledge is gained in the field of research?” When going horizontal in this methodology, is it critical to compare the different methods [x] and [y] on the same problem to elicit their relative merits? “What are the advantages and weaknesses of method [x] as compared to method [y]?” It may be the case that method [x] is more efficient than method [y], whereas method [y] is more accurate, by some measure of accuracy, than method [x]. It 68 CRAFtING YouR ReSeARCh FutuRe might also be true that method [x] is better in reducing the error rate, if we con- tinue with the cost-sensitive learning example, or that method [y] performs better in some other measure of success such as AUC in ranking. In other words, many exciting research questions can be raised and answered by conducting this research horizontally, and as a result, many top-quality research papers can be written. Likewise, we can also go vertically from top-down in this matrix (see the vertical arrow in Figure 4.1), by considering applying the same method to a variety of related problems in one focused area. This is preferred if you have a very good grasp on the method’s inner strengths and weaknesses. As an example, suppose we choose the decision-tree learning method in machine learning, and wish to apply this solution to various subproblems of cost-sensitive learning. Then we may ask whether the method performs as expected on unbalanced class classification problems, on cost-sensitive learning problems when we have no good knowledge on the cost function, and on cost-sensitive learning when human feedback (which are also costly) are considered in the learning process for future data. We can compare the decision-tree based methods to all other methods that others have tried before on this problem, and if possible, we can find out why the decision-tree based method can perform better or worse than these methods. In this way, we can find out the method’s true merits and weaknesses in various learning problems that involve costs. Like the horizontal research methodology, this top-down process also al- lows you to truly brand yourself in your research community, and make a name for yourself. A popular analogy in many research circles is that a research method is like a hammer, whereas a research problem is like a nail. In this analogy, the horizontal methodology is akin to finding different hammers for the same nail, where as the vertical methodology is like finding different nails to hammer on by the same hammer. As the saying goes, “once you have a hammer, everything looks like a nail!” Finally, a better solution is if you can identify both a hammer and a nail, by going both horizontally and vertically (e.g., a submatrix from cell# (1,1) to CoNduCtING SoLId ReSeARCh 69 FIGuRe 4.2: A tree of research results. cell# (3,3) in Figure 4.1). If you can truly practice this “hybrid methodology,” you may already have a research career at hand, and a tree of fruits will grow with the associated publications, as demonstrated in Figure 4.2. 4.6 eMPIRICAL vS. theoRetICAL ReSeARCh The above discussion naturally brings us to a popular question raised by many students: should I do theoretical research or empirical research? In engineering, the corresponding question is: should I do fundamental research or application- oriented research? As we discussed so far, the researchers’ job is to uncover the causal relations between factors that may be hidden in nature, and this job can be accomplished either theoretically or experimentally. Generally speaking, theoretical research fits better for areas where well-founded assumptions can be formulated to allow inferences to be drawn from, to verify one or more phenomena under observation. In contrast, empirical research is when such assumptions are difficult to come up with, thus requiring experimental verification and data collection. In traditional 70 CRAFtING YouR ReSeARCh FutuRe science such as physics, the boundary between theoretical and empirical research was clearer. Nowadays, especially in engineering science and practice, the line between theory and experimental research is less clear. Add to this gray area the term “system oriented research,” which may indeed confuse some beginners and even seasoned professors. We have more than once heard some senior professors and researchers proclaim: “we have built this system, which is my research.” We wish to clarify, however, in this section, that building a system without subsequent analysis is not research, yet. But, if you have a hypothesis, say “Method X is better than Method Y under conditions Z,” this hypothesis can be verified by building systems to realize X, Y under Z and evaluate the hypothesis with these systems. This way of proving or disproving a hypothesis is research. Let’s start with empirical research, which is often associated with concepts such as system building, gaining experiences, and making observations. Often, empirical research starts with a hypothesis, which is a prediction or proclamation about the world. As an example, the claim that “it is possible to fly faster than the speed of sound” is a hypothesis. It can be proved, or disproved by building a plane that can break the sound barrier, which provides evidence that is observable. In science and engineering, hypotheses and empirical research are often tightly coupled, but they may not be raised and verified by the same person or the same group of researchers. Theoretical research proposes models and hypotheses that can be generalized and tested. They often state a fact that goes beyond the current set of observations using methods of induction. Once the models are built, theories should have the ability to deduce new facts about the future. Thus, good theories have the generalization ability. Empirical and theoretical research also often go hand in hand; in fact, in physics, the theoretical and empirical research works are often done by theoretical physicists and experimental physicists, respec- tively, who are often two separate groups of people. How do we get the initial ideas in empirical research? One often-practiced first step is learning by repeating some other researcher’s work and rebuilding their systems. For example, if you decided to build a search engine system for scientific CoNduCtING SoLId ReSeARCh 71 literature, then perhaps a good system to try to build is the PageRank algorithm that underlies the Google search engine. There are several advantages in doing this. First, to get one’s hands dirty and to understand the details of system build- ing is very important in system and engineering oriented research. By repeating others’ work in your own environment, you will understand what is stated in their research papers much more deeply, and even be able to understand what was left out of their papers; in some cases, many important details are left out either un- intentionally or because of space limitation. However, unless you try building the systems on your own, you will not be able to fully understand these details. Second, building these systems allows you to appreciate the complexity and scope of the problems at hand, and think hard on how to plan for your own research in the fu- ture. Often, one cannot understand fully the issues and resources that are involved in completing a project. It might be the case that, just by reading about a system in a research paper, one often underestimates the scope of the project. This is particu- larly troublesome for beginners, as a major delay in system building can disrupt the long-term plan for one’s Ph.D. study. Third, building a system allows you to have an important resource at hand: the baseline or benchmark system, against which you can later compare your more superior system to and demonstrate the validity of your future hypotheses. Finally, and perhaps most importantly, going through an entire process of building a system allows you to reveal many of the weaknesses or oversights of a prior work, and allows you to propose your own hypothesis and formulate an innovative idea. Back to our earlier search-engine example: you might find that the original PageRank algorithm did not take into account the individual users’ preferences and interests, and decide to develop a personalized search engine for scientific literature in response. To see whether you as a researcher should become a theorist or an ex- perimental scientist, consider that in science and engineering, the development of theories have been serving two strikingly different purposes. The first purpose is for experiments to confirm or disprove a preceding theory, and the second one is vice versa. 72 CRAFtING YouR ReSeARCh FutuRe In the first scenario, on the one hand, theory comes first, which should intrigue a sufficiently large number of subsequent researchers, who then build systems and conduct experiments to prove or disprove the proposed theory. One example of this mode of research is Artificial Intelligence. In his fa- mous article, “Computing Machinery and Intelligence,” Alan Turing put forward a grand hypothesis for all to see: that digital computers built based on Turing machine can be made intelligent on par with humans. This hypothesis cannot be proven or disproven by theory only, just like the hypothesis that the Earth goes around the Sun cannot be verified based on theory alone. One should actually build an intelligent computer to pass the Turing test to be claimed intelligent, and this is both systems work and experimental research. The theory is testable and is also decomposable, thus we have various branches of AI that includes computer vision, machine learning, planning, game theory and computer games, etc. This is an example of theory before experiments. On the other hand, we can have experiments before theory in many other examples. This used to be largely how physical science was done. You do experi- ments, and produce results that do not connect with, or cannot be explained by, a current theory. You now have something about which to posit a theory. The Michelson–Morley experiment performed in 1887 created a “crisis” for classical physics, and then Einstein proposed Special Relativity (a new theory) that can explain the experiment outcome. Here is a more recent example in the develop- ment of modern machine learning theories. In the early 1980s, there was great excitement about the fact that digital computers could be made to learn from ex- amples. Many schools of learning algorithms and systems flourished, each backed by a number of successful applications. Noticing this diverse development in the computational learning field, and the inability of existing theories to unify the seemingly different learning algorithms, Leslie Valiant from Harvard University developed the PAC learning theory, which stands for probably approximately cor- rect learning. According to this theory, learning is simplified as the ability for a system to make fewer and fewer mistakes with higher and higher likelihood, given CoNduCtING SoLId ReSeARCh 73 that more examples are input. Several assumptions are made on how the examples are drawn, how the mistakes are measured, and how to define when the learning is successful. In most of the real-world machine learning applications, these assump- tions are not necessarily true, or cannot be easily verified. Nevertheless, the theory was abstract, elegant, and simple, and very useful in explicating the differences between different learning algorithms. For this and other works, Valiant obtained the 2011 Turing Award. Are you more like Alan Turing or Leslie Valiant? The answer is that most likely you will need both abilities in your work. As a beginning researcher, you need to have a keen eye on the way the general field is going, and able to see the theoretical underpinning in the trend. At the same time, you need to cultivate a keen eye on how to unify different empirical research and various theories with a simple and elegant theory of your own. This may happen in a computer science thesis on machine learning, where one can propose a new learning problem, offer a solution, experimentally compare different approaches, and develop a theory to prove the algorithm’s convergence and efficiency, under certain assumptions. In other words, the world has become more complex that one had better become both a theoretician and an experimental scientist. Now we return to the question of the value of building systems. As stated earlier, one cannot claim that one is a researcher by way of building systems only. However, one can become a researcher while building a system with a hypothesis in mind. The fact that you build an airplane is to prove that heavier-than-air ma- chines are able to fly in air. Likewise, the fact that we build a computer system is to prove that the machine can be made to accomplish one or more of the intelligent tasks that, before the system was built, humans were still better at these tasks. An example is the IBM’s WATSON system, which beats human champions in the TV game of Jeopardy, which before WATSON was only achieved with smart humans. Thus, before building your system, ask yourself: what are you trying to prove? In our example of Students A, B, and C, the difference between theoretical versus empirical research can be reflected in the choices of A and B, who prefer 74 CRAFtING YouR ReSeARCh FutuRe theoretical and empirical research, respectively. Let a particular instance of Student A be Student A2. Student A2’s research focus is in how to learn a better model by learning from examples that can come from very different source domains, where these other domains may use a different feature representation. Student A2 further decides to use a method of ensemble model learning as a solution. To proceed, he first asks the question: “is it possible to transfer useful knowledge between any pair of sources and target learning domains?” To answer this question, he consults the theoretical works in computer science and mathematics, and formulates a set of sufficient and necessary conditions with theoretical proof of transferability. This set of theorems then guides his search for a better empirical solution, which he then verifies further with large data sets. In contrast, Student B2 (an instance of Student B) prefers to follow an em- pirical approach from the beginning in the research area of knowledge transfer. To do this, he finds a specific application domain of online product recommendations, and realizes that the main challenge in this area is to come up with a scalable set of algorithms that can work both accurately and efficiently. He then consults research papers in this area, which he extends into an innovative algorithm. He tests the algorithm on several large data sets obtained from online product recommenda- tion and advertising companies, on which he realizes good performance. 4.7 teAM woRk ANd MuLtI-dISCIPLINARY ReSeARCh A long, long time ago, research used to be a one-person affair. Leonardo da Vinci studied animal and human anatomy, architecture, and physics alone. Galileo Galilei studied the motion of objects and planets, Newton published his three laws of physics, and they published their works all by themselves. This situation has dramatically changed today: open any issue of nature, and you will notice many co-authors for each paper; sometimes the authorship takes up an entire page. In milder cases, look up any author in engineering science, in Google scholar or DBLP, and you will find an active researcher who has likely co-authored several, CoNduCtING SoLId ReSeARCh 75 if not many, research papers with dozens of other people. In today’s science and engineering research, teamwork and collaboration have become commonplace. Enough has been said about effective team work, especially in business and management sections of bookstores online and in airports. For scientific research, however, collaboration often takes some unique conditions. We can summarize these conditions as: common goals, communication, complimentary skill set, and social cohesiveness. A most common team setting is a student-advisor combination. There can be variations where an advisor is replaced by a committee member, and the student by a student group. In this setting, the student is often the main risk taker, taking the initiative in seeking out new research topics, conducting surveys, inventing algorithms, and carrying out the experiments needed if the work involved is em- pirical in nature. In this case, the advisor acts as a consultant, giving feedback to students from time to time and making sure that the student is on the right track. At the beginning, the advisor is often the generator of the initial ideas, defin- ing an area where the advisor has experience in, and listing out several potential broad topics for the student to choose from. Later, the student becomes the main idea generator. In weekly meetings, for example, the advisor often asks “have you checked this paper out?” “Why not consider this other approach?” Or, “have you talked to so and so in our department, for he or she might have a solution for your problem?” When it is time for paper writing, the advisor often acts as an editor, especially for the first versions of the research paper. In fact, an effective advisor can help a student choose a better title, formulate a better abstract, and a better introduction, which are often the most difficult tasks to do for a beginner. See Section 5.6 for some other effective approaches with which your supervisor can help you improve your paper writing quickly. These points are particularly important when dealing with multi- disciplinary research, where team members come from different disciplines. This is when your teammates are most likely your peers. Bear in mind that multi- disciplinary research is often the most rewarding, because it allows each researcher 76 CRAFtING YouR ReSeARCh FutuRe to “think outside the box” of his or her own research field. This can happen in bioinformatics, computational physics, or environmental sustainability fields. The authors had the pleasant experience of traveling far into China’s west together with some of Asia’s best ecologists and computer scientists in seeking ways to un- derstand birds’ migration patterns via GPS5 trajectories. In a series of eye-and-ear opening workshops, researchers from different disciplines pleasantly discovered what each could do to achieve the goal of environmental sustainability. In multi-disciplinary research, many new challenges exist. While it is fun to work with researchers elsewhere, it does take time to learn each other’s objectives, tools, and terminologies. Sometimes it feels like getting a second Ph.D. degree. This period of re-education might last one or more years, after which one can find many exciting new horizons. Thus, we highly encourage Ph.D. students to be will- ing to drop in each other’s seminars and conferences to learn something entirely new. You will be pleasantly surprised! • • • • 5 Global Positioning System. C H A P T ER 5 77 writing and Publishing Papers In Chapter 3, you learned how to find novel and interesting research ideas and topics, and in Chapter 4, you learned how to conduct solid research to demon- strate your ideas. Assume that you have accumulated enough novel and significant results in your research. The next important task, for researchers and graduate students, is to write and publish high quality papers in order to tell the world about your contributions in research. Albert Einstein, for example, was awarded the 1921 Nobel Prize in Physics largely due to his published paper on the pho- toelectric effect (which gave rise to quantum theory) in 1905. In fact, Einstein published three other papers on Brownian motion, the special theory of relativity, and E = mc2 in 1905. It is those four publications that contributed substantially to the foundation of modern physics and changed the world since. In general, a research work and outcome can be very roughly categorized into top-notch (say top 5%), very good (top 5–25%), good (top 25–50%), and so- so (bottom 50%), based on its novelty and significance. Your effort (finding novel ideas and conducting solid research, as discussed in Chapters 3 and 4), is to “up- grade” your research outcome from so-so to good, to very good, and to top-notch, whenever possible. Which category a finished research shall fall into is, in fact, a highly complex issue. Experienced researchers, such as your supervisors, may have a better sense where your research outcome fits in. But let us assume that this can be done for now. Ideally, you should obtain at least good or very good research outcome before considering writing and publishing a paper. We can also roughly categorize journals and conferences into the same four classes based on many factors (such as the Impact Factor, competitiveness, and so on). Again, this is a highly complex issue, but assume that this can be done. Then, 78 CRAFtING YouR ReSeARCh FutuRe good writing is to ensure that a research outcome will be published in a publication venue of the corresponding category. For example, a very good research outcome should be published in a very good publication venue, instead of being “down- graded” to good or even so-so ones, after repeatedly rejected by very good venues due to poor writing. Sadly, we have seen this type of down-grading happening too often in young researchers. Chapters 5 and 6 of this book will hopefully guide you to change this. Most graduate students will have written essays and reports by the time they enter graduate programs. Some may have written newsletter articles, novels, poems, promotional flyers, and speeches. They will surely have written tons of emails, instant messages, and online chat. But most may have never written aca- demic research papers, which are quite different from the other forms of writing mentioned above. As the late Turing Award winner and Nobel Lauriate, Herb Simon1 was known to tell his students: to write a good paper, “you decide on what you want to say, say it, and then choose a good title!” There are many details embedded in this statement, which is the topic of this chapter. In particular, this chapter discusses the key elements of writing research papers, and emphasizes the main differences between scientific writing versus other forms of writing. 5.1 “PubLISh oR PeRISh” As we have seen, publishing high-impact, top-quality papers in top, peer-reviewed venues in a sustained manner is extremely important for researchers, especially faculty members in universities and researchers in research labs. It is the most important means to share with the research community your contributions in research, and your papers will hopefully bring impact to the field. In addition, your academic promotion is also critically hinged on your high-impact publica- tions. The same can be said about your research grants and projects. Thus, in the research circle, there is a phrase: “publish or perish”! 1 Herbert A. Simon (1916–2001) was a professor at Carnegie Mellon University. He was a founder of many disciplines, including artificial intelligence. He received ACM’s Turing Award in 1975 and the Nobel Memorial Prize in Economics in 1978. wRItING ANd PubLIShING PAPeRS 79 FIGuRe 5.1: Illustrating h-index: an author’s h-index is when the publication count line crosses the citation curve, given that the papers are sorted from more to less on the X-axis. Indeed, the pressure for publishing high-impact papers is very high in universities in North America, and in many countries around the world. This pressure tends to have some adverse effects, including producing “salami” papers (see Chapter 3) that are not highly impactful and overlooking the other important responsibilities (such as teaching) of university professors. We are certainly against publishing many unimportant papers just to pad your resume. Despite the negative connotations associated with the phrase “publish or perish,” publishing high-quality papers that report novel and significant research results is the duty of researchers. Here, we emphasize that a researcher’s goal is to publish high-impact papers that others can use to build their own research pro- grams. One indication of impact is citation numbers, which counts the number of references others have made in their papers when referring to your work. Today we have many ways to count citations. Some count citations by journal articles only; for example, the Science Citation Index, or SCI, is an often-used index on journals from the Institute for Scientific Information (ISI), which is owned by Thomson Reuters. Instead of just counting a limited number of journals, other citation 80 CRAFtING YouR ReSeARCh FutuRe services may include most open-source publication venues, including conferences. Examples include the Google Scholar and the CiteSeerX services, which are in- creasingly being used to judge the impact of papers and researchers. A particularly important measure is the h-index, which is a measure de- signed by Jorge E. Hirsch on both the productivity and the citation numbers of a paper. According to Wikipedia2: a scholar with an index of h has published h papers each of which has been cited in other papers at least h times. For example, a researcher with an h-index of 20 means that the researcher has 20 papers that are cited by others for 20 times or more, and the rest of the papers published by the researcher are cited less than 20 times. The h-index, as shown in Figure 5.1, reflects both the quantity of publications and the quality of publications, which can be viewed via a chart. We sort the publications of an author from the most cited to the least cited, and take this list as the X-axis. The Y-axis is the count value: we can plot the number of citations for each paper, which gives one curve (marked as “Citation Count”). Similarly, we can plot the diagonal straight line as the number of papers, which is denoted by “Paper Count.” When the line and the curve cross each other, the corresponding X-value gives the h-index value (which is 17 in this example). However, publishing top-quality papers is not an easy task. This leads to our next question: why is publishing top-quality papers hard? 5.2 whY PubLIShING toP-QuALItY PAPeRS IS hARd There are usually two major avenues of publications: conferences and journals. Most good conferences and journals want to maintain their reputation of only publishing a limited number of top-quality papers. At the same time, most re- searchers want to publish in those top conferences and journals, because their papers will have a high visibility. Thus, the competition is very stiff. 2 http://en.wikipedia.org/wiki/H-index wRItING ANd PubLIShING PAPeRS 81 In computer science and some other disciplines, there are many top-rated conferences that publish full-length papers (e.g., 6 to 12 pages of double-column, condensed texts). The acceptance rate can range from 10 to 30%. Many top spe- cialty journals in science and engineering also have an acceptance rate of about 10–30%. Some broad top-of-the-heap journals in science (such as Science and nature) have very low acceptance rates. Some students tend to “try their luck” when they submit their papers to those top conferences and journals. “30% is not too bad, and is much higher than winning a lottery!” They further explain mathematically: if I submit a paper to 20 conferences and journals with an acceptance rate of 30%, the probability that none of them accepts my paper is 0.720, which is about 0.014. Thus, the chance that at least one conference/journal accepts my paper is 98.6%! We usually give those students the following advice: first, do not submit “lousy” papers to a good conference or journal just to try your luck, or just to get reviewer comments about the paper. Doing so will easily damage your reputation. Second, it is academic misconduct to simultaneously submit the same or very similar papers to multiple places (see Section 5.4 on plagiarism). 5.3 whAt MAkeS A GReAt PAPeR? What makes a great paper? What ingredients will ensure that your paper will get accepted? As you have probably guessed, there is no absolute answer to these ques- tions; it is relative to the conference or journal you submit to, and the answer is also subjective by individual reviewers. When reviewers evaluate papers, they take into account the overall quality of the conferences and journals that you submit to. Despite these factors, there are some common elements that reviewers often use to judge and rank papers. We will review them below. First, you need to understand the review process. Almost all conferences and journals recruit a pool of established researchers to review submitted papers. For each submission, 2–5 reviewers (usually 3) in the same or closely related areas are selected to review your paper. Sections 5.8 and 5.9 will discuss paper reviews for conferences and journals in detail. These reviewers often need to provide a set 82 CRAFtING YouR ReSeARCh FutuRe of “scores” for rating the quality of the paper, along with a detailed justification of their scores. As mentioned earlier, reviewers are always anonymous, thus, they often review papers with a critical eye. Scores are usually integers between 1 to 5, or between 1 to 10. The following is a typical list of questions that reviewers must answer with scores: Please use an integer from 1 to 5 to answer each question below (1 for defi- nitely NO, 5 for definitely YES): 1. 2. 3. 4. 5. 6. Are the research and results novel? Are the results significant? Is the paper technically sound? Is the paper clearly written and well presented? Should the paper be accepted? Are you highly confident about you.r review? Clearly, Questions 1 and 2 are about novelty and significance of the research we have been talking about throughout this book. Question 3 is about research methodologies (see Chapter 4). The research must be technically sound to support the main claim of the paper. If the idea is not novel, the result is not significant, or the research method is flawed, the scores on Questions 1–3 would be low, and the chance for your paper to be accepted would be low, no matter how well you write your paper. However, too often we see young researchers, including Ph.D. candidates, who have conducted novel and significant research, but have difficulty in writing their papers well. That is, their papers would receive a low score for Question 4 above. This also means that it is difficult and frustrating for reviewers to make an accurate judgment about Questions 1–3. For a high-quality and competitive conference or journal, reviewers are usually critical and cautious—if they are not sure about the novelty and significance of a paper, they tend to give low scores for Questions 1–3. Such a paper would then likely be rejected. As we have been organizers of many competitive international conferences, often as Program Committee Chairs, we can say that among rejected submissions, wRItING ANd PubLIShING PAPeRS 83 at least half of them were negatively influenced by poor writing. This happens to many papers written by native English speakers. Chapter 6 describes many language- independent common misconceptions and flaws that often weaken the submitted papers significantly. If authors adhere to guidelines and methods that we propose in this and the next chapters, those papers would be better judged, and would have a better chance of being accepted. We will start with several basic, untold truths about research papers. 5.4 A Few uNtoLd tRuthS About ReSeARCh PAPeRS We would like to first lay down a few basic “ground truths” or postulates about research papers. These postulates are so basic and well accepted in the research community that your supervisors (or other researchers) may never explicitly spell them out for you. However, many early researchers learn these postulates in the hard way. The first and most important ground truth about a research paper is that it must be truthful, honest, and accurate. Unlike commercial ads and product pro- motion, authors of research papers should be as unbiased as possible, discussing both strengths and weaknesses of their work in the paper. The experimental results must be truthful and accurate. Material, data, and results should be kept for a cer- tain period of time (usually several years) after the paper is published for possible future verification by other researchers. If researchers intentionally falsify the re- sults or mislead the readers, serious questions may be raised about the researchers’ credibility; in the worst case, academic fraud may be charged. Occasionally we hear news about research misconduct where data and research results are fabricated, or the published results cannot be replicated. This often results in published papers being retracted from the journals, and/or researchers being dismissed from their research institutes. Honest mistakes are allowed, but strong due diligence should be applied to avoid mistakes that could have been avoided. Another common form of research misconduct is plagiarism. This includes many forms. One of them is called citation plagiarism. This is when authors fail 84 CRAFtING YouR ReSeARCh FutuRe to cite and credit previous work that is similar to their work, and give readers an impression that the work is original and done by themselves. We understand that many authors may not wish to do this on purpose; often they may not find certain previous publications to know that their work has actually been done and published before. In many cases, reviewers can understand such unintentional omission, and will point out such previous papers. As authors, you must then study and cite these and other published papers, and discuss how your paper is different from them. If the previous work is indeed very similar or identical to yours, then you should not submit your paper anymore, until you improve it to show that it is better than the previous work, at least in some aspects. In Section 3.2, we mentioned that you should do a thorough literature search, as thorough as you can before you start your research on a chosen topic or problem. This would help prevent you from wasting time and effort in “reinventing the wheel.” When you make a claim in your paper on novelty, you may also say “to the best of our knowledge, our work is original . . .” to reflect your best effort. Another form of plagiarism is multiple publications of the same or very similar content in different conferences and journals. Many conferences and jour- nals explicitly ask authors to submit only original work, and forbid simultaneous submissions even if the authors intend to withdraw others should one submission be accepted. Multiple submissions and publications can be discovered easily (espe- cially with modern electronic submission systems), and will easily damage authors’ reputations. When you include others’ writings as your own, you run the risk of violat- ing copyright law. Some graduate students copy many sentences or even several paragraphs from other papers, often from previous work or a general introduction to a topic, in their own papers. True, the description of previous work or a well- established topic is pretty much the same. But still, you cannot copy sentences from other papers into yours as if you wrote them. The “other papers” may actually include your own published papers. The publication agreement of your previous papers may stipulate that anyone, including you, needs to get a written permission if any part of the paper is reproduced. If you need to quote the whole sentences or paragraph as fair use in your paper, put them in quotation marks, and cite the wRItING ANd PubLIShING PAPeRS 85 sources. An easy way to avoid copyright infringement, when you write similar con- tent as in other papers, is to wait for a few hours (or days) after you read the other papers, and write the description in your own words. This way, your content will be similar, but the wording will be quite different. The last often-untold truth about research papers is that it must reveal the full details of your research so that other researchers can replicate your results independently after reading your published paper. In Chapter 1, we described re- search as making novel and significant contributions with repeatable and verifiable results. Thus, it is your responsibility to reveal technical details of your work as fully and as clearly as possible in your paper. If other researchers require additional details of your published paper, you are obliged to supply them. Indeed, research in science is “self-regulating” and “self-correcting,” where published results and papers will be analyzed, replicated, verified, and improved upon by other research- ers. It is an open (fully revealing), fair (relatively speaking), and free (i.e., academic freedom) community. If your work contains trade secrets or methods with poten- tial commercial gain, you can choose not to publish it, or you can secure patents or other intellectual property protections before the paper is submitted. When you are ready to write your first papers, you should certainly get your supervisor involved. You may have a proofreader (e.g., a native speaker) to review and revise the paper. What are the roles of you (Ph.D. candidate), your supervisor, and the proofreader in a paper writing process? 5.5 the RoLeS oF You, YouR SuPeRvISoR, ANd PRooFReAdeR Quite a few graduate students are from abroad, where their native language is not English (such as Chinese, Persian, Spanish), but they need to write papers in English. “Since my native language is not English, my supervisor should write the 86 CRAFtING YouR ReSeARCh FutuRe papers, while I am doing the experiments,” some may say. Or, students just write a first draft, give it to their supervisor or proofreader to revise and polish the paper to “perfection.” These viewpoints are certainly not correct. You must learn to write papers well by yourself by the end of your Ph.D. study, regardless of whether your native language is English or not. In fact, many native English speakers do not know how to write research papers well. One of our Master’s students, who is a native English-speaking Canadian, almost failed the thesis defense due to his poor writing. There are many language-independent misconceptions and flaws (see Chapter 6) in writing research papers, and they are often harder to overcome than grammatical errors. Your supervisor will play an important role in correcting them. A good understanding of the roles of you, your supervisor, and proofreader is important in writing a high-quality research paper. Here is a list of roles that the supervisor may play in paper writing: • • • • Help you to understand the goals, logic flow, organization, and argu- ments in writing research papers. Help you to identify specific misconceptions in writing research pa- pers, and you must learn to correct them quickly. Make high-level suggestions on how to improve the presentation and argument of the papers. Make a final check of the paper before it is submitted. Your role in paper writing: • • Work with your supervisor closely for the first 1–2 papers, and learn to write papers well quickly (see Section 5.6 for advice for supervisors). Become independent quickly, and be able to write the whole paper well by yourself. Proofreader’s role: • After a paper is largely finished (with excellent structure, flow, argu- ment, organization, and presentation) by you and your supervisor, a proofreader can be asked to further improve the paper and correct wRItING ANd PubLIShING PAPeRS 87 minor English errors. Other graduate students in the group or in the department would be good candidates. We want to emphasize that the role of proofreaders, unless they are also researchers in the similar area, is quite minimal. Often they cannot help you strengthen the logical flow, arguments, or organization of your paper. They can only point out minor English errors (such as the question of whether “the” should or should not be used in a certain place, and the use of prepositions). You and your supervisor are most crucial for writing a high-quality research paper. So, how can you and your supervisor can work together most effectively in improving your paper writing? We answer this question in the next section. 5.6 SuPeRvISoRS: how to IMPRove YouR StudeNtS’ wRItING MoSt eFFeCtIveLY This section is mainly written for supervisors, who wish to improve their graduate students’ writing most effectively. If you are a graduate student and want to work with your supervisors to improve your writing skills quickly, talk to your supervi- sors to see if they can use the method we suggest here. Many supervisors first ask their students to write paper drafts, and correct them on papers (e.g., with red ink). They pass the corrected drafts to students to “input” the corrections in the paper. This process may be repeated many times. Unbeknownst to supervisors, their students often have a hard time reading their handwriting, and do not know why these changes have been made. The improve- ment in the students’ writing skill is often minimal in each such writing-revision iteration. We have found that the following method can very quickly improve students’ writing skill, to the point that they can write well by themselves after writing only 1 to 2 papers. We call the method the PI method, or the Progressive Improvement method. It may take a bit more time in the beginning, but the extra effort at the beginning will be paid back many times during their Ph.D. study. The PI method works roughly as follows. When it is time to write a research paper, you can ask your student to write a few sections first, or about half of the 88 CRAFtING YouR ReSeARCh FutuRe first draft. These sections may include the Abstract, Introduction, and a section on your new theory or methods. Why not ask him to write the whole paper? Well, if this is the student’s first paper, it is likely that the draft needs be completely rewrit- ten. Thus, the student does not need to waste too much time in writing a complete draft that will not be used in the future. You then sit with your student, and work closely with him, word by word, for the first page (just one page) of the paper. For a student who is a native English speaker, you may focus on high-level structure, logic flow, and how to make con- vincing arguments in the paper. For a foreign student, you may also need to work on detailed sentence structures and choice of words. You need to provide detailed explanations about why you revise the paper this way. Ask your student to write down each writing principle and each type of mistake your student made. You then tell your student to learn and generalize from these principles and mistakes, and apply them to revising the rest of the paper (and to write new sections). You ask him to review the notes often, take time to revise the paper carefully, and try not to make the same mistakes again. Your student may come back in a few days with the revised paper. You can first quickly review the previous page(s) you have worked on, and offer further advice on improvements. Then you work with him, word by word, on the next new page (still, just one page). You should notice that the number of mistakes and needed improvements might be cut by half. If your student makes the same mis- take as the last time, you should give him a serious warning. Your student should write down new tips and mistakes, and then go away to revise the rest of the paper, and come back to you in a few days. This process goes on progressively (thus called Progressive Improvement), until the whole paper is improved once. By that time, the writing skill of your student should have improved tremendously. It is often necessary to go over this whole process two or more times. In the second and third rounds you and your student may focus more on the overall structure and logic flow of the paper, adding experiments to make the results more convincing, adding examples to make it easier to understand, and so on. Again, you work closely with your student, but only on 1–2 issues, or only on 1–2 pages wRItING ANd PubLIShING PAPeRS 89 at a time. Then, you may ask him to apply the ideas to improve the whole paper. Several such iterations are often needed to produce a highly polished and satisfac- tory paper, to be submitted to competitive conferences or journals. By the time the first paper is finished (usually in several months), you student should improve his writing tremendously, and be ready to write a reasonably good paper by himself. Your student will also learn how you have tried to make their paper as per- fect as possible. Keep each version of the revisions so that your student can see how many changes have been made, and learn from this process after the paper is submitted. In Chinese there is a saying: it is better to teach people to fish, rather than giving them a fish. (The conventional English translation of this is: Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.) By spending some extra time teaching your students to write their first paper at the beginning of their graduate study, they learn to write good papers by themselves for the rest of their research career and life. This in turn frees your time for working on other important research problems. Often, we have several graduate students who are learning to write papers, and we use the following methods to be even more efficient. We will distribute the first draft of a paper to these students, and ask them to review and revise the first page carefully on their own. We will then use Skype (a software for online group voice chat) and Teamviewer (a software that allows several people to view the same screen where the paper is actually revised) to discuss and revise the paper simultaneously. This way, all of our graduate students can contribute, revise, and learn how to write better research papers, even when we are in different places or countries. Below, we will first discuss where to submit the paper after it is written. 5.7 wheRe to SubMIt: CoNFeReNCe oR JouRNALS? In some disciplines, such as biology and statistics, conference papers are usually very short and in the form of an extended abstract, and the acceptance rates are 90 CRAFtING YouR ReSeARCh FutuRe usually high. The purpose of the conferences in these disciplines is to let research- ers meet and present their most recent work, usually as posters. Often thousands of researchers go to such conferences each year. Complete work is often published only in journals. In some other disciplines, such as Computer Science, confer- ence papers are full-length with 6 to 12 pages of condensed text, often in double columns, reporting on novel contributions. The reviews for such conferences are more rigorous, and thus, the acceptance rates are typically quite low. If a paper is accepted, authors often have 20 to 30 minutes to present their work orally in a conference session, sometimes as a poster as well. Often, such conference papers are regarded as important as journal paper publications, although different depart- ments, schools, and universities may put them under different weights. Here are some other differences between full-length conference and journal papers: • Conference papers often have a shorter review time than journals, and their review processes are also different (see Sections 5.8 and 5.9). Thus, conference papers are suitable for reporting the most current work with rapid progress. Going to conferences also allows you to meet other researchers and build up your academic network. • Annual conferences have submission deadlines while journals do not. Thus, conference deadlines are often taken as drivers and landmarks for making progress in research. • Conference papers, including the full-length ones, usually have page limits, while most journals do not. Thus, journal papers are usually longer, extending full-length conference papers to report complete work, and thus are often regarded as “archival.” One way to enter a research field is to attend a top or main conference in that field. In computer science, for example, each subfield such as artificial intel- ligence or machine learning has its own “top conference.” Here you will meet with the leaders of the field, hear the latest progress in the field, and meet numerous wRItING ANd PubLIShING PAPeRS 91 people who are active researchers in the field. Soon, you will want to be an author yourself, and start to look for a conference to submit your paper to. If your paper is accepted, you can present your paper in conferences while others listen and learn about your work. It will be a boost to your confidence in research, and make you a mature researcher. Which conferences and journals will you select to submit your papers? Each discipline has a set of conferences and journals; usually some are considered top-tiered, while others so-so. You have probably heard about some humorous (yet true) stories about nonsensical computer-generated papers being accepted by peer-reviewed conferences and journals. You certainly do not want to submit your papers there! Here are some general guidelines in choosing conferences and journals to publish your work. If a conference is the main conference in the field where most important researchers go, where “importance” can be measured by citation numbers, h-index, or leadership in an area, then you may consider submiting a paper or poster even if the acceptance rate is high. Otherwise, choose the main conferences in a field with an acceptance rate around or below 1/3. For journals, it is hard to specify an Impact Factor (IF) as a guide to determine where to submit your papers, as IF varies a lot for different disciplines. One general guideline is to choose the top tier, or the top 25%, of the journals in the field in terms of IF. You may also talk to your supervisor who should know well which conferences and journals belong to top-tier. After you submit a full-length paper to the conference, you might ask: how are conference papers reviewed? 5.8 how ARe FuLL-LeNGth CoNFeReNCe PAPeRS RevIewed? Many prestigious and competitive conferences in computer science require that the names and affiliations of authors remain anonymous in the submission, such that the reviews can be more fair—reviewers will judge the papers only based 92 CRAFtING YouR ReSeARCh FutuRe on the contents, not the authors. Some conferences, however, do not have this requirement precisely because author information can also provide some credit- ability of the work. In both cases, it is usually quite fair when your submissions are reviewed by other researchers. Let us consider the process in which a top conference reviews and accepts full-length papers. The authors of this book have been conference reviewers, pro- gram committee (PC) members, senior PC members, PC chairs and conference chairs. Naturally, we are in a good position to answer this question. First, when the conference paper deadline closes, typically the conference chairs will start to filter out the papers that obviously do not make the cut. Some are rejected right away due to their wrong format, such as being longer than the page limit. Typically, there are also a number of senior PC (SPC) members; each oversees the review process for a subset of the papers and provides comments and recom- mendations for PC chairs at the end. A paper is often reviewed by three reviewers, who are at arm’s length from the authors. Often, this means that the reviewers are not current and former colleagues, students, advisors and friends of the author. What do reviewers look for when they review a paper? Section 5.3 described briefly what makes a great paper. Again, the most important attributes are novelty and significance, as mentioned many times in the book. Reviewers would want to find out what is new in this paper, compared to established literature and practice in the field. If they cannot find what is new about the paper, say in the abstract and introduction of your paper, they might start looking for reasons to reject the paper. Another important thing in paper review is to look for evidence to back up what the author claims are the innovative aspects of the paper, to ensure that there is real impact and significance in the research. For example, the author might claim that the paper presents a new method for learning communities in a large- scale social network in the abstract and introduction of the paper. However, if the experiments deliver only tests on a small-scale data set, or if the experiments do not compare with some well-known methods in the literature, then there will be enough grounds to reject the paper. Section 5.3 discussed what makes a great wRItING ANd PubLIShING PAPeRS 93 paper, and reviewers need to give scores to assess a paper’s originality, significance, technicality, and presentation. Generally, to reject a paper is often easier than to accept one, because there are many reasons a paper can be rejected, and only one of them needs to be found. In other words, a paper might have many critical points where things can go wrong, and if one of these critical points is not handled properly, the paper might be rejected. We can simulate the process of rejecting a submitted paper by pretending that we are reading a freshly received submission. First, a reviewer can read the abstract of the paper and search for the term “In this paper . . .” or an anchor place where the authors state what their main contributions are. The reviewer can then take this contribution statement and start looking for elaborations (that is, by following the top-down refinement discussed in Chapter 6), beginning with a reading of the introduction section. If the reviewer cannot find any elaboration, it is a sign that the paper was not written in a logical way, and it is very likely that the paper is poorly written. If similar patterns can be found in many other parts of the paper that shows that the paper contains too many logical confusions or syntactic mistakes, then the reviewer may consider these facts as strong evidence that the paper should be rejected for a thorough rewrite. Subsequently, if the paper clearly states its innovations in both the abstract and introduction sections of the paper, but if the author has not followed up with strong evidence to back up these contribution claims (i.e., the author did not state how he did his solid research, as we mentioned in Chapter 4), then the paper again can be rejected. If the research results can be in place, but the author has not discussed or cited some very relevant works in related literature, then it may be a sign that the author is not sufficiently familiar with the established literature in the field, and it may be another ground to consider this as a major weakness, which may lead to a rejection. Summing up the above procedure, the process of a quick scan on a paper can be rather strict, but fast: it may take 20 minutes for a reviewer to check all of the above points, before a rejection decision is made due to a lack of logical flow, 94 CRAFtING YouR ReSeARCh FutuRe clarity, sufficient related works or research results. If, however, the paper survives the above screening process, it may still not mean that the paper will be accepted. The reviewer might take another 30 minutes or longer to carefully read the techni- cal parts of the paper, go through the derivations, theorems, and results, check the relevant literature, and perhaps even ask the opinion of another expert in the area, before giving a recommendation on the paper. In recent years a reviewer’s workload is increasing each year. For example, a typical computer science conference can easily receive nearly 1,000 submis- sions. A reviewer might have to review 10 papers in several weeks. The time they spend on each paper is usually rather short. Each reviewer needs to provide the reviewing scores, as well as detailed justification and suggestions. In Chapter 6 we will discuss how to make papers easy to read, so that your paper can pass the so-called “10/30” test. Some conferences allow authors to view the reviews and input their feedback online before final decisions are made. If such an opportunity is given, you should try your best to provide succinct, clear, and strong statements about reviews, espe- cially if you believe some aspects of the reviews are not correct. The final acceptance decision of each paper will be made by the senior program committee member (SPC) and the program chairs. Once the decision is made in a conference, which is usually just “Accept” or “Reject,” the decision is final, and usually cannot be appealed. There is no room to formally reply to the reviews and to submit a revised version, as most journals would allow. So, how are journal papers reviewed? 5.9 how ARe JouRNAL PAPeRS RevIewed? Journal papers are peer-reviewed by other researchers, in a similar way as a confer- ence paper. The EIC (Editors-in-Chief ) of the journal may assign each submis- sion to one of the Associate Editors (AE) of the journal. The AE in charge of your paper will recruit reviewers and oversee the reviews of your submitted paper. The final decision is usually made by the EIC. wRItING ANd PubLIShING PAPeRS 95 Compared to conference papers, major differences exist that make journal papers much “deeper.” First, a journal usually does not have a very strict page limit, making it possible for authors to fully express themselves. Thus, authors can go much deeper in a journal paper than in a conference paper in describing their research results. Second, the process of paper review for a journal paper is often longer than a conference paper, going through several “rounds” of comments and response between the reviewers and authors. This process makes it possible for authors to submit a revised paper to address all reviewers’ concerns. More specifically, after the first round of review, authors may receive one of the following four decisions: accept as is, accept with minor revisions, accept with major revisions, and reject. In the middle two cases, authors need to prepare a revision within a certain time limit to resubmit to the journal. Accompanying the revised manuscript, authors also need to prepare a clear and detailed point-to- point reply to all reviewers’ comments, especially on the negative ones, in a response letter. Here authors can give a detailed rebuttal if they believe that the reviewers are wrong. When authors believe that the reviewers have made good suggestions, they should improve the paper, and specify how and where in the article they have addressed these comments. The response letter can be long (e.g., 10 pages), and should be carefully written. If the paper is initially accepted with major revision, after the revised paper is submitted, the paper will usually be handled by the same AE (Associate Editor), and reviewed by the same reviewers. The second-round revision can still be re- jected, if reviewers are not convinced and satisfied with your revision, or it might result in a second major revision (only in rare cases), minor revision, or acceptance (happy ending!). If the second-round decision is a minor revision, you should submit the revised paper, and another point-to-point response letter, similar to the one for the major revision; but this one can be shorter than that for a major revi- sion. Usually, the revised paper will be checked by the associate editor in charge, along with a few designated reviewers, only to see if all of the minor concerns are addressed. If so, the paper will be accepted. 96 CRAFtING YouR ReSeARCh FutuRe Occasionally, during these rounds of review you may think that you are being treated unfairly. In that case, you can always write a letter to the EIC to complain. Compared to conference papers, the process of submitting and revising a journal article is often lengthy, but it provides very good training for a student and researcher alike. It is in this process that more detailed weaknesses of the manu- script can be brought out and addressed. Thus, despite the lengthier time delay in getting a paper published, it is still worthwhile to submit an extended version of a conference article to a journal, in order to “close the book” after fully exploring an idea. For this reason, journals are often considered to be archival. When extending a full-length conference paper to a journal article, how much extra material is often included? On this question, the answer varies from journal to journal. In some conferences, such as the computer graphics conference ACM SIGGraph,3 most conference articles can be directly transferred to a cor- responding journal, such as the ACM Transactions on Graphics journal in this example. This is done under the agreement between the conference and journal on copyright matters, and on how papers are cited, so that one of the conference or journal articles will be cited at a time and citations will not be counted twice. In other cases, full-length conference papers need to add at least an additional 25 to 30% of new material before being considered for journal publications. This ad- ditional material can be more experimental results, more theoretical results, more discussions and comparisons with related works, or a combination of the above. In this case, we suggest that you write a cover letter to the EIC detailing what is new in the journal submission compared to the published conference paper. As you can see, the process of paper review in a typical journal is quite dif- ferent from that in conference. While review of conference papers is a “one-shot” process, meaning that the review results cannot be disputed once the final decision is made, for a journal paper the authors can often engage in rounds of communi- 3 Association of Computing Machinery, Special Interest Group on Graphics and Interactive Techniques; http://www.siggraph.org wRItING ANd PubLIShING PAPeRS 97 cations via the response letters, and thus the decision process is more interactive. In addition, because a journal is often longer in page count, authors can write more thoroughly about a subject. Thus, we strongly suggest that Ph.D. candidates should try their best to submit and publish 1–2 top-quality journal papers reflect- ing their Ph.D. work, especially if they plan to enter the academia. • • • • 99 C H A P T ER 6 Misconceptions and tips for Paper writing In the previous chapter, we have given an overview on the process of paper writing, submission, and reviewing. In this chapter, we focus on some common and major misconceptions and flaws that junior researchers and graduate students often have when they write their first research papers. These flaws are language-independent — that is, native English speakers often make them too. Ironically, it is often much harder to correct those language-independent flaws than grammatical errors in English, and thus, supervisors may need to be forceful in correcting them, and correcting them early, before the Ph.D. thesis is written. Publishing a series of papers in competitive journals and conferences during Ph.D. study is the best way to validate not only the thesis topic, but also the good presentation style of the papers. 6.1 “It’S So obvIouS thAt ouR PAPeR IS GReAt” One common weakness of papers is that the authors do not make a strong argu- ment for the research in their paper. They might think that the reviewers can see and conclude easily that the paper is great. This may be due to the culture and environment that they grew up in; e.g., some cultures believe that “we should be modest,” and thus we should not stress the importance of our work too much. However, as we saw earlier, publishing in top journals and conferences is highly competitive, and thus it is your responsibility and to your benefit to argue, as strongly as you can but not exaggerate, that your work is novel and significant. 100 CRAFtING YouR ReSeARCh FutuRe Indeed, a research paper is essentially an argument about one central theme: our research work makes novel and significant contributions. This central theme is almost always supported by the following logical steps: • • the problem is important in advancing knowledge. If the problem you study is not important, then why study and write about it? Previous works A, b, . . . have been done, but they have certain weaknesses. Most likely some previous works have been done, and if they are already perfect, there is no need for you to study it. • we propose a new theory/method/design/process z. You should emphasize the novelty of your work. Is it the first time that Z is pro- posed? Is Z intriguing and surprising? If so, you should say it in the paper. • we prove/demonstrate that z is better (at least in some aspects) compared to A, b, and others. Can you prove it theoretically? Do you run extensive experiments to demonstrate the superiority of Z compared to previous works and the state-of-the-art (see Chapter 4)? This supports the high impact and significance of your work. • discuss z’s strengths and weaknesses. You should also be upfront about the weaknesses of Z. A research paper is not like product promotion—it must be honest, fair, and accurate. The weakness also leads to future work of Z, usually described in the Conclusion section of the paper. Each component should be further supported and justified, as strongly as you can, by your paper. For example, when you claim that the problem is impor- tant, you can support it by showing who else also claimed this importance in the past, citing many previous publications on the problem, or referring to its use in real-world designs, engineering work, and applications. When you claim that your new theory or method is better than a previous one, you should be able to prove it theoretically, or run extensive experimental comparisons and perform statistical MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 101 significance tests on the results (see Chapter 4 for how to justify the superiority of your work). If you show that your new method has been deployed in practice, such as industrial applications, it would be even better. The more support you have for your argument, the more convincing the paper will be, and the greater the chance that the paper would be accepted. If you are the first one to propose the new theory, paradigm, or method, you should claim it in your paper: “To the best of our knowledge, we are the first to propose . . .”. Be explicit and forceful, and avoid ambiguity. Use the active-voice sentence structure to describe what you have done (we propose . . . ; we demon- strate . . .); a passive voice (it was proposed . . .) is confusing as it is unclear who actually proposed it. Make sure to distinguish what your paper is proposing and solving from what previous works have proposed or solved. Note that making a strong argument for your paper does not mean that you should exaggerate your claims. In fact, you should never claim anything more than what you can support and justify in the paper. Opposite from the statement “I am modest,” we sometimes see the mistake of claiming “I am the greatest.” Some au- thors make a grand claim (such as “We have solved the AI problems completely”), but grossly fail to support it. This casts a very negative opinion about the paper, which can be easily and quickly rejected. Note that while making a strong argument about the superiority your research, use a polite tone, such as “to the best of our knowledge,” “as far as we know.” Similarly, use a polite tone when discussing the weaknesses of previous works, such as “it seems that the previous work . . .”. Back up your claims with strong evidence. If you plan to submit your paper to a specialized conference or journal, you may not have to say, literarily, that the problem we are studying in this paper is important. This can be implied in the description of the problems. But none of the above logical components should be missing in the paper. To summarize, your paper is an argument, and should have one central theme: your paper contains novel and significant contributions. You should 102 CRAFtING YouR ReSeARCh FutuRe emphasize your contributions. You should argue for your paper, as strongly as you can, and at the same time, not exaggerate your contributions. It is a tricky balance. Be positive, accurate, upfront, and balanced. 6.2 “It IS YouR ReSPoNSIbILItY to uNdeRStANd MY PAPeR” Very often, when early researchers (including Ph.D. candidates) write their papers, they unintentionally make their papers hard to understand by reviewers and future readers. They often believe that it is the reviewers’ responsibility to understand their papers (hence the title of this section). They often blame reviewers for not having enough knowledge or putting in enough time to understand their papers (“Reviewers should read my paper more carefully and check out my published papers cited, to fully understand this paper.” Or “Reviewers are so careless. They point out . . . but it is clearly stated at line 23 of the right column on page 5!”). Furthermore, some researchers even think it is a “good thing” to make their papers hard to read (“If my paper is easy to understand, it must be too simple!”). They might think that it is natural for research papers to be hard to understand (“My paper should be hard to understand—it is based on many years of research and my Ph.D. thesis!”). In the last section, we describe one objective of writing a paper: to make an argument, as strongly as you can, for the novelty and significance of your paper. Here, we want to add another objective: you need to do so as clearly and as simply as you can. The two objectives are, surprisingly, not contradictory to each other. Why is the objective of clarity so important? A major reason is that review- ers are very busy researchers themselves, and they won’t spend hours to understand every page of your paper. If reviewers don’t quite understand your paper due to your poor writing, they tend to be frustrated, and give you low scores and nega- tive recommendations (Section 5.3). The other reason is that after your paper is published, as we discussed in Section 3.3, readers, who themselves are researchers, need to get your main ideas and results quickly. Research papers should be written MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 103 in a straightforward, direct, simple, and clear manner anyway. It is a significant milestone in a graduate student’s career when he or she can consider “This paper is so simple,” as a compliment rather than a criticism, as long as the simpler de- scription addresses the same problem. As we will show you, it is actually not too hard to do. 6.3 the 10/30 teSt Whenever you are writing a research paper, or a report or thesis for that matter, you must remember at all times that you are writing for your readers, such as re- viewers, other researchers, and thesis examiners.You know your work so well after many years of research, but this is not true for your reviewers. Often it is because you know your work so well that it is hard for you to write for others. You must put yourself in reviewers’ shoes, so to speak. This is the same as designing prod- ucts for your target clients and customers—you must think from the perspectives ofyour end users. To write for reviewers, you must first gauge the knowledge level of average reviewers. If you are submitting your paper to a general conference or journal, a gentle introduction to the problem you study is needed. You should assume that the reviewers have little knowledge on the specific research problems you work on. You should certainly assume that reviewers have never attended your weekly research meetings, nor have they heard your presentations on the work! All they have at hand is this paper that they are reading. If they have questions while re- viewing your paper, they cannot ask and communicate with you! One way to check if your paper is clearly written is to judge if it can pass what we call the “10/30 test”: for average reviewers, can they get a good idea of what the problem you are studying is and what your main contributions are within 10 minutes? In addition, can they get a very good understanding of your paper (assuming a 10-page conference paper) to make an acceptance decision within a further 30 minutes? Most likely reviewers will not spend more than one to two hours to review your paper (including writing the reviews). 104 CRAFtING YouR ReSeARCh FutuRe Before you submit your paper, give it to some colleagues who are familiar with the area but have not worked on your problems, to see if it can pass the 10/30 test with them! It is somewhat a “dilemma” that the more novel your work is (which is a good thing), the harder that you can convince the reviewers. You must introduce your work “gently” and support it strongly with technical details and convincing results (such as definitions, theorems, proof, designs, methods, data, experiments, and applications). How can you do these two “opposite” tasks well? The question turns out to be a key point in writing research papers, and we will present it in the next section. 6.4 toP-dowN ReFINeMeNt oF PAPeRS Top-down refinement, briefly speaking, means that you must present your work in the general-to-specific style. This can be facilitated by a top-down section structure of papers. Recall that, in Section 3.3, we discussed a typical structure of a research paper (duplicated here in Figure 6.1) and described how such a struc- ture can help you to read the papers quickly to get the main ideas and results. You should write your paper in this way too, so that others, especially reviewers, can get the main ideas and results of your paper quickly and easily. Let us now explain this key issue in more detail. First, recall that your paper should have the following logical steps supporting the central theme, briefly, • • • • The problem is important Previous works have been done but they have certain weaknesses We propose our new theory/method/design/process We prove/demonstrate that ours is better than previous works In your research paper, you need to “tell your story” to reviewers of these central criteria several times (4 times, actually) with different levels of details. That is, you need to tell your story in 10 words (as in the title), 200 words (in Abstract), 1,000 words (in Introduction), and 5,000 words (the main body), with increasing levels of details. More specifically: MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 105 title: The title of the paper is the highest level of summary of the central theme. It may contain a few to a dozen or so words (say 10 words), and it must be at a very high level (i.e., not too technical). It should convey a positive and exciting tone by using, for example, words such as “improving,” “novel,” or the “hot” topic that your paper is about, such as “social networks.” If writing a paper is hard work, then creating a good title is an art. The title of your paper gives the reader a first impression, and this is why some seasoned researchers even go as far as say that the title equals half the paper. A first rule of thumb is that you want your paper to stand out in a pool of many other papers of the same type, either as a paper in an issue of a journal, which might consist of 10 or 20 papers, or in conference proceedings with 100 or more papers. Another rule of thumb to follow is that your title is no longer than one line; a long title gives an indication that the work might be too specific, or the authors are not good at sum- marizing their work. Another rule of thumb is to ensure that no one has published the same or very similar title before. This rule can be enforced by checking on a search engine, which often returns a list of closely matched titles. You may try to enter some potential titles in a search box and see how many hits you will get as a result, and whether the returned results resemble the paper you are writing. Abstract: The Abstract of the paper may contain a few hundreds of words (say 200 words). It must be a high-level 200-word summary of the complete central theme, telling readers about your work. In Figure 6.1, we use a “200-word story” and “elevator pitch” to describe the Abstract. That is, the Abstract must be at a high level, positive, simple, and it tells a complete “story” about your work in 200 words. It should attract people’s attention, like an elevator pitch when you tell investors (reviewers here) how great your product (your paper) is within a few minutes. Here is a sample Abstract. We add some comments in [. . .]. General web search engines, such as Google and Bing, play an important role in people’s life. [The problem is important] However, most of them return a flat list of webpages based only on keywords search. [Previous works have certain weaknesses] It would be ideal if hierarchical browsing on topics and keyword 106 CRAFtING YouR ReSeARCh FutuRe FIGuRe 6.1: Outline of a sample paper, and an illustration of top-down refinement. search could be seamlessly combined. In this paper we report our attempt toward building an integrated web search engine with a topic hierarchy. We implement a hierarchical classification system and embed it in our search engine. [A very high- level summary of our work] We also design a novel user interface that allows users to dynamically request for more results when searching any category of the hier- archy. [Emphasizing novelty and usefulness] Though the coverage of our current search engine is still small, [be upfront on the weakness of the work] the results, including a user study, have shown that it is better than the flat search engine, and it has a great potential as the next-generation search engine. [Using positive words to show the significance and impact of the work.] As you can see, the abstract presents a complete line of argument of the central theme at a very high level without using technical jargons. It also casts a positive and exciting tone about the novelty and significance the work. Introduction: The Introduction section usually takes 1–4 pages (on average, 2 pages) to write. In the Introduction, you will re-tell your central theme again with more explanations on every component of the argument than the Abstract. MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 107 The Introduction should also emphasize the background, namely, why the prob- lem is important; who has studied it; who should read the paper, and where have similar techniques been used, etc. The Introduction should still be written at a high level, avoiding technical terms and details as much as you can. What is the relation between the arguments, such as “the problem is im- portant,” in the Abstract and Introduction sections? Simple! each argument in the Introduction is simply a refinement of a corresponding one in the Abstract, in the same order. A simple and rough rule of thumb is that each sentence in the Abstract can be expanded and refined into roughly three to 20 sentences in the Introduction (20 sentences can form a paragraph). If the Abstract consists of sentences A, B, C, . . . , then the Introduction will be A1, A2, . . . B1, B2, . . . C1, C2, . . . The set of sentences Ai, i = 1, 2, . . . , is simply an expansion of A. The same applies to B, C, and so on. If the sentences and logic flow in the Abstract are modified in a revision, then be sure to remember that subsequent revisions should be made in the Introduction to reflect the changes. Here are the beginning sentences in the Introduction that accompanies the sample Abstract we mentioned earlier in this section. Again, our comments are included in [. . .]. General web search engines (such as Google and Bing) play an important role in people’s lives in helping people to find information they want. According to SEMPO (2009), more than 14 billion searches are conducted globally in each month. However, most of them return a flat list of webpages based only on key- words search. As queries are usually related to topics, simple keyword queries are often insufficient to express such topics as keywords. Many keywords (such as china, chip) are also ambiguous without a topic. It would be ideal if hierarchical browsing and keyword search can be seamlessly combined, to narrow down the scope of search, and to remove ambiguity in keywords. The original Yahoo! Search Engine is a topic directory with hierarchy for easy browsing. However, . . . [back- ground about search engine development] 108 CRAFtING YouR ReSeARCh FutuRe You can see that the first two sentences in the Introduction are further elaborations of the first sentence in the Abstract. The following sentences are fur- ther elaborations of the second and third sentences in the Abstract section. The Introduction also provides the background on search engines, and the motivation and rationale of this research. At the end of the Introduction you usually describe the layout of the rest of the paper. You tell the readers what each section of the paper will describe very briefly. Be sure to use an active voice as much as you can. For example: We orga- nize the rest of the paper as follows. In Section 2, we discuss previous work on . . . In Section 3 we describe. . . . Finally, in Section 4 we show . . . etc. Previous work: You may have a section on reviewing previous works, such as Section 2 in Figure 6.1. This is a further expansion of the corresponding part in the Introduction, which in turn expands from the Abstract. The key here is to demonstrate to the readers that you are familiar with the state of the art, so that your further statement on your contributions has credibility. Reviews of previous works do not need to be long, but you must draw the difference between previous works and your work. Sections on your work: Your main original work will be described here. As it may be quite lengthy, you may need several sections for it. These sections make a detailed argument on your central theme. These sections describe what your novel theories, methods, or processes are (Section 3 in Figure 6.1) and why they are sig- nificant; that is, why they are better than previous works and the state-of-the-art (Section 4 in Figure 6. 1). You can have more sections (such as new theory, deploy- ment, and so on) for your work. The overall structure of these sections is simply a further top-down refinement of the corresponding parts in the Introduction. In fact, you should apply the top-down refinement at all levels in these sec- tions. Your top-down refinement should be supported by the organization of the paper. That is, you create high-level subsections (such as Sections 3.1 and 3.2), to MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 109 describe the high-level ideas, and then use low-level subsections (such as Sections 3.1.1, 3.1.2) to describe more technical details, as shown in Figure 6.1. The top-down refinement is often used within each paragraph. Usually one paragraph should have one central idea. It often starts with a summary sentence (such as “Active learning has been shown to reduce the number of labeled exam- ples significantly”). Then you further elaborate this summary sentence by showing why and how in the rest of the paragraph. Conclusion: After you describe your contributions in great length, near the end of your paper, you need to write a summary or conclusion section. In this section, you re-tell the whole story again at a high level. The Conclusion section can be similar to the Abstract, with more details on your novel and significant contributions now that you have presented all the specifics, and future works. With this top-down refinement structure, it becomes very easy for reviewers, and future readers, to understand your ideas. At the same time, they can go deeper into your technical details and results to any level of detail they wish. Reviewers can spend 10 minutes on the Abstract, Introduction, and some top-level descrip- tions to understand the main contributions of your work at a high level. This helps them understand quickly the rest of the paper by spending 30 minutes or so to hover between high-level subsections, and if they want to, go deeper into techni- cal details at low-level subsections. Only this way can your paper possibly pass the “10/30 test” described earlier in the section. Do you find that our book is easy to understand? That is because of how we framed it: we have been using the top-down refinement in writing this chapter, and the whole book.Now, please do the same in your papers! 6.5 CReAte A hIeRARChY oF SubSeCtIoNS ANd ChooSe SeCtIoN tItLeS CAReFuLLY As we have seen the importance of writing research papers in a top-down refine- ment fashion, it is thus extremely important to create levels of (sub)sections, and 110 CRAFtING YouR ReSeARCh FutuRe choose section titles very carefully to reflect the overall logic structure of the paper. Note that in some fields and journals, papers often have a fixed structure and sec- tion titles (such as sections on Introduction, Hypothesis, Methods, Results, and so on). If this is the case, you should follow the convention. Avoid a very long section without subsections. For example, if the Review section is very long, split it into several subsections (Sections 2.1, 2.2, etc.), each perhaps discussing one type of previous work. On the other hand, avoid very deep subsections (such as 3.1.2.1.1). Usually you should not go deeper than 3 or 4 levels in structure. If you have to use deeper subsections, consider including two or more first-level sections (for example, Section 3 for the new theory and Section 4 for the new method) rather than putting them into one big section. At the beginning of each section and subsection, you should write a brief summary or introduction to this section. Thus, between Section 3 and 3.1, there should be some introductory or summary paragraph(s) about Section 3. Similarly, you should write some introductory paragraphs for Section 3.1, before you create and use Section 3.1.1. This is exactly the top-down refinement you apply at all levels in the paper. The writing process itself can be a top-down refinement process. When our graduate students are ready to write their second or third papers by themselves, we usually work with them on the Abstract carefully, together with a 2-3 level outline (including subsection titles and some very brief contents) for the whole paper. This will make the whole paper logical, consistent, and coherent. Then we ask our students to “fill in” details in each section, also in the top-down manner. This will make it easy for your students to write great papers. 6.6 tIPS FoR PAPeR wRItING Above we discussed a number of language-independent misconceptions in paper writing and how to correct them. Here we offer a number of tips for writing good papers, resulting from our own experiences as well as extensive interactions with other authors and reviewers alike. MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 111 6.6.1 use Certain words to Signal Readers When you describe your work at a high level (in the top-down refinement pro- cess), use certain keywords to signal readers so they know which part is important and which part can be skipped. The following are some examples. We underline those keywords here for illustration. “We will first describe our method at a high level here. It consists of four major steps. We will describe them briefly below.” “The intuition of our method is that . . .” “We will describe a proof sketch first to give some intuition about the theo- rem and the proof.” “Generally speaking, our method is . . . .” When you start describing technical details, after a high-level description, you should also signal readers about this. You can use keywords such as: “More specifically, . . .” “For example, . . .” “We provide details of Step 3 as follows. . . .” “Below we give a detailed breakdown of our experimental results.” These words basically signal reviewers that if you are comfortable with the general idea, you can skip the details here! 6.6.2 use Simple Sentences, but Not Simpler Einstein once famously said: “your theory should be as simple as possible, but not simpler.” The same can be said in writing papers. Often, when beginning research- ers write papers, they use long and complex sentences to describe their ideas and work.Most of the time, writing can be simplified to improve readability greatly. Here is a paragraph from a draft paper written by a capable non-native English- speaking Ph.D. student: “There are two basic functionalities that we expect our system to offer: an effective knowledge organization model to represent the panorama of knowledge in levels and scales, named MKN model; a multi-faceted eBook retrieval system 112 CRAFtING YouR ReSeARCh FutuRe based on MKN model to ease the searching and cognitive process for users, named MIQS, using Facet Grouping, Multi-scale Relevance Analysis, and Information Visualization to overcome the difficulties above.” You will notice that the whole thing is just one sentence! Maybe grammati- cally it is correct, but it is certainly hard to follow. Interestingly, when we asked the student why he wrote such a long and complex sentence, he replied that he had been preparing for the Graduate Record Examinations (GRE) test. It is a required standardized test for admission to many graduate schools, and it includes tests for reading comprehension. Do you really want to test reviewers’ reading comprehen- sion level with your paper? We revised the long and complex sentence to the following eight short and simple ones: “There are two basic functionalities that we expect our system to offer. The first functionality is an effective knowledge organization model. It represents the panorama of knowledge in levels and scales. We call it the MKN model. The second functionality is a multi-faceted eBook retrieval system. It is based on the MKN model to ease the searching and cognitive process for users. We call it MIQS. It uses facet group- ing, multi-scale relevance analysis, and information visualization to overcome the difficulties mentioned earlier.” Reviewers will certainly appreciate simple, straightforward, and logical sen- tences in your paper. Even when the ideas, methods, or results you want to express are complex, you should try your best to explain them using as simple ways as possible. Often figures and diagrams can be created to help this effort, and analogies can be drawn to simplify the explanation. 6.6.3 use a Small Set of terms throughout the Paper Another important method to make your paper easy to understand by reviewers and readers is to use a small set of technical terms throughout the paper. Often MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 113 several technical terms are equivalent in meaning, and different authors may use different terms in their paper. Unlike writing novels and poems in which you would try to avoid using the same terms, in research papers, it is actually better to keep using the same technical terms. Using different terms for the same thing would confuse readers greatly. For example, in the Information Retrieval area, a re- search field that concerns how documents can be indexed and searched effectively, we often talk about the “precision on the test data.” But other terms are also used in other papers, such as “precision on testing data,” “precision on validation set,” “test-set precision,” “percent of correct retrieval on test set.” If you use all of these interchangeably in your paper, you will cause a huge amount of confusion. Thus, it is best to stick to one term for the same meaning and use it throughout the whole paper. If your choice is unconventional, you can formally or informally define the terms early in the paper, or even include a table of term definitions early in the paper, and then use them throughout the paper. 6.6.4 use examples early and use them throughout the Paper When you explain some abstract concepts or complex modeling processes, it is often best to use one or two concrete examples. Use examples early in the paper. That is, do not overwhelm readers with too many abstract concepts and complex processes before showing examples. By then, the reviewers may have gotten lost (and worse, they may lose interest in your paper). A good approach is to introduce one or two examples early, and to further develop the same example(s) throughout the paper. This is why they are often called “running examples.” You can see that we have been using several graduate students as examples throughout the paper, and hopefully our approach has made our book easier and fun to read! 6.6.5 use Figures, diagrams, Charts, Photos, tables Just as examples can greatly enhance the comprehension of your paper, so too can diagrams, flow charts, photos, figures, drawings, illustrations, tables, and so on. Use them lavishly in the paper. You will find that we have used many figures in this book. “A picture is worth a thousand words.” Often it is much faster to view and 114 CRAFtING YouR ReSeARCh FutuRe understand charts and images than reading hundreds of words that explain the same thing. When you make your paper easy to understand and save reviewers’ time, they will appreciate it. 6.6.6 write about Your Motivations and Justifications As we emphasized earlier, it is extremely important that you write your paper for your reviewers and readers. You must write from their perspective. They may know the area well, but they may know little about the specific research problem studied in your paper. Thus, when you write about your novel theories, methods, processes, and so on, you should write about the motivations—why they work—at least intuitively. If there is a new mathematical equation, explain why you choose its particular form and parameters. Writing about motivations may not be so easy, as you have worked on your research problem for months or even years. Try to recall your initial motivations, or try to explain your work to some colleagues who do not know your research problem. Or, you can keep track of the motivations and write them down as you go, as part of your overall documentation for your research process, so you can refer to them and look them up later. Similar to motivations, you must justify certain important choices you made in your research. For example, why did you choose those particular parameters in your experiments and datasets? Why did you combine those processes but not others? For each choice you made, you should try your best to justify it, at least briefly. Reviewers may not “buy” your justifications completely, but if do not see them, they can easily raise questions and cast negative views of your paper. 6.6.7 Pose Potential Questions and Answer them Yourself As you are writing for your reviewers who would be reading your paper for the first time, you must think hard about one thing: what questions would they have while reading my paper? These questions can come up anywhere in the paper. For ex- ample, in the Introduction, after you briefly describe the problems and your novel MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 115 solutions, reviewers may wonder why you did not use some previous methods, perhaps with some obvious modifications, that could be effective in solving your problems. In the experiment section, reviewers may wonder why you did not use a different material, method, or a different optimization process. Writing about motivations and justifications will answer some of those questions. However, sometimes there is no natural place to answer some of these questions. In these cases, you can pose these questions yourself, at the most likely place that reviewers may ask, and then answer them by yourself ! The easiest way to pose such questions is “One might wonder . . . ,” or “One might argue that . . .” Then provide a succinct answer. If you raise questions at the same time as reviewers would while they are reading your paper, and you provide satisfactory answers, you cannot imagine how satisfied the reviewers will be after reading your paper! 6.6.8 emphasize and Reiterate key Points in Your Paper Often we hear graduate students complaining about reviewers’ apparent careless- ness when reading their paper. They point out a question from the reviewer but the answer actually appeared in the paper. As we discussed earlier, reviewers are very busy researchers themselves, and they often have very limited time in reading and reviewing papers. If certain mes- sages are very important, you should emphasize them, and reiterate them several times in the paper, especially in high-level subsections. It may also be worthwhile to present the information in multiple ways, as part of sentences, diagrams, lists, or headings. This allows you to reinforce important information and concepts.How many times and in how many different ways have we reiterated the key point that you should use top-down refinement in writing papers in this book? This should give you an example. If your method has some small but key differences from the previous methods, and you think reviewers can easily overlook them, you must point this out, and emphasize these key differences. You should also reiterate such key 116 CRAFtING YouR ReSeARCh FutuRe differences several times in the paper, including perhaps in the Introduction and Conclusions. 6.6.9 Make Connections throughout the Paper Another important approach, which is often overlooked by young researchers, is to make ample connections within your paper. In our book there are many places we use “See Section . . . for more details,” “As we discussed in Section . . . ,” “Recall that . . . ,” and so on. In fact, whenever you write about something that has been mentioned earlier, or will be mentioned later in the paper, you can consider making a connection there. This makes your paper coherent, consistent, and easy to understand. 6.6.10 Format Papers for easy Reading We have presented many approaches and tips on how to make papers easier for reviewers and readers to understand. There are more such tips, but we will not go over them now. Instead, we want to talk about some formatting details. This shows that even “trivial” matters such as formatting should be considered when you write your papers. One annoying thing we often encounter when we review papers is that figures, charts, and the text explaining them are not on the same page. This can happen easily when you use LaTexTM to format the paper, which arranges the fig- ures or charts automatically. Imagine that reviewers have to flip your paper back and forth to match the text with the diagram—a frustrating process. We often try to reformat the paper manually so the figures and accompanying texts are on the same page, and even near each other. Another related issue is figure captions and tables. Often you can choose to put explanation texts either in the main text of the paper, or in the captions. We prefer the explanation texts to be put in captions. Captions are always very near (at the top or bottom of ) the figures or tables. Yet another issue is the font size. Often in figures or tables, the fonts are too small to be viewed easily. This is often due to the amount of content presented MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 117 FIGuRe 6.2: An example of a paper with too many results on the page. in the figures and tables. Many authors want to present as much information as possible in figures and tables to show “how much” work they have done. Often too many figures are jammed in a small space, too many curves in each figure, and too many rows and columns in the table. All of these result in small font sizes. Not only are small fonts hard to view, with too much information in one figure or table, reviewers can be confused about where to look! Remember you cannot point out with your finger which column to look at while reviewers are reviewing your paper! Here is an example of a paper with too many results on the page (see in Figure 6.2). Young researchers are often eager to present as much information as they can fit in the limited space, thinking that perhaps this helps show that they have done a lot of work. In reality, it is often beneficial to only present a smaller amount of most relevant and key information, especially in figures and tables, with adequate font sizes. 6.7 otheR MISCoNCePtIoNS ANd FLAwS There are many other misconceptions and flaws in writing research papers. However, as this book focuses mainly on the overall process of doing research for graduate students in science and engineering, we selectively present some key ones here. We plan to write a book exclusively on research paper writing in the future to give this topic complete coverage. Here are some of the other often encountered misconceptions and questions: 118 CRAFtING YouR ReSeARCh FutuRe • “My work is really elegant and beautiful. It has a lot of math:defini- tions, theorems, and long proofs. Don’t blame me if reviewers cannot understand it!” • “To emphasize that our method is so much more superior, I use a lot of old, italics, exclamation points, and super strong language in the paper. My supervisor removes most of them. Is he insane or what??!” • “My supervisor always corrects little things in English that appear ev- erywhere even in newspapers, books (even this book), and magazines. For example, he would change ‘it can’t . . .’ to ‘it cannot . . .’. It’s really a waste of time, isn’t it?” • “I am putting so many new contributions in the paper, including new theory, proofs, algorithms, experiments, and even an implemented system, so that it cannot be rejected by reviewers.” • “My supervisor asked me to revise the paper further. I think it is al- ready perfect. Besides, I wrote it, so it is hard for me to find my own errors and make further improvement.” • “My work is so much better than previous work, but it still got re- jected. I can tell from the reviews that the reviewers are authors, or friends of authors, of the previous work I compared to. How can re- viewers accept my paper if their own work is inferior to mine? Is it clearly a conflict of interest?” • “The reviewers of my journal submission are so unreasonable. I don’t think I can ever revise the paper to satisfy their demands. I should try another journal.” 6.8 SuMMARY The two chapters on paper writing (Chapters 5 and 6) are quite long, but they are extremely important for young researchers. Too often young researchers write papers that are unnecessarily hard to understand, and they believe that it is the reviewers’ responsibility to understand their papers. Clearly this “flaw” is not re- MISCoNCePtIoNS ANd tIPS FoR PAPeR wRItING 119 lated to English or any specific language they are using. A lot of effort can and should be put into writing an easy-to-follow paper that can pass the “10/30” test we mentioned earlier in the chapter. This actually should also be true for writing essays, homework assignments, reports, or any long documents. Thus, it is not reviewers’ responsibility to understand your paper; it is your responsibility to make it easy to understand. You can do that using these ap- proaches and tips we have discussed in Chapters 5 and 6, from the top-down refinement strategy to “trivial” formatting details. Notice that we have presented two objectives of paper writing: one is to make an argument, as strong as you can, for your paper; the other is to present your arguments and results as clearly and as simply as you can. These two objec- tives are not conflicting, and a huge amount of time and effort can be put in to optimize them. Unfortunately, the “global optimal solutions” for these objective functions are unknown, and can never be reached completely. That is, there are always ways to improve your papers (including research results in the papers). The more time and effort you put in, the better the paper will be. Thus, doing research and paper writing are a never-ending optimization process. When we submit a paper, it is not because it is already perfect; rather it is because we have put in as much effort as we can before the deadline (most conferences have deadlines), or we believe that the paper is on par with, or better than, the quality of published papers in the same journals or conferences, and we want to put a closure to the current work. • • • • 121 C H A P T ER 7 writing and defending a Ph.d. thesis In previous chapters, we discussed how to conduct effective research and publish research papers. We have discussed how to find good ideas for a thesis in Sec- tion 3.5, and how to set up a thesis plan early in Section 3.7. In this chapter, we put all these ideas together and give an overview of one of the most important functions of Ph.D. study: to successfully write and defend a Ph.D. thesis. You will find that writing a thesis is quite similar to writing a research paper (see Chapters 5 and 6), but many important differences also exist. 7.1 theSIS ANd dISSeRtAtIoN A Ph.D. thesis or dissertation is the most important piece of work in your early career. It is a logically organized document that convincingly states your solution to a challenging problem. It should be logically organized such that your commit- tee members should understand and appreciate it. The committee of the thesis examiners is tasked to find holes in your thesis, and a Ph.D. defense is organized so that in the space of two or more hours you must bravely and convincingly de- fend it, in front of the examiners. Your entire graduate life is essentially condensed to this activity! Sounds tense and terrible? Actually it is not. If we take you as a product, your Ph.D. program as a piece of software, then the difference between when you first entered the program, and when you exit successfully from the program, is a person (you!) who is more confident, logical, knowledgeable in a focused area of research, with knowledge of your problem and solution inside out. When you 122 CRAFtING YouR ReSeARCh FutuRe enter your Ph.D. defense, you are the most knowledgeable person in the proposed area of research (more than most thesis examiners), and you are there to tell your committee just that. In the traditional sense, a thesis is a hypothesis or statement about the world. For example, a thesis might be that “the Earth goes around the Sun, but not the other way around.” Another example of a thesis might be that “a distance measure on the data differences can be found to help build a piece of classification software that performs better than existing classifiers.” However, a dissertation is an organized presentation of your thesis, in which you present the thesis and its entire context, present how others have approached the thesis, and your particular solution. A dissertation includes all evidence you have to defend the thesis, and all your thoughts that arise as a result of the thesis. Despite this difference, we often treat them the same. Thus, we often hear advisors and students say, “I am writing my thesis.” In Section 3.5, we briefly discussed the process of going from research ideas to a thesis topic, in which we mentioned that, among the many factors, passion for research, technical strengths, and the area popularity can be important factors for you to consider in choosing a thesis topic. In Section 4.2, we further discussed how to systematically filter the potential thesis ideas based on impact, importance, and knowledge of how to break down a complex problem into simpler ones. When you enter the actual process of writing a Ph.D. thesis, you will find that all of these skills and conditions will play an important role. The procedures in writing and defending your thesis are all different in different universities and countries, but the main parts are the same. There are basically two ways to organize your thesis: top-down or bottom-up. 7.2 theSIS oRGANIzAtIoN: toP dowN oR bottoM uP By the time the student sits down and writes the thesis, typically the student will have accumulated a number of documents as resources. These might include the student’s published conference or journal articles, some accepted and some just wRItING ANd deFeNdING A Ph.d. theSIS 123 submitted. They also include the student’s proposal documents, and other drafts that the student has written. Now the task for the student is to organize them into a coherent Ph.D. thesis. First, consider the top-down process (also refer to the top-down process of paper writing in Section 6.4). The top-down approach starts from a central thesis; for example, for a computer science student, a problem such as “How to include a human in the loop when constructing a text classification model?” can be the the- sis. It should be simple and concise, and easy to state even to non-domain experts. This is particularly important for you to convince the external Ph.D. committee members when defending your thesis, because by rule the committee must include someone outside of your area of study. For example, a Physics professor might be asked to be the external examiner for a Computer Science Ph.D. student. Then, using the Research Matrix Method that we described in Section 4.3, the thesis might be broken down horizontally or vertically into several subproblems, each with a coherent introduction, existing solution survey, and your proposed solution, along with all experimental and theoretical evidence for you to defend it. Each subproblem can then be further broken down into subsections, each focusing on a sub-subproblem of its own, but all connected in some logical fashion. This is similar to the “thesis plan” we mentioned in Section 3.7. This top-down approach, illustrated in Figure 7.1, has the following advantages: • • • • It allows the student and advisor to know about the central thesis early in the program. It can easily reveal missing problems and solutions early in the study, so that a remedy can be designed accordingly early in the program. It allows the student to have good training in grant proposal writing, and ensures good management style. It makes it easy to define coherent terminology and symbols used throughout the thesis. However, the top-down approach is also not without weaknesses. It is often very challenging for a junior researcher to foresee all subproblems and 124 CRAFtING YouR ReSeARCh FutuRe FIGuRe 7.1: The top-down approach. solutions early in the process, as research planning is typically iterative: you plan and then you use the feedback of your plan execution to replan, until the plan is satisfactory. In contrast to the top-down process of organizing your thesis, a bottom-up process is often favored by many (see Figure 7.2). This applies when the student has published several research papers and has some written resources scattered around. A student using this strategy acts as a gold-miner looking for nuggets in FIGuRe 7.2: A bottom-up process for building a thesis. wRItING ANd deFeNdING A Ph.d. theSIS 125 a pile of rocks. Like a miner, the student has to discover a subset of the material that has a coherent theme in the writing. Again like a miner the student may not take all the raw material in for the content of the thesis, and instead will pick and choose. This is where the student has to have a keen eye on what is necessary to compose the thesis, and what is not. A risk is for the student to mistakenly take the thesis as a job report that includes all that the student has done, thus including some material that has been published by the student, but has little to do with the main theme of the thesis. Summarizing, the advantages of the bottom-up process are: It gives the student more flexibility in exploring different potential themes early in the program. The student has a “fat” CV to take to job interviews after completing the thesis, where the diversity adds to advantages in job hunting. • • Some of the disadvantages of the approach include: • There is the risk that the student compiles all published papers as the thesis without selection, thus destroying the coherence of the dissertation. • The student might spend more time threading together the works reported in papers, and put in much effort unifying the symbols and terminologies used in different papers. In the end, whether the student prefers a top-down or a bottom-up ap- proach is entirely a personal choice. Let’s consider the earlier examples of Students A2, B2, and C2, where A2 prefers theoretical research, B2 prefers empirical and system-oriented research, while C2 prefers research that can lead to patents and start-up companies. As an example, Student A2 wishes to follow the top-down method for thesis writ- ing and organization, and in so doing he finds a topic to work on first using the matrix method presented in Chapter 4. After isolating the thesis topic to be in the area of “transferability for knowledge transfer between domains of different 126 CRAFtING YouR ReSeARCh FutuRe feature spaces,” he divides the problem into several subproblems, such as defining a robust distance function, learning a representative subspace, and then transfer- ring between two or more domains with different weights attached to the learning models. These weights are further learned from the source and target data. As a top-down style researcher, Student A2 pursues the problem by breaking it down into finer and finer details. In contrast, Student B2 pursues his research agenda in a bottom-up manner. Recall that Student B2 is interested in scalable online recommendation algorithms that are both efficient and effective. He publishes several papers on different as- pects of the problem, each focusing on a different scalability or accuracy issues associated with his methods. When he accumulates a sufficient number of publi- cations, he then takes stock of what he has accomplished, trying to summarize it into a coherent whole. He finally decides that he will use the material of scalable architecture for online recommendation as his main topic for the thesis, based on which he selects and extends the rest of the subtopics into his thesis as separate chapters. Finally, Student C2, who favors applications that lead to patents and start- up companies, may select a combination of top-down and bottom-up way of organizing his thesis plan. For example, the student may start by working on a data-mining competition that also leads to several publications and patents. The student then finds the topic of social network analysis to be new and fascinating, and decides to plan for a thesis in this area. He designs a top-down plan to com- plete the thesis, and works on each part in turn. In the end, the thesis appears like a hierarchically organized “island” of works among several pieces of finished, but different works that are not included in the thesis. 7.3 deFeNdING YouR theSIS Before the student celebrates the successful ending of a long student career, there is one more hurdle to cross: the thesis defense. This is where the student has to demonstrate to the experts and non-experts that he or she has proposed a thesis, wRItING ANd deFeNdING A Ph.d. theSIS 127 knows all the previous major works related to the thesis, and has accumulated convincing evidence on the thesis. In addition, the student has to demonstrate that he or she can effectively communicate the thesis. In many universities, a Ph.D. defense consists of a student presentation (45 minutes to one hour long), followed by a (closed door) question and answer period; the latter part can go in two rounds. Thesis presentation is unlike any conference or seminar presentations the student has done before, as it summarizes a major project of the student. In a way, your thesis presentation should convince the committee that in the previous five or so years of Ph.D. program, you have contributed to world knowledge by one or more of the following: • • • Developed a better solution to an existing challenging problem. Identified a new problem and designed its formulation, and offered a new solution, such that in effect you opened up a new area. Developed a new methodology that unifies many major approaches in the area, and offers your own new insight. A thesis presentation should demonstrate that you have understood the problem well including its implications in the real world and that you: • • • Know all the previous major approaches to the same problem and can discuss their pluses and minuses with ease. Know how to design a solution as well as evaluate its merits and weaknesses. Have mastered the skill of presenting the same problem to different audiences, at different lengths and in different contexts. This last point is particularly important, as presentation skill is one of the distinguishing criteria that separate a Ph.D. from the rest. In this view a Ph.D. must be able to sell his or her thesis, much like a salesperson or a business account manager sells his products. In 40 minutes to 1 hour, the student must convince the committee that the work holds water. The student should be able to summarize 128 CRAFtING YouR ReSeARCh FutuRe the work succinctly in one sentence, three sentences, one paragraph, and several paragraphs, depending on the context in which the presentation is made. In the actual presentation, the student needs to go through these points: • • • • what the problem is, why the problem is important to solve, what the related work solves, how does it solve it, what merits does it have, and what weaknesses does it have. how the student has solved it better than others. These points are similar to the logical steps in any research paper, as de- scribed in Section 6.1. When comparing to previous work, you should be as objec- tive as possible, without personal sentiment. Avoid saying overly broad things like, “But their method is ineffective since it cannot scale up.” A thesis presentation is usually followed by an hour-long question-and- answer period. Be prepared, but also be aware that you cannot anticipate all ques- tions. When meeting new and startling questions, pause for a moment before you answer them. Some points to keep in mind: • Questions can be highly critical from some examiners, but it usually does not mean that they intend to fail you. It is normal that commit- tee members will drill as deeply as they can, in order to see how well you actually know your area. They also wish to see if you can handle tough questions before they let you graduate; after all, they are the “safety guard” for the university’s good name. • Questions from non-experts in a field can be general and be from dif- ferent, unexpected angles. Don’t be afraid to say, “I don’t know about this, and I will look into it later.” • • Make sure you know the basics of your thesis very well. If examiners find that you misunderstood some basic concepts, they can fail you. If you can use slides during a defense, prepare your answers to poten- tial questions with extra slides, just in case questions come up during the Q&A period. wRItING ANd deFeNdING A Ph.d. theSIS 129 Don’t be afraid to pause, think about a question, and discuss how it is rel- evant to your thesis. You need to be sure you understand what is being asked of you before answering it. It also helps if you prepare some generic questions that keep popping up in thesis defenses everywhere: • • • • • Summarize your main contributions in one to three sentences. What is the problem you are trying to solve? What are the main contributions of your thesis? Which one is ground-breaking? What is one major weakness of your solution? If you were to do your Ph.D. study again, how would you do it differently? You may still be very nervous before your thesis presentation and defense, especially if your native language is not English. The best advice we can give is to rehearse it several times before the actual defense. Ask your supervisor to invite a few colleagues, postdocs, and other graduate students to act as examiners, and stage a “mock defense” for you. As supervisors, we sometimes even video-recorded the whole mock defense process for some of our previous Ph.D. students, and they found it extremely helpful. They became highly confident, and did an excellent job in the thesis defense. As graduate students, we all hear anecdotes about some famous questions all the time. In the case of one author of this book (Yang), there was a famous professor who was on his committee with a reputation for falling asleep during the student presentation and then waking up, asking: “So, how do you apply this thing?!” This turned out to be the killer question in many of his exams. • • • • 131 C H A P T ER 8 Life After Ph.d. When we were young, becoming a professor seemed to be the ideal thing to do. You become a teacher with your graduate students. You have summer and winter breaks. You get to go to different places for conferences. On top of all this, you are admired by many. In fact, this picture is only partially true. In this chapter, we try to demystify the life of a professor, and give readers a realistic picture of life after Ph.D. 8.1 A dAY IN the LIFe oF A tYPICAL PRoFeSSoR Suppose that you have completed your Ph.D. degree. Now what? One of the authors (Yang) had the following story to tell: after his defense at the University of Maryland, his supervisor Professor Dana Nau congratulated him with a smile: Congratulations! Now you have to write a Ph.D. thesis every year! This is actually not true. The truth is that after the Ph.D., one typically has to write one Ph.D. thesis every three months! This includes writing grant propos- als, preparing and teaching classes, meeting students and mentoring them, serv- ing for conference and journal organizations, attending and sometimes chairing committee meetings, balancing budgets for research groups, and reviewing others’ grant proposals. Besides these, you are constantly reading papers, discussing with students, and learning new things. See the list of activities and tasks for researchers in Chapter 1. This seemingly confusing set of roles does not seem so attractive un- less they are put in perspective. Here is a picture of a day in the life of a professor in the university. 132 CRAFtING YouR ReSeARCh FutuRe 7:00 a.m.: After getting up and having breakfast, and saying goodbyes to family members, the professor heads to the computer to catch up on a few urgent emails that need to be handled right away. 8:00 a.m.: The professor heads for the swimming pool or gym. A 30-minute exercise adds infinite energy to the professor’s brainpower. It is essential for a researcher to have a clear mind when working on a research problem. It is good for anyone to have a healthy body. Students often believe that putting more time on a problem may eventually lead to a desired result, no matter how tired and exhausted they are. However, pouring more time and effort onto a problem is less effective than spending your time and energy wisely. Having at least 30 minutes of physical exercise will allow one to gain much more than spending five times more time on a problem while the mind is murky. 8:30 a.m.: The professor heads for office, gets a cup of coffee or tea along the way, and reads more emails and reviews the slides before the 9am class. 9:00 a.m.: An undergraduate class starts. A class usually lasts 1.5 hours. A faculty member is expected to teach between two to four classes a week. To prepare for the classes, the professor needs to spend more time preparing notes, slides, and other class material, or work with teaching assistants on preparing for assignments, projects, and exami- nations. Professors are also asked to teach new courses, especially in fast-changing disciplines such as computer science and engineering. In this case, more time needs be spent on the course preparation. Teaching is an integral part of a researcher’s career. Teaching allows the research to communicate smoothly with students, honing one’s ability to explain a difficult concept in plain language, and to illustrate com- LIFe AFteR Ph.d. 133 plicated solutions on a variety of easy-to-understand matters. Often professors can also identify exceptional students in the class for collab- orative research, and inspire them to become researchers in the future. Communication ability is important for a researcher, as it is part of the researcher’s job to write research papers and explain new find- ings to peers and to people in other fields. It is also important for the researcher to work with more junior researchers and cultivate future generations. Thus, teaching should not be taken as a distraction, but rather, it should be an essential ingredient of being a good researcher. 10:30 a.m.: During the class, a few students asked questions that required further explanations. The professor invites them to his office to continue the discussion after class. 11:00 a.m.: The professor joins a committee meeting on graduate admission matters. A faculty member is expected to do a certain amount of service work. Before getting his or her tenure, a professor is expected to join one or two departmental committees in a light-load mode. After tenure, which typically earns him an associate professor title, the committee work load of a professor is expected to increase, sometimes involving committees beyond his or her own department on matters concerning the school or the university as a whole. The duties of these committees typically involve student admission, scholarship, faculty tenure and promotion, university research grant distribution and proposal ranking, etc. They can range from one to six hours for a senior professor per week. 12:00 p.m.: The professor has his lunch. Some professors schedule lunch meetings with their students, so that they can discuss in a more relaxed atmo- sphere, and at the same time, save time. 134 CRAFtING YouR ReSeARCh FutuRe 1:00 p.m.: The professor attends a student Ph.D. defense session. In his career, a professor is expected to join many students’ committees, ranging from undergraduate studies to Ph.D. programs. Sometimes, a professor is called upon to be an external member of a university wide Ph.D. com- mittee, serving on the Ph.D. defenses for students in other depart- ments. On these occasions, he may have to listen to the presentations of members outside their area of expertise. 3:00 p.m.: The professor meets his Ph.D. students in a group meeting. This is when the professor has the most fun. The professor first listens to a student’s presentation of recently conducted experiments, and then raises several questions and discusses possible answers with the stu- dents. The professor then works out the next steps in their research with the students, and agrees to send the students some references related to the topic of discussion. 4:30 p.m.: The professor joins his students and colleagues to attend a depart- mental seminar. Attending seminars is a typical activity of an aca- demic. This is how professors can learn about others’ work, and how they can disseminate their work to others. Sometimes, these seminars are given by job applicants, in which case the professor will be asked to interview and rank the candidates. 5:30 p.m.: Proposal writing: a professor has to constantly apply for new projects and grants in order to support his group of students, postdoc fellows, and research assistants, and to support his group members when they go attend conferences. All research activities, ranging from computer usage to travel related to conferences, need support. Thus, it is critical that the professor writes successful grant proposals, and writes them LIFe AFteR Ph.d. 135 often. This is because a typical grant application has a low success rate that can range between 5% to 25%, depending on where you are in the world and the type of grant you apply for. We discuss some tips on how to write a successful grant proposal in Section 8.2. 6:30 p.m.: The professor returns home for dinner with his family. 8:30 p.m.: The professor starts working on a research paper that he jointly writes with his students or colleagues. This may be mixed with phone calls, emails, Skype, or in person meetings in research labs. 10:30 p.m.: The professor starts to book his trip to attend the next conference. He sends emails to his travel agent . . . As you can see, the professor’s day is full of different types of activities, all centered around learning and helping others learn. There are also times when there are too many of these activities that demand attention all at once, which can be distracting. Because of this, a good professor should be highly effective, and also be a good time manager. Of course, there is more freedom associated with being a researcher. When the class is finished and papers are submitted, most professors can relax a bit. They can also go to different conferences, visit other universities, and chat with other researchers on ideas for future research. This brings us back to Chapter 1, where we discussed the pros and cons of being researchers. 8.2 APPLYING FoR ReSeARCh GRANtS One of the major activities in a professor’s career is to apply for research grants. As we described before, these grants are the major funding sources for supporting all ac- tivities around a research project, including paying for students’ and staff members’ salary, lab equipment, computers and printers, and travel expenses to conferences 136 CRAFtING YouR ReSeARCh FutuRe and visits. In the United States, grants are also essential in paying the summer salaries of a professor, since many universities pay for only the teaching terms of a professor’s salary. Research grants are typically applied through granting agencies. These granting agencies are typically divided into the following categories: • University grants: these are the internal grants where a small amount of funds are made available typically to allow new faculty members to get started, or to encourage faculty members to take on a new research direction. • Government funding agency: these include the National Science Foundation in the US and in China, NSERC in Canada, A-star funding in Singapore, European union grants, and Research Grants Commission in Hong Kong and National Science Foundation of China, and the European Research Council, to name a few. • Industrial or military research grants: These are sponsored by industry or the military organization, usually with a particular mission in mind. The objectives of these grants or projects are usually more specifically focused on building of prototype products. Stringent constraints on spending and milestones apply. For a researcher, applying for research grants is a part of everyday life. For most researchers, the size of the grant is an important factor that determines how far you can reach in achieving your research goal. To be a successful grant appli- cant, the researcher has to be more than a scientist or engineer; he or she must also be a good market researcher in order to understand the needs of the society, a good salesman to present his ideas well, a good writer and presenter, and a good manager in case the project involves more parties. For one person to have all these qualities is challenging, but a successful grant applicant must possess at least some of these attributes. Often for each type of grant, grant proposals are called for once a year. Applying for a project is similar to submitting a paper to a conference, in that LIFe AFteR Ph.d. 137 both grants and conferences have deadlines. However, major differences exist. This is underscored by the fact that, often, we hear complaints from even seasoned researchers: “if I have been very successful in getting papers accepted by very pres- tigious conferences and journals, why do I still fail to get my proposals accepted?!” This is a valid question: why is writing good grant proposals so hard? The key to understanding the difference between research papers and pro- posals is that their readership can be very different. While a research paper at a prestigious venue is often reviewed by two to three very qualified experts in one’s field of study, a proposal is often reviewed by a much larger pool of people, where only a small subset of them are domain experts and the rest are from a more di- verse range of areas (although still in the general area of one’s field). Most of the others are there to help assess the general impact and quality of the proposal, and while these reviewers are known in the general areas of research, they may not be experts with the same depth as the author. Thus, if they cannot understand your proposal, the proposal will be ranked low. Another difference between a proposal and a research paper is that a pro- posal must motivate the goals and convince the reviewers that the goals are both grand and achievable, without going too much to either extreme. On the one hand, a proposal has to show that the goals to be achieved are challenging, such that few others have tried them before, and thus the goals are innovative. On the other hand, these goals are not so out of reach, at least for this researcher, that the means to reach the goals are viable. This is a fine balance of two competing extremes, and indeed it is very difficult to attain. However, for a research paper, reviewers have the problem and solution in front of him or her from the content of the research paper, thus the balancing act between motivating the problem and solving the problem is less of a problem. In contrast, for a research proposal, it is often impossible to reveal all details of the solution, since otherwise the need for the proposal would be in question. One of the most important aspects of a research grant proposal is its title. While short, a title is truly a window into the whole proposal. A good title is 138 CRAFtING YouR ReSeARCh FutuRe critical in helping the reviewer form a first impression on the entire proposed project. Recall that in many cases, reviewers themselves are not necessary specific domain experts in the proposed domain; for example, a computer architecture researcher may be called upon to review a proposal on data mining. Thus, the title part should also serve well for the generalist. A rule of thumb is that the title should contain several components, including the target problem (e.g., a learn- ing algorithm for image understanding), the proposed method or solution (e.g., a Bayesian method) and the application area in which the method will be used to solve the problem (e.g., images and text from social media or social networks). A title such as “Image Understanding based on Bayesian Methods for Socially Tagged Images Under Uncertainty and Incomplete Data Environments” might not be a good title, because it is a bit too long. In contrast, “Image Understanding for Socially Tagged Images Under Uncertainty” is more succinct and better. Similar to the title, the abstract and objectives part of the proposal provides a slightly more detailed window into the proposal, where the aim is to guide the reviewer into the proposal in a more structured manner once the reviewer has been convinced that the proposal is sufficiently interesting by reading the title. Thus, the abstract should state the problem, tell the reader why these problems are challenging and new, and then state in general terms what the proposed solutions are. This is followed by a few sentences on the impact of the solution should the project be funded and succeed. We have given similar advice on paper writing in Chapters 5 and 6. In a similar vein, the objective part of a proposal should state clearly what the proposed tasks and aims are for the project to accomplish. If there are several objectives in the statement, it is important that there is a main objective, which, like the title, should be designed so as to impress the reader. This main objective can be stated at the beginning of the list of objectives, or at the end. It may often be the case when the writer of the proposal has done some preliminary works, that he might wish to use the first objective as a lead-in to the rest of the proposal. This is fine as long as the researcher has an overview sentence to tell the reader about LIFe AFteR Ph.d. 139 the case. If the main objective is stated first, then the rest are sub-objectives and should be grouped as subtasks under the first important objective. This forms a top-down taxonomy for the reader to follow. In general, a research proposal is broken down into several functional sec- tions, each serving a different purpose: • The abstract explains the proposed project even to an outsider, making clear in one or two sentences the main problem, the target audience, the open challenges and open problems, motivations related to these chal- lenges and problems, proposed solutions at a high level, and the impact your solution will bring should the project be funded and succeed. • An overview of the objectives that describes the main things you wish to achieve, along with an indication that your work is important not only for your own research field, but for society as a whole. The ob- jectives should be hierarchically organized so that readers can follow each path to other important parts of the rest of the proposal. Readers can use this to conduct a review of the proposal in a non-sequential manner, jumping to parts that they wish to see efficiently. • A review of previous works and background research that describes the context of the proposed project as well as what the investigators and other people have done in the proposed research area in the past. It is important to stay focused in the background discussion so as not to diverge into too many irrelevant details and marginally related fields. The main purpose of this part is, first, to convince the readers that the researchers are true experts in the field of study; second, to show that there are not many prior works addressing the same problem being proposed; and third, to demonstrate that the investigators themselves have done preliminary work leading to the proposed projects. • The methodology and research plan part, discusses in detail the re- search method, subtasks, research schedule, and evaluation methods. 140 CRAFtING YouR ReSeARCh FutuRe Important in this part are the references back to previous sections that discuss specific research subtasks and steps to the keywords indicating the major objectives in the title, abstract, and objectives part; these can be served by sentences such as “recall in Section 1, we discussed the importance of designing a new method for ABC; in this section we describe the details of ABC.” The more tightly connected these parts are via references like this, the easier it is for reviewers to master the main points of the proposal, and thus the better the outcome. • The budget and research schedule part, should be carefully proposed rather than going to either extremes of asking for too much funding or too little. In one extreme, if too much funding is requested, it is difficult to justify the proposal in terms of its scope. But if too little is asked, reviewers will question the feasibility of the proposed project as well. To help the reader understand the full scope of reviewing criteria, here we quote the proposal review criteria from the U.S. National Institute of Health (NIH), a well-known funding agency, as an example. This set of criteria is fairly typical of all criteria of many major grant agencies across the world1: • overall Impact. Reviewers will provide an overall impact/priority score to reflect their assessment of the likelihood for the project to exert a sustained, powerful influence on the research field(s) involved, in consideration of the following review criteria and additional review criteria (as applicable for the project proposed). • Significance. Does the project address an important problem or a critical barrier to progress in the field? If the aims of the project are achieved, how will scientific knowledge, technical capability, and/or clinical practice be improved? How will successful completion of the 1 See http://grants.nih.gov/grants/peer/critiques/sbir-sttr.htm#sbir-sttr_01 LIFe AFteR Ph.d. 141 aims change the concepts, methods, technologies, treatments, services, or preventative interventions that drive this field? Does the proposed project have commercial potential to lead to a marketable product, process, or service? • Investigator(s). Are the PD/PIs (Project Directors and Principle Investigators), collaborators, and other researchers well suited to the project? If Early Stage Investigators or New Investigators, or in the early stages of independent careers, do they have appropriate experi- ence and training? If established, have they demonstrated an ongoing record of accomplishments that have advanced their field(s)? If the project is collaborative or multi-PD/PI, do the investigators have com- plementary and integrated expertise? Are their leadership approach, governance, and organizational structure appropriate for the project? • Innovation. Does the application challenge and seek to shift current research or clinical practice paradigms by utilizing novel theoretical concepts, approaches or methodologies, instrumentation, or interven- tions? Are the concepts, approaches or methodologies, instrumenta- tion, or interventions novel to one field of research or novel in a broad sense? Is a refinement, improvement, or new application of theoretical concepts, approaches or methodologies, instrumentation, or interven- tions proposed? • Approach. Are the overall strategy, methodology, and analyses well- reasoned and appropriate for accomplishing the specific aims of the project? Are potential problems, alternative strategies, and bench- marks for success presented? If the project is in the early stages of development, will the strategy establish feasibility and will particularly risky aspects be managed? • environment. Will the scientific environment in which the work will be done contribute to the probability of success? Are the institutional support, equipment, and other physical resources available to the 142 CRAFtING YouR ReSeARCh FutuRe investigators adequate for the project proposed? Will the project ben- efit from unique features of the scientific environment, subject pop- ulations, or collaborative arrangement? What are some of the typical mistakes made by the writers of grant pro- posals? The following is an excerpt of some of the comments summarized from reviewers’ comments by Hong Kong’s natural sciences and engineering research agency, or the RGC (research grants council).2 Note that these are examples of generalized (negative) comments from many proposals accumulated in several years: originality • • • • There is only limited innovation. This is an incremental research. There is lack of evidence of new breakthrough. Objective 1 is not exciting. Objective 2 seems to be a part of Objective 3. Overall the proposal lacks new ideas to investigate. The objectives, even if achieved, are not exciting. Methods • • • It is unclear how the data will be collected and analyzed in task 1. Difficult to see how the research design/methodology will achieve the project objectives. The PI (principle investigator) needs to write the design and meth- odologies more clearly. For this purpose, step-by-step procedures, diagrams, and equations would be helpful. Feasibility • The Principle Investigator (PI)’s track record is a concern to this re- viewer, as he has not published any paper or patent in the area of re- search in this proposal. 2 http://www.ugc.edu.hk/eng/rgc/index.htm LIFe AFteR Ph.d. 143 • • • • • This proposal on <topic> was submitted before and was not supported. Some arguments have been provided, but do not seem convincing. The PI has limited understanding of <research area>, which is very important to the second objective. The PI should have involved co-Is to contribute missing expertise. No preliminary results are provided to support the hypothesis. This work is not properly based on existing published knowledge in the subject area. The objectives of this proposal are too wide. I believe too much has been promised in this proposal for two years of work. Likely contribution to discipline • • • The PI failed to clarify how the proposed technique can achieve any better performance than other state-of-the-art techniques. It is stated that an understanding of <topic> is of paramount impor- tance. You need to describe for whom this is important and why. I am not optimistic that the proposed research will generate signifi- cant publications in main-stream journals. others • This proposal is full of ambiguities and I do not think the applicant has a clear mind where he is heading. Basic concepts and many tech- • • • • nical details are unclear. The proposal has three objectives. These objectives are not integrated; they appear disjointed. The manpower planning is poorly put together. The proposal is too qualitative when it should be a quantitative topic. There is no sufficient information in the proposal about the analytical framework, theoretical foundation, model specification, estimation strategy, data source, and potential economic impact to Hong Kong and beyond. 144 CRAFtING YouR ReSeARCh FutuRe • I don’t think the current title properly reflects what the authors intend to do. 8.3 teChNoLoGY tRANSFeR A professor’s life is not just teaching and research. Often times, a professor, and his students and colleagues, might invent something useful for society, and this is when they start thinking about how to move the technology and ideas from their labs to the real world in areas such as industry and the market place. This process of moving knowledge away from labs, conferences, and journals, to practice is known as technology transfer. A researcher can conduct technology transfer at any point in time. He or she may transfer knowledge while still being a graduate student. He or she may be a postdoc fellow or a professor, or an industrial researcher working in an industry lab such as Google, Microsoft Research, General Electric, Huawei, or pharmaceutical companies such as Pfizer, etc. Technology transfer may take one’s time away from pure academic research for a while, but it is a very satisfying process, especially after seeing one’s ideas and work being used by people. There can be several ways in which technology transfer can happen. The simplest way is licensing, where, with the help of a legal consultant, one can sign an agreement with a company such that the company can use the technology in a limited manner. If the technology is a piece of software, then the agreement will state clearly what the software includes and does not include, what happens when the software refers to some other people’s software that they themselves have lim- ited use clauses, and what happens when the software breaks. That is why a legal expert is often needed to assist in negotiating and drafting a licensing agreement. The process of defining these terms can be lengthy and tedious. Fortunately, many universities and research labs have offices that are designated for this use, and in many cases this costs the researcher very little or nothing, since the legal services can often recuperate their costs through a percentage of the agreed fee as part of the agreement. LIFe AFteR Ph.d. 145 When reading a legal agreement, such as a licensing agreement, for the first time, a researcher is often inundated with jargon and clauses that are quite foreign to the researcher. When this happens, do not worry, since a legal document is not very different from a research paper. Similar to a research article, the documents often start with definitions in upper case; these are the terms that will be used repeatedly and unambiguously in the subsequent texts. The legal terms are similar to a set of logical rules and statements. While a lawyer is helpful, it is also the researchers’ task to ensure that these statements are consistent and the coverage is appropriate. Mathematical logic does help here. An important aspect of licensing is the terms of use of the product to be licensed. The term can be limited by geography, such as the Asian or European market, or by time, such as number of years. In some extreme cases, the researcher might agree to give all rights of use to the company, in which cases the term might refer to “exclusive use,” which forbids the researcher to transfer the same technology to others, essentially preventing competitors from having access to the same technology. In such cases, the benefit to the researcher is usually higher than non-exclusive use clauses. Patents are another kind of technology transfer. Patents are statements of a new invention, be it a process or a product design that is associated with a right assigned to the inventor. When filing patents on an idea, a researcher goes through a process that is almost the same as doing research. First, the researcher should define what the idea is in the simplest and most unambiguous terms. Then, the re- searcher goes through a literature search to prove that other similar ideas or tech- nology are in fact different from the one concerned, in one way or the other. This is like writing a related work section of an article or a Ph.D. dissertation. Often there are patent databases in a library to help one go through this search process, sometimes with a fee, but many search engines today provide look-up services to the public for free. Like a research article, a patent application should reference many research papers in citations. In addition, the researcher should give the full details on the design of the idea, such as how it might be used in practice, and so 146 CRAFtING YouR ReSeARCh FutuRe on. A patent lawyer, who will assist in the filing process, often reviews this docu- ment. The filing time may in fact be quite long, sometimes two years, and the fee can range from thousands of US dollars to tens of thousands. When filing a pat- ent on an idea, there is a requirement that no prior publication has been made on the same idea, thus the researcher is often forbidden to publish a research article on the same idea until the patent is approved by the patent office. In some cases, however, a patent can be filed while a paper is being reviewed by a conference or a journal, but researchers should consult a lawyer about this. Sometimes a researcher spends some time working for a company on a limited time basis. In such cases, we say that the researcher is consulting with the company. Often, universities encourage researchers to do some consulting work while being employed at a university. For example, many universities in the US, Canada, and Hong Kong allow a faculty member to spend one day per week to consult with a company. Consulting activities vary greatly from person to person. In one case, a faculty might answer questions from the people working in the company that they consult with. In other cases, a faculty member might actually sit in at the company as if he or she was an employee of the company. The most complicated, but also most rewarding offshoot of technology transfer is spinning off a company. We hear many legends of spin-off companies, such as Google, which was formed by two Ph.D. students who invented a new search technology. Universities often turn on a green light for faculty members and students to go create spin-off companies, by allowing them a “leave of ab- sence.” This is a term that refers to the practice of allowing a faculty member to leave the university for a specified time period, often one or two years, in which the researcher is not paid a salary by the university, but the position is kept for the person. This is why the researcher needs to find the funding required to support him or herself during the spin-off company creation process. Spin-off companies can be created with or without a faculty member. In the case of Student C, for example, the student may decide to form a spin-off company with the help of the university Technology Transfer office, taking advise LIFe AFteR Ph.d. 147 from the supervisors as well as industrial partners. For example, student C might find his new algorithms to perform much better than previously known algo- rithms in an e-commerce area, and may decide to create a spin-off company in order to commercialize this algorithm. He and his supervisor may decide to leave the university for a while, and formulate a business plan and marketing plan to extend his algorithms to more industrial applications. His previously filed patent on the algorithm would have helped a lot when talking to potential venture capital companies, many of whom decide to take a portion of the company’s share and provide funding. Furthermore, the venture capital companies may have access to a large network of experienced business people, from whom Student C selected a few as the new companies’ business development officers, such as Chief Executive Officers (CEOs) or Chief Financial Officers (CFOs). The student might take the position of a Chief Technology Officer (CTO), which allows the student to further expand his talent in product development. However, what we often don’t hear is the amount of work that these suc- cessful, or unsuccessful, companies require. While it sounds nice to be able to hand others a business card with a title of CEO or CTO, in fact, before deciding on spinning off a company, the researcher should take many factors into careful consideration, as the risk is also the greatest among all options of technology transfer. A necessary first step in finding venture capital to support a spin-off com- pany is to write a business plan. When writing a business plan, first and foremost, researchers should describe their objectives in sufficient depth so that funding parties can be sufficiently convinced that there is indeed an untapped market out there for the technology. This process is very much similar to describing one’s ideas in a research article. Writing this up is also akin to writing the Introduction section of a paper (see Chapter 6). The researcher himself or herself should be firstly convinced of the existence of the market. Then, the researcher should prepare a thorough literature study, like build- ing a related work section of their paper, in showing that despite the existence of 148 CRAFtING YouR ReSeARCh FutuRe such a lucrative market, in fact few competitors have tried exactly the same ideas before. This requires a detailed argument and analysis, often with many citations and quotes. Subsequently, the researcher has to discuss the methodology itself and a business model in which he or she will specify how this company can survive based on the revenue received by selling this product after taking cost into consideration. There is a wide spectrum of operating methods which a company can rely on, ranging from building up a service and sales channel for the product to reach a larger audience, to facilitating a strategic alliance with other companies to mutu- ally benefit from the sales. Note that in a business plan, the technology description part is needed and this part is similar to writing a research paper; however, unlike a research paper, the technology part of a business plan only occupies a small por- tion, as a strong argument is needed in analyzing the market and the competitors. It is sometimes estimated that technology often occupies only five to ten percent of an entire business building process. Even so, the reward far out-runs the hur- dles, since otherwise we would not have seen so many successful examples. There is also the management aspect to consider. At this point, the re- searcher has to think like a manager, as a team of experts will be needed to work in sync. This team is known as a “management team,” which includes not only the researcher, but a person with business management experience as a CEO, a finan- cial and accounting expert known as a CFO, a publicity expert known as a Chief Information Officer (CIO), etc. The team is in fact the most critical part of the spin-off company, and because of this, a venture capital company sometimes will assemble such a team for the researcher, by inviting other experienced people to join in. This is when the researcher will see his or her own shares in the company shrink, but in fact the whole pie might become much larger. Thus it is a worth- while practice in many cases. With the help of these experts, the researcher will further complete a financial plan and a marketing plan for the spin-off company. One of the stickiest issues when creating a spin-off company is the IP, or intellectual property. This refers to the content of the technology, a specification LIFe AFteR Ph.d. 149 of who owns it and a claim that it has never been done before. In some universi- ties and research labs, the university owns partial IP for any invention created therein. When creating a company, legally the university can claim a portion of the company’s share. In this case, it is important for the researcher to negotiate with the company early in the process, so that the university or the research lab also bears a part of the cost in early stages of the company’s creation, such as providing subsidized office space, computing facilities, and other legal services. • • • • 151 Summary In this book, we have systematically discussed how to do research, from setting one’s goals for a research career, to getting research ideas, reading and critiquing papers, formulating a research plan, writing and publishing research papers, and to writing and presenting one’s thesis. We also discussed what life is like after one gets a Ph.D. degree. We hope the examples, lessons, and experiences presented in this book demystify a researcher’s life, so that young and inspiring students can set the right goals in life, and young and beginning researchers have something to rely on. We will succeed if this book can offer some guidance to students and junior researchers alike to help them succeed in a fruitful and adventurous research life. Indeed, research is full of adventures and fun if you master the secrets of doing it right. In our life we totally enjoyed doing research ourselves. We certainly hope that you do too. • • • • 153 References [1] Advice on Research and Writing. Mark Leone. http://www.cs.cmu .edu/~mleone/how-to.html [2] Advice to a Beginning Graduate Student. Manuel Blum. http://www -2.cs.cmu.edu/%7Emblum/research/pdf/grad.html [3] “A Ph.D. is Not Enough.” Peter J. Feibelman. Addison-Wesley, Reading, MA, 1993. [4] The Craft of Research (Guides to Writing, Editing, and Publishing). Wayne C. Booth, Gregory G. Colomb, and Joseph M. Williams, The University of Chicago Press. [5] How to Research. Loraine Blaxter, Christina Hughes, and Malcolm Tight. Open University Press. [6] ‘How to Write a Research Paper.’ Martyn Shuttleworth, LuLu.com. Au- gust 2010. [7] Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character, Richard Feynman, Ralph Leighton (contributor), and Edward Hutchings (editor). W W Norton, 1985. doi:10.1119/1.14087 [8] Advice to a Young Scientist. Peter Brian Medawar. Harper & Row, 1979. 155 Author biographies Charles Ling has been a professor at the Western University in Canada since 1989. He obtained his BSc. in Computer Science from the Shanghai Jiaotong University in 1985, and then graduated with his Masters and then Ph.D. in Computer Science from the University of Pennsylvania, USA, in 1987 and 1989, respectively. He specializes in data mining and machine learning, and their applications in Internet, business, healthcare, and bioinformatics. Overall, he has published over 120 research papers in peer-reviewed conferences and journals. Charles Ling has also engaged in much professional service in the above areas. He has been an asso- ciate editor for several top journals and an organizer for several top conferences in computer science. He is also a Senior Member of IEEE and a Lifetime Member of AAAI (Association of Advancement of Artificial Intelligence). Charles Ling is the director of the Data Mining and Business Intelligence Lab at Western University, where has been involved in several technology transfer projects. Charles Ling is also a specialist in child gifted education. He integrates his research in Artificial Intelligence and cognitive science, and develops a full range of thinking strategies that improve children’s intellectual abilities. These thinking strategies embrace, enhance, and connect with math, science, and other areas. He can be reached at [email protected]. Qiang Yang is a professor in the Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China. He is an IEEE Fellow, IAPR Fellow (International Association of Pattern 156 CRAFtING YouR ReSeARCh FutuRe Recognition) and an ACM Distinguished Scientist, for his contributions to Artificial Intelligence and Data Mining, which are also his research interests. Qiang Yang graduated from Peking University in 1982 with BSc. degree in Astrophysics, and obtained his PhD degree in Computer Science from the University of Maryland, College Park, in 1989. He was an assistant and then as- sociate professor at the University of Waterloo, Canada between 1989 and 1995, and an associate and then a full professor and NSERC Industrial Research Chair at Simon Fraser University in Canada from 1995 to 2001. He is an author of two books and over 300 publications on AI and data mining. His research teams won several prestigious international competitions on data mining. He was an invited speaker at several top conferences, and a founding Editor in Chief of an ACM journal (ACM TIST), as well as an editor for several top journals. He has also been an organizer for some top conferences in computer science. Besides academic research, he has engaged in several industrial projects with IT companies, and been sitting on several research grant panels. In his spare time, he enjoys sports, reading and traveling. He can be reached at [email protected].
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=7416054.pdf&bkn=7416053&pdfType=book	Series ISSN 1939-5221 S a e e d B . i N k u Engineering Principles in Everyday Life for Non-Engineers Saeed B. Niku, California Polytechnic State University This book is about the role of some engineering principles in our everyday lives. Engineers study these principles and use them in the design and analysis of the products and systems with which they work. The same principles play basic and influential roles in our everyday lives as well. Whether the concept of entropy, the moments of inertia, the natural frequency, the Coriolis acceleration, or the electromotive force, the roles and effects of these phenomena are the same in a system designed by an engineer or created by nature. This shows that learning about these engineering concepts helps us to understand why certain things happen or behave the way they do, and that these concepts are not strange phenomena invented by individuals only for their own use, rather, they are part of our everyday physical and natural world, but are used to our benefit by the engineers and scientists. Learning about these principles might also help attract more and more qualified and interested high school and college students to the engineering fields. Each chapter of this book explains one of these principles through examples, discussions, and at times, simple equations. This book can be a general reference book for learning about engineering for all audiences, especially for college students in majors other than engineering, or used in general education classes for technical content, or for encouraging high school students into thinking about STEM (science, technology, engineering, and mathematics), or general non-fiction reading. Many books are supposedly written for “dummies.” This is not one of them. The assumption within is that people are intelligent and with perseverance and patience they can learn about new subjects. It is for anyone interested in learning how the world works. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Synthesis Lectures provide concise Library of Engineering and Computer Science. original presentations of topics, published information, visit our website: quickly http://store.morganclaypool.com in digital and print formats. For more important research and development store.morganclaypool.com i i E n g n e e r n g P r n c p l e s i i i n e v e r y d a y l i f e F o r N o n E n g n e e r s i - Engineering Principles in everyday life for Non-Engineers Saeed B. Niku Engineering Principles in Everyday Life for Non-Engineers Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 e Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: e Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 e Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 e Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 iv Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering ermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape ermal Optimization Using Bejan’s Constructal eory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and rive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 v Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: e DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2016 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku www.morganclaypool.com ISBN: 9781627058582 ISBN: 9781627058599 paperback ebook DOI 10.2200/S00699ED1V01Y201601ENG026 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #26 Series ISSN Print 1939-5221 Electronic 1939-523X Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku California Polytechnic State University San Luis Obispo SYNTHESIS LECTURES ON ENGINEERING #26 CM&cLaypoolMorganpublishers&ABSTRACT is book is about the role of some engineering principles in our everyday lives. Engineers study these principles and use them in the design and analysis of the products and systems with which they work. e same principles play basic and inﬂuential roles in our everyday lives as well. Whether the concept of entropy, the moments of inertia, the natural frequency, the Coriolis acceleration, or the electromotive force, the roles and eﬀects of these phenomena are the same in a system designed by an engineer or created by nature. is shows that learning about these engineering concepts helps us to understand why certain things happen or behave the way they do, and that these concepts are not strange phenomena invented by individuals only for their own use, rather, they are part of our everyday physical and natural world, but are used to our beneﬁt by the engineers and scientists. Learning about these principles might also help attract more and more qualiﬁed and interested high school and college students to the engineering ﬁelds. Each chapter of this book explains one of these principles through examples, discussions, and at times, simple equations. KEYWORDS engineering concepts, entropy, thermodynamics, thermodynamic cycles, combined cycle power generation, moments of inertia, stepper motors, DC motors, AC motors, transformers, engines, rotary engines, 2-cycle engines, hybrid cars, vibrations, nat- ural frequency, hearing, guitars, signal transmission, Coriolis acceleration, vectors, weather systems, electromagnetic force, EMF, back-EMF ix Dedicated to Shohreh, Adam, and Alan for their patience with me Contents xi Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 Entropy: Natural Orders, ermodynamics, Friction, Hybrid Cars, and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Entropy and Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 1.3 Is it Possible to Defy Entropy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Why Do We Get Older? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Entropy as Described by an Equation: ermodynamics . . . . . . . . . . . . . . . . . . . 7 1.5 1.5.1 e First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5.2 e Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Hybrid Cars Anyone? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Common Misconceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.7 2 Natural Frequencies: Vibrations, Hearing, Biomechanics, and Guitars . . . . . . . 23 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1 2.2 System Response to External Forces at Diﬀerent Frequencies . . . . . . . . . . . . . . 26 2.3 Natural Frequency of Other Common Systems . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3.1 Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.2 Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.3 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Applications and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4.1 Guitars, Pianos, and Other Stringed Instruments . . . . . . . . . . . . . . . . . . 35 2.4.2 Speaking and Vocal Cords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.3 Tuning to a Radio or TV Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.4 Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4.5 Walking and Running, Hearts and Lungs . . . . . . . . . . . . . . . . . . . . . . . . 53 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4 2.5 3 Coriolis Acceleration and its Eﬀects: Bikes, Weather Systems, Airplanes, and Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 xii 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.2 Vector Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.4 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.5 Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.6 Rotating Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Coriolis Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Inertial Reaction to Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Air and Water Circulations (Convections) Due to Heat . . . . . . . . . . . . . . . . . . . 72 Coriolis Acceleration and Weather Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Accelerations Due to Combined Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.7.1 Riding Bicycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.7.2 Oscillating Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.7.3 Airplanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.7.4 Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.7.5 Movements of a Spacecraft in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.3 3.4 3.5 3.6 3.7 4 ermodynamic Cycles: Refrigeration, Air Conditioning, Engines, and Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1 4.2 4.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Spark-Ignition Power Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.3.1 4-stroke Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.3.2 2-stroke Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.4 ermodynamic Representation of the Spark-Ignition Power Cycle . . . . . . . . 114 4.5 Compression-Ignition Diesel Engine Power Cycle . . . . . . . . . . . . . . . . . . . . . . 118 4.6 ermodynamic Representation of Compression-Ignition Power Cycle . . . . . 119 Rotary (Wankel) Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.7 Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.8 4.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.10 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5 Moments of Inertia: Mass and Area Moments of Inertia, Accelerations, Inertial Forces, Strengths, and Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.1 5.2 Second Moment of the Area (Area Moment of Inertia) . . . . . . . . . . . . . . . . . . 126 5.3 Deﬂections of a Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Parallel Axis eorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.4 Polar Moment of Inertia (Polar Moment of the Area) . . . . . . . . . . . . . . . . . . . 138 5.5 Strength of Materials: Stress, Strain, and Modulus of Elasticity . . . . . . . . . . . 142 5.6 5.7 Role of Moments of the Area in Stress Calculations . . . . . . . . . . . . . . . . . . . . . 146 5.8 Mass Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6 Electromotive Force: Motors, Transformers, AC and DC Currents . . . . . . . . . 155 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.1 6.2 Introductory Terms: Voltage, Current, and Resistance . . . . . . . . . . . . . . . . . . 155 6.3 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.4 Electromotive Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 6.5 DC Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 AC Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.6 Stepper Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6.7 6.7.1 Canstack Stepper Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6.7.2 Hybrid Stepper Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 6.8 6.9 DC Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.10 AC Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 6.11 Back-emf Issues in Motors and Transformers: Laminated Iron Cores . . . . . . . 182 6.12 Back-emf in DC Motors: Servomotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.13 Advantages and Disadvantages of Diﬀerent Motors . . . . . . . . . . . . . . . . . . . . . 186 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Prologue xv Almost every aspect of our lives is governed or aﬀected by some engineering concept. Most people do not know about these concepts or are oblivious to them. We take it for granted that at any time, we have cold drinks and safe foods in our refrigerators. is was not true a few decades ago. e principles on which refrigeration is based have existed forever, but we did not know how to use them properly. We take it for granted that wherever we go, a mixture of oxygen and nitrogen is present. We do not suﬀocate from a lack of oxygen in one location while burning in pure oxygen in another. And we take it for granted that we age—but why? We can walk for hours without really getting tired, but cannot run for long without getting tired. Why is it that cities on the Atlantic coast get snow, but the ones on the Paciﬁc coast do not? Tree branches get smaller in diameter as their distance to the trunk increases, but why? And a telephone book can be easily bent, but not a piece of cardboard. Why? Most hybrid cars have better gas mileage in the city than on freeway driving. Why do airplanes ﬂy, how do engines work, and how do we hear? Why is it that we can select the broadcast from one station at a time without mixing information from hundreds of others? So how are these issues related to engineering (or as some would call it, physics)? Simple principles govern why and how things happen. If we learn these principles we can understand how diﬀerent phenomena aﬀect our daily lives, why certain things happen as they do, and how we can use them to our beneﬁt. ere are too many engineering principles to discuss for non- engineers. is book covers a few of these principles that are more general and directly apply to our understanding of natural phenomena. A few equations are used in the discussion to better understand the issues. I hope this will not be a distraction. I envision that whether or not you are an engineer or scientist, you will be able to follow them. is book can be a general reference book for learning about engineering for all audiences, especially for college students in majors other than engineering, or used in general education classes for technical content, or for encouraging high school students into thinking about STEM (science, technology, engineering, and mathematics), or general non-ﬁction reading. Many indi- viduals from all walks of life have made encouraging comments about how they enjoyed reading the manuscript and how they have learned from it, and I thank them for their time. Not knowing about a subject does not make a person dumb. Many books are supposedly written for dummies. e assumption in this book is that people are intelligent, even if they do not know about certain ﬁelds; as long as they have the perseverance and are patient they can learn about new subjects. So this book is not for dummies. It is for intelligent individuals who are interested in learning new material. xvi PROLOGUE I would like to foremost thank Alan Niku for his thorough and thoughtful editing of the manuscript, his comments, his humor, and his photography. I would also like to thank Joel Clay- pool for his courage in taking on this project and Dr. C.L. Tondo for his work on the project, and Hila Ratzabi for editing the manuscript. In addition, my sincere thanks go to Daniel Raviv, James LoCascio, Patrick Lemieux, Frank Pekar, William Murray, Steven Klisch, Julia Wu, Jesse Maddren, Glen orncroft, Ahmad Naﬁsi, Larry Coolidge, Sina Niku, and others whom I may have forgotten by now, for their assistance during the writing of this project. Let’s get to work. We will look at a few concepts and see how they relate to our lives every day. I hope you will enjoy the book and learn something new from it. Saeed Benjamin Niku Mechanical Engineering Cal Poly, San Luis Obispo January 2016 C H A P T E R 1 1 Entropy Natural Orders, ermodynamics, Friction, Hybrid Cars, and Energy 1.1 INTRODUCTION Imagine walking into a room and ﬁnding out that all of the oxygen in the room has separated into one side and all the nitrogen and other gases in the opposite side, and consequently you can either not breathe or you almost get burned in the pure oxygen. Certainly this does not happen in nature. In reality, even if you design a chamber with a membrane in the middle, ﬁll one side with oxygen and the other side with nitrogen, and then pull out the membrane, the oxygen and nitrogen completely mix after a while. e natural world does not like this artiﬁcial order; thanks to entropy, it will mix them together into a uniform mixture. Unless other forces and characteristics (such as diﬀerences in density, non-mixing ﬂuids) intervene, things get mixed up into uniform states. In fact, this is true for any artiﬁcial order created against the natural disorder of things. We may build a solid structure; nature will destroy it one way or another. We come into living; nature will eventually ﬁnd ways to kill us. Mountains and valleys are formed by other forces of nature; the mountains eventually wash oﬀ into the valleys to ﬁll them into a natural disorder or uniformity. Boiling water will cool to the same temperature as the environment. Only natural orders remain, to some extent. So what is entropy? Entropy is a measure of the level of organization (or disorganization) in a system; a degree of its organization or randomness; the probability of knowing where the molecules of a medium are at any given time. When order is increased and the system becomes more organized, entropy decreases (yes, decreases). When order is decreased, entropy increases. In all natural systems, there is a tendency for entropy to increase. When an artiﬁcial order is imposed on a system the entropy decreases. Can entropy eventually increase to inﬁnity? Perhaps. But we know that it increases when order is reduced. In the following examples, we will investigate the role entropy plays in reducing order. 2 1. ENTROPY Example 1.1 Ice in Warm Water Imagine a glass of water at your bedside overnight. If you measure the temperature of the water in the morning, it will be the same as the room’s temperature; there is no diﬀerence between these temperatures, and therefore, no heat is transferred from one to the other. Even if the water was originally warmer than the air, or colder than it, after some time, heat would have transferred from one to the other to bring both media to the same temperature. Now drop an ice cube into a glass of warm water. Similarly, since there is a temperature diﬀerence between the ice and the water; heat is transferred from the water to the ice until they are both at the same temperature. e concentrated amount of thermal energy in the water compared to the ice is not natural; in natural systems, heat is transferred in the direction of higher-to-lower temperature from one system to another until they are all at the same temperature, whereas here, the ice is cold and the water is warm. erefore, there is an “un-natural” order in this system. We have deliberately created a system that has a particular order to it; entropy will destroy this order through the transfer of heat between them. Not only is it impossible to wake up one day and see that the glass of water you left at your bedside has transformed itself into a glass of warmer water plus an ice cube in the glass (by transferring heat from a portion of the water into the rest to make an ice cube), even if you create this order, entropy will nullify it. e same is true in other systems. Cold air versus warm air, a hot plate and a cold dish on it, a stove and a pot of water, a heater and the cold air surrounding it, and the air-conditioned building and the warm weather outside. In all these examples, heat ﬂows in the direction of higher-to-lower temperature until they are the same as the temperature of the place in which they are and achieving equilibrium, therefore eliminating the order caused by the diﬀerence in temperatures. Example 1.2 Mountains and Valleys Mountains are above the average horizon and valleys are below, therefore creating an order. Even though mountains and valley are themselves created by natural forces, this diﬀerence creates a particular un-natural order. rough diﬀerent mechanisms, nature will try to break down the mountains and ﬁll up the valleys to destroy this order, even if it takes millions of years. We cannot expect the dirt to simply rise to create mountains in the opposite direction. What are some of these mechanisms? As air is heated and the energy of its molecules increases, the distance between these molecules increases too, making the air less dense. As a result, the warmer (and less dense) air rises. Since entropy does not favor the creation of a new order (leaving empty the space that the warm air previously occupied), cold air moves in to ﬁll the empty space, thus creating winds and currents. e wind moving through the mountains erodes the mountains ever so slowly and moves the material away to reduce it. To this, we should also add ﬂowing waters when it rains and snow melts, or when rivers cut through the dirt and carry it along. e Nile River is famous for ﬂooding at its delta every year and fertilizing the area with new and nutrition-ﬁlled dirt from the mountains above. Figure 1.1 shows the erosion of earth due to these mechanisms at work at Petra. 1.1. INTRODUCTION 3 Figure 1.1: e washed out, worn out Petra valley. Most materials expand when heated and contract when cooled, including when frozen. is is due to the fact that as the temperature decreases, so does the energy of the molecules, and therefore, they get closer to each other, reducing the volume of the material and making it denser. However, exceptions exist, including Bismuth and water; they expand when frozen. e density of water is maximum when it is at about 4(cid:14)C at sea level. e volume of water increases when it freezes and when it is heated; this is why you should not place a closed water container in the freezer; it may rupture. You can see the result of this expansion by observing the surface of an ice cube. If you mark the surface of water in a plastic container and place the container in a freezer, you will notice that when frozen, the surface of the ice will have risen above the original line. However, if you use a metal container (and cover the surface with a piece of cardboard to prevent the direct blowing of cold air onto the surface) you will notice that the surface of the ice is somewhat conical in shape (although shallow), as in Figure 1.2. In most refrigerators, the cold air is blown throughout the freezer compartment. When a plastic container is used, since it is not a very good heat conductor, the water freezes at the surface ﬁrst, and therefore, as the water expands, it pushes up the surface as it continues to freeze. However, since the metal container is a good conductor, it causes the water to start freezing at the perimeter of the surface and around the walls. As it continues to freeze and expand, the surface rises slowly and continues to freeze at slightly higher levels until it ﬁnishes with an apex in the middle, just like a hill (the complete mechanism at work here is more complicated though). Water pipes may also rupture in the winter when they freeze. In places where the winter temperatures are very low, water pipes are buried a few feet underground to keep them warmer 4 1. ENTROPY Figure 1.2: In a metal container, as water freezes around the perimeter towards the center, it expands and pushes the water level up slowly, creating a conical shape with an apex. and prevent their rupture. e same is true for the water that gets in between crevices of rocks and other rigid material, whether on a mountain or not. When the water freezes, it cracks the rock or breaks it apart, and therefore, eventually destroys the order that exists. And what happens to the tree branch that falls in the forest when a hurricane passes through or when the tree is diseased? Microorganisms, beavers, termites, and other agents eventually break it down and destroy it. Example 1.3 What Happened to the Flagpole? So, you had a ﬂagpole in the yard, and after a few years, it rusted and eventually failed. e same is the fate of the sign pole at the bus-stop. ey rust because there is an order in the system that is un-natural. Entropy demands that the order be destroyed. One may try to postpone the rusting by painting the pole or embedding it in concrete, or keeping away the moisture whenever possible. But rusting, or oxidation, is another natural mechanism for reducing the artiﬁcial order of things. Just think about the radiator in your car. It will eventually rust and fail. But then what shall we say about the steel used in an engine, where it is constantly lubricated and moisture is kept away? It hardly rusts. In this case, friction and rubbing action between the diﬀerent moving parts will eventually erode the material, eventually reducing it into nothing (although the engine will stop long before this state is reached, and therefore, oxidation takes over in the junkyard). So do all metals oxidize? Not really. Stainless steel is almost rust-proof (although not all types and all qualities are rust-proof. Less expensive stainless steel that lacks enough chromium will rust. Check out your barbeque). Gold does not rust either, but it wears out. So it is not impervious to entropy. And what happens to that plastic part that does not rust? e ultraviolet 1.2. ENTROPY AND EFFICIENCY 5 light will help in its decomposition, ﬁrst by fading, then hardening and cracking, and eventually decomposing. Is this not what happens to most paints too? Nature, in its arsenal of mechanisms for reducing order, has countless other weapons, in- cluding insects, animals, microorganisms, viruses, diseases, ﬁre, wind, ﬂoods, and many others, each with a unique capability to do its work. 1.2 ENTROPY AND EFFICIENCY Reducing entropy will increase the eﬃciency of a system by increasing the order within the system. To understand this, let’s look at the following case. Example 1.4 Going to the Oﬃce Naturally, one may need to sleep longer one day due to being tired, less another day due to sickness or having to take care of a chore. It seems more natural that people who all participate in similar activities in the same place like an oﬃce or classroom or a factory may like to go to work or to class when they feel like it or when they can. Wouldn’t it be nice to be able to go to a classroom any time you prefer? Except that such a system is not eﬃcient. A teacher would have to repeat the same material countless times every day as students showed up randomly when they wanted. One might go to a bank for a transaction. However, if the tellers and bank managers came to work as they wished, chances that the work got done would be very low. Meetings would never work either if participants would arrive when they wished. ink what would happen if the workers of a factory took vacations as they wished instead of all taking the same days oﬀ. e factory would not be eﬃcient either. However, we will create an un-natural situation by requiring that everyone, regardless of how long they have slept, whether they are tired or not or whether they like it or not, must go to a class or be present in the oﬃce or participate in a meeting at the same designated time. But as a result, the teacher will have to teach once, the customer can make a transaction with the oﬃce staﬀ, and everyone knows when they can expect to see someone for an appointment. Is this not more eﬃcient? Yes, but it is not natural. e tendency in this system is also to reduce order; people skip work, get sick, do not come to work on time, and appointments are not kept. To maintain eﬃciency, we need to sacriﬁce comfort or desires. Otherwise, natural chaos would abound. 1.3 IS IT POSSIBLE TO DEFY ENTROPY? Yes. Simply by creating order, we defy entropy. By doing so we increase order, and consequently, eﬃciency. As a result, we create systems that do things for us, from which we beneﬁt even if we need to constantly ﬁght entropy. As an example, take the engine of a car. e design of an engine forces a particular sequence of events to repeat thousands of times a minute for hundreds of thousands of miles of travel. Each time the air is sucked into the cylinders, it is compressed, fuel is injected into the hot air causing 6 1. ENTROPY an explosion and creating useful work that turns the engine, and the burnt fuel-air gases are forced out (see Chapter 4). is is not a natural sequence and does not happen by itself, but precisely because of that, it is eﬃcient (useful to us). Entropy tends to create situations to reduce this order when components break, rust, or wear out and as accidents happen. But as long as the order is maintained, the system is a useful entity. If you think about any other system, including living systems, the fundamentals remain the same. A completely chaotic system is natural. However, everything has a particular order in it that makes it useful. We, and everything we create, are under the control of this fundamental phenomenon, even if we learn to defy it. 1.4 WHY DO WE GET OLDER? As mentioned previously, living systems are also subject to the same entropy. Humans, for ex- ample, are very sophisticated and orderly systems. Nature, based on entropy, uses a variety of mechanisms through which it destroys this order, including disease, accidents, and aging. We get older because our systems have to eventually stop. Obviously, here I will not discuss the inherent mechanisms that the body uses to cause aging (such as the natural DNA markers that measure our age and turn on or oﬀ diﬀerent functions of our DNA). Whatever these mechanisms, they are just tools through which entropy does its work. However, even if we do our best to take care of our bodies and stay healthy, even if we never contract a disease, never smoke or drink, always exercise, eat right, and always make prudent decisions, we still get old and our bodily functions eventually stop, some sooner, some later. Physiologists and engineers can derive equations that describe this phenomenon mathe- matically as well. For example, considering caloric intake (how much energy is consumed by an individual through the food the person eats) versus the expenditure of energy by a person, one can calculate the eﬃciency of the human body and the food eaten. Of course, the eﬃciencies of diﬀerent food systems are diﬀerent. However, this waste of energy can be mathematically related to entropy generation. erefore, one can actually estimate the increase of entropy of the system of human body. Now think about the fact that when a child scratches her knee, when a person cuts his ﬁnger while cooking, or even after surgery, the body heals itself. But why should it? Is that not against entropy? Yes it is. When it heals, the body adds to its order, reducing entropy. So healing, and in fact life itself, are against entropy. As long as we are alive, our bodies have learned to defy entropy and to heal, overcome diseases, grow bigger, re-produce, and create new life. Each one of these phenomena is against the fundamental principles of entropy, disorganization, and the randomness of nature. But we are born (regardless of our will and against entropy), we grow bigger and taller and stronger, we get better after illness, and we go on living for a period of time. Each one of these reduces the overall entropy of the universe until we eventually die, when it increases once again. Planting a seed and growing it into a tree is the same. e secret of life in the seed can 1.5. ENTROPY AS DESCRIBED BY AN EQUATION: THERMODYNAMICS 7 defy entropy, causing it to sprout, grow, create fruits and seeds, and resist death for a while. But eventually, all vegetation and trees come to an end too. 1.5 ENTROPY AS DESCRIBED BY AN EQUATION: THERMODYNAMICS ermodynamics is the study of thermal systems, resulting in the transformation of diﬀerent forms of energy, the creation of useful work, heat transfer, and the dynamics involved. ermo- dynamics is built on two basic laws, appropriately referred to as the ﬁrst law and the second law. (ere is also a zeroth law that indicates that if two bodies are at thermal equilibrium with a third body, they are also at thermal equilibrium with each other. Kind of obvious, but necessary.) ere is also a third law of thermodynamics, stating that entropy is zero at absolute-zero temperature. In any system, both the ﬁrst and second laws of thermodynamics must be satisﬁed, not just one. 1.5.1 THE FIRST LAW e ﬁrst law of thermodynamics relates to the fact that energy is not created, but only transformed from one form to another. erefore, for every system (we refer to it as a closed system, separated from the environment or other systems), the total energy remains the same because we cannot produce any energy and we cannot destroy any energy, but only transform it into other forms. For example, in our cars, we transform into mechanical energy some of the chemical energy stored in the fuel by ﬁrst transforming it into thermal energy (combustion). e remaining part of the energy is rejected from the engine through the exhaust and the radiator (if water-cooled) and by direct radiation of heat into the atmosphere. e mechanical energy of the engine is also transformed into other forms, for example kinetic energy of the car moving at a particular speed, or the potential energy of the car going uphill (we will talk about these later). is potential energy is once again converted to more kinetic energy (going faster) if we continue downhill. All of this energy is eventually converted into thermal energy through the brakes, air resistance, and friction in the system (we eventually slow down and stop). e total amount of chemical energy going to the engine is equal to the total mechanical energy plus the rejected heat. is can be described by: or Efuel D Emechanical Erejected C Ein D Eused C Erejected; (1.1) (1.2) where Ein is the input energy, is the Eused energy that is converted into a useful form such as mechanical energy, and is the Erejected thermal energy rejected to the environment. You might see this equation containing the word work as well, such as the work done by the engine. Work is another form of expressing energy. When a force moves, it works. erefore, when the force created by 8 1. ENTROPY an engine at the point of contact between the wheels and the ground pushes the car forward, it is doing work. Work, which can be transferred into mechanical energy, can be calculated by multiplying the force by the distance travelled or a torque by the angle rotated. is is usually expressed as: W F d; (cid:1) D (1.3) where F is the force and d is displacement (how much the object has moved). is is true for the human body too. If you consider the human body as a system, then the total energy intake (from the foods we eat) should be equal to the generated work, the stored energy in the body (such as by fat), and the rejected heat. So imagine that a person takes in 2,000 Calories of energy in one day. Suppose that the person uses 900 Calories to walk, think, perform bodily functions, talk, etc. Also imagine that the person loses 900 Calories of heat through radi- ation and convection. Our bodies, when warmer than the environment, lose thermal energy. We must lose the thermal energy generated by our muscles and physiological functions to not only remain comfortable, but to even stay alive. e opposite is true in temperatures warmer than our body temperature; not only does the body get warmer, it cannot reject its extra thermal energy through convection or radiation. e reason we perspire is to increase heat loss from the body by evaporating the sweat on our skin (it takes thermal energy from the body to evaporate, therefore transferring our body heat into the environment. In damp environments where humidity is high and the body cannot easily evaporate the sweat, we feel warmer. Similarly, when there is a breeze, we feel cooler because it increases heat loss from the body). Without this heat loss, we may die (should we use anti-perspirants in hot weather?). e remaining 200 Calories that are not rejected and are not used otherwise will be stored by our bodies in the form of fat. At 9 Calories per gram of fat, this is about 22 grams of fat added to the body, a weight gain. On the other hand, if the energy intake is less than the work produced plus the heat loss, our bodies will convert the body fat into energy supply, therefore causing a net weight loss. e energy equilibrium requirement is maintained through this dynamic. It should be mentioned here that this is a very simpliﬁed model of the human body. In general, each person has a diﬀerent metabolic rate that is aﬀected by many factors, including heredity, age, and so on. Some of the food we eat is not digested at all, and is rejected as waste. When we suddenly reduce our energy intake (say by dieting), the body assumes there may be a supply problem, like a famine, and slows the metabolic rate, storing more fat for future emergen- cies. If we start eating more again, it will convert more to fat. If we eat as usual but work more (burn more calories), there is less left for conversion to fat. erefore, the aforementioned model should be used for understanding the energy equilibrium and not a complete picture of human metabolism or dieting. In general, reducing energy intake should have the same eﬀect as doing more work (more walking, exercising, swimming, etc.). However, doing more activities, even in light of eating more calories, is more fun! By the way, you may have noticed that in the preceding section, we used Calories and not calories. Each Calorie is in fact one kilocalorie or 1,000 calories. In food science notation, the 1.5. ENTROPY AS DESCRIBED BY AN EQUATION: THERMODYNAMICS 9 unit used is Calorie. It is generally assumed that carbohydrates and proteins are approximately equivalent of 4 Calories per gram, or 4,000 calories per gram. Fat is approximately 9 Calories per gram, or 9,000 calories per gram. One calorie is the energy needed to raise the temperature of 1 cc (cubic centimeter) of water by 1 degree Celsius (or 1.8 degrees Fahrenheit). erefore, one Calorie is the energy needed to raise the temperature of one liter of water by one (cid:14)C. Consequently, 2,000 Calories consumed by one person in one day can heat up 2,000 liters of water by one (cid:14)C. A person requiring 2,000 Calories per day for maintaining constant weight, who fasts for 24 hours (no food intake whatsoever, except water), and who still performs routine work as everyday life 222 grams or a little less than 0.5 pounds. that burns 2,000 Calories of fat, will lose 2,000/9 Now calculate how many days one would have to fast, completely, and maintain the same level of activity, to lose a desired amount of body fat. D So, can we cool down a room during the heat of the summer by placing an air-conditioning unit or a refrigerator with its door open inside the room? Do either of them not produce cooler air that can make the room cooler? e answer is no. e room will actually be hotter. is is because there is friction in every system, regardless of what we do. So we need energy to overcome this friction. We also need energy to transfer the heat from one part of the system to another. Remember, energy is neither produced, nor destroyed, but only transferred (or converted) from one form to another. e cooler air of the refrigerator or the air-conditioning unit is the result of a thermodynamic cycle (we will discuss this in Chapter 4) which removes the thermal energy through one part of the system called an evaporator (and therefore, making that part cooler) and transferring it to another part of the system through the condenser (and therefore, making it hotter). e net result is that we have spent energy in order to do this transfer. If the evaporator part of the system is outside of the room, and therefore, transfers the additional thermal energy to the ambient air, the net result is that the room or the refrigerator will be cooler inside at the expense of being hotter outside. If the whole system were within the room, the net result would be a hotter room. Note how we have created a particular order within this system that against the expected outcome (that heat ﬂows from a hotter place to a colder place) transfers the heat from a colder place to a hotter place by the additional work we do. It is necessary to mention one thing here. If you look at a dictionary, the word heat is deﬁned in terms such as “energy associated with the motion of atoms or molecules in solids and capable of being transmitted by convection and ra- diation,” as a “form of energy possessed by bodies,” the “perceptible sensible or measurable eﬀect of such energy so transmitted,” etc. In vernacular con- versations we also refer to heat as energy. However, in thermodynamics, heat is the transfer of energy from one medium to another, which is diﬀerent. Al- though in the realm of thermodynamics equating these to each other is not correct, we still use the word as if it is an energy term and refer to heaters, .. 10 1. ENTROPY heat exchangers, heat pumps, heat absorption and heat rejection, and similar terms. Inadvertently, the word is also used here as if it were energy because we normally refer to it as such. Understanding that although correct deﬁnitions are diﬀerent, we may sometimes use the word “heat” as if it were thermal or internal energy. .. 1.5.2 THE SECOND LAW e second law of thermodynamics relates to the quality of this energy transformation. But ﬁrst a word about energy types. Rub your hands against each other for a few seconds. ey will feel warm. Burn a small stick of wood. It will give oﬀ thermal energy. Turn on a light bulb (especially an incandescent light bulb that gives oﬀ light through a heated element) and it gets hot. Run the engine of your car, and it too will get hot. Now try to do the opposite: use the heat to move your hands, to recreate the stick of wood, regenerate the electricity that turned on the light, or recreate the gasoline that went into the engine. You will need to create a system composed of many elements to move your hands, spend the energy for a long time to nurture and raise a tree, make a power-plant or design a device like an engine, or use a chemical reactor to re-make the gasoline. is is because thermal energy is the lowest-quality energy. All other forms of energy tend to reduce to thermal energy unless we do something drastic. Natural systems go toward the lower-quality thermal energy. For example, what happens to the energy of your voice as you speak? Your voice will vibrate countless diﬀerent systems in your vicinity, including surfaces and molecules of air through which the energy eventually converts to thermal energy. In fact, the sound can only emanate in air by vibrating the molecules of air; sound does not transfer in vacuum. And all that mechanical energy in the form of vibrating elements converts to thermal energy. And what happens to the sound level if you speak to someone while you are inside and the other person is outside of a room? e reason the level of your voice heard outside is lower is that part of the energy is absorbed and converted into thermal energy by the walls, the doors and the windows, and the furniture and other things in the room. Additionally, the eﬃciency of converting other energy forms into thermal energy versus converting thermal energy into other forms of energy is very diﬀerent. Not only is it easier to convert electrical energy to thermal energy, it is also more eﬃcient. erefore, the best eﬃciency one might expect from a power plant that converts lower-quality thermal energy (chemical energy of the fuel converted to thermal energy during burning) into higher-quality electrical energy is about 40% (see the discussion about “combined cycles” in Section 4.8), whereas converting electrical energy into thermal energy is very eﬃcient (almost all electrical energy is converted into thermal energy in a lamp). is is also very much related to entropy, but we will not get into it for now. e eﬃciency of converting electrical energy into mechanical energy (such as in an electric motor) 1.5. ENTROPY AS DESCRIBED BY AN EQUATION: THERMODYNAMICS 11 can be over 90%. Similarly, electrical-to-electrical conversion of energy such as in a transformer or a charger can also be about 90% or so. Another important issue is the value or utility (usefulness) of energy. What matters is not only the total amount of energy that is available, but also at what temperature it is (this is called exergy). A high temperature medium is higher in value or utility than the same medium in low temperature. For example, the total energy stored in the waters of a lake is tremendous, but since its temperature is about the same as the ambient temperature, this energy cannot readily be used. A small mass of ﬂuid at high temperature may have the same energy as a large tank of the same ﬂuid at ambient temperature. We cannot easily use the energy of the larger mass at near ambient temperature, but the energy of the high-temperature small mass can be used readily (for example, to heat a glass of water) and, therefore, it has more utility. As mentioned earlier, both the ﬁrst and second laws of thermodynamics must be satisﬁed. Imagine a cup of hot coﬀee left in a room. Eventually, the heat transfers from the coﬀee into the room, and therefore, the energy lost from the coﬀee is gained by the room, satisfying the ﬁrst law. However, if it were up to the ﬁrst law alone, it should also be possible that some energy from the room transfers itself to the now-cooled cup of coﬀee and heats it again; if it were left to the balance of energy transfer alone, both scenarios would satisfy the ﬁrst law and either one would be possible. But we know this does not happen, because it violates the second law. Based on the second law of thermodynamics, it is impossible for the heat to transfer from a cold source into a hot source on its own. A very common blessing and curse of everyday life is friction. Friction is a blessing when we need it, and a curse when we do not need it. Examples abound, but for instance, when we brake, it is friction that stops our car or bicycle. In this case, more friction generally makes a better brake. e same is true in walking; we can only walk because there is friction. Just think of walking on ice or with roller skates and how hard it is even though the friction is low, not zero. And we can grab a fork and eat only because there is friction. In all these cases we win because there is friction. But we lose when there is unwanted friction, for example in the mechanical components of our car, air friction (drag) as we move through the air, and friction on the ﬂoor when we push heavy objects. However, in both cases, whether a blessing or a curse, friction always opposes motion and therefore it always converts part of the energy (or all of a speciﬁc form of energy such as kinetic energy) in the system into thermal energy, the lowest form of energy. Since every real system has friction, every real system creates wasted heat, whether a car, a fan, a computer, or our bodies. ere is no escape from this. erefore, as every system operates, it will lose some of its energy into thermal energy, and consequently, there can never be a 100% eﬃcient system (this is also directly related to entropy and is expressed as a thermodynamic equation that is used in the analysis and design of systems, but is beyond the scope of this book). In fact, based on the preceding argument, perpetual machines are fundamentally impossi- ble. Since every system has friction in it, it is impossible to drive a system indeﬁnitely without supplying some energy into it; the friction in the system converts the added energy into ther- 12 1. ENTROPY mal energy. Without it, the machine will not move, and even if the system is given some initial energy (like a ﬂywheel which is already rotating) the stored energy will soon be converted into thermal energy and rejected due to the friction in the system. Based on this fact, next time you hear someone’s idea of a novel, innovative, and unique perpetual machine, go ahead and bet that it will not work and challenge them to make it if they insist that you just don’t understand. So what is the second law of thermodynamics anyway? e second law states that the trans- fer of energy from one system to another is in the direction of lower-quality energy. For example, a hot glass of water left in a room will lose its energy to the cooler air in the room until they are at equilibrium and there is no more transfer of energy. What is the chance (probability) that the energy in the cooler room would somehow collect itself into the glass of water and make it hotter than the room temperature? Zero. Is this not what we already said about entropy anyway? 1.6 HYBRID CARS ANYONE? Hybrid cars have recently become very popular, and rightly so, due to their very high eﬃciency as compared to other vehicles with regular internal combustion (IC) engines. For cars of a similar size and weight, typical fuel consumption may be in the 25–30 MPG in the city and 30–40 MPG on freeways, whereas for a hybrid it might be 50–60 MPG in the city and about 40–45 MPG on freeways. Obviously, hybrid cars are much more eﬃcient, even if the numbers are strangely confusing in that hybrids use more gasoline in freeway driving than city driving. First, let’s see why non-hybrid cars are more eﬃcient in freeway driving than in city driving. As previously discussed, the total energy of the fuel spent is converted into the kinetic energy of the car and into thermal energy due to friction, drag, sounds and vibrations, as well as the huge amount of energy rejected by the engine through the exhaust, radiator, and heat loss through the body of the engine (and due to the second law of thermodynamics, it is impossible to eliminate this loss). e eﬃciency of the best engines is lower than 40%; this means that less than 40% of the total energy is converted into useful energy such as kinetic energy, while the rest is lost as thermal energy. is is even worse when the engine runs without the car moving, such as behind a traﬃc light or in congested traﬃc. In these situations, there is no kinetic energy, and therefore all the fuel energy is wasted. e kinetic energy stored in a car of mass m at a velocity of v is: E D mv2: 1 2 So, in stop-and-go driving in the city, every time we speed up, we convert less than 30%–40% of the spent fuel energy into kinetic energy. In a non-hybrid car, when we brake, this energy is converted to additional thermal energy and is rejected to the environment, causing more loss. In fact, sometimes the thermal energy of braking can be so much that it may damage the brake’s rotor assembly. e rotor gets so hot that, due to what is called residual stresses that remain in it as a result of manufacturing operations, it can bend, requiring that it be grinded to prevent pul- sations when the brake is applied. e more we accelerate and gain speed and then slow down by (1.4) 1.6. HYBRID CARS ANYONE? 13 braking, the more energy we waste, leading to higher gasoline consumption in the city compared to freeway driving where we drive at a more steady speed. In this case, since we do not slow down or completely stop as much as we do in city driving, there is much less waste, and therefore better eﬃciency. Engines require an injection of extra fuel to accelerate when we speed up, further re- ducing the eﬃciency in city driving. As a result, more uniform speeds in freeway driving increase eﬃciency, reducing the need for additional gasoline. To make matters even more complicated, since most drivers like to have plenty of power available to accelerate quickly, more powerful en- gines are installed in cars; in freeway driving, when accelerations are lower (smaller changes in speeds in freeway driving), only a fraction of the available power of the engine is used. Since engines have diﬀerent eﬃciencies at diﬀerent power levels, the total eﬃciency of the engines is aﬀected by the power it generates. In purely electric cars (also called Zero Emission Vehicles or ZEV, Battery Electric Vehicles or BEV, Electric Vehicles or EV ), instead of an engine, the source of energy is a large set of batteries. e car is propelled by converting the electrical energy stored in the batteries (actually in the form of chemical energy) to mechanical energy through electric motors that rotate the wheels. Like in a conventional car it is possible to stop an electric car by braking, and therefore, converting the kinetic energy of the car into thermal energy and rejecting it into the atmosphere. However, due to a phenomenon called electromotive force (or EMF), the kinetic energy can be recaptured and converted back to electrical energy that can be used to recharge the batteries. Of course, this is not 100% eﬃcient either and some energy is lost during conversion (in fact, due to safety concerns, there is always some braking mixed in with regeneration to ensure that the vehicle stops when needed, especially at low speeds). erefore, since a lot of the kinetic energy is captured and converted back into electrical energy and stored in the batteries (or ultra-capacitors), the eﬃciency of the system is much higher than when an internal combustion engine is used. As a result, the total eﬃciency of an electric car can be much better than a regular engine-equipped car. A Word about Electromotive Force (EMF) Imagine that a conductor (for example a wire) is placed within a mag- netic ﬁeld (for example between the two poles of a magnet) as in Figure 1.3. With an electric current ﬂowing through it, the conductor will experience a force (or a torque in rotational systems) called electromotive force, which is perpendicular to the plane formed by the current and the ﬁeld. Similarly, if the conductor is moved (or rotated) within the ﬁeld (for example, by applying a force or torque to it and causing it to move), a current will be induced in the conductor. e same is true if the magnetic ﬁeld is turned on and oﬀ or is changed in magnitude or direction. is simple principle governs how elec- tric motors work, how electric generators generate electricity, and even how transformers change the ratio of voltage and current for electrical energy dis- .. 14 1. ENTROPY tribution systems. More on this in Chapter 6, but for now suﬃce it to say that an electric motor and an electric generator (such as the generator in your car that recharges your battery after you drain it a bit by starting the engine, and which if it fails, your battery will drain, stranding you in the middle of worst places when you need to restart your engine!) are the same thing (with minor diﬀerences for managing the DC and AC currents). Figure 1.4 shows the sta- tor coils of an AC induction motor and its rotor. e rotor is a collection of conductors that move within the magnetic ﬁeld, generated by the stator coils. Figure 1.3: A wire carrying a current, placed within a magnetic ﬁeld, will ex- perience a force in a direction normal to a plane formed by the current and the ﬁeld. is means that if a current passes through a motor’s coils, the electro- motive force will cause it to rotate, acting as a motor. However, if you rotate the shaft of the motor, either by attaching it to something else that is rotating or by turning it manually, it will have a current induced in it, acting as a gen- erator. Figure 1.5 shows a ﬂashlight in which the user can rotate the handle to charge the energy-storage unit within the ﬂashlight. In this case, instead of a rechargeable battery, a large-capacity capacitor may be used. .. CurrentFieldForceNSForce1.6. HYBRID CARS ANYONE? 15 Figure 1.4: An AC motor with its stator coil and rotor. Figure 1.5: In this ﬂashlight, a crank is used to rotate a generator in order to con- vert mechanical energy into electrical energy. is is either stored in a rechargeable battery or in a large capacitor. However, as explained earlier, the mechanical energy is converted into electri- cal energy through the generator (which is really a small motor) and stored in the capacitor. Similarly, in a hybrid car, the same motor that rotates the tires when powered by the current from the batteries can also function as a gen- erator and produce a current that recharges the batteries when it is forcefully rotated by the wheels (while the current from the batteries is cut oﬀ ). Since a torque is needed to turn the generator, it converts the kinetic energy of the car into electricity, and consequently acting as a brake. Obviously, electronic .. 16 1. ENTROPY circuits are used to control the ﬂow and the charging of the batteries and how much force is applied. So, in electric and hybrid cars instead of braking by mechanical means and wasting the energy into thermal energy, the kinetic energy is recaptured and converted back to electric form, stored in the battery, and used again later. .. It should be mentioned that, when charged by plugging into the electric grid, the energy stored in the batteries comes from a power plant that also burns fuel, so it is not that much more eﬃcient than an engine; the diﬀerence is that power plant energy conversion systems are some- what more eﬃcient than engines, perhaps a little over 40% or so (see Section 4.8 for additional notes on this). Electricity can be “generated” (or more accurately, converted) by burning gas or coal (less expensive), by solar panels, through nuclear or hydroelectric power plants, wind energy systems, etc. erefore, the total system is more eﬃcient than an engine. Electric cars have many advantages in addition to their eﬃciency. Since there is no engine, there is no need for oil changes, maintaining the water level in the radiator (there is no radiator for cooling the engine anyway), and almost no need for replacing brakes. ey also do not have a gear box or a clutch (or transmission). Figure 1.6 shows a Tesla Motor S-Type car without the body. It shows how there are very few parts to the car. However, electric cars have a fundamental drawback. When the battery is drained, it must be recharged, whether at home, at work, outside shopping malls, or at charging stations. Unless the car is driven short distances, for example between your house and your place of work or school or shopping, and time is available to recharge the batteries at night or while you shop, or if charging stations are readily available to charge the batteries on a regular basis (which requires time), you may run out of energy and not be able to drive your car. is severely limits the range of an electric car and limits its usefulness to only short trips. Some companies have proposed, and have attempted at great expense, to create battery-exchange stations as common as gas stations, into which you may drive your car, automatically exchange your battery with a similarly charged unit, pay for the energy used, and quickly get on your way again. Until such a time when there are suﬃcient stations everywhere, the recharging of batteries will remain an issue. A huge advantage can be created if a relatively small engine is also added to the purely electric system to recharge the batteries at a constant rate while we drive. ese cars are referred to as Range Extended Electric Vehicles or Plug in Hybrid Electric Vehicles (PHEV). In this case, the car has a complete electric drive system, including batteries, drive motors and generators for brakes, and control systems, but also an engine, fuel tank, and associated hardware. However, in general, the power required to constantly recharge the batteries is a fraction of the power needed to propel the car at high accelerations. erefore, a small engine can be designed and used to generate electricity at its maximum eﬃciency to recharge the batteries. is way, the driver may drive the car just like a regular car without regard to range limitations. Since most of the energy is recaptured during braking, and because they can be charged at night, the eﬃciency of these cars 1.6. HYBRID CARS ANYONE? 17 (a) (b) (c) Figure 1.6: Tesla Motors S-Type chassis (a), drivetrain (b), and steering mechanism (c). Due to its nature, an electric car is very simple, with very few parts, compared to a conventional car or a hybrid. e batteries are placed in the middle part of the car under the seats. in terms of needed gasoline is very large. However, if the intention for the engine is to propel the car in extended driving situations like a regular engine capable of large accelerations, the engine will have to be larger and its eﬃciency will be lower. For example, the 2012 model Chevrolet Volt has an 84-horsepower engine. e engine of the 2013 Toyota Prius is 138 HP. So then what is a hybrid electric vehicle (HEV )? A hybrid car is the combination (hybrid) of both systems that share the power generation duties. Although it sounds even more ineﬃcient to have both an engine and a set of usually heavy and expensive batteries with limited lives, and drive motors and control systems, hybrids oﬀer something that electric cars lack: the convenience of having gasoline available to burn regardless of how long a drive might be, as well as the desired 18 1. ENTROPY accelerations available when needed, all at a much better gas mileage. It should be mentioned here that there are many diﬀerent combinations of gasoline and electric drive duties used in hybrids, each with their own characteristics (for example, parallel systems, series systems, and power-split systems). Regardless, in hybrid cars, when not plugged in to recharge the batteries, a regular engine converts the chemical energy of the gasoline into electrical energy which is used to charge the batteries or assist in powering the vehicle. e electrical energy is used to drive the electric motors to propel the vehicle, and the EMF is used to convert much of the kinetic energy of the car back to electrical energy when we brake. As long as the speed of the car is relatively low (up to about 30–35 miles per hour) and the batteries are charged, the electrical energy is used to drive the electric motors and propel the vehicle. When the battery is drained, the engine automatically starts to charge the battery and also help propel the car. At higher speeds the engine starts and participates in propelling the car. In freeway driving, it is mostly the engine that drives the car. Still, the kinetic energy of the car is recaptured and used to charge the batteries during braking. Since the engine does not principally drive the car in most cases, and since it does not normally start the car from rest where the most torque is needed, and therefore does not need to be hugely powerful to provide large accelerations that are needed only a fraction of our driving time, the engine can be much smaller and can mostly run at a constant rate at its most eﬃcient state. erefore, it will have the best possible eﬃciency at the lowest possible weight (although manufacturers are increasing the size of engines to satisfy our hunger for more power, albeit at the cost of fuel eﬃciency!). So why is it that the eﬃciency of a hybrid vehicle is even better in city driving than in free- way driving? Do we not accelerate, decelerate, and brake more often in city driving and therefore waste more energy? Should it not be that gas consumption in freeway driving should be even less than in city driving? en why is it larger for hybrids? ere are two reasons for this anomaly. One is that hybrids switch to their engines in free- way driving. erefore, the eﬃciency is that of the engine. However, the more important reason is drag resistance. When an object moves through the air—regardless of its shape—the faster it goes, the larger the air resistance. e very simpliﬁed equation describing this phenomenon is: FD D 1 2 (cid:26)Cd Av2; (1.5) where FD is the drag force indicating resistance to movement, is the density (cid:26) of the ﬂuid (in this case, air), Cd is the coeﬃcient of drag, a measure dependent on the shape of the object, A is the frontal area of the object (the area of the vehicle if you were to look at it directly from the front), and v2 is the square of the velocity of the vehicle. Coeﬃcient of drag varies for diﬀerent shapes; airplanes have a much smaller coeﬃcient of drag than buses because they are more aerodynamic. Coeﬃcient of drag for cars also varies depending on their shape. e most important element of Equation (1.5) is speed because it is squared. erefore, as the speed increases, the drag force increases quadratically. For example, for the same car, when everything else remains the same, as the speed goes from 30 miles an hour to 60 miles an hour, the drag increases four times as much. 1.7. COMMON MISCONCEPTIONS 19 At 75 miles an hour, the drag is 6.25 times as much. erefore, in freeway driving, the engine has to provide more power to compensate for the drag force at a much higher value than city driving where speeds are low. Unlike stop-and-go driving conditions where much of the kinetic energy is converted back to electrical energy and restored into the batteries, all the energy is used to compensate for drag force and not recaptured in freeway driving, and therefore, the eﬃciency of hybrids in freeway driving is less than in city driving. Strange, but true. 1.7 COMMON MISCONCEPTIONS Since we are talking about energy, let’s also talk about some misconceptions people have about it. I. Heating a room faster by setting the thermostat higher: Some people think that if a room is very cold, they can warm it faster if they set the thermostat at a higher temperature. Unless they have variable-rate furnaces with multiple burners, variable-rate or multiple fans, and a smart controller, this is not true (most systems are simply on-oﬀ systems). Let’s say the room is at 60(cid:14)F and the desired temperature is 72(cid:14)F. If you set the thermostat at 72(cid:14)F, the heater will pump heat into the room until it gets to 72(cid:14)F and stop (depending on the settings of the furnace, some systems slow down a bit when the temperature is near the desired value to prevent overshooting and to allow the furnace to cool down). Setting the thermostat at 85(cid:14)F will not increase the rate of heating the room to 72(cid:14)F because the furnace works at its maximum power regardless of the set temperature. So, the temperature of the room will not increase any faster; it just continues to increase until it reaches the desired temperature. So, if you initially set the thermostat to 85(cid:14)F and subsequently reduce it to 72(cid:14)F as it reaches this desired value, the rate of heating will be same as if you were to initially set it at 72(cid:14)F and be done with it. II. Cooling a room by leaving the refrigerator door open: On a hot summer day, when it is diﬃcult to bear the heat, it is tempting to leave the refrigerator door open in order to blow cool air into the room, and some people do so because they think they are generating cool air that can reduce the temperature of the room. As was discussed earlier, this is a misconception too. Although the refrigerator does blow cool air into the room, as long as the whole unit is inside the room, the total net eﬀect is more heat. Leaving the door of a refrigerator open will actually make the room warmer, not colder. is is due to the fact that the refrigerator is colder than the room because the heat is transferred from it and added to the air that is blown over its condenser. Due to the ever-present friction and ineﬃciencies in every system, it takes a net positive amount of energy to do this, therefore adding more thermal energy to the room and further warming it. We will see about thermodynamic cycles, including refrigeration cycles in Chapter 4, but for now let it suﬃce to say that leaving your refrigerator door open does not make the room cooler. In fact, it is the same if an air-conditioning unit is completely enclosed inside a room. So how do air conditioners normally make a room cooler? By placing their condensers, where the hot air is blown out, outside of the room, whether a traditional AC unit, a unit installed in a window, or a unit whose evaporator is inside the room and its condenser is outside. All you are doing is moving the thermal energy from inside the room plus the work done by the system 20 1. ENTROPY to the outside environment; the net eﬀect is more heat. Figure 1.7a shows the evaporator of an air-conditioning system inside the room, where the thermal energy of the room is transferred to the coolant, thereby making the room cooler. Figure 1.7b shows the condenser unit of the same system outside of the room, where the thermal energy is rejected into the outside air. (a) (b) Figure 1.7: Even though the evaporator part of the air conditioning unit is inside the room where it cools the air, the condenser part is outside in order to dissipate the thermal energy to the environment. Similarly, a running fan inside a room will also make the room warmer because the energy spent by the motor is added to the room. However, since the moving air helps evaporate sweat from the body, and therefore cools it, it makes the person feel better. Nevertheless, the temperature rises as a result of running the fan. III. e hand dryer in the restroom blows cold air when it starts: You may have noticed that when you use blown air to dry your hands in a public restroom, it feels that at the beginning, when we believe it should be hot to dry our hands quickly, the blower blows cold air. Later, when the hands are almost dry, it blows hot air. However, if you try to pass them under the blower when your hands are dry, you will notice that the air is warm from the beginning. e reason we feel the air is cold at the beginning is that when our hands are wet, the air evaporates the moisture on our hands, cooling it in the process. What our hands feel during this process is the consequence of evaporation and the transfer of heat from the hands while the moisture evaporates. IV. Food cooks faster in boiling water if you turn up the heat: If your food is cooking in already-boiling water, turning up the heat will not increase the temperature of the water, and as long as the water remains boiling, it will not cook any faster. is is because when water or other ﬂuids boil, the temperature remains constant at the boiling point. For water at sea level, this is 212(cid:14)F or 100(cid:14)C. is means that if you increase the amount of thermal energy through burning more gas or more electrical energy passing through the heating element, the additional energy 1.7. COMMON MISCONCEPTIONS 21 will make the water boil faster, not hotter, and therefore, it will convert to steam at a faster rate, but the temperature will remain the same. At pressures lower than the air pressure at sea level (for example, if you go to Denver), the boiling temperature decreases as well, cooking the food slightly slower. So what is the right way to increase the temperature of the water and cook faster? Using a pressure cooker, in which the lid is completely sealed causing the pressure in the pot to increase. is will raise the boiling temperature, therefore cooking faster. However, you cannot remove the lid without ﬁrst letting out the steam to reduce the pressure equal to the atmospheric pressure in order to taste the food or check it. Otherwise, it may blow up in your face! Each time you do this, a lot of energy is wasted too. e same is true in steam locomotives. In order to increase the temperature of the water and generate more steam and more power, a pressure vessel is used. is increases the boiling temperature and increases the total energy that the steam carries, therefore achieving more power transmission. e downfall is that pressure vessels are heavier and more dangerous. e same principle is also used in the design of a novel coﬀee cup that keeps your coﬀee at a constant temperature for a comparatively long time. e cup is double-walled, where the space between the two walls is ﬁlled with a chemical compound that boils at about 180(cid:14)F, a desired temperature for hot coﬀee. If the freshly poured coﬀee is hotter than this temperature, the extra energy is transferred through the metal wall of the coﬀee cup to the ﬂuid in between and heats it up to a boiling temperature. e remaining energy will boil the compound into steam. Since the heat capacity of boiling the compound is more than heating it, much of the initial excess heat energy of the coﬀee will be stored in the chemical compound in the form of steam at a constant temperature. As the coﬀee gets cooler, the heat energy of the compound is transferred back to the coﬀee, keeping it at the desired temperature for a longer time. Enjoy your coﬀee without the danger of pouring it over your legs and burning them while you drive! C H A P T E R 2 23 Natural Frequencies Vibrations, Hearing, Biomechanics, and Guitars 2.1 INTRODUCTION Imagine that you are sitting at home on a ﬁne morning when suddenly your whole house starts shaking. You look outside and realize a train or airplane has just passed by. You are at a rock concert and the drummer starts playing a bass beat so heavy you feel like your heart is actually vibrating inside your chest. Or you are stopped at an intersection and the car next to you is blasting reggae music with sub-woofers and your whole car starts to shake along with the beat. But how can an object have such a powerful eﬀect on another object with which it does not even have physical contact? What about the tires of a car shaking vigorously if they are not balanced and your cell phone vibrating when there is an incoming call? I know someone who claims that his back molars vibrate when he hums a D# note. He uses this vibration to tune his instruments when he does not have access to a tuner. What causes these vibrations? e phenomenon that causes all of these is called natural frequency. In this chapter we will study natural frequency, vibrations, and many other related issues and see how to reduce unwanted vibrations and beneﬁt from them when we need to and how they aﬀect our everyday lives. Imagine that you attach a small weight m to a spring (with spring constant k, see below), as shown in Figure 2.1 and hang the spring. Obviously, the weight will pull down the spring until the force in the spring equals the weight. Since it is in equilibrium, the mass will stay where it is without motion Now imagine that you pull down the weight extending the spring and then let go; it will start to go up compressing the spring, stop, come down stretching the spring, stop again, and start to go up again, oscillating up and down repeatedly at a constant rate. How long will it continue to oscillate? is depends on a number of diﬀerent factors, including the internal friction in the spring and air resistance (that converts the kinetic energy of the weight to heat, as discussed in Chapter 1), also referred to as damping. In the absence of any factors that will convert this energy into heat, the mass will theoretically oscillate forever, converting its potential energy P (energy stored in the spring as it is stretched or compressed) into kinetic energy K of the mass as described by: K D 1 2 mV 2; (2.1) 24 2. NATURAL FREQUENCIES Figure 2.1: A weight hanging from a spring in a stable condition. where V is the velocity of the mass. Of course, nothing in nature is completely frictionless, and air resistance exists unless there is an absolute vacuum. So in reality, after a few oscillations, the mass will eventually stop when all its initial energy is converted to heat. Where did that initial energy come from? From pulling the spring down, stretching it, and storing the energy in a form called potential energy or elastic energy: P D 1 2 kd 2; (2.2) where k is the spring constant and d is the displacement or the stretch in the spring from its free (unstretched) length. Spring constant is the force necessary to stretch or compress a spring one unit of length. In the metric system it is the force (in Newtons) necessary to stretch a spring one meter. In English units, it is the force necessary in lbs to stretch the spring one inch or foot. e displacement can be easily calculated from: mg k ; d D (2.3) where g is the acceleration of gravity (for example, 32.2 ft/sec2 or 9.81 m/sec2), and therefore, mg is the weight of the mass. It is important to notice that the little energy given to the system will cause the mass to oscillate for a long time—perhaps forever—if there is no friction or air resistance. e frequency at which the mass oscillates is called natural frequency. So what is natural frequency? e natural frequency of a part or system is the frequency at which it will oscillate theoretically without any (or in reality with little) outside energy. e rate kmof natural frequency, in the absence of damping (such as friction) can be described as: 2.1. INTRODUCTION 25 f D 1 2(cid:25) r k m Hz; (2.4) where the term 1 2(cid:25) is a constant of conversion, k is the spring constant, and m is the mass of the part (not its weight). Hz (read Hertz) is the unit used to describe frequencies (for example, your radio station may be at 90.5 MHz, or 90.5 Mega Hertz of oscillations per second). Let’s ﬁrst explore this concept before continuing. It should be clear from Equation (2.4) that as k increases, the natural frequency increases too. Conversely, as m increases, the natural frequency decreases. As engineers refer to this, when a system is stiﬀer (larger k), the natural frequency is higher and the oscillations are quick, whereas when the system is more massive (larger m), the natural frequency is lower and oscillations are slow. For example, imagine that we have two springs, one with a spring constant of 5 lb/in, one with 10 lb/in, and the weight used is 1 lb. To get the mass of this weight, we will use: W D mg or m W g D 1 386 lb in=sec2 D D 0:0026 lb:sec2=in: (2.5) (Note the unit used for mass in English system. In SI units, the unit of mass is kg, but in English units, there is no real unit for mass, so we use this unit which comes from dividing the unit of force lb by the unit of acceleration in/sec2). For the combination of the 5 lb/in spring and the 0.0026 lb.sec2=in mass (1-lb weight), the natural frequency of the system will be: f D 1 2(cid:25) r 5 0:0026 D 7 Hz or that one full oscillation will take 1 the natural frequency will be: 7 (cid:138) 0:14 seconds. For the second spring, with the same mass, f D 1 2(cid:25) r 10 0:0026 D 9:87 Hz and the time required to fully oscillate once is about 0.1 seconds. As you see, when the spring is stiﬀer (harder, requiring more force to pull or push), the natural frequency is higher too, taking less time to complete one oscillation; the mass moves faster. Now let’s take the same 5 lb/in spring, but attach a 2-lb weight (m 0:0052 lb.sec2/in) to it. e natural frequency will be: W g D 2 386 D D f D 1 2(cid:25) r 5 0:0052 D 4:94 Hz with the time required for a complete oscillation at 0.2 seconds. 26 2. NATURAL FREQUENCIES To see how this relates to real-life products, consider sub-woofer and tweeter speakers. e sub-woofer is usually a larger, relatively heavy speaker with a more massive cone. erefore, its natural frequency is lower, and as a result it is more appropriate for generating low-frequency bass sounds. e tweeter is usually small, such as the speaker used in your computer or cell phone, with a very light-weight diaphragm, which has a higher natural frequency that is suitable for generating higher frequency treble sounds. We will see more about these and other examples shortly. Since systems can oscillate very easily at their natural frequency, it means that if there is a changing force that is near the natural frequency of the system, it will induce large oscillations into the system. When it is to our beneﬁt, we take advantage of this phenomenon, whereas when it is to our detriment, we try to reduce or control it. erefore, any time there are forces present that oscillate near the natural frequency of a system, we must watch out for large, sometimes out-of-control oscillations in the system. If the inducing force varies at a frequency that is not close to the natural frequency, the system will not oscillate freely; it requires much more energy to oscillate a system or a part at frequencies other than the natural frequency. 2.2 SYSTEM RESPONSE TO EXTERNAL FORCES AT DIFFERENT FREQUENCIES Figure 2.2 shows the response of a system to varying-amplitude force (like a sine wave) at diﬀerent frequencies. Although in reality, input forces may be very diﬀerent, engineers use known inputs such as a sine wave to study the output of a system and understand its behavior. e x-axis shows the ratio of the frequency of the external force relative to the natural frequency of the system. So when this ratio is !=!n 1, the frequency of the external forcing function is the same as the natural frequency of the system. At other values, the frequency of the external force is either higher or lower than the natural frequency of the system. D e y-axis shows the response of the system, also called the magniﬁcation factor. It indi- cates how large the response of the system is relative to the amplitude of the force. So when the magniﬁcation factor is equal to 1, the amplitude of the vibration of the system is the same as the external force, and therefore, there is no magniﬁcation. When it is larger than 1, the system oscillates at a larger amplitude than the external force (it is magniﬁed), and when it is smaller, it indicates that the vibration is reduced. is is an important factor in the design of systems where we might wish to increase or decrease the amplitude of the vibration. Another important factor in Figure 2.2 is the damping ratio, shown as (cid:16) (Greek symbol zeta). We already mentioned that all systems have some friction, air resistance, or other damping (such as shock absorbers in your car) in them. (cid:16) indicates the level of this damping. A larger damp- ing ratio indicates quicker conversion of the system’s energy to heat, and consequently, reducing the amplitude of the vibration and how long it oscillates. What is important about Figure 2.2 here is that it shows how the system responds as the frequency and damping ratio change. Note that around !=!n 1 (when the frequency of the external force is the same as the natural frequency), the amplitude of the response is very large, D 2.2. SYSTEM RESPONSE TO EXTERNAL FORCES AT DIFFERENT FREQUENCIES 27 Figure 2.2: e response of a system to an external driving force at diﬀerent frequencies and ampli- tudes and damping. especially when the damping ratio is lower. eoretically, in the absence of any damping, the amplitude of the response could be inﬁnite, a theoretically devastating result. is would mean that the system could disintegrate as it is subjected to an external force at the natural frequency. However, although every system has some damping, when it is low, the amplitude of the response can be very large, many times larger than the input. As the damping increases, the amplitude of 1:00, also called critical damping, the amplitude of the the response deceases. At the value of (cid:16) response varies between 1 (when the input frequency is zero) and zero as the frequency increases. is indicates that with critical damping, the amplitude of the response is always smaller than the input, and therefore, the vibration is always reduced. We will see more about this later, but as an example, the suspension system of a car is designed to have a critical damping value to prevent excessive oscillations when it encounters a bump or similar external force. If the shock absorbers (that provide the damping in your car) get old or are damaged, the car can oscillate many times before the vibration dies out. Similarly, our bodies have a lot of damping. Consequently, our body parts are largely shielded from external vibrations. Although there is still a danger present when body parts are subjected to frequencies near their natural frequencies, the damping in the body reduces this danger signiﬁcantly. Next time you are taking a picture in a moving car try to place D ζζζζζζωω28 2. NATURAL FREQUENCIES the camera somewhere on the body of the car (dashboard, side of the doors, etc.) and see how much vibration is transmitted to the camera, to the point of making it impossible to take a good picture. But when you hold the camera in your own hands, the vibration is dampened signiﬁcantly, allowing you to take nice pictures. e same is true with reading a book in a moving car. Placing the book on the body of the car might make it impossible to read due to vibrations. Also notice how the amplitude of the response increases as the frequency of the input approaches the natural frequency, but reduces signiﬁcantly as the frequency of the external force increases beyond the natural frequency. For example, as the ratio of !=!n approaches 2 or larger, the amplitude of the response of the system approaches zero, indicating that the system does not vibrate. It is only at around the natural frequency that the response is large. is is very important, as it indicates that we can prevent large vibrations if the frequency of the external force is larger than the natural frequency. We will later see how this plays a pivotal role in our hearing mechanism and the design of certain systems. e following examples can help us better understand some of these concepts. Example 2.1 Balancing the tires of a car To make the ride of a car more comfortable, the tire assembly is attached to a suspension system consisting of a spring and a damper (also called a shock absorber). e suspension may take diﬀerent forms, but in most cases it is a spring and a shock absorber. Figure 2.3 shows two typical suspension systems for cars, one with a leaf spring and shock absorber, one with a coil spring and shock absorber. e shock absorber is designed to exert a force proportional to the velocity of the oscillation in the opposite direction of the motion, therefore dampening the oscillation and stopping it; the larger the velocity of the oscillation, the larger the force will be. But as far as we are concerned, the tire-spring assembly is very similar to the system of Figure 2.1. erefore, it has a natural frequency at which it oscillates vigorously when the frequency of the input force is close to it. Where does this force come from? e force may come from an imbalance in the tire or the tire assembly as a result of man- ufacturing processes; no manufacturing process is ever perfect. erefore, tires may be slightly heavier at one point compared to another, resulting in an imbalanced tire. e extra heaviness on one side of the tire, although sometimes very small (perhaps a few grams only), induces an outward force in the tire when the tire is rotating, referred to as centrifugal force. (Mechanical engineers and physicists do not refer to this name. We prefer to talk about an inward acceleration called centripetal acceleration, pointed toward the center of rotation. Due to the inertia of the tire, there is a reaction to this acceleration, pushing outwardly. Please see Chapters 3 and 5 for a more thorough discussion about inertia.) For example, the centrifugal force is the same force that lets you rotate a weight attached to a string without it falling, as in Figure 2.4. e same force dur- ing the spin cycle of a washing machine will force out the water. At much higher values (due to extremely rapid rotations) this force also separates uranium from other impurities, and therefore, concentrates it at higher purity levels. 2.2. SYSTEM RESPONSE TO EXTERNAL FORCES AT DIFFERENT FREQUENCIES 29 Figure 2.3: Typical spring-damper assembly of automobile suspension systems. Figure 2.4: A weight, attached to a string, will not fall when it is rotating around a ﬁxed point due to the outwardly pushing centrifugal force. Although the centripetal acceleration is inward, the reaction to this acceleration is outward. Since this force is always outward, the direction of this force changes as the tire rotates, sometimes facing down, sometimes facing up, to the left or to the right. Especially when the force is pushing down or pushing up, it pushes against the spring, deﬂecting it. is is exactly the same as in Figure 2.1 where a weight (a force) is attached to a spring, causing it to oscillate. As shown in Figure 2.2, as long as the frequency of this force is not similar to the natural frequency of the suspension system and the tire assembly, the tire will not oscillate much. But when the frequency of the alternating force is close to the natural frequency of the system, even the small force caused by a few grams of the weight imbalance is enough to violently oscillate the tire, shaking the car with everything in it; it only takes a small amount of force to introduce large oscillations at the natural frequency. However, the oscillations are much smaller if the frequency of the force is below or above the natural frequency of the system. a30 2. NATURAL FREQUENCIES In this case, our goal should be to eliminate this undesirable vibration. To do so, we elim- inate the source of the force, the tire imbalance. is is why the tire is tested for imbalance by placing it in a machine that rotates it and measures the force exerted by the imbalance as well as its location. e technician places a counter-balance weight on the tire assembly across from the center, therefore balancing it. Since the source of the oscillating force is eliminated, so are the resulting vibrations at the natural frequency. e same is true for any other device that rotates this way, be it the blades on the turbine of a jet engine, the tub of a washing machine when clothes are loaded in it, the driveshaft of a car, or even its engine. For example, if the blades on the turbine of a jet engine are not carefully balanced across from each other, the turbine, rotating at very high rates (perhaps 50,000 to 80,000 revolutions per minute) will generate tremendously high forces that can vigorously shake the engine. e driveshaft of your car that connects the gearbox (in the front) to the diﬀerential (placed in the rear of the car in rear-axle driven cars) must be balanced too; otherwise it will shake when rotating at the natural frequency range. And if you place a heavy jacket, a heavy article of clothing, a rug, or a blanket into a washing machine without other articles to counterbalance it, the machine may shake out of control during the spin cycle, causing it to move and break away from the water lines and cause severe water damage to its surroundings. And although it is slightly diﬀerent from this exact example, even an engine has forces that must be counterbalanced to prevent excessive vibrations in it. Except for certain conﬁgurations (such as a V-6 engine that is naturally balanced), the counterbalance weights are integrated into the crankshaft. Example 2.2 Shakers and Oscillators In Example 2.1 we looked at a system in which our desire was to eliminate vibrations (oscillations). In many other systems we may actually want to take advantage of the oscillations at the natural frequency. ree examples (and there are many more) are a cell phone vibrator, a hand-held massager, and electric shavers. In all cases, either a mass-spring or a rotating mass system is designed with a particular natural frequency. A vibrating force, either electromagnetic or mechanical (an imbalanced-weight rotating), is applied to the system at the same frequency, whereupon the mass oscillates vigorously although the force is very small. Since little energy is needed to induce vibrations at the natural frequency rate, the cell phone vibrator, the massager, or the electric shaver head operate with little expenditure of energy. 2.3 NATURAL FREQUENCY OF OTHER COMMON SYSTEMS Natural frequency is not just a characteristic of a mass-spring system or a rotating system. Many other systems have similar frequencies at which they oscillate with little or no external force. One such system is a pendulum. Others include wires, attached at both ends, and cantilevered beams. We will now discuss these systems because they also play an important role in many systems we often use. 2.3. NATURAL FREQUENCY OF OTHER COMMON SYSTEMS 31 2.3.1 PENDULUM Imagine a pendulum, a mass m attached to a string (or bar) l and hung at one end as in Figure 2.5a. If you move the pendulum to one side (for accuracy, assume the angle is small) and release it, since the mass now has potential energy at an unstable state, it will move down to the bottom, gaining speed as its potential energy is converted to kinetic energy. As the mass continues to the opposite side, the kinetic energy converts back to potential energy until the mass stops, repeating the process indeﬁnitely until, either due to friction or air resistance, the energy is lost in the form of heat. eoretically, in the absence of friction and air resistance, the oscillation will go on forever; in reality, it will oscillate a few times before it stops. Similar to the aforementioned case with a mass and spring, if you desire to oscillate the mass at a rate other than this rate, you will have to exert a force on it, whereas at this rate, there is no need for additional input force. Similarly, this is the natural frequency at which the system oscillates with little to no external force. (a) (b) Figure 2.5: A pendulum’s oscillation has a natural frequency that is independent of its mass. Although it is easy to derive the equation describing the natural frequency, suﬃce it to say that the natural frequency of a simple pendulum with a point mass (not the bar) at small angles is: f D 1 2(cid:25) r g l Hz: (2.6) Notice that the mass does not aﬀect the natural frequency (m is not part of this equation). is means that regardless of the size of the mass, the natural frequency of a simple pendulum is only aﬀected by the length of the string (or more accurately, the distance between the center of the mass and the point of suspension), and of course, the acceleration of gravity. erefore, unless you move to a diﬀerent planet, or move up a mountain, etc., the natural frequency of the pendulum will remain the same unless l changes. Where is this used? An example of an application of this system in everyday life is a grand- father clock. Because the natural frequency of a pendulum is ﬁxed, it can be designed (with appropriate dimensions and lengths) to have a period of exactly one second (or its multiples). mll,m32 2. NATURAL FREQUENCIES erefore, at that rate, it requires very little force supplied from the spring winding, a mass hung from a chain, or an electric ﬁeld, to oscillate it for a very long time. Have you ever seen how a grandfather clock is adjusted? A small screw on the bottom of the pendulum is turned to move in or out just a bit. e change in weight distribution (not the total weight) changes the location of the center of mass of the pendulum (causing a change in l) and changing the natural frequency and the period of oscillation. e same is true in another very important part of our lives: walking and running. We will discuss this a little later together with other body parts. Example 2.3 A child in a swing is mechanically very similar to a pendulum. Based on the size of the swing and the weight distribution of the child, the swing will have a certain natural frequency at which it tends to oscillate. It requires a lot of force to swing the child at another rate (you would have to grab the swing and move it back and forth at all times to force it to oscillate at other frequencies). 2.3.2 CANTILEVERED BEAMS Now imagine a cantilevered bar—a bar that is attached to a rigid body (like a wall) at one end, but is free at the other end—as in Figure 2.6. If the bar is pulled down a bit and released (plucked), the bar will oscillate up and down until the stored energy in it is converted to heat due to damping or internal friction in the material or because of air resistance. Here too, if you desire oscillations other than the natural frequency rate, you will need to exert a force on the bar; it does not need any additional force to oscillate at this rate. Figure 2.6: Oscillations of a cantilevered bar. m,LLhbe equation describing the ﬁrst natural frequency of a cantilevered beam is: 2.3. NATURAL FREQUENCY OF OTHER COMMON SYSTEMS 33 1 2(cid:25) (cid:20) 3:5156 L2 (cid:21) s EI (cid:26) ; f1 D (2.7) (cid:2) where L is the length of the beam, is (cid:26) the density (or mass per unit length), and I is the area mo- ment of inertia (see Chapter 5 for more details). e moment of inertia is discussed in Chapter 5, but for a beam with a rectangular cross section of width b and height h, as shown in Figure 2.6, it is: 1 12 E is the modulus of elasticity, a measure of the hardness or stiﬀness of the material. If you pull a piece of material, it stretches. Modulus of elasticity is a representation of this relationship and describes how stiﬀ a material is (see Chapter 5 for more detail). e Modulus of elasticity for steel is about 30 106 psi (in engineering terms, it is the ratio of stress over strain). bh3; (2.8) D I e important issue in Equations (2.7) and (2.8) is that the natural frequency of a beam is aﬀected by the properties of the material (E and (cid:26)), the length of the beam, its thickness and width. If any of these factors change, the natural frequency will change too. erefore, conceivably, we can make a series of beams with diﬀerent dimensions and tune them to all have diﬀerent natural frequencies as we want them. Are there any examples of where this is used? Of course there are, including the vibrations of a reed in an oboe or clarinet, a tuning fork, and our hearing mechanism. e reed of an oboe, a fundamental part of it that makes the sounds, is essentially a cantilevered bar (see Figure 2.7). As the musician forces an air-stream over it, it vibrates and generates the sound we hear after it is ampliﬁed by the body of the oboe. As the speed or pressure of the air stream changes, so does the vibration frequency of the reed. In a tuning fork too, when the legs of the u-shaped fork are struck, they vibrate at their natural frequency. rough the choice of dimensions and material used, the fork is designed to vibrate at a desired frequency. e same principle is used in the design of a particular tachometer with no moving parts (see Figure 2.8a). Tachometers measure how fast something rotates (for example, an engine shaft). Most tachometers are based on the back-emf principle discussed in Chapters 1 and 6. e tachometer is very similar to a small electric motor that is connected to the rotating machine, and which generates a current/voltage proportional to how fast it is rotating. A gauge measures the voltage. However, this particular device has a number of small cantilevered beams of diﬀer- ent thicknesses next to each other, each with a unique natural frequency that is slightly diﬀerent from the neighboring ones. By placing the tachometer on a rotating machine, its vibrations are transferred to the tachometer, forcing only one of the beams to vibrate vigorously when its natural frequency matches that of the rotating machine. erefore, with no moving parts, the number of revolutions per minute of the rotating machine can be measured. Figure 2.8b shows how this tachometer indicates the speed of the motor of a drill press at 2,000 rpm. 34 2. NATURAL FREQUENCIES Figure 2.7: e reed of a clarinet. 2.3.3 STRINGS Finally, consider a string that is attached to a rigid body at one end and kept taut with an axial force acting on the other, as in Figure 2.9. Plucking the string will also induce oscillations in it at its natural frequency that requires no more external force until it dies out due to internal damping and other frictional forces. e equation [1] describing the natural frequency for the string is: 1 2L s F (cid:26)A ; f D (2.9) where L is the length of the string, A is the cross sectional area, (cid:26) is the density of the material (mass per volume, or how heavy each unit volume of the material is), and F is the tension or force in the string. When the tension is increased, the natural frequency of the string increases as well, creating a higher pitch (this is how a guitar is tuned). As the length of the string increases, the natural frequency decreases. erefore, when the length of the string is reduced by fretting, the pitch increases (notice how the lengths of the strings in a harp are diﬀerent in order to produce diﬀerent pitches). For larger cross sections A, the natural frequency decreases as well. erefore, thicker strings have a lower pitch range. Heavier materials (steel versus nylon) also produce lower pitch vibrations. erefore, combinations of length, thickness, material, and tension can create any natural frequency we desire. 2.4 APPLICATIONS AND EXAMPLES e following sections show the applications of natural frequencies in a multitude of systems and devices. In each case, you will notice how the same engineering principles apply and how they are 2.4. APPLICATIONS AND EXAMPLES 35 (a) (b) Figure 2.8: A tachometer with no rotating parts. Figure 2.9: Oscillations of a string, attached ﬁrmly at both ends. used, whether in devices and systems that we design and build, or natural systems created through natural forces. 2.4.1 GUITARS, PIANOS, AND OTHER STRINGED INSTRUMENTS As the previous discussion indicated, large ranges of pitches can be produced by strings depending on their length, thickness, material characteristics, and tension. In a piano many strings are used, each with a speciﬁc length and thickness, practically all the same material. However, to tune the Vibrating at2000 Hz.FL,A,m36 2. NATURAL FREQUENCIES piano, an expert tuner adjusts the tension in order to create an exact pitch (natural frequency). In a piano, when a key is pressed, a hammer hits a string, and therefore, depending on how hard it hits the string, the volume of the sound varies. It is also possible to dampen the sound by pressing a damper against it. In harpsichords, the string is plucked just like a guitar; otherwise it is very similar to a piano. Harps are the same; each string at a diﬀerent length produces a diﬀerent pitch. e sound is adjusted by adjusting the tension. A harp is also plucked with the ﬁngers. In many stringed instruments, from guitars, violins, and violas to cellos and basses, all lengths are equal (some other instruments have varying lengths strings). However, the thicknesses of the strings are diﬀerent and so are the materials used (Figure 2.10). Some strings are steel, some are nylon, and some are wound with a wire (nickel) for a lower pitch. e tone of the open string is adjusted/tuned by changing the tension. Subsequently, the instrument is “played” by changing the natural frequency through fretting or ﬁngering. is is even more sophisticated in instruments such as a violin, where vibrato is common. In some electric guitars a tremolo bar is used to change the tensions of all strings simultaneously, thereby changing the pitch of all of them (see Figure 2.11). In this case, instead of attaching the strings to the body of the guitar, they are attached to the bridge. Since the bridge has a spring-loaded hinge, it can be moved slightly by the musician to change the tension. Can you guess how musicians use a tuning fork to tune a guitar or violin? Why does it work? Figure 2.10: Strings of a guitar produce pitches based on their lengths, the force pulling them at one end (including the changes in the force through the tremolo bar), the material from which they are made, and their cross sections. 2.4. APPLICATIONS AND EXAMPLES 37 Figure 2.11: A tremolo bar is used to change the tension on all strings simultaneously, thereby chang- ing their natural frequency and their tone. How Tension is Applied in String Instruments: Worm Gears: To apply ten- sion to the strings in a string instrument either friction–based pegs or a worm gear-based tuning key is used. For a violin or a viola, where the tensions are lower and the instrument is not plucked constantly, the strings are tensioned by turning the pegs or tuning keys. ese pegs are held in place through fric- tion. e pegs and the holes are tapered at a shallow angle, and therefore, by pushing them into the hole, enough friction is generated to keep the pegs from loosening (Figure 2.12). However, in guitars and most other instruments that are plucked, the forces are larger and friction may not be enough. In that case, worm gears are usually used (Figure 2.12). So what is a worm gear? Although worm gears are not related to the subject of vibration, let’s look at the way they work before continuing. is will show us how most engineering subjects are inter-related too. .. 38 2. NATURAL FREQUENCIES Figure 2.12: In a violin, tension is provided by a tuning peg, which is held by friction. In a guitar, since the forces are larger, tension is provided by a worm gear–based tuning key. Worm Gears: Worm gears are very common in devices for reducing speed and increasing torque, including in automobile steering mechanisms, jacks, wenches, and others. Like other pairs of gears, they provide reductions or increases in angular velocities and torques. But they also have other char- acteristics that make them useful in particular instances. Figure 2.13 shows a simple worm gear. Depending on whether the worm is a right-handed or left-handed worm (turning the worm in the direction of your curled ﬁngers of the right or left-hand will move the thread forward along the direction of your thumb; also see Chapter 3), the worm gear will rotate counter-clockwise (CCW) or clockwise (CW). .. 2.4. APPLICATIONS AND EXAMPLES 39 Figure 2.13: A simple worm gear. First a word about gear ratios. In all gear systems, the reduction or in- crease in angular speed or torque is proportional to the gear ratio (the ratio of the number of teeth on each gear, usually called the driver gear and the driven gear). erefore: ; N2 N1 !1 !2 D T2 T1 D where !1; T1; N1 and !2; T2; N2 are the angular velocity, torque, and number of teeth of each gear, as shown in Figure 2.14. Notice how these are related. e larger a gear, the slower it rotates, but the larger the torque. erefore, by selecting the appropriate number of teeth on a pair of gears we can increase or decrease the angular speed and torque. (2.10) So why is it that when a gear rotates faster, the torque on it is lower, and vice versa? Of course we can answer this question by calculating the moments on each gear and by drawing free body diagrams as well, but here we will consider the principle of work and energy. As we have already discussed, the total energy in a system is constant unless we add energy to it or remove energy from it. is is called conservation of work and energy. Assuming that the friction in the system is small enough to be negligible, the total work or energy into and out of the system of gears is constant. However, work is equal to force multiplied by linear displacement, or equal to a torque multiplied by angular displacement. erefore, the total input and output should be equal, or: .. W T1 !1 (cid:2) D D T2 (cid:2) !2; (2.11) WormWorm gear40 2. NATURAL FREQUENCIES where W is the work. is is the same result as Equation (2.10). Consequently, as the angular speed is reduced, the torque is increased, and vice versa. is is exactly what happens in an automobile gear box as well. In the ﬁrst gear, the output angular speed is reduced through higher gear ratios, creating larger out- put torques that can start a car moving. When the speed of the car increases, we shift into second and third, etc., increasing the speed, but lowering the output torque. Figure 2.14: A gear reduction system. Although worm gears look somewhat diﬀerent, they are kinematically the same. ey provide a large gear ratio for their size, but usually have more friction as well. However, depending on their helix angle, they can be self- locking, an important characteristic. So what is the helix angle? In fact, if you look closely, the worm looks like a screw. A screw is nothing more than a triangle, wrapped around a cylinder, as shown in Figure 2.15. e angle of the triangle at the tip is the helix angle. is determines how many threads are present in any given length (e.g., 20 threads per inch in a 1=4-20 screw). In reality, when a screw is rotated, the nut moves up or down on this (inclined) plane. A larger helix angle means that the nut moves faster, but it requires a larger force to move up. Imagine that the angle is large, creating a steep incline. What will happen to a box on a steep inclined plane if the force behind it is removed? As shown in Figure 2.16, in the absence of friction large enough to stop the motion, the box will slide down. With smaller helix angles the box tends to stay and not slide. If you translate this concept into a screw, and if the .. ωω2.4. APPLICATIONS AND EXAMPLES 41 helix angle is small, the nut will not move down on a screw when the load is removed, causing a self-locking mechanism. If the angle is steep, it is possible that as the force is removed, the nut may automatically move down, making it not self-locking. But which one is better? Imagine you use a jack to raise your car by applying a torque to the handle. One common design for automobile jacks is equivalent to a nut moving on a screw, raising or lowering the car. How would you like it if the car you just raised would comeback down as soon as you released the handle? Here we want to make sure the nut on the jack is self-locking. In other applications such as in a hand-press we want to make sure that as soon as the handle is released the press returns without external eﬀort by the operator. is will increase the eﬃciency of the system. Here, a not-self-locking screw is better. Consequently, based on our needs, we can design the screw to be self-locking or non-self-locking. For the guitar, we obviously want the tensioner to be self locking; other- wise, as soon as the tuning keys are released the tension will be lost. Although other ways exist to do this, worm gears are commonly used because they can easily be self-locking, even at large tensions. Figure 2.15: An inclined plane wrapped around a cylinder creates a screw. Figure 2.16: A box moving up an inclined plane. .. Helix angleHelix angle42 2. NATURAL FREQUENCIES 2.4.2 SPEAKING AND VOCAL CORDS Humans speak and produce sounds by expelling (or modulating) air from their lungs through vocal cords (also called vocal folds) situated in our larynxes. e air causes the cords (actually folds) to vibrate. As in a guitar or violin, the sound resonates within the larynx, sometimes with additional harmonics, creating an audible and unique voice. e shape of the cords, their thickness and size, and the shape of the larynx create each person’s unique voice as well as the diﬀerent frequencies of each sound. For example, the average fundamental frequency is about 210 Hz for women, about 125 Hz for men, and more than 300 Hz for children. By changing tension in the cords, humans can alter their frequency and produce diﬀerent sounds, pronounce diﬀerent letters, and sing. e production of sound is not the only characteristic that follows the engineering princi- ples we have already discussed. We can also see the eﬀect of similar variables in the system. For example, generally adult males’ voices are lower-pitched than those of women or children. As we might expect, the male vocal cords are longer, ranging between 1.75 and 2.5 cm (0.75 to 1 inch) versus 1.25 and 1.75 cm (0.5 to 0.75 inch) for women. We have already seen that longer strings (and cantilevered beams) have lower natural frequencies and produce lower-pitched sounds than shorter strings. As a child grows and his or her cords elongate, his or her voice changes too. Figure 2.17 shows typical vocal folds. Figure 2.17: e vocal cords and folds. 2.4.3 TUNING TO A RADIO OR TV CHANNEL e tuning of a radio or TV to diﬀerent channels or stations is in fact related to natural frequencies as well, although in this case it relates to the natural frequency of an electronic circuit’s output. ere are certain circuits that are speciﬁcally designed so that their output voltage oscillates, e.g., like a sine wave. Although most circuits are too complicated to discuss here, we can consider a 2.4. APPLICATIONS AND EXAMPLES 43 very simpliﬁed set up to study the fundamentals. is will teach us how a tuning system works. So ﬁrst let’s talk about this, then about tuning. Imagine a very simple electric circuit composed of a coil or inductor L and a capacitor C as in Figure 2.18. As was discussed in Chapter 1, since the coil is a conductor, when a current passes through it, a magnetic ﬁeld is developed. Conversely, when the coil is placed within a varying magnetic ﬁeld, a current is induced in it. ese are called electromotive force (emf ) and back-emf. e important thing to realize is that these can happen as a result of each other. Figure 2.18: An R-L-C circuit and its response. e voltage oscillates at the natural frequency rate of the circuit. A capacitor is another electronic element that can store electrical energy and discharge it back into the circuit when the voltage of the load is less than the voltage across the capacitor. eoretically, if there is absolutely no loss of energy in the circuit due to electrical resistance, when the circuit is initially energized, the ﬂow of the electrons in the circuit will cause the coil to generate a back-emf voltage which charges the capacitor. When the voltage in the coil becomes less than the capacitor, the capacitor discharges its energy back into the coil, causing the same back-emf. is repeats forever, creating an oscillating voltage. In real life, every electrical element has some resistance R, so every time the current goes through, part of the energy is converted to thermal energy, and consequently, the oscillation of the voltage in the circuit dies very quickly. However, just like a mechanical device, such as a grandfather clock where the energy loss is compensated by the energy stored in a weight or a spring, the energy stored in a battery or similar device can DCInductor CoilCapacitorResistorDC source− +44 2. NATURAL FREQUENCIES compensate for the lost energy in the circuit. erefore, we can expect that the R-L-C system may continue to oscillate indeﬁnitely as long as we have a source of external energy to compensate for the loss. In most systems a crystal is used for this purpose, but the principles stay the same. Figure 2.18 shows the schematic of an R-L-C circuit, a simple circuit consisting of a coil and a ﬁxed capacitor put together for testing, and the output of the system as seen on an oscilloscope when an impulse signal is applied to the circuit. Notice how quickly it dies out due to the electrical resistance in the wires. e frequency at which the voltage in the system oscillates is a function of the capacitance of the capacitor C (a measure of charge-storing capability of the capacitor) and the inductance of the coil L as: f D 1 2(cid:25) r 1 LC : (2.12) Changing the value of L or C will change the oscillating frequency of the circuit. is is exactly what is done in manually tuning an old-style radio by a knob. Turning the tuning knob moves a set of plates within a capacitor relative to the counterpart ﬁxed plates, changing how much energy is stored between the plates (Figure 2.19). Although the same can be accomplished by other means (such as the use of a quartz crystal), the basic idea is to create an oscillating voltage in a circuit. Figure 2.19: A schematic drawing of a variable capacitor. How is this related to tuning to a radio or TV station? To see this, imagine a pendulum oscillating at a particular rate, in front of which is a plane with a hole, also oscillating as in Fig- ure 2.20. An observer is looking through the hole trying to see the pendulum. If the rate of the movements of the pendulum and the plane are exactly the same and they start at the same time, the observer will continually see the pendulum through the hole. However, if the rates are not the same, even if they start exactly at the same time, the observer will actually not see the pendulum, except by chance when they happen to be at the same location at the same time. When the two Rotatable platesStationaryplateshave the same frequency of oscillation, we can say that they are tuned (synchronized) with each other, moving at the same rate. Stay tuned, as we are not there yet. Now we need to see how diﬀerent broadcasts are coded for distinction. 2.4. APPLICATIONS AND EXAMPLES 45 Figure 2.20: An observer behind a plane with a hole may or may not see the pendulum moving depending on whether or not the pendulum and the plane have the same frequency of motion. ere are hundreds of stations that broadcast radio and television programs. Without some unique feature to distinguish one signal (or station) from another, every receiver would capture the combined broadcasts from all the stations at once, obviously a completely useless system. is would happen if the information broadcast by any station (radio, TV, the Police, etc.) consisted of only the intended signal (for example the music) without a distinguishing signature to diﬀerentiate it from another. However, to create multiple stations with multiple channels of broadcast, each with a unique signature, the signal is modulated with a carrier signal before broadcast, either based on amplitude modulation (AM) or frequency modulation (FM). We will not get into too much detail about this, but let’s see what this means. Imagine that f .t / (some function of time, which in general can be anything, including music, video, or any other signal) is the signal that is to be broadcast. Figure 2.21 shows a sim- ple sinusoidal function f1.t/ D 0:5 0:5 cos.50t/ as shown Figure 2.22a (a cosine that oscillates between 0 and 1 instead). e frequency of this signal is 50 times as large as the sine function of Figure 2.21. Similarly, Fig- ure 2.22b shows a similar signal, but at a frequency of 100 instead of 50. Notice how the two signals look the same, but one is faster at a higher oscillation frequency. sin.t/ as an example. Now consider another function f2.t/ D C Modulating (combining, in this case multiplying) the two signals together will result in a signal that has the overall shape of the lower frequency signal f1.t/, but with the higher frequen- 46 2. NATURAL FREQUENCIES Figure 2.21: A simple sine function signal of f .t/ sin.t/. D (a) f .t/ 0:5 C D 0:5 cos.50t/ (b) f .t / 0:5 C D 0:5 cos.100t / Figure 2.22: A higher frequency carrier signal at the frequency of 50 and 100 cycles per second. cies of the second function f2.t/. Figure 2.23 shows the result of modulating these functions at diﬀerent frequencies of 50 and 100 as: F .t/ f1.t/ f2.t/ sin.t/ (cid:140)0:5 (cid:2) C D (cid:2) D 0:5 cos.50t/(cid:141) and F .t/ f1.t/ f2.t/ sin.t/ (cid:140)0:5 (cid:2) C D (cid:2) D 0:5 cos.100t/(cid:141) : What is interesting is that the same can be done at any other frequency, all resulting in the same overall shape of f1.t/, but at diﬀerent frequencies. 2.4. APPLICATIONS AND EXAMPLES 47 (a) F .t/ sin.t/ (cid:140)0:5 (cid:2) C D 0:5 cos.50t/(cid:141) (b) F .t/ sin.t/ (cid:140)0:5 (cid:2) C D 0:5 cos.100t/(cid:141) Figure 2.23: Modulated signals of a simple sine function and higher frequency cosine functions result in the same basic overall shape of the sine function, but at a higher frequency of the carrier signal. Figures 2.24 and 2.25 show another signal and its modulated signals at two diﬀerent fre- quencies. Similar to the previous case, the original shape of the signal is preserved but when modulated, the signal contains the higher frequencies of the carrier signals. Figure 2.26 shows two additional signals and their modulated versions for comparison. en how is this used as a unique signature for each broadcasting station? Imagine that each station is granted a particular frequency that it uses as its carrier frequency, used to modulate its particular signal. Whether music, dialogue, pictures and video, or any other data, the signal is modulated with the station’s signature frequency. erefore, the broadcast signal will have the basic information in it, but is broadcast with a carrier frequency unique to the station. Now look back at Figure 2.20. As with the pendulum and the plane with a hole, where they are either in tune or out of tune, your receiver (TV, radio, or other device) may be in tune with a particular signal frequency or out of tune with it. If it is in tune with a signal, it will “see” the signal continuously and will therefore receive it. Since it is out of tune with all other signals it will not “see” any of them. All it takes for your receiver to tune in is to have the same frequency as the carrier frequency of the signal (or station). In other words, if the receiver has a frequency similar to the carrier frequency of the broadcast signal, it will receive it; if not, it will not see the broadcast signal. is is done by an oscillating circuit such as in Figure 2.18 and Equation (2.12). A variable capacitor in an R-L-C or similar circuit changes the natural frequency of the receiver, matching it with the frequency of the carrier signal of the particular station in which one is interested. When the two are in tune, the receiver will receive only that signal. A low-pass ﬁlter eliminates the high carrier frequency (called de-modulation), ending up with the original signal that is ampliﬁed and played back as music, dialogue, video, etc. 48 2. NATURAL FREQUENCIES Figure 2.24: e signal f .t/ sin.t/ C D 1 3 sin.3t/. (a) (b) Figure 2.25: e result of modulating the signal of Figure 2.24 with a carrier signal at two diﬀerent frequencies as F .t/ 0:5 cos.100t/(cid:141). 0:5 cos.50t/(cid:141) and F .t/ sin.3t/(cid:141) sin.3t/(cid:141) (cid:140)sin.t/ (cid:140)sin.t/ (cid:140)0:5 (cid:140)0:5 C C D C C D (cid:2) (cid:2) Frequency modulation is somewhat more complicated. Instead of modulating the ampli- tude of the signal with the frequency of the carrier signal, the frequency of the carrier signal is changed based on the amplitude. As the amplitude of the signal changes, the amplitude of the carrier signal remains the same, but its frequency changes within a certain range. e rest is the same. We will not discuss the details of FM modulation here. 2.4. APPLICATIONS AND EXAMPLES 49 Figure 2.26: Two additional examples of signals f .t/ and their modulated signal F .t/ (cid:140)0:5 C signal. (cid:2) 0:5 cos.100t/(cid:141). Notice how the shapes of the signals are preserved at the frequency of the carrier f .t/ D Realistically, the modulating frequencies are very high, in the hundreds of thousands (kHz) for AM, and in the millions (MHz) for FM. Amplitude modulation is prone to noise, but has a better range, while FM is less prone to picking up noise, but does not travel very far. is is why most available out-of-town stations where cities are not close by are AM, not FM. 2.4.4 HEARING e hearing mechanism in humans (and most animals) is also related to natural frequencies. To see this relationship, let us ﬁrst examine the human ear and its parts, then we will discuss the mechanism of hearing. 50 2. NATURAL FREQUENCIES e human ear has three distinct parts: the outer ear, the middle ear, and the inner ear, as schematically shown in Figure 2.27. Each section has a diﬀerent function. Figure 2.27: Schematic drawing of the human auditory system. e outer ear has the following roles: 1. e pinna is a distinct feature of the human face, giving it a certain beauty and making the human face look as we have come to know and love. 2. It is sensitive to touch, temperature, and other stimuli. 3. It acts as a radiator to dispense of excess heat when needed. ere are a lot of blood vessels in this organ. When the body needs to dispense heat, blood ﬂow to the outer ear increases. is is why the ears turn red when the person is hot or nervous. 4. It collects sound. e sound we hear is the result of the reaction of our hearing mechanism to the vibration of molecules of air. e pinna increases the ability of the system to sense these vibrations. 5. It helps in determining the direction of the sound. Humans hear in stereo; this means they can sense the approximate location of the source of sound in space. is is because the distance from a source of sound to each ear is slightly diﬀerent. e very small diﬀerence in the time that it takes for the sound to reach each ear is detected by the brain, helping it Auditory canalTympanicmambraneHammerAnvilStirrupSemi-circularcanalsCochleaEustachiantubePinnaOuter earMiddle earInner ear2.4. APPLICATIONS AND EXAMPLES 51 to determine the location of the sound. However, we can also determine if the source is in front of or behind us, even with closed eyes, because of the unique shape of the outer ear. Since its shape relative to the front or rear is diﬀerent, it can detect whether the source is in the front or rear. Sound energy (a mechanical type of energy) travels through the ear canal (also called the auditory canal) to the tympanic membrane (ear drum). e tympanic membrane is a thin skin layer that is vibrated by sounds ranging in frequencies between about 20 Hz to about 20,000 Hz, an amazing range. is is why we can hear sounds within this approximate range. We cannot hear sounds with frequencies above this range (called ultrasound) or below it. Other animals can. Dogs, bats, and many other rodents can hear frequencies far above this range. Can you guess why? Primarily, it is the ability of their (smaller and therefore higher natural-frequency) tympanic membranes to oscillate at higher frequencies that enables them to hear those frequencies. is characteristic is used to drive rodents away from houses and farms without aﬀecting humans. Since humans do not hear ultrasonic vibrations, a device that is plugged into an electrical outlet or pushed into the ground creates loud ultrasonic sound bites annoying rodents and bats and ground squirrels and driving them away without humans even hearing it. If lower frequencies of ultrasound were used domestic animals might also hear the sound and be annoyed. e vibrations of the tympanic membrane are transferred to the middle ear. e middle ear consists of three bones (Ossicles) called the hammer, anvil, and stirrup. ese bones are held together by tiny muscles. ey bridge the tympanic membrane on one side and the cochlea of the inner ear on the other, creating a physical connection between the outer ear and the inner ear. Stirrup bone touches the cochlea at the oval window, where the vibrations of the stirrup are transferred to the liquid within the cochlea. A narrow tube called the Eustachian Tube connects the nasopharynx (throat cavity) to the middle ear. e middle ear has four distinct functions as well: 1. It helps in isolating the inner ear from the tympanic membrane. ere are many cases where the tympanic membrane may be damaged by external factors such as extreme sounds or intentional operations (e.g., when a doctor inserts a plug into the tympanic membrane to help young children with drainage of the middle ear when it is infected). If the inner ear were directly attached to the tympanic membrane, any physical damage to the tympanic membrane, whether intentional or accidental, would permanently damage the inner ear resulting in permanent hearing loss. But with this arrangement, where the middle ear acts as a safety device, damage to the outer ear will not result in a permanent loss of hearing. 2. e Eustachian tube helps with the equalization of air pressure between the outer and mid- dle ear. Without this equalization, not only would the middle ear ache terribly, as the out- side air pressure changes, the pressure diﬀerence between the outer and middle ear would prevent us from clearly hearing sounds. By swallowing, we force the Eustachian tube to open, therefore equalizing pressure in the middle ear. If an individual with a cold or ﬂu or 52 2. NATURAL FREQUENCIES allergies cannot equalize the air pressure due to inﬂammation of the Eustachian tube, he or she may have pain and may not hear well. Physicians may even suggest that the individual avoid ﬂying. 3. e speciﬁc arrangement of the three bones allows the middle ear to amplify sound vibra- tions. is ampliﬁcation helps in hearing lower threshold sounds. 4. e three bones of the middle ear transfer the vibrations to the inner ear. In the presence of very loud sounds, the vibration of these bones becomes very large too. As a safety device, and to prevent the inner ear from permanent damage, the tiny muscles connected to the hammer, anvil, and stirrup bones contract, reducing the amplitude of the vibrations, the severity of the sound, and hearing damage. If you have ever experienced a heavy feeling in your ears when exposed to loud noises (such as a loud concert or gunshot), it is because the middle ear muscles were contracted. is in itself is an indication of damage to the inner ear, even if not as severe as it might have been without this safety feature. Consequently, sound vibrations are transferred to the inner ear. e inner ear consists of the cochlea and the semicircular canals. We will discuss the func- tion of the semicircular canals shortly, but they are not part of the hearing mechanism. e cochlea is a spiral canal, about 2 5 8 turns, with a complicated structure whose individual functions are not yet fully understood. Within it are three passages, two of which are separated by a membrane called basilar membrane. Unlike the cochlea, the basilar membrane is thicker and narrower at the base of the cochlea near the oval window and thinner and wider at the apex (end). As the ﬂuid inside the cochlea is vibrated by the ossicles (hammer, anvil, and stirrup), the basilar membrane vibrates with it. However, since the input to the cochlea is only through the oval window as one signal only, the cochlea has to decompose and codify the sound into diﬀerent frequencies that can be recognized by the brain. is is the job of the basilar membrane. Since the width and the thickness of the basilar membrane varies throughout its length, each location on it has a particular natural frequency. As the sound vibrations go through the cochlea, one location on the basilar membrane vibrates in synch with the particular frequency of the sound. It is as if each location is tuned to vibrate at one frequency, higher frequencies at the base where the basilar membrane is thicker and narrower (resulting in a higher natural frequency) and lower frequencies toward the apex where the membrane is thinner and wider (resulting in lower natural frequencies). As a result, although only one set of vibrations enters the inner ear, the basilar membrane “decomposes” the sound into individual frequencies at each location. Along the membrane are rows of inner and outer hair cells (which are not really hair, but very thin cell-structures) that are extremely sensitive to motion. e outer hair cells (numbering about 12,000) help with tuning the basilar membrane for its decomposition task. e inner cells, numbering about 3,500 in a single row, detect the vibrations of the basilar membrane and send a signal to the brain through the auditory nerve, where the sound is heard and recognized (the 2.4. APPLICATIONS AND EXAMPLES 53 mechanism by which the brain interprets and understands the sound and the meaning of sounds is beyond the scope of this book). All sounds can be decomposed into a collection of simple sine and cosine sounds at par- ticular frequencies (called the Fourier Series). erefore, the collective vibrations of the individual hair-cells within the cochlea will enable us to hear and understand the sound about us. If a hair- cell does not send the proper signal, we will not hear the corresponding frequency. is is why people who lose their hearing ability will have a diﬃcult time understanding sounds even if it is ampliﬁed by a hearing aid; they do not hear the sounds correctly. As we age, we naturally lose our ability to hear higher frequency sounds. However, expo- sure to loud noises can also eventually damage hair-cells permanently, and consequently, hearing ability. 2.4.5 WALKING AND RUNNING, HEARTS AND LUNGS Have you noticed that your arms and legs are in fact very similar to pendulums? Granted, each arm or leg has two oscillating portions, the upper part and the lower part. is is called a double pendulum. One fortunate thing is that the motions of both arms and legs are relatively limited; they move less than 150(cid:14). Otherwise, their motions would be more complicated. Nonetheless, each arm or leg functions as a pendulum, and like pendulums, they have a natural frequency. Equation (2.6) for Figure 2.5 is the natural frequency of a pendulum like in a grandfather’s clock, with the mass concentrated at one point. e arms and the legs are more like bars with distributed mass. e natural frequency of a bar can be expressed as: f D 1 2(cid:25) r mgr Io ; (2.13) where I0 is the second mass-moment of inertia (see Chapter 5), m is the mass of the bar, g is the acceleration of gravity, and r is the distance from the pivot point to the center of mass of the bar. Both the length of the arm or leg (as in r) and the mass are important factors, as is the mass- moment of inertia which is a measure of the distribution of mass. ere are relatively simple ways of measuring the mass of the arm or leg and calculating its mass moment of inertia even for living humans. erefore, we should be able to calculate what we need. However, what is of interest to us is not the calculation, but understanding natural frequency and its role in our everyday life. A person may be able to walk for hours without getting tired. But if he or she is walking briskly or carrying a weight in his or her hands while walking, even if it is only a couple of pounds, it becomes much harder to walk more than a short time before the person feels tired. Why? When walking, we tend to move our legs and arms in about their natural frequency rates. Our arms move in the opposite direction of our legs in order to help us with balance as we move forward. At these rates, it takes little energy to move the legs and arms, so a person can do it for a long time without tiring much. However, moving at a brisk rate will change this situation; now you are forcing arms and legs to move at rates diﬀerent from their natural frequencies. erefore, much more energy 54 2. NATURAL FREQUENCIES Figure 2.28: e Tacoma Narrows Bridge (Prelinger Archives). is needed to do this. If you are trying to exercise or burn calories, this is the right thing to do. If you want to walk longer, perhaps to have a nice walk along the beach, then brisk walking is not the right thing. Similarly, if you carry a small weight in your hand as you walk, it is not the weight that causes you to burn calories or get tired; it is how the weight adds to the moment of inertia and how the natural frequency of your arm changes. erefore, even if you move at a normal rate, you still burn additional calories because at your normal rate of walking, you are no longer moving your arms at the previous natural frequency rate. Have you noticed how physical activity experts prescribe exactly the same things—to walk briskly or to carry a light weight in your hands—as you walk? is is why. It is actually very similar for the lungs and the heart. We breathe at the natural frequency of our lungs; therefore little energy is needed to do so. But now try to breathe at a diﬀerent rate, and you get tired quickly. e same is true with a heart if it beats at a rate above the natural frequency rate. By the way, dogs pant at a high rate compared to, for example, humans. Can you tell why? An adult human heart beats at about 70 times per minute. However, for infants, it is about 120 and for young kids, it is about 90 beats per minute. Why? Since the mass of an infant’s heart is smaller, its natural frequency is larger (as we have seen with other systems). As the heart grows, the rate decreases. By the way, in a 65-year lifetime, the heart beats at least 70 2:4 109 times. is is 2.4 billion times. Not too bad. 365 60 65 24 D (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) Example 2.4 Tacoma Narrows Bridge In 1940, the brand new Tacoma Narrows Bridge in Puget Sound, Washington, collapsed due to a phenomenon called wind-induced ﬂutter. e fundamental reason for the violent move- ments was that the girders (deep I-beams used in the construction) moved as a reaction to the high winds in the narrows because the sides of the bridge were closed and the wind could not freely move through them. Since the frequency of the variations in the wind happened to be close to the natural frequency of the bridge, the motions became larger and the bridge swayed more until it collapsed. Fortunately, since this had happened from the time of construction (but never to this extent), the bridge was closed and there was no traﬃc on it. A new bridge was dedicated in 1950. at bridge still stands. 2.5. BIBLIOGRAPHY 55 2.5 BIBLIOGRAPHY [1] Dimarogonas, Andrew: Vibration for Engineers, 2nd ed., Prentice-Hall, NJ, 1996. 34 C H A P T E R 3 57 Coriolis Acceleration and its Eﬀects Bikes, Weather Systems, Airplanes, and Robots 3.1 INTRODUCTION Oregon, Washington, and California on the West Coast of the U.S. are next to an ocean as are their East Coast counterparts, including New York, Florida, the Carolinas and New England states. However, their weather patterns are signiﬁcantly diﬀerent. For example, except for the high altitudes of the mountainous areas of California, the rest of the state does not get any snow in the winter and is relatively dry in the summer, but New York gets a lot of snow in the winter and is very humid and warm in the summer. For example, during the month of February in 2015, the eastern half of the U.S. experienced record low temperatures and record amounts of snow, even as far south as Florida, which plunged to low 20-degrees F. At the same time, the western states had a record dry season and high temperatures. e cities in the east were in single-digit temperatures even without the eﬀects of wind-chill while California was enjoying temperatures in the 70s and 80s F. Looking at weather maps, you could clearly see how the so called Siberian Express air mass, moving over the North Pole and traveling south over the North America veered eastward inun- dating the eastern part of the U.S. Why? Weather patterns are aﬀected, among other things, by altitude, latitude, longitude, and proximity to large bodies of water, but also by a phenomenon called Coriolis Acceleration that pushes the air-mass, the jet-stream, and the prevailing winds to- ward east. In this chapter, we will learn about Coriolis acceleration and also discuss gyroscopic eﬀects and accelerations caused by rotating frames that explain why a bicycle does not fall when riding, why you will fall if you turn the handle of a bicycle or a scooter rather than leaning right or left, and why an airplane may rotate unexpectedly when in ﬂight. To learn about these concepts and understand the basics, we will need to ﬁrst make a few deﬁnitions and go over some introductory issues. After that, we will return to learn how Coriolis acceleration aﬀects our everyday lives. But along the way, we will learn a lot about mechanics and how these concepts are part of our lives too. 58 3. CORIOLIS ACCELERATION AND ITS EFFECTS 3.2 DEFINITIONS Since Coriolis acceleration, like all other accelerations, is a vector, let’s start by deﬁning vectors. 3.2.1 VECTORS A vector is a mathematical expression possessing a magnitude, a direction (also called line of action), and a sense. Values that are not vectors are scalars. For example, a quantity such as $10 is a scalar. It has no direction; it is only a magnitude. Bags of fruit are also scalars. Time is a scalar too; it has no direction. So is the speed of travel. It only indicates how fast one moves. However, velocity is a vector. Not only does it specify a magnitude (the speed) of travel, it also indicates the direction (and sense) of travel. For example, the line of action of the velocity vector may be 30(cid:14) up from horizontal. erefore, we know in what direction the object is moving. However, this does not yet specify the sense of travel, whether it is moving away from us or getting closer to us. erefore, we also specify the sense at which the vector acts through an P with its length representing the magnitude, its direction arrowhead. Figure 3.1 shows a vector E (30(cid:14) up from horizontal), and its sense (going to the right). With the same magnitude and line of action, if the sense is reversed, the object moves in the opposite direction and the location of the object will be completely diﬀerent as time goes by. Figure 3.1: A vector with its magnitude, direction, and sense. Force, acceleration, and distance travelled are also vectors. For example, indicating that a car moved 10 ft does not indicate in what direction it moved. To completely specify the motion, it is necessary to also specify the direction and the sense of the motion. Force is a vector too because if you pull an object it gets closer to you, and if you push the object it gets away from you. So force P is speciﬁed has a direction and a sense, and consequently, it is a vector. Notice how a vector E with an arrow above it. ere are also other common notations used for indicating vectors such as bold letters (P) or (P ). 3 apples Unlike scalars that can be simply added, subtracted, or multiplied, vector addition, subtrac- tion, and multiplication require more and may yield very diﬀerent results. For example, 5 apples 8 apples, but a 5-lb force plus a 3-lb force may or may not be equal to 8 lbs de- C pending on the directions and senses of the two forces. Figure 3.2a shows how a parallelogram is used to add vectors. As shown, the summation of the two vectors (also called the resultant) is equal to the diagonal of the parallelogram that is formed by the two vectors. e resultants of the D θV1 and E V2 are diﬀerent when the directions and senses of the vectors change. same two vectors E As you can see in Figure 3.2b, adding two vectors with equal magnitudes acting on the same line of action will result in a vector twice as large if they have the same sense, but zero magnitude if they have opposite senses because they will cancel each other. 3.2. DEFINITIONS 59 (a) (b) Figure 3.2: Vector additions. Vectors are fundamentally important in engineering. Many subjects of study use vector notations and vector analysis for proper results. Examples abound, from the forces acting on the wings of an airplane in ﬂight to the forces acting on buildings, and from hydrodynamics to space ﬂight, motors, and robotics. For example, the force generated by a jet engine is the same as the resultant of the drag forces and lift forces that keep an airplane aﬂoat. e forces shown in Figure 3.2a are exactly applicable to the way a ship is pulled by tugboats. e forces of the tugboats will pull the ship in the direction of the resultant force. 3.2.2 VECTOR MULTIPLICATION Vectors can be multiplied, but not like scalars. For example, for scalars, 3 12. But for vec- tors, the result of multiplication is not the same. ere are two types of vector multiplication called Dot Product . R/. e result of a dot product is a scalar, a simple number. But the result of a cross product is another vector (note the diﬀerence in notations). At least for our discussion here, we need to learn about cross products. R/ and Cross Product . V2 (cid:2) E V2 (cid:1) E D E V1 E V1 E D D (cid:2) 4 60 3. CORIOLIS ACCELERATION AND ITS EFFECTS V1 and E V1 R D E E V2: e cross product of two vectors E V2 is another vector (read it as V1 cross V2): (3.1) (cid:2) E R is perpendicular to the plane formed by the two vectors E V2, and e direction of vector E its sense follows the right-hand-rule. e right-hand-rule means that if you curl the ﬁngers of V2, your thumb will indicate the sense. e your right hand in the direction of going from E right-hand-rule convention (and this is a convention only) is a very common and useful indicator, used in many diﬀerent situations. Figure 3.3 shows the result of the cross product of two sample vectors. Notice the direction and the sense of the resultant vector. Also note that this is a three- dimensional or spatial ﬁgure, not planar, so you must use your imagination in seeing the vectors in three-dimensional space. Cross products will be used to explain many of the concepts related to accelerations, including Coriolis. V1 and E V1 to E Figure 3.3: e cross product of two vectors. For math-oriented minds, the magnitude of the dot product for simple cases is: and the magnitude of the vector representing a cross product in simple cases is: R D V1V2 cos (cid:18); R D V1V2 sin (cid:18); (3.2) (3.3) where V1 and V2 are the magnitudes of the two vectors and (cid:18) is the angle between them. One important result we can derive from Equation (3.3) is that since sin (cid:18) 0, when two vectors are parallel (and therefore the angle between them is 0), their cross product will be 0. Similarly, when two vectors are perpendicular to each other, their dot product is zero. 0 when (cid:18) D D ×3.2. DEFINITIONS 61 In practice, both dot and cross products are important and very useful. For example, imagine F for a distance Ed as in Figure 3.4. As mentioned earlier, both force that you push a box with force E and distance (we usually refer to distance as displacement) are vectors; they have a magnitude, but also a direction and a sense. e energy required to move the object is called work. Work, like energy, is a scalar; it has a magnitude but no direction. Obviously, the larger the force or distance, the more energy is required to move the object. To calculate the work needed to move F and Ed , which yields a scalar, as the object, we can take the dot product of the two vectors E expected. erefore: W D Ed F (cid:1) E D dF cos (cid:18): Figure 3.4: e work or energy needed to move an object is the dot product of the force and the displacement. As mentioned earlier, when two vectors are perpendicular to each other, their dot product is zero. e weight of the box of Figure 3.4 is a vector that is directed downward (due to gravity). F , the weight does not do any work because it is As the box is pushed to the right by force E perpendicular to the displacement; it only does work when the box moves in the same direction, downward (we refer to this as a change in potential energy). Now imagine that you are tightening a bolt using a wrench as in Figure 3.5. Obviously, if you exert a larger force or if you use a longer wrench, increasing the distance of the force to F and Ed is another vector the bolt, the bolt tightens more. e cross product of these two vectors E called moment or torque. is torque is what tightens the bolt, and is perpendicular to both vectors, and its magnitude is: T (cid:12) (cid:12) (cid:12) D Ed (cid:12) (cid:12) (cid:12) E F (cid:2) E D dF sin (cid:18): So, although in both cases, the vectors involved are E together can be drastically diﬀerent. F and Ed , the result of multiplying them Can you ﬁgure out the direction of the torque vector? For Figure 3.5, it is into the page (as if an arrow is shot into the page). Notice how your thumb, with the curled ﬁngers of your F , points into the page. Most common bolts have right-hand threads right hand going from Ed to E Frdr62 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.5: e torque caused by a force E F applied at a distance Ed . (when you rotate the bolt or a nut in the direction of your curled right-hand ﬁngers, the bolt or the nut moves forward in the direction of your thumb). erefore, this torque moves the bolt forward, thus tightening it. A left-hand threaded bolt will move backward. Consequently, turning it in the same direction will loosen the bolt. 3.2.3 ROTATIONS Now let’s see how a rotational motion is deﬁned. If you imagine a plate rotating, the direction of the rotation can be speciﬁed as clockwise (CW) or counterclockwise (CCW), depending on which side you look at (see Figure 3.6). If you are not familiar with these terms, it is probably because you have always had a digital clock. Nonetheless, we can also specify the rotational motion of the plate as a vector perpendicular to the motion. e vector is conventionally assumed to be directed in the direction of your thumb if your right-hand ﬁngers curl in the direction of rotation (right-hand-rule). erefore, looking straight at a clock and curling your ﬁngers in the direction of rotation (CW) will point your right thumb in the direction toward the clock. e opposite rotation (CCW) will point your right thumb outward away from the clock. Looking at a bicycle too, when the tires rotate, the rotation of each one can be described by a vector as shown in Figure 3.7. is vector (and its direction) is very important in understanding why we can ride a bicycle without falling. Similarly, the rotations of the propellers of an airplane or the turbine of a jet engine can be characterized by vectors in the same fashion. 3.2.4 ACCELERATION Acceleration is the change in either the magnitude of velocity, its direction, or both. For example, if you are currently going at a rate of 50 mph traveling south on a straight road, but your speed increases to 60 mph, you have a positive acceleration in the same direction as your travel, as FrdrFrdr3.2. DEFINITIONS 63 Figure 3.6: Rotation of a plate in clockwise or counterclockwise directions. Figure 3.7: A bicycle’s tire rotations can be speciﬁed by a vector. indicated by the fact that your body is pushed back in the opposite direction of the acceleration. Similarly, if you continue to travel at 50 mph but follow a turn in the road and change your direction, you experience an acceleration as indicated by the fact that your body moves in the opposite direction of the change (we will discuss the reaction of the body to acceleration later). If your speed decreases from 50 mph to 40 mph, it creates an acceleration in the opposite direction of your travel, slowing you down. Strictly speaking, this is not a negative acceleration, but is called deceleration. And in fact, there is a diﬀerence between negative acceleration and deceleration. Deceleration means you are slowing down. Negative acceleration means that the acceleration vector is in the negative direction relative to a reference frame (or positive axis). In other words, if the positive direction of an axis is to the right, and if the direction of the acceleration is in the negative direction (to the left), then this vector is negative. It may still be an acceleration (increasing the velocity to the left) or a deceleration (slowing down while still going 64 3. CORIOLIS ACCELERATION AND ITS EFFECTS to the left). Deceleration is in the opposite direction of your velocity or direction of motion, and therefore, it slows you down. Consequently, if your motion is in the negative direction and you decelerate (slow down), your acceleration is in the opposite direction of motion (which is the positive direction) and therefore, a positive acceleration. You should always look into the direction of the acceleration vector in relation to a reference frame to decide if it is positive or negative acceleration, as compared to whether your speed is increasing or decreasing to decide if it is an acceleration or deceleration. ere are many diﬀerent types of acceleration. For example, consider a point on a rotating plane as shown in Figure 3.8. At the instant shown, the point P travels exactly to the left, and therefore, its velocity is also pointed to the left. However, from experience we know that a little later it will end up at point P 0, traveling down, with its velocity pointed down. Obviously, the direction of the velocity between these two points changes, even if the magnitude remains the same. erefore, in addition to possibly changing in magnitude, the direction of the velocity vector has changed. is must have been caused by an acceleration too. is is called centripetal acceleration and is a function of the square of the angular velocity of the plate !2. As we will discuss shortly, Coriolis acceleration is another type of acceleration, and together with all other accelerations that may exist, constitutes the total acceleration of the object of interest. Figure 3.8: e rotation of a plate and how the direction of the velocity of any point on it changes as it rotates, causing centripetal acceleration. 3.2.5 REFERENCE FRAMES Reference frames are used to describe the position, orientation, and motions of objects in a plane or in space as depicted in Figure 3.9. In two dimensions (on a plane), we usually use two axes, x and y. In three dimensions (space) we use three axes x, y, and z. For example, when in a plane, point P is at a distance of a from the x-axis and b from the y-axis. In three-dimensions (space) a point Q is expressed by three values of a distance a from the x-axis and b from the y-axis for the projection of Q on the x-y plane, and c from the x-y plane. Similarly, we can deﬁne the orientation of an object relative to these axes. Motions can also be deﬁned relative to these axes within the reference frame. e axes of frames are always mutually perpendicular to each PPVrVr''other, and they follow the same right-hand-rule we saw earlier. erefore, the z-axis will be in the direction of your thumb if you curl your ﬁngers in the direction of going from the x-axis to the y-axis, or x E y (cid:2) E z. D E 3.2. DEFINITIONS 65 Figure 3.9: Two- and three-dimensional reference frames. We can also consider an extension to this, which helps us with the next sections as well. e two reference frames shown in Figure 3.9 are stationary; they are ﬁxed and do not move, and therefore we refer to other things relative to them. However, it is possible to also have additional frames that move relative to the ﬁxed reference frame. We call them moving frames. For example, z0 to a bike at the hub of the front tire as shown in y0 (cid:0) imagine that we attach a frame x0 (cid:0) z will Figure 3.10. As the bike moves, the location of the frame relative to the ﬁxed frame x change. However, unlike the location of the rider relative to x0 (cid:0) z0 which does not change, y0 (cid:0) z0 does the position of any point P on the tire (for example, the valve stem) relative to x0 (cid:0) change. is distinction will play an important role in the next section. (cid:0) (cid:0) y0 (cid:0) y 3.2.6 ROTATING FRAMES Figure 3.11 shows a wheel that is rotating about a shaft. As we discussed in Section 3.2.3, the rotation of the wheel can be described by a vector perpendicular to it. In this ﬁgure, a ﬁxed ref- erence frame x z is attached to the center of the wheel (the z-axis is perpendicular to the (cid:0) plane of the wheel, indicating its direction of rotation) while x0 (cid:0) z0 is a frame attached to z0 frame does not stay at one location when the the wheel at point P . If you notice, the x0 (cid:0) wheel rotates; the frame rotates with the wheel. is is called a rotating frame. y0 (cid:0) y0 (cid:0) (cid:0) y Looking at the same wheel from above, we will see both the ﬁxed frame and the rotating frame. When the wheel rotates, the rotating frame moves to new locations and its position and orientation (the directions of its axes) change. Figure 3.12 shows the wheel from above. You can z0 also see how the same applies to a rotating bar. When the bar rotates, the frame x0 (cid:0) attached to it rotates with the bar. y0 (cid:0) We can attach a ﬁxed frame x In fact, the same applies to the rotation of planet Earth and everything that moves with it. y0 elsewhere y to the center of the Earth as well as frames x0 (cid:0) (cid:0) yzxycbaQabxPxyz66 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.10: A moving frame and its motion relative to a ﬁxed frame. Figure 3.11: A rotating frame. (Figure 3.13). As the Earth rotates, the frames attached to it also rotate. is rotation is very slow, one revolution every 24 hours. However, since the average radius of the Earth is 3,960 miles (6,370 km), the speed of a point on the equator is 2(cid:25).3960/=24 or over 1,000 miles per hour (2(cid:25).6370/=24 or over 1,600 km/hr). erefore, although the frame rotates slowly, its position changes vastly. Nonetheless, the frame is rotating and this does matter when we talk about the weather. y1 Let’s take this one step further as it will shortly help us with our analysis. Suppose that z. a frame x1 Now also assume that a second rotating bar is attached to the ﬁrst bar, and a frame x2 z2 is attached to this bar, as shown in Figure 3.14a. When both bars rotate relative to each other, not only do these frames rotate relative to the ﬁxed frame, the second frame rotates relative to z1 is attached to a rotating bar, rotating relative to a ﬁxed frame x y (cid:0) y2 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) Pxyx'y'z'zx'y'z'Pxyz3.2. DEFINITIONS 67 Figure 3.12: Rotating frames attached to a wheel or a bar. As the wheel or the bar rotate, the position and orientation of the rotating frame changes. Figure 3.13: e Earth and a frame attached to it. e frame rotates with the rotation of the Earth. (cid:0) y1 the ﬁrst one. e way we look at this in mechanics is to assume that you are located on the ﬁrst bar (let’s say there is a chair attached to this bar and you are sitting on it). en you may not feel that frame x1 z1 attached to your chair is rotating, but you will see that the second frame x2 z2 is rotating relative to you. erefore, there is motion between these frames relative y2 to each other. In fact, this is what happens to us on Earth. Since we are attached to the Earth, we do not necessarily feel that we are rotating, but we see other objects (frames) move relative to us. However, an observer outside of planet Earth (e.g., in a spaceship or a satellite) will see us rotating and other objects moving relative to us. e same is true if you are sitting in an airplane (cid:0) (cid:0) (cid:0) xyx'y'x'y'x'y'x'y'xyx'y'xyzx'y'z'x'y'z'68 3. CORIOLIS ACCELERATION AND ITS EFFECTS and someone walks in the aisle. Regardless of whether or not you feel the motion of the airplane (which is moving very fast), you see the person is getting closer to you. However, you both move relative to an outside frame (or object). Please note that although in Figure 3.14 both arms move in the same plane, generally they may move in three-dimensional motion. Figure 3.14b shows a robot with its linkages moving relative to each other in three dimensions. (a) (b) Figure 3.14: Motions of moving frames relative to a ﬁxed frame and relative to each other. Neither motions nor frames representing them have to necessarily be rotational. A move- ment void of any rotation is called a translation. For example, Figure 3.15 shows two simple examples where in (a), a slider simply slides (translates) on a bar while a second bar, attached to it, rotates. In case (b) the bar rotates while a slider slides over the bar. In contrast with the two-bar system of Figure 3.14 where two bars rotate relative to each other, in this case a slider translates while the bar rotates. Once again, this will be an important issue when we talk about Coriolis acceleration and the weather. In Figure 3.15 frames are attached to the bars and sliders. In case (a), frame x1 z1 (the z-axis is perpendicular to the page, but not shown) is attached to the slider and translates with it while x2 z1 is z2, attached to the slider, rotates attached to the bar and rotates with it while frame x2 with the bar but also slides (translates) with the slider relative to x1 z2, attached to the bar, rotates relative to it. In case (b), frame x1 z1. y1 y1 y1 y2 y2 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) Although these two cases seem similar to each other, they are in fact very diﬀerent. In z1 rotates. z1 only translates, while in (b), frame x1 case (a), the ﬁrst frame x1 y1 y1 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) xy1x1y2x2y3.3. CORIOLIS ACCELERATION 69 (a) (b) Figure 3.15: Combined rotations and translation with a bar and a slider. Although these two systems have similar components, the motions are very diﬀerent. It is therefore a rotating frame. Consequently, frame x2 z2 also rotates with it. So, it is important to note that when a frame is rotating, and within it there are other motions (either translations or rotations), the rotation of the ﬁrst frame will rotate the subsequent frames. is change in the direction of the velocity of the subsequent frames creates an acceleration component called Coriolis acceleration that does not exist when the frame does not rotate. Now that we have endured a long set of introductions, we are ready to look at this acceleration and see what it does. y2 (cid:0) (cid:0) 3.3 CORIOLIS ACCELERATION Coriolis acceleration is one of the components of the total acceleration of a particle or a rigid body. e total acceleration is the vector addition of all the changes in the magnitude and the direction of the velocity of the object, each caused by something diﬀerent. However, the Coriolis acceleration is present when there is a velocity within a rotating frame. erefore, the ﬁrst requirement is that there must be a rotating frame, within which there is another motion. ese two requirements must be present for the Coriolis to exist, and it is the result of the changes in the direction of the velocity of the second motion caused by the rotating frame. Otherwise, if the frame is not rotating, or if there is no motion present on the rotating frame (therefore no velocity), there will not be a Coriolis acceleration present. Looking once again at Figure 3.15a, notice that the ﬁrst frame is not rotating, and conse- quently, even though the bar is moving relative to it, there is no Coriolis acceleration, whereas in xy1x1y2x2yrωxy1y1x2x2yurω70 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.15b since there is a rotating frame upon which there is a velocity acceleration. u, there will be Coriolis E Coriolis acceleration, like all other components of acceleration of a body, is a vector with magnitude and direction. For mathematically oriented minds, the magnitude of the Coriolis ac- celeration is: 2 D ac E (3.4) ! E ac is the Coriolis acceleration component, E u; (cid:2) E ! is the angular velocity vector of the rotating where E u is the linear velocity of the frame that moves relative to it. As you may remember, frame, and E ! is the representation of the rotation of an object, and it follows the right-hand-rule; if you curl E the ﬁngers of your right hand in the direction of rotation, your thumb will show the direction u is the vector showing the direction of the of the vector representing the rotation. Similarly, E linear (translational) motion of the slider. As we discussed in Section 3.2.1, the cross product is another vector whose direction also follows the right-hand-rule. erefore, if the ﬁngers of your u, your thumb will be in right hand are curled in the direction of going from vector E the direction of the Coriolis acceleration. ese vectors, shown in Figure 3.15b, are drawn again in Figure 3.16 with the corresponding directions of Coriolis acceleration when the direction of ! changes. Notice how the direction of Coriolis acceleration changes with a change in the vector E u changes. We will shortly see how this direction of E is an important factor in weather systems. !. e same will happen if the direction of E ! to vector E Figure 3.16: e direction of Coriolis acceleration. 3.4 INERTIAL REACTION TO ACCELERATION Imagine you are sitting in a car and the driver presses on the gas. What happens to your body as the car accelerates? You probably have noticed that as the car accelerates forward, your body is 3.4. INERTIAL REACTION TO ACCELERATION 71 pushed back against the seat. Similarly, if the driver brakes, creating a deceleration (or a negative acceleration, pointing in the opposite direction), your body will be thrown forward. is is why when a car is in a head-on collision the passengers are thrown forward, and if not restrained by either a seat belt or airbag, they can collide with the windshield and be severely injured. Why is it like this? Because as we will see in Chapter 5, the inertia of a body (its mass) tends to resist changes in movement; it does not want to go faster or to slow down. If it is not moving, it tends to stay that way. If it is moving at a particular speed, it tends to continue at that speed. e only reason it might be forced to move or change its speed is if a force or torque is applied to it. In that case, the body reacts to the acceleration in the opposite direction of the acceleration. If it is pushed forward, it tends to want to move backward. If is it pushed backward, it tends to want to go forward, resisting change in its motion. In mechanics, we do not really write our equations like this; instead, we draw what is called a free-body diagram and a mass-acceleration (or inertial-reaction) diagram, and set them equal to each other in order to solve the problem. But this is beyond the scope of this book. We will just look at the reaction of the mass or inertia, which is to resist motion, always trying to move in the opposite direction of an acceleration. We can also see the same phenomenon when a mass, attached to a string, is rotated. In rotational motions, the so-called centripetal acceleration is always pointed toward the center of rotation. erefore, the mass always tends to move away from the center (this is referred to as centrifugal force). If it were not for the string applying a force to it, the mass would ﬂy away from the center. erefore, the mass continues in a circle as long as the string applies a force to it. You may realize that this is also the same as what happens to fabrics in a washing machine during the spin cycle: water particles, free to move without much restraint, tend to move away from the center of rotation while the fabric is spun fast, separating from the fabric outwardly. e same is also true in other centrifugal devices that separate solid particles from a mixture, including blood samples and Uranium concentrators used for enrichment. In fact, this can also be applied to societies. Since each society (a family, community, city, country) has a “mass,” it usually resists change unless something forces it, and even at that, the society reacts to it due to its inertia. Some societies have larger inertia (regardless of their size), some smaller inertia. e larger the inertia of a society is, the larger the resistance to change. More traditional societies have larger inertia; they do not like to change their traditions as much because of the value they see in it. In many cases, in order for a society to accept changes some large force (inﬂuence) is needed. ese may be economic forces (such as periods of growth or depression), natural disasters, wars, great leaders, dictatorships, or huge social eﬀects. Similarly, small changes in society can be accomplished with more ease because reaction to change will be smaller. In some instances, when a great change is forced on a society it may result in disastrous reactions, break-downs of the fabric of society, or revolutions. We will see the same phenomenon as we discuss weather systems shortly. 72 3. CORIOLIS ACCELERATION AND ITS EFFECTS 3.5 AIR AND WATER CIRCULATIONS (CONVECTIONS) DUE TO HEAT Before we embark on learning about the relationship between Coriolis acceleration and the mo- tions of air masses, it is necessary to also understand one other phenomenon: the circulation of air and water due to heat injection (have you noticed how many diﬀerent issues are at work for this phenomenon?). Imagine a pot of water on a stove. As the pot heats up, the water warms up as well. But the hottest point on the pot is where it is the closest to the source of heat. At that location, the water adjacent to the hottest point receives maximum heat. As the molecules of water warm up, due to the increased kinetic energy, the distance between molecules of water increases, increasing the volume and decreasing the density of water (making it lighter) adjacent to the hottest point. e lighter water now rises up toward the surface (as for example, a piece of wood might do when placed in water—since its density is lower than water, it ﬂoats up). However, rising water cannot leave a vacuum behind; something else has to replace it. Consequently, colder water from the surrounding area will rush in to replace it. As shown in Figure 3.17, water rises near the heat source and colder water rushes in to replace it, creating a double (actually donut-shaped) circulation all around. Figure 3.17: Circulation of water in a pot. e same is true with air; as warmer but lighter air rises, colder air from elsewhere rushes in to replace it. Otherwise, we end up with vacuum (and the possibility that people in a warm place may not have enough air to breathe). is is the root cause of wind, and why in general, wind is cooler. is is also why beaches are generally windy. When the earth warms up due to sunshine, air rises. e cooler air from the ocean blows in to replace it. If you stand next to an open ﬂame like a BBQ pit, the warm air rises and colder air replaces it, and consequently, although you may 3.5. AIR AND WATER CIRCULATIONS (CONVECTIONS) DUE TO HEAT 73 feel warmer on your frontside where the radiation heat from the ﬁre warms you, you may feel relatively colder on your back due to the wind. Sometimes ﬁreﬁghters try to control ﬁre by ﬁre. is means that to combat an advancing brush ﬁre, they start a new ﬁre at a safe distance in advance of the burning ﬁre. e air above the original ﬁre, being hot, rises, pulling the air from around for replacement. is will cause the new ﬁre, set by the ﬁreﬁghters, to move in the direction of the old ﬁre until they merge. Since the brush is already burned by the new ﬁre, the original one runs out of fuel and dies out. is is possible only because of the direction of the wind. .. e faster the air moves, the lower its pressure (this is why airplanes can ﬂy, as we will see later). erefore, the warmer air that rises will create a lower pressure region. e region with colder air that is not moving has higher pressure (which in meteorology is considered stable air). e air from the higher pressure region ﬂows toward the lower pressure region, creating wind. Most materials expand as they are heated. is is due to the increase in the ki- netic energy of their molecules, resulting in increased distance between them. erefore, the density of these materials decreases as they are heated. How- ever, there are certain materials that do not abide by this rule. For example, Bismuth, a naturally occurring element with atomic number 83, gets smaller when heated, and therefore, more dense. Water is the same. Water expands when heated and contracts when cooled until about 4(cid:14)C. At this temperature, it is at its smallest volume, and therefore, its densest. As it is cooled further and freezes, it actually expands. is expansion has many important consequences: 1. Due to this expansion when water freezes, the volume increases. is means that as water freezes it requires more space. If there is no room for this expansion, the resulting forces can be very large. For example, a bottle which is relatively full of water and is capped well may explode if left in a freezer. Similarly, exposed piping in cold environments can burst when water freezes. 2. Since water expands when frozen, it becomes lighter. Consequently, when making ice cubes, you may notice that the center of the ice cube rises as it freezes and becomes lighter and lighter. .. 74 3. CORIOLIS ACCELERATION AND ITS EFFECTS 3. Water is densest at 4(cid:14)C. is means that the water in large bodies of water like pools or lakes is densest just near freezing, but not yet frozen. Because it is the densest, the water at this temperature sinks to the bot- tom. is keeps the ﬁsh and other living creatures safe. Otherwise, if ice were denser, it would sink down to the bottom, freezing and killing all its ﬁsh and other living organisms. Is it not nice that Nature thinks of these things? .. e same happens with air surrounding the Earth at the macro level. As the air warms under the inﬂuence of the sun, it rises, pulling in colder air to replace it. However, wind patterns change as the Earth rotates around the sun, inﬂuenced by its tilt. Earth has a tilt of approximately 23:45(cid:14) relative to its elliptical path (see Figure 3.18). Due to this tilt, the total amount of sunshine received at each location changes during the year, causing the seasons. e Equator divides the Earth into two equal halves. e Tropic of Cancer is 23:45(cid:14) above the Equator, and the Tropic of Capricorn is 23:45(cid:14) below it. It is on these two tropics that the sun’s energy is the greatest in the summer for the Northern Hemisphere and winter (their summer, even though it is January and February) in the Southern Hemisphere because each is perpendicular to the radiated energy from the sun. Many of the deserts of the world are also located on these two tropics. For this reason, wind directions change in diﬀerent seasons, aﬀecting Coriolis acceleration. Imagine a summer day in the Northern Hemisphere; the most intense heat radiation from the sun over the Earth occurs around the lower 1/3 of the Northern Hemisphere, both on land and on bodies of water. Very similar to the pot of water on a stove, as the air and water warm up, the air and the moisture within it rise, creating a low pressure area, causing the air from the high pressure area to rush in to replace it. is creates an almost constant circulation of air throughout the Earth with circulating winds (called cells). However, due to other inﬂuences, instead of a double circulation pattern, there are three circulatory patterns over the Northern Hemisphere and three over the Southern Hemisphere (see Figure 3.19). ese are called Hadley, Ferrel, and Polar cells. Notice that the winds go in opposite directions near the surface versus the upper atmosphere. e expectation would be that there should only be one cell in each hemisphere; hot air rises, and is replaced by cold air. However, both Poles are huge heat sinks; they are very cold, with cold air that sinks down, creating Polar cells. In general, the weather between 0 and 30 degrees is heavily inﬂuenced by the relatively stable Hadley cell, as is the weather between 60 and 90 degrees by the relatively stable Polar cells. It is the areas between 30–60 degrees, inﬂuenced by the Ferrel cells, that are more unstable. e Ferrel cells are somewhat secondary in nature, existing as a result of the Hadley and Polar cells. As a result, the Ferrel cells, also known as the Zone of Mixing, change much more than the other cells. Notice that most of the land mass in the Northern Hemisphere is in this region, 3.6. CORIOLIS ACCELERATION AND WEATHER SYSTEMS 75 Figure 3.18: e position of Earth relative to the Sun during the year. including the U.S., the southern half of Canada, most of Europe, most of Asia, including China, and the southern half of Russia. 3.6 CORIOLIS ACCELERATION AND WEATHER SYSTEMS Coriolis acceleration aﬀects many other systems too, but since we have studied so much to get to this point, let’s talk about the eﬀects of Coriolis acceleration on weather systems. So, once again, why is it that the states along the West and East Coast of the U.S. are all adjacent to large bodies of water (oceans), but their weather patterns are so diﬀerent? One would expect that being next to an ocean, the weather is heavily inﬂuenced by moisture, and therefore, all these states should have similar weather patterns, both in the summer and in winter. However, we know they do not have similar weather patterns. North east states receive signiﬁcant snow during winter season while south east states do not; those states are generally warmer. Similarly, 76 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.19: e continuous air circulation patterns of Hadley, Ferrel, and Polar cells in the Northern and Southern Hemispheres. north west states receive more snow (although not as much as the eastern states) than the south western states. Summers in Florida are very humid, but not in California. As you see, it is not simply the latitude or longitude that causes diﬀerences in weather patterns. Additionally, there are somewhat constant world-wide winds (the jet stream, prevailing winds, trade winds, etc.) that almost always blow in the same direction, and although they do dip down or move up as the weather and seasons change, they predominantly blow in the same direction (which has been used for sailing for millennia). What causes these winds? And what causes cyclones? Coriolis acceleration. As we saw in Section 3.3, when there is (linear) motion within a rotating frame, there is a component of acceleration called Coriolis, which is perpendicular to both the rotation vector and the motion (velocity) vector, and it follows the right-hand-rule. Here, we have the perfect recipe for this too, where the rotating frame is the Earth, and the motions are of the aforementioned cells. e combination of the two together causes Coriolis acceleration. However, notice that since the winds are in diﬀerent directions, the directions of the Coriolis accelerations vary too. It should be clear that the wind directions at the surface and at higher altitudes are op- posites, and therefore, the directions of Coriolis accelerations will also be opposite. But to avoid confusion, let’s only look at these directions on the surface; the opposite will be true for higher elevations. First let’s look at the Polar cell in the Northern Hemisphere. Figure 3.20 is a closer look at the Polar cell. e rotation of the Earth is represented as an upward vector, and the velocity vector of the air moving within the Polar cell near the surface is southward, moving away from the Pole. u, the Coriolis acceleration will be toward the ! 2 Remembering the Coriolis equation of E ac E (cid:2) E D Hadley CellFerrel CellPolar cell3.6. CORIOLIS ACCELERATION AND WEATHER SYSTEMS 77 east. However, just like the reaction of your body to a forward acceleration due to its inertia (see Section 3.4), which pushes your body backward, the air mass will react to this acceleration, causing it to move toward the west, creating Polar Easterly winds (coming from the east). e air mass, instead of simply moving down from the high pressure area to the low pressure area, generally moves west in the 60–90 degree region. Figure 3.20: Within the Polar cell, the direction of the winds near the surface is southward. e Coriolis acceleration is toward the east, forcing the winds to react and go westward, creating Polar Easterly winds. e rest is similar. If you look at the Ferrel cell, the motion near the surface is northward toward the Pole. Since the rotation vector is still the same, the direction of Coriolis will be to- ward the west and the reaction of the air mass will be toward the east, creating the Westerly winds within the 30–60 degrees region. Once again, instead of simply moving from high to low pressure areas, the winds shift toward the east. What is interesting is that as the Westerlies and the Polar Easterlies run into each other, they create all sorts of weather patterns, aﬀecting regional climates. Westerlies bring warm and moist air from the oceans to the west coasts of the continents, de- scribing why the weather on the East Coast of the U.S. is so diﬀerent from the West Coast. Due to these Westerlies, the general pattern of air mass movements in the U.S. is eastward; air masses move from the west to the east. West Coast weather is inﬂuenced by the air coming from the Atlantic Ocean, a marine climate that is warmer and moister in winter, not causing snow until higher altitudes, whereas the East Coast weather is inﬂuenced by continental air from the land- mass where it is colder, causing snow in winter. If the air would be moving straight down from Direction of the windin the Polar cell at thesurfaceDirection of CoriolisaccelerationRotation of theEarthwindEarth'srotationCoriolis78 3. CORIOLIS ACCELERATION AND ITS EFFECTS high to low pressure areas without the inﬂuence of Coriolis acceleration, the weather patterns on both coasts of the continents would be similar. For the Hadley cell too, the direction of motion of the wind at the surface is southward, Coriolis acceleration is to the east, and the reaction to it causes the winds to shift toward the west, creating the Northeast Trade winds. Trade winds are the steering winds of the tropical cyclones near the Equator; they determine the direction that the cyclones take as they travel westward. Southern Hemisphere winds follow the same rules too, creating the Polar Easterly winds at the Polar cell, the Westerly winds within the Ferrel cell, and the Southeast Trade winds within the Hadley cell. See Figure 3.21 for the directions of these winds. Figure 3.21: e prevailing winds shift due to Coriolis acceleration within each cell. Note how the Easterlies and Westerlies create almost constant cycles in the Northern and Southern Hemispheres. ese cycles have been used in sailing for millennia. ey enable ships to sail from continent to continent. Similarly, depending on whether an airplane ﬂies into a prevail- ing wind or against it, ﬂight times can change signiﬁcantly. Flying from San Francisco to New York usually takes less time than ﬂying from New York to San Francisco, perhaps as much as one hour depending on diﬀerent current conditions. Figure 3.22 shows the general directions of the winds over the continents. Please remember that these are general directions. ese wind directions are heavily inﬂuenced by seasons, bodies of water, mountains, and temperatures, therefore inﬂuencing regional and local weather patterns. Still, you can see how these winds inﬂuence the general weather patterns. It is interesting that the same also happens on a smaller scale in your car. Next time you are driving in a car and the fan is on, try to notice what happens as .. Polar easterly windsNortheast trade windsWesterly windsSoutheast trade windsWesterly windsPolar easterly winds3.6. CORIOLIS ACCELERATION AND WEATHER SYSTEMS 79 Figure 3.22: e general direction of the prevailing winds over the continents. the car turns. If the blower is blowing the air to your face, as soon as you turn, the air’s direction changes and you will not feel the air on your face. When you straighten out, the air blows in your face again. Why? Just like before, when the car turns, it becomes a rotating frame within which there is air moving. If you do the same cross product, with the vector representing the rotation of the car in the up-down direction and the blowing air in the direction toward you, the cross product of the resulting Coriolis acceleration will be to the left or right, deﬂecting the air sideways. When the car goes straight and the rotation vector is zero, the air moves directly toward you. .. And now to our original question of why the weather of the West Coast is so diﬀerent from the East Coast. As you may see in Figure 3.22, the general weather of California is heavily inﬂuenced by the Westerlies, which are commonly moist and warm due to the Paciﬁc Ocean. erefore, it does not snow until the mountains because the air is warmer and more humid, whereas, due to the same Westerlies that pass over a huge landmass, by the time the air reaches the East Coast, it is cold and therefore snows. e same is also true when the polar easterlies dip down and bring cold air from the north into those states. As you move down to the Southern Gulf states, both the Westerlies and the Easterly trade winds bring moisture to those states, so the air is warm and humid. Of course, other local issues aﬀect local winds and weather too. ese include sea and land breezes during the day, mountains and valley breezes, and high mountain thermal ﬂows that aﬀect local winds (see Figure 3.23). An important issue to notice is that the angular velocity (rate of rotation) of the Earth is very low (one revolution per 24 hours). Consequently, only long motions are aﬀected by it over large 80 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.23: Rows of trees in San Luis Obispo, near the coast in California, all leaning to the east due to the inﬂuence of regular on-shore sea-breeze winds from the Paciﬁc Ocean. distances. Small motions we normally make like walking or throwing a ball are hardly aﬀected by Coriolis at all. e idea, that the rotation of the water in a toilet bowl or when the water drains in a bathtub is due to Coriolis, is wrong; the water in a toilet rotates because it is deliberately designed with lateral openings to rotate the water as it is discharged to increase eﬃciency. e rotation of the water as it drains in a bathtub is due to the conservation of angular momentum, a subject that we have not covered here. But neither is due to Coriolis, and therefore, neither will necessarily go the opposite way in the Southern Hemisphere. e importance of Coriolis acceleration varies based on latitude (the angle between the location and the Equator, deﬁning north-south locations). Figure 3.24 shows the velocities of the surface winds within the Polar and Hadley cells again. Notice that since the winds follow the surface, the directions (line of action) of these velocities are not exactly the same, but follow the curvature of the Earth. 3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 81 Figure 3.24: Surface wind directions of the Polar and Hadley cells. Now let’s look at the Coriolis acceleration of these two cells. Notice that as Equation (3.4) shows, Coriolis acceleration is the cross product of the angular velocity of the Earth and the wind velocity. But also as we saw earlier in Section 3.2.2, due to the nature of cross products, only ! counts; the cross the component of the velocity that is perpendicular to the angular velocity N ! is zero. As Equation (3.3) shows, product of the component of the velocity that is parallel to N the magnitude of the cross product is a function of sin.(cid:18)/, which is zero when two lines are parallel. As Figure 3.24 shows, the velocity of the surface winds in the Polar cell is nearly perpendicular ! representing the rotation of the Earth. However, the velocity of the surface winds in to vector N !. erefore, the Coriolis acceleration and its eﬀect the Hadley cell is pretty close to parallel to N is much more pronounced in the Polar cell compared to the Hadley cell near the Equator. 3.7 ACCELERATIONS DUE TO COMBINED MOTIONS Gyroscopic motions are closely related to this subject and we will see a couple of applications where they are used later, but due to their complicated nature, we will not cover gyroscopic mo- tions in this book. However, when there are multiple simultaneous rotations about diﬀerent axes, they result in additional accelerations that cause interesting results. Since we have already dis- cussed many of the elements related to these, let’s go a bit further and also discuss these and their eﬀect on the objects that many of us use regularly. 3.7.1 RIDING BICYCLES One of the ﬁrst things a child must learn for riding a bicycle is that turning the handle to the right or left will throw the rider to the side; instead he or she must lean to one side or the other Hadley CellPolar cell82 3. CORIOLIS ACCELERATION AND ITS EFFECTS to force the front tire to turn to one side. is is because, in addition to other factors such as the head-tube angle and the oﬀset (called rake angle) and location of the center of gravity and friction, the combined rotations of the tire and the handle-bar create an additional acceleration similar to Coriolis acceleration that aﬀects the turning (as mentioned earlier, this can be explained by gyroscopic motions, but we will not discuss that here). While riding a bicycle there are two rotating frames, one turning within the other, causing acceleration. To see how this works, let’s look at Figure 3.25. Imagine that a disk rotates about the x-axis as represented by vector !1. Now imagine that this disk is also rotating about the z- axis as represented by !2. As you can imagine, as time goes on, as a result of the rotation !2, vector !1 changes direction to !10 (and beyond). is change in direction, which in fact is the acceleration, is shown as (cid:1)! (read delta-omega, meaning change in !). Although we are not showing it here, this change is actually perpendicular to both of these vectors (along the y-axis) and its magnitude is !1!2. As we have seen before, this is the same as the cross-product of these two vectors. erefore, the change (cid:1)! a can be shown as: D N a N !2 D N !1: (cid:2) N (3.5) is means that as one vector rotates due to a rotation, the resulting acceleration is perpendicular to both vectors. Now let’s see how this translates into the bicycle ride. Figure 3.25: Rotations within a rotating frame cause acceleration. a N !2 D N Referring to Figure 3.26, Section 3.2.3, we see that the rotations of the tires of a bicycle can be represented by the vector !1 about the x-axis. If the handle-bar is rotated about the z-axis as !2 at the same time, there will be an acceleration perpendicular to both of these about the y-axis !1. A reaction to this component of the acceleration due to inertia will tend to throw as the rider to the right. Conversely, with the same !1 representing the rotation of the tires, if the rider leans to one side, there will be a rotation !2 along the y-axis, causing an acceleration along the z-axis that causes the handle-bar to rotate. As was mentioned earlier, there is a lot more to the total reaction of a bicycle, but this simple analysis shows how the bike reacts to rotations. (cid:2) N xyz11xyz1x'y'121ωωωωωω∆ω3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 83 Figure 3.26: Rotations of a bicycle’s tires and handle-bar and the resulting acceleration. Why we can ride a bike without falling over: When the tires of a bicycle rotate, the rotation creates a vector perpendicular to the motion. is vector represents the angular momentum of the tire, and is a function of the weight of the tire, the way this weight is distributed (called moment of inertia), and how fast it rotates. Nonetheless, angular momentum is a vector whose direc- tion follows the right-hand-rule. Although we have not discussed angular mo- mentum yet, let it suﬃce to say that this vector likes to maintain its direction. In other words, changing the direction of this vector requires an attempt, an external torque. Otherwise, the direction and magnitude of this vector tend to remain the same. External factors such as friction eventually reduce the angu- lar momentum. is is why a rotating wheel eventually comes to a stop. is is true for the direction too; the direction of an angular momentum vector tends to remain the same unless forced to change. is is called preservation of angular momentum and is an important subject in dynamics. But what is important about this? e important thing is that due to this resistance to change, barring external inﬂuences, the direction of an angular momentum vector will not change. erefore, as long as the tires of a bicycle are rotating (suﬃciently) the direction of the vector resists changing. As a result, the tire will not fall over. In some instances, if the rider brakes very hard, both tires may lock and stop rotating while they slide on the road before completely stopping. Unfortunately, this causes the bike to fall over because there is no longer any .. xyz12aωω84 3. CORIOLIS ACCELERATION AND ITS EFFECTS angular momentum. To prevent this, especially in motorbikes, the rear brakes are designed to never create forces large enough to lock the wheel. Since the contribution of braking force on the rear wheel is lower anyway, this generally does not signiﬁcantly diminish the braking ability of the total system, but prevents the bike from falling over. .. 3.7.2 OSCILLATING FANS An oscillating fan is in fact very similar to a bicycle. e rotating blades create a vector !1 perpen- dicular to the plane of the blades, as shown in Figure 3.27. Now imagine that you also turn on the oscillation mechanism that oscillates the fan to the right and left, as represented by a vector !2. Of course, the direction of !2 changes as the direction of oscillation changes. erefore, the resulting !1 also changes direction. is means that as the fan oscillates either to acceleration the right or left, the forces generated by this acceleration will tend to push the fan’s base forward, backward, or sideways. Note that here too, the magnitude of vector !1 representing the rotation of the blades is much larger than the magnitude of !2 representing the oscillations. erefore, the resulting acceleration is relatively small. !2 D N (cid:2) N a N Figure 3.27: e rotations and oscillations of a fan and their representations. 12ωω3.7.3 AIRPLANES 3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 85 An airplane motions can be described by attaching a frame to it as shown in Figure 3.28. Although other conventions exist, the rotation of the airplane along an axis through its fuselage pointing forward is generally called roll. A rotation about an axis through the wings is called pitch, while a rotation to the left or right along a vertical axis pointing down is called yaw. As before, the three axes of the reference frame are mutually perpendicular. Conventionally, the x-axis is assigned to the roll axis, the y-axis is assigned to the pitch axis, and the z-axis is assigned to the yaw axis. z. Notice how in this common convention for airplanes the positive direction y erefore, (cid:2) E of the yaw axis is downward. D E x E Figure 3.28: Motions of an airplane can be described through a frame attached to it. First a word about how an airplane becomes airborne. An engineering principle called Bernoulli’s principle indicates that when a ﬂuid moves faster, its pressure drops. You can simplify this by looking at the total energy of a system, including both its potential and kinetic energies (see Chapters 1 and 2). Unless there is a net positive energy into the system, the total should remain the same due to the conservation of energy law. erefore, as the kinetic energy of the sys- tem increases due to its higher speed, its potential energy (translated into its pressure) drops. is is used in many places and systems, for example in measuring the airspeed of an airplane or in the old carburetors that were used to mix gasoline with air and supply it to the engine. Take the airplane: a small pipe called a pitot tube is attached to the wing of the airplane and directly into the airstream. As the airplane ﬂies, the air that is pushed into the pitot tube comes to a stop be- cause the tube is closed at its opposite end. erefore, the total kinetic energy of the air converts to potential energy, and as a result, pressure increases. As the plane goes faster, the pressure in the pitot tube increases. is pressure is measured and calibrated into the speed that the speed indicator shows. In the old-style engine carburetors a venturi was used to take advantage of the rollpitchyaw86 3. CORIOLIS ACCELERATION AND ITS EFFECTS same principle. A venturi is essentially a tube whose diameter reduces at some point (see Fig- ure 3.29). Since the same amount of gas or ﬂuid passes through the smaller cross section, speed must increase, reducing pressure. erefore, the pressure within the smaller cross section is lower than before or after. is was used to suck the gasoline from a small tank next to it, mixing it with the air and supplying the engine with the fuel-air mixture. Many other systems are also based on this principle. However, for an airplane, the increase in speed comes from the shape of the wing’s cross section. Figure 3.29: As the ﬂuid moves through a venturi, within the smaller cross section, its speed increases and its pressure decreases. Looking at Figure 3.30 you will notice that as the airplane moves through the air, due to the asymmetric shape of the cross section of the wing which has a longer length on the top than it does on the bottom, the air has to travel faster above the wing than it does below in order to maintain continuity. As a result, the pressure above the wings is lower than the pressure below. is creates a positive upward force that ﬂoats the airplane. Notice that since the pressure above can never approach zero, the maximum diﬀerence between the pressure below and above is only a fraction of the total atmospheric pressure. However, since the wings are large, the pressure diﬀerence multiplied by the large area creates enough upward force to ﬂoat the plane. By the way, you can test this by holding a piece of paper in your hands at one edge, letting the other edge hang freely. If you blow air over the paper it moves up. is is because the air moving over the paper has a velocity larger than the air below it. is reduces the pressure above the paper, lifting it. We will discuss control surfaces and how airplanes’ motions are controlled shortly, but ﬁrst let’s see how these surfaces work. A control surface is a portion of the wing or the rudder of an airplane which moves independently of it. Control forces are generated by moving the control surfaces into the air stream in diﬀerent directions, resulting in controlled motions. Figure 3.31 shows a control surface that is lowered into the airstream. e air pushes against the surface and creates a force as shown, trying to “straighten” the obstruction. is force can be resolved into two forces, one horizontal, one vertical. e horizontal force is called drag and it works against the forward motion of the airplane, increasing demand from the engine to overcome it. e vertical force tries to move the surface and with it, the wing, upward. Similarly, if the control surface is Higher speed,lower pressureLower speed,higher pressureLower speed,higher pressureFluid inFluid out3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 87 Figure 3.30: An airplane becomes airborne due to the pressure diﬀerence below and above the wings, caused by the increased velocity of air traveling above the wings. Due to Bernoulli’s principle, as the air speed increases, its pressure decreases. moved up into the airstream, the resulting force will be downward and the wing will move down with it too. ese control surfaces control the motions about the three axes. As you see, if the surface is lowered, the force will be upward. If the surface is lifted up, the force is downward. What happens if one surface is lowered while the opposite one is lifted up simultaneously? ere will be a pair of forces, one downward, one upward. ese two forces together create a torque (a couple) that causes rotation. is torque will rotate the airplane about the roll axis. In order to rotate the airplane along each axis a set of control surfaces are used, as shown in Figure 3.32, called ailerons, the rudder, and elevators. Motion along the roll axis is controlled by control surfaces on the rear edge of wings close to the tips called ailerons. Ailerons move in opposite directions, developing forces that are also in opposite directions as the airplane moves through the air. e aileron that is up creates a downward force; the one that is down creates an upward force. As we saw in Section 3.2.2 these two forces will create a moment along the roll axis and will roll the airplane along that axis. Obviously, for controlled motions during ﬂight, small forces are used to roll the plane slowly. But imagine a ﬁghter airplane that rolls quickly to shun an incoming missile. e forces will be larger, requiring great skill on the pilot’s part to control the plane. Motion along the yaw axis is controlled by the rudder attached to the vertical tail ﬁn, the large vertical control surface on the back of the airplane. e rudder moves to the left or right, creating a force to the right or left, rotating the airplane along the yaw axis. You may have noticed that the surface of a road is usually raised on one side along a turn. is is a lot more obvious in race tracks where race cars travel at very high speeds. is is necessary to keep the car on the road when during the turn, it is subject to centripetal acceleration (or what is referred to as centrifugal force which is really the reaction of inertia to centripetal acceleration as we discussed earlier). Similarly, airplanes are intentionally banked a little by rolling them along the roll axis during turns to prevent particles inside the airplane from ﬂying outwardly (for example, if you have a glass of water on your tray in an airplane when it turns, without this banking, the glass will slide Longer path, higher speed, lower pressureShorter path, lower speed, higher pressureAir88 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.31: As the control surface is moved down into the airstream, a force is generated that can be resolved into drag and an upward force that lifts the wing on one side. e opposite happens if the surface is moved up into the airstream. oﬀ the tray). In order to do this, the pilot usually combines the motions of the rudder with that of the ailerons to bank the airplane along the roll axis during a turn along the yaw. Motion along the pitch axis is controlled by elevators. Elevators are really part of the rear tail surfaces (called stabilizers) that move upward or downward, either attached to the fuselage or attached to the top of the vertical ﬁn. Alternately, a single control surface called stabilator may be used to do the same. Elevators and stabilizers are also used to level the airplane during the ﬂight. In general, a pilot needs to make sure that the center of gravity of the plane is in front of the center of lift (usually indicated by a minimum and maximum distance), which is on the wings. In smaller airplanes before take-oﬀ the pilot makes sure that the luggage in the tail part of the airplane is moved around until the center of gravity is in front of the center of lift. is way, if the plane stalls, it will nose-dive (and not tail-dive). After the plane gains some speed, the pilot can try to level the airplane again and continue ﬂying. Otherwise, as a plane stalls, it may crash. airstreamforcegeneratedaileronwing cross sectionaileron up,force downaileron down,force upDragupwardforce3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 89 Figure 3.32: Control surfaces of an airplane. As a control surface is pushed into the airstream, the air presses against it, creating a force that attempts to push it back. In some airplanes, the vertical ﬁns and the stabilizers are combined into two tail surfaces that are at an angle relative to the wings (like a “v”). If you know how to make a paper airplane, make one. By bending both the wing tips up or down, one up and one down, or bending the rudder’s tip, you can force the airplane to roll, pitch, or yaw in any combination. How to Make a Paper Airplane: Figure 3.33 shows one way to make a simple paper airplane. Figure 3.33: A simple way to make paper airplanes. .. rollpitchyawaileronrudderelevatorstabilizervertical fin90 3. CORIOLIS ACCELERATION AND ITS EFFECTS As we discussed earlier, any time there is motion within a rotating frame, there will be an additional acceleration component caused by the cross products of the two motions as shown by Equation (3.5) repeated here: a N !2 D N !1: (cid:2) N Like bicycles and fans, since the blades (or in the case of a jet engine, the turbines) rotate along the roll axis, there is a relatively large vector present in that direction. Whenever the airplane is rotated along the roll axis the same vector is present too. If at the same time the plane rotates along the pitch or yaw axes, there will be an acceleration component in the direction perpendicular to both. erefore, anytime the pilot rotates the plane about the pitch axis, he or she has to also make a correction about the yaw axis, and whenever there is a rotation about the yaw axis, he or she needs to make a correction about the pitch axis. In most cases though, since the rotations are very slow, the resulting acceleration is very small and it may not be necessary to do much about it. However, in faster maneuvers or during take oﬀ (when the nose is pulled up by a rotation along the pitch axis) and landing, when these rotations are larger, corrections are necessary in some cases. Pilots are taught to look at the “ball in the race” instrument that indicates if the net acceleration vector is oﬀ to one side or not, and to “step on the ball” to keep this vector along the pilot’s spine, thus keeping him or her straight in the seat, and not pushed to one side or the other. In larger airplanes the automatic control system of the airplane automatically takes care of these corrections. You may have noticed that as airplanes touch the ground, the tires, which at that instant are stationary, rub against the tarmac until their speed is equal to the speed of the airplane, making noise and smoking. In this process, the tires wear as well. One common tendency is to suggest that the tires be rotated just before landing by attaching a small motor to each tire, therefore eliminating this rubbing and smoking. e problem is that since the tires rotate along the pitch- axis, as the pilot tries to correct the airplane’s roll or yaw, additional motions are created along the other axes, making it diﬃcult to control the airplane. ere is a story that one airliner used tires that had small scoop-like extensions on the tires to force them to rotate when the landing gear was lowered before landing. Due to this phenomenon, the pilots used to cut the scoops out of the tires by a knife to prevent this rotation. Auto-pilots are based on gyroscopes, which also involve the same ideas we have discussed. A gyroscope has a ﬂywheel-type rotating mass, which due to its relatively large mass and high speed of rotation, creates a large angular momentum. is momentum resists a change in its direction. erefore, anytime it is subjected to rotation in a direction other than the direction of the angular momentum vector, it resists the motion. Gyroscopes can be used in two ways, one to steady the motions of a system, another to automatically control its motions, called auto pilot. e same is true for ships and other water-vessels. For example, if a large gyro is mounted on a ship, it will resist motions along the other two axes that are perpendicular to the direction of the angular momentum vector. As a result, the gyro will steady the motion of the ship against waves. Additionally, based on Equation (3.5), since the gyro moves about an axis perpendicular to the motion induced in it, through sensors such as a potentiometer, a signal may be measured that can 3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 91 be used to move the control surfaces of the airplane to correct the induced motion. erefore, except during take-oﬀ, landing, or emergencies such as sudden turbulences, while the airplane cruises at high altitudes the auto-pilot can be in control of the airplane. 3.7.4 ROBOTS Robot manipulators, similar to the ones used in industry to manufacture and assemble parts and products, have multiple joints (degrees of freedom or DOF) that enable them to move to any position or orientation within their reach (see Figure 3.34). is is usually translated into a hip joint, a shoulder joint, an elbow joint, and three wrist joints (if the robot is a 6-DOF or 6-jointed robot. Fewer DOF or joints are also common, but they are not as versatile). Clearly, when all joints rotate together to move the robot to a new position or orientation, a similar situation like the bicycle, fan, or airplane exists; every rotation within another rotation creates an additional acceleration component perpendicular to the two rotations. Since the robot has up to six joints, it is possible that joints 1 and 2 may be moving simultaneously. erefore, there will be an acceleration !1!2. Now suppose that joints 1, 2, and 3 move simultaneously. In this case, there will still be an acceleration component caused by the rotation of !2 (the shoulder) within !1 (the waist) as !1!2. However, there will also be another acceleration component caused by the rotation of joint 3 (the elbow) within the waist as !1!3, but since joint 3 also moves within joint 2, there will be an acceleration !2!3. erefore, the total acceleration includes all three components. Similarly, if all six joints move together, since joints 2, 3, 4, 5, and 6 all move within joint 1, there will be acceleration components !1!2, !1!3, !1!4, !1!5, !1!6, and since joints 3, 4, 5, and 6 move within joint 2, there will be accelerations !2!3, !2!4, !2!5, !2!6, as well as !3!4, !3!5, !3!6, as well as !4!5, !4!6, and !5!6. Each acceleration, multiplied by its own corresponding mass or moment of inertia produces a Coriolis force that has to be dealt with. In most robots that move slowly, these accelerations are small and can be ignored. But for fast-moving robots, these can become signiﬁcant and must be considered in the design of the robot. To experience the same phenomenon yourself, ﬁrst turn about your waist while your arm is stretched outward. Next move your arm up and down while still stretched. en move your arm up and down while you rotate about your waist. You will notice how you feel an additional force against your arm, stemming from the Coriolis-type acceleration. 3.7.5 MOVEMENTS OF A SPACECRAFT IN SPACE e following excerpt is from NASA’s Gemini-VIII spacecraft mission journal, written by astro- nauts Neil Armstrong and David Scott (see https://www.hq.nasa.gov/alsj/alsj-Gemini VIII.html). After station-keeping for about 36 minutes, docking with the Gemini Agena Target Vehicle was accomplished. e ﬁnal docking maneuver was begun when a distance of about 2 feet separated the two vehicles. A relative velocity of about three-fourths of a foot per second was achieved at the moment of contact. e nose of the space- 92 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.34: A robot and its joint movements. craft moved into the docking adapter very smoothly and the docking and rigidizing sequence took place very quickly and with no diﬃculty. e docking sequence was completed at 6:33:22 ground elapsed time, with the two vehicles rigidized together. For a period of 27 minutes after docking, the stability and control of the docked vehi- cles was excellent. At approximately 7:00:30 ground elapsed time, the crew noted that the spacecraft-Gemini Agena Target Vehicle combination was developing unexpected roll and yaw rates. e command pilot was able to reduce these rates to essentially zero; however, after he released the hand controller, the rates began to increase again and the crew found it diﬃcult to eﬀectively control the rates without excessive use of spacecraft Orbital Attitude and Maneuver System propellants. In an eﬀort to isolate the problem and stop the excessive fuel consumption, the crew initiated the sequence to undock the spacecraft from the Gemini Agena Target Vehicle. After undocking, the spacecraft rates in roll and yaw began to increase, indicating a spacecraft problem which the crew attempted to isolate by initiating malfunction-analysis procedures. When the rates reached approximately 300 degrees per second, the crew completely deactivated the Orbital Attitude and Maneuver System and activated both rings of the Reentry Control System in the direct-direct mode. After ascertaining that spacecraft rates could be reduced using the Reentry Control System, one ring of the system was turned oﬀ to save fuel for reentry and the spacecraft rates were reduced to zero using the other ring. e crew continued the malfunction analysis and isolated the problem area to the No. 8 thruster (yaw left-roll left) in the Orbital Attitude and Maneuver System. e circuitry to this thruster had failed to an “on” condition. Joint 1, waistJoint 2, shoulderJoint 3, elbowJoint 4, wristJoint 5, wristJoint 6, wrist3.7. ACCELERATIONS DUE TO COMBINED MOTIONS 93 is report relates to many of the principles that we have discussed in this chapter. To better understand these, let’s start with thrusters and their role. Large rockets are used to apply large forces (and acceleration) on spacecraft for rapid move- ments, but small motions and rotations are accomplished by ﬁring small thrusters for short periods of time. Imagine a spacecraft, schematically shown in Figure 3.35, moving in space. Also imagine two pairs of opposing thrusters attached to it in one plane as shown. If thrusters A and B are ﬁred simultaneously (usually for a very short time), the spacecraft will accelerate in the direction shown due to the force exerted by the thrusters. To slow down or return the spacecraft to its previous speed, thrusters C and D are ﬁred simultaneously to exert similar but opposing forces to the craft. To rotate the craft in the counter-clockwise direction, thrusters C and B are ﬁred simul- taneously. In this case, the forces of these thrusters are opposing and cancel each other, and consequently, the summation of forces is zero and the craft will not accelerate linearly. However, since these forces create a torque in the counter-clockwise direction, there will be a torque in that direction, resulting in a rotation. Similarly, to rotate the craft in a clockwise direction, thrusters A and D are ﬁred simultaneously. In either case, to slow down the rotation or to stop it, the opposite pairs of thrusters are ﬁred. Figure 3.35: Depending on which pair of rocket thrusters is ﬁred, the spacecraft may move in one direction, rotate clockwise, or rotate counterclockwise. Since a spacecraft is free to move in three dimensions, it must have a similar arrangement of two pairs of thrusters in each plane to allow controlling its motions along the x-, y-, and z- axis as schematically shown in Figure 3.36. A similar arrangement is used for maneuvering spatial movements of astronauts in space walks. What happened with the spacecraft in the earlier story was that one of the thrusters had malfunctioned in the “on” position, and was consequently applying a torque to the vehicle and accelerating it to about 300 degrees per second, a very large value that induces dizziness in as- tronauts and can eventually destroy their vehicle. e astronauts had separated the two crafts to ﬁnd which one was at fault. After ascertaining that the docking vehicle was the reason, they ﬁred another series of thrusters that are used for controlling reentry to counter the malfunctioning MovesforwardRotatesCCWRotatesCWABCDABCDABCD94 3. CORIOLIS ACCELERATION AND ITS EFFECTS Figure 3.36: Pairs of thrusters are used in diﬀerent planes (x-y, x-z, and y-z) to move a spacecraft along or rotate a spacecraft about its axes. thruster. Eventually, the astronauts turned oﬀ the automatic system that was supposed to keep the vehicle running and took over the piloting of the vehicle themselves. Notice that in spatial movements, since the object can rotate along all the axes, there are Coriolis accelerations along diﬀerent axes as well. erefore, quick rotations that increase Coriolis are more diﬃcult to control. Rocket propelled human ﬂight systems follow the same rules, except that gravity is present. erefore, thrusters or jet packs are only needed for lifting while gravity exerts a downward force. e rotations are accomplished by pairs of thrusters. But watch out for Coriolis acceleration. Hopefully, you have noticed how all these issues are inter-related. Whether a bicycle, an airplane, the air coming out of a vent in your car, the weather, a fan, a robot, or a spacecraft, engineering principles govern how systems behave and react. Engineers use these principles in the design and analysis of systems that we use every day. Knowing them allows the engineer to not only create useful devices and systems, but also to protect users against adverse reactions that might occur as a result of these principles. Front viewSide viewC H A P T E R 4 95 ermodynamic Cycles Refrigeration, Air Conditioning, Engines, and Power Cycles 4.1 INTRODUCTION When I was a junior in an engineering college my uncle asked me, “Do you know how a refriger- ator works? Can you repair one?” I replied yes, I know how it works. But whether I can repair one or not depends on a lot of other things. What I meant was that as engineering students, we learn thermodynamics, in which we study the principles that govern how a refrigeration cycle works, and based on that we can design the system. However, each company uses somewhat diﬀerent sets of components to achieve about the same results. Based on experience with those compo- nents, you may or may not be able to ﬁx a broken system or even recognize exactly what a part does; a certiﬁed technician can do that better than an engineer. But a technician cannot design the system or create a new one. e same is true with engines. You learn how an engine works and how to design it to ensure that it works properly, but as an engineer, you may or may not know how to ﬁx it depending on your experience. To see this relationship and to understand why it is important to learn the basics and the principles of engineering let’s look at refrigeration and power development systems and how the principles and the practical devices map into each other. If you have access to a bicycle pump do the following exercise (if not, a simple balloon will do): Firmly place your ﬁnger at the output valve of the pump and press down on the plunger (down-stroke), pressurizing the air inside, and hold it (with the balloon, blow it up and hold the tip to prevent the air from escaping, but do not tie it with a knot). If you touch the body of the pump you will notice that it is a bit warmer (the balloon will most probably not get noticeably warm because of its size). Why do you think it is warm now? is is because we perform “work” on the air to pressurize it (as was discussed in Chapter 3, work is force multiplied by distance. As a force moves, it does work, which also means that it adds energy to the system. In this example, we exert a force on the plunger to compress the air, and we move it in the same direction, doing work and adding energy to the system). e added work will increase the temperature of the pressurized air. e same happens when the air inside a tank is pressurized by a pump; the tank body’s temperature rises a little because the air inside gets warmer. In mechanical engineering, the relationship between pressure, volume, and temperature of a gas 96 4. THERMODYNAMIC CYCLES can be expressed by an equation of state. e most common one for gases is called ideal gas law. Tables containing the detailed properties of real gases are also available. Equation (4.1) shows the ideal gas relationship between pressure, speciﬁc volume, and temperature. In this equation, temperature is the slave to the pressure and volume. R is called the speciﬁc gas constant and is known for diﬀerent gases. For air, R is 0.2870 kJ/kg.K (kilo-Joules per kilogram Kelvin, where Kelvin is 273. C is the temperature in degrees Celsius). In English the absolute temperature, or K(cid:14) D units, R 53:34 ft-lbf/lbmR (feet, pound-feet per pound-mass Rankin, where Rankin is the absolute temperature in English units or R(cid:14) D P v 460 where F is in Fahrenheit). F(cid:14) C RT: C(cid:14) C D (4.1) D In this equation, P is the pressure, v is the speciﬁc volume (volume/mass), R is the gas constant, and T is the absolute temperature. Due to the added work and as a result of Equation (4.1), the temperature of the air within the bicycle pump rises. We will see more about this shortly, but assuming that the ratio of the original volume of the pump to its ﬁnal volume is 4:1 without any leaks, the ﬁnal pressure can be about 7 times as much. Assuming a temperature of air before compression of 20(cid:14)C (68(cid:14)F), the ﬁnal temperature can be as high as 237(cid:14)C (460(cid:14)F). You may ask why the pump warms up only a bit if the air itself is this hot? e answer is that the weight of the compressed air compared to the pump is very small. erefore, although the temperature of the air increases a lot, the total energy is not much, increasing the pump’s body temperature only a little. A colleague of mine has designed a simple pump from glass in which the air can be quickly compressed about 20 times, raising its temperature to about 700(cid:14)C (1290(cid:14)F) and instantly combusting a small piece of paper that is placed at the bottom of the pump. Although the air inside becomes very hot, enough to burn the paper, the total energy is barely enough to warm up the body of the pump. .. Now imagine that while you continue to hold the pressure, you let the bicycle pump (or the balloon) cool down. Here, while the air is under pressure, it cools down by losing its heat energy, and although the pressure drops somewhat, the air is at a higher pressure than when we started. Next imagine that you release the plunger of the pump while you still hold the pump’s outlet oriﬁce (or let go of the balloon’s tip to let the air out). Since the air is under pressure, it will push back the plunger, and as a result, the air’s pressure returns (almost) to the original value before it was pressurized (in reality, the air is now doing some work and therefore loses some more energy). Lastly, what happens at this point is that since the air returns to its original pressure and in the process has lost a net sum of energy, its temperature also reduces to something lower than what it was at the beginning; the pump will feel a little cooler at the bottom (and the balloon also 4.1. INTRODUCTION 97 feels cooler). erefore, since it is now cooler than the environment, the air can absorb the heat from the environment and make it cooler. In this process, we forced the system to absorb heat from one environment, transfer the heat to another, and reject it there. e net eﬀect is a lower temperature in one place and a higher temperature somewhere else. is is exactly what happens in any refrigerator or air conditioning system. Neither of these systems “create” coldness; they just transfer the heat from one environment to another such that one becomes colder, one becomes hotter. Remembering our discussion about entropy in Chapter 1, is this not in the opposite direction of what natural systems would do to increase entropy? Should we assume that the net eﬀect is zero? In fact, we should not. Since we need to employ work (add energy) to compress the air and since all systems have friction (they waste energy, even if we were not compressing air but just moving the plunger), we add to the energy of the system which ultimately has to be rejected. erefore, we will need to reject more heat at a higher temperature than we absorb at a lower temperature, making the higher-temperature source even hotter. In other words, as we discussed in Chapter 1 with entropy, the eﬃciency of the system can never be 100%. is is why if you run a refrigerator inside a room, even with its door open, the room will eventually become hotter not cooler; the total heat transferred to the room is equal to the heat from inside the refrigerator plus the electric energy used to run the compressor and the fans. What the refrigerator accomplishes is to keep its interior compartment cooler at the expense of a higher exterior temperature. Now let’s see what this means in engineering terms. First, notice that this is a cycle: we compress the gas that is at a particular temperature, let it cool down, then expand it which further cools it down, and in turn it absorbs the heat and warms up to its original state. We repeat the process. is is called a thermodynamic cycle. ere are many diﬀerent types of thermodynamic cycles, each with their own speciﬁc characteristics and applications, including cycles that trans- late into power development (such as in power plants), engines, and refrigeration systems. ese cycles are usually described with graphs, including a graph of temperature versus entropy .T s/, pressure versus volume .P h/. In this book we will use the pressure versus volume .P V / diagram for its simplicity, even though it is somewhat limited in its usefulness. V /, and pressure versus enthalpy or energy .P (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) Figure 4.1 shows the P V diagram for the ﬁrst phase of this process. e x-axis shows the volume of the air at any state while the y-axis shows the corresponding pressure. Each of the isotherm lines show the relationship between the volume and pressure at a constant temperature. In this case, if the temperature of the gas is kept constant, as the pressure increases, the volume will decrease according the isotherm line. Now let’s see how our process maps into this diagram. Let’s say we start at point 1 at a particular pressure and volume. In the case of the pump, this indicates the atmospheric pressure and the volume of the pump. Segment 1-2 shows the compression of the air; we compress the air in the pump, and as a result, its pressure increases, its 98 4. THERMODYNAMIC CYCLES Figure 4.1: e pressure versus volume .P experiment. (cid:0) V / diagram of the ﬁrst segment of the bicycle pump volume decreases, and it becomes hotter. As shown, point 2 is at a higher pressure, lower volume, and at a higher temperature than point 1. Segment 2-3 in Figure 4.2 shows the cooling of the air as we maintain the volume, but we let the air cool down (here, we are assuming that as the air cools down, its volume does not change. In reality, the volume decreases a little as it cools down). Notice how the line indicates the changes in the state of the gas. Its volume is (almost) constant, its pressure is lower, and the temperature is also lower as indicated by a lower-temperature isotherm, in this case the same as the original temperature. Segment 3-4 in Figure 4.3 indicates the release of the plunger, where the pressure returns (almost) to the previous level and the volume is a little lower too (due to the decrease in tem- perature). However, notice that point 4 is at a lower temperature than point 3 (lines 1-2 and 3-4 follow a constant entropy line). Segment 4-1 in Figure 4.4 is the absorption of outside heat energy into the system, which returns the system back to its original state. ese four segments constitute a cycle that can be repeated. In the process, we transfer heat from one environment into another by applying external energy to the system, with a negative net eﬀect. 4.2 REFRIGERATION CYCLE e way a refrigerator works is very similar to the bicycle pump example, except that as an en- gineered device, it is designed to be much more eﬃcient and to work continuously. Each part of Volume, VPressure, PLines of constanttemperature (isotherms)12coolerhotter1-2: Compress the air.4.2. REFRIGERATION CYCLE 99 Figure 4.2: e pressure versus volume .P pump experiment. (cid:0) V / diagram with the second segment of the bicycle Figure 4.3: e pressure versus volume .P experiment. (cid:0) V / diagram with the third segment of the bicycle pump the cycle is accomplished by a particular component. Let’s see what these components are and how they work and how the cycle diﬀers from Figure 4.4. Unlike the bicycle pump, where the medium was air, the medium in most refrigeration systems is a chemical with favorable characteristics such as boiling point and heat capacity. For decades, the refrigerant of choice was Freon-12, a chloroﬂuorocarbon (CFC), and it worked very Volume, VPressure, P1231-2: Compress the air.2-3: Cool down.coolerhotterVolume, VPressure, P12341-2: Compress the air.2-3: Cool down.3-4: Expand the air.coolerhotter100 4. THERMODYNAMIC CYCLES Figure 4.4: e complete pressure versus volume .P cycle. (cid:0) V / diagram of the bicycle pump experiment well due to its physical characteristics. Freon-12 was also freely used as a propellant in sprays. However, since Freon had an adverse eﬀect on the upper-atmosphere Ozone layer, it was banned in the mid 1990s. It was replaced with tetraﬂuoroethane (R-134a). Although R-134a works well too, due to the size of its molecules, it leaks more easily and needs to be replaced more often. It turns out that R-134a also has adverse eﬀects on global warming (as much as 2,000 times more than CO2) and is being phased out. A big diﬀerence between the bicycle pump example and a refrigeration system is that instead of air, which is always a gas, Freon switches states between gas and liquid. is helps in maintaining a desired and almost constant temperature in the refrigerator and freezer and increases the eﬃciency of the system. Figure 4.5 shows a typical refrigeration system. e system consists of four operations; compression, condensation, expansion, and evaporation. ese operations are accomplished by components (conveniently) called a compressor, a condenser, an expansion valve, and an evapo- rator. e compression segment of the cycle is accomplished by a compressor. A compressor is a combination of an electric motor and a pump, both integrated together and hermetically sealed to prevent leakage. e function of the compressor is to compress the refrigerant. As a result, the refrigerant becomes a pressurized hot gas. In many cases, a small fan is installed next to the compressor to blow air on it to keep it cool; otherwise the heat may damage the compressor. Remember that in order to compress a gas, we need to do work on it, adding to the energy of the system. is work, supplied by the compressor motor, eventually turns into heat and is ultimately wasted. Figure 4.6 shows a typical compressor and cooling fan next to it. Typically, the compressor is in the rear-bottom part of the refrigerator and can be accessed from the back. Volume, VPressure, P1234coolerhotter1-2: Compress the air.2-3: Cool down.3-4: Expand the air.4-1: Absorb heat.4.2. REFRIGERATION CYCLE 101 Figure 4.5: A typical refrigeration system and its components. Figure 4.6: A typical compressor and cooling fan next to it. e second component of the system is a condenser. In reality the condenser is a simple heat exchanger; it is a series of tubes that transfer the heat of the high-pressure hot refrigerant out to the ambient air. As a result, the compressed and overheated refrigerant cools down, and eventually becomes a liquid (and this is why it is called a condenser, because it condenses the superheated gas into liquid). erefore, at point 2 in Figure 4.5, the refrigerant is in liquid form. To increase heat transfer from the condenser, it is possible to add a fan to blow air over the condenser and EvaporatorCondenserCompressorExpansion valveWorkHeat transferred fromrefrigerated spaceHeat transferred to theambient air1234102 4. THERMODYNAMIC CYCLES cool it down. In older refrigerators, the condenser was usually placed vertically on the back of the unit in order to take advantage of convection heat exchange; the warm air would simply rise and escape from behind the unit. In modern units, the condenser is usually under the refrigerator. In reality, the small fan that is used to cool down the compressor is designed to suck in the air from the front of the refrigerator at the bottom, pass it over the condenser and the compressor, and blow it out the back, in eﬀect cooling both of them together. Condensers are very prone to dust accumulation that greatly reduces their eﬀectiveness. erefore, it is advisable to clean the condenser once in a while. It should be mentioned that for larger systems, water cooling, larger fans, and other assistive devices are added to remove larger heat loads. Figure 4.7 shows typical condensers in a household refrigerator (a) and in an industrial unit (b). (a) (b) Figure 4.7: Typical condensers in refrigerators (a) and industrial units (b). e third component of the system is an expansion valve. Typically, the expansion valve is a long capillary (very narrow) tube. When the liqueﬁed refrigerant passes through it, due to the large pressure drop in the capillary tube, the high-pressure liquid loses its pressure and becomes a mixture of gas and liquid at low pressure. Just like the bicycle pump example, when the cooled refrigerant is allowed to lose its pressure, its temperature drops signiﬁcantly. erefore, at point 3 in Figure 4.5, the liquid entering the evaporator is very cold, and consequently, the evaporator will also be very cold. Figure 4.8a shows a typical expansion valve. In larger systems the expansion valve can be an actual valve, which similarly reduces the pressure of the liquid as it passes through (Figure 4.8b). e fourth component of the system is an evaporator. In reality, the evaporator is also a simple heat exchanger just like the condenser, and is similarly made of tubes. e cold refrigerant mixture of gas and liquid absorbs the heat of the refrigerator and boils into gas, which is then sent back to the compressor. In this process, the heat of the refrigerated area is absorbed and 4.2. REFRIGERATION CYCLE 103 (a) (b) Figure 4.8: Typical expansion valves. transferred to the outside. To increase the eﬀectiveness of the refrigerator in modern systems a fan blows air over the evaporator and then into the freezer which is typically at about 4(cid:14)F ( 15(cid:14)C). e refrigerator area is cooled through the freezer air and is typically at 35(cid:14)–40(cid:14)F (1–4(cid:14)C). In most systems, the evaporator is behind the freezer area and cannot be seen. In older refrigerators, the evaporator coils were embedded into the freezer box area. (cid:0) (cid:0) Figure 4.9 shows a typical thermodynamic P V (pressure vs. volume) refrigeration cy- cle. As expected, it includes the same compression, condensation, expansion, and evaporation segments. Segment 1-2 in Figure 4.9 shows the thermodynamic representation of compression. During compression, pressure increases, volume decreases, and temperature increases. Although not entirely accurate, it is usually assumed that the entropy of the system remains the same dur- ing this operation. is is not an important issue for our discussion here, as we have not really studied this subject. However, the assumption helps us determine how this segment behaves in the P V diagram. All points under the curve are mixtures of gas and liquid. All points to the right of the dome are gas. erefore, at point 2, the refrigerant is in gas form. Segment 2-3 shows the condensation, where the refrigerant condenses by losing heat and becomes a mixture. In this process, pressure remains the same, but since the gas liqueﬁes, the volume decreases. Segment 3-4 is the expansion, where volume increases a small amount, but pressure drops and temperature decreases. Segment 4-1 is evaporation, where the liquid evaporates by absorbing the outside heat at constant pressure and its volume increases. (cid:0) 104 4. THERMODYNAMIC CYCLES Figure 4.9: ermodynamic representation of the refrigeration cycle. While designing a system, which is what many engineers do, the designer has to choose components of the system so that they collectively work as desired. e thermodynamic cycles such as Figure 4.9 allow the engineer to design the system, pick appropriate speciﬁcations (such as temperatures, pressures, volumes, etc.) and choose appropriate components that work together and produce the desired results. is includes the size, capacity, and power of the compressor, the size of the fan, the dimensions of the condenser and evaporator, the ranges of temperature and pressures, and so on. Without these thermodynamic tables and material behavior charts, it would be impossible to design a system that is eﬃcient and works well. It should be mentioned here that modern refrigerators have other added features. For ex- ample, huge layers of ice would form on the freezer walls of old refrigerators that doubled as an evaporator. is is because when the air cools and its temperature drops the moisture in the air condenses to water and freezes over the cool surface. To prevent this, about every 22 hours, refrigerators switch oﬀ and the freezer walls are heated slightly for a short time to thaw the ice, which drops down into a tray at the bottom of the refrigerator. e water eventually evaporates into the outside room. is action keeps the freezer ice-free, but uses energy to heat the freezer wall and melt the ice, but also to cool it down again. Air-conditioning systems are essentially the same as refrigeration systems, except that the components may be put together somewhat diﬀerently to cool down an environment instead of the limited volume of the refrigerator. ese systems also include a compressor, condenser, expansion valve, and evaporator. e heat of the system is transferred to the outside by a fan, whereas the air from the room is sucked in by a fan, blown over the evaporator to cool down, and returned to the same environment. In this process, since the air is cooled down, some of the moisture in the air condenses on the evaporator, and therefore the humidity of the air is reduced Pressure, PVolume, V1234CompressionCondensationExpansionEvaporation4.3. SPARK-IGNITION POWER CYCLE 105 too. In the summertime, this is a good thing because moist air feels warmer. Consequently, the air feels better because it is cooler and also drier. However, like refrigerators, the condensed water has to be drained. You may have noticed that in many air-conditioning systems, it appears that the unit is leaking. at is in fact condensed water and not a leak. e same is true in automobile air- conditioners. Other than these diﬀerences, an air-conditioning system and a refrigeration system are thermodynamically very similar. 4.3 SPARK-IGNITION POWER CYCLE A spark-ignition cycle approximates the cycle of power development by an internal combustion engine with spark plugs. is is also similar to what is referred to in thermodynamics as an Otto Cycle which is an ideal cycle (an ideal cycle is approximate. Real cycles diﬀer somewhat from ideal cycles. But to learn the principles, we always start with an ideal cycle, then modify the cycle to a more realistic model). Conversely, a compression ignition cycle approximates a diesel engine, where the air is compressed much more and consequently, it becomes much hotter to the point that when the fuel is injected into it, it explodes and burns without the need for a spark plug. We will discuss the diﬀerences between these two engines later. An internal combustion engine in general refers to any type of engine in which the com- bustion of the fuel and air within a closed environment produces the gases that generate the mechanical work, and includes regular gasoline engines, diesel engines, rotary engines, and jet engines. Conversely, steam engines are not internally combusting engines; in steam engines, the ﬁre is outside of the engine and instead, combustion products boil water into steam in a boiler and the steam is used to power the engine. Common gasoline and diesel engines are called recip- rocating IC engines because the piston reciprocates (moves up and down) in a cylinder, rotating a crankshaft that is connected to it via a crank and a connecting rod. Wankel (rotary) engines and jet engines do not reciprocate (in fact, they do not have pistons and connecting rods and cranks); instead Wankel engines have rotary 3-sided rotors that revolve within a chamber, and jet en- gines have compressors, combustion chambers, and turbine rotors that always rotate. We should remember that in this section our discussion revolves around reciprocating internal combustion engines even if we just refer to them as IC engines. First let’s see how an engine works, then we will look at the thermodynamic cycle repre- senting it. It should be mentioned here that there are two types of gasoline reciprocating internal combustion (IC) engines—2-stroke and 4-stroke. As we will see shortly, 2-stroke engines are less eﬃcient and more polluting than 4-stroke engines. Four-stroke engines are cleaner, more eﬃcient, and vastly more popular, but as we will see, they develop power in every other cycle. Except in speciﬁc cases such as small motorbikes, model airplane engines, some lawn-mower engines and the like, almost all engines are 4-stroke. 106 4. THERMODYNAMIC CYCLES 4.3.1 4-STROKE ENGINES Figure 4.10a shows the schematic of a one-cylinder, 4-stroke, spark-ignition reciprocating internal combustion engine (notice all the qualiﬁers that are used to deﬁne it). In kinematics, this is called a slider-crank mechanism (Figure 4.10b) because it consists of a slider (the piston) and a crank, connected together by a coupler. However, unlike the slider-crank mechanism where the slider simply slides on a surface, in the internal combustion engine the piston oscillates inside a cylinder with a cylinder head which enables it to compress the air inside. e engine schematic shows the engine block and cylinder head, the piston, the connecting rod (coupler), the crank and crankshaft, the spark plug, the fuel injector, and two valves on the top. One valve is on the intake manifold and allows the outside air to be sucked into the engine; the other is on the exhaust manifold and allows the burned gases to be pushed out to the atmosphere. (a) (b) Figure 4.10: A single-cylinder reciprocating internal combustion engine and a slider-crank mecha- nism. In 4-stroke engines the complete cycle occurs within two complete rotations of the crankshaft (720(cid:14)), causing the piston to move up and down twice within the complete cycle (Fig- ure 4.11). ese are called the intake, compression, power, and exhaust strokes. Let’s assume that the piston is at the top (called top-dead-center or TDC) and is at the beginning of a cycle (intake stroke). At this point the intake valve is open, and as the piston moves down, it sucks in ﬁltered air, as shown in Figure 4.11a. In older cars, the air would move through a device called a car- buretor. Carburetors are no longer used in cars, but they are still around in older cars (even into the 90s). As discussed in Chapter 3, when ﬂuids or gases move faster, their pressure drops. A carburetor has a Venturi that, due to its reduced cross section, increases the speed of air, dropping PistonEngine blockCylinder headValveSpark plugFuel injectorConnecting rodCrankshaftValveCrankSliderCrankCoupler4.3. SPARK-IGNITION POWER CYCLE 107 the pressure. e pressure diﬀerence through the Venturi sucks in some fuel from a small tank at the side of the carburetor, causing fuel (gasoline) to be mixed into the air-stream. In fact, for this reason, the faster the engine rotates, the better the fuel mixes with air. e fuel-air mixture con- tinues to the cylinder. In newer engines, an injector is used to inject a precise amount of gasoline into the cylinder as the piston moves down, mixing with the air (other possibilities exist). When the piston is almost at the bottom (called bottom-dead-center or BDC), the intake valve is closed. (a) (b) (c) (d) Figure 4.11: e four strokes of a 4-stroke gasoline engine. e second stroke is compression. As the piston moves up, since both valves are closed and the fuel-air mixture is trapped inside the cylinder, it compresses causing both the pressure and temperature to rise (Figure 4.11b). In most gasoline engines, the compression ratio, the ratio of the air volume at the beginning and end of this stroke .V1=V2/, varies between about 8 and 11. A compression ratio of about 11 raises the temperature of the air to the point that it will require premium gasoline with higher octane; otherwise, the fuel-air mixture may ignite at an improper time, potentially damaging the engine (called detonation or knocking). At compression ratios of about 8 the temperature is still low enough to not combust prematurely; therefore regular gasoline can be used. It should be mentioned here that the ignition, combustion, and burning of the fuel-air mixture is a very complicated and involved issue that is beyond the scope of this book. We simplify Intake stroke:- Intake valve open- Fuel injectedCompression stroke:- Both valves closed- Spark near top dead centerPower stroke:- Both valves closedExhaust stroke:- Exhaust valve open108 4. THERMODYNAMIC CYCLES this process greatly here. In fact, one of the major issues in an internal combustion engine class in engineering programs is the process of combustion and its mechanisms. Gasoline Octane Number: e gasoline octane number relates to the tem- perature at which gasoline auto-ignites in an engine. e higher the octane number, the higher this temperature will be. Gasoline octane numbers vary between 87 and 91. Gasoline with octane number 87 is called regular, 89 is medium grade, and 91 is premium gasoline, not in quality but in the auto- ignition temperature. e auto-ignition temperature of gasoline is between 246–280(cid:14)C (475–536(cid:14)F) depending on its grade when measured in open air. In engines, the temperature at which the gas may ignite prematurely is much higher, at about 747 40(cid:14)F) [1]. ese numbers do not re- (cid:6) late to the quality or cleanliness of the gasoline at all. Higher octane in a fuel is achieved by mixing diﬀerent hydrocarbons and by adding chemicals to the gasoline that increase its ignition temperature, and therefore, make it more ex- pensive. However, all grades have the same heat energy value. If your engine’s compression ratio is higher, say 11, it will require higher octane gasoline. If it is about 8-9, it can safely work with regular 87-octane gasoline. 22(cid:14)C (1380 (cid:6) Should you use the higher octane gasoline in an engine with compres- sion ratio of about 8-9 as some suggest, thinking it is a better gasoline? e answer is no. Higher octane gasoline will not provide more energy, will not burn better or cleaner, and will not keep your engine cleaner. erefore, for more money, you will get the same result. Using higher grade gasoline in a car that does not require it will make no diﬀerence except in unnecessary higher cost. e only exception is when an engine has carbon deposits in it that cause it to continue to turn even when turned oﬀ, or if the carbon deposit causes pre-ignition. is happens to older engines in which after a long pe- riod of time, carbon deposits accumulate in the cylinder; when the engine is hot, the deposits cause the air-fuel mixture to combust before the piston gets to the ignition point when the spark plug sparks. is premature ignition causes the mixture to burn prematurely, increasing pressure to unsafe levels. is may damage the engine permanently. Additionally, in some engines the same carbon deposits cause the mixture to ignite although the engine is turned oﬀ, continuing to rotate. Higher octane gasoline may improve the situation by decreasing the probability of the mixture igniting prematurely. Otherwise, continue to use the grade that the manufacturer recommends. .. 4.3. SPARK-IGNITION POWER CYCLE 109 Most typical engine management systems found in modern cars have a knock sensor that monitors if the fuel is pre-igniting. In modern computer con- trolled engines, the ignition timing will be automatically altered by the engine management system to reduce the knock to an acceptable level. However, this should not be a reason to use regular gasoline in a high-compression engine that requires premium grade either. .. e third stroke is the power stroke. Within the two rotations of the crankshaft, this portion is the only one that actually delivers power to the engine. As the piston nears the top-dead- center, the spark plug is ﬁred to generate a strong spark within the fuel-air mixture, causing it to combust and burn quickly as the piston clears the top-dead-center. Combustion creates a very high-pressure mixture, which when multiplied by the area of the piston, translates to a very large force, pushing down the piston in its down-stroke and generating a large torque at the crankshaft. Both valves remain closed during this stroke. Just a note here. Do you remember the deﬁnition of work (force multiplied by distance)? Here, the force of combustion gases on the piston pushes it down, therefore moving the piston. Consequently, we have a force that displaces, creating work, or energy. e force is not constant, therefore the rate of work generated is also not constant. Finally, the fourth stroke is the exhaust. As the piston starts to move up again, the exhaust valve is opened, allowing the piston to push out the hot, burned gases, almost completely clearing the cylinder of the spent fuel-air mixture and preparing it for the repetition of the ﬁrst stroke, sucking in fresh air as the exhaust valve is closed and the intake valve is opened. e cycle repeats until the engine is shut oﬀ. What is the purpose of higher compression ratios if they require more expensive gasoline? In general, the higher the compression ratio, the better the eﬃciency of the engine. Engine ef- ﬁciency percentages range from the 20s to the low-30s. As the compression ratio is increased, it compresses the same air more compactly, increasing its temperature and reducing its volume. As a result: 1. e mixture burns better at higher temperatures. 2. Because compression and combustion happen in a smaller volume, the fuel mixes better and burns more quickly and completely. 3. Higher pressures produce larger forces. 4. More power is squeezed from the combustion gases. When an engine operates at high altitudes, since the air is thinner, less air enters the cylin- ders. As a result, compression pressure is lower and the engine delivers less power. Turbochargers are used to increase the intake pressure and push more air into the cylinder, especially at higher altitudes. 110 4. THERMODYNAMIC CYCLES For ideal gases, the ratio between the pressure at bottom-dead-center P1 and top-dead- center P2 can be calculated as a function of compression ratio rc (ratio of volumes at bottom- dead-center V1 and top-dead-center V2 or rc D V1=V2) as: n (cid:19) ; P2 P1 D (cid:18) V1 V2 (4.2) 1:4 for ideal gases. erefore, we can see that for a compression ratio of 8, the pressure where n ratio will be about 18 whereas for compression ratio of 11, the pressure ratio increases to 28, a signiﬁcant increase. (cid:25) Except in speciﬁc applications such as 1-cylinder lawn mower or power tool engines and some small cars with 2- or 3-cylinder engines, most automobile engines have at least 4 cylinders. Five, 6, 8, and even 12 cylinders are also common. In multiple-cylinder engines each cylinder and piston combination operates exactly as mentioned before. However, all connecting rods are at- tached to a common crankshaft. Consequently, the movements of the pistons are all coordinated. For example, in a 4-cylinder engine, if one piston is at top-dead-center and is at the beginning of its intake stroke, another piston might be at bottom-dead-center and at the beginning of its upward motion to compress the fuel-air mixture. A third cylinder may be at TDC and at the beginning of its power stroke, while the fourth is also at BDC and ready for its exhaust stroke. e same sequence continues between all four, and as a result, in every stroke, one of the cylinders is at its power stroke. As mentioned earlier, in 4-stroke engines, the total cycle for each piston requires two ro- tations of the crankshaft or 720(cid:14), and therefore, each stroke is one-quarter of this, or 180(cid:14). Con- sequently, in a 4-cylinder engine, one power stroke occurs at every 180(cid:14) of the crankshaft rota- tion. As a result, the multiple-cylinder arrangement will make the output power much smoother than if there were only one larger cylinder. For a 6-cylinder engine, the power stroke is at every 90(cid:14). erefore, even for the 720(cid:14)=6 same size engine, a 6 or 8-cylinder engine will run much more smoothly than 4-cylinder engines. Notice that since one cylinder at a time produces power the output is more uniform, whereas if they were all arranged to ﬁre simultaneously (which is possible if they are all connected to one crank), the output would vary much more, causing a much rougher ride. 120(cid:14), and for an 8-cylinder engine, it is at every 720(cid:14)=8 D D It should be mentioned here that it is extremely crucial that the valves close and open at exact proper times. e valves are opened and closed by pear-shaped cams on a camshaft (Fig- ure 4.12). To coordinate the valve timing with the position of the pistons, the camshaft is run directly by the crankshaft through gears, a timing belt, or a timing chain at half the speed. As the camshaft rotates, the cams on it turn and open the valves; springs close the valve. All these mo- tions require work, which comes from the crankshaft (part of the power developed by the power stroke). erefore, part of the energy of the engine goes into running its internal parts. Later- model engines may have two valves for intake and two valves for exhaust in order to speed up the process of intake and exhaust. Consequently, a 4-cylinder engine may have 16 valves (speciﬁed as DOHC engine for double-overhead-cam engine). In these engines, since the four valves can be 4.3. SPARK-IGNITION POWER CYCLE 111 in four corners of the combustion chamber in the shape of a plus sign, there is room in the middle for the spark plug. As a result, the combustion starts in the middle of the chamber with equal distance to the perimeter, more completely burning the fuel-air mixture. erefore, these engines produce less pollution and are more eﬃcient too. Figure 4.13 shows the same cylinder-head block with the valve arrangement and the camshafts on it. (a) (b) Figure 4.12: A cam opens and closes the valve as it rotates. 112 4. THERMODYNAMIC CYCLES Figure 4.13: e valve arrangement and the camshaft on a cylinder-head block. To facilitate quicker passage of air in or out of the cylinder, the designer of the engine should want to open the valves as much as possible. However, there is a limit to how much this can be because when the piston gets to top-dead- center, the remaining volume is very small and we do not want the piston to run into the valves. However, there is an additional concern. Like any other mechanical device, it is possible that the timing belt or chain may break. In that case, some valves may remain open while the piston continues to travel to the top, eventually running into them. is can be disastrous to both the piston and the valves, and should be avoided at all costs. is is why manufacturers recommend that every so often, the timing belt be replaced before it breaks. Others use a timing chain, which in general can last much longer without failure. .. IntakevalvesExhaustvalvesSpark plugopening4.3. SPARK-IGNITION POWER CYCLE 113 Additionally, it is possible to design the engine in such a way to ensure that the pistons and the valves will not collide at all. ese engines are referred to as non-interference engines versus interference engines in which the pistons and valves may collide if the timing belt breaks. In non-interference engines, although the engine stops working if the belt breaks, it remains safe and as soon the belt is replaced, the engine can be used again—a minor repair that can be done easily. In interference engines, if the timing belt breaks, the engine may require major overhaul. Find out what the engine in your car is and how often you need to replace the timing belt. .. As you may imagine, there is a very large amount of heat generated in an engine, a large portion of which must be transferred to the environment; otherwise, the engine parts will overheat and will be damaged. In order to keep the engine cool, most engines have a water-cooling system and a radiator that transfers excess heat to the environment. To do this, there are water passages throughout the engine block. A water pump forces the water around the cylinders and the engine body, and later, through the radiator. With the aid of a fan, the radiator transfers the heat out. To keep a constant range of temperatures, a thermostat is used to stop the ﬂow when the coolant is cold, and open when it gets hot. Alternately, some engines, including some automobile engines as well as airplane engines, are air-cooled. In this case, the ﬂow of air over the engine ﬁns cools the engine. e other major issue in engines is friction between the contact surfaces, including the piston and the cylinders, the connecting rod and the cranks, and the cranks and the crankshaft. e friction causes additional heat that must be removed as well. To reduce friction and to cool down these engine parts they are constantly lubricated with engine oil. e crankcase, the big reservoir at the bottom of the engine block, is ﬁlled with oil. An oil pump, sometimes inside the crankcase, pumps the oil between these contact surfaces and also splashes some oil onto the inner surfaces of the cylinder when the piston is at the top, lubricating the contact surface as the piston slides down. Of course, the pumping of the oil also takes away a little more of the engine power. 4.3.2 2-STROKE ENGINES So far we have studied 4-stroke engines. However, as mentioned earlier, there are also 2-stroke engines that are used with simpler systems such as motor bikes or model airplanes. In this case, all necessary parts of the cycle have to happen within two strokes (one complete revolution of the crankshaft) or within 360(cid:14). ere are advantages and disadvantages to 2-stroke engines. One advantage is that since the power stroke happens at every 360(cid:14), we should expect that the power development per cycle is more dense in a 2-stroke engine than in a 4-stroke engine, where the power development is once every 720(cid:14). But due to other ineﬃciencies of the 2-stroke engine, this ratio is not twice as much. Another advantage of a 2-stroke engine is that since it lacks the similar valve arrange- 114 4. THERMODYNAMIC CYCLES ment necessary in a 4-stroke engine, it is usually much simpler with fewer parts. erefore, it is an appropriate design for model airplanes and other applications where cost, space, and weight are important issues. However, as we will see, due to their construction, these engines are more polluting and wasteful, and due to the lack of an oil pump, they require that the oil be added to the fuel. erefore, the engine burns a mixture of oil and gasoline, which makes it even more polluting. It is expected that the mixture lubricates the engine as it goes through the system. Two-stroke engines do not have intake and exhaust valves. Instead, there are two openings on the lower part of the cylinder body that are normally closed when the piston is up and covers them, and open as the piston moves down. In 2-stroke engines, the crankcase is also closed except through a valve, as depicted in Figure 4.14. When the pressure in the crankcase is lower than the outside, it opens and air is entered into the crankcase; when the pressure in the crankcase is higher, it simply closes. erefore, as the piston moves up and creates relatively lower pressure in the crankcase, air is sucked in. As the piston moves down, the valve closes and the air that is trapped in the crankcase is pushed up into the cylinder through the intake opening, all the while sucking a little gasoline-oil mixture with it into the cylinder (see the previous discussion about venture eﬀect). Unlike 4-stroke cycles, more than one thing happens simultaneously during each stroke of the 2-stroke cycles. erefore, we need to start at some arbitrary point, follow all that happens, and eventually end at the same point in order to see how this engine works. Imagine that the piston is moving down and is close to its bottom-dead-center as in Fig- ure 4.15a. By this time, the intake valve in the crankcase is closed due to the increased pressure in the crankcase, the exhaust port is opened and the consumed fuel-air mixture is mostly out, and as the piston continues its downward motion, the intake opening on the cylinder opens as well, and the somewhat-compressed fuel-oil-air mixture in the crankcase is pushed into the cylinder. As the piston starts its upward motion (Figure 4.15b), it closes the intake and exhaust openings, opens the crankcase intake valve bringing new fuel-oil-air mixture into the crankcase for the next cycle, and compresses the mixture in the cylinder until it reaches near the top-dead- center. At that point, a spark combusts the mixture, starting the downward power cycle. Once again, as the piston moves down, it closes the crankcase intake valve, opens the ex- haust and the intake openings in short sequence, and repeating the cycle until the engine stops. Clearly, before all the exhaust gases escape, a new fuel-oil-air mixture starts entering the cham- ber and mixing with it. is reduces the eﬃciency of the engine and also lets some of the new unburned mixture out the exhaust, polluting the air. As was mentioned earlier, these engines are simple, with fewer moving parts, and with more frequent power cycles, but are more polluting and less eﬃcient. 4.4 THERMODYNAMIC REPRESENTATION OF THE SPARK-IGNITION POWER CYCLE Similar to the refrigeration cycle, where we compared the actual work of the system with its thermodynamic representation, we can do the same for power cycles. is can help engineers 4.4. THERMODYNAMIC REPRESENTATION OF THE SPARK-IGNITION POWER CYCLE 115 Figure 4.14: Schematic of a 2-stroke engine. design engines with desired speciﬁcations, calculate the power developed by diﬀerent size engines, and help them design more eﬃcient and better engines. It is crucial for an engineer to work with thermodynamic representations. (cid:0) (cid:0) (cid:0) s/ representations. Figure 4.16a shows the .P Once again, it is very useful to also study the temperature-entropy .T s/ diagram as well as the pressure-volume .P V / diagram. However, since we have not studied entropy as a V / diagram for an tool, we will skip the .T idealized power development cycle. Segment 1-2 represents the compression cycle, and as shown, while volume decreases, pressure increases as the piston moves up toward the top-dead-center. Segment 2-3 represents the combustion of the fuel-air mixture in the chamber. In the idealized cycle, this combustion of the mixture is assumed to be very quick, so fast that ideally (reality is close to this but not exactly) the volume is not changed, but there is a huge increase in the pressure. Segment 3-4 is the expansion of the gases, the development of power in the engine, when high- pressure gases push down the piston and create the force or moment that rotates the crankshaft. As shown, the pressure decreases while volume increases as the piston moves down. At this point, the exhaust valve is opened and the remaining gas escapes, rejecting the remaining heat. Ideally, this also happens instantaneously, and therefore, at constant volume. e diﬀerence between an (cid:0) Spark plugFuel-oilmixtureExhuast portIntakeopeningAirDeflector116 4. THERMODYNAMIC CYCLES (a) (b) Figure 4.15: e strokes of a 2-stroke engine. actual 4-stroke engine cycle and the thermodynamic cycle representation is the remaining two strokes of exhaust and intake. In 4-stroke engines the piston moves up and exhaust gases are pushed out (which require a little more energy), and subsequently the piston moves down and fuel- air mixture is pulled in (also requiring a little more energy). However, the ideal thermodynamic cycle does not show these; actual thermodynamic cycle representation in Figure 4.16b includes an additional section to represent the exhaust (segment 4-5) and intake (segment 5-1) strokes. Also notice that in reality, volumes change during ignition and heat rejection. In reality, combustion requires time to complete. Ideally, it is best to start the combustion before top-dead-center and allow it to complete at the same volume that it started. erefore, in reality, the spark ignition occurs as much as 20(cid:14) before top-dead-center, and ends as shown in Figure 4.16b at about the same volume. e area surrounded by the four segments in the P As mentioned earlier, the ideal thermodynamic representation only represents two of the four strokes of the engine. You may notice that a 2-stroke engine more closely matches this repre- sentation, even though the compression and exhaust are not instantaneous as the cycle assumes. V diagram represents the power de- veloped by the engine at each complete cycle (this is the same as pressure multiplied by volume at each instant. e volume of a cylinder is the area of the base multiplied by its height. In an engine, the volume is the piston area multiplied by the stroke of the piston. Conversely, pressure multi- plied by an area is force, and force multiplied by distance is work. erefore, pressure multiplied by volume is the same as force multiplied by distance, both representing work). An engineer can (cid:0) Spark plugExhuastoutMixture tothe cylinderSpark plugAir to thecrankcasecompression,then ignitionFuel-oilmixture4.4. THERMODYNAMIC REPRESENTATION OF THE SPARK-IGNITION POWER CYCLE 117 (a) (b) Figure 4.16: ermodynamic representation of the spark-ignition power cycle. use this graph to estimate or calculate the power output of the engine. e ratio of the power de- veloped with respect to the chemical energy of the input gasoline determines the eﬃciency of the engine, and can be estimated from the graph. In reality, the eﬃciencies are measured under more realistic conditions. It should be mentioned here that fuel injection has increased the eﬃciency of modern engines. However, there is a large set of desirable characteristics and undesirable con- sequences that play an important role in the eﬃciency of engines and cars in general. e shape (aerodynamics) of a car, the desired acceleration and power, the weight of the car, the accessories that are operated by the engine, etc., all aﬀect the eﬃciency of the car and its MPG rating. High accelerations and high power output means that the engine is very powerful when needed, but in most conditions, its power is excessive and not used, reducing its eﬃciency signiﬁcantly. At the same time, we desire to reduce pollution, and therefore add limiting devices and pollution reduc- tion systems to engines that limit their performance and reduce other desirable characteristics. erefore, like many other engineering decisions, the design of the engine and the chosen size and power characteristics are compromises, based on marketing and engineering considerations. 1-2 Compression2-3 Ignition3-4 Expansion4-1 Heat rejection1234Pressure PVolume VIdealizedPressure PVolume VIgnitionExhaustIntakeCompressionExpansion12345End of combustionRealistic118 4. THERMODYNAMIC CYCLES On a side note, you may have noticed how you were repeatedly asked to imag- ine certain things in order to visualize motions and other happenings in a still picture or ﬁgure throughout the book. It is very common in engineering to vi- sualize motions in still pictures and drawings and to see things in one’s mind. Whenever we design something new that does not exist we see it in our mind’s eye. Some individuals may already be good at this, others learn to do it. In en- gineering problem solving one needs to visualize things that do not exist and see motions and happenings that are not shown. Whether an engine, a mech- anism, a robot, or a thermodynamic cycle, we see much more in a drawing than is shown. .. 4.5 COMPRESSION-IGNITION DIESEL ENGINE POWER CYCLE Compression-ignition diesel engines are quite similar to spark-ignition 4-stroke engines. ey are predominantly 4-stroke, similarly structured to have intake, compression, power, and exhaust strokes. ey also have similar valve operation and construction. e major diﬀerence between them is in the way fuel is delivered; in spark-ignition engines, the fuel and air are mixed and com- pressed before the mixture is ignited by a spark plug ahead of the piston reaching the top-dead- center, whereas in compression-ignition engines only air is compressed and the fuel is injected into it toward the end of the compression stroke. In diesel engines, compression ratios are much higher than in gasoline engines, and therefore, there is no need to use a spark plug to ignite the mixture; it auto-ignites when the fuel is injected into the hot air. In diesel engines, due to the large compression ratios of 14–20 (even higher in larger sys- tems), the air (and not a fuel-air mixture) is compressed to a high degree, signiﬁcantly increasing its temperature. Equation (4.3) shows the resulting temperature as air is compressed (tempera- tures are in Kelvin, (cid:14)K 273 or in Rankin (cid:14)R 460): D (cid:14)C C C D (cid:14)F 0:4; T2 D T1Cr (4.3) where Cr is the compression ratio and T1 and T2 are temperatures before and after compression. Table 4.1 shows the pressure ratios and corresponding temperatures for initial temperature of 20(cid:14)C 68(cid:14)F for diﬀerent compression ratios from Equations (4.2) and (4.3). D When the compression ratio increases, the temperature increases too. For a compression ratio of 8, the approximate temperature will be about 400(cid:14)C (752(cid:14)F), whereas for a compression ratio of 15, it will be 592(cid:14)C (1100(cid:14)F). Since the auto-ignition temperature of diesel fuel is lower than that of gasoline, it can even ignite without a spark at these temperatures. erefore, instead of a spark plug (and its support system) the fuel is injected into the hot, compressed air. 4.6. THERMODYNAMIC REPRESENTATION OF COMPRESSION-IGNITION POWER CYCLE 119 Table 4.1: Compression ratios and associated pressure ratios and temperatures e ﬁrst stroke of a diesel engine is the intake stroke, when the intake valve is opened and air is sucked in. With turbo-charging, the air is pushed into the chamber at slightly higher pressure; this is very helpful at higher elevations where the air pressure is a little lower. As the piston moves toward the top-dead-center in the compression stroke, the air is compressed, increasing its pressure and temperature. Near the top-dead-center, diesel fuel is injected at high pressure into the chamber, and due to the high temperature of the air compared to the auto-ignition temperature of the diesel fuel, it ignites immediately and burns as the piston continues its downward power stroke, creating the torque at the crankshaft. During the fourth stroke, as the piston travels up to the top-dead-center, the exhaust valve is opened, allowing the burnt cases to escape. e valve closes as the piston moves down again while the intake valve is open, repeating the cycle. Advantages of a diesel cycle include higher eﬃciencies due to higher compression ratios, lack of an ignition system, and lower cost of diesel fuel (in most places). Diesel engines are usu- ally powerful and are used for trucks, locomotives, marine applications, factories (to generate electricity and run other machines), and even in some power plants. Disadvantages include the lack of availability of diesel fuel as compared with regular gasoline in gas stations (at least in the U.S.), lower power delivery at higher altitudes, more noise, and diﬃculty starting the engine in cold temperatures. Many diesel engines include a heating element in the combustion chamber for cold-starting the engine. Diesel engines are also more polluting, although they have improved in recent years. However, due to the availability of plenty of air in the mixture, diesel engines produce less CO and more CO2. 4.6 THERMODYNAMIC REPRESENTATION OF COMPRESSION-IGNITION POWER CYCLE Similar to the thermodynamic representation of the spark-ignition power cycle, and for the same reasons, we can also represent the compression-ignition cycle (also called constant pressure com- bustion cycle) with both (T V ) thermodynamic graphs. Figure 4.17a shows the ideal compression-ignition diesel cycle. Segment 1-2 represents the compression of the air in the s) and (P (cid:0) (cid:0) Compression ratioCrPressure ratioP2/P11829446690 811152025ApproximateTemperature T2°C(°F)400(752)490(914)592(1100)698(1288)789(1450)120 4. THERMODYNAMIC CYCLES cylinder as the piston moves up toward the top-dead-center, at which point fuel is injected into the cylinder. Segment 2-3 represents the combustion. e ideal cycle assumes that combustion occurs at constant pressure because fuel continues to burn as the piston moves down. erefore, the pressure increase due to combustion compensates for the pressure loss due to increase in the volume. Segment 3-4 represents the expansion of gases (development of power), and segment 4-1 represents the rejection of remaining heat or exhaust. Figure 4.17b shows a more realistic diesel cycle where the compression/combustion and expansion is broken into two segments. As in the case of gasoline engines, we can also add the intake and exhaust strokes to the diagram. (a) (b) Figure 4.17: ermodynamic P (cid:0) V representation of the compression-ignition cycle. Have you noticed the particular noise that diesel trucks make as they travel downhill at high speeds? is noise is due to braking the truck with the engine instead of powering it with the engine. As we have discussed in previous chapters, kinetic energy of a body is: K D 1 2 mV 2; (4.4) where m is the mass and V is the velocity. Trucks are massive, especially when fully loaded. When they travel at high speeds, their kinetic energy is tremendously large. Slowing a truck in a downhill stretch of the highway is almost impossible without damaging the brakes, assuming they even 1-2 Compression2-3 Injection/combustion3-4 Expansion/power development4-1 Heat rejection1234Pressure PVolume VIdealizedPressure PVolume VRealistic4.7. ROTARY (WANKEL) ENGINES 121 work. To control the speed of a truck in downhill stretches and to slow it down to manageable values, the engine is practically shut down by cutting oﬀ fuel to it while still keeping it engaged with the transmission, forcing it to rotate. As a result, the engine acts as a pump, not an engine, requiring work to turn. is work is provided by the kinetic energy of the truck, slowing it down. In other words, in order for the engine to keep turning without fuel, it takes the kinetic energy of the truck and slows it down. To increase this eﬀect, it is possible to alter the opening and closing of the valves and increase the work still required to turn the engine. All these alterations can be studied and designed using the same thermodynamic representations. It should be mentioned here that we have only looked at three thermodynamics cycles. However, there are many others that relate to other systems, including Stirling and Ericsson cycles, the Carnot cycle, and the Brayton cycle. 4.7 ROTARY (WANKEL) ENGINES Rotary engines follow a similar thermodynamic cycle, but are mechanically diﬀerent from re- ciprocating internal combustion engines. ey have an intake, compression, ignition, expansion, and exhaust segments. However, instead of the usual slider-crank mechanism (piston and cylin- der, connecting rod, and a crank) rotary engines include an epitrochoid-shaped housing with two openings for intake and exhaust and a three-sided rotor as shown in Figure 4.18. e rotor both rotates and orbits around the ﬁxed geared shaft called the eccentric-shaft (e-shaft) with a 1/3 ratio such that for every three rotations of the eccentric shaft, the rotor rotates only once. is forces the three corners of the rotor to always remain in contact with the housing. Spark plugs ignite the compressed fuel-air mixture at the proper time. ese engines are simpler, smaller and lighter, and provide a better power-to-weight ratio. However, they are relatively new compared to the reciprocating engines, and therefore, there is less experience available with the design and service aspects of these engines. As shown in Figure 4.18, at any given time, multiple segments of the cycle happen si- multaneously. For example, in Figure 4.18a, the engine is at the end of its intake, in the middle of its power development, and in the exhaust stroke all at the same time. In Figure 4.18b, it is compressing the fuel-air mixture, developing power, and ﬁnishing exhaust. In Figure 4.18c the engine is taking in the air mixture, the spark plugs initiate combustion, and exhaust has started. Figure 4.19 shows the rotor of an actual engine in the combustion chamber. 4.8 POWER GENERATION (cid:0) s) and pressure versus volume Although engineers use similar temperature versus entropy (T V / diagrams to design and analyze power generation systems (such as in a power plant), .P we will only discuss the principles of these systems here because in real life, these systems can be complicated and there are too many variations that make each system uniquely diﬀerent from another, therefore changing the eﬃciency of the system. (cid:0) 122 4. THERMODYNAMIC CYCLES (a) (b) (c) (d) Figure 4.18: Rotary (Wankel) Engine operation. IntakeExhaustPower(a)CompressionPowerExhaustIgnitionIntake(d)4.8. POWER GENERATION 123 Figure 4.19: A rotary engine’s combustion chamber and rotor in diﬀerent positions similar to posi- tions shown in Figure 4.18. As was mentioned earlier, energy is neither created nor destroyed; it is only converted from one form to another. When we speak of power generation in a power plant, we actually mean the conversion of one form of energy such as thermal or hydraulic or chemical energy into electrical. Power generation, among others, includes conversion of energy from coal, gas, or other hydro- carbon and fossil fuels, nuclear, wind, hydraulic, and solar into electrical energy. In each of these systems, a generator is turned at a constant speed to convert the energy into electrical form (see Chapter 6 about generators and motors). e power needed to rotate the rotor of the generator is provided by one of the aforementioned systems. One of the most common systems used is a steam generator. In these systems, fossil fuel is burned in order to turn water into steam at high pressure and temperature, raising its energy to a very high level. e pressurized and hot steam is then pushed through a steam turbine, causing it to turn. e shaft of the turbine is connected to the generator, and thus, it rotates. e energy needed to boil the water into steam may come from burning coal, gas, other hydrocarbons, nuclear reaction, or similar. Coal is inexpensive and plentiful, but it is very dirty and creates a lot of pollutants, including carbon dioxide. Coal is used all over the world, but in certain countries that use it extensively, the level of air pollution is also very high. Since in recent years gas has become much more available and much cheaper, but burns much more cleanly, many systems have been converted to burn gas. An important issue here is that, as was discussed earlier, due to the second law of thermo- dynamics, it is impossible to assume that all the energy of the steam can be converted to electrical power. is will defy the second law. erefore, at best, the eﬃciency of a power plant can be as high as low-40s percent. is means that close to 60% of the power in the fuel is wasted as rejected heat. Another popular system is to turn the generator of a power plant by a jet engine; here, fuel is burned in a jet engine just like the way it is burned in an airplane engine in order to ﬂy it. However, instead of the jet engine pushing through the air to ﬂy the plane, the shaft is connected 124 4. THERMODYNAMIC CYCLES to the generator, rotating it to generate electricity. e burned air/fuel mixture leaves the system still with high level of energy left in it because it is still very hot and has much kinetic energy (it comes out of the jet engine at a very high speed). erefore, like most other systems, the eﬃciency of the jet engine is low and most of the energy is wasted as rejected heat. An alternative, originally designed decades ago but becoming more popular only recently, is a combined-cycle. In a combined cycle, a generator is powered by the jet engine as described earlier. However, the high energy left in the burnt gas is captured by using it to boil water into steam just like the steam power systems. Since more of the energy is captured between the two systems compared to either of them alone, the eﬃciency of such a system can be more than 60%, a signiﬁcant increase. is indicates how engineering principles can be used to make a system better, more eﬃ- V / diagrams can be cient, and less polluting. ermodynamic cycles and the .T s/ and .P used to design and tune the system to its best possible performance level. (cid:0) (cid:0) 4.9 CONCLUSION As you have probably noticed, the intention of this chapter was not to discuss refrigerators or engines or power generation, but how the study of thermodynamics is necessary in order to know what these cycles are and how they are used by engineers to design and improve these systems. ere is, of course, a lot more to thermodynamics than what is discussed here. But hopefully this discussion shows the importance of thermodynamics in our everyday technological lives. ere are over a billion cars in the world. Imagine if through thermodynamic studies we could improve their eﬃciency by a couple of percentage points. Imagine how much energy we would save and how much less pollution we would have to deal with. 4.10 BIBLIOGRAPHY [1] Gluckstein, M.E and Walcutt, C. “End-Gas Temperature-Pressure Histories and eir Re- lation to Knock,” Transactions of SAE 69, 529, 1961. 108 C H A P T E R 5 125 Moments of Inertia Mass and Area Moments of Inertia, Accelerations, Inertial Forces, Strengths, and Strains 5.1 INTRODUCTION If you think of any classic cartoons, it is inevitable that at some point a beloved animal character will slowly crawl on the branch of a tree as it is pursued by its nemesis, bending the branch more and more until it breaks. Have you ever wondered what would happen if the animal had some knowledge of engineering and could calculate how far it could go before the branch would break (knowing about engineering principles makes cartoons even more interesting)? In real life, we can actually predict the strength of the part we are loading and calculate how much load it can safely carry without breaking. Extending the idea of cartoons to real life we can ﬁnd countless examples where the situation is the same. Simply think of the load on the wings of an airplane. It is actually similar to the situation mentioned earlier. is chapter discusses these relationships and how these ideas are related to each other. Let’s start with the following experiment. Please take a ruler or a piece of wood or similar object and place it between two raised points (perhaps two cups or books) and then press it in the middle as in Figure 5.1a. You will notice that bends. A larger force exerted by you will cause the ruler to bend more. Now turn the ruler 90(cid:14) on its side and repeat as in Figure 5.1b. You will notice that the ruler, under the same force, does not bend at all (or bends very little). So why is it that although it is the same object, with the same dimensions, the same mass or weight, and the same strength, that in one orientation it bends more easily than in another orientation? e reason is that the moment of inertia of the object, in this case the area moment of inertia, is diﬀerent between the two orientations. Although everything else is the same, the area moments of inertia are not. e same is true when we deal with the motion of objects, where mass moment of inertia is a factor. In this chapter we will examine how moments of inertia aﬀect the behavior of objects, both as they relate to static (not moving) and dynamic (moving) situations. It should be mentioned here that area moment of inertia is not an accurate description of this entity, but it is a name which we commonly use. A better name would be second moment of the area. 126 5. MOMENTS OF INERTIA (a) (b) Figure 5.1: How much a ruler bends under the same load depends on its area moment of inertia (second moment of the area) in that orientation. In fact, we can deﬁne both the ﬁrst and second moments of an area. e ﬁrst moment of area is used to calculate the center of the area, and although this has many applications, we will not discuss it here. We will ﬁrst discuss the area moment of inertia; mass moment of inertia will be discussed second. 5.2 SECOND MOMENT OF THE AREA (AREA MOMENT OF INERTIA) Second Moment of Area (or Area Moment of Inertia) is a representation of the dimensions of an area and its distribution (thin, tall, round, square, hollow). Among others, second moment of the area is a measure of how much a body resists bending under a force or resists rotation under a torque (such as in the rotation of one end of a shaft relative to the other end when twisted). Let’s consider a simple bar with a rectangular cross section as shown in Figure 5.2. Although it is very easy to derive the second moment of a rectangular area by integration, we will skip this derivation here. Let it suﬃce to say that the second moment of a rectangular area about the x-axis is: Ix D 1 12 bh3; (5.1) where b is the length of the base of the rectangle and h is its height. Notice that the second moment of the area is independent of the length of the bar. In order to get a feel for the numerical value of the second moment of the area of a rectan- gular beam we need to look at a few examples with real numbers. Please stay with the numerical examples as they clarify the point much better than a simple equation. So let’s assume that the base of the beam is one inch and the height is 4 in. e second moment of the area of the beam 5.2. SECOND MOMENT OF THE AREA (AREA MOMENT OF INERTIA) 127 Figure 5.2: e rectangular cross section of a beam. will be: Ix .1/.4/3 5:33 in4: 1 12 D D Notice that the unit for the second moment of the area is in4 (or cm4, etc.). Also notice that this is a measure of the area and its distribution, meaning the size of the area and its relative width and height, but that it has nothing to do with what kind of material it is or how strong it is. Note also that for this example, the area of the cross section is 1 4 in2. 4 Now let’s do the same, but this time we will turn the beam on its side such that the base 4 in2, but this will be 4 in while the height is 1 in. Notice that the area is still the same 4 time, the area moment of inertia will be: D (cid:2) 1 (cid:2) D Ix D 1 12 .4/.1/3 D 0:33 in4: As you notice, even though the beam is exactly the same, with the same dimensions and the same area, its second moment of area has changed signiﬁcantly, in this particular example a ratio of 5.33/0.33 or more than 16/1, all because we simply turned it around. To better understand this, let’s now consider a beam with a square cross section of 2 4 in2 as before, but the area moment of inertia is: Here too, the area is the same 2 2 (cid:2) D 2 in. (cid:2) Ix D 1 12 .2/.2/3 D 1:33 in4; and the ratio, compared to the previous case, is 5.33/1.33 or 4/1. Once again, factors inﬂuencing the magnitude of the second moment of an area are both the actual dimensions of the area and their distribution. bhxybhl128 5. MOMENTS OF INERTIA We can also deﬁne the area moment of inertia of the same cross section about the y-axis (we will see the application of this shortly). In this case, as in Figure 5.2, relative to the y-axis the height h will be the base and the base b will act as the height, and therefore: Iy D 1 12 hb3: Substituting the same dimensions as before, we will get the second moment of area about the y-axis as 0.33 in4. Notice that the second moment of area about the x-axis for our ﬁrst case 4 is the same as the second moment of area about the y-axis for the second case when b 1. when b 1; h 4; h If we calculate the approximate second moments of area of the ruler of Figure 5.1 where D D D D the ruler is 0.075 in thick and 1.175 in wide, we get the following: For Figure 5.2a: For Figure 5.2b: Ix Ix D D 1 12 .1:175/.0:075/4 12 .0:075/.1:175/4 1 0:000003 in4 0:0119. D D e ratio is 0:0119=0:000003 3,840. is means it will take 3,840 times as much force to bend the ruler of Figure 5.1a the same amount as Figure 5.1b, an amazing diﬀerence (meaning that most probably, the ruler will break before it bends). D Before we continue our discussion of the second moment of area, let’s see how it is used in calculating the deﬂection of the beam under a load as well as its stresses. 5.3 DEFLECTIONS OF A BEAM Deﬂection relates to how much a beam bends; it is usually calculated at its maximum, in this case, in the middle of the beam. e maximum deﬂection for a simple beam, supported at the two ends (like the ruler of Figure 5.1) and a single force in the middle can be calculated by: ymax D (cid:0) FL3 48EI ; (5.2) where ymax is the maximum deﬂection at the center of the beam, F is the load, L is the length of the beam, E is called modulus of elasticity, a material property (which we will discuss later), and I is the second moment of the cross sectional area of the beam, as shown in Figure 5.3a. e negative sign indicates that the beam bends down (below the reference frame x-axis). Since the second moment of the area I is in the denominator, as it gets larger the deﬂection decreases. As you can see, when the ruler of Figure 5.1 is turned 90(cid:14), the only thing that changes in this equation is the second moment of the area of its cross section; otherwise, the load, the modulus of elasticity, and the length remain the same. If the second moment of the area is 3,840 times as large, the deﬂection will be 3,840 time smaller compared to the ﬁrst case, and this is exactly what we see. is fact is used extensively in the design of structures and machine elements in order to limit or increase deﬂections as necessary. For example, a roof beam should not deﬂect much, and therefore, the beam is laid in the direction of the maximum second moment of the area, whereas in the leaf spring of Figure 5.4, used at the rear axle of a truck, the beam (each leaf of the spring) is laid on its base to increase the deﬂections, therefore acting as a spring. 5.3. DEFLECTIONS OF A BEAM 129 (a) (b) (c) Figure 5.3: e deﬂection of a beam under a load at its center. Figure 5.4: A leaf spring used in a truck. e second moment of the area used in Equation (5.2) is Ix. So when do we use Ix and when Iy? It depends on about what axis the beam bends. For example, if the beam of Figure 5.2 LFymaxxyymaxxyLFymaxxyL130 5. MOMENTS OF INERTIA is loaded with a force in the vertical direction, causing it to bend about the x-axis, we use Ix. If the beam were loaded with a horizontal force causing it to bend about the y-axis, we would use Iy. Now assume that instead of one ruler we would use two of them on top of each other as in Figure 5.3b. In this case, since they both bend under the same load, we can assume that each one will carry almost 1=2 of the load, and therefore the deﬂection will be 1=2 of the ﬁrst case, or similarly, that the total second moment of the area is twice as much for two of them, and therefore: ymax D (cid:0) FL3 48E.2I / : Notice that this means that the two rulers slide over each other as they bend. is can be likened to bending a telephone book. As you bend the book, all the pages bend together and slide over each other, but they all maintain their original lengths. Now let’s assume that instead we use a similar ruler or beam, but twice as thick. In this case, the total amount of material would be the same as using two thinner rulers or beams, and the overall dimensions would be similar. However, the second moments of the area are diﬀerent. Whereas with two rulers, the total second moment of the area is: Itotal 2 (cid:2) D 1 12 bh3 D 1 6 bh3; the total second moment of the area for a beam twice as thick (with its height equal to twice the height of the original beam) is: Itotal 1 12 D b.2h/3 1 12 D b.8h3/ 2 3 D bh3; which is four times as large as the ﬁrst case with a deﬂection four times smaller. Notice that unlike the ﬁrst case where the two beams slide over each other, in this case there are no separate layers to slide over each other; the beam bends as one piece. is small diﬀerence is the reason for the diﬀerent magnitudes of deﬂection (and as we will see later, stresses). It is as if you held all the pages of the telephone book together while trying to bend it, if they were all glued; it would strongly resist bending. e sliding of the layers of the beam over each other is called shear. When the layers slide over each other and consequently there is no resistance between them, there is no shear force; when they are prevented from freely sliding over each other, there is a shear force between the layers, and consequently, the book does not bend. Figure 5.5 shows this diﬀerence between a telephone book whose pages are prevented from sliding by two large paper clips versus free sliding of the pages. is also explains why a cardboard is much stronger (stiﬀer) than individual papers with the same thickness. e paper layers in a cardboard are glued together, therefore preventing them from sliding over each other. Plywood is made of thin layers of wood, glued together. ey are strong and resist bending too. However, plywood is also used in the 5.3. DEFLECTIONS OF A BEAM 131 Figure 5.5: When the pages of a telephone book are prevented from sliding over each other, it does not bend as much due to the diﬀerences in second moments of the area. manufacture of bent surfaces such as in modern furniture. In this case, the thin layers are ﬁrst bent to shape, then glued together. erefore, they maintain their shape. So why does the sliding of layers over each other matter? To understand this, let’s once again look at the cross section of the beam, in this case a rectangle. As you see in Figure 5.6, the centerline of the cross section is called neutral axis which is through the center of the area (called centroid). For symmetrical cross sections such as a rectangle or a circle, the neutral axis is in the middle. At the plane of the neutral axis the length of the beam does not change during bending. is means that as the beam bends, its length remains the same at the neutral axis, while all other layers change length. In the case of a beam loaded from above as shown in Figure 5.6, all layers of the beam above the neutral axis must shorten while all layers of the material below the neutral axis must lengthen. e farther away a layer is from the neutral axis, the larger the increase or decrease in its length. Now imagine how much larger the increase and decrease will be when the cross section increases in height. is is why the bending of the beam decreases signiﬁcantly as the height of the beam increases, which is reﬂected as h3 in the second moment of the area equation. Now compare this with doubling the number of beams instead of doubling the height. In the case of two beams, the lengths of the layers of each beam increase or decrease independently based on the beam’s height, while each one slides over the other beam. (ink about the layers of the upper beam below its neutral axis which lengthen, while the layers of the lower beam above its neutral axis which shorten. At the interface, one is shortened, one is lengthened. Consequently, they slide over each other.) Because the height of each individual beam is less, the increase or decrease in length of the layers is much less. Once again, think about the telephone book and how the lengths of the pages must increase or decrease when glued together versus the pages sliding over each other when not glued. However, when the height of the beam is doubled, there 132 5. MOMENTS OF INERTIA Figure 5.6: e neutral axis of a rectangular cross section. is no sliding of the layers; the farther away a layer is from the neutral axis, the larger its shortening or lengthening. Obviously, it is possible to have cross sections other than a rectangle. Examples include cir- cular (such as a shaft), hollow circular (such as a tube), hollow rectangular, I-beams, C-channels, L-shaped angles, and many more. ere are either formulae for calculating the second moments of area for these shapes, or they can be found in tables. e second moment of a circular area is: Ix Iy D D 1 4 (cid:25)r 4; (5.3) where r is the radius of the circular cross section. Notice that due to the symmetry of a circular area, the second moments about the x-axis and y-axis are the same. e second moment of the area for a tube can easily be calculated by subtracting the second moment of the inner area (treated as missing material or as a negative moment) from the second moment of the total area as: Ix D 1 4 4 (cid:25)ro (cid:0) 1 4 (cid:25)ri 4; (5.4) where ro and ri are the outer and inner radii of the tube as shown in Figure 5.7a. e same can be done for a hollow rectangular tube or other shapes. Similarly, we can add second moments of the area together for shapes that are combinations of elements with which we are already familiar. For example, suppose that two rectangular beams of the same size are placed next to each other as shown in Figure 5.7b. e total second moment of the area about the x-axis for both will be the summation of the moments, or: Ix D 1 12 bh3 1 12 C bh3 D 1 6 bh3: (5.5) If you have ever worked with electrical wires you have probably noticed that multi-strand wires are much easier to bend than single-strand wires of the same gauge (thickness). e reason bhNeutral axisLengthsincreaseLengths decreaseLengths increaseLengthsdecreaseF5.3. DEFLECTIONS OF A BEAM 133 (a) (b) Figure 5.7: Second moments of the area for combined areas. is that multi-strand wires consist of many thinner wires that can slide over each other. e total second moment of the area is the summation of the moments of each strand. However, the second moment of the area for the thicker single-strand wire is much bigger than the second moment of the area for the multi-strand wire, and consequently, it is stiﬀer. e same is also true for a steel cable versus a steel bar of the same diameter. Cables are much easier to bend than bars because the second moment of the area for a bar is much bigger too. e strands of the cable can slide over each other; the layers of the bar cannot. Tree branches are the same. icker branches have a larger diameter which increases the area moment of inertia, reducing deﬂection under the force of winds and the weight of its fruit, other branches, animals, and leaves. Being as smart as it is, nature provides adequate strength as necessary. Because the loads decrease as we get closer to the top of the tree or to the tip of each branch, its thickness reduces as well. is reduces the weight and optimizes the design; there is basically enough material to take the load as needed. Second moments of the area for most common standard building beams such as I-beams are available in manufacturers’ tables where engineers readily ﬁnd them. However, for shapes that are not included in tables or are not common, we can easily calculate the second moments of area, some by mathematical integration, others by combining formulae used for common shapes. To understand this, which also helps in further understanding the idea of the second moment of area, let’s consider the Parallel Axis eorem. xyorirbhxyb134 5. MOMENTS OF INERTIA 5.4 PARALLEL AXIS THEOREM As you may have noticed, we calculated the second moment of the area about the neutral axis (we placed the origin of the reference axes at the center and calculated the moments relative to the x-axis and y-axis). However, for many diﬀerent reasons (which will become clear shortly) we may need to calculate the second moment about other axes away from the neutral axis. e second moment of the area about another axis x0, parallel to the neutral axis, can be found from: Ix0 D Ix C Ad 2; (5.6) where A is the area and d is the distance between the two axes. In other words, the second moment of the area about x0 is equal to the second moment about an axis through the centroid plus the area multiplied by the square of the distance between the two axes. is is called parallel axis theorem. For example, the second moment of the area of a rectangle about the bottom of the rectangle instead of its centerline (Figure 5.8) is: Ix0 D Ix C Ad 2 1 12 bh3 .bh/(cid:18) h 2 C D 2 (cid:19) 1 12 bh3 1 4 C D bh3 D 1 3 bh3: Figure 5.8: Parallel axis theorem. Now let’s see where this can be used. Imagine that we model an I-beam (Figure 5.9b), a very common structural beam element whose second moment of area is often needed for stress and deﬂection calculations, as three rectangular-shaped areas attached to each other as shown in Figure 5.9a. e vertical portion is called a web and the horizontal portions are called ﬂanges. In this case, the total second moment of the area about the neutral axis x is the summation of the second moments of each of the three areas, all about the neutral axis x. e second moment of the web can easily be calculated by Equation (5.1). However, the second moments of the ﬂanges must also be calculated about the same x-axis that was used for the web, which is a distance of d away from each ﬂange. erefore, we will need to use the parallel axis theorem Equation (5.6) to calculate the contribution of the ﬂanges to the total second moment. e total second moment bhx'yx5.4. PARALLEL AXIS THEOREM 135 of area for the I-beam about the x-axis is: e second moment of the web about the x-axis is: Itotalx D Iwebx C 2Iﬂangex : Iwebx D 1 12 .t/.h3/: e second moment of each ﬂange about its own axis x0 and x00 is: Iﬂangex 0 D Iﬂangex 00 D 1 12 .b/.t 3/: But since we need the second moment about the x-axis, we use parallel axis theorem and get: Iﬂangex D Iﬂangex D Iﬂangex 1 12 bt 3 Ad 2 1 12 D 0 C .b/.t 3/ C .bt/.d 2/ btd 2: C erefore, the total second moment for the I-beam is: Itotalx D 1 12 th3 2 (cid:18) 1 12 C bt 3 C btd 2(cid:19) : (a) (b) Figure 5.9: (a) A simpliﬁed model of an I-beam, (b) An actual I-beam. To see the signiﬁcance of this let’s assume we make an I-beam out of three pieces similar 4 in. If the three were laid next to each other as in Figure 5.10a, the to our previous example, 1 (cid:2) thdxx''x'ydbtWebFlangeFlange136 5. MOMENTS OF INERTIA total second moment of the area would be the summation of their individual moments about the x-axis: 2Iﬂange Itotal D D Iweb 1 12 C .1/.4/3 2 (cid:18) 1 12 C .4/.1/3(cid:19) 6 in4: D However, if they were assembled (and glued/welded together) into an I-beam as in Fig- ure 5.10b, the second moment of the area would be: Itotal 1 12 1 12 D D th3 C .1/.4/3 bt 3 2 (cid:18) 1 12 2 (cid:18) 1 12 C btd 2(cid:19) C .4/.1/3 C .4/.1/.2:5/2(cid:19) 56 in4: D (a) (b) Figure 5.10: An I-beam versus its constituent parts next to each other makes a huge diﬀerence in the total second moment of the area. is is over nine times as large. e fact that the ﬂanges are at a distance away from the x-axis signiﬁcantly adds to the total second moment as compared to the ﬂanges on the x-axis. is is why the distribution of the material, and not the total area, is important in how much load a beam carries or how much it deﬂects under the load. is example shows the importance of the shape of the beam and how much load the same material carries in a structure or a machine. Now suppose that the same amount of material is used either as a ﬂat sheet or as an I-beam by cutting it into three strips and gluing the pieces together in the shape of an I-beam (Figure 5.11). Even though they are the same amount of area (same material), the I-beam will carry a much larger btxtbbthdxx''x'dbt5.5. POLAR MOMENT OF INERTIA (POLAR MOMENT OF THE AREA) 137 Figure 5.11: A strip of material versus cutting and gluing it into an I-beam. e I-beam carries sig- niﬁcantly more load than the strip. load. Engineers can design structural elements that are much more eﬃcient with less material because they use these engineering principles in their designs. Another major example of where the second moment of the area is increased by distributing the material farther away from the neutral axis is the use of a truss. Because the distance of the element of the truss from its neutral axis is increased, its moment of inertia is also increased signiﬁcantly, enabling it to carry larger loads, especially at larger spans. Figure 5.12 shows an example of a truss used as the main load-carrying element in a ceiling. Look for it in a bridge next time you see one. Figure 5.13 shows a common dish rack. Can you tell why the body is designed this way? In addition to their eﬀect on the shape of the rack, the two sets of semi-circular welded horizontal members create a much larger second moment of area than if they were added together as a thicker rod, were laid next to each other, or were free to slide over each other. Figure 5.14 shows two corrugated pieces of cardboard. Looking at their cross sections and the diﬀerences between their construction, can you tell why the one in Figure 5.14a rolls easily in one direction for wrapping purposes (but not in the perpendicular direction), whereas the corrugated cardboard of Figure 5.14b is stiﬀ in all directions? 5.5 POLAR MOMENT OF INERTIA (POLAR MOMENT OF THE AREA) So far we discussed the role of the second moment of the area in bending. Now imagine a similar situation, but here we intend to twist a bar by applying a moment or torque to one end as shown in Figure 5.15. is twisting of the bar is called torsion. As in bending, when a bar is twisted, one end of the bar rotates relative to the other end. is twisting of the bar is called angular deﬂection. 138 5. MOMENTS OF INERTIA Figure 5.12: A truss used as a load-carrying element in a ceiling. e second moment of the area of the truss is signiﬁcantly larger due to the way the elements are distributed farther away from the neutral axis. Figure 5.13: e two sets of semi-circular horizontal members of the dish rack increase the second moment of the area, decreasing its deﬂections. In torsion, we use the polar moment of the area (polar moment of inertia), J , which for a round shape is: J D 1 2 (cid:25)r 4: (5.7) 5.5. POLAR MOMENT OF INERTIA (POLAR MOMENT OF THE AREA) 139 (a) (b) Figure 5.14: Corrugated cardboard is stiﬀ due to its increased area moment of inertia. Figure 5.15: Torsion of a bar. Iy Notice that this is twice as large as Ix (Equation (5.3)), which makes it equal to Ix (for a symmetrical cross section). e polar moment of the area can be similarly calculated for other shapes, including with the use of the parallel axis theorem. C Similarly, we can also deﬁne modulus of rigidity G, a material property similar to the modu- lus of elasticity E that was used in calculating deﬂections in Equation (5.2). In torsion, the angular deﬂection (angle of twist) is: T L J G ; (cid:30) D (5.8) where (cid:30) is the angular deﬂection, T is the applied torque, and L is the length of the bar. When torque or the length of the bar increase, the angular deﬂection increases as well. However, as the polar moment of the area increases, the angular deﬂection decreases. Similar to bending, the polar moment of the area directly aﬀects the twisting of the bar. TorqueAngular deflectionAngle of twist140 5. MOMENTS OF INERTIA e polar moment of the area for a hollow bar is: J D 1 2 (cid:25) r 4 o (cid:0) 1 2 (cid:25) r 4 i ; (5.9) where ro and ri are the outer and inner radii of the bar. is is the polar moment of the larger area, minus the polar moment of the missing (hollow) area. Now imagine a solid shaft with a radius of 0.5 in. e polar moment of the area will be: J D 1 2 (cid:25) r 4 o D 1 2 (cid:25).0:5/4 D 0:098 in4: e cross sectional area of the shaft will be: (cid:25)r 2 A D D (cid:25).0:5/2 D 0:785 in2: Now imagine that we use the same amount of material (same cross sectional area), but we make the shaft hollow. In this case, the outer diameter of the shaft will have to increase to accommodate the hole and still have the same area. ere are countless diﬀerent choices available for the inner and outer diameters to achieve the same area. Let’s choose the outer diameter of 0.75 in. In that case, the inner diameter will be: 0:785 ri D D (cid:25).0:75/2 0:56: (cid:0) (cid:25).ri /2 erefore, the shaft will be a hollow tube with 0.56 and 0.75 inner and outer radii as shown in Figure 5.16. e polar moment of the area with the new dimensions will change to: 1 2 (cid:25) r 4 i D 1 2 (cid:25).0:75/4 1 2 (cid:0) (cid:25).0:56/4 (cid:25) r 4 1 2 0:343: o (cid:0) J J D D Notice how much larger the polar moment of the area is although the same amount of 3:5 times as large. material has been used. e new polar moment of the area is 0:343=0:098 As long as we do not make the new shaft’s wall thickness so small that it will collapse under the load, increasing diameter also increases the polar moment of the area. Obviously, this is much more eﬃcient in material use. D An example of this is the driveshaft of an automobile. When the engine of a car is in the front but the car is rear-wheel driven (examples include many older cars, some larger cars, and most trucks), a driveshaft connects the transmission (in the front) to the diﬀerential (in the back) as shown in Figure 5.17. In order to increase the eﬃciency of the system and lower the weight and the cost of the car, the shaft is hollow. So far we only discussed the role of second moment of the area (and polar moment of the area) in deﬂections. Actually, although in certain applications deﬂection calculations might be the 5.6. STRENGTH OF MATERIALS: STRESS, STRAIN, AND MODULUS OF ELASTICITY 141 Figure 5.16: e polar moment of the area increases signiﬁcantly as the shaft is made hollow but with the same area. Figure 5.17: e driveshaft of a car connects the transmission to the diﬀerential. primary concern, in most cases stress calculations are even more important because stress calcu- lations determine whether or not a structural or mechanical element can carry the load to which it is subjected. Before we discuss this issue, let’s ﬁrst look at the material strength characteristics and see how they are related to moments of the area and mechanical stress. 5.6 STRENGTH OF MATERIALS: STRESS, STRAIN, AND MODULUS OF ELASTICITY If you attach a weight to a spring it will stretch (elongate). For larger weights, the stretch will be larger. If you plot the weights versus elongations, you will notice that for the most part, the r = 0.5 inA = 0.785 in2J = 0.098 in4r = 0.75 inA = 0.785 in2J = 0.343 in4r = 0.56 in142 5. MOMENTS OF INERTIA relationship is linear. is means that for example, if the weight is doubled, the elongation will be doubled too. erefore, we can deﬁne a relationship between the weight (which is a force) and the elongation as: F d ; k D (5.10) where F is the force (or weight) in lb or N (Newton, a unit of force in SI system of units), d is the elongation in inches or meters, and k is the spring constant in lb/in or N/m. k is a measure of the stiﬀness of the spring; the larger the stiﬀness, the harder it is to stretch or compress the spring. Now imagine that you continue to add to the weight until the spring stretches to its fullest. At that point, the spring does not stretch as freely as before. erefore, the relationship between the force and deﬂection changes at this point and it becomes much stiﬀer, a non-linear relationship. Figure 5.18 shows a simpliﬁed depiction of this behavior. Figure 5.18: e spring stiﬀness is the ratio of applied force and the resulting elongation. A similar thing happens to a metal bar. Figure 5.19 shows a typical bar that is used to study the characteristics of many materials, including metals. e bar is placed in a machine that pulls the two ends, applies a force to the bar, and measures the elongation of the bar under the load. In this example the bar was pulled until it broke. Note how the area that broke was reduced in diameter before breaking. As it may be clear to you, the bar’s elongation is inﬂuenced by how thick it is; the thicker the bar, the smaller the elongations for the same force. erefore, to measure the strength of the material without the inﬂuence of its size, the force is normally divided by the area. is is called stress. It may also be clear that the longer the bar is, the larger the total elongation will be (think of a short rubber band and a long one; the long rubber band stretches more than the short one). erefore, in order to eliminate the eﬀect of length and measure only the material property, the elongation is divided by the length of the bar. is is called strain. Consequently, we can study the relationship between stress and strain. is way, the relationship is about the ForceElongationk5.6. STRENGTH OF MATERIALS: STRESS, STRAIN, AND MODULUS OF ELASTICITY 143 behavior of the material without regard to its thickness or length. erefore: F A ; (cid:27) D (5.11) where (cid:27) (read sigma) is the stress, F is the applied force, and A is the cross sectional area of the bar, and: l 0 l ; " D (5.12) where " (read epsilon) is the strain, l is the original length, and l 0 is the elongation. Figure 5.19: A typical material testing specimen. Calculation of the stress in any structural or machine element is crucial in ensuring that the structure or the machine will be able to take the load to which it is subjected. If stresses exceed the strength of the material, it will fail. Stress calculations are among the most important activities that a design engineer might perform. At other times, not just the stresses but also the deﬂections are considered because excessive deﬂections may also cause failure. erefore, it is not just the calculation of stresses and strains, but also the understanding of the behavior and strengths of the material used that are extremely important in engineering design and analysis. Figure 5.20 shows the relationship between stress and strain for steel. As you see, when a force is applied to steel, it stretches; when the force is removed, it returns to its original length. erefore, a steel bar acts just like a spring, albeit it is much stiﬀer. is is an extremely important characteristic that is used in many engineering calculations to ensure that a part can carry the load to which it is subjected. As shown in Figure 5.20, to a certain point, the steel bar will elongate proportionally to the applied force, at which point its behavior changes. is is called proportional stress limit Sp and it is a very important characteristic. e ratio of stress over strain within this limit (the slope of the line) is also a very important characteristic of materials, called the modulus Diameter dArea ALength lForce FElongation l'Force F144 5. MOMENTS OF INERTIA of elasticity, E: E D (cid:27) " : (5.13) Figure 5.20: e relationship between the stress and strain of steel. Modulus of elasticity for common steel is about 30 106 psi or 200 GPa (Giga-Pascal) in SI units. is means that although a steel bar behaves like a spring, it requires 30 million lbs of force per square-inch of the area to elongate it 1 in/in. (cid:2) Up until the proportional limit, steel behaves linearly. For small additional forces, the elon- gation is not linear, but when the force is removed, the bar still returns completely to its origi- nal length without any permanent change in its length. is limit is called elastic limit or elastic strength or yield strength, Sy. However, if the force is increased beyond this limit, the bar will per- manently elongate, although when the force is removed the bar shortens an amount representing the elastic elongation. So for example, if a machine part is subjected to a force large enough to take it beyond the elastic limit, it will permanently change (and this is why it is called yield strength, because at this point the material yields to a new shape or length). is change is called plastic deformation. When the load is removed, it shortens an amount equal to the elastic deformation, but with a permanent elongation that no longer goes to zero. In many situations in design, this is considered a failure of the part, even if it has not broken. Imagine a part of an engine permanently elongating while rotating; the engine will no longer function properly even if no parts are broken. However, most parts are designed with a safety factor to ensure we do not reach the yield strength. And this is why we dare load a car with large loads, but still do not expect it to plastically change forever. We know it deforms under the additional load, but since it is elastic, as soon as the load is removed, it returns to its original shape. If the force is increased further, even for relatively smaller amounts, the steel bar will elon- gate in much larger amounts until it eventually approaches the maximum stress it can take, called StressStrainSFSuSpSy5.6. STRENGTH OF MATERIALS: STRESS, STRAIN, AND MODULUS OF ELASTICITY 145 ultimate strength, Su. At that point, the cross section of the area becomes smaller (because it plastically yields) and the material breaks and fails at SF . Other types of steel behave somewhat diﬀerently. For example, a piece of high-carbon steel is much stronger, but also very brittle, and therefore, does not elongate as much although it can take higher loads. erefore, the stress-strain graph representing it, as well as its proportional, yield, and ultimate strengths and its modulus of elasticity will be diﬀerent. Similarly, other metals (aluminum, brass, copper, stainless steel, and other alloys) all behave a little diﬀerently, but follow similar patterns. Additionally, other materials such as glass, concrete, wood, and plastics can also be characterized similarly even though the numbers and the patterns of behavior may be diﬀerent. For example, glass is a very hard but brittle material. erefore, it does not yield much, and if subjected to bending it suddenly breaks before any permanent elongation or yielding has occurred. As shown in Figure 5.20, when a part is subjected to loads beyond its yield strength, it permanently deforms, although the elastic deformation is recov- ered when the load is removed. However, what happens here is that if the same part were to be subjected to a new load, the load would have to be larger than before in order to permanently deform the part again (shown as the dot- ted line). is is because, as you may notice in Figure 5.20, the portion of the graph between the yield strength and ultimate strength has a small upward slope, and therefore, every time the load must be larger to have the same ef- fect. is means that the material actually becomes harder and stiﬀer every time it is loaded beyond the yield strength. is is called cold-working, and is a common method of strengthening parts. For example, cold-rolled steel is stronger than hot-rolled steel because if it is heated, the material is softer and it does not require as much force to yield it. It is interesting to note that human nature is somewhat similar. People who never work hard or never endure hardships behave diﬀerently than people who experience diﬃculties and hardships and learn from these experiences. A broken toe, an illness, lost belongings, failures, and social diﬃculties all con- tribute to our resilience. Every experience that involves some hardship beyond our “yield limit” will make us tougher. We even have a name for people who have never had hardships. We call them spoiled. And just like metals, where if the loads become too large for the material it will break and fail, we hope that the hardships to which humans are exposed will not be beyond their ca- pability, causing complete failure. Otherwise, experiences with hardships are good for us; they make us stronger. .. 146 5. MOMENTS OF INERTIA 5.7 ROLE OF MOMENTS OF THE AREA IN STRESS CALCULATIONS Now that we have learned about stresses, we can go back to the previous discussion about moments of the area. In Sections 5.3 and 5.5 we discussed the linear deﬂection of a beam in bending and angular deﬂection of a bar in torsion and saw how we can calculate these deﬂections for simple elements. Similarly, we can calculate the stresses in bending and torsion (and of course in more complicated loading situations that we will not discuss here). For a bending beam as in Figures 5.3 and 5.5, the maximum stress (which happens to be in the middle of the beam) is: M C I ; (cid:27) D (5.14) where (cid:27) (read sigma) is the stress, M is the moment, C is the distance to the top or bottom of the beam from the neutral axis (for maximum stress), and I is the second moment of the area. e second moment of the area also plays a fundamental role in the calculation of stresses as it does for deﬂections. e larger the second moment of the area is, the smaller the maximum stress will be. Also notice that if we let C 0, indicating a distance of zero from the neutral axis, Equation (5.14) shows that the stress on the neutral axis will be zero (and consequently, there is no deﬂection either); it linearly increases as we move away from the neutral axis to the top or bottom. D Similarly, for torsion, the maximum (shear) stress in the bar of Figure 5.15 is: T r J ; (cid:28) D (5.15) where (cid:28) (read tau) is the shear stress, T is the applied torque, r is the radius of the bar, and J is the polar moment of the area as discussed in Section 5.7. Once again, polar moment of the area is a fundamental element in the calculation of stresses as well as deﬂections. e larger the polar moment of the area is, the smaller the shear stress will be. is also shows that the stress at the center of the bar (where r 0) is zero, increasing as we get closer to the outer edge. In fact, the material closer to the center is almost wasted; it carries little load (because stresses are low). is is another good reason to use a hollow shaft rather than a solid one. e same material spread out into a hollow shaft will have a larger polar moment of inertia and will also save on wasted low-stress material. D e diameter of tree branches becomes smaller closer to the tip compared to the base as shown in Figure 5.21. Since the load on the branch is smaller closer to the tip, the diameter and the moment of inertia of the branch are smaller, resulting in less weight and increasing the tree’s eﬃciency. e second moment of the area and the polar moment of the area are very important con- cepts in engineering. Understanding the role of moments of the area in this process is a funda- mental requirement for engineers. 5.8. MASS MOMENT OF INERTIA 147 Figure 5.21: Tree branches become smaller closer to the tip because the load on the branch is smaller too. 5.8 MASS MOMENT OF INERTIA As area moments of inertia (including the polar moment of the area) are a representation of the distribution of the area, mass moments of inertia are representations of how the mass is dis- tributed. So, even though two diﬀerent parts may have the same total mass, depending on their shape, their mass moments might be very diﬀerent. Similarly, as the area moments of inertia directly impact how the material reacts under the inﬂuence of external loads and how large the stresses and strains are, mass moments of inertia directly aﬀect the way the mass reacts to acceler- ations, causing it to move diﬀerently depending on not just the mass, but its distribution too. is has a direct eﬀect on our daily lives and the way things move and react as we work with them. So let’s ﬁrst talk about the context in which mass moments of inertia play a role before we learn what they are and how to calculate them for simple cases. In Chapter 3 we had a discussion about linear accelerations and how mass reacts to accel- erations (please review if necessary). As mentioned there, imagine that you are sitting in a car, accelerating forward. You will notice that you are pushed back against the seat. In this case, since the acceleration vector is forward (causing the car to speed up in the forward direction), the mass of your body reacts to this acceleration; due to its inertia (sluggishness), the body tends to stay in the condition it is in and not change, and therefore, reacts to a push forward by resisting it. e same is true in other conditions. For example, if a body is moving at a constant speed it tends to remain at that speed and reacts to speeding up or slowing down. erefore, when braking and consequently having a backward acceleration, the body tends to move forward to react to it unless it is restrained. In fact, if this deceleration happens very quickly (such as in an accident when the slow-down is extremely quick, creating a huge backward acceleration), the body may spring forward enough to hit the front windshield. is is why we have seat belts and airbags to restraint 148 5. MOMENTS OF INERTIA the body and keep it from hitting the windshield. Please see Sections 3.2.4 and 3.4 for additional discussions. e discussion above is about the relationship between a force, linear acceleration, and mass. A similar relationship exists in angular motion. In this case, the relationship is between a moment or torque (instead of a force), angular acceleration (instead of linear acceleration), and a, we F mass moment of inertia (instead of mass). erefore, similar to the linear case with E E can write an equation that describes the angular version as: D m T E I (cid:11); E D (5.16) T is the torque, I is the mass moment of inertia, and (cid:11) is the angular acceleration vector. where E E is means that the torque induces an angular acceleration in a body proportional to the mass moment of inertia that causes it to rotate. A larger torque creates a larger angular acceleration. However, if the mass moment of inertia is smaller, the angular acceleration will be larger for the same torque, and vice versa. For example, consider a fan with the blades attached or removed. If the blades are not attached to the motor when it is turned on, the motor shaft rotates quickly in a very short period of time. is means that its angular acceleration is very high, and therefore it speeds up from zero to its maximum velocity very quickly. However, when the blade is attached to the motor and it is turned on it takes a relatively long time before the blades reach their maximum speed. Although it is true that the blades are also trying to push out the air and therefore add to the load on the motor, the much-lower angular acceleration is due to the much larger mass moment of inertia of the blades. Assuming that the torque of the motor is essentially the same, because the mass moment of inertia is larger, the angular acceleration is lower, requiring much more time to speed up to its maximum. It may appear that the lower angular acceleration might just be the result of adding mass to the motor. However, if we were to add a metal ball with the same total mass equal to the blades to the motor and repeat the test, we would ﬁnd that although the angular acceleration would be lower than no mass, it would still be much higher than with the blades. is indicates that it is not only the mass that matters but how it is distributed. In fact, we might mention that the rotor of the motor also has a mass moment of inertia that aﬀects the angular acceleration of the rotor. Even when there are no blades attached to the rotor, the moment of inertia of the rotor is still present. We simply add to it when we attach the blades. e actual mass of the rotor may be much larger than the mass of the (plastic) blades, but the mass moment of inertia is much less compared to the blades. And this is why if we just add a ball with a mass equal to the blades, it will be as if the rotor were a bit heavier with little eﬀect. But with the blades attached, the mass moment of inertia is increased signiﬁcantly, aﬀecting the angular acceleration signiﬁcantly. So let’s see how this can be analyzed and calculated. is analysis will help us understand what mass moment of inertia really is. As shown in Figure 5.22, the mass moment of inertia for a plate of radius r, thickness t, and mass m about an axis x going through its center is: 5.8. MASS MOMENT OF INERTIA 149 Ix D 1 2 mr 2: (5.17) Figure 5.22: Mass moment of inertia for a plate. Assume that a plate is 4 inches wide (2 inches in radius) and 1 inch thick. Its mass can be calculated by multiplying the volume by its density. e volume of the plate is its area multiplied by its thickness, or: Vol (cid:25)r 2t (cid:25).2/2.1/ 12:57 in3: D D D e speciﬁc weight of steel is 490 lb/ft3 (0.2837 lb/in3). is means that the density of steel 0.000734 lbs2/in4 (this strange looking unit is the result of expressing the mass in English 0.00783 kg/cm3 in SI units. erefore, the mass of the plate is: is (cid:26) units). is is equivalent of (cid:26) D D m Vol (cid:26) (cid:2) D D .12:57/.0:000734/ 0:0092 lbs2=in: D e mass moment of inertia of the plate is: Ix D 1 2 mr 2 1 2 D .0:0092/.22/ D 0:0184 lbs2in: Now let’s take the same amount of material as before (same thickness, area, volume, and mass), but make it into a ring with an outside diameter of 5 inches and an inner diameter of 3 inches (outside and inside radii of 2.5 and 1.5 inches), as shown in Figure 5.23a. e area of the ring with ro as its outer radius and ri as its inner radius is: Vol t (cid:0)(cid:25) r 2 o (cid:0) D (cid:25) r 2 i (cid:1) D 1 (cid:0)(cid:25).2:52 1:52/(cid:1) (cid:0) D 12:57 in3; which is the same as before, as will be its mass (0.0092 lbs2/in). However, the mass moment of inertia of the ring is: Ix D m (cid:0)r 2 o C r 2 i (cid:1) : (5.18) 1 2 xtr150 5. MOMENTS OF INERTIA Substituting the new radii in this equation gives us: Ix D 1 2 .0:0092/.2:52 1:52/ C D 0:0391 lbs2in; which is more than twice as large as the solid plate. Although we did not use any more material, simply by changing the size (a diﬀerent distribution of mass), we more than doubled the mass moment of inertia. (a) (b) Figure 5.23: e mass moment of inertia of a ring is changed as the distribution of the material changes. Now consider a third version: Assume we still use the same amount of material, but this 4:58 inches as shown in Figure 5.23b. 5 and ri time form the ring to have dimensions of ro In this case, too, since the area of the ring and its thickness are the same, so is its mass of 0.0092 lbs2/in. However, the new mass moment of inertia will be: D D Ix 1 2 1 2 D D r 2 i (cid:1) m (cid:0)r 2 o C .0:0092/.52 4:582/ C D 0:211 lbs2in; D which once again is nearly 0.211/0.0184 11.5 times as large. is is the power of the way the mass is distributed. As the material is pushed outwardly, the mass moment of inertia increases. Figure 5.24 shows a typical way this is used in the design of machinery. In this ﬁgure, instead of attaching a uniform-thickness plate to the air motor, the same amount of material is made into the shape of a ﬂywheel with a much larger mass moment of inertia. e larger moment of inertia is needed for smooth operation of the air motor, but it is provided without using a massive plate. In a typical ﬂywheel, most of the mass is moved into the rim, which is connected to the hub with a xtrorixtrirothin plate. e same design is used in reciprocating internal combustion engines (used in all cars) to smooth out the variations in the thermodynamic cycle. See Chapter 4 for more discussion. 5.8. MASS MOMENT OF INERTIA 151 Figure 5.24: A typical ﬂywheel is designed to have a larger mass moment of inertia without being too heavy by pushing most of the material outwardly to the rim. If you were to turn on a fan with the blades attached, as in Figure 5.25a, you would notice that the blades take a while to reach their maximum rotational speed. However, if the blades were removed as in Figure 5.25b, the motor shaft would reach its maximum speed much more quickly, in a fraction of the time needed with the blades. As we discussed earlier, Equation (5.16) shows the relationship between the mass moment of inertia and angular acceleration. A fan motor without the blades has much less moment of inertia (of the rotor) than with the blades, especially since the mass moment of inertia of the blades, with their outwardly distribution, is relatively large. erefore, the angular acceleration at the shaft without the blades is much larger than with the blades, and consequently, the motor reaches its maximum rotational speed much more quickly. is is even more apparent in ceiling fans, where the mass moment of inertia of the long blades is even higher. Many bicycle enthusiasts look for a lightweight bike, usually at much higher cost, thinking that it is easier and faster to ride. Although the weight of the bike is a factor, the acceleration and how quickly the maximum speed is achieved are more importantly aﬀected by the weight, size, and weight distribution of the tires. As you might guess by now, since bike tires rotate, their mass moment of inertia directly aﬀects the angular acceleration, and consequently, how quickly the maximum speed is achieved. erefore, skinnier tires used in racing bicycles that are lightweight 152 5. MOMENTS OF INERTIA (a) (b) Figure 5.25: A fan motor accelerates much more slowly when the fan blades are attached as compared with the blades removed. will have lower mass moment of inertia compared with fatter and heavier tires used in mountain bikes. Some bike owners go as far as drilling holes in the sprockets of their tires, thinking they are reducing the moments of inertia (as well as mass). How much eﬀect do you believe this will have on the overall mass moment of inertia of the tires? Almost none. However, reducing the weight of the rim and the weight of the rubber used in the tire will signiﬁcantly aﬀect the moment of inertia. Now let’s look at a diﬀerent situation. e propellers of airplanes and helicopters also rotate about the shaft, and like the aforementioned examples, we should expect their mass moments of inertia to aﬀect the torque needed to rotate the propeller and the accelerations achieved. So ﬁrst let’s look at how we can calculate their approximate mass moments of inertia. To do this, let’s model the shape of a propeller as a slender bar. is approximation is useful for seeing what is important, but not accurate enough in practical terms. e actual mass moment of inertia can be found either experimentally or by writing more complicated equations. Figure 5.26a shows a slender rod (the length is much larger than the diameter). Assume that the rod is attached to an axis at its center and rotates in a plane. Equation (5.16) still applies here; the applied torque is equal to the mass moment of inertia times the angular acceleration. e mass moment of inertia of a slender bar is: 5.8. MASS MOMENT OF INERTIA 153 1 12 I D mL2; (5.19) where m is the mass and L is the total length of the slender bar. Now suppose that the bar rotates about one end, not the center. In this case, we need to calculate the moment of inertia about the end, not about the center. As with the second moment of the area about an axis other than the centroidal axis, we need to use the parallel axis theorem to calculate the mass moment of inertia about an axis other than the one at the center of the mass. is, similar to Equation (5.6) for area moment of inertia, can be written as: IB Io C D md 2; (5.20) where IB is the mass moment of inertia about an axis B away from the center of mass, Io is the mass moment of inertia about the center of mass, and d is the distance between the two axes. erefore, for the slender bar of Figure 5.26b, the mass moment of inertia about one end will be: IB Io 1 12 D D 2 (cid:19) m(cid:18) L 2 C mL2 1 4 C mL2 1 3 D mL2: Obviously, this moment of inertia is 4 times as large, resulting in an acceleration that is 4 times as slow, or requiring 4 times as large a torque to rotate the bar at the same rate. Figure 5.26: e mass moment of inertia of a slender bar. Just to clarify this in a diﬀerent way, let’s recalculate the mass moment of inertia of the slender bar about its center of mass by assuming that it is the summation of two bars, each with a length half as much and a mass half as much, attached together at one end. erefore, the total mass moment of inertia will be twice the moment of inertia of a bar at half the length and half LL/2LL/2BO154 5. MOMENTS OF INERTIA the mass, calculated at its end, or: 2 (cid:0)I 0(cid:1) 2 1 3 (cid:18) 1 2 m(cid:19) (cid:18) L 2 D 2! (cid:19) 1 12 mL2; IO D D which is exactly the same as before for the mass moment of inertia of a slender bar about its center of mass. erefore, when propellers are longer or heavier, their mass moments of inertia increase. In helicopters, where the propellers are much longer than in airplane engines, it is almost impossible to turn them as fast as in an airplane; their mass moment of inertia is much larger, putting a much larger load on the engine. As you can see, both the second area and mass moments of inertia play a fundamental role in many things in our daily lives. For example, you can see the eﬀects of the moment of inertia of the wings of a bird both in terms of their strength under the weight of the bird as well as how much force (or moment) is needed to ﬂap them and in the eﬀects of the moments of inertia of the legs of diﬀerent creatures, including humans, in running. You can hopefully imagine these same eﬀects considered in the design of a bridge, the ﬂight of an airplane, the rotating parts of an engine, and countless other devices and machines we use every day. Understanding these concepts helps us both control their eﬀects and use them to our advantage. C H A P T E R 6 155 Electromotive Force Motors, Transformers, AC and DC Currents INTRODUCTION 6.1 Each of the two generators of the Diablo Canyon nuclear power plant in San Luis Obispo County generates over 1,100 megawatts of power, enough for about 3 million people. e Ames Research Center national full-scale subsonic wind tunnel in Mountain View, California, is 40 80 ft and creates winds of up to 350 mph (560 km/h), large enough to test a real, full-scale Boeing 737. e fans and the motors running these fans are enormous. And yet, the generators used to recharge a hand-held ﬂashlight are the size of a large olive and the motors used in small remote-control servomotors are about ¼ inch in diameter. What is important is that the largest and the smallest of motors and generators are actually very similar in the way they work and that they all follow Faraday’s Law which we will study later. (cid:2) When you simply plug in an electric motor (whether as part of a device or stand-alone) it simply turns and provides a torque that allows the device to do its job. e same is true for a DC motor that is connected to a battery. You may also use a simple charger (or transformer) to recharge your batteries, whether in a cell phone, camera, computer, hybrid car, or toy. In fact, you may have heard that the high voltage (as large as 500,000 volts) of electric power is lowered to the household voltage (110 volts) with a transformer before it is delivered to your place of residence or work. All these examples are based on a phenomenon called electromotive force or emf. A similar phenomenon that works in the opposite way, called back-emf, is also an important issue that aﬀects the way these systems work or are designed. In this chapter we will study these two phenomena, how they are used, and where they appear to aﬀect our daily lives. But ﬁrst let’s learn the diﬀerence between voltage and a current, and their relationship. ese terms appear in all issues related to circuits and electric devices. 6.2 INTRODUCTORY TERMS: VOLTAGE, CURRENT, AND RESISTANCE Equation (6.1) shows the relationship between voltage (V ), current (I ), and resistance (R). But what is the physical meaning of these terms? To understand it, let’s make an analogy. We will look at a simple ﬂuid system to show how they are related. IR: V D (6.1) 156 6. ELECTROMOTIVE FORCE Imagine a tank of water with a pipe attached to it, full of water as shown in Figure 6.1. At the bottom of the pipe there is a valve, closed at this time, which prevents the water from ﬂowing in the pipe. e pressure at the bottom of the pipe is a function of the density of water and its height. Larger heights (h) will increase the pressure at the bottom of the pipe. Figure 6.1: A tank-pipe-valve system shows the analogy between hydraulic and electric systems. Now imagine that we open the valve just a bit. As a result, water will start to ﬂow slowly at the bottom. e amount of water ﬂowing is a function of the pressure and the opening of the valve. At this point, the valve provides resistance to the full ﬂow of the water. Further opening the valve will increase water ﬂow until it is fully opened, at which time the ﬂow is at its maximum rate. Obviously, at higher pressures, the ﬂow will be larger too. Notice that regardless of the valve opening, the ﬂow is also a function of the diameter of the pipe. Smaller diameters provide more resistance to the ﬂow. For example, if the pipe were a hose with a small diameter, the ﬂow would be less than if it were a large pipe. erefore, the pipe diameter also introduces resistance to the ﬂow. Electrical systems can be explained the same way. e water pressure is analogous to the voltage. e ﬂow of the water is analogous to the current which represents how many electrons pass a cross section of the wire. e valve represents a variable resistance similar to resistors that are used in circuits to control current. e resistance of the pipe too represents the electrical re- sistance of wires and conductors. As shown in Equation (6.1), when the resistance of a circuit increases, the current decreases. By changing either the voltage or the resistance, the current ﬂow can be controlled. For a system (for example a motor) where the resistance is constant, when the voltage changes, the current changes accordingly. In mechanical systems the equivalent analo- gous elements are force and voltage, velocity and current, and viscous coeﬃcient of friction and hresistance. To understand this, think of walking in a pool. You need to exert yourself to move in the water. e thicker the ﬂuid, the harder it will be to move. 6.3. MAGNETIC FIELDS 157 6.3 MAGNETIC FIELDS Imagine that there is a magnetic ﬁeld present. is can happen if you have a permanent magnet or if you wrap a wire into a coil and run a current through it, as shown in Figure 6.2. In the vicinity of the coil or the magnet, there will be a magnetic ﬁeld such that if we bring another magnet close to either of them, similar poles (both north or both south) repel each other and the opposite poles attract even before they touch. Since the strength of the ﬁeld (ﬂux density) at any point, among other things, is related to the square of the distance from the source, the ﬁeld strength reduces quickly as you move away from the source. erefore, with most simple magnets, this is felt when you are close. e same can be felt at larger distances when you experiment with a stronger magnet. Figure 6.2: A permanent magnet and coils (when electricity ﬂows through them) create a magnetic ﬁeld around themselves. You can actually visualize a magnetic ﬁeld by peppering small pieces of iron (ﬁlings) onto a piece of paper over a magnet as shown in Figure 6.3a. e lines formed by the iron ﬁlings show the shape of the ﬁeld between the poles. Figure 6.3b shows the general shape of magnetic ﬁelds. Magnetic ﬂux lines always close between the poles. Unless they are somehow concentrated by other means, they surround the magnet in all directions. is is similar to having a source of light that illuminates in all directions equally. As a result, the strength of the magnetic ﬁeld is distributed and low. However, like a ﬂood light whose light intensity is concentrated in a small angle by reﬂectors, the strength of the magnetic ﬁeld around a magnet or a coil can be increased locally by concentrating them with an iron core. is is why we almost always see an iron bar within a coil; the coil generates the electromagnetic ﬁeld, but it is distributed all around and consequently, it is very weak. e iron core inside it concentrates the ﬁeld causing it to be much 158 6. ELECTROMOTIVE FORCE (a) (b) Figure 6.3: e shape of a magnetic ﬁeld around magnets and coils. Iron ﬁlings, peppered within the ﬁeld will line themselves up to follow the magnetic ﬂux lines. stronger around the bar. For the same reason too, all motors are invariably made with a metal casing to concentrate the magnetic ﬁeld within the casing. As a result, even if you bring a small piece of steel near the body of a motor, the magnet within the motor does not attract it. is is an important characteristic of magnets and coils and is used in almost all transformers and motors as well as magnetic devices used as sensors such as a Linear Variable Diﬀerential Transducer (LVDT ) used to measure distances. We will later discuss the additional eﬀects of the iron cores in a transformer, how they can be a detriment to the eﬃciency of the system, and how we can overcome that. Before we explore the subject of electromotive force, let’s ﬁrst study magnetic ﬂux a bit more. is will help us understand the subject much more easily. SolenidMagnetWire loope strength of the magnetic ﬂux is the product of the ﬂux density (the level of the con- centration of the magnetic ﬂux in any area) and the area, or: 6.3. MAGNETIC FIELDS 159 F B (cid:1) D A; (6.2) where F is the ﬂux, B is the ﬂux density, and A is the area. As expected, the ﬂux changes as a result of any variations in either the ﬂux density or the area. As we will shortly see, what is important in the generation of electromotive force is not just the strength of the ﬁeld but the changes in it with respect to time. ese changes come about as a result of the changes in the ﬂux strength or the area. For example, in a transformer the strength of the ﬂux (ﬂux density) changes due to the nature of the alternating current (AC) power. e AC current or voltage follows a sine function as shown in Figure 6.4. e voltage changes from zero to a maximum level, then decreases back to zero, then follows to a maximum with the opposite polarity (negative direction), ﬁnally returning to zero again, and repeating the pattern 50 times a second (or 60 times a second outside of the U.S. and Canada). As the voltage changes, so does the ﬂux density. As a result, when a coil is connected to AC power, its ﬂux density varies continuously. Figure 6.4: e sinusoidal nature of AC power creates a continuous change in the ﬂux density of a coil. Now imagine that we have a permanent magnet or a coil (connected to a DC source of power which does not vary) with constant ﬂux density. If we pass a conductor (e.g., a piece of wire) through the ﬂux, the conductor will disrupt the ﬂux, eﬀectively changing its area. is means that as a result of passing the conductor within the ﬂux and crossing its lines, we cause a change in its area, creating variations in the ﬂux. e eﬀect is the same as when the ﬂux density changes. Either one of these two will change the ﬂux strength. TimeVoltage160 6. ELECTROMOTIVE FORCE 6.4 ELECTROMOTIVE FORCE Electromotive force relates to the interactions between a magnetic ﬁeld and an electrical current through a conductor (such as a wire). According to Faraday’s Law, when there is a change in the magnetic ﬁeld, the interaction results in the generation of a force if the conductor is carrying a current, or induction of a voltage (or current) in a closed-loop conductor if it is moved (by a force). A series of simple experiments by Michael Faraday in England and by Joseph Henry in the U.S. in 1831 helped formulate this phenomenon. Figure 6.5 shows a galvanometer (which measures a current) in series with a simple conductor coil. If a bar magnet is moved toward the coil, the galvanometer deﬂects, indicating a current in the conductor. If the bar is stopped, the galvanome- ter goes back to zero. If the bar moves back, the galvanometer deﬂects in the opposite direction, indicating a current in the opposite direction. If the magnet is reversed, all these indications also reverse. e same will happen if the magnet is kept stationary but the coil is moved relative to it. erefore, as shown, when the magnet is moved within a coil it generates a current. is is called an induced electromotive force or emf. Figure 6.5: A magnet moving toward a coil induces a current in the coil. is is called induced elec- tromotive force or emf. Similarly, as shown in Figure 6.6, if the galvanometer and the coil are stationed close to another stationary coil that is connected to a power source (battery), when the switch is closed or opened the galvanometer deﬂects momentarily in opposite directions, but not if the switch is left on or oﬀ. It is only as a result of the switch turning on or oﬀ that the galvanometer deﬂects, indicating that the change in the current causes an electromotive induction in the coil. is is the principle behind the generation of electrical power in a generator. is interaction between a magnetic ﬁeld, a conductor, and relative motion (caused by a force that creates the motion) is interchangeable. is means that as in Figure 6.5, in the presence of a current through the coil, the magnet will experience a force that moves it relative to the coil (still called the electromotive force). e same principle is the basis on which all motors operate too. 6.4. ELECTROMOTIVE FORCE 161 Figure 6.6: Whenever the switch is closed or opened the galvanometer deﬂects, indicating a momen- tary induction of electromotive force in the coil. e opposite of the same phenomenon is called back electromotive force or back-emf. We will discuss this a bit more later. Now let’s see what this means in practice. Notice that as we just saw in Section 6.3, the change in the ﬂux can come from a change in its density or from a conductor crossing its lines. Also note that a closed-loop conductor means that the wire is continuous or attached to a load. For example, let’s say we attach the two sides of the wire to a lamp. In that case, the circuit is closed-loop or continuous, and therefore, the voltage which is induced can travel through the wire to the load (lamp) and return. is creates a current in the wire. Otherwise, if there is a voltage but the wire is not continuous or attached to a load, there is no current ﬂow and nothing happens. As a side note, I remember a group of ﬁrst-year students who had designed and constructed a device which, based on this principle, was supposed to re- duce vibrations in a pendulum as it passed through a magnetic ﬁeld. However, the device was not working and the students had assumed that it was not con- structed well. What they had not realized was that since the pendulum was insulated and not attached to a load to actually use the voltage induced in it, there was no current and as a result there was no damping of the pendulum. .. As mentioned previously, this is the principle that governs the operation of all motors, generators, and transformers. Although these are seemingly diﬀerent devices, the diﬀerent inter- actions of the same elements of Faraday’s Law are at work for each one. Now let’s see how each one works. First let’s see about motors. Imagine that there is a magnetic ﬁeld generated by a permanent magnet (where the ﬂux intensity is constant). Now imagine that we take a conductor such as a wire and pass a current through it. As a result of Faraday’s Law, the interaction between the ﬂux VRs162 6. ELECTROMOTIVE FORCE and the current-carrying conductor is a force on the conductor, pushing it away. We will see how an actual motor works continuously, but for now, as you can see, a force is generated that pushes away the conductor. Now take the same system mentioned previously, but instead of supplying a current through the conductor, assume that we move the conductor through the ﬂux (which is caused by a force we supply). e crossing of the ﬂux also creates a change in the ﬂux (area), and based on Faraday’s Law, this will induce a current in the conductor. is system is a generator (and we will see the details later). Note that a generator and a motor are the same; in one, we supply the current and it moves, in the other we supply the motion and it induces a voltage (or current). It should be mentioned that although the workings of a DC and AC motor and their details are diﬀerent, they all follow the same principles. Next consider a transformer. ere are no moving parts in it. Instead, two coils interact with each other. e supplied current to one coil is AC power which varies constantly and changes the ﬂux. Consequently, as a result of the changes in the ﬂux and based on Faraday’s Law, a voltage is induced in the second coil. erefore, although these devices are diﬀerent and each one is designed for a diﬀerent application, they all follow the same rules. Now let’s see how AC and DC motors, generators, and transformers work. 6.5 DC MOTORS DC stands for Direct Current, meaning that the polarity (direction of ﬂow) does not change. If a battery is used, the magnitude does not change either. DC power is usually supplied by batteries or by circuits that deliver a direct current. erefore, a DC motor requires a DC source and will not work with AC power. ese motors are powerful, their direction of rotation can be changed, and their speed can be controlled relatively easily as we will discuss later. However, their power- to-weight ratio is lower than AC-type motors and they cannot tolerate high temperatures as much as AC-type motors. As expected, DC motors operate based on the principles of electromotive force. A per- manent magnet (called a stator) provides a magnetic ﬁeld whose lines are crossed by a current- carrying conductor (called a rotor). Since the eﬀective area of the ﬂux is disrupted, a force is generated that pushes the coil rotor as shown in Figure 6.7a. Since the conductor is attached to a shaft, it rotates to the middle as a result of the force. e same thing happens to the second coil which is now receiving the current. erefore, the rotation continues. In order to provide the current to the coils sequentially when needed, a set of commutators and brushes are used. e coils are connected to the commutators. e brushes, carrying the current from the power source, slip over the commutators and supply the coils with a current. In reality, the rotor coils are formed around iron cores, creating magnets. We may describe the motion of a DC motor through the pulling of opposite poles and pushing of similar poles between the poles of the stator magnet and the rotor magnets. When the current is supplied to a coil, the core develops a north pole and a south pole that are pulled or pushed by the poles of 6.6. AC MOTORS 163 (a) (b) (c) Figure 6.7: e components of a DC motor. the stator, causing the rotor to rotate. However, as soon as one coil rotates away, power is cut oﬀ and instead, the next coil is powered which repeats the process until the power is cut oﬀ. In order to make the motion of the motor smooth, most DC motors have rotors with three coils (Figure 6.7c). Either one or two of the three coils are powered at any given time. Figure 6.7b shows the rotor, stator, commutators, and brushes of a small DC motor. 6.6 AC MOTORS AC motors are simpler in their construction and operation and are therefore more rugged. ey are made of a permanent magnet (PM) rotor or a simple cage (such as squirrel cage rotor) and a coil stator. AC motors do not have brushes or commutators because AC power automatically NSMagnetsCommutatorsRotor coilsBrushes on springpower conectorsContacts to thepower source164 6. ELECTROMOTIVE FORCE provides a changing magnetic ﬁeld and consequently, there is no need for external switching of the direction of the current for continuous rotation. Imagine that a permanent magnet is mounted on a shaft to form a rotor as shown in Fig- ure 6.8. e stator is a coil in which the current ﬂows. Let’s assume that the rotor is situated such that both the north and south poles are aligned with poles of the coil which at this instant is not magnetized yet. Imagine that at the instant shown, the AC current starts from zero in the positive direction ﬂowing into the coil. is will create a magnetic ﬁeld such that both north poles and both south poles of the rotor and stator will repel each other, forcing the rotor to rotate in the direction shown in order to bring the north of the rotor closer to the south of the stator and the south of the rotor to the north of the stator. As the AC current increases to its maximum level, the repelling and attracting forces between the poles increase. Eventually, the AC current starts to decrease toward zero, but still provides the same forces in the same directions. As soon as the poles of the rotor and stator align themselves with each other’s opposite poles, the direction of the AC current changes its polarity, thereby switching the directions of the poles on the stator. is will create the exact situation as before, but at the new location, repelling the now-similar south poles and north poles toward the opposite side. With this complete cycle, the rotor rotates once. But as soon as it reaches the opposite side, the AC switches again, forcing the motion to continue, repeating indeﬁnitely until the motor is shut down. ere is no need for commutation, switching, or brushes. Figure 6.8: A permanent magnet AC motor. Notice how the rotor follows the stator’s moving ﬁeld. Due to the nature of AC power, the ﬁeld continually switches directions, and the rotor follows it. erefore, the speed at which it rotates is a function of the line frequency. For example, the line frequency in the U.S. is 60 Hz. Depending on the number of poles used, the speed of an AC motor with permanent magnets will NNSSAC current6.6. AC MOTORS 165 be 1,800, 3,600, etc. e same motor in many other countries whose line frequency is 50 Hz will be 1,500, 3,000, etc. ese are usually referred to as synchronous motors because they have a ﬁxed speed that is a function of the line frequency. is speed, to a large extent, stays constant as the load increases or decreases, but the angle between the rotor and stator changes a little to increase or decrease the load. If the load increases more than the motor can handle, instead of slowing down as a DC motor does, it simply stops. Another type of AC motor is called an induction motor. Induction motors are very similar to synchronous AC motors but instead of the permanent magnet rotor, they simply have a metal rotor in the form of a number of longitudinal bars that are connected together like a cage. erefore, the rotor is usually called a squirrel cage rotor as shown in Figure 6.9. Notice that the rotor is not powered by any electrical current; it is simply a metal cage. Similar to other AC motors, the stator is made of coils that are powered by an AC current. In this case, due to back-emf, the varying ﬂux induces a current into the cage. However, since there is a current in the cage’s conductors, a force is generated that rotates the rotor. However, in this case there are no poles that exactly follow the magnetic ﬁeld, and consequently, the rotor can rotate at any speed as the torque and current change. ese motors, also called asynchronous motors, are rugged, powerful, long lasting, simple, and economical. ere are no brushes, magnets, or commutators. ey are used in most AC applications. eir basic disadvantage is that they always rotate in the same direction. erefore, they can only be used in applications where the motor does not need to change direction (e.g., washing machines, dryers, fans, pumps, etc.). ey cannot be used as drill motors because unlike DC motors, they cannot be reversed. Figure 6.9: An AC induction motor’s stator and rotor. e rotor is a simple non-magnetic cage with no power supplied to it. AC power is supplied to the stator coil only. One exception is called a reversible AC motor, where the coil is center-tapped as shown in Figure 6.10. In this case, only 1=2 of the coil is used for each direction, producing 1=2 of the torque. erefore, for the same power rating, these motors need twice as much winding, making 166 6. ELECTROMOTIVE FORCE them heavier and more costly. To reverse the direction of rotation, the AC current ﬂows from the center to only one side of the coil, thereby going left to right or right to left, creating a ﬁeld that is the opposite of the other case. As a result, the rotor will rotate in one direction or another. Figure 6.10: A reversible AC motor can switch directions because the stator coil is center-tapped. As a result, the current ﬂows in opposite directions depending on which route is chosen, creating ﬁelds that are in opposite directions and forcing the rotor to rotate in opposite directions. For devices like drill motors that require direction change but where DC power is not available unless it is rectiﬁed and lowered to suit common low-voltage DC motors, a universal motor is used. Universal motors are a combination of DC principles and AC power. Instead of permanent magnet stators like those in DC motors, they have coil magnets as in AC motors that need to be supplied with an AC current. e rotor is a coil with brushes and commutators that is also powered by an AC current. In this case, the magnetic ﬁeld caused by AC power in the stator coil changes direction 60 times a second, but because the rotor is also supplied with the same AC current, its direction also changes the same 60 times per second at precisely the same time. Since they both switch directions at the same time, it is as if it were a DC current. e additional switching through the brushes and commutators causes the rotor to rotate like a DC motor. erefore, although powered by an AC current, the motor’s direction of rotation can be switched like a DC motor. In other types of motors such as stepper motors and brushless DC motors, the attempt is to do the opposite; to run a DC motor with the construction of an AC motor with no brushes or commutators. is makes the motors more rugged and longer lasting. We will study these motors next. 6.7 STEPPER MOTORS Unlike DC and AC motors that start rotating continually when they are connected to a power source, stepper motors do not; they only move one step when the ﬁeld is ﬁeld rotation is usually accomplished by a dedicated circuit, a computer, a microprocessor, a PLC (Programmable Logic Controller) or similar means. erefore, the movements of the rotor are under complete control of an external device. 6.7. STEPPER MOTORS 167 To understand the way a stepper motor works let’s consider a simpliﬁed version ﬁrst. Fig- ure 6.11a shows a permanent magnet rotor and a coil in oﬀ position with their poles aligned. As soon as the coil is turned on, the similar north and south poles will repel each other (Figure 6.11b) until the poles of the magnet line up with the opposite poles of the coil (Figure 6.11c). At this point, the rotor will stay here without movement, even if we turn oﬀ the coil. is is called the point of least reluctance, a stable position. In this position, even if we apply a torque to move the rotor it will resist. If we once again turn on the coil in the opposite polarity of the ﬁrst case, the similar poles will repel each other again (Figure 6.11d), forcing the rotor to rotate again until the opposite poles align and it stops again. In this process, every time we turn on the coil in proper polarity, we force the rotor to rotate half of a full circle or 180(cid:14). However, although we can force the rotor to only rotate this ﬁxed amount, there are two problems with this set up: (1) that the step size is large, and (2) there is no control over the direction of motion that the rotor takes. When we turn on the coil, the rotor may rotate either clockwise (CW) or counter-clockwise (CCW). (a) (c) (b) (d) Figure 6.11: A simple stepper motor set up. To improve this situation let us consider the set up in Figure 6.12 where we have added a second coil. In this case, assume that we start as before, when both coils are oﬀ and the rotor is aligned with the poles of coil-1. Now assume we turn on coil-2 such that its poles will be as shown in Figure 6.12b. As a result, the rotor will rotate to align itself with the poles of coil-2. If we next turn oﬀ coil-2 and turn on coil-1 as shown in Figure 6.12c, the rotor will rotate until its poles align with the poles of coil-1. Once again, we turn oﬀ coil-1 and turn on coil-2 in the opposite polarity, forcing the rotor to rotate again. Continuing to turn on and oﬀ coils-1 and -2 sequentially in proper polarity we can force the rotor to rotate clockwise or counterclockwise as much as we want. In this case, the step size is reduced to a quarter of a turn or 90(cid:14) and we know the rotor’s direction of rotation; unlike the ﬁrst case it is not left up to chance, which is a big improvement. Also notice that by selecting how many times we turn each coil on and oﬀ we can ensure that the stepper motor rotates exactly as much as we wish, no more, no less. Additionally, NSSNNSNSNSNSSN168 6. ELECTROMOTIVE FORCE by selecting how fast we turn the coils on and oﬀ we can control how fast the rotor rotates; if they are turned oﬀ and on more quickly, the rotor will also rotate more quickly and vice versa. So we are in complete control of the magnitude of rotation, the speed of rotation, as well as the direction of rotation. (a) (b) (c) (d) Figure 6.12: Employing two coils instead of one will improve the stepper motor behavior and char- acteristics. We can improve the situation and cut the size of the step in half if we employ another variation. As shown in Figure 6.13b, suppose that instead of turning oﬀ coil-2 at this instant and turning on coil-1 we would keep it on while we turn on coil-1. With both coils on, since the rotor’s magnet needs to balance itself at the point of least reluctance, it will align itself in the middle of the arc between the two, thereby rotating only 45(cid:14) (Figure 6.13c). If we then turn oﬀ coil-2 it will rotate the remaining 45(cid:14) to complete the step (Figure 6.13d). is is called half stepping and is common in many applications. erefore, without adding any new coils or other components, simply by controlling when the coils are turned on and oﬀ we can reduce the step size by half. e only remaining problem is that for most applications, even 45(cid:14) is a large displacement. is is NS1221NS122SN1N122SSN1NS122SN16.7. STEPPER MOTORS 169 because although we have control over displacement, speed, and direction of rotation, we actually have no control over the location of the rotor in between the poles when it is under load. erefore, it is desirable to reduce the size of these steps even further. However, there is a limit to how many coils we can add. In the following section, we will see how two diﬀerent methods are employed to reduce the step size of common stepper motors signiﬁcantly without adding a signiﬁcant number of coils. (a) (b) (c) (d) Figure 6.13: Schematic of an improved stepper motor. 6.7.1 CANSTACK STEPPER MOTORS Canstack motors are rugged and simple in construction. e motor is comprised of a permanent magnet rotor made of a ﬂexible sheet magnet that is similar to the type that is used for refrigerator magnets. ese magnets, called halfback array magnets, are made by embedding (powder) steel ﬁlings in a ﬂexible resin and magnetizing them with a machine. To understand the diﬀerence NS1221NS122SN1NS122SNSN1NS122SN1170 6. ELECTROMOTIVE FORCE between these magnets and a regular steel magnet, turn one of these magnets on its back and try to stick it to any steel material. You will notice that the magnet does not stick. is is not due to the fact that many of these magnets have a sheath of plastic, used for advertising, on them. It is because these magnets are magnetized only on one side. Figure 6.14 schematically shows how these magnets are a series of magnets next to each other with all their poles on one side; the opposite side is not magnetic. Figure 6.14 also shows the construction of the rotor of the stepper motor and a real rotor. e rotor is made of the same type of magnet, rolled into a cylinder. erefore, the rotor will have a series of south and north poles sequentially located next to each other. Figure 6.14: e magnetic ﬁeld of the rotor of a canstack stepper motor possesses a series of magnets next to each other. Figure 6.15 shows the stator of a canstack stepper motor. It is made up of two electromag- nets, stacked over each other, each made up of two plates and a coil. Each plate has, in this case, 12 little ﬁngers or tabs on it as shown. When a current ﬂows in the coil, each of these plates becomes either a north or douth pole. erefore, there will be 12 tabs of north and 12 tabs of south created when a current ﬂows in each coil. e coils can be turned on and oﬀ indepen- dently of each other in either polarity by center-tapping the coil as was discussed in Section 6.6, Figure 6.10. Notice that this means that when a coil is turned on, it creates an equivalent of 12 magnets (24 poles), or a total of 48 tabs and 48 poles around the stator when both coils are turned on. But instead of having to make 24 individual coils within the motor and turning them on and oﬀ sequentially, we only need to turn two magnets on and oﬀ. But notice that although we only have two electromagnets, since each coil is center-tapped, we eﬀectively have four coils, referred to as Coil-1, Coil-2, Coil-3, and Coil-4. Coil-1 and Coil-2 are the same coil, but with opposite polarity, etc.). N SN SN SN SN SN SN SN SN SN SSNSSSSNNNSNSSSSNNNCross section of the magnet6.7. STEPPER MOTORS 171 Figure 6.15: Canstack stepper motor is comprised of a permanent magnet rotor and a stacked, two- stage stator with repeating poles that are staggered from each other to provide small step sizes. Let’s call the plates (and thereby the tabs attached to each) A and B for the ﬁrst electro- magnet (Coil-1 and Coil-2) and C and D for the second electromagnet (Coil-3 and Coil-4). Table 6.1 shows their magnetic poles for each polarity: Table 6.1: e poles of the stepper motor electromagnets versus the polarity of the current e trick is that these plates are assembled such that the tabs form a staggered set so that they will have a sequence of A, C, B, D, A, C, B, D, A, C,: : : : : : . Figure 6.16 shows this arrange- ment in a linear fashion. So, what is the eﬀect of this arrangement? Suppose that we turn on Coils 1 and 3 at the same time. is means tabs A and B will be N and S, and tabs C and D will be N and S. erefore, the sequence of A, C, B, D, A, C, B, D, A, C,: : : will result in N, N, S, S, N, N, S, S, etc. (please follow this carefully). Similar sequences will form as we turn the coils on and oﬀ. Table 6.2 shows the pattern when the coils are switched six times. Notice that in Table 6.2, as highlighted, the ﬁeld rotates in one direction. For example, any two south poles next to each other advance one step as the coils are switched on and oﬀ RotorStatorSingle platewith tabsTabs ATabs BTabs CTabs DCoil-1NSCoil-2SNCoil-3NSCoil-4SN172 6. ELECTROMOTIVE FORCE Figure 6.16: e four plates that constitute the two magnets of a canstack stepper motor are staggered relative to each other such that their tabs are sequentially repeating in an A, C, B, D, A, C, B, D, A, C,: : : : : : . fashion. Table 6.2: e sequence of magnetic poles of stepper motor tabs as the coils are sequentially turned on and oﬀ sequentially, as do the rest. erefore, if the rotor is aligned with the tabs such that its north is between the two souths, the rotor moves with the sequence as shown in Figure 6.17. e continuous motion of the stepper is accomplished by simply repeating the sequence of switching coils 1 through 4 in 1-3, 1-4, 2-4, 2-3 order as shown in Table 6.2. Reversing the sequence will force the rotor to turn backward. Since there are 48 tabs, each step will be 360(cid:14)=48 D n where n is the number 7:5(cid:14). Consequently, the total rotation of the rotor will be equal to 7:5(cid:14) (cid:2) of switchings. e faster we switch, the faster the rotor rotates. is way, we are in complete control of the total angular displacement, angular speed, and direction of rotation of the rotor. If a microprocessor is used to run the stepper motor, as is the case in most devices, the microprocessor turns four switches on and oﬀ that provide a current to each coil in a 1-3, 1-4, 2- 4, 2-3 sequence, which is extremely simple to program with a microprocessor. Figure 6.18 shows a schematic of this set up. ACBDACACBDACBDCoil-1, Coil-3NNSSNNNNNNNNSSCoil-1, Coil-4NSSSSNCoil-2, Coil-4SSNNSSNNCoil-2, Coil-3SSSNNSCoil-1, Coil-3SSNNSSCoil-1, Coil-4NSSNNSSN6.7. STEPPER MOTORS 173 Figure 6.17: e rotor follows the ﬁeld as the ﬁeld is advanced in the stator of a stepper motor. For simplicity, only some of the tabs are shown. Figure 6.18: e schematic of a simple set up to run a stepper motor with a microprocessor. It should be mentioned here that there is much more to stepper motor drives, control schemes, eﬃciency, and other issues that are beyond the scope of this discussion. SSSSSSNNNNNNSTabs ATabs BTabs CTabs DNSSSSNNNNNSNSTabs ATabs BTabs CTabs DMicroprocessoroutput portsSteppermotorcoilcontactss4s1s2s3SwitchesVin174 6. ELECTROMOTIVE FORCE 6.7.2 HYBRID STEPPER MOTORS ese stepper motors usually have a much smaller step size, for example 1:8(cid:14) at full step and 0:9(cid:14) at half step. is translates to 200 and 400 steps per revolution respectively. However, this is achieved with the same number of coils. To understand how this works, let’s look at a simple principle that is not only used here, but also in calipers that are used for measuring dimensions more accurately. Imagine that a bar A with a certain length is divided into 10 portions as shown in Fig- ure 6.19. Obviously, each portion will be 1/10th. Also imagine that bar B with the same length is divided similarly into 10 portions. erefore, the divisions of both bars A and B will be exactly the same. If at any time the division marks of A and B are aligned, one of the bars would have to move one full division in order to align the next set of division marks. For example, if division marks 2 on A and B are aligned, the next possibility for alignment will be if B is moved one full division until 3 on A will be aligned with 2 on B. Figure 6.19: Aligning division marks of similar lengths requires one full-length motion. Now imagine that we take the same length bars A and B, divide A into 10 portions as before, but divide bar B into 11 divisions as shown in Figure 6.20a (other numbers of divisions are perfectly ﬁne too. Each number will result in a diﬀerent proportion, but they are all ﬁne). Also imagine that at one point, division mark 3 on bar A is aligned with division mark 3 on B (Figure 6.20b). Unlike the previous case where the division marks were all the same length, here they are slightly diﬀerent. Consequently, all it takes to align the next set of division marks is for bar B to move only about 1/10th of this distance, or about 1/100th of the total length until division mark 4 on A aligns with division mark 4 on B (Figure 6.20c). In other words, since the divisions are no longer the same, bar B only has to move the distance of the diﬀerence between the two, or .1=10/ 0:01. is means that we have made the divisions so much smaller without having to draw 100 lines. is principle is used in calipers to measure dimensions to about 1/100th of an inch. It should be mentioned here that it does not matter what the number of divisions are .1=11// (cid:138) (cid:0) 012345678910012345678910AB012345678910012345678910ABas long as they are not equal. So we could achieve similar results (albeit diﬀerent values) with 10 and 8, 8 and 7, 20 and 21, or any other unequal pairs. 6.7. STEPPER MOTORS 175 (a) (b) (c) Figure 6.20: e unequal number of divisions on equal lengths allows for measuring much smaller distances as in a caliper. (cid:0) .1=50/(cid:141) Figure 6.21 shows the construction of the rotor and stator of a hybrid stepper motor. Notice how the rotor and the stator have teeth or divisions on them. In this particular example, the rotor has 50 divisions, and the stator has the equivalent of 40 divisions. Just like the caliper, in order to move the rotor to align with the next division at any location, the rotor has to only move an angle of (cid:140).1=40/ 1:8(cid:14), which is much smaller than 0:02/ the canstack step size. Combining these two seemingly unrelated concepts beneﬁts us very much. e rotor of a hybrid stepper motor is a simple magnet with one north and one south pole. To reduce the back-emf current in it as it rotates, the rotor is made of laminated layers attached together to form the rotor as is shown in Figure 6.21. e stator has four coils in it that can be individually turned on and oﬀ. erefore, exactly like the canstack motors and with a similar schematic as in Figure 6.18, a sequence of 1-3, 1-4, 2-4, 2-3 or its reverse drives the hybrid stepper motor forward or backward with complete control over its displacement, speed, and direction. 360(cid:14) D 360(cid:14) D .0:025 (cid:0) (cid:2) (cid:2) 012345678910A012345678910B11012345678910A012345678910B11012345678910A012345678910B11176 6. ELECTROMOTIVE FORCE Figure 6.21: A hybrid stepper motor and its rotor and stator construction. 6.8 TRANSFORMERS Transformers are used to increase or decrease voltages and currents. ey function based on the same principles we have already discussed although there are no moving parts in them. ey are composed of a primary coil, a secondary coil, and an iron core to concentrate the ﬂux and increase the eﬃciency of the device. e primary and secondary coils are simple coils with diﬀerent number of turns (loops) in them designated as N1 and N2. An AC current is fed into the primary coil which creates a varying ﬂux. According to Faraday’s Law, since the ﬂux intensity is changing due to the AC current, it induces a voltage into the secondary coil. In general, without an iron core to concentrate the ﬂux, the level of induced voltage is very low and most of the energy is wasted. However, in the presence of a core, the eﬃciency of the system can be increased to 90% or better. Figure 6.22 shows the schematic drawing of two ways transformers may be built. Figure 6.23 is a typical transformer. e primary and secondary coils, the iron core, and the connections for diﬀerent levels of voltage can clearly be seen. e induced voltage can be expressed as: Vout D Vin(cid:11) .N2=N1/ cos (cid:12); (6.3) where Vout is the voltage in the secondary and Vin is the supplied voltage in the primary. e constant (cid:11) represents the eﬀects of the coupling between the primary and secondary coils as a result of the iron core concentrating the ﬂux and can vary from near zero to a maximum of 1 under the best conditions. Larger values of (cid:11) indicate a better and more eﬃcient transformer. (cid:12) is the angle between the primary and secondary coils. N1 and N2 are the number of turns in the primary and secondary coils. 6.8. TRANSFORMERS 177 Figure 6.22: Schematic drawing of two ways a transformer may be built. Figure 6.23: A typical transformer with its coils, iron core, and connections. Varying the Vin will proportionally change Vout. Since AC voltage varies between zero and a maximum value in both positive and negative directions, it follows that the induced voltage in the secondary also varies between zero and a maximum value in both directions. Consequently, the output of a transformer is also AC unless we do something else to rectify it. In certain applications (such as automotive or charging batteries where the battery requires a DC current) the AC output of the generator is rectiﬁed using diodes. e positive polarity current goes through directly, but the negative portion is switched back into positive. Consequently, the current becomes DC. In transformers used for increasing or decreasing voltage the primary and secondary coils are usually kept parallel, and consequently, the angle between them is zero. As a result, cos (cid:12) primarycoilSecondarycoilIron corePrimarycoilSecondarycoilIron coreConnection pointsfor different voltages178 6. ELECTROMOTIVE FORCE is 1 and the induced voltage achieves its maximum value. However, in other applications such as resolvers, the angle may be changed by rotating one of the coils relative to the other, changing cos (cid:12) and inﬂuencing the output voltage. Resolvers are used as sensors to measure the angle of rotation of shafts and joints in systems such as robots. e output voltage is also proportional to the ratio of the primary and secondary coils as N2=N1. is means that if the number of turns in the secondary coil is larger than the primary coil, the output voltage is larger than the input voltage and vice versa. is is the primary application of transformers; by selecting the ratio of the number of turns in the primary and secondary coils, we can achieve any desirable voltage ratio. As mentioned earlier, if N2=N1 is larger than 1, the output voltage will be increased. If it is smaller than 1, it will be decreased. Assume that we use a ratio of 10/1. is means that the output voltage will increase by a factor close to 10. Does this mean that we have increased the power of the system at no cost? Obviously if this were true, we could use a transformer to “generate” additional power indeﬁnitely at no cost, which is impossible. So what else should we expect? Instead of considering only the voltage we must consider the power, which for electrical systems is deﬁned as: P V I; (6.4) D where P is the power in watts, V is the voltage and I is the current. In other words, the power of an electrical system is the product of its voltage and current. We have seen that, except for losses (which are always present, and the best we can do is to approach 100% eﬃciency, but never reach 100%), the power should remain the same; output power should be equal to input power because we do not generate power or energy out of nowhere. erefore, we should expect that when we increase the voltage, the corresponding current of the system reduces proportionally, and when we decrease the voltage, its current increases proportionally. As an example, and assuming almost 100% eﬃciency, if we increase the voltage by a factor of 10, the current in the secondary will be 1/10th of the current in the primary. And this is exactly what a transformer does. It increases or decreases the voltage at the expense of the current. We are not changing the total power (or energy) available; we are just transforming the ratios of the voltage and current at each other’s expense. Electric power transmission is the main application of this system. To better understand this, let’s ﬁrst look at electrical power loss in electrical systems. All electrical conductors, even the best materials (like copper), show some resistance to the free ﬂow of electrons. is means that as electrons move in a conductor, some of the energy they have is converted to heat energy. e power lost as heat energy in a conductor is expressed by: Plost RI 2; (6.5) D where I is the current and R is the resistance. Clearly, since I is squared, it is a much more important factor than resistance. In other words, in order to reduce power loss in conductors, it is more important and more eﬀective to reduce the current than it is to reduce resistance. Resistance 6.8. TRANSFORMERS 179 can be reduced by increasing the cross section of the conductor (thicker wires) which increases the weight and the cost of the wire, sometimes prohibitively. However, reducing the current at the same rate reduces power loss much more signiﬁcantly. And this is exactly why transformers are used. Electrical power generation is usually accomplished in power plants in locations where they make the most sense. For example, hydroelectric power plants do not require fuel such as oil or gas, generating (actually, converting the potential energy of the water behind a dam into) electri- cal energy at very low cost; the power comes from the kinetic and/or potential energy of the water running through the turbines. However, dams are usually not close to cities or communities where electricity is needed and consequently, the power must be transmitted. Another concern might be pollution, noise, and economics (cost of the land). In most cities it is impossible to operate a power plant within the city limits. Power plants are in the outskirts and their power must be trans- mitted. And perhaps most importantly, it is very uneconomical to have small power plants in each neighborhood for the consumption of the small community around the plant; large power plants are much more eﬃcient and economical. erefore, a few large power plants generate enormous amounts of electrical energy that are transmitted to large areas for consumption. Nowadays, al- most all plants, whether hydroelectric, fuel based, or solar and wind, are interconnected through a grid which feeds all communities. Consequently, it is crucial to be able to transmit huge amounts of electrical energy from one place to another. However, as we saw, when power is transmitted through a conductor, some of it inevitably converts to heat energy due to electrical resistance in the conductor. To reduce loss, we can either use heavy-gauge copper wires at enormous weight and cost or try to reduce the current. To un- derstand this issue, suppose that a power plant generates electricity at 100 volts of potential and 100 amps of current, yielding 100 10,000 watts of power. In this case, the loss of power in a length of wire with 1 ohm of resistance will be Plost 10,000 watts, an enormous amount, basically wasting all the power that was generated. .1/.100/2 RI 2 100 D D D D (cid:2) D Now suppose that using a transformer, we increase the voltage to 10,000 volts. is means that, assuming there is no loss, the current will be reduced to 1 amp, still yielding 10,000 watts. In this case, the power loss for the same length of wire equaling 1 ohm will be Plost D .1/.1/2 1 watt. So the loss is 1/10,000th of the ﬁrst case, allowing the power to be distributed to a very large area. is means that the power at the point of consumption is at 10,000 volts and 1 amp, which is completely useless; we need high-current power at 110 volts (220 volts in many other countries) to run our machines, appliances, and devices. However, if another transformer with the opposite ratio of the ﬁrst one is used to once again reverse the transformation, we can recover the same 100 volts and 100 amps at the point of consumption and deliver appropriate power to the user. is is exactly what is done. In the ﬁrst part of the transmission journey over rural transmission towers and lines for long distances, the voltage may be increased to hundreds of thousands of volts with very little current (in the U.S., there are power lines with 115, 138, 161, 230, 345, and 500 kV). In sub-stations, this is reduced to tens of thousands of volts for local RI 2 D 180 6. ELECTROMOTIVE FORCE transmission, and ﬁnally, reduced again by local transformers in neighborhoods to 110 volts and delivered to users. Figure 6.24 shows typical transmission towers and transformer units on top of an electrical pole, reducing electric power from tens of thousands of volts to 110 volts. Figure 6.24: Typical transmission lines and transformers on power poles that reduce electric power from tens of thousands of volts to 110 volts for domestic consumption. However, all this is possible because we deal with AC power which provides the necessary variation in the ﬂux density needed for Faraday’s Law to work. DC power would not provide this opportunity because it does not change; to induce a voltage in the secondary coil, there would have to be a motion present which is not the case for transformers (otherwise, it becomes a generator which we will see later). Nowadays, it is possible to electronically switch on and oﬀ a DC current and cause it to induce a voltage in the secondary coil, and consequently, have a DC transformer. But this was not the case in the past. e story is that omas Edison had spent a lot of money to establish local DC-generating power plants in diﬀerent neighborhoods of New York City and to transmit them via copper wires to households. e ﬁrst one was in 1882 on Pearl Street in lower Manhattan. However, as discussed, to reduce power loss in the wires, he had to use very thick wires for the transmission of low voltage, high current electricity. At the time when he started transformers did not exist anyway, but even if they did, they would have been ineﬀective .. 6.9. DC GENERATORS 181 with a DC current. Later Tesla designed and built prototype transformers with AC power. George Westinghouse, an entrepreneurial inventor and pio- neer of Edison’s era, seized the opportunity to generate low cost hydroelectric AC power at Niagara Falls, and by transforming it to high voltage and using very thin wires, transmit the power to New York City at very low cost and compete with Edison. e rivalry was intense, and at one point Edison had his engineers design and build what is now known as the electric chair (which is used for execution) in order to scare people from using AC power. How- ever, this did not work, and Westinghouse became a huge company, at one time employing more people than any other company in the U.S. .. In reality, there are three lines of transmission for three-phase power (needed for higher voltages and currents in larger plants and certain applications like three-phase motors). Each of the three phases is treated exactly the same, but carried on a separate wire. To reduce the electromagnetic eﬀects of these high voltages, the wires are usually drawn in a braided manner (they never touch; in fact they are apart from each other far enough to prevent arching between them, but braided). Chargers we use to recharge our batteries are miniature transformers too. eir primary and secondary coils are designed to provide the proper voltage needed. Some chargers provide DC output. is is done externally by diodes, rectiﬁers, and capacitors, etc. In other words, although the output of the transformer is an AC current, diodes and rectiﬁers eliminate or switch the negative polarity portion to a positive one, and capacitors or other averaging circuits modify the rectiﬁed output close to a DC (see Section 6.10). In some transformers the secondary coil is tapped at diﬀerent counts of turns, generating a variety of voltages which are accessible to the user. erefore, the user may choose a variety of diﬀerent voltages depending on the application. Figure 6.23 shows such a transformer. 6.9 DC GENERATORS For most cases, a generator is nothing diﬀerent than a motor. Instead of supplying a current to the motor and expecting it to rotate and provide a torque, a generator is rotated externally (by a torque) and is expected to provide a current (or voltage) as long as it is connected to a load such as a lamp. Otherwise, since it is not in a complete circuit, it will rotate without resistance and no power will be generated. is is still within the parameters of Faraday’s Law; because we are changing the ﬂux intensity by rotating the rotor, a voltage is induced in the conductors. A DC generator is the same as a DC motor. Since we intentionally use brushes and com- mutators, as discussed earlier, the output of a DC generator is discontinuous and choppy. is means that although the current is always in one direction and the polarity is always the same, the current does ﬂuctuate. However, for most purposes such as charging batteries this is not a 182 6. ELECTROMOTIVE FORCE problem. But for a true DC current that, similar to the current from a battery, does not ﬂuctuate, the output must be smoothed. 6.10 AC GENERATORS As with DC generators, for most cases an AC generator is also the same as an AC motor. When the rotor is rotated by an external torque, the magnetic ﬁeld induces a voltage or current in the stator as long as a complete circuit exists. erefore, when attached to a load, it can operate the device. However, in order to use an AC generator for charging batteries the current must be rec- tiﬁed; the reverse polarity section of the current must be switched to forward polarity (remember Figure 6.4 and how the polarity of an AC current reverses every 1/2 cycle). Simple diode arrange- ments called rectiﬁers are used to do this, and therefore, although the current is not constant, it can be used to charge batteries. is is the set-up used in automobiles too. e generator is usu- ally an AC generator with rectiﬁers in it. Figure 6.25 shows a simple rectiﬁer circuit made up of four diodes in the form of a bridge. In the forward polarity portion the current ﬂows through diode B, through the load, through diode D and back to the source, forming a complete circuit. For the reverse polarity portion of the current notice how the direction of the positive/negative is now reversed. As soon as the polarity reverses, diode B no longer allows the current through. Instead, the current ﬂows through diode C, through the load, through diode A, and back to the source. However, notice how in both cases, the direction of the output feeding through the load is the same. As a result, the output is now rectiﬁed and is always positive. Once again, notice that although the current is rectiﬁed, it is not constant. To create a constant-magnitude current that resembles the current from a battery it is necessary to remove the variation. To do this a simple circuit made up of a resistor and capacitor can be used to ﬁlter out the changes (this is called a low-pass ﬁlter). is simple combination of a resistor and capacitor reduces the variations to a large extent and makes the current smooth. e capacitor charges up when the voltage is higher and discharges back into the circuit when it is lower, smoothing the current. If too much current is drawn from the source this smoothness reduces and shows ripples in the output. It should be mentioned here that since AC induction motors (squirrel cage) do not have magnets, they do not generate a voltage unless something else is done. is includes a capacitor to give an initial charge to the rotor to start the current, which, as long as the rotor turns at or above the nominal speed, will continue to generate electricity. 6.11 BACK-EMF ISSUES IN MOTORS AND TRANSFORMERS: LAMINATED IRON CORES An interesting consequence of Faraday’s Law is that it is also present in reverse even when it is undesirable. As we discussed earlier, due to the electromotive force phenomenon, when a current is supplied to the rotor of a motor, it rotates. Conversely, due to back-emf, when the rotor is turned by an external torque, the same Faraday’s Law causes an induction of a current in the stator. And 6.11. BACK-EMF ISSUES IN MOTORS AND TRANSFORMERS: LAMINATED IRON CORES 183 Figure 6.25: A rectiﬁer is used to change the direction of the negative portion of the AC current into positive, thereby converting it to a DC current. as we saw, a transformer also functions based on the same electromotive force and Faraday’s Law. However, both in motors and transformers, since we need to concentrate the ﬂux, we use a metal core or a metal rotor. Based on the back-emf and the presence of varying ﬂux, caused by an AC current or as a result of using brushes and commutators, a current is also induced in the core of the transformer or the rotor of a motor (also called eddy current). If the core is solid iron, due to its low electrical resistance, the current can be large, creating a lot of heat (this is used in induction heating, where food is cooked when the bottom of the pot or a pan is heated by eddy currents). is is a huge waste of energy and a cause of concern to dissipate the heat. In order to reduce the eﬀects of this back-emf in the core of the transformer or the rotor we need to reduce the ﬂow of the back-emf current. To do so, the core of the transformer or the rotor is usually made up of thin layers of metal, laminated together, that are insulated from each other. Because the current Load+_ACgeneratorAC currentinput+_Load+_ACgeneratorAC currentinput+_ForwardportionReverseportionDC currentoutputDC currentoutputABCDABCD184 6. ELECTROMOTIVE FORCE ﬂows in very thin layers that have higher electrical resistance, and consequently lower currents, heat generation is eﬀectively eliminated. e layers are laminated together by pins, rivets, and welds, or pressed together. Figure 6.26 shows (a) the stator of an induction motor, (b) the rotor of a small DC motor, (c) a transformer core, and (d) the magnetic rotor of a stepper motor. All of these are made of thin layers laminated together, but insulated from each other, to form the required shape. (a) (c) (b) (d) Figure 6.26: e rotors of motors and the cores of transformers are usually made of thin layers of the metal that are insulated from each other and connected by pins, rivets, screws, or welds to take the required shape and ﬁght back against the induced back-emf due to the changing ﬂux. 6.12. BACK-EMF IN DC MOTORS: SERVOMOTORS 185 6.12 BACK-EMF IN DC MOTORS: SERVOMOTORS Back-emf plays a signiﬁcant role in the performance of all motors, but especially DC motors. To understand this issue ﬁrst recall our discussion about the relationship between an applied torque, mass moment of inertia, and angular acceleration as described by Equation (5.16), repeated here: (cid:11) E As we discussed, when a torque is applied to a rotating body, it accelerates and rotates faster in proportion to its mass moment of inertia. As long as the torque is present and exceeds friction and other resistive torques, the body will continue to accelerate and rotate faster. T E D I Now consider a DC motor that is connected to a battery. As the current ﬂows through the motor and the electromotive force exerts a torque on the rotor, it will start to rotate. In proportion to the mass moment of inertia of the rotor, it will continue to accelerate and rotate faster as long as the torque is present (and of course, for lighter rotors, the acceleration is higher and vice versa). However, since this torque continues to be present, should we not expect to see the rotor’s speed continue to increase, theoretically to inﬁnity? In other words, while the current continues, so does the torque and the acceleration, increasing the angular velocity indeﬁnitely until the rotor disintegrates. But we know from experience that if we connect a motor to a battery, when it reaches its nominal value, the velocity no longer increases. Why? is is due to the same back-emf. Once again, let’s imagine that we connect a DC motor to a battery. Since there is a torque, the rotor accelerates and its angular velocity increases. However, as mentioned before, since the rotor contains coils that are moving in the presence of a magnetic ﬁeld, a back-emf voltage (or current) is induced in the coil which is in the opposite direction of the supplied current. As a result, it reduces the eﬀective current to a value that is smaller than the supplied value. As the rotor increases its speed, the back-emf current increases and eﬀectively reduces the supplied current until such a time that the supplied current and the back-emf current equal each other, but in opposite directions; the eﬀective current at that speed is zero. erefore, the eﬀective torque at that speed goes to zero as does the resulting angular acceleration, and the velocity no longer increases. As a result, the DC motor continues to run at that nominal speed until conditions change, not increasing to inﬁnity. Now imagine that we engage a load, for example a fan blade or a wheel, to the motor. Since the eﬀective torque on the rotor at the nominal speed is zero but we have added an external load, there will be a negative acceleration (deceleration) which will slow down the rotor. However, as it slows down, the back-emf will be lower, increasing the eﬀective current, which increases the torque. erefore, as we increase the external load on the motor, it will slow down until the torque generated by the motor equals it. At this point the motor will rotate at a constant speed that is lower than when it was not loaded. If we increase the load, the motor will further slow down to decrease the back-emf, increasing the eﬀective current and increasing the torque supplied. is process continues as the load changes; with an increased load the motor slows down, and with a decreased load it speeds up to match the back-emf with the required torque. You may have 186 6. ELECTROMOTIVE FORCE experienced this phenomenon when dealing with DC motors, whether in appliances, toys, or other devices. In many applications it is necessary to maintain an exact speed regardless of the load on the motor. For example, the speed of the motors of a robot arm that moves in space for welding two pieces together must be very exactly controlled; otherwise the welds will either be too thick, too thin, or non-uniform. However, the load of the arm changes as it moves through the workspace. Without a control system to maintain correct velocities it would be impossible to perform a sat- isfactory job. In order to control the speed or maintain a constant speed we must use a controller that, through the use of an appropriate sensor, measures the velocity of the rotor and compares it to the desired value. If the speed is lower than desired, it will increase the supplied current (or voltage) to the motor, increasing the eﬀective current and increasing the speed. If the speed is too high, it will decrease the supplied current (or voltage) to the motor, reducing the eﬀective current and torque and slowing down the motor. is process continues as long as the motor is running. Such a system is called a feedback control system. It feeds back the sensed information to the controller which compares it with the desired value, and makes appropriate adjustments as necessary. Feedback systems are not just for controlling a motor but for countless devices and systems and may take many shapes and control many other factors. But their principal intent is to control some characteristic of a device through this sensed state of aﬀairs and to make adjustments to control the output. A motor that is equipped with such a controller is called a servomotor because its velocity can be controlled. In fact, by an additional position-sensor feedback, we can easily measure how much the rotor rotates, and turn it oﬀ as it approaches the desired angle of rotation. So, the total displacement and the speed of rotation of servomotors can both be speciﬁed and controlled. But the main point of this discussion is that the back-emf continues to play a pivotal role in the way a motor responds to always-varying loads and the way it is controlled. Without the controller, the desired speeds of motors must be maintained manually. 6.13 ADVANTAGES AND DISADVANTAGES OF DIFFERENT MOTORS Diﬀerent types of motors have diﬀerent characteristics, advantages, and disadvantages that make them unique in their applications and utility. In this section we will look at each type and learn about their characteristics. e major issues related to motors are heat rejection, reliability and life expectancy, torque rating, ability to reverse direction, and control of displacement and speed. Heat rejection is an important issue in motors. As we discussed before, when a current ﬂows through a conductor, due to the ever-presence of some resistance in the wires, heat is generated according to Equation (6.5). is heat increases as the current or the resistance increases. If not rejected or dissipated, the heat can severely damage the motor. Heat production is more prominent when the motor is under load. As we discussed, when the load on a motor increases, it slows down, the back-emf is lower, and the eﬀective current is higher to provide additional torque. But the 6.13. ADVANTAGES AND DISADVANTAGES OF DIFFERENT MOTORS 187 higher current also means higher heat production. e worst case is when the load is so high that the motor eventually stops due to the lack of enough torque, even though the back-emf is zero. is is called stall condition, when heat generation is at its maximum. Stall condition can burn a motor if it is not prevented. In DC motors the current ﬂows through the rotor coils and heat is therefore accumulated in the rotor. is heat has to ﬂow from the rotor through the air gap into the stator, and through the stator and the body of the motor, out to the environment either by radiation (if you are close to a motor, you may feel its heat even if you do not touch it), convection (air circulating around the motor’s body and taking the heat with it as it warms up), or in some cases by conduction (when the motor is attached to something else and the heat ﬂows through it). is is a long path with high resistance provided by the air gap (air is a very good heat insulator compared to metals). On the other hand, heat generation in AC motors is in the stator because the current ﬂows through the stator coil. erefore, heat only has to ﬂow through and out of the body. e heat path is much shorter and simpler as shown in Figure 6.27. erefore, AC-type construction where the stator carries the current is more rugged, can withstand a much higher current, and consequently, produce a larger torque. As a result, AC-type motors are generally more powerful than their counterparts in DC. Notice that stepper motors have an AC-type construction where the current ﬂows through the stator although they operate on a DC current. erefore, they can generally handle larger currents. Figure 6.27: Heat rejection path for AC- and DC-type construction. Permanent magnetor squirrel cagerotorCoil statorPermanentmagnetstatorCoil rotorAC-typeDC-type188 6. ELECTROMOTIVE FORCE Reliability and life expectancy results from simplicity in design and using fewer parts. DC motors have more parts, including commutators, brushes, and springs. Of more concern are the brushes that wear out and need replacement once in a while. As a result, AC-type motors, steppers motors, and brushless DC motors that do not employ commutators and brushes are generally more rugged and longer lasting. Torque rating relates to the response of the motor in relation to the supplied current. e generated torque of DC motors is nearly proportional with the supplied current. AC motors can handle larger currents and as a result can be more powerful for the same coil sizes and dimensions. However, stepper motors are generally the weakest. e largest torque they develop (called holding torque) is when they do not rotate at all. As they start to rotate, their torque decreases rather rapidly to the point that if they rotate fast, the torque becomes so small that the motor will miss steps. Since steppers do not usually have feedback systems, the controller will not be aware of their missed steps; this can have unacceptable consequences. e main reason for this behavior is that since the ﬁelds in the stepper coils are turned on and oﬀ very rapidly as their speed increases, the back-emf current ﬁghts the supplied current and severely aﬀects the torque. ere are remedies to minimize the eﬀects of back-emf (such as micro-stepping and the application of zener-diodes, etc.) at an added cost. e ability to reverse direction is a major factor. In many cases there is no need to reverse the direction of rotation of the motor (such as a fan). In that case, AC-type motors have many advantages. But when direction control is important, the choice is either a reversible AC motor or a DC motor (including universal motors). Because of this, most servomotors are of DC-type. Displacement and speed control is another deciding factor in the choice of motors. For example, stepper motors and brushless DC motors are run one step at a time, and consequently, it is easy to count the number of steps (or actually command the controller to send a known number of signals to the motor to move the rotor an exact number of degrees) and how fast the signals are sent and therefore control the displacement and speed of the motor. erefore, there is no need for a controller system or feedback sensors to measure the motion of the motors. However, these motors do require circuitry to operate with the added cost. Additionally, if these motors miss a step, there is no control system involved and no feedback system to determine the error and correct the motor. As a result, they can only be used for situations where there is little chance of missing a step or when they are reset often, like in a printer where the motor’s position is reset at the end of every line. DC and AC motors simply rotate as long as there is a current, and therefore, there is no control over their motion unless we employ a control system that through the use of sensors, measures both the rotational displacement and speed of the rotor and provides control over them (namely a servomotor). In this case, there is no need for drive circuitry as in a stepper motor or brushless DC motor, but there is a need for a control system. So depending on the application, the users must select the best choice based on their needs. 6.13. ADVANTAGES AND DISADVANTAGES OF DIFFERENT MOTORS 189 ese characteristics are also present in other types of motors. Depending on their char- acteristics, you can determine their utility and application. For example, any motor that does not have a rotor through which current ﬂows will not have to deal with heat rejection issues. Un- less other means are provided, AC currents from an outlet cannot be modiﬁed, and therefore, AC-type motors cannot be reversed. So even if we have not discussed other motors here, you can determine their characteristics by comparison with these fundamental types. Next time you see a motor or a transformer, especially if you have the chance to open it up and see its inside, see if you can determine what type of a motor it is and why it is used for that particular purpose. Electromagnetism and electromotive force are an important part of our daily lives in countless ways. Author’s Biography 191 SAEED BENJAMIN NIKU Saeed Benjamin Niku is a professor of mechanical engineering at California Polytechnic State University (Cal Poly), San Luis Obispo, California. He has taught courses in mechanics, robotics, design, and creativity, and has been involved in the design of many products, including many assistive devices for the disabled and new robotic devices. Dr. Niku’s publications include a statics workbook, an introduction to robotic analysis book (in its second edition), and a creative design of products and systems book. He enjoys making furniture and utilitarian products as well as artistic artifacts with wood, metals, glass, leather, and other materials. He received a B.S. mechanical engineering from Tehran Polytechnic in 1975, an M.S. mechanical engineering from Stanford University in 1976, and a Ph.D. in mechanical engineering from the University of California, Davis in 1982. Dr. Niku is a licensed professional engineer in the State of California. 193 Index absolute zero, 7 AC current, 159, 164, 176, 181, 189 AC motor, 163, 188 acceleration, 25, 57, 62, 84, 91, 147 acceleration, angular, 148, 151 acceleration, centripetal, 28 aileron, 87 altitude, 57 amplitude modulation, AM, 45 angular acceleration, 148, 151 angular deﬂection, 137, 139 angular momentum, 83 Arctic Circle, 75 asynchronous motor, 165 auditory canal, 51 auditory nerve, 52 Autumnal Equinox, 75 back-emf, 155, 161, 182, 185, 188 basilar membrane, 52 Bernoulli, 85 Bismuth, 3 bottom-dead-center, 107, 110 brushless motor, 188 caliper, 174 Caloric intake, 6 Calorie, 8, 54 canstack stepper motor, 169 cantilevered beam, 32, 42 capacitance, 44 capacitor, 15, 43, 182 center-tapped, 165 centripetal acceleration, 28, 64, 71 centroid, 131 chemical energy, 7 coeﬃcient of drag, 18 coeﬃcient of friction, 156 cold working, 145 combined cycle, 124 commutator, 162 compression ratio, 108, 118 condenser, 9, 101 connecting rod, 106 conservation of energy, 85 convection, 72 Coriolis acceleration, 57, 69, 75, 91 crankshaft, 106 critical damping , 27 cross product, 59 current, AC, 14 current, DC, 14 damping, 23 damping ratio, 26 DC current, 159, 177, 181 DC motor, 188 deceleration, 63, 185 deﬂection, 128, 142 detonation, 107 Diesel, 118 dot product, 59 194 INDEX ear, 50 eccentric shaft, 121 eddy current, 183 Edison, omas, 180 eﬃciency, 5, 10, 16, 97, 117, 158, 173, 176 elastic energy, 24 elastic limit, 144 elastic strength, 144 electric car, 16 electric energy, 179 electric power, 160 electromotive force, 13, 155, 161 elongation, 142 EMF, 13, 18, 155 energy conversion, 11 entropy, 1, 97, 115 epitrochoid, 121 equilibrium, 23 Eustachian tube, 51 evaporator, 9 exergy, 11 Faraday’s Law, 160, 182 feedback control, 186 Ferrel cell, 74-81 ﬁlter, low pass, 47 ﬁrst law, 7, 11 ﬂux, 157, 176 ﬂywheel, 90, 150 Fourier series, 53 Freon-12, 99 frequency modulation (FM), 45 friction, 11, 19, 25, 37, 97 fuel-air, 6, 107, 118 Gemini Agena, 92 generator, AC, 182 generator, DC, 181 grag, 86 gyroscope, 90 gyroscopic motion, 81 Hadley cell, 74-81 halfback array magnet, 169 half-stepping, 168 hardening, 145 harmonics, 42 hearing, 23 heat exchanger, 10, 102 heat loss, 8 heat rejection, 186 helix angle, 40 hybrid, 12 hybrid stepper motor, 174 hydroelectric powerplant, 16 ideal gas, 96 inductance, 44 induction heating, 183 induction motor, 165 internal combustion engine, 12, 105, 151 Joseph Henry, 160 Kelvin, 118 kinetic energy, 11, 15, 23, 31, 72, 120, 179 knock sensor, 109 knocking, 107 larynx, 42 latitude, 57 life expectancy, 188 longitude, 57 low-pass ﬁlter, 182 LVDT, 158 magnetic ﬁeld, 157 magnetic ﬁeld current, 13 magniﬁcation factor, 26 mass moment of inertia, 147, 151, 153 mechanical energy, 7 metabolic rate, 8 micro stepping, 188 microprocessor, 172 modulus of elasticity, 33, 128, 141, 144 modulus of rigidity, 139 moment of inertia, 53, 61, 125 motor, AC, 163, 188 motor, asynchronous, 165 motor, brushless, 188 motor, canstack stepper, 169 motor, DC, 188 motor, hybrid stepper, 174 motor, induction, 165 motor, reversible AC, 165 motor, servo, 185, 188 motor, squirrel cage, 165 motor, stepper, 166 motor, synchronous, 165 motor, universal, 166 natural frequency, 23, 31, 42, 49, 53 nature, 6, 73, 133 neutral axis, 131, 146 non-interference engine, 113 North Pole, 57 nuclear powerplant, 16 Octane number, 108 ossicle, 51 oval window, 51 Ozone layer, 100 parallel axis theorem, 133, 153 pendulum, 31, 44, 53, 161 Petra Valley, 3 pinna, 50 pitch axis, 85 INDEX 195 pitot tube, 85 plastic deformation, 144 PLC, 166 Polar cell, 74-81 polar moment of inertia, 137, 138 potential energy, 23, 31, 61, 179 power plant, 10, 16, 121, 179 prevailing winds, 57 programmable logic controller, 166 proportional stress limit, 143 radiation, 7 Rankin, 118 rectiﬁer, 182 reliability, 188 reluctance, 167 residual stress, 12 resolver, 178 resultant, 58 reversible AC motor, 165 right-hand-rule, 60 robot, 68, 91 roll axis, 85 rotary engine, 105, 121 rotating frame, 65, 69 rotor, 162, 175, 183, 187 rudder, 89 scalar, 58 second law, 7, 10, 12 second moment of the area, 125, 146 self locking , 41 servomotor, 185, 188 shear, 130, 146 Siberian Express, 57 slider crank mechanism, 106 solenoid, 158 sound energy, 51 spark-ignition, 105 196 INDEX speciﬁc gas constant, 96 speciﬁc volume, 96 speciﬁc weight, 149 spring constant, 23, 142 squirrel cage motor, 163, 165, 182, 187 stabilator, 88 stabilizer, 88 stainless steel, 4 stall condition, 187 stator, 162, 164, 175, 182, 187 stepper motor, 166 strain, 141 stress, 141, 146 Summer Solstice, 75 synchronous motor, 165 tachometer, 33 Tacoma Narrows bridge, 54 Tesla Motor, 16 thermal energy, 7, 12, 20 thermodynamics, 7, 11, 95, 116 thruster, 93 top-dead-center, 106, 110 torque, 61, 87, 139, 182, 188 torque, holding, 188 torsion, 137 transformer, 162, 176, 179, 183 translation, 68 tremolo, 36 tuning fork, 33 tympanic membrane, 51 ultimate strength, 145 ultra capacitor, 13 ultraviolet light, 4 universal motor, 166 vector, 58, 70 vehicle, battery, 13 vehicle, electric, 16 vehicle, plug-in hybrid, 16 vehicle, zero emission, 13 venturi, 85 Vernal Equinox, 75 vibration, 23 vocal cords, 42 Wankel engine, 105, 121 Westinghouse, George, 181 wind induced ﬂutter, 54 Winter Solstice, 75 work, 7, 61, 96, 109 worm gear, 37 yaw axis, 85 yield strength, 144 zener diode, 188 zero emission, 13 zeroth law, 7 zone of mixing, 74
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813538.pdf&bkn=6813537&pdfType=book	SYNTHESIS LECTURES ON ENGINEERING Series ISSN: 1939-5221 Systems Engineering Building Successful Systems Howard Eisner, The George Washington University This book provides an overview of systems engineering, its important elements, and aspects of management that will lead in the direction of building systems with a greater likelihood of success. Emphasis is placed upon the following elements: • How the systems approach is defined, and how it guides the systems engineering processes • How systems thinking helps in combination with the systems approach and systems engineering • Time lines that define the life cycle dimensions of a system • System properties, attributes, features, measures and parameters • Approaches to architecting systems • Dealing with requirements, synthesis, analysis and cost effectiveness considerations • Life cycle costing of systems • Modeling, simulation and other analysis methods • Technology and its interplay with risk and its management • Systems acquisition and integration • Systems of systems • Thinking outside the box • Success and failure factors • Software engineering • Standards • Systems engineering management Together, these top-level aspects of systems engineering need to be understood and mastered in order to improve the way we build systems, as they typically become larger and more complex. About SYNTHESIs This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com Mor gan Cl aypool Publishers & ISBN: 978-1-60845-701-4 90000 w w w . m o r g a n c l a y p o o l . c o m 9 781608 457014 E I S N E R S Y S T E M S E N G I N E E R I N G M o r g a n & C l a y p o o l & CM& Mor gan Cl aypool Publishers Systems Engineering Building Successful Systems Howard Eisner SYNTHESIS LECTURES ON ENGINEERING Systems Engineering: Building Successful Systems Copyright © 2011 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Systems Engineering: Building Successful Systems Howard Eisner www.morganclaypool.com ISBN: 9781608457014 paperback ISBN: 9781608457021 ebook DOI 10.2200/S00349ED1V01Y201104ENG014 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #14 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X Synthesis Lectures on Systems Engineering: Building Succesful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 iv Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Systems Engineering: Building Successful Systems Howard Eisner The George Washington University SYNTHESIS LECTURES ON ENGINEERING #14 CM& Morgan & cLaypool publishers ABSTRACT This book provides an overview of systems engineering, its important elements, and aspects of management that will lead in the direction of building systems with a greater likelihood of success. Emphasis is placed upon the following elements: (cid:129) How the systems approach is deﬁned, and how it guides the systems engineering processes (cid:129) How systems thinking helps in combination with the systems approach and systems engineer- ing (cid:129) Time lines that deﬁne the life cycle dimensions of a system (cid:129) System properties, attributes, features, measures and parameters (cid:129) Approaches to architecting systems (cid:129) Dealing with requirements, synthesis, analysis and cost effectiveness considerations (cid:129) Life cycle costing of systems (cid:129) Modeling, simulation and other analysis methods (cid:129) Technology and its interplay with risk and its management (cid:129) Systems acquisition and integration (cid:129) Systems of systems (cid:129) Thinking outside the box (cid:129) Success and failure factors (cid:129) Software engineering (cid:129) Standards (cid:129) Systems engineering management Together, these top-level aspects of systems engineering need to be understood and mastered in order to improve the way we build systems, as they typically become larger and more complex. KEYWORDS systems engineering, systems approach, systems life cycle, system measures, architecture, synthesis, analysis, cost-effectiveness, system costing, technology, risk management, software engineering, systems acquisition, integration Contents vii 1 2 3 4 5 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Deﬁnitions and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Deﬁnitions and Difﬁculties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The Systems Engineer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 1.3 Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Director of Systems Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Systems Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Additional Related Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Systems Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 The Fifth Discipline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1 Thinking in Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Systems Thinking and Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Systems Thinking and Special Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 3.5 General Systems Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Key Elements of Systems Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1 Other Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 The Life Cycle Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.1 Generic Life Cycle Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 A DoD Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.2 A NASA Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.3 Systems Engineering Across the Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 viii 6 7 8 9 System Properties, Attributes and Features (PAFs) . . . . . . . . . . . . . . . . . . . . . . . . . . 21 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Measures and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Architecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Functional Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 9.1 9.2 9.3 9.4 A Simple Computer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A C4ISR System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Earth-Observing System (EOSDIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 FAA’s NextGen System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 10 Requirements Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 10.1 Requirements Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 10.2 Derived Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 10.3 Some NASA Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 10.4 Top Half Dozen Requirements Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 11 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 11.1 Supporting Tables and Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 12 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 12.1 Deeper Levels of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 12.2 Analysis of Alternatives (AoA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 13 Cost-Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 13.1 Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 ix 14 Life Cycle Costing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 14.1 Life Cycle Cost Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 14.2 Bottoms-Up and Top Down Cost Estimation Notions . . . . . . . . . . . . . . . . . . . . . . 53 14.3 Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 14.4 NASA and Cost Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 15 Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 15.1 Four Illustrative Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 15.2 15.3 Domains of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 15.4 Modeling and Simulation in the DoD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 16 Other Analysis Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 16.1 System Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 16.2 Errors as Requirements or Speciﬁcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 16.3 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 16.4 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 “Subjective” Analysis and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 16.5 16.6 Other Topics of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 17 The Role of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 17.1 Ofﬁce of Technology Assessment (OTA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 17.2 The Department of Defense (DoD) and Technology . . . . . . . . . . . . . . . . . . . . . . . . 64 17.3 Criticisms and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 17.4 Technology Readiness Levels (TRLs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 17.5 The Technology Readiness Assessment (TRA) Deskbook . . . . . . . . . . . . . . . . . . . 66 17.6 A Closing List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 18 Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 18.1 Basic Risk Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 18.2 Risk Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 18.3 NASA and Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 x 18.4 Additional Risk Management Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 19 Testing, Veriﬁcation, and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 19.1 Test and Evaluation (T & E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 19.2 Veriﬁcation and Validation (V & V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 20 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 21 22 20.1 Brief Deﬁnition of Systems Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 20.2 Systems Integration Core Competencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 20.3 The Stovepipe Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 20.4 Evolutionary Development and Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 20.5 20.6 Integration Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Integrability? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 20.7 The Bottom Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Systems Engineering Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 21.1 The SEMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 21.2 The SEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Project Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 22.1 Goals, Objectives and Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 22.2 Task Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 22.3 Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 22.4 Organization and Stafﬁng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 22.5 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 22.6 Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 22.7 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 22.8 Earned Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 22.9 The Project Manager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 xi 23 24 25 Software Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Software Development Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 23.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 23.2 The Capability Maturity Model 23.3 COCOMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 23.4 Top Ten for Software Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Systems Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 24.1 The 5000 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 24.2 Defense Acquisition Performance Assessment (DAPA) Report [4] . . . . . . . . . . . . 97 24.3 Weapon System Acquisition Reform Act of 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 24.4 Greater Efﬁciency and Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 24.5 Evolutionary Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Systems of Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Some Perspectives Regarding Systems of Systems . . . . . . . . . . . . . . . . . . . . . . . . . 100 25.1 25.2 Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 25.3 The Ubiquitous Department of Defense (DoD) . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 26.1 26.2 26 Thinking Outside the Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Inside the Box 1: Build systems so as to maximally integrate all stovepipes . . . . 104 Inside the Box 2: It’s not possible to make changes so as to achieve more than marginal improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Inside the Box 3: Requirements should be considered ﬁxed and inviolate . . . . . . 105 Inside the Box 4: There is no silver bullet that can ﬁx a poorly performing acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 26.5 Nine Suggestions for Thinking Outside the Box . . . . . . . . . . . . . . . . . . . . . . . . . . 106 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 26.3 26.4 27 Ten Failure Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 27.1 One—Unrealistic Schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 27.2 Two—Unrealistic Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 27.3 Three—Too Many Risks in the Performance Dimension . . . . . . . . . . . . . . . . . . . 110 27.4 Four—Lots of Risk Analysis, Not Enough Risk Mitigation . . . . . . . . . . . . . . . . . 110 xii 27.5 Five—Lip Service to “The Learning Organization” . . . . . . . . . . . . . . . . . . . . . . . . 110 Six—Poor Requirements Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 27.6 Seven—Failure to Buy Into Evolutionary Development . . . . . . . . . . . . . . . . . . . . 111 27.7 27.8 Eight—Insufﬁcient Communications and Teamwork . . . . . . . . . . . . . . . . . . . . . . 112 27.9 Nine—Slippage in the Practices of Systems Engineering . . . . . . . . . . . . . . . . . . . 112 27.10 Ten—We Know What to Do; Why Won’t We Do It? . . . . . . . . . . . . . . . . . . . . . . 112 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 28 A Success Audit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 29 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 29.1 Military Standard 499B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 29.2 IEEE P1200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 29.3 EIA 632 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 ISO/IEC 15288 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 29.4 IEEE/EIA 12207 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 29.5 IEEE P1471 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 29.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Preface This book basically provides a top-level overview of Systems Engineering. As such, it may be considered a Primer on systems engineering, looking at some 30 main topics that tell a good part of the story. It leans heavily upon the views of a few government agencies and how they perceive and practice systems engineering. These agencies tend to drive as well as use systems engineering on the numerous projects that they sponsor. They are major customers, and we note that listening to customers is usually a very good idea. These 30 main topics represent what the students and practitioners of systems engineering need to know. It is expected that readers, after a quick perusal of the entire book, will want to “drill down” into subjects of special interest. Many other sources are identiﬁed for these purposes, both at the end of each chapter as well as in the Bibliography (Chapter 30). It is further noted that the book’s subtitle is “Building Successful Systems”. In a real-world context, that’s what systems engineering should be all about. There’s no one formula that will ensure this outcome. Pointers in that direction appear throughout the book, and two chapters focus more sharply on how we might be more successful. Respectively, they look at “doing it wrong”, and “doing it right”. These chapters are the following: (cid:129) Chapter 27 - Ten Failure Factors (cid:129) Chapter 28 - A Success Audit This book has been designed also for introductory courses in systems engineering at either the undergraduate or graduate level. A follow-up more intense treatment, as per a 2nd course in systems engineering, may be found among the chapter references as well as the citations in the Bibliography (Chapter 30). I am appreciative of the fact that my Publisher, Joel Claypool, immediately saw the need for this book, and its top-level approach. I am also appreciative of the constant encouragement from my wife, June Linowitz, who has been supportive of all of my writing adventures in and around the world of systems engineering and related disciplines. A Good Day to All, Howard Eisner April 2011 C H A P T E R 1 1 Deﬁnitions and Background 1.1 DEFINITIONS AND DIFFICULTIES This is a book about building relatively large systems using a discipline known as systems engineering. Many deﬁnitions of this discipline have been suggested, as for example: (cid:129) Systems engineering is “an interdisciplinary approach and means to enable the realization of successful systems” [1]. (cid:129) Systems engineering is “an iterative process of top-down synthesis, development, and operation of a real-world system that satisﬁes, in a near-optimal manner, the full range of requirements for the system” [2]. (cid:129) Systems engineering is a “methodical, disciplined approach for the design, realization, technical management, operations, and retirement of a system” [3], and a system is deﬁned as “a construct or collection of different elements that together produce results not obtainable by the elements alone.” (cid:129) Systems engineering is “an interdisciplinary management process to evolve and verify an inte- grated, life cycle balanced set of system solutions that satisfy customer needs” [4]. This source also deﬁnes a system as “an integrated composite of people, products, and processes that provide a capability to satisfy a stated need or objective.” In this book, considerable attention is paid to elaborating upon these short-form deﬁnitions and providing a rationale for the explanations. We note, however, that despite the fact that we have considerable background on what systems engineering is, and how it should be applied, we still experience great difﬁculties in building large systems. A sense of some of these problem areas can be gleaned from looking at some of the reports produced by such groups as the GAO (Government Accountability Ofﬁce). Here are some of their observations [5]: 1. We did not have sufﬁcient technology maturity to justify moving forward. 2. Knowledge with respect to design and production, at important milestones, was lacking. 3. We were using high-risk contracting procedures with insufﬁcient accountability. 4. We had poor cost estimating methods. 2 1. DEFINITIONS AND BACKGROUND 5. We had been experiencing unacceptable cost growth in too many of our important systems. In addition, there are other reports that suggest there is considerable room for improvement. A rather well known analysis, known as the Standish Report, provides some data points for us to consider [6]: (cid:129) Only about 16% of all information technology projects were concluded on time and within the allocated budget (1999 data). (cid:129) About 30% of the above programs were canceled prior to their scheduled completion (1999 data). (cid:129) Results in 2009 revealed a decrease in the success rates of projects, with these rates in the vicinity of 32% of all projects (on time, budget, and with proper features). (cid:129) The 2009 data indicated “the highest failure rate in over a decade.” An internally-directed look at systems engineering problems from the NDIA (National De- fense Industrial Association) gave us yet another perspective [7], summarized below. (cid:129) Urgent user demand requires ﬁelding capabilities more rapidly than we are doing today. (cid:129) The systems engineering expertise is wanting in both quality and quantity. (cid:129) Practices known to be effective are not consistently applied. (cid:129) Technical decision makers do not have the proper information at the proper times. (cid:129) Poor impacts are resulting from lack of technical authority. These issues are known to adversely affect our ability to build successful systems, especially in the government and defense worlds. So – we continue to look for better ways to understand and apply principles of systems engineering to the systems we are building. If we are able to do so, we expect that we will be more successful as we move forward, and that the systems themselves will operate more successfully. 1.2 THE SYSTEMS ENGINEER The systems engineer is in considerable demand, and in a 2009 survey was cited as ranking ﬁrst in terms of the “best job in America” in the Information Technology Sector [8]. This source claimed that demand was soaring, moving from a niche position in the aerospace and defense industries to an expanding set of potential employers ranging from “medical device makers to corporations like Xerox and BMW.” The median salary at that time for experienced people was $87,100, with a top pay of some $130,000 per year. From these data alone, it is easy to see why many technical folks would try to qualify as systems engineers. 1.3. PROCESS 3 We cite in Table 1.1 ten of the attributes that are sought in terms of a highly qualiﬁed systems engineer. Although we may know all the details of the systems engineering processes, it is the competent systems engineer who makes it all happen. Having said that, however, we must also recognize that the individual systems engineer cannot do it alone. In today’s world of building large systems, the engineers are part of a team, and it is the highly functional team that leads to success. Put another way, if the competent systems engineer is embedded in a poor team, the results are not likely to be acceptable. For that reason, we pay a great deal of attention to the matter of building high performance teams (HPTs) in attempting to construct successful systems. 1.3 PROCESS As we explore the various aspects of systems engineering in this book, we will note an emphasis on “process.” For example, some of the cited standards have basically identiﬁed all the processes that need to be properly executed in an attempt to build successful systems. Here, we acknowledge process as critically important but claim that it is still a necessary but insufﬁcient condition. In our search for the latter, we look in the direction of subject matter expertise. We look for the systems engineer who deeply understands systems engineering, but who also has the subject knowledge that is critical to success in this world of large and complex systems. 1.4 DIRECTOR OF SYSTEMS ENGINEERING In completing this ﬁrst chapter, we note that there is a Director of Systems Engineering (DSE) that deals with key issues within the Department of Defense (DoD) [9]. This ofﬁce, as of this writing, has adopted a set of priorities, as listed below: Table 1.1: Selected Desirable Attributes of the Systems Engineer. 1. Broad technical skills – the ability to solve problems in several technical domains. 2 Open-minded – willing to change one’s mind and modify any pre-conceived notion. 3. Facilitator – noticeably assists in group problem-solving 4. Excellent listener – is receptive to hearing the views of others. 5. Integrator – is able to bring ideas together to formulate new solutions. 6. Superior people skills – relates very well to all members of the team as well as bosses. 7. Inquisitive – often explores information at the “edges” of the immediate problem. 8. Analytical – thinks logically and with precision and persistence. 9. Team Player – willingly listens to and supports other team members. 10. Technical leader – is competent and able to take a lead position on technical matters and problem solving. 4 REFERENCES (cid:129) “Support the current ﬁght; manage risk with discipline. (cid:129) Grow engineering capabilities to address emerging challenges. (cid:129) Support realistic program formulation through the application of development planning and early systems engineering. (cid:129) Increase focus on reliability, affordability, and total ownership cost. (cid:129) Champion systems engineering as a tool to improve acquisition quality. (cid:129) Develop future technical leaders across the acquisition enterprise.” This ofﬁce has a signiﬁcant inﬂuence in the world of systems engineering and is likely to continue to play an important role in the years to come. REFERENCES [1] International Council on Systems Engineering (INCOSE), www.incose.org 1 [2] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 1 [3] “NASA Systems Engineering Handbook,” NASA/SP-2007–6105, NASA Headquarters, Washington, DC. 1 [4] “Systems Engineering Fundamentals,” Defense Systems Management College (DSMC), Oc- tober 1999, Fort Belvoir, VA. 1 [5] GAO Highlights, “Assessment of Selected Major Weapon Programs,” March 2005 and March 2006, see also www.gao.gov 1 [6] Standish CHAOS Reports, standishgroup.com, 1999, 2010. 2 [7] www.ndia.org 2 [8] “Best Jobs in America,” Number 1. Systems Engineer, CNNMoney.com, money.cnn.com 2 [9] www.acq.osd.mil/se/ 3 C H A P T E R 2 5 The Systems Approach In this chapter, we deﬁne what is referred to as the “Systems Approach.” We will look at some deﬁnitions in the literature but, ultimately, will accept and expand upon this author’s deﬁnition. In this regard, the seven elements of the “systems approach” have been set forth as cited and discussed below [1]: 1. Establish and follow a systematic and repeatable process. A proven process is emphasized and must be able to be carried out by different teams in differing environments. New processes can be introduced but only after they have been established as close as possible to best practices. 2. Assure interoperability and harmonious system operation. The internal components of a system must interoperate, and these must also interoperate with other systems if they are designed to do so. We are striving for internal as well as external harmonious operations such that stresses are minimized. 3. Be dedicated to the consideration of alternatives. A central feature of the “systems approach,” we construct and evaluate alternative approaches and designs, whenever feasible.This notion applies both at the architectural design level as well as the detailed sub-system design level. Failure to do this can lead to trying to use yesterday’s solutions to today’s problems. 4. Use iterations to reﬁne and converge. We recognize the complexity of building large systems and use iteration and recursion to allow us to move forward, even when we do not have a solution immediately at hand. We are able to use the “TBD” (to be determined) in a systematic way, and iterate to ultimately ﬁnd what we believe to be a best solution. 5. Create a robust and slow-die system. We insist upon having our systems, as best we can, not be subject to single-point catastrophic failures. As parts (e.g., components) of our systems fail, performance may be degraded, but a little at a time. 6. Satisfy all agreed-upon user/customer requirements. 6 2. THE SYSTEMS APPROACH Requirements may change and “creep” during the development process, but when they become stable and agreed-upon, there is an obligation to satisfy these requirements. Developers and acquisition agents must ﬁnd new and better ways to negotiate appropriate solutions to this often controversial area. 7. Provide a cost-effective solution. The over-riding consideration in the systems approach is to develop a cost-effective solution to the customer’s problem. This usually involves the appropriate consideration of alternatives, from which the most cost-effective solution is selected. We will now expand the above seven features to a total of ten. On that basis, we add the following three items, along with a short discussion of each: 8. Assure the system’s sustainability. The new systems we are building must not lead to massive depletion of our resources. They must be sustainable, in the long run, even though we may need to invest disproportionately in the short run. This is more than a dollars and cents issue: applying as well to natural as well as man-made resources, and the rates at which we use them. 9. Utilize advanced technology, at appropriate levels of risk. History has shown that many of our most important large-scale systems (e.g., telephone, electrical power grid, transportation, defense) have moved forward only as a result of the technology that we have been able to develop and apply. Technology is thus a basis for many of our new systems, and we need to ﬁnd the proper balance, every step of the way, between advanced technology and level of risk. 10. Employ systems thinking. “Systems thinking” is considering the development, operation, and maintenance of our systems in a holistic sense. It is a perspective that allows us to go beyond the views of individual compo- nents and sub-systems, to total systems as well as systems-of-systems. Due to its importance, and also its lack of intuitive precision and clarity, the next chapter is devoted to exploring this topic in a more comprehensive manner. The basic claim in this book is that the well-considered use of the systems approach will help to increase the likelihood of success in building systems. The Department of Defense, in its consideration of recommended acquisition practices, makes the point as below with their own perspective as to what constitutes the total systems approach [2]: “Total Systems Approach – The Project Manager (PM) shall be the single point of account- ability for accomplishing program objectives for total life-cycle systems management, including sustainment. The PM shall apply human systems integration to optimize total system performance (hardware, software and human), operational effectiveness, and suitability, survivability, safety, and 2.1. ADDITIONAL RELATED FACTORS 7 affordability. PMs shall consider supportability, life cycle costs, performance, and schedule compa- rable in making program decisions. Planning for Operation and Support and the estimation of total ownership costs shall begin as early as possible…” Yet another view of the “systems approach” is provided by NASA in their systems engineering handbook [3]: (cid:129) The systems approach is “the application of a systematic, disciplined engineering approach that is quantiﬁable, recursive, iterative, and repeatable for the development, operation, and maintenance of systems, integrated into a whole throughout the life cycle of a project or program.” We also have a quite interesting and coherent exposition on the systems approach from one of our gurus in the overall ﬁeld of systems engineering. This exposition took the form of a long paper entitled “The Systems Approach,” and was co-authored by Simon Ramo [4], whose name was included in the company title known as “TRW” (i.e.,Thompson-Ramo-Wooldridge). Dr. Ramo makes many points, among them the following: (cid:129) The systems approach uses objectivity, logic, and automated common sense. (cid:129) It typically uses a team of experts, dignifying the problem and the implied methodology. (cid:129) A skillful team will zero in on the problem (and its solution). (cid:129) The systems approach has the potential for solving many of our most important and vexing problems if we can ﬁnd and develop the appropriate practitioners and have a forum for listening and implementing solutions. 2.1 ADDITIONAL RELATED FACTORS We cite now a few factors that relate to the systems approach, and we may well become an integral part of it (i.e., on our “top ten” list). Stakeholders. As we try to ﬁnd the best system, we must ask the question: best for who? This raises the notion that many of our systems have a large number of stakeholders, and the interests of these stakeholders may be in conﬂict. The systems approach should be able to account for possible disparate interests and none-the-less ﬁnd a solution that most, if not all, will accept. Tradeoffs at the Systems Level. Connected to the above idea is the notion that we need to look at the various tradeoffs that exist at the top-most level in question. To illustrate - who gets the service and who makes the proﬁt are but two of many questions that need to be explored. Architectures and Balance. Architectures are crucial features of our systems, and systems approach considerations in that respect are “simpliﬁcation, compromise and balance” [5]. How is that to be achieved? See Eb Rechtin’s seminal book on systems architecting [5]. Design for Integration. If we are to be more successful bringing whole systems together, we need to do better in our designs to account for, and facilitate, the downstream integration. Conversely, 8 REFERENCES systems not designed to be integrated are not likely to be amenable to such considerations or goals. This is a problem area that needs considerable work in the future, given our tendencies to look for ways to integrate “stovepipes.” REFERENCES [1] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 5 [2] DoD Directive 5000.1, “The Defense Acquisition System,” May 12, 2003, Department of Defense, Washington, DC. 6 [3] NASA/SP-2007–6105, Rev. 1, “NASA Systems Engineering Handbook,” December 2007, NASA, Washington, DC, p. 276. 7 [4] Ramo, S., and Robin K. St. Clair, “The Systems Approach,” www.incose.org 7 [5] Rechtin, E., System Architecting, Prentice-Hall, 1991. 7 C H A P T E R 3 Systems Thinking 9 We recall, from the previous chapter, that “systems thinking” is listed as one of the features of the systems approach. Thus, systems thinking helps us to carry out that approach as part of the overall discipline of systems engineering. In broad terms, systems thinking involves looking at the system we are building, or analyzing, as a whole, rather than as an assemblage of parts. Systems thinking leads us to considering the behavior of the total system in its current environment or in a situation that may change from time to time. Systems thinking takes us away from a reductionist viewpoint to one that is more holistic. In this chapter, we look at what several students and teachers of systems thinking have espoused and attempt to apply some of these notions to systems engineering. 3.1 THE FIFTH DISCIPLINE There is no better place to begin to explore systems thinking than to go to the work of Peter Senge [1] called “The Fifth Discipline.” The overall topic of the “art and practice of the learning organization” is examined in some detail, with the conclusion that there are ﬁve disciplines that need to be mastered in order to create and sustain “the learning organization,” namely: 1. Building a shared vision. 2. Personal mastery. 3. Mental models. 4. Team learning, and, 5. Systems thinking (the ﬁfth discipline). The nature of systems thinking is thus examined, with the following key observations: (cid:129) “systems diagrams” represent and help us understand the behavior of systems. (cid:129) Reinforcing and balancing feedback and delays are among the building blocks of systems thinking. (cid:129) A bottom line of systems thinking is the creation of leverage. (cid:129) Each of the ﬁve learning disciplines depends upon thinking at the levels of (a) practices, (b) principles, and (c) essences. 10 3. SYSTEMS THINKING (cid:129) Essences depend upon holism and interconnectedness; principles depend upon structure, policy and leverage; practices depend upon system archetypes and simulation. Senge’s approach, in part, is based upon a well-known modeling and analysis procedure known as System Dynamics, originally developed by Forrester [2]. This procedure is used to study and characterize the behavior of organizations. It is also directly applicable to systems of all types. In the latter sense, we may think of Forrester’s work as one of many tools that the systems engineer is able to use to explore the behavior of a variety of systems. 3.2 THINKING IN SYSTEMS We see further systems thinking perspectives in the work of Donella Meadows [3], who along with her husband Dennis, studied “limits to growth” and was a strong purveyor of the System Dynamics approach to systems thinking and analysis. Some of the ideas set forth in her book on systems thinking include the following: (cid:129) A system consists of three types of things: elements, interconnections and a function or purpose; the latter often has the greatest inﬂuence on system behavior. (cid:129) A system, typically, is more than the simple sum of its parts. (cid:129) Information feedback is critical to the stability of systems. (cid:129) The resilience of systems is very important, and it has its limits. (cid:129) Models are our ways of thinking about and evaluating systems, but they are still models and not reality. (cid:129) Most of our systems exhibit extreme non-linearities, which make them very difﬁcult to analyze. (cid:129) One of our challenges is still to “go for the good of the whole.” 3.3 SYSTEMS THINKING AND HEURISTICS A rich supply of systems thinking in relation to systems engineering and architecting can be found embedded in the subject of system “heuristics.” And perhaps the most outstanding developer of system heuristics was E. Rechtin [4]. In his classic book on system architecting, Dr. Rechtin gave us the beneﬁt of some of his systems thinking, represented in the short sample of heuristics cited below: 1. “Except for good and sufﬁcient reasons, functional and physical structuring should match; 2. No complex system can be optimum to all parties concerned, nor all functions optimized; 3. Build in and maintain options as long as possible in the design and implementation of complex systems; 4. A model is not reality” (see a similar comment above from Meadows). 3.4. SYSTEMS THINKING AND SPECIAL TOPICS 11 Undoubtedly, the above and other heuristics came forth from his keen observations about systems over a period of some 50 years. And his “systems perspective” was likely derived from his integration skills that allowed him to focus upon the top-level behavior of systems and the teams that were building these systems. 3.4 SYSTEMS THINKING AND SPECIAL TOPICS Over the years, systems thinking has gravitated to a series of topics that have been difﬁcult to contemplate and resolve. Researchers continue to make progress, but additional systems thinking would be most welcome with respect to the partial list of such matters as cited below: ◦ system complexity, ◦ measures of interoperability and integrability, ◦ emergent properties, ◦ resilience, ◦ adaptation, ◦ self organization, ◦ reﬂexivity, ◦ transformative factors and features, ◦ total system models and simulations, ◦ a breakthrough general systems theory. Having pointed to the above, however, we need to understand that our current state-of-the-art in systems thinking is extensive, with several “sub-schools” of thought within the overall ﬁeld. 3.5 GENERAL SYSTEMS THEORY Many of the aspects of systems thinking are traceable back to yet another classic work, that of Bertalanffy’s “General System Theory” [5]. Many of the researchers in a general systems theory point back to Bertalanffy as the source of their thinking, and inspiration. As we look at systems theory and systems thinking from the perspective of systems engineering, we are aware of one top-level aspiration: (cid:129) That if we had a stronger and more coherent base of systems theory and thinking, we would do a better job at systems engineering, and thus would be able to be more successful in our systems engineering undertakings. Systems thinking and theory thus provide a challenge for the “systems” community. That challenge is to put the pieces together such that all of the related ﬁelds, including systems engineering, are illuminated.To that end, we provide here as the last reference a long list of researchers [6] that can be accessed by the reader to explore their contributions, and the possibility that a totally integrative treatment is within our grasp, not too far down the road. 12 REFERENCES REFERENCES [1] Senge, Peter, The Fifth Discipline – The Art & Practice of the Learning Organization, Double- day/Currency, 1990. 9 [2] Forrester, Jay, System Dynamics, Pegasus Communications, 1968. 10 [3] Meadows, D., Thinking in Systems, Chelsea Green Publishing, 2008. 10 [4] Rechtin, E., Systems Architecting, Prentice Hall, 1991. 10 [5] Bertalanffy, Ludwig von, General System Theory, George Braziller, 1968. 11 [6] Systems Researchers: R. Ackoff, W. R. Ashby, B. Babathy, G. Bateson, K. Boulding, S. Beer, F. Capra, P. Checkland, C. W. Churchman, R. Flood, H. Foerster, J. Gall, R. Hutchins, M. C. Jackson, Klir, E. Laszlo, I. Prigogine, A. Rapoport, A. Sage, L. Skyttner, F. Vester, J. von Neumann, M. Weber, G. Weinberg, N. Wiener, B. Wilson, (see, also chapter thirty). 11 C H A P T E R 4 13 Key Elements of Systems Engineering The key elements of systems engineering depend upon which approach one takes to the overall application of systems engineering. Three such approaches can be identiﬁed: 1. The Process-Oriented Approach (POA). 2. The Model-Based Approach (MBSE), and, 3. The Tailored Activity Approach (TAA). In this chapter, we explore in some detail the latter approach, such that each activity represents a basic element of systems engineering. Less emphasis is placed upon the former two approaches. An overview of this approach can be explored by deﬁning four aspects of systems engineering that tend to be both large and important in scope and correlated with a system’s life cycle. These four aspects are the following: A. System Architecting. B. Subsystem Design. C. Construction, Test and Evaluation. D. Operations, Maintenance and Reengineering. A critical aspect of systems engineering is the ﬁrst part of the design process known as System Architecting. It is during this activity that the design team comes to terms with, and deﬁnes, the overall system design. Errors here propagate throughout the design and can be fatal to the overall effort. Once the architecture is formulated and agreed to, the Subsystem Design proceeds. These ﬁrst two aspects constitute the overall design activity for the system [1]. An accepted design, down to the subsystem level, allows the team to build the system with speciﬁc implementations of hardware, software, and the human element. At the end of this Construction process, Test and Evaluation conﬁrms that the physical system satisﬁes the stated requirements, and the system is able to move forward into Operations, Maintenance, and Reengineering. This overview becomes the background for the more formal deﬁnition of the elements of sys- tems engineering, using the Tailored Activity Approach. The overall notion is depicted in Figure 4.1. 14 4. KEY ELEMENTS OF SYSTEMS ENGINEERING Table 4.1: Six Categories and Thirty Elements of Systems Engineering. Category A: Developer Design-Related 1. System Architecture 2. Analysis and Evaluation of Alternatives 3. Technical Performance Measurement 4. Life Cycle Costing 5. Risk Analysis and Mitigation 6. Hardware, Software and Human Engineering Category B: Developer Integration and Test 7. Integration 8. Veriﬁcation and Validation 9. Test and Evaluation Category C: Key Support Elements 10. Concurrent Engineering 11. Speciﬁcation Development 12. Interface Control 13. Computer Tool Use 14. Technical Data Management and Documentation 15. Integrated Logistics Support and Sustainment 16. Reliability, Maintainability and Availability 17. Quality Assurance 18. Conﬁguration Management 19. Specialty Engineering 20. Preplanned Product Improvement Category D: Fielding, Operations and Support 21. Training 22. Production and Deployment 23. Operations and Maintenance 24. Operations Evaluation and Reengineering 25. System Disposal Category E: Customer-Deﬁned Elements 26. Needs, Goals and Objectives 27. Mission Deﬁnitions 28. Requirements 29. Functions Category F: Overall Management 30. Management of All the Above Elements Systems(cid:3)Engineering(cid:3)Aspects(cid:3) (cid:3)(cid:3)(cid:3)Implemented(cid:3)Via(cid:3)30(cid:3)Elements(cid:3) 4.1. OTHER APPROACHES 15 - (cid:882)System(cid:3)Architecting(cid:3) (cid:882)Subsystem(cid:3)Design(cid:3) (cid:882)Construction,(cid:3)Test(cid:3)&(cid:3)Evaluation(cid:3) (cid:882)Operations,(cid:3)Maintenance(cid:3)and(cid:3) Reengineering(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)In(cid:3)Six(cid:3)Categories(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(see(cid:3)Table(cid:3)4.1)(cid:3) Figure 4.1: Aspects, Categories, and Elements of Systems Engineering. The representation of the six categories, and the 30 elements, is shown below in Table 4.1 [2]. The above construction of systems engineering is considered to be part of the Tailored Activity Approach (TAA) since the amount of effort to be devoted to each element is to be determined explicitly by the project management that is responsible for the system that is being designed and built. This project management can be thought of as consisting of three people: the Project Manager (PM), the Chief Systems Engineer (CSE), and the Project Controller [3].Thus, it is both possible and critical that this team decide which elements are funded, and by how much. Not all projects require all of the elements, and depending upon size, complexity, and other factors, the project management must tailor the systems engineering activities to the overall program needs and constraints. 4.1 OTHER APPROACHES The above discussion leaves open the question as to what the elements are for the Process-Oriented Approach (POA) and the Model-Based Systems Engineering (MBSE) approach. We will not give a deﬁnitive answer to this question in this text. However, it is clear from the work of INCOSE [4] and the ISO/IEC 15288 Standard [5] that the Process-Oriented approach is based upon twenty-ﬁve speciﬁc processes in the categories of: agreements, enterprises, projects, and technical considerations. With respect to the Model-Based Systems Engineering approach, we refer the reader to the work of Friedenthal [6], Estefan [7], and others [8]. Some of the key ideas in the MBSE approach are listed below: - It represents a movement from a document-based method to a model-based method. - It has the potential to improve the quality and uniformity of how systems engineering is executed (e.g., in the ﬂow-down of requirements). 16 REFERENCES - In applications to date, we see the use of the Systems Modeling Language, which itself rep- resents an improvement over the Uniﬁed Modeling Language [6]. - There are several noteworthy MBSE methodologies [7]. Whichever approach selected by the systems engineering team, we note strong support for the use of systems engineering [9], and evidence that with its proper application, the likelihood of success is increased [10]. REFERENCES [1] Eisner, H., “System Design, Architecting and Heuristics,” International Conference on In- dustrial Engineering and Systems Management, IESM 2009, Montreal, Canada, May 13–15, 2009. 13 [2] Eisner, H., Managing Complex Systems—Thinking Outside the Box, John Wiley, 2005. 15 [3] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 15 [4] Systems Engineering Handbook, vers. 3.2, INCOSE, www.incose.org 15 [5] Systems Engineering – System Life Cycle Processes, (2002), ISO/IEC 15288, Geneva, Switzerland. 15 [6] Friedenthal, S., A. Moore and R. Steiner, A Practical Guide to SysML: The Systems Modeling Language, Elsevier, 2008. 15, 16 [7] Estefan, J., Survey of Model-Based Systems Engineering Methodologies, INCOSE MBSE Initia- tive, INCOSE, May 23, 2008, www.incose.org 15, 16 [8] Wymore, A. W., Model-Based Systems Engineering, CRC Press, 1993. 15 [9] DoD Directive 5000.1,The Defense Acquisition System, Department of Defense (DoD), Wash- ington, DC, May 12, 2003. 16 [10] www.ndia.org 16 C H A P T E R 5 17 The Life Cycle Dimension Most systems are built and put into service on a well-deﬁned time line. Most agencies and companies have a well-deﬁned understanding of the time lines they tend to use, and the various phases that are part of the time lines. In this chapter, we look brieﬂy at three of these time lines and phases. 5.1 GENERIC LIFE CYCLE PHASES An example of what might be called a set of generic life cycle phases is displayed in Figure 5.1 below [1]: Need(cid:3) Develop(cid:882) ment(cid:3) Concept(cid:3) Definition(cid:3) Concept(cid:3) Validation(cid:3) Engineering(cid:3) Development(cid:3) Pro(cid:882) duction(cid:3) Opera(cid:882)(cid:3) tions(cid:3) Figure 5.1: Generic Life Cycle Phases. Here we see the system phases described as: - Need Development. - Concept Deﬁnition. - Concept Validation. - Engineering Development. - Production, and - Operations. The program is formally approved after the need has been veriﬁed; at which time, the team begins work on deﬁning the concept, in detail. During this phase, there is also an SRR, a system requirements review. Proceeding into concept validation, there is a system design review (SDR). After validation, we move into engineering development. During this key phase, there are two reviews: the PDR (preliminary design review) and CDR (critical design review). Just about all life 18 5. THE LIFE CYCLE DIMENSION cycle representations include formal reviews of critical importance to the success (or lack of it) in a program or project. An interim operational capability (IOC) is typically achieved during production, with a ﬁnal operational capability (FOC) available at the start of operations. 5.2 A DOD EXAMPLE As one might expect, the DoD has been clear about its life cycle phases, which are deﬁned as part of its Defense Acquisition Management System [2]. A representation of that system is shown here in Figure 5.2. User(cid:3)Needs(cid:3)and(cid:3) Technology(cid:3) Opportunities(cid:3) A B C Materiel Sol. Analysis Technology(cid:3) Development(cid:3) Eng. & Manuf. Development Production(cid:3)and(cid:3) Deployment(cid:3) Operations(cid:3)and(cid:3) Support(cid:3) Concept(cid:3) Decision(cid:3) Program(cid:3) Initiation Figure 5.2: Life Cycle Phases With Emphasis on Technology [2]. The phases of interest here are: - Materiel Solution Analysis. - Technology Development. - Engineering and Manufacturing Development. - Production and Deployment, and - Operations and Support (O & S). The ﬁrst phase accepts “user needs” and “technology opportunities” as inputs, explicitly stress- ing the importance of technology in our military systems. This point is reinforced by the second phase that formalizes, and even develops, the technology needed for the system.The program cannot be initiated until it is completely clear, so that the selected technology is, or will be, available when 5.3. A NASA EXAMPLE 19 it is called for. The formal “systems acquisition” process starts with engineering and manufacturing development and continues on into production and deployment. That is followed by the operations and support (O & S) phase. One important difference between the DoD and the generic life cycle phases can be seen by the inclusion of a “technology” emphasis in our defense world. This is entirely appropriate as we must assure that our military systems have the state-of-the-art technologies for the conﬂicts of the day. As in the generic case, the DoD has many reviews during which progress can be assessed. Listed below are eleven reviews that are part of the process: - Initial Technical Review (ITR). - Alternative Systems Review (ASR). - System Requirements Review (SRR). - System Functional Review (SFR). - Preliminary Design Review (PDR). - Critical Design Review (CDR). - Test Readiness Review (TRR). - System Veriﬁcation Review (SVR). - Production Readiness Review (PRR). - Operational Test Readiness Review (OTRR). - In-Service Review (ISR). 5.3 A NASA EXAMPLE The NASA approach to deﬁning life cycle phases is provided in their Systems Engineering Hand- book [3], which shows a total of seven life cycle phases: - Pre-Phase A: Concept Studies. - Phase A: Concept and Technology Development. - Phase B: Preliminary Design and Technology Completion. - Phase C: Final Design and Fabrication. - Phase D: Assembly, Integration and Test; Launch. - Phase E: Operations and Sustainment. 20 REFERENCES - Phase F: Closeout. A considerable amount of work is accomplished prior to formal “approval,” which is needed before ﬁnal design and fabrication. As with the DoD, we see a strong role for technology and the need for its development and completion before approval. Another difference is the ﬁnal phase for program closeout. Despite some minor differences, we also see a considerable amount of “up front” design work in an attempt to assure that the system is sound before we write software and “bend metal.” 5.4 SYSTEMS ENGINEERING ACROSS THE LIFE CYCLE From chapter four, we can see that the elements of systems engineering are needed throughout the system’s life cycle. This is reinforced in one of the more important DoD acquisition Instructions [2], as follows: “Rigorous systems engineering discipline is necessary to ensure that the Department of De- fense meets the challenge of developing and maintaining needed warﬁghting capability. Systems engineering provides the integrating technical processes to deﬁne and balance system performance, cost, schedule, and risk within a family-of-systems and systems-of-systems context. Systems engi- neering shall be embedded in program planning and be designed to support the entire acquisition to support the entire acquisition life cycle” [2, enclosure 12]. REFERENCES [1] Eisner, H., Computer-Aided Systems Engineering, Prentice-Hall, 1988. 17 [2] DoD Instruction 5000.02, “Operation of the Defense Acquisition System,” Dec. 8, 2008, Department of Defense, Washington, DC. 18, 20 [3] “NASA Systems Engineering Handbook,” NASA/SP-2007–6105 Rev. 1, NASA Headquar- ters, Washington, DC, December 2007. 19 C H A P T E R 6 21 System Properties, Attributes and Features (PAFs) We tend to characterize systems by their properties, attributes and features. Some of these can be quite general, like maintainability, and some tend to pertain to various kinds or types of systems. To illustrate, Table 6.1 lists some of these PAFs for (a) an automobile, (b) a house, and (c) a radar system. We will generally treat properties, attributes and features as more-or-less the same. As can be seen from the above table, users and purchasers of these systems have a strong interest in under- standing the PAFs, often in quite a lot of detail. Failure to do so can easily lead to purchases that are regretted from the point of view of buying an inferior system or buying the wrong system. All of this points us in the direction of wanting to have more information about these PAFs. We cannot be good users or purchasers when we don’t have the right kinds of information. And the providers of our systems don’t necessarily work hard at supplying the appropriate information. Here are a couple of examples in this respect. You buy a TV and eventually lose the remote clicker for it. So you go out and buy another generic remote. Now you have to program the new remote to a code for your TV. What is the code number? Where is it written down? Who knows? You buy a vacuum cleaner and a piece of it breaks. So you try to buy a replacement part. How do you describe the part? What’s its name? What’s its part number? Who knows? The information age is upon us and is manifested in all types of ways and for all kinds of systems. In the world of systems, we also ﬁnd PAFs that are both interesting as well as possibly obscure. Here are a few of them, along with a ﬁrst-order description: - System resilience: the ability of a system to recover to normal operation, or to a form of degraded operation, after some type of signiﬁcant stress has been placed upon the system. - System complexity: a level of extreme complication represented by the system and its behavior. - Emergent behavior: one or more new forms of behavior of the system under stress and/or after the system has been in its operating environment for some period of time. - Sustainability: the degree to which a system is able to continue to operate without massive infusions of new types of energy that are not cost-effectively provided. 22 6. SYSTEM PROPERTIES, ATTRIBUTES AND FEATURES (PAFS) Table 6.1: Selected Properties, Attributes and Features of (a) automobile, (b) a house, and (c) a radar. (a) An automobile Weight Length Color Type (e.g., sedan, convertible) Cost Fuel Efﬁciency Maintainability Horsepower Capacity (e.g., for people) (b) A House Type (e.g., colonial, ranch…) Number of Rooms, by type Number of Square Feet Construction (e.g., brick, wood…) Cost Color Age Location (e.g., district, neighborhood…) (c) A Radar Transmitted Power Location (ground, airborne…) Frequency of Operation Type (pulse, continuous…) Directivity Resolution Bandwidth Size of Antennae Cost - Self-Regulatory: the degree to which a system has the internal property to remain in a stable domain of operation over the long haul. - Vulnerability: the extent to which the system will fail to carry out its main functions when subjected to severe stresses. Is this the approximate opposite of resilience? This small sample will give the reader some idea as to the perplexities that face the systems engineer from time to time. REFERENCES 23 Ultimately, the systems engineer would like to have a precise deﬁnition of these PAFs, and also a means of measuring them. If the engineer and the customer can agree on such a precise deﬁnition, there is a much greater chance that a system will be built (some day) such that both parties have a win-win proposition and venture. That’s the “end game” - a system for which both parties have done it correctly, and a “happy customer” (as well as a good reference) is the result. And as we saw in an earlier chapter, this is by no means what is happening, with high likelihood, in that real world out there. So now we come directly to the matter of measurement. When we see a set of PAFs, we try to ﬁnd a way to measure them, to the maximum extent possible or practicable.The easier and more widely accepted the method of measurement, the happier we are. The more subjective, the unhappier. But we don’t leave it at that. There are times that we almost insist upon “measuring the unmeasurable.” Other times, we rely on a research-oriented program whose objective is to ﬁnd an appropriate measure down-the-road. It’s all good, and often it’s also quite complicated. For example, if we look at a system, we still don’t have a good way of measuring its complexity. So we are studying the matter. On the other hand, we do have a way of measuring the complexity of software. Some years ago, in a seminal paper, Tom McCabe suggested a software measure that is called McCabe’s Cyclomatic Complexity for software [1]. It was a brilliant contribution, and it led to a quite successful company that Mr. McCabe built, all around the matter of measuring the complexity (as well as other attributes) of software. Perhaps, in the near future, we will have a comparable story to tell about systems. More about this matter of measurement, an important part of systems engineering, is in the next chapter. REFERENCES [1] McCabe, T., (1976), “A Complexity Measure,” IEEE Computer Magazine (February). 23 24 C H A P T E R 7 Measures and Parameters The last chapter cited a variety of PAFs (properties, attributes, features) that were of interest for three types of systems. It was indicated that some of these are measurable and some are not, at least for now. The systems engineer pays special attention to making measurements; this activity represents a serious part of having the appropriate “tools of the trade.” We need to make these measurements, so that we can be precise and correct about what it is that we are building. We need these measurements, also, to prove to our customers (and ourselves) that we have satisﬁed their requirements. We tend to give a special name to those measures that receive special attention, and they are referred to as technical performance measures, or TPMs. The lists below illustrate TPMs for four types of systems, (a) a transportation system, (b) a communication system, (c) an on-line transaction processor, and (d) a radar system (Table 7.1). These are all “technical” measures and therefore do not refer to systems costs by deﬁnition. Matters of cost will be considered in a later chapter. You may also note that there might be other TPMs that come to mind as you read the above lists. Try adding two more to each category. When the systems engineer has enumerated a number of TPMs for the system in question, it is also usual to look at them more deeply and decide which of them can be further categorized as Key Performance Parameters (KPPs) for the system. One of the important documents dealing with the acquisition of systems says that we should identify a “minimum” set of KPPs for the system [1]. These are used as a basis for building and testing the system, and also tracking progress as to how we are doing during the system’s development. We also note that the identiﬁcation is for a “minimum’ set, not a maximum set. We want to continually try to manage these difﬁcult programs and systems by a sharp focus on what is most important, not on everything we can think of. That perspective, we recognize, may make the difference between success and failure. In this connection, we can ponder a quote from Dr. Eberhardt Rechtin as he constructed a set of useful “heuristics” for systems: “amid a wash of paper, a small number of documents become critical pivots around which every project’s management revolves…” [2]. We also recognize that having deﬁned these important TPMs and KPPs, we need to then address the matter of how we are going to calculate these measures and parameters. In some cases, the issue is relatively straightforward. In others, we may have to build a model of the system to do the calculation. That model might include the notion of simulation of prospective system behavior on one or more computers. Two examples of relatively simple and well-accepted calculations are Table 7.1: Illustrative Technical Performance Measures (TPMs). 25 (a) A Transportation System Capacity Trip Time Frequency of Service Energy Efﬁciency Throughput (b) A Communication System Capacity Signal-to-Noise Ratio Bandwidth Number of Users Error Rate Quality of Service Speed of Service (c) An On-Line Transaction Processor (OLTP) Response Time Accuracy Number of Simultaneous Users Security Level (d) A Radar System Range Probability of Detection False Alarm Probability Transmitted Power Frequency Band of Operation Signal-to-Noise Ratio those of system reliability and system availability, using the formulas below: Reliability = exp(−λ t) Availability = A = MTBF MTBF + MDT Where λ is the failure rate in failures per unit of time (e.g., hours) and MTBF = Mean-Time-Between Failures, hours, and MDT = Mean Down Time, hours. Much more complex relationships are brought into play for large and complex systems such as air defense, air trafﬁc control and networked communications systems. 26 REFERENCES There are times, for good and sufﬁcient reason, when we attempt to “measure the unmeasur- able,” as suggested in the last chapter. Some examples will illustrate the point without stretching the overall credibility of the endeavor. In the ﬁrst case, we have created a set of “Capability Maturity Models” in the systems and software (and other) domains. In doing so, we identify key process areas (KPAs), and we associate levels of achievement in these areas with speciﬁc numbers. So in the original CMM for software, if an organization demonstrates competency in six important KPAs, then it has achieved level 2 on the CMM scale [3]. In another example, we are estimating the level of effort (in person months) required to carry out a software development program [4]. The overall relationship can be simply stated: PM (effort) = A (size)B . Where PM is the effort measured in person-months, A is found by considering a set of “effort multipliers” and B represents several “scale factors.” These scale factors, speciﬁcally, are the following: 1. Precedentedness. 2. Development ﬂexibility. 3. Risk resolution. 4. Team cohesion. 5. Process maturity. Each of these scale factors is evaluated on the basis of a six level scale, namely: Very Low, Low, Nominal, High, Very High and Extra High. When this is completed, a “table lookup” yields a value for “B,” which lies between 1.01 and 1.26 for the COCOMO II early design and post-architecture models. So in this way, we are able to move from a somewhat subjective set of estimates to a precise value of the scale factor variable. This type of estimation process is not physics, but it does move us a step on down the road in estimating effort levels for software, a quite valuable activity. Success in constructing large scale systems, in fact, depends upon having these types of procedures available to the systems engineering team. REFERENCES [1] DoD Instruction 5000.2, “Operation of the Defense Acquisition System,” May 12, 2003, Department of Defense (DoD), Washington, DC. 24 [2] Rechtin, E., Systems Architecting, Prentice-Hall, 1991. 24 [3] Paulk, M. B. Curtis and M. B. Chrissis (1991). “Capability Maturity Model for Software,” CMU/SEI-91-TR-24, Pittsburgh, Software Engineering Institute. 26 [4] Boehm, B., et al, Software Cost Estimation with COCOMO II, Prentice-Hall, 2000. 26 C H A P T E R 8 Architecting 27 The overall conception of a system and how it works is set forth in the system’s architecture. Ar- chitecting, a process that leads to the selection of a preferred architecture, is the “front-end” of the system design activity. The “back-end” is simply called the subsystem design [1]. One way to understand the difference between the ﬁrst step of design (the architecting) and the second step (subsystem design) is to draw an analogy between what tasks are carried out, approx- imately, in an A & E (architect and engineer) ﬁrm. The Architects do the front-end architecting, which is then followed by the engineers who ﬁll in the important engineering subsystems and details. The latter is generally not undertaken until the overall architecture is well-deﬁned and approved by the client. Clearly, different skills and training are required to carry out these far-ranging activities. Dr. Eberhardt Rechtin, a pioneer in examining the matter of system architecting, provided his insights into the process of architecting by exploring such topics as [2]: who and what is the system architect, an approach to building the system, acceptance testing, modeling and simulation, tools that the architect uses, boundaries and interfaces, and a quite instructive as well as useful list of “heuristics.” Several top-level features will help to further explain the nature of an architecture. If we look at a large-scale communications system, two distinguishing aspects would be whether the system employs frequency division multiplexing (FDM) or time division multiplexing (TDM). These are two signiﬁcantly different features, and, typically, the architecture employs one or the other, but not both. Other approaches in the multiplexing domain might also be alternatives, such as code division multiplexing (CDM). Yet another broad “dichotomy” is centralized vs. decentralized command and control. A choice of one or the other is typical although one can conceive of a “hybrid” approach. A third dichotomy might well be an “open” or a “closed” (specialized) architecture. These are but three examples of names that we give to different architectural approaches or alternatives. In 1997, the Department of Defense (DoD) published a C3I Architectural Framework that was eventually re-named the DoDAF [3]. At this time, the DoDAF remains the centerpiece of the DoD approach to architecting. It is largely based upon the construction of the following three “views” of an architecture: 1. The operational view. 2. The systems view, and 3. The technical view. 28 8. ARCHITECTING The DoD has also described their six aspects of actually developing an architecture [3], and they are cited below: 1. Articulate the intended use of the architecture. 2. Establish the scope, context, environment, and any other assumptions of the architecture. 3. Determine which characteristics the architecture needs to capture. 4. Establish which architecture views and supporting products should be built. 5. Build the needed products. 6. Use the architecture for its intended purpose. Although these are interesting and informative steps, they are not sufﬁciently deﬁnitive, so that one would expect two persons to actually follow the same process, resulting in similar products. The DoDAF approach has become quite far-ranging, and the three “views” originally pre- sented have been expanded and described in a great amount of detail. In the defense domain especially, and as expected, the DoDAF procedure is widely accepted and understood. Another architecting approach, set forth by this author, has been called the EAM (Eisner Architecting Method [4]). This approach focuses on examining the cost-effectiveness of alternative architectures. Explicit calculations are made of the cost and effectiveness levels of alternatives, and the results are compared. The most cost-effective solution, given the situation at hand, is called the “preferred” architecture. There are four key steps that constitute the EAM approach, as listed below: 1. Functional decomposition and requirements allocation. 2. Synthesis. 3. Analysis. 4. Cost-effectiveness comparisons. These steps have been deﬁned, generally, such that the output of each step implies the process yielding that output, and vice versa. The word used here to describe this type of situation is to say that the steps and the outputs are “congruent.” This is considered to be a highly desirable feature of this architecting procedure. Each of these four steps is also described in some detail in later chapters. A very short citation of these steps follows. Functional Decomposition and Requirements Allocation. In this step, the overall system is decomposed according to the functions that the system is to perform. Each function is typically also decomposed into sub-functions. There is no attempt during this step to deﬁne the manner in which the functions and sub-functions are to be instantiated, i.e., implemented in hardware, software and/or the human element. The system requirements are then allocated to the functions and sub-functions to which they pertain. REFERENCES 29 Synthesis. In this step, design approaches for all sub-functions, and for several alternatives, are deﬁned. This is the essence of this architecting procedure. The precise manner in which this is done is described in chapter eleven, a most important explanation of the overall technique. Analysis. The essential purpose of this step is to evaluate the architectural alternatives from a cost-effectiveness point of view. Thus, it is during this step that we actually calculate numerical values for the cost and effectiveness of the various alternatives. Cost-Effectiveness Comparisons. We enter this step, ideally, with measures of the cost and effectiveness of the alternatives under consideration. We compare these data as well as examine system constraints (like budget limitations) to try to ﬁnd a preferred architecture. We look also at sensitivities and tradeoffs that might lead to a preferred solution. Substantially, more about these important steps is provided in chapters eleven through four- teen. By way of an interim summary, we are now in a position to deﬁne what we mean by an architecture. In this regard, we will use most of what this author constructed as a deﬁnition in a previous work [5]: An Architecture is a construction of a set of design choices for the various sub-functions of the overall system where these choices are believed to be interoperable and also satisfy the stated user requirements. In addition to the above discussions of architecting and architectures, there are still other approaches that the reader may wish to explore to round out his or her understanding of this complex and important topic. These include [5] the following: 1. MoDAF. 2. Enterprise Architecture (EA). 3. Service-Oriented Architecture (SOA). 4. IEEE explanation of Architectures. 5. Zachman approach to architecting. Architectures and architecting are considered to be critical aspects of building successful systems. If you get it wrong, there, typically, is no end to the trouble you will encounter. Getting it right usually means that the pieces tend to fall into place, leading to an often elusive but very welcome success story. REFERENCES [1] Eisner, H., “System Design, Architecting and Heuristics,” International Conference on In- dustrial Engineering and Systems Management, IESM 2009, Montreal, Canada, May 13–15, 2009. 27 30 REFERENCES [2] Rechtin, E., Systems Architecting, Prentice-Hall, 1991. 27 [3] C4ISR Architectural Framework, version 2.0, U. S. Department of Defense (DoD), Washing- ton, DC, Dec. 18, 1997. 27, 28 [4] Eisner, H., “Eisner’s Architecting Method (EAM): Prescriptive Process and Products,” Tuto- rial, INCOSE 2003, Arlington, VA, 29 June – 3 July 2002. 28 [5] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd edition, John Wiley, 2008. 29 C H A P T E R 9 31 Functional Decomposition The system design process begins with functional decomposition. That is, all of the system’s func- tions are identiﬁed and further broken down into sub-functions. One is careful to deal only with functionality and not the suggested or implied instantiations of these functions. The functions are the “what” is to be part of the system and not the “how” each function is to be built. This distinction is very important. We do not want to pre-judge the technical solutions, which are to be deﬁned later in the design process. Some examples of functional decomposition follow. 9.1 A SIMPLE COMPUTER SYSTEM Here is a short list of most of the important functions of a computer system: 1. Input. 2. Storage. 3. Processing. 4. Output. 5. Operating Software. 6. Applications Software. 7. Security. 8. Network Connectivity. 9. Power Supply. 10. Physical Structure. Note the absence of even a hint as to how these functions are to be designed. That will be part of the synthesis activity. 9.2 A C4ISR SYSTEM Seven functions are immediately suggested from the title of this type of system: 1. Command. 32 9. FUNCTIONAL DECOMPOSITION 2. Control. 3. Communications. 4. Computation. 5. Intelligence. 6. Surveillance. 7. Reconnaissance. If we extend the system to air defense, for example, we may add some additional functions, such as the following: (cid:129) Threat assessment. (cid:129) Scanning. (cid:129) Detection. (cid:129) Tracking. (cid:129) Missile/Target assignment. (cid:129) Launch. (cid:129) Target Kill. (cid:129) Damage assessment. 9.3 EARTH-OBSERVING SYSTEM (EOSDIS) A system that NASA developed was initially structured into Segments and Functions [1]. These can easily be reiterated in the form of functions and sub-functions, as illustrated in Table 9.1: 9.4 FAA’S NEXTGEN SYSTEM The FAA (Federal Aviation Administration) has been planning the Next Generation System (a system of systems) for some time [2]. Basic functions of NextGen have been described largely (but not exclusively) in terms of “services,” as follows: 1. Interaction Services. 2. Mission Services. 3. Support Services. 9.4. FAA’S NEXTGEN SYSTEM 33 Table 9.1: Functions and Subfunctions for the Earth Observing System (EOSDIS) [1]. Function 1—Flight Operations Subfunction 1.1—Mission Control Subfunction 1.2—Mission Planning and Scheduling Subfunction 1.3—Instrument Command Support Subfunction 1.4—Mission Operations Function 2—Science Data Processing Subfunction 2.1—Data Processing Subfunction 2.2—Data Archiving Subfunction 2.3—Data Distribution Subfunction 2.4—Data Information Management Subfunction 2.5—User Support for Data Information Subfunction 2.6—User Support for Data Requests Subfunction 2.7—User Support for Data Acquisition and Processing Requests Function 3—Communications and System Management Subfunction 3.1—Distribution of EOS Data to Nodes Subfunction 3.2—Distribution of Data Among Active Archives Subfunction 3.3—Interface with External Networks Subfunction 3.4—Network/Comms Management and Services Subfunction 3.5—Conﬁguration Management Subfunction 3.6—Site Processing Assignment and Scheduling Subfunction 3.7—Performance, Fault and Security Management Subfunction 3.8—Accounting and Billing 4. SOA Core Services. 5. Security Services. 6. Technical Infrastructure Services. 7. Administrative Services. 8. Services Provisioning Management. 9. Enterprise Governance. 10. SOA Governance. As a point of information, the FAA cites these Services as part of the Systems View framework that is recommended in the DoDAF approach to architecting [3]. In this case, the overall architecture has been selected as the SOA, or service-oriented architecture. 34 REFERENCES Several additional points are made here with respect to functional decomposition. The ﬁrst is that the functions need to be deﬁned as independently as possible from one another. The second is that ultimately we will wish to know what the possible interactions might be between functions, as in data/information ﬂows. Another related point was suggested by Rechtin in his articulation of system heuristics, namely [4, p. 313]: “Do not partition by slicing through regions where high rates of information exchange are required.” Yet another point is that we will also be associating a set of requirements with each and every function and subfunction, to the maximum extent possible, as part of the requirements engineering process. Finally, there remains a question as to how many levels of decomposition are appropriate. At this point, the answer is twofold: (a) it depends upon the size of the system, and (b), often, for purposes of architecting a relatively small system, a breakdown to functions and subfunctions is workable. This is where the experience factor comes into play when architecting a real world system. REFERENCES [1] H. Eisner, Essentials of Project and Systems Engineering Management, 3rd edition, John Wiley, 2008. 32, 33 [2] www.faa.gov/nextgen 32 [3] C4ISR Architectural Framework, version 2.0, U. S. Department of Defense (DoD), December 18, 1997. 33 [4] E. Rechtin, Systems Architecting, Prentice-Hall, 1991. 34 C H A P T E R 10 35 Requirements Engineering The area of requirements has been a problem for many years. It seems to be one of the weak points in the systems engineering process, and, collectively, we have had great difﬁculty in terms of ﬁnding real solutions. For example, the NDIA (National Defense Industrial Association) cites “Inadequate Require- ments Engineering” as one of the top ﬁve systems engineering problems [1].The GAO (Government Accountability Ofﬁce) does very much the same in terms of reasons why our systems are not be- ing built and delivered within acceptable cost, schedule and technical performance proﬁles [2]. The DoD (Department of Defense, DUSD, 2006) claims that requirements engineering is one of our key software issues [3]. Finally, in terms of this presentation, we have the DAPA (Defense Acquisition Performance Assessment) report that conﬁrms “requirements” as one of six broad problem areas [4]. Just about all of our systems engineering processes include the deﬁnition of requirements as an early milestone. After all, how can we proceed with designing and building a system without a clear set of requirements that have been deﬁned “up front”? The basic answer is that we do an articulation of requirements up front, but it is at that very time that we know the least about a system. However, having written these requirements, they tend to be cast in stone, and many program managers are very hesitant to change them, for a variety of reasons. Indeed, one of the issues with requirements, viewed as one of the reasons we get into trouble, is known as “requirements creep.” So despite our tendency to keep requirements ﬁxed, they somehow creep, leading to difﬁculties. This author takes the view that, in many cases, requirements need to be challenged and changed as we become smarter about the system we are trying to build. Indeed, a good systems integration company should recommend changes when they appear to be the correct course of action, Further, if the customer agrees, it should be possible to make such changes in an expeditious manner. This point is made by this author in a text dealing with these types of matters [5]. One of our leading software engineers, Barry Boehm, tells a story that provides a sharp focus on this matter of reconsidering and changing requirements [6]. His company was building a “search” system with a requirement to have a query response time of one second. After working on the system and the one second response time matter for some time, the company concluded that in order to meet this requirement, the system cost would have to increase from $30M to $100M. However, if the response time requirement were changed to 4 seconds (90 percent of the queries were all right with 4 seconds), the system could be delivered at the original budget of $30M. In other words, moving the response time from one second to four seconds would “save” some $70M. This led to changing the requirement, with all parties pleased with the ultimate decision. 36 10. REQUIREMENTS ENGINEERING 10.1 REQUIREMENTS ALLOCATION We wish to relate requirements engineering with the previous topic of functional decomposition. After the latter is achieved, and a complete requirements document written, the next step is to allocate each and every requirement to one or more of the system functions and/or sub-functions. This is a crucial step, allowing one to proceed with the selection of design alternatives for the functions and sub-functions. Without knowing the requirements for these functions, there is typically not a good way to proceed. It is at this point, however, that we run into difﬁculties, generally of two types. In one case, we wind up with functions or sub-functions for which no requirements have been deﬁned. Broadly speaking, there are two ways to solve this problem. The ﬁrst is to select a design approach that reﬂects the state-of-the-art. The second is to derive a requirement when none was explicitly stated. Hence, we have the topic of derived requirements as a subject of interest, to be referred to again below. Another possibility is that we have requirements that appear to “have no home.” That is, we cannot see exactly how to allocate these requirements to the functions and/or sub-functions. In such a case, we typically need to re-structure the functional decomposition to accommodate the “extra” requirements. Sometimes this step simply means that the requirement applies but at a lower and not precisely deﬁned part of the decomposition. 10.2 DERIVED REQUIREMENTS If the user/customer develops a set of requirements, and many functions and/or sub-functions have no associated requirement, then it is usually the responsibility of the systems integrator to derive a set of “missing” requirements. This set is then submitted for approval by the customer. When ﬁnally approved, the process can continue such that we have a “complete” set of requirements. This step is a critical one as can be seen especially when we are deriving an error budget for a system in which errors need to be precisely deﬁned as well as controlled. This can be illustrated by reference to a simple error model in which there is an overall “pointing” error, T, which is one half of one degree (the stated requirement as a standard deviation). Here is a simple set of derived errors if we have four independent and additive errors that contribute to the overall error: T = W + X + Y + Z (error variables are additive and independent) Var(T ) = Var(W ) + Var(X) + Var(Y ) + Var(Z) (variance of sum is sum of variances) (.5)2 = .25 = .05 + .06 + .06 + .08 . Deriving new requirements, not previously stated, is an important part of the responsibility of the systems integrator. 10.3 SOME NASA PERSPECTIVES NASA has been working with high-tech requirements for many years. Accordingly, they have a rather well-deﬁned set of procedures dealing with requirements as part of their system engineering 10.4. TOP HALF DOZEN REQUIREMENTS RECOMMENDATIONS 37 discipline [7]. As just one example, Table 10.1 shows a partial allocation and ﬂow-down of science pointing requirements. The ﬂow-down implies an overall error model: Table 10.1: Partial Allocation and Flow-down of Science Pointing Requirements [7]. SCIENCE POINTING REQUIREMENTS 1. Spacecraft Requirements 1.1 Attitude Determination Requirements 1.1.1 Total Gyro to Star Tracker Error 1.1.2 Attitude Estimation Error 1.2 Science Axis Knowledge Requirements 1.2.1 Instrument Boresight to Science Axis 1.2.2 Science Axis to Attitude Control System Reference 2. Ground Requirements Here are four very speciﬁc requirements statements that NASA points to in relation to a Thrust Vector Controller (TVC): - The TVC shall gimbal the engine a maximum of 9 degrees, plus or minus 0.1 degrees. - The TVC shall gimbal the engine at a maximum rate of 5 degrees/second, plus or minus 0.3 degrees per second. - The TVC shall provide a force of 40,000 pounds, plus or minus 500 pounds. - The TVC shall have a frequency response of 20 Hz, plus or minus 0.1 Hz. Other illustrative numerical requirements that one might see in a requirements document include the following: - The system shall have an overall availability of 0.98. - The system shall have an overall mean-time between failures (MTBF) of 500 hours. - The system shall have a response time of not more than 5 seconds, 90 percent of the time. - The system shall have a bit error rate (BER) of no worse than (10) −12. - The system shall have a probability of detection of at least 0.98. 10.4 TOP HALF DOZEN REQUIREMENTS RECOMMENDATIONS We now suggest some six notions having to do with the appropriate treatment of requirements. 38 REFERENCES 1. Make sure to allocate requirements. One should seek to allocate each and every requirement to the system functions and sub- functions, as well as the overall system, as appropriate. This allows the synthesis process to proceed such that all design engineers know what the requirements are. 2. Derive new requirements when appropriate. New requirements need to be derived when there are functions and/or sub-functions that have no requirements associated with them during the above allocation process. These derived requirements need to be approved by the customer before they are fully accepted. 3. Locate and track all high risk requirements. This necessitates a deep review of all requirements to see which ones are likely to lead to trouble downstream.Those conﬁrmed as high risk need to be questioned, and alternative requirements suggested. We are trying to reduce risk, all the time. 4. Carry out a trade-off analysis of important and difﬁcult requirements. As changes in requirements may be suggested, we need to determine the possible impacts of such changes. We are looking for changes in schedule, costs and/or performance. A previously discussed situation in this chapter noted that an increase in system response time from 1 to 4 seconds resulted in a projected decrease in system cost of $70 million. This is a situation worth noting! 5. Use the principle of “iteration” with respect to requirements. The notion here is that when we don’t have a solid requirement, we insert and accept a temporary “TBD” (to be determined). That is a place-holder that triggers a deeper look at what the appropriate requirement should be. When that look is completed, we come back to the TBD and put in the appropriate number. 6. Use “Requirements Tools” when warranted. As systems have become larger and more complex, we need to use an automated “requirements tool” to help us manage the overall requirements engineering process. The companies that provide these tools have proven their value. Look for tools like “Core” or “Doors,” as well as others with these kinds of capabilities. REFERENCES [1] www.ndia.org 35 [2] www.gao.gov 35 REFERENCES 39 [3] Schaeffer, M. D. (2006). “DoD Systems and Software Engineering – Taking It to the Next Level,” Systems and Software Engineering, Ofﬁce of the Deputy Under Secretary of Defense (A & T), October 25, 2006. 35 [4] Department of Defense (DoD), “Defense Acquisition Performance Assessment,” Kadish Re- port, January 2006, Washington, DC. 35 [5] Eisner, H., Managing Complex Systems – Thinking Outside the Box, John Wiley, 2005. 35 [6] Boehm, B., “Unifying Systems and Software Engineering,” Computer Magazine, March 2002, pp. 114–116. 35 [7] “NASA Systems Engineering Handbook,” NASA/SP-2007–6105 Rev. 1, NASA Headquar- ters, Washington, DC, December 2007. 37 40 C H A P T E R 11 Synthesis This is a most crucial step in the process of constructing an architecture for the system. Both the functional decomposition and the requirements engineering are preparatory steps. The essence of synthesis is to develop a set of design alternatives for all of the sub-functions that have been deﬁned for the system. The simplest way to take this step is to envision and then ﬁll out a table that shows these design alternatives in a clearly understandable form. Such a table is illustrated below: Table 11.1: Synthesis Construction. FUNCTIONS SUB- FUNCTIONS “Low-End” System Moderate Upgrade Major Upgrade F1 F2 FN F1.1 F1.2 F1.3 F2.1 F2.2 FN.1 FN.2 FN.3 FN.4 We note that the suggested table has the functions and sub-functions listed as the rows, and three alternative system architectures are listed as the columns. At this point, the alternatives can be thought of as the following: 1. A “low-end” system. 2. A moderate upgrade beyond the “low-end” system. 3. A major upgrade above the “low-end” system. Another way to envision these alternatives is explored in a later chapter. For now, we think in terms of constructing three alternative architectures, with increasing performance or effectiveness. All three alternatives satisfy the stated requirements for the system. An example of how the design entries might be stated, for a simple computer system, is shown in Table 11.2. 41 Table 11.2: Illustrative Computer Design Alternatives as Part of the Synthesis Process. FUNCTION “Low-End” system Moderate Upgrade Major Upgrade INPUT Keyboard Mouse CD Drive USB Telephone Keyboard Mouse CD Drive USB Telephone Touchpad Video Microphone PROCESSING X GHz MEMORY R GB (X+Y ) GHz (R+S) GB Keyboard Mouse CD Drive USB Telephone Touchpad Video Microphone Touch Screen Voice Recognition Voice Recording Fiber Optic (new) (X+Y+Z) GHz (R+S+T) GB Only three functions for the computer system are illustrated - the input, the processing, and the memory. We develop the table by working on a row at a time, moving from left to right. Each time this is done, we envision improvements in the performance, or effectiveness, of the approach. After all rows have been completed, we take the columns, one at a time, and look at them from top to bottom. In doing so, we are verifying that the entries are interoperable with one another. When all this is completed, we have a synthesis “product” that is what we want and also implies the process by which it was constructed. This means that when we see the completed table, it is easy to envision the manner in which it was developed. By deﬁnition, each of the three alternatives is an architecture, deﬁning the principal ways in which the functions and sub-functions are instantiated. If the design team wishes to consider more than three alternatives, there is no a priori constraint against doing so. Also, the suggested process is one in which the best design/architecture members of the team spend whatever time is necessary, working together, to construct the table. It is truly a team approach to building the systems architecture, in a team setting. 42 11. SYNTHESIS When the table is complete, for all system functions, the stated alternatives are the best that the design team is able to construct. If some very good approach is not included, it is a failing of the design team. If the PM and Chief Systems Engineer wish to guard against that possibility, the synthesis step can be the following: - Carried out by two parallel and independent teams, and/or - Have the results reviewed in detail by a set of senior consultants. Other variations on these themes can also be considered. The basic notion here is that we wish to construct the best possible alternative architectures as part of our solution to the overall problem. Making a serious mistake in architecting is very likely to be fatal to the overall success of the project and system. Another interesting question about this process: what happens if it is discovered that one or more sub-functions have been missed? The basic answer is that at the point of discovery, the team needs to go back and include the missed sub-function and its instantiations. A further question: can some of the architectures include functions that the others do not include? The answer to that is, “no,” since in such a case, we would be using different requirement sets for the different alternatives. In the world of both mandatory and optional requirements, however, this result is an acceptable, and even expected, possibility. At this point, there has been no formal evaluation of the alternatives against one another. That evaluation is reserved for the “analysis” step that follows, and it is explored in some detail in the next chapter. However, if the formal analysis reveals serious ﬂaws in the deﬁnition of the alternatives, then one returns to the synthesis step and makes the suggested improvements. In this fashion, we are using one of the key aspects of the systems approach, i.e., to make progress and improvements through “iteration.” This is one of the important places in which iteration works for the project team, and it is necessary to allow time for such a contingency. In other words, we have a type of loop between synthesis and analysis that should be a natural part of how we build large complex systems. 11.1 SUPPORTING TABLES AND VIEWS The synthesis chart is central to the design of alternative architectures [1, 2]. It is simple and easy to understand. That is one of its virtues. However, it is also suggested that the design/synthesis team consider adding additional information that provides support to the process. This information can come in the form of tables and views that help to explain and document what is meant by each of the alternatives. For example, the three DoDAF views (operational, systems, technical) views can be added here, as can other recommended views. These are more explanatory at this point then they are evaluative. We do not, in general, want to divert attention from the main tasks of synthesis and analysis, as described here, in order to come up with a preferred architecture. The development of additional information should ﬂow from the need for such information, as perceived by the design team. Now we move on to the next step, the formal process of “analysis.” REFERENCES [1] Eisner, H.,“Eisners Architecting Method (EAM): Prescriptive Process and Products,” Tutorial, INCOSE 2003, Arlington, VA, 29 June - 3 July 2003. 42 [2] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 42 REFERENCES 43 44 C H A P T E R 12 Analysis The primary focus of the “analysis” activity discussed here is to evaluate the architecture alternatives that are synthesized as part of the previous chapter’s design work. As such it is necessarily limited. But at the same time, due to its narrow scope and perspective, the analysis can address the matter of which architecture has the highest levels of performance and effectiveness. Ultimately, we are interested in selecting a preferred architecture for the system under consideration. During this ﬁrst iteration of the analysis, our primary interest is in comparative (vs. absolute) results. In a second or third iteration, we will be in a position to deepen our analysis since we generally will have more time, and likely more resources to apply to the problem. We take as a given input the three (or more) alternatives that we have constructed during the synthesis step. These remain: 1. The “Low-End” System. 2. The Moderate Upgrade, and 3. The Major Upgrade. The immediate consideration is to decide upon the evaluation criteria that we will use in assessing the merits of the three alternatives. Criteria that we tend to use for generic classes of transportation and communication systems are listed below in Table 12.1. In the evaluation suggested here, which is one of the least complex assessment procedures, we will basically look at a rating and weighting scheme for comparative analysis. The analysis takes the form of Table 12.2 as below. In Table 12.2, we are showing the three alternatives (columns) against a set of nine evaluation criteria (rows). The rating scheme is on a scale of 0 − 10, and the weights are selected in the interval 0 − 1 (adding to unity). We evaluate each alternative on the given scale and multiply the ratings by the weights to yield the comparative results in Table 12.2. We also interpret the “bottom-line” numbers as measures of the effectiveness (MOEs) of the alternatives. This represents the ﬁrst-order calculation of the effectiveness of each of the alternatives. The numbers in Table 12.2 suggest that the moderate upgrade represents about a 12% im- provement over the “low-end” system, and that the major upgrade is (a) about a 5% improvement over the moderate upgrade and (b) about a 17% improvement over the “low-end” system. As a ground-rule, all systems satisfy the designated requirements. We note that this type of rating and rating evaluation scheme: a. Represents a preliminary assessment of the alternatives. Table 12.1: Typical Evaluation Criteria for Transportation and Communications Systems. TRANSPORTATION SYSTEM CRITERIA COMMUNICATIONS SYSTEM CRITERIA 45 Capacity Speed Frequency of Service Risk Reliability Safety Trip Time Environmental Effects Growth Capability Capacity Bandwidth Grade of Service Connectivity Security Survivability Risk Expandability Availability EVALUATION CRITERIA Table 12.2: An Evaluation Framework for Alternative Transportation Systems. “Low-End” System Rating/ Product Moderate Upgrade Rating/ Product Major Upgrade Rating/ Product Weights (%) Capacity Frequency Risk Reliability Safety Trip Time Environment Growth Availability 15 10 20 10 15 5 10 5 10 SUMS 100 6/.9 8/.8 9/1.8 7/.7 7/1.05 7/.35 6/.6 6/.3 7/.7 7.2 7/1.05 8/.8 8 8/1.6 8/.8 8/1.2 8/.4 9/.9 8/.4 9/.9 8.05 9/1.35 8/.8 7/1.4 9/.9 9/1.35 8/.4 9/.9 8/.4 9/.9 8.41 b. Will ultimately be followed by a more detailed quantitative procedure. c. Needs to be subjected to a “sensitivity analysis,” e.g., seeing how the results change if the weights are varied; seeing how the results change if a new group of evaluators provide the ratings, etc. d. Needs to be followed by a cost analysis of the alternatives, resulting in speciﬁc cost estimates. 46 12. ANALYSIS 12.1 DEEPER LEVELS OF ANALYSIS The world of “systems analysis,” of which the above is just a narrow sliver, is wide and deep. Many claim that it was born during the “Whiz Kids” regime under Robert McNamara in the Department of Defense during the Kennedy administration [1]. Accordingly, there are many techniques and approaches that can be said to be part of systems analysis [2, 3]. As a result, this author has reserved two additional chapters in this book that will elaborate further on this topic, a critically important one in the “systems” world. These chapters are the following: - Chapter 15: Modeling and Simulation. - Chapter 16: Other Analysis Relationships. These treatments will give the reader a broader understanding of the “analysis” world and its con- stituent elements. 12.2 ANALYSIS OF ALTERNATIVES (AOA) The analysis of alternatives was implied by the various aspects of the “systems approach,” as presented in chapter two of this book. To the maximum extent feasible, we are always asking the question: is there a better approach or alternative? In this case, we are looking at alternative architectures and asking this same question. The notion of an “analysis of alternatives” (AoA) was made very concrete as the DoD set forth its acquisition instructions and directives [4]. An AoA plan is required during the system reﬁnement activities, and it is used to guide the process. The preferred solution is derived from an AoA. AoA precepts were incorporated in an “AoA Handbook,” produced by an Air Force group dealing with aerospace studies [5]. Important aspects of this work included the following: - An AoA deﬁnition: the evaluation of the performance, operational effectiveness, operational suitability, and estimated costs of alternative systems to meet a mission capability. - Key AoA components dealing with the operational environment, alternative developments, effectiveness analysis, cost analysis, risk analysis and cost-effectiveness analysis. - An articulation of analysis types, namely, analyses of (a) risk, (b) suitability, (c) sensitivity, (d) risk, (e) trade space, and (f ) comparative analysis. The above, and other AoA activities, especially in the federal government, are critically important in bringing the consideration of alternatives into play to the maximum extent possible, within the constraints of any program. This is absolutely necessary for success as we continue to build larger and more complex systems. REFERENCES 47 REFERENCES [1] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 46 [2] Gibson, J., W. Scherer and W. Gibson, How To Do Systems Analysis, John Wiley, 2007. 46 [3] Buede, D., The Engineering Design of Systems, John Wiley, 2000. 46 [4] DoD Instruction 5000.2, “Operation of the Defense Acquisition System,” May 12, 2003, Department of Defense (DoD), Washington, DC. 46 [5] AoA Handbook, www.oas.kirtland.af.mil 46 48 C H A P T E R 13 Cost-Effectiveness Recall that we are attempting to construct a cost-effective solution to our client’s problem. Thus, cost-effectiveness is a dominant consideration, as is the notion that we should be selecting a preferred architecture from among a set of alternative architectures. The cost-effectiveness perspective forms the basis for the recommended architecting approach in this book. It is also reinforced by a simple statement in a key Department of Defense (DoD) Directive, a part of the so called “5000 series” [1]. That statement says that those dealing with the acquisition of large-scale systems “shall seek the most cost-effective solution over the system’s life cycle.” In general, terms, we consider three overall domains for architecting, such domains having the descriptive names: (a) The low cost domain. (b) The high effectiveness domain, and (c) The best value domain. These domains, looking at effectiveness plotted vs. system cost, are depicted in Figure 13.1. In the low cost domain, we are speciﬁcally architecting a low-cost solution that still satisﬁes the overall customer needs and requirements. In the high effectiveness domain, we are looking for very high performance, with cost not representing a dominant factor. In the best-value domain, we are searching for the “knee-of-the-curve” such that we obtain large increases in effectiveness per dollar expended, to the point at which the curve starts to show diminishing returns. Each of these domains has its place in the building of both government and commercial systems. Here are some examples. In the low-cost domain, the government is often looking for a “plain-vanilla” personnel track- ing system that does not push the state-of-the-art, saving more substantial funding for less de- manding applications. In the high effectiveness domain, the government might be looking for a high performance ﬁghter that has no equal anywhere in the world. In the best-value domain, the government might be trying to obtain the “best bang for the buck” and can likely go beyond the minimum cost system in order to get to the “knee-of-the-curve.” The domain of interest, in any particular case, may ultimately depend upon the speciﬁc program requirements and constraints. For example, a severely limited budget or a schedule constraint both point toward a low cost domain solution. A need to have the best technological solution pushes toward the high effectiveness domain, but the need must be accompanied by a supporting budget 49 High(cid:3) Effectiveness(cid:3) (cid:3) s s e n e v i t c e f f E (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) Knee(cid:3)of(cid:3) Curve;(cid:3) Best(cid:3) Value(cid:3) Cost(cid:3) Low(cid:3) Cost Figure 13.1: Low Cost, High Effectiveness and Best Value Domains. and schedule. Without the latter, risk begins to skyrocket, and the program starts to be headed toward failure. It is recommended here that the “best-value” domain be used to the maximum extent possible. This approach tends to be justiﬁed on its own merits, and it tends also to support technology and system upgrades if such are part of the overall plan for the system. Once the cost-effectiveness domain is established, the need remains for the consideration of alternatives within that domain. For example, if one is budget constrained and therefore in the low-cost domain, it is still both appropriate and important to consider two to three alternatives from which to ultimately select a best or preferred architecture. This notion is accepted as a matter of principle even at the subsystem design level. As an example in the high-effectiveness domain, we ultimately held a competition for the Joint Strike Fighter ( JSF) between Boeing and Lockheed-Martin. The latter won that competition, but both ﬁghter designs were clearly in the high-effectiveness domain, for good and sufﬁcient reasons. The low-cost, knee-of-the-curve, and high effectiveness domains show themselves in terms of how consumers buy automobiles, as an example. At the low-end, there are many cars that sell in the $9,000 to $14,000 range, and many purchasers are completely comfortable with these low-cost offerings. At the same time, there is a quite healthy domain that consists of automobiles at about twice these prices. Many would identify that area as containing best-value solutions. Finally, although most basic transportation needs can be satisﬁed by these two domains, there is also a clear market for 50 13. COST-EFFECTIVENESS the $80-100K automobile and its associated high-effectiveness domain. Today’s systems engineer must be prepared for projects and systems that can operate at any point on the cost-effectiveness scale. 13.1 VIEWS The cost-effectiveness graph in Figure 13.1 is the principal overview of the merits of each alternative. Typically, however, we will want to develop other “views” of the alternatives, such that these views provide insight into key system relationships, parameters and tradeoffs. Table 13.1 below provides a list of other views that might be used in order to more clearly characterize the system alternatives under consideration [1]. Table 13.1: Other Views That Might Be Used to Evaluate Alternative Systems and Architectures [2]. A. Requirements Satisfaction B. Risk and Requirements C. Cost by Function, and by Requirements D. E. Effectiveness vs. Human Factors F. G. Effectiveness vs. RMA Effectiveness vs. Risk Sensitivity to Changes in Criteria Weights We note the tendency toward measurement in looking for other views. As best we can, we wish to formulate an objective and quantitative understanding of the systems under examination. Each view adds information that will help to quantify and also clarify the situation at hand. As we complete this chapter, it is worth noting two key observations made by Eberhardt Rechtin, cited earlier in this book (i.e., Chapters 2 and 3) in reference to the overall topic of archi- tecting. These statements are as follows [3]: - “no complex system can be optimized to all parties concerned,” and - “the choice between architectures may well depend upon which set of drawbacks the client can handle best.” The factors that go into the calculation of effectiveness, and especially their weights, may well differ, depending upon who is doing the architecting and who is acquiring the system. In short, various stakeholders see the system differently. This point was reinforced on a consulting assignment of this author some years ago. In support of nine members of the Aviation Advisory Commission (AAC), the question was raised as to what weights they would give to a set of criteria associated with alternative aviation systems of the future. Table 13.2 below shows the diverse views of the evaluators in regard to each of the speciﬁc criteria [4]. We also note that the evaluators decided that investment and operating costs had to be part of the process, whereas in many other frameworks, cost is taken to be an independent variable. REFERENCES 51 Table 13.2: Weights (in %) Given to a Set of Criteria Used to Evaluate Alternative Aviation Systems [4]. Criteria E1% E2% E3% E4% E5% E6% E7% E8% E9% Average Social Environmental Service Quality System Capacity Human Factors Internat’l Economic Investment Cost Operating Cost 5 20 20 10 5 5 15 20 10 40 10 10 10 10 5 5 15 10 10 10 10 5 20 20 10 15 15 15 5 10 15 15 15 20 20 20 5 5 5 10 5 5 15 20 10 15 15 15 10 15 15 15 5 10 15 15 21 8 19 15 1 10 12 14 8 12 18 13 6 13 14 16 11.0 16.1 15.8 14.2 6.3 9.2 12.9 14.4 What all this means is that the systems engineer must not lose sight of the fact that various measures of the system’s effectiveness will differ in their importance, depending upon the vantage point of the observer/evaluator. The systems engineer must therefore always be prepared to exam- ine the sensitivities of the solutions to these factors. At the same time, this does not change the basic notion that the “bottom line” is to seek the most cost-effective solution from among a set of alternatives. REFERENCES [1] DoD Directive 5000.1, “The Defense Acquisition System,” May 12, 2003, Department of Defense (DoD), Washington, DC. 48, 50 [2] Eisner, H., “New Systems Architecture Views,” 25th National Conference of the American Society of Engineering Management (ASEM), Alexandria, Va, Oct. 20–23, 2004. 50 [3] Rechtin, E., Systems Architecting, Prentice-Hall, 1991. 50 [4] Eisner, H., Computer-Aided Systems Engineering, Prentice-Hall, 1988. 51 52 C H A P T E R 14 Life Cycle Costing It is clear that we need to estimate the costs of systems in order to carry out the cost-effectiveness analysis cited in Chapter 13. We also need to understand the trade-offs associated with various design choices in terms of their costs. And the ultimate budgets for systems are based upon our agreement, or not, that systems can be built for a designated set of costs. There also has been great concern regarding the escalation of costs over time and, therefore, the affordability of the systems that we build and buy. This implies that we need to know not only what today’s costs are, but what tomorrow’s costs are likely to be. This might turn out to be one of the most serious unknowns and challenges that need to be faced by a system’s project manager (PM) and also the Chief Systems Engineer. 14.1 LIFE CYCLE COST MODEL STRUCTURE The overall approach, in the context of systems engineering, is to take a “life cycle” view of the issue of system costing. That is, we estimate the costs of systems over their entire life cycles, and we compare alternatives on the same basis. We will use the “three by three” approach as designated by this author and described below. There are three categories of cost that we use in our life cycle cost model (LCCM), namely: 1. Research, development, test and evaluation (RDT&E). 2. Procurement (or acquisition). 3. Operations and Maintenance (or Support). The ﬁrst category deals with all the costs that are expended before we actually purchase or acquire one or more copies of the system. The second includes the dollars spent for the acquisition. The third funds the operations and support phase, usually the longest (and most expensive) part of the life cycle. The details of subordinate costs can be found in an earlier text of this [1] and other [2] authors. The other aspects of the model are the three dimensions: 1. The three cost elements (as above). 2. The speciﬁc years of the system’s life cycle, and 3. The sub-systems of which the overall system is constructed. 14.2. BOTTOMS-UP AND TOP DOWN COST ESTIMATION NOTIONS 53 These three dimensions can be seen to ﬁt very well into the structure of a 3-dimensional spreadsheet for which the rows are the cost elements, the columns are the years, and the “sheets” are the various sub-systems. Thus, the “three by three” designation refers to the three categories of cost and also the three dimensions of the overall life cycle cost model. 14.2 BOTTOMS-UP AND TOP DOWN COST ESTIMATION NOTIONS If we look at the above “three by three” model, we are able to get some idea as to the number of data elements that might be part of such a model. If we assume 25 cost elements, 15 years of the system’s life cycle, and 8 sub-systems, then we have (25)(15)(8) = 3,000 data “cells,” each containing a cost estimate. Estimating such costs is not an impossible task, but it takes time and some “digging” to develop these estimates. Following this approach is basically a “bottom’s up” procedure to building a life cycle cost model. It is data-intensive, and we have a great deal of visibility into elements of cost. But it also requires good databases that we can access in order to retrieve data from systems that are similar to the one we are building. In addition to the above approach, there is a top-down approach. In such a case, we look at similar systems, and we use real data from these systems in order to extrapolate to the system in question. These extrapolations are generally called “cost-estimating relationships” (CERs), and they allow for the estimation of only a few key parameters, or variables, in order to develop a cost estimate at the “aggregated” or “system” level. Table 14.1 shows a few examples [1]. Table 14.1: Illustrative Cost Estimating Relationships [1]. Cost Estimated for Primary Cost Drivers A Computer Aircraft Engine A Radio A Radar System An Antenna Software Speed, Storage Capacity Bypass Ratio, Thrust Frequency, Power, Number of Channels Frequency, Bandwidth, Weight, Output Power Frequency, Size Delivered Source Instructions, Environment (see brief discussion of COCOMO below) We can illustrate a well-known CER area by a brief examination of the Constructive Cost Model known as COCOMO. This model focuses upon the costs of software and has taken the simple form: PM = A (KDSI)B Where PM = person-months, which is easily converted into a dollar amount, and KDSI = thousands of delivered source instructions. 54 14. LIFE CYCLE COSTING A is called an effort multiplier, and B is referred to as a scale factor [3, 4]. The latter is a function of ﬁve variables, and the former is a function of seven or seventeen other variables, depending upon the situation [5]. So we have a relatively simple way to estimate the costs of software, with “delivered source instructions” remaining as the key independent variable. Extensions of this notion allow us to further calculate the recommended development time, the productivity and the required manpower levels. 14.3 PRICE PRICE is a series of cost models that originated with the company RCA, and it survives as an important independent source of cost information, based upon real world data and its analysis. There are several PRICE models as cited below: (cid:129) PRICE H—focused upon the cost of hardware (cid:129) PRICE HL—expands to the hardware life cycle, including cost-effectiveness and system availability (cid:129) PRICE M—oriented to the costs of electronic systems. PRICE, as well as many other formal sources of parametric life cycle cost information, provides the systems engineer with several alternatives in terms of data on real systems that would otherwise not be readily accessible. 14.4 NASA AND COST MANAGEMENT NASA has been very active over the years in dealing with cost estimation and management. Some years ago, they started several new initiatives in order to “strengthen cost estimating and project cost management”[6]. NASA has also produced a Cost Estimating Handbook [7], an excellent idea that helps to deﬁne their approach to this important matter. Some of the main topics addressed by NASA include the following: Cost Estimating. (cid:129) The role of cost estimating. (cid:129) Cost estimating at NASA. (cid:129) The Cost estimating process. Cost Risk. (cid:129) Cost risk. (cid:129) Cost risk approaches. REFERENCES 55 (cid:129) Model Summaries/Overview. (cid:129) Risk Handbook Summaries. Economic and Supporting Analyses. (cid:129) Economic analysis. (cid:129) Other Cost Estimating considerations. We note the scope of these topics as well as the expansion into economics. It is interesting also that NASA highlighted “cost risk” in their overall deliberations. Both economics and risk are appropriately part of the cost estimation and management issue. REFERENCES [1] Eisner, H., Computer-Aided Systems Engineering, Prentice-Hall, 1988. 52, 53 [2] Blanchard, B., and W. Fabrycky, Systems Engineering and Analysis, 5th Edition, Prentice-Hall, 2011. 52 [3] Boehm, B., Software Engineering Economics, Prentice-Hall, 1981. 54 [4] Boehm, B. et al, Software Cost Estimation with COCOMO II, Prentice-Hall, 2000. 54 [5] usc.sunset.edu 54 [6] Gregory, F., NASA Deputy Administrator, “Implementation of Cost Management References Initiatives,” December 23, 2004, NASA, Washington, DC. 54 [7] NASA Cost Estimating Handbook, 2008, NASA Headquarters, Washington, DC. 54 56 C H A P T E R 15 Modeling and Simulation One of the principal reasons we use modeling and simulation (M & S) is to be able to predict the performance of systems before we actually build these systems. The results, therefore, can strongly inﬂuence and contribute to our design of these systems. Or at least, we hope so. To the extent that this is not the case, M & S canstill play a valuable role for systems in the process of being developed and tested, and for systems that are being integrated. The “modeling” part of M & S can range far and wide since there are numerous interpretations of what a model is and what it is not. This author see models as a way to represent and explore, in one way or another, the behavior of the system that is to be built. So we produce a model, or a replica, of the system, in one or more domains of the system. We then subject the model to trade-offs and testing, believing that we are learning something about the real system. If we are good “modelers,” then we are learning. Bad modelers, unfortunately, learn very little about the real system. Whether good or bad, we need to keep in mind one of the heuristics suggested by Eberhardt Rechtin, one of our best systems engineers [1]. He appropriately reminded us that “a model is not reality.” This means we need to know what our model can do for us, and what it may not be able to do, i.e., its limitations. 15.1 FOUR ILLUSTRATIVE MODELS We will use four speciﬁc examples in order to illustrate the notion of a model. The ﬁrst will be a system “computational model,” as discussed below. We have stressed the importance of being able to compute (calculate) the technical perfor- mance measures (TPMs) as well as the key performance parameters (KPPs) of a system.To assist us in this endeavor, we can construct what this author has called a “Parameter Dependency Diagram”[2]. Such a diagram represents a computational model of the system in question. One begins by identify- ing the key parameters and measures that are of interest to compute. A long list is made of these and prioritized. The highest priority parameters and measures are examined, and for each, the question is raised: what does this parameter depend upon? One answers the question by deciding, for example, that parameter A depends upon parameters X, Y, and Z (see Figure 15.1). The same question is then asked about parameters X, Y, and Z, with the answers shown in diagrammatic form, following Figure 15.1. This process is continued until the diagram displays the dependencies between all important parameters and measures. The dependencies, ultimately, are converted into quantitative relationships (i.e., formulas for computation). X Y Z 15.2. SIMULATION 57 A(cid:3) Figure 15.1: A Step in Constructing a Parameter Dependency Diagram. For the information ﬂow model, we focus initially upon the functional decomposition of the system (see Chapter 9). We then ask the question: what is the nature of all information ﬂows between all functions and sub-functions? The results are then entered into a table that has these functions and sub-functions as both its rows and columns. Several information ﬂow descriptors can be used as the cell entries (e.g., type, rate of ﬂow, security level, etc.) Yet another model is itself a descriptor of the systems engineering process.This model is called the systems engineering “Vee” model [3]. It is formulated as a “V,” such that the downward stroke of the “V” has the early systems engineering activities that move from requirements to design speci- ﬁcations, and the upward stroke completes design engineering and moves through the construction and integration of system conﬁguration items. A fourth model is called the “Spiral Model,” and it too depicts major parts of the systems engineering process but in the form of a spiral [3, p. 18]. By means of its spiral structure, it demon- strates the fact that we tend to iterate parts of the process rather than proceed in a totally linear manner. Numerous other “models” have been developed with specialized purposes that help us to build better systems. Often, these have been based upon some type of diagram, for example: functional ﬂows and data descriptions, ﬂow charts, state transition diagrams, IDEF charts, GERT charts, and many others. Another touchstone for modeling, especially relevant to the main subject of this book, is the work on model-based systems engineering (see also Chapter 4). This is based upon the notion that models form an excellent foundation for carrying out systems engineering.Two prominent aspects of this approach include the UML (uniﬁed modeling language) and the SySML (systems engineering modeling language) [2]. 15.2 SIMULATION This descriptor is used when we attempt to actually simulate the behavior and operation of the system in question. A simulation is a model, but a model is not necessarily a simulation. There are generally two approaches in the simulation world. We can build a new simulation, writing all the software “from scratch.” Or, we can use an existing software “package” that is provided by a commercial 58 15. MODELING AND SIMULATION vendor. As an example of the ﬁrst approach, we might build our own simulation if we wanted to capture the possible behavior of a new Metro system that we wanted to build for a city with such a need. In the second case, numerous packages are available to us, depending upon the problem we are trying to address. A book by this author [2] provided a list of such software, along with a set of potential suppliers. The latter approach works very well when the user determines that the software in question applies (for sure) to the problem at hand. The short Table 15.1 below illustrates the type of software that is available, along with the problem domain and the name of the vendor. Table 15.1: Selected Modeling or Simulation Packages Available From Suppliers. Software Name Problem Domain Vendor GPSS/H LANNET II.5 PROMOD SIMFACTORY SLAM Mathematica 7 GAMS Mathematical SAS CORE System General Purpose Systems Local Area Network General Systems Factory Operations General Systems Mathematical Analyses Programming Statistics & Optimization Requirements Wolverine CACI Promod CACI Pritsker Wolfram GAMS Dev. Corp. SAS Institute Vitech 15.3 DOMAINS OF INTEREST Table 15.1 provides only a small sample of the domains that have been addressed by Modeling and Simulation. Table 15.2 lists another dozen such domains in which a systems engineer can obtain assistance in evaluating the performance of a variety of systems of interest. 15.4 MODELING AND SIMULATION IN THE DOD The DoD has embraced M & S , ﬁnding it extremely useful with respect to building complex systems. There is a Modeling and Simulation Information Analysis Center (MSIAC) that provides support to developers and users. Their overall mission is to “access, acquire, collect, analyze, synthesize, generate, and disseminate scientiﬁc, technical and operational support information in the area”[4]. The MSIAC is oriented to providing the above type of support to its customers. M & S is considered to be a key enabler such that data and related services are accessible across the various parts of the agency. The management of M & S is especially important in helping the DoD achieve its goals by [5]: (cid:129) Leading investments in M & S. (cid:129) Helping with collaborative R & D. Table 15.2: A Dozen Domains Which Have M & S Support Packages. REFERENCES 59 • Operations Research • Control Systems Analysis • Decision Analysis • Queuing Theory • Linear and Non-Linear Systems Analysis • Reliability, Availability and Maintainability • Probability and Statistics • War Gaming • Forecasting • Risk Assessments • System Dynamics • Process Reengineering (cid:129) Maximizing commonality, reuse, effectiveness and efﬁciency. The DoD also pays special attention to M & S veriﬁcation, validation and accreditation (VV&A). Many of our successes in M & S are traceable to the DoD. At the same time, it can be said that we have a vibrant and productive commercial M & S industry that is very important to the world of systems engineering. REFERENCES [1] Rechtin, E., Systems Architecting, Prentice-Hall, 1991. 56 [2] Eisner, H., Essentials of Project and Systems Engineering Management, 2008, 3rd Edition, John Wiley, 2008. 56, 57, 58 [3] Buede, D., The Engineering Design of Systems, John Wiley, 2000, page 10. 57 [4] Modeling and Simulation Information Analysis Center, www.dod-msiac.org 58 [5] DoDD 5000.59, “DoD Modeling and Simulation (M & S) Management,” August 6, 2007, Department of Defense, Washington, DC. 58 60 C H A P T E R 16 Other Analysis Relationships In this chapter, we explore a limited number of analysis relationships that are ﬁrmly “tools of the trade” for the systems engineer. These relationships tend to be focused on calculations of the system technical performance measures rather than on evaluating alternative systems architectures, as in the analysis of Chapter 12. They also tend to relate to some of the modeling and simulation methods examined in Chapter 15. 16.1 SYSTEM ERRORS All systems are capable of making errors, and we pay a great deal of attention to understanding and controlling system errors. Two classic types of errors: 1. The system fails to do what it is designed (intended) to do. 2. The system does one or more things that it was not supposed to do. We look at the former as a failure in the performance or effectiveness domain. The latter is usually called a “false alarm.” A simple example is the automobile air bag system. It clearly can fail to “go off ” when a bad accident is occurring (error 1 above). Or it can “go off ” when no accident has occurred (error 2 above). Both are very bad news, with different consequences. For many systems, we characterize, calculate and control the errors. A failure to do so may well make the system inoperative or even dangerous to use. In doing do, we create a “model” of the system errors, which is basically a roadmap for how to calculate and control. We usually characterize errors as the standard deviation (σ ) of a probability distribution. Its square is the error expressed as a variance (σ 2). If the error model consists of a total error as the sum of a set of independent random variables, then the deﬁning total error variance is calculated: σ 2(T ) = σ 2(x) + σ 2(y) + σ 2(z) where the overall error variable (T ) is the sum of three other random variables, x, y, and z. Ex- pressed another way, the total error variance is the sum of the variances of the three subordinate and independent error variables. If the error variables are not independent but correlated in some way or another, the above relationship does not hold. Instead, one needs to account for covariance terms in a formula that can be found in most books on probability and statistics. Dealing with covariance terms is a well known part of a well-developed theory. 16.2. ERRORS AS REQUIREMENTS OR SPECIFICATIONS 61 16.2 ERRORS AS REQUIREMENTS OR SPECIFICATIONS Two cases are cited here whereby errors are deﬁned as requirements or speciﬁcations. The ﬁrst is the case of a radar system such that the detection probability is designated as 0.98, and the false −6. The ﬁrst limits one error to (1 − .98) or 2 percent. Thus, we fail to detect alarm probability is 10 a target when a target is present no more than 2 percent of the time. For the second error, the false alarm rate is limited to 1 time in a million. The second case is that of an on line transaction processor (OLTP). Here we can focus upon the response time and specify that the response time be less than 15 seconds, for 90 percent of the transactions. We can expand that, if we wish, to also say that the response time be less than 25 seconds, for 95 percent of the transactions. This also means that the response time may be greater than 25 seconds, for only ﬁve percent of the time (one out of 20 transactions, on the average). So there are many ways to express error bounds, and the systems engineering team must be prepared to build a system that satisﬁes these types of statements. 16.3 RELIABILITY The reliability of a system is deﬁned as the probability that a system will operate without failure to a speciﬁed time “t.” It is given by the formula: R = exp(−λt) . Where R is the reliability, “t” is the time in question, and λ is the system failure rate. The failure rate is also the reciprocal of the system mean-time-between-failure (MTBF). With the above straightforward equation, it is a simple matter to calculate the likelihood that a system will operate successfully to its MTBF. The operation is shown below: R = exp(−λt) = exp(−t/MTBF) = exp(−MTBF/MTBF) = exp(−1) = 0.368 . It immediately follows that the probability that a system will operate without failure to twice its MTBF is exp(−2) = 0.135. The above formula holds when the system in question has independent subsystems and when the failure rate is approximately constant (the system has “no memory”). Systems with demonstrable wear-out violate this constraint, and one cannot use the exponential distribution in such a case. The recommended approach in such a situation is to use the Weibull distribution.This is a two-parameter distribution which has a density function of f (t) = αλt α−1 exp(−λt α). When α = 1, this reduces to the exponential case. We are able to improve or increase reliability by placing systems, or components of systems, in a parallel redundancy conﬁguration. This basically means that both of the components need to have failed in order to have the overall system fail. For example, if you have a small business running out of your home ofﬁce, and you are concerned about having a computer working (along with a printer) with high reliability, then it makes sense to buy two computers and two printers. One set is kept in 62 16. OTHER ANALYSIS RELATIONSHIPS “parallel,” so that in the case of failure, a back-up is present. We are able to demonstrate how this works with two simple formulas: R (series) = R∗R = R2 where R is the reliability of a component R (parallel) = 1 − (1 − R)(1 − R) . If the basic reliability of one component is 0.9, the series and parallel reliabilities are found: R (series) = (0.9)(0.9) = 0.81 R (parallel) = 1 − (1 − .9)(1 − .9) = 1 − (.1)(.1) = 1 − .01 = 0.99 . The redundant arrangement has thus improved the reliability from 0.9 to 0.99, but it comes with a price. This is the essence of a trade-off whereby we wish to improve a feature of the system, with a cost that is acceptable. 16.4 AVAILABILITY The Availability of a system is deﬁned as the probability that a system will operate successfully when called upon to do so. It is given by the formula: A = MTBF/(MTBF + MDT) . Where A is the availability, MTBF is the mean-time-between failure, and MDT is the system mean down time. If, for example, the MTBF is 500 hours and the MDT is 4 hours, the availability is calculated as: A = 500/(500 + 4) = 500/504 = 0.992 . Thus, we see that being able to detect a failure and then repair it quickly (low MDT) will improve the system’s availability, which is what our intuition tells us about such a matter. 16.5 “SUBJECTIVE” ANALYSIS AND MEASUREMENT In the world of building real systems, many “subjective” methods are used that lead to progress. For example, the various forms of capability maturity models are largely based upon “subjective” assessments that deﬁne levels of capability in several domains (e.g., systems engineering, software engineering, etc.). Two additional areas include evaluating the extent to which systems are interop- erable and integrable [1]. Progress is being made in terms of measuring and evaluating important features such as system complexity, resilience and sustainability. Often, the early steps in such ﬁelds start with a type of subjective analysis. This is also, at times, characterized as “soft” science, as contrasted with “hard” science or their equivalent engineering forms. 16.6. OTHER TOPICS OF INTEREST 63 16.6 OTHER TOPICS OF INTEREST Under the overall topic of analysis, there is a large body of knowledge known as linear systems theory. We know a great deal about how to analyze linear systems, and usually we use mean-square error (variance) as a key parameter. However, when the system exhibits non-linear behavior, we have greater difﬁculty with both the underlying theory as well as ease of calculation. In many cases, we go to the world of modeling and simulation to ﬁnd a solution, as discussed in an earlier chapter. Another area of no small interest is the topic of System Dynamics, formulated by Jay For- rester [2], and moved forward by many others. Subtopics include such features as stocks, ﬂows, causal loops and the necessary equations to tie all these together, supported by a diagrammatic representa- tion. A related and well-known simulation package called DYNAMO has been available for users from a variety of ﬁelds. Finally, we are able to see analysis topics of interest as represented in one of our earliest treatises on systems engineering [3]. These include: • Design of experiments. • System logic. • Queuing theory. • Game theory. • Linear programming. • Cybernetics. • Information Theory. • Servomechanism theory. • Human engineering. • Group dynamics. Clearly, there are numerous dimensions to the world of analysis. And although the systems engineer cannot be an expert in even a large proportion of these, it is necessary to know when and where each of the analysis methods are able to be used to solve a systems problem. REFERENCES [1] Eisner, H., “Toward Measures of Interoperability and Integrability for System Architectures,” 2008 INFORMS Telecon Conference, University of Maryland, College Park, MD. 62 [2] Forrester, J., System Dynamics, Pegasus Communications, 1968. 63 [3] Goode, H. and R. Machol, System Engineering, McGraw-Hill, 1957. 63 64 C H A P T E R 17 The Role of Technology Most large-scale systems today lean heavily upon technology for their performance, from automobiles to air trafﬁc control to the Internet to the telephone. Technology has made it possible to achieve our high levels of productivity, as well as our overall quality of life. And technology is absolutely crucial to our superiority in the defense and security of our nation. In terms of building new systems, we look to technology to provide higher levels of perfor- mance. These new levels keep us competitive. However, as we look at advanced technology we ask at least these three questions: (cid:129) Is this technology necessary to meet the performance requirements of the system? (cid:129) Does this technology increase the level of risk in terms of cost and schedule constraints? (cid:129) Does this technology come to us at increasing, decreasing or the same costs, as compared to other alternatives? Thus, we see potential trade-offs between better technology, risk and the overall costs of that im- proved technology. Project managers and chief engineers need to grapple with that problem every time a higher performing technology is under serious consideration. 17.1 OFFICE OF TECHNOLOGY ASSESSMENT (OTA) The importance of technology to this country is underscored by the fact that an Ofﬁce of Technology Assessment was operative over the time period 1972 to 1995. The purpose of that Ofﬁce was to look at all aspects of technology on behalf of Congress. Public Law 92-484 established the Ofﬁce, and it was extremely valuable in examining the advantages and disadvantages of various types of technology. Many of the publications of the OTA have been made available through Princeton University, and a form of technology assessment took root in Europe after the OTA closure in the United States. Today, technology remains no less important, and it may turn out that the old OTA is resurrected down the road, in one form or another. 17.2 THE DEPARTMENT OF DEFENSE (DOD) AND TECHNOLOGY We are easily reminded of the role of technology in terms of defense by looking at the latest DoD system acquisition guidance. It is recalled that in Chapter 5, we brieﬂy examined the system life 17.3. CRITICISMS AND TECHNOLOGY 65 cycle and a DoD Instruction [1] that pertained to the phases of that life cycle. In particular, we note that a “Technology Development Phase” (TDP) was inserted between the initial Materiel Solution Analysis Phase and the Engineering and Manufacturing Development (EMD) Phase.This expresses the important notion that technology is to be analyzed in great detail, and it needs to be conﬁrmed that the technology selected for large systems will be appropriate and available. The cited purpose of the TDP is cited: (cid:129) To reduce technology risk, as well as determine and mature the appropriate set of technologies to be integrated into a full system. (cid:129) To have a continuous technology discovery and development process that demonstrates close collaboration between the S & T (science and technology) community, the user and the system developer. (cid:129) To assure iteration to assess the viability of technologies while also reﬁning user requirements. The Instruction continues to describe the Phase in detail and cite the exit focus: (cid:129) Exit when an “affordable program or increment of militarily useful capability has been iden- tiﬁed.” This strengthens the accepted notion of providing a system in an evolutionary manner. More about that later in the book. 17.3 CRITICISMS AND TECHNOLOGY The Government Accountability Ofﬁce (GAO), for several years, has been evaluating the practices of various executive agencies, especially in regard to systems that they consider not to be successful. For example, one report looked at 18 large-scale NASA projects with a total life cycle cost over $50 billion and saw “signiﬁcant cost and/or schedule growth”[2]. Problems were cited especially with respect to developing new technologies or retroﬁtting old technologies, as well as understanding the risks tied to these technologies. Another GAO report looked more-so at “technology transition” processes on the part of the DoD [2], concluding that they routinely accepted “high levels of technology risk,” often in the form of including technologies before they were ready to be transitioned. Shortcomings in the technology domain are considered to lead directly to certain “poor cost and schedule” outcomes. In many of their assessments, the GAO examined programs from the points of view of (a) technology maturity, (b) design, and (c) production. A relatively large number of problems in these programs were attributed to lack of technology maturity. That leads us to looking more closely at this topic and the closely related subject of “technology readiness.” 66 17. THE ROLE OF TECHNOLOGY 17.4 TECHNOLOGY READINESS LEVELS (TRLS) Both the DoD and NASA (and others) have accepted the notion of “Technology Readiness Level” as a way of speciﬁcally measuring the extent to which various technologies can be brought into the systems they are building. Table 17.1 below brieﬂy describes nine such levels [3]. Table 17.1: Short Descriptions of Nine Technology Readiness Levels [3]. Technology Readiness Level Brief Description 1. Basic principles observed and reported. 2. Technology concept and/or application formulated. 3. Analytical and experimental critical function and/or characteristic proof of concept. 4. Component and/or breadboard validation in laboratory environment. 5. Component and/or breadboard validation in relevant environment. 6. System/subsystem model or prototype demonstration in a relevant environment. Scientiﬁc research begins to be translated into applied research and development. Invention begins. Application is speculative. Components not yet integrated. Active research and development is initiated. Includes analytic and laboratory studies. Basic technological components are integrated. Low ﬁdelity compared to eventual system. Fidelity of breadboard technology increases signiﬁcantly. Basic components integrated. Model tested in relevant environment. 7. System prototype demonstration in an operational environment. 8. Actual system completed and “ﬂight qualiﬁed” through test and demonstration. 9. Actual system “ﬂight proven” through successful mission operations. Prototype near or at planned operational system. Major step up from TRL 6. Technology proven to work in its ﬁnal form and under expected conditions. Represents end of true system development. Actual application of technology in its ﬁnal form and under mission conditions. Having this set of deﬁnitions deﬁnitely helps in terms of understanding where a program might stand in terms of incorporating various kinds of technology into real systems. 17.5 THE TECHNOLOGY READINESS ASSESSMENT (TRA) DESKBOOK The above Technology Readiness Levels can be used as a basis for a formal Technology Readiness Assessment (TRA). Quoting the intention [4]: 17.6. A CLOSING LIST 67 (cid:129) “A TRA is a formal, systematic, metrics-based process and accompanying report that assesses the maturity of technologies called Critical Technology Elements (CTEs) to be used in sys- tems. CTEs can be hardware or software.” The way it works is that an independent review team (IRT) with the appropriate subject matter expertise uses the TRLs as a metric to assess the maturity of the CTEs. All of this has the purpose of making sure that the technologies selected for a system are sufﬁciently mature and that they are ready to be part of that system, with minimum risk. A detailed explanation of how this works is provided in the cited references dealing with technology readiness and assessment. 17.6 A CLOSING LIST As we close this chapter, we take note of some every-day high-technology systems and components that have come into the lives of most of us, and thereby inﬂuence us in a positive way as we go about our chores at home and at work: • The hybrid automobile. • The GPS receivers and position trackers. • The Internet. • New arrays of phones. • Very low price computers. • Massive storage devices, like ﬂash drives. • Fiber-optic connectivity. • Pods, Pads, Nooks and Kindles. Try making a short list of those technology areas that tend to support your own life, both at home and at work. New ones seem to be appearing almost every day. REFERENCES [1] Department of Defense (DoD) Instruction 5000.02, “Operation of the Defense Acquisition System,” December 8, 2008, USD(AT&L). 65 [2] www.gao.gov 65 [3] DoD 5000.2-R, “Mandatory Procedures for Major Defense Acquisition Programs (MDAPS) and Major Automated Information Systems (MAIS) Acquisition Programs,” April 5, 2002, Department of Defense. 66 [4] “Technology Readiness Assessment (TRA)” Deskbook, Department of Defense (DoD), July 2009, Prepared by the Director, Research Directorate (DRD), Ofﬁce of the Director, Defense Research and Engineering (DDR&E). 66 68 C H A P T E R 18 Risk Management The previous chapter brieﬂy explored the role of technology in our systems, as well as the notion that when technology is used in a system and that technology is not yet mature or ready, the risk to all is increased. This “technology risk” leads to one or more of what we might call the four generic risks in a system: (cid:129) Performance Risk. (cid:129) Cost Risk. (cid:129) Schedule Risk. (cid:129) Societal Risk. In this chapter, we examine various approaches to limit these risks, otherwise known as risk man- agement (RM). We also note that as part of the process, we almost always try to measure risk, one way or another. 18.1 BASIC RISK PERSPECTIVE A fundamental perspective regarding risk is that it consists of two major components: (cid:129) The likelihood (or probability) that an exceedingly bad event will occur, and (cid:129) The consequences of the occurrence of that event. We have several notable examples to cite here but not examine in detail. The ﬁrst is the BP oil spill in the Gulf, which was very upsetting to many people and businesses in that area as well as other impacted locales. It took a while to “cap” the leaking oil, with apprehension and anger growing almost every day. It was a low probability event, with quite high consequences. Another well-known set of events was that of losing manned spacecrafts in both the Columbia and Challenger missions. This was heart-wrenching as the nation mourned the loss of these very brave astronauts. In terms of nuclear facilities, we have the Chernobyl incident in Russia as well as the Three Mile Island case in the United States. We very seriously guard against nuclear problems of this type, but yet they occurred. Finally, you may remember that we lost a spacecraft on a mission to Mars (Mars Climate Observer) due to an inconsistency in the use of the metric vs. the English system of measurement. We saw it happen, and we assume that measures were taken that will make such an event one of very low likelihood for any and all future missions. Looking at the above, and factoring in several experiences of this author, we pause here to suggest four actions that are likely to improve any given “risk” situation: 1. Look in detail for cases in which a single point of failure will almost immediately lead to mission failure. 18.2. RISK MATRIX 69 2. Fix these cases (mostly through design changes) before the design is “frozen.” 3. Review the risk situation, in a systematic matter, every month. 4. Carry out the above with the very best and proactive systems/risk engineers. 18.2 RISK MATRIX A convenient way to examine the probability-consequence approach is to construct a “risk matrix” such as that shown below in Table 18.1 [1]. Table 18.1: Risk Matrix: Rows are Levels of Likelihood; Columns are Levels of Consequence; Higher Numbers Are Greater Likelihoods and Consequences. L5-C1 L4-C1 L3-C1 L2-C1 L1-C1 L5-C2 L4-C2 L3-C2 L2-C2 L1-C2 8 L4-C3 L3-C3 L2-C3 L1-C3 9 8 L3-C4 L2-C4 L1-C4 10 9 8 L2-C5 L1-C5 In the risk matrix, we see ﬁve levels of likelihood (rows) mapped against ﬁve levels of conse- quences (columns). The top right corner of some six “cells” represent areas of greatest concern since both the probabilities and the consequences are high. As shown, numbers can be assigned to these cells as the sums of the likelihood and the consequence levels. For these six situations, therefore, it is of utmost importance to dig deeply into ways to decrease both the probabilities as well as the consequences, if possible. Often, the emphasis is to re-design the system so that the probabilities are decreased and multiple failures are necessary before the system stops working. 18.3 NASA AND RISK MANAGEMENT NASA has reacted well to the Challenger, Columbia and other risk events and has done extremely well in terms of its programs and perspectives with regard to risk management. They continue to deﬁne and reﬁne risk management procedures [2] adopting what appears to be a continuous im- provement approach. This approach leans heavily upon Risk-Informed Decision Making (RIDM) 70 18. RISK MANAGEMENT and Continuous Risk Management (CRM). The former has three main parts, including (1) identi- ﬁcation of alternatives, (2) risk analysis of alternatives, and (3) risk-informing alternative selection. The latter has six elements: 1. Identify: what are the main contributors to risk? 2. Analyze: estimate the likelihoods and consequences. 3. Plan: the risk disposition, including mitigate plans. 4. Track: monitor progress in all of the above. 5. Control: verify effectiveness of mitigation plans and actions. 6. Communicate and Document: throughout the process. NASA has recognized the role that knowledge management (KM) plays in the domain of risk man- agement. In doing so, they have emphasized such activities: (a) continuous risk management, (b) risk management case studies, (c) knowledge capture and transfer, (d) wiki-enabled teams, (e) knowledge- based risks, and (f ) decision support [3]. NASA has also championed a ﬁeld known as “Quantitative Risk Assessment” (QRA) that has carefully deﬁned methods and procedures for numerical analyses of risks. This has involved, among others, some of the notions and schema listed below: 1. The precise formulation of physical and functional hierarchies. 2. Separation of mission phases. 3. Event sequence diagramming. 4. Event and fault trees. 5. Common-cause failure modeling. 6. Construction of binary decision diagrams. 7. Probability modeling and analysis. NASA’s approach is therefore both comprehensive and quantitative. It also takes account of the need to convert qualitative and quantitative assessments to real-world decision making. 18.4 ADDITIONAL RISK MANAGEMENT PERSPECTIVES Earlier discussions have indicated that the GAO, in some respects, has taken the DoD to task for using “immature” technology and thus placed some programs at risk. Despite that, however, this author believes that the DoD has an excellent perspective on the matter of risk and the management thereof. Here, for example, are some key features of the DoD’s risk management process [4]: REFERENCES 71 (cid:129) Continuous process over system life cycle. (cid:129) Organized methodology. (cid:129) Measuring unknowns and implementing risk mitigations. (cid:129) Continuous monitoring and assessments. They have deﬁned and implemented a “risk management process model” consisting of the following important ﬁve steps: 1. Risk identiﬁcation. 2. Risk analysis. 3. Risk mitigation planning. 4. Risk mitigation plan implementation. 5. Risk tracking Finally, the DoD has looked in considerable detail at what works and what does not in terms of an effective risk management approach. Listed below are some of their suggestions [4]: (cid:129) A process integral to a sound acquisition approach. (cid:129) Complete risk analyses and follow-up mitigations. (cid:129) Continuous and iterative risk assessments. (cid:129) Well-deﬁned thresholds and success criteria. (cid:129) Technical reviews as early as possible in the life cycle. Risk management is a topic that we clearly understand quite well, but we do not always implement in accordance with what our plans and reviews are telling us. Too many of our failures in this domain, unfortunately, can be attributed to human error. How do we reduce human error? The answer points to two areas: better training, and more intense monitoring. REFERENCES [1] NASA Systems Engineering Handbook, NASA/SP-2007–6105 Rev 1, December 2007, NASA Headquarters, Washington, DC. 69 [2] NASA Procedural Requirements, NPR 8000.4A, December 16, 2008, “Agency Risk Manage- ment Procedural Requirements,” Ofﬁce of Safety and Mission Assurance, NASA, Washington, DC. 69 72 REFERENCES [3] “Integrated Risk and Knowledge Management Systems,” D. Lengyel, ESMD Risk and Knowl- edge Management Ofﬁcer, Exploration Systems Mission Directorate (ESMD), NASA Head- quarters, Washington, DC. 70 [4] “Risk Management Guide for DoD Acquisition,” 6th Edition, August 2006, OUSD(AT&L), The Department of Defense, Washington, DC. 70, 71 C H A P T E R 19 73 Testing, Veriﬁcation, and Validation This chapter considers testing as well as veriﬁcation and validation (V & V), three topics that are critical to systems engineering and building successful systems. Testing will be dealt with in two contexts that can be expressed as testing in the small and testing in the large. For the former, we are concerned with integrating small units (components, conﬁguration items) and then testing them to see if they work after the integration. In that sense, we see many “integration and test” (I & T) instances that are a natural part of building a system, piece by piece. Over the years, many have adopted the view that the best way to handle this type of testing is to accept the notion: “build a little, test a little.” This incremental approach is a good one that tends to lead to more than acceptable results. However, one possible problem shows itself in this regard. In putting together the master project schedule, not enough time is allocated to this multi-cycled integration and test set of activities. So what often happens is there are failures that need to be ﬁxed (the test fails), and these are not really accounted for. It is rare to have many (I & T) cycles during which no failures are experienced. This is easily remedied by using experience factors to leave more time for cases in which the tests fail. Testing in the large, for this text, will mean testing within the context of Test and Evaluation (T & E). Some of the features of this very important topic of T & E will be explored below. 19.1 TEST AND EVALUATION (T & E) Two critical aspects of T & E are Development T & E (DT&E) and Operational T & E (OT&E). The overall strategy regarding T & E is formulated relatively early, i.e., during the Concept and Technology Development Phase. The notion of early planning for T & E has now been widely accepted, and doing so is an important part of overall project success. OT&E is the “last” key milestone that needs to be achieved in order to have the overall system accepted. Thus, it is crucial for both the “customer” as well as the “contractor.” There are special problems associated with OT&E that may not be obvious. During this “exit” activity, which may last for quite a long time, the overall system is being tested and evaluated in terms of satisfying operational requirements of the system “in the ﬁeld.” This means that one must either place the system “in the ﬁeld” or try to simulate an operational environment as best as possible. Further, in no small number of cases, demonstration of operational performance is extremely difﬁcult. For example, if a weapon system has a kill probability of “X,” then it is literally impossible to prove this by running a large number of targets during the 74 19. TESTING, VERIFICATION, AND VALIDATION testing to statistically make the case. So a procedure short of achieving absolute statistical validity is needed. This requires considerable creativity, imagination and engineering acumen as well as management judgment. T & E has a lot of history in the Department of Defense (DoD). In that sense, one might say that the DoD is an excellent source of good information about how to conduct T & E successfully. There are lots of “lessons learned” that have been acknowledged and accepted by this important Department that takes an integrated view, describing the purpose of T & E as “to provide knowledge to assist in managing the risks involved in developing, producing, operating and sustaining systems and capabilities”[1]. We note that this statement of purpose brings us to a connection with risk management, as discussed in the previous chapter. A prominent part of carrying out T & E is to produce a Test and Evaluation Master Plan (TEMP), which: “shall describe planned development, operational, and live-ﬁre testing, including measures to evaluate the performance of the system during these test periods, an integrated test schedule, and the resource requirements to accomplish the planned testing”[1]. It is to be noted that another aspect of T & E is todeal with matters of interoperability, a key area that has given us trouble over many years. Interoperability requires that we understand the systems with which we need to interoperate, which, in turn, means that our testing needs greater integration and collaboration. This notion has been called “integration testing,” characterized as the “collaborative planning and collaborative execution of test phases and events to provide shared data in support of independent analysis, evaluation and reporting by all stakeholders, particularly the developmental (contractor and government) and operational test and evaluation communities”[2]. The acting Director of the Developmental Test & Evaluation activity in the DoD has deﬁned key issues in three principal areas: (1) sharing and access to data, (2) control of test events, and (3) possible overreaction to interim test results [3]. He also notes that solutions to these types of issues are mostly cultural, and also solvable. 19.2 VERIFICATION AND VALIDATION (V & V) Veriﬁcation and Validation (V & V) has come to be a well-known method for assuring that a system meets all aspects of its requirements. It has come upon the scene largely in the software arena where we were (and still are) experiencing many development problems. Overview deﬁnitions of V and V [4]: Veriﬁcation is a set of activities conﬁrming that the products of a phase of development satisﬁes the requirements from an earlier phase, and Validation is directed toward conﬁrming that various subsystems, or the overall system, complies with the overall requirements 19.2. VERIFICATION AND VALIDATION (V & V) 75 Some have suggested that an appropriate way to look at V & V is to say that validation is concerned with whether or not one is constructing the right product, whereas veriﬁcation addresses the matter of whether or not it is being constructed the right way. The IEEE has been a great supporter of the need for V & V, especially with respect to software [4]. An overview of their perspective: Software veriﬁcation and validation processes determine whether the development products of a given activity conform to the requirements of that activity and whether the software satisﬁes its intended use as well as established user needs. When the V & V is carried out by an independent party, it is called IV&V. This is also a well established practice whose basic purpose is to add a level of assurance and avoid self-serving or conﬂict of interest situations. NASA has set up a separate IV&V facility that is focused upon software [5]. Key activities at that facility include: (cid:129) Carrying out IV & V on safety and mission critical software. (cid:129) Providing software expertise to other groups at NASA. (cid:129) Reducing program and project risk as it relates to software. (cid:129) Carrying out research that can enhance the methods used in software assurance and software IV & V in general. The Argonne National Laboratory (ANL) has made IV & V a core competency and area of focus, attempting to assure that the IV & V is ﬂexible, applied at the systems level, tailored to the client’s needs, and of the correct level of effort, especially when there are high-consequence projects to be addressed. They deﬁne IV & V as a “systems engineering process used for evaluating the integrity and quality of the process and products of a systems development effort”[6]. Their IV & V efforts can be characterized as being rigorous, adaptive, integrated and self-improving. As the cornerstones of their programs, they tend to focus on (a) integrity, (b) surety, and (c) competence, especially with respect to requirements, development and testing. A previous discussion (chapter ﬁfteen) has dealt with modeling and simulation (M & S). The need for V & V in that connection has also been well recognized. That is, we know it is critically important to verify and validate the methods, assumptions and results of M & S sothat we can use them in an appropriate way. As an example, the Coast Guard has set forth an instruction dealing with veriﬁcation, validation and accreditation (VV & A) of models and simulations [7]. The DoD is also well aware of such a need [8]. This chapter has brieﬂy discussed testing and veriﬁcation and validation. These are attempts to assure that we have a quality system that satisﬁes the agreed-upon requirements. Both are also connected to ways of managing risk. We have learned, at times rather painfully, that there is little substitute for putting the real system through its paces in order to conﬁrm that it works, and will continue to work, over its full mission. 76 REFERENCES REFERENCES [1] DoD Instruction 5000.02, “Operation of the Defense Acquisition System,” December 8, 2008, Department of Defense (DoD), Washington, DC. 74 [2] Defense Acquisition Guidebook, Test and Evaluation (T & E) Chapter, Department of De- fense (DoD), Washington, DC. 74 [3] DiPetto, C.,“Implementing Integrated Testing,” International Test and Evaluation Association (ITEA) Journal, September 2009. 74 [4] IEEE 1012–2004, IEEE Standard for Software Veriﬁcation and Validation, 8 June 2004, IEEE, Piscataway, New Jersey. 74, 75 [5] NASA IV & V Facility, 100 University Drive, Fairmont, WV 26554, www.nasa.gov/ centers/ivv 75 [6] Argonne National Laboratory (ANL), U. S. Department of Energy Laboratory, managed by UChicago Argonne, LLC, www.anl.gov 75 [7] Commandant Instruction 5200.40, Veriﬁcation, Validation and Accreditation (VV&A) of Models and Simulations, 22 December 2006, U. S. Coast Guard, Department of Homeland Security, 2100 Second Street, SW, Washington, DC. 75 [8] DoD IV&V for M & S(Modeling and Simulation), DoD Instruction 5000.61, December 9, 2009, U. S. Department of Defense (DOD), Washington, DC. 75 C H A P T E R 20 Integration 77 As with testing, integration can be thought of in the “small” and in the “large.” For the former situation, we are simply integrating components, assemblies, units, and the like, and then testing them to see if the integrated products work. For the latter case, integration is part of “Systems Integration,” and many of our largest companies present themselves as “Systems Integrators” (SIs). This is entirely appropriate since they do in fact have the expertise to integrate all aspects of systems about as well as such an activity can be accomplished. This expertise might also be thought of as a set of core competencies. These are considered here, after a short deﬁnition of systems integration. 20.1 BRIEF DEFINITION OF SYSTEMS INTEGRATION Systems Integration (SI) is a set of processes whereby subsystems are identiﬁed, developed, and connected such that they inter-operate harmoniously and represent a cost-effective solution to the problem and needs set forth by a customer. 20.2 SYSTEMS INTEGRATION CORE COMPETENCIES In broad terms, systems integration requires the skills that are part of both systems engineering and project management. Looking more closely, the following dozen areas are named here as the critical core competencies: 1. Dealing constructively with the customer. 2. Requirements engineering. 3. System architecting. 4. Project and program management. 5. Life cycle costing. 6. Technical performance measurement. 7. Risk Management. 8. Test and Evaluation. 9. Interface Analysis and Control. 10. Software engineering. 11. Building highly productive teams. 12. Systems engineering management. Other areas that may represent the next level of capability are (a) rapid prototyping and deployment, (b) evolutionary design, and (c) architecting systems of systems. 20.3 THE STOVEPIPE ISSUE There is considerable pressure in the U.S. for the Systems Integrator (SI) to build “fully integrated” systems. This is often extended to situations where there are several “stovepipes.” The instruction to 78 20. INTEGRATION the SI is to maximally integrate such stovepipes, with a goal of 90% integration, or more. In other words, the more integration, the better. For this author, this is not an appropriate perspective or instruction. What is the reason? For some systems/stovepipes, integration is well-advised and feasible. For others, integration is virtually impossible and therefore not well advised. The desirability of high levels of stovepipe integration depends strongly upon the speciﬁc design features of the stovepipes. Only one general rule should be applied to this “stovepipe integration issue:” (cid:129) Integrate stovepipes such that the resultant system represents the most cost-effective solution to the customer’s problem. In other words, maintain the architecting perspective that even in the case where there are existing stovepipes, we are still seeking an overall system that is most cost-effective. If that overall system has a minimal level of integration, so be it. This conclusion has been reached with the aid of several personal experiences as well as observations of the scene relative to stovepipe integration attempts. In one noteworthy experience, an integration approach was abandoned after the program missed several key cost and schedule milestones. It was just too hard to integrate the stovepipes, and stay within budget and schedule constraints. 20.4 EVOLUTIONARY DEVELOPMENT AND INTEGRATION Today’s approach to building large-scale systems has been called “evolutionary,” which is entirely appropriate. The ﬁnal overall system is successfully constructed through the planned integration of several “builds,” such that these builds themselves represent a truly functioning capability. This may be illustrated by a simpliﬁed example. Suppose an overall system has been designed to have some nine functions, one through nine. The system architects ultimately decide upon an overall architecture consisting of three builds: (cid:129) Build One provides functions 2, 5 and 6. (cid:129) Build Two provides functions 1, 4 and 7. (cid:129) Build Three provides functions 3, 8 and 9. The overall architecture is considered to be the most cost-effective solution and the three builds represent well-deﬁned and needed capabilities that will ultimately be built, integrated and delivered. The customer does not have to wait for deployment of the whole system; early builds are provided that serve more immediate needs. Thus, evolutionary development and pre-planning for integration go hand-in-hand. The system is designed such that the builds can be integrated at the appropriate level of integration. Designing for integration, at whatever level, is generally a whole lot better than trying to integrate after the fact. 20.5. INTEGRATION READINESS 79 20.5 INTEGRATION READINESS The notions of System Readiness as well as Integration Readiness have been explored by various researchers in Systems Engineering, paving the way toward a better understanding of readiness, in general. In moving from “TRL to SRL” (technology readiness level to systems readiness level), several authors have deﬁned an “Integration Readiness Level” (IRL) whose purpose is to evaluate the risk of integration [1]. In this investigation, seven integration readiness levels are deﬁned, with the following key words for the various levels: Level 7 – veriﬁed and validated integration of technologies. Level 6 – technologies can accept, translate and structure information. Level 5 – control between technologies. Level 4 – detail in the quality and assurance of the integration. Level 3 – compatibility between technologies. Level 2 – speciﬁcity regarding interaction. Level 1 – interface between technologies identiﬁed. We note that the System Readiness is a function of both the Technology Readiness Level and the Integration Readiness Level. Research of this type continues to shed light upon ways in which technologies and integration inter-relate in terms of the readiness of the system in question. 20.6 INTEGRABILITY? Another approach considers the formulation of a metric for the ways in which parts of a system may integrate with other parts, or systems with systems [2]. That approach suggests speciﬁc ways to measure what is called “integrability,” using subjective analytic techniques. An example is shown that develops percent integrability measures for four stovepipes taken two at a time (six pairs). This author suggests that we will eventually be formulating and using this type of metric to deal more effectively with the pervasive issue of integrating stovepipes, or any sets of systems and subsystems. This same paper also sets forth a method for developing interoperability indices that are relevant to another integration problem, that is, the interoperability of systems and subsystems. 20.7 THE BOTTOM LINE The bottom line here is that Systems Integration (SI) can be one of the most difﬁcult aspects of building successful systems. Forcing stovepipes, subsystems, COTS and GOTS together , when they have not be designed to inter-relate, is basically not a good idea. Is there a better idea? The answer is “yes,” and it lies in holding ﬁrmly to an over-arching design that is the most cost-effective solution, chosen from among a set of well-deﬁned alternatives. Despite all the rhetoric about integrated systems and solutions, we would do better to design systems to be integrated rather than try to “crunch” them together after the fact. Building successful systems may ultimately depend upon our understanding of this notion. 80 REFERENCES REFERENCES [1] Sauser, B., Dinesh Verma, J. Ramirez-Marquez, and R. Gove,“From TRL to SRL:The Concept of Systems Readiness Levels,” Stevens Institute of Technology, Hoboken, New Jersey, Paper #126. 79 [2] H. Eisner, “Toward Measures of Interoperability and Integrability for System Architectures,” 2008 INFORMS Telecom Conference, University of Maryland, College Park, MD. 79 C H A P T E R 21 81 Systems Engineering Management There is clearly a need to manage the varied activities that represent the elements of systems en- gineering. Generically, this would be called Systems Engineering Management (SEM), and one of the keys to success is to be able to carry out such management efﬁciently and effectively. Some of the most important attributes that contribute positively to successful SEM include the following: Ability to Communicate – This shows up on virtually every list. Management, at all levels, is all about communicating, and in all directions. And, of course, we are talking about solid, honest and inclusive communications that reaches people in a positive way. Effective Team Building and Operation – Today’s manager needs to have the skills to build a team that is highly functional, motivated and productive. Having an assemblage of very smart people in a room is not necessarily constructing a team. A good team needs to be built, and it does not magically appear just as a result of bringing a group of people to a problem-solving session. Creative and Adaptive – In the world of large and complex systems, many unforeseen hap- penings occur. The systems engineering manager, in the midst of such happenings, must ﬁnd creative solutions, generally one at a time. And he or she must also be highly adaptable to new situations and environments. If the previously planned path is clogged, for whatever reason, a new path must be found. Technical Understanding – The best managers of systems engineering have a solid technical background and understanding. With such skills, they are usually held in high regard for both their managerial as well as their technical contributions. This, in turn, makes for a more solid systems engineering team. Persistence and Dedication – A large and complex system has numerous activities that are being executed simultaneously and in rapid ﬁre. The manager needs to tackle all of the issues that come to his or her desk one at a time, and with patience. This takes being persistent and dedicated to a well-considered pace. Good decisions require time to collect data, think and confer with others on the team. 82 21. SYSTEMS ENGINEERING MANAGEMENT Systematic and Organized – In the above scenario, it is clearly necessary to organize all the pieces and deal with them in a systematic manner. A friend, as well as others, has suggested the three “C” approach: remain calm, cool and collected. This overall area, relative to the requisite skills of a manager, is explored further in the chap- ter on Project Management. And beyond such management skills, there is a critical document in Systems Engineering Management. Several years ago, that document was called a Systems Engi- neering Management Plan (SEMP). Now, it is called the Systems Engineering Plan (SEP). Both are discussed in some detail in the text that follows. 21.1 THE SEMP The major components of the SEMP have been set forth [1]: (cid:129) The Systems Engineering Process. (cid:129) Systems Analysis and Control. (cid:129) Technology Transition. (cid:129) Technical Integration Teams. Of special note are the last two items on this list. The next to last reinforces the need to consider the technologies in the system, and how they are to be transitioned. The last item listed supports an emphasis on two notions: teams and integration. We deeply understand that our systems must be built by highly functional teams. We are not, however, always able to achieve this goal. 21.2 THE SEP The SEP was basically mandated in February 2004 by the Deputy Under Secretary of Defense as a crucial part of how Systems Engineering was to be carried out in the Department of Defense [2]. In that context, the plan was to do the following: (cid:129) Describe the program’s overall technical approach, including processes, resources, metrics, and applicable performance incentives. (cid:129) Detail the timing, conduct and success criteria of technical reviews. This same charter became a requirement in a key acquisition instruction [3]. Going beyond the above, the DoD suggested that the SEP be organized to cover ﬁve major focus areas [4]: (cid:129) Program requirements. (cid:129) Technical stafﬁng and organization planning. REFERENCES 83 (cid:129) Technical baseline management. (cid:129) Technical review planning, and (cid:129) Integration with the overall management of the program. The SEP is an important document that is updated appropriately depending upon which phase of the program one is carrying out. The SEP is to be available for each milestone review and thereby remains a most important way to try to manage the program. In addition, the discipline of systems engineering is reinforced and embedded in the technical design of the system and the various technical reviews that are so critical to program success. Another important part of the overall SEP is the role of the Systems Engineering Working-level Integrated Product Team (SE WIPT) which includes key systems engineers that bring their best ideas and talents to the system and program in question. Finally, modeling and simulation (M & S) is recognized as a “key enabler throughout the acquisition life cycle.” As considered in a previous chapter, M & S remains an integral part of predicting the performance of complex systems even when not a part of the system has actually been built. The SEP has an associated preparation guide that can be used by the program manager and the chief systems engineer. Some of the more important notions cited in that guide [5]: (cid:129) The SEP is a blueprint for the overall management of the technical aspects of a program. (cid:129) The SEP has a preferred format, but is to be tailored. (cid:129) The SEP is to be continuously updated. (cid:129) The SEP is to identify linkages with other relevant technical and programmatic activities. (cid:129) A sound systems engineering strategy is crucial. (cid:129) The SEP details the critical technical issues as well as how they are to be addressed and solved. The SEP remains one of the most critical documents for technical management and thus plays a crucial role if one is to achieve program and system success. REFERENCES [1] “Systems Engineering,” Military Standard 499B (1971), U.S. Department of Defense (DoD), Washington, DC. 82 [2] M. W. Wynne, Acting DUSD for AT&L, “Policy for Systems Engineering in DoD,” February 20, 2004. 82 [3] DODI 5000.02, “Operation of the Defense Acquisition System.” December 8, 2008, U. S. Department of Defense (DoD), Washington, DC. 82 84 REFERENCES [4] ODUSD (A & T) “Systems and Software Engineering Enterprise Development,” Technical Planning for Mission Success, version 2.01, U.S. Department of Defense (DoD), April 2008. 82 [5] SEP Preparation Guide, version 0.95, December 2004, Department of Defense (DoD), Wash- ington, DC. 83 C H A P T E R 22 85 Project Management Systems, large and small, are typically built as a part of a project. The project is run by a Project Manager (PM). The Chief Systems Engineer as well as the Project Controller typically report to the PM. In that sense, the PM, Chief Systems Engineer and the Project Controller can be thought of as a triumvirate that manages all aspects of the project. The classical four elements of projects are the following: (cid:129) Planning. (cid:129) Organizing. (cid:129) Directing, and (cid:129) Controlling. At times, the “controlling” element is called “monitoring” since control can be achieved by combining monitoring and directing. In the context of this book, the primary activity of the project is to build a system for which the key discipline is systems engineering. As implied above, the ﬁrst need is to formulate a project plan. This document can be said to contain seven parts, as (1) Goals, Objectives and Requirements (GORs), (2) Task Statements, (3) Technical Approach, (4) Organization and Stafﬁng, (5) Schedule, (6) Budget, and (7) Risk Analysis. Each is brieﬂy discussed below. 22.1 GOALS, OBJECTIVES AND REQUIREMENTS Objectives are usually sub-sets of goals, as shown by the following example: Goal 1—Assure the ﬁnancial stability of the enterprise. Objective 1.1: Build and install a ﬁnancial management system. Objective 1.2: Install a COTS project cost monitoring system. Objective 1.3: Upgrade to a COTS accounting system. Goal 2—Enhance the technical capabilities of the enterprise. Objective 2.1: Establish an internal technical training program. Objective 2.2: Provide and support an external training program. 86 22. PROJECT MANAGEMENT Objective 2.3: Establish a technical mentoring and information exchange program. The objectives can be made more quantitative by adding, for example, milestone dates. Re- quirements are much more speciﬁc and relate directly to the functionally decomposed elements of a system. See chapters nine and ten for more about this area. 22.2 TASK STATEMENTS These deﬁne the work elements to be carried out. They can also be called parts of a work breakdown structure (WBS). Here are some generic task statements relative to building a model: Task One - Conceptual design of the model. Task Four - Installing the Model. Task Two - Building the model. Task Three - Validating the model. Task Five - Using the Validated Model. 22.3 TECHNICAL APPROACH This section of a plan describes the main points in terms of approach to each of the task statements. For the above statements, the key questions to be answered are the following: - What is the suggested approach to conceptualizing the model? - How is the model construction to be approached? - How is the model to be validated? - How is the model to be installed in all the ofﬁces? - What are the plans for using the model? 22.4 ORGANIZATION AND STAFFING This part of the plan typically has two parts: (1) what is the organization of the project, and (2) which people are assigned to each task? The latter is often shown as a task responsibility matrix (TRM) that lists the percent of time each person is assigned to each of the tasks. Additional information can be appended, such as more detail about the tasks (such as sub-tasks) and the people (such as how to contact, what is their home organization, etc.). Summations yield estimates of the overall effort that is being applied to each of the tasks. 22.5 SCHEDULE A key part of the plan is the project schedule. For a large and complex effort, a PERT diagram is often used to capture the schedule. This approach has many excellent features, such as showing task dependencies and also the critical path. For a relatively small project, the Gantt chart is still used. Examples of both of these charting procedures are available in the references cited at the end of this chapter. 22.6. BUDGET 87 22.6 BUDGET Every project carries with it a budget, which is the maximum expenditure that will be allowed. The direct labor component can be constructed by starting with the task responsibility matrix. As indicated above, total person-weeks is a typical output, leading directly to an estimate of labor costs. An overhead cost is usually a percentage of that cost, including fringe beneﬁt costs. Then we add other costs such as expected travel costs, and apply appropriate G & A(general and administrative) costs to that total. Then a fee, or proﬁt cost, is added to obtain the overall project cost plus fee. That number is usually called the price of the project. The budget is typically shown by month, detailing the amount of money that is planned to be spent every month. As the actual monies are spent, the remaining funds to be spent are re-allocated by month. 22.7 RISK ANALYSIS This section of the project plan identiﬁes risks and also plans for mitigating such risks. Typical risks fall into the categories of schedule risk, cost risk and performance risk. Experienced systems engineers usually do well with being able to look realistically at such risks and putting into place very speciﬁc mitigation strategies as well as tactics. The above seven elements represent the overall plan for the project, and it should be up-to- date and as short as necessary to do the job. New employees can be brought up to speed by reading the plan, and management can obtain a top-level view of the key aspects of the project. Of course, the plan is a very good way of keeping top management informed and apprised of progress. 22.8 EARNED VALUE A well-accepted element of project management is the method of earned value analysis (EVA). The basic idea of EVA can be illustrated by an example. Suppose a project is at the 6 month point of a 12 month overall schedule. One looks at the project cost reports and ﬁnds that half of the budgeted funds have been spent. So we are half-way through the schedule and half-way through the available dollars. One might conclude that all is well. However, has the project made the technical progress that it was supposed to achieve? A deeper look at this matter reveals that only a quarter of the work to be performed has actually been carried out. So the project is actually in trouble in terms of work that was planned. The EVA quantiﬁes this area, and it estimates where the project is likely to wind up in terms of schedule, cost and work accomplished. 88 22. PROJECT MANAGEMENT 22.9 THE PROJECT MANAGER A great deal of a systems engineering program’s success, or lack of it, depends upon the Project Manager (PM). The PM must have an appropriate set of skills to make it all work. We cite below some nine characteristics of an effective PM, as set forth in an IEEE Engineering Management Review [1]. 1. Leads by Example. The members of a team are always watching the PM as to what will happen next. The solid PM shows the way and, hopefully, sets a good example as to what to do and what not to do. 2. Is a Visionary. Although this attribute tends to be applied more to leadership traits, it applies as well at the project level. The good PM is constantly reﬂecting a positive vision as to where the project is going and what it takes to be successful. 3. Is Technically Competent. A PM that knows the subject matter of the project is more likely to be successful than the one who does not. Often, the project personnel will not respect a leader (the PM) who is not technically competent. 4. Is Decisive. The successful PM knows when it is time to stop discussing and gathering data (as well as opinions) and make a decision as to which way to go. 5. Communicates Well. This is on everyone’s list in terms of effective management as well as leadership. 6. Motivates. The effective PM knows how to motivate his or her people, going beyond the “standard tools” such as salary increases and bonuses. The centerpiece of this is often ﬁnding the correct and elegant solution for the customer as well as pride in the team’s accomplishments. 7. Stands Up to Upper Management. The ability to do this, when necessary, is very important in terms of the team’s solidarity as well as performance. 8. Supports Team Members. Every member of the team needs to feel valued and needs to be productive. Support from the PM is an essential ingredient in both. 9. Encourages New Ideas. All the good ideas do not reside in the brain of the PM. It therefore behooves the PM to understand that and to elicit the best ideas from all team members. There are, of course, many other factors that go into being an excellent PM. The reader is encouraged to go beyond the above listing and into the references that explore this interesting and important topic in considerably more detail. The ﬁrst of the references cited below refers to the key attributes of a Project Manager. The following references are recommended with respect to covering the scope and intricacies of project management. There are, of course, many other worthy texts in this densely populated ﬁeld. REFERENCES 89 REFERENCES [1] Zimmerman, T. and Yasin, M., “A Leadership Proﬁle of American Project Managers,” IEEE Engineering Management Review, Vol. 26, No. 4, Winter 1998, pp. 5–11. 88 [2] Kerzner, H., Project Management, 10th Edition, 2009, John Wiley. [3] Forsberg, K., H. Mooz and H. Cotterman, Visualizing Project Management, John Wiley, 2000. [4] Keszbom, D., D. Schilling and K. Edward, Dynamic Project Management, John Wiley, 1989. [5] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd Edition, John Wiley, 2008. 90 C H A P T E R 23 Software Engineering In this book, as well as most others, software engineering is considered a part of (a subset of ) the overall topic of systems engineering. However, it occupies a critical space in systems engineering due to the fact that (a) many of our systems are composed of large segments of software, and (b) a relatively large number of problems are encountered in these software segments. As an example, we see references to software problems and issues in many of the reports issued by the GAO (government accountability ofﬁce), as cited below [1]: (cid:129) Defense attempting to address major software challenges. (cid:129) NASA’s software development approach increases safety and cost risk. (cid:129) Embedded computer systems: signiﬁcant software problems need to be addressed. (cid:129) Immature software development processes increase risk. In addition to the above sampling, from time to time, we see a particular system with software difﬁculties singled out and reported in the daily media. Such was the case with the FBI’s Sentinel System which caught the public’s attention with quotes like [2]: (cid:129) The system is approximately $100 million over budget and two years behind schedule. (cid:129) It could cost $350 more and an additional six years to complete. (cid:129) Some 90% of the $451 million budget for the entire system was already spent, with delivery of only two of the program’s four phases. (cid:129) Much of the above is attributable to software issues and problems. So – even though software is a very ﬂexible building block of systems, it remains a key problem area that still requires a lot of attention. 23.1 SOFTWARE DEVELOPMENT STEPS The major steps that are needed to develop software are deceptively simple: 1. Formulating the system requirements. 2. Deriving the software requirements from the system requirements. 23.2. THE CAPABILITY MATURITY MODEL 91 3. Constructing and validating the software architecture. 4. Building, integrating and testing to the conﬁrmed architecture. 5. Passing the overall acceptance tests for the system. 6. Installing the system with the appropriate O & M training. We have found that the so-called “waterfall model” for software development does not work, and we have accepted the “spiral model” as largely developed by Barry Boehm [3]. That has been an appropriate step forward but perhaps not well enough understood in all of its dimensions. Basically, this model incorporates iterations to assure that the system is on track from an overall cost, schedule, risk and performance point of view. 23.2 THE CAPABILITY MATURITY MODEL One of the early steps taken to try to improve software development was to formulate a Capability Maturity Model (CMM) [4]. This well accepted advance put forth the notion that we could measure the extent to which an organization was capable of producing correct software. This model deﬁned 5 levels of capability in the software domain, and set forth some 18 Key Process Areas (KPAs) that were most important in demonstrating that capability. Since these early days, the basic model has been expanded to what is known as the “integrated” model, the CMMI [5]. This model expanded from software and on into other system development areas such as systems engineering and inte- grated product and process development (SE/SW/IPPD). Version 1.0 had 186 speciﬁc practices, 54 goals and 24 process areas. The latter are shown below in Table 23.1. In today’s world, the soft- ware developers need to demonstrate their capabilities in the larger integrated context. The mature “systems” enterprises have been stepping up to that challenge. 23.3 COCOMO Measuring important aspects of software has been one of the key elements of software engineering. Key measures have included size, progress at milestones, resource utilization, amount of reuse, stafﬁng levels, numbers and types of problems (including defects), requirements creep, complexity and cost. The latter measure has been the domain of a model known as COCOMO, the Constructive Cost Model. It is so central to the matter of software engineering that a short explanation is set forth here. COCOMO has been described in two books [6, 7] as well as a USC website [8]. The simplest form of COCOMO, known as COCOMO I, has taken the form of the following four equations: PM = A (KDSI)x. TDEV = B (PM)y. PROD = DSI/PM. FTES = PM/TDEV, where 92 23. SOFTWARE ENGINEERING Table 23.1: CMMI Twenty-Four Process Areas [5]. Category: Process Management Organizational Process Deﬁnition Organizational Process Focus Organizational Training Organizational Process Performance Organizational Innovation and Deployment Category: Engineering Requirements Management Requirements Development Technical Solution Product Integration Veriﬁcation Validation Category: Project Management Project Planning Project Monitoring and Control Supplier Agreement Management Integrated Project Management Risk Management Integrated Teaming Quantitative Project Management Category: Support Conﬁguration Management Process and Product Quality Management Measurement and Analysis Decision Analysis and Resolution Organizational Environment for Integration Causal Analysis and Resolution PM = person-months, KDSI = thousands of delivered source instructions, TDEV = development time, PROD = productivity, DSI = delivered source instructions, FTES = fulltime equivalent staff, A and B are multipliers, and x and y are scale factors. For a particular set of software development conditions (the organic mode), we will take the following values for the multipliers and scale factors: A = 2.4, B = 2.5, x = 1.05, and y = 0.38, and a project with DSI equal to 80,000, as below: PM = 2.4(KDSI)1.05 = 2.4(80)1.05 = 2.4(99.6) = 239 person-months. TDEV = 2.5(239)0.38 = 2.5(8.01) = 20 months. PROD = 80000/239 = 334.7 DSI per person-month. FTES = 239/20 = 11.95 persons. Additional information regarding COCOMO II has been provided in Chapter 14. It is clear that COCOMO remains an important contribution to software engineering, especially with respect to costs and the various factors that affect costs. 23.4 TOP TEN FOR SOFTWARE ENGINEERING We close this chapter with the author’s “Top Ten” for the overall ﬁeld of software engineering. ONE—IDENTIFY AND TRACK PROGRESS ON ALL BUILDS EVERY WEEK, WITH A PROMINENT DISPLAY One of the more important actions that can be taken on a software development program is to make sure that progress is sharply deﬁned and measured, each and every week. This would seem like overkill, but it generally is not, considering how fast one can fall behind. In addition, this suggestion also calls for a prominent display (on a prominent wall) of current status as compared with planned status. Problem areas are not likely to be overlooked, especially when they are staring at everyone in red on an extremely large chart. 23.4. TOP TEN FOR SOFTWARE ENGINEERING 93 TWO—USE COCOMO AND OTHER CERS As seen above, the use of COCOMO provides critical estimates of software cost that can be used independently and also compared with more conventional build by build estimates of cost. The most advanced form of COCOMO should be used, consistent with the availability of input information on the various effort multipliers and scale factors. Other cost-estimating relationships (CERs) are recommended, depending upon the type of system one is working on. For example, function point analysis is a CER that has proven to be useful on some programs. THREE—ASSURE MULTIPLE AND INDEPENDENT ESTIMATES All software related models (such as COCOMO or software reliability) require input estimates. A critical input for COCOMO is an estimate of KDSI, or thousands of delivered source instructions. For all such estimates, one should obtain multiple and independent values from different people on your team. An example is to obtain three estimates of critical parameters from three groups who are not to confer on the numbers or the process. We are trying to have the best possible inputs and avoid the GIGO (garbage in–garbage out) problem. FOUR—ACCEPT THE CMMI NOTIONS AND DISCIPLINE The CMMI principles are good ones and need to be followed by all serious software development organizations. Tailored approaches are acceptable in order to match the processes used to the par- ticulars of a given program, and avoid “overkill.” Successful team practices should be accepted and used as models for all relevant parts of an organization. Trends toward agile development need to be taken seriously. So do the process areas shown in Table 23.1 here. FIVE—ASSURE A SOFTWARE “TEAM” Software engineering, as is the case with systems engineering, is a team endeavor. The PM and lead systems and software engineers need to build the appropriate teams that lead to high productivity and a sense of accomplishment as well as commitment. People who refuse to join the team need to be shown their errant ways, as well as the door. SIX—KEEP TIME AND COST RESERVES IN CASE OF TROUBLE Reserves should be SOP (standard operating practice) for difﬁcult software developments. A risk analysis will tend to reveal areas of probable troubles, but resources need to be set aside to deal with such troubles. The PM will appreciate that kind of help, in distinction to “let’s all now go to a 60 hour work week.” 94 REFERENCES SEVEN—IDENTIFY AND FOLLOW BEST PRACTICES Each software development team should know what works for it and what does not, as best practices in their particular environments.This does imply that various teams may have different best practices, and that is true. But tailored best practices is not another way of describing a free-for-all. There are also many sources that can be accessed that will reveal recommended practices that have worked for other teams and organizations. EIGHT—LEAVE EXTRA TIME FOR INTEGRATION AND TEST (I & T) AND ITERATIONS THEREOF History on software programs suggests that not enough time is typically allocated to iterations of the integration and test (I & T) cycles. The expectation is that most, if not all, tests will be positive. That is rarely the case. Failures require changes in the original code, most of which were not predicted or anticipated. These unexpected iterations can lead down some dark alleys so a good countermeasure is simply to leave extra time to achieve the appropriate I & T results. NINE—PAY SPECIAL ATTENTION TO THE HW-SW INTERFACES AND TRADEOFFS Systems tend to fail at the interfaces, and the hardware-software interface is one of the most impor- tant. In addition, there are often trade-offs to be explored in terms of design choices as well as what should be implemented in hardware and what in software. The answers here tend to not be obvious, and they often require additional attention. TEN—PROVIDE SPECIAL CARE (& FEEDING) OF YOUR BEST SW ENGINEERS While we are paying special attention, we must recognize that it is the software engineers that are ultimately making all the good things happen. They often need special treatment and will deliver for the project if this treatment is forthcoming. Such is life. Software is a domain that needs extra attention, and so do the folks who ﬁnd the right answers for the project. REFERENCES [1] www.gao.gov 90 [2] J. Stein, “Report Criticizes FBI on Computer Project,” Washington Post, October 21, 2010. 90 [3] Buede, D., The Engineering Design of Systems, John Wiley, 2009. 91 [4] Paulk, M., B. Curtis and M. B. Chrissis (1991), “Capability Maturity Model for Software,” CMU/SEI-91-TR-24, Pittsburgh, Software Engineering Institute. 91 [5] Ahern, D., A. Clouse and R. Turner, CMMI Distilled, Addison-Wesley, 2001. 91, 92 [6] Boehm, B., Software Engineering Economics, Prentice-Hall, 1981. 91 [7] Boehm, B., et.al, Software Cost Estimation with COCOMO II, Prentice-Hall, 2000. 91 [8] www.sunset.usc 91 REFERENCES 95 96 C H A P T E R 24 Systems Acquisition Systems are acquired under various sets of rules. System acquirers need to know these rules and also need to be improving the processes they use, whenever possible. The U. S. government, for obvious reasons, documents its acquisition rules, often in great detail. In this chapter, we take an overview look at some of these acquisition rules, perspectives, and concerns, especially those promulgated by the Department of Defense (DoD).The systems engineering community, including the ever-present systems integrators, need to know all the actual and implied acquisition guidance in order to do the best job they can for their customers. 24.1 THE 5000 SERIES The so-called “5000 series” represents a DoD Directive [1] as well as an Instruction [2]. In Tables 24.1 and 24.2 below, we list some of the more important points that are made in these two signiﬁcant documents. Table 24.1: Key Points in the DoD Directive: The Defense Acquisition System [1]. • The primary objective is to acquire quality products that meet user needs at a reasonable price. • Use competition to innovate, reduce costs, and increase quality. • Deal appropriately with system responsiveness, ﬂexibility, discipline, information assurance, interoperability, and integrated test and evaluation. • Multiple concepts and alternative ways to meet user needs shall be considered. • Seek the most cost-effective solution over the system’s life cycle. • Apply a systems engineering approach that optimizes system performance and minimizes total ownership costs. • Utilize a “Total Systems Approach.” Many additional points are made by the 2008 version (an eighty page document) of the above Instruction [3] that the reader may wish to examine. These include further details regarding integrated test and evaluation as well as systems engineering. The latter conﬁrmed the importance of systems engineering and its role in systems acquisition. 24.2. DEFENSE ACQUISITION PERFORMANCE ASSESSMENT (DAPA) REPORT 97 Table 24.2: Key Points in the DoD Instruction: Operation of the Defense Acquisition System [2]. • Provide an analysis of alternatives (AoA) as the basis for the Technology Development strategy. • The Technology Development Phase will reduce technology risk. • Approve a minimum set of key performance parameters (KPPs). • Operations and Support (O & S) shall sustain the system in the most cost-effective way over its full life cycle. • Develop integrated plans and capability roadmaps. • Maintain the continuous application of a robust systems engineering methodology. 24.2 DEFENSE ACQUISITION PERFORMANCE ASSESSMENT (DAPA) REPORT [4] Continuing concern regarding the acquisition process within the DoD was the basis for the 2006 DAPA report. This report looked at 42 important areas of concern and results were presented in the following areas: 1. Organization. 2. Workforce. 3. Budget. 4. Requirements. 5. Acquisition. 6. Industry. This report provided a clear indication of what needed to be improved and how to go about doing so, as of that time. Despite this rather well-deﬁned prescription, major concerns continued to be expressed about the acquisition system. So shortly thereafter, we have the Weapon System Acquisition Reform Act of 2009 (WSARA) [5]. 24.3 WEAPON SYSTEM ACQUISITION REFORM ACT OF 2009 Many of the key aspects of the WSARA of 2009 can be gleaned from the subjects of some of the sections under titles 1 and 2, as below in Table 24.3. Each of the weapon systems produced and used by the DoD need to be appropriately supported in the ﬁeld. Such support hopefully leads to greater efﬁciency as well as more cost-effective readiness outcomes. The DoD is looking for improved operations in these eight principal areas: (1) product support business model, (2) industrial integration strategy, (3) supply chain operational strategy, (4) governance, (5) metrics, (6) operating and support costs, (7) analytical tools, and (8) human capital. 98 24. SYSTEMS ACQUISITION Table 24.3: Sections of Weapon System Acquisition Reform Act (WSARA) of 2009. Title One – Acquisition Organization Section 101 – Systems Engineering Capabilities Section 102 – Developmental Testing Section 103 – Technological Maturity Testing Section 104 – Independent Cost Assessment Section 105 – Combat Commanders Title Two – Acquisition Policy Section 201 – Trade-offs of Cost Schedule and Performance Section 202 – Preliminary Design Review Section 203 – Life-Cycle Competition Section 204 – Nunn-McCurdy Breaches Section 205 – Organizational Conﬂicts of Interest Section 206 – Acquisition Excellence 24.4 GREATER EFFICIENCY AND PRODUCTIVITY If we move into September of 2010, we see important messages conveyed to all acquisition profes- sionals. One was from the DUSD (A, T & L) of the DoD, and it emphasized the need to “do more without more”[6]. At the same time, Secretary of Defense Gates issued a memorandum calling for new ways to increase efﬁciency and productivity [6]. Five speciﬁc areas are emphasized, including: 1. Affordability and control of cost growth. 2. Incentivizing productivity and innovation in industry. 3. Promoting real competition. 4. Improving tradecraft in services acquisition. 5. Reducing non-productive processes and bureaucracy. This latter initiative from the Secretary of Defense has some 23 subordinate points within the above ﬁve categories. Overall, the objective is to provide guidance as to how to achieve greater efﬁciency and productivity, and thereby obtain better buying power. 24.5 EVOLUTIONARY ACQUISITION From the above, one can see enormous efforts to reform the acquisition system, and one can achieve greater performance with reduced expenditures. As this chapter closes, however, one other important perspective was accepted earlier as an important part of the systems acquisition process, namely, evolutionary acquisition. This approach mandated that we were to build systems incrementally and get these increments out to the war-ﬁghter as soon as possible. This activity, coupled with the several systemic changes in the acquisition system identiﬁed above, will likely tell much of the acquisition “story” for years to come. Will it all lead to greater success in building our large systems? This author believes that it will, but only if we actually implement a reasonable number of changes that have been mandated and demanded by the Secretary of Defense and his Deputy Undersecretary for A, T & L. REFERENCES 99 REFERENCES [1] DoD Directive 5000.1, “The Defense Acquisition System,” May 12, 2003, Department of Defense (DoD), Washington, DC. 96 [2] DoD Instruction 5000.2, “Operation of the Defense Acquisition System,” May 12, 2003, Department of Defense (DoD), Washington, DC. 96, 97 [3] DoD Instruction 5000.02, “Operation of the Defense Acquisition System,” December 8, 2008, Department of Defense (DoD), Washington, DC. 96 [4] “Defense Acquisition Performance Assessment (DAPA) Report,” Kadish Report, January 2006, Department of Defense (DoD), Washington, DC. xi, 97 [5] Weapon System Acquisition Reform Act (WSARA) of 2009, Public Law 111–23. May 22, 2009. 97 [6] Ashton Carter, “Memorandum for Acquisition Professionals,” September 14, 2010, DUSD (A, T & L), The Pentagon, Department of Defense (DoD),Washington, DC. 98 100 C H A P T E R 25 Systems of Systems As systems have become larger and more complex, there has been a formal acknowledgment that true “systems of systems” have indeed come upon the scene. And the question immediately behind that is: what does the systems engineering and integration community need to do to successfully build and maintain these systems of systems? There are numerous examples of systems of systems. One that is readily apparent is our national air trafﬁc control (ATC) system. This system is a central part of what might be called our National Aviation System (NAS), and it clearly has subordinate systems dealing with navigation, radars, aircraft landing, communications, and others, including massive display systems in the air and on the ground. Other domains for systems of systems include our national telecommunications system, our highway system, our train system, our defense system and our energy delivery system. 25.1 SOME PERSPECTIVES REGARDING SYSTEMS OF SYSTEMS In 2001, Sage and Cuppan examined the systems engineering and management of systems of systems (SoS) and federations of systems (FoS) [1]. One result of this examination was the conclusion that such systems and federations possessed the “characteristics of complex adaptive systems.” They also reinforced points made about ﬁve characteristics of systems of systems, namely: (cid:129) Operational independence of the constituent systems. (cid:129) Managerial independence of the systems. (cid:129) Geographic dispersion. (cid:129) Emergent behavior. (cid:129) Evolutionary development. The emergent behavior is of special interest, meaning that the overall system of systems can exhibit patterns of behavior that are not present in any one of the individual systems. Also, the latter-listed item implies that the system of systems may be continuously growing under general principles of evolutionary development. A couple of years later, a group of researchers published their work regarding “System of Systems Engineering”[2]. One of the points of interest is their comparison between conventional systems engineering and system of systems engineering (SoSE), in eight domains, i.e., (1) focus, 25.1. SOME PERSPECTIVES REGARDING SYSTEMS OF SYSTEMS 101 (2) objective, (3) approach, (4) expectation, (5) problem, (6) analysis, (7) goals, and (8) boundaries. Their “bottom line” is that System of Systems Engineering (SoSE) may be deﬁned as the following: “The design, deployment, operation and transformation of higher level metasystems that must function as an integrated complex system to produce desirable results. These metasystems are themselves comprised of multiple autonomous embedded complex systems that can be diverse in technology, context, operation, geography, and conceptual frame”[2]. The above paper also sets forth four unique and distinct system contexts that need to be considered. These are the following: (1) new system design, (2) existing system transformation, (3) operation and maintenance, and (4) evaluation and evolution. This is followed by suggestions for research in the domain of system of systems engineering. A third approach to matters concerning systems of systems, and the engineering thereof, was set forth by this author, working with other colleagues in the industry. This approach was documented, in summary form, in a textbook dealing with project management and systems engi- neering [3]. The ﬁrst area of focus was to deﬁne the “elements” of system of systems engineering, under the following 3 major categories: 1. Integration Engineering. 2. Integration Management. 3. Transition Management. A total of 15 subordinate elements were established under these three topics. The basic notion was, and remains, that “integration” was a key issue under a System of Systems perspective, and it had to be approached from both an engineering as well as a management point of view. Further, “management” was also very important, showing up in “integration” as well as “transition” issues. The 15 elements that become critical areas in SoSE focus upon the most important activities, given that each of the systems that are part of an SoS have a coherent systems engineering methodology that has already been applied. Stated another way, the matter of SoSE tends to zero in on “systems” issues having to do primarily with integration and transition. As part of the aforementioned third approach, the authors also formulated a facilitating concept they called “Rapid Computer-Aided System of Systems Engineering” (RCASSE) [3]. As can be inferred by the title, the focus here was rapid or agile systems engineering, as applied to systems of systems, and with special attention to how the computer could be used to make the entire process more efﬁcient. The basic steps of RCASSE were deﬁned: 1. Mission engineering. 2. Baseline architecting. 3. Performance assessment. 4. Specialty engineering. 5. Interfaces/compatibility evaluation. 6. Software issues/sizing. 7. Risk deﬁnition/mitigation. 8. Scheduling. 9. Pre-planned product improvement. 10. Life-cycle cost issue assessment. 102 25. SYSTEMS OF SYSTEMS Following these steps is recommended in order to deal with a complex system of systems and the often stringent demands of schedule. These demands are usually also coupled with cost con- straints. The overall point is that RCASSE is an example of how conventional systems engineering needs to evolve so as to be viable in the domain of complex systems of systems. 25.2 COST ESTIMATION An important question is that of estimating the development effort and costs of a system of systems. We have COCOMO (and other approaches, such as Function Points) for more conventional systems. What might we have for systems of systems? As it turns out, the same COCOMO group, under the direction of Barry Boehm, has tackled this problem, and offers an approach by the name of COSOSIMO [4]. Key inputs are set forth as size drivers and scale factors. The former is determined to be a function of the following: (cid:129) Number of SoS interface protocols. (cid:129) Number of independent system component organizations. Each of these is weighted in terms of expected complexity. Scale factors have been selected: 1. SoS architecture maturity. 2. Cost/schedule compression. 3. Integration risk resolution. 4. Component system maturity. 5. Component system readiness. 6. Integration team capability. 7. Maturity of the integration processes. The current status of COSOSIMO can be ascertained by exploring the website for the CO- COMO team [5]. Implicit in the work on estimating costs for systems of systems is the notion of the SoS Lead System Integrator (LSI), what the LSI does in terms of activities, and how this might differ from more conventional systems engineering activities [6]. But a bottom line in this investigation is to view SoS LSI teams as complex adaptive organizations and to derive from that a set of ways to possibly improve success rates and efﬁciency with systems of systems. A sampling of these ways includes [6]: (cid:129) Planning for risk-driven spiral processes. (cid:129) More up-front architecting and engineering. (cid:129) Support for innovation and learning. (cid:129) More mission-driven and change tolerant. 25.3. THE UBIQUITOUS DEPARTMENT OF DEFENSE (DOD) 25.3 THE UBIQUITOUS DEPARTMENT OF DEFENSE (DOD) 103 We end this chapter on systems of systems by recognizing that the DoD, as in many areas of systems engineering, was on the scene early to formulate some guidance and perspectives so as to try to increase success rates. The DoD Systems Engineering Guide for Systems of Systems [7] is an excellent source for additional reading. Its short roadmap provides, for example, pointers to the following material: (cid:129) A description of types of SoS. (cid:129) A comparison of systems and SoS. (cid:129) A high level overview, as well as detailed description, of SoS systems engineering core elements. (cid:129) How the systems engineering processes support SoS core elements. (cid:129) A high level summary of the Guide. It seems clear that we will see many papers, studies and case histories of how to build and manage systems of systems as we continue on down the road in this complex area. REFERENCES [1] Sage, A. and C. Cuppan (2001), “On the Systems Engineering and Management of Systems of Systems and Federations of Systems,” Information, Knowledge, and Systems Management, 2(4): 325–345. 100 [2] Keating, C., et al. (2003), “System of Systems Engineering,” Engineering Management Journal, 15(3). 100, 101 [3] Eisner, H., Essentials of Project and Systems Engineering Management, (1998, 2002, 2008), John Wiley. 101 [4] Lane, J. A., “Estimating System-of-Systems Development Effort,” Software Tech News, DoD, Vol. 9, No. 1, March 2006. 102 [5] sunset.usc.edu 102 [6] Lane, J. A. and B. Boehm, “Systems of Systems Lead System Integrators: Where Do They Spend Their Time and What Makes Them More or Less Efﬁcient?.” Systems Engineering, Vol. 11, Number 1, Spring 2008. 102 [7] “Systems Engineering Guide for Systems of Systems,” version 1.0, August 2008, Director, Systems and Software Engineering, DUSD (Acquisition and Technology), Department of Defense, Washington, DC. 103 104 C H A P T E R 26 Thinking Outside the Box The many problems we have had with building successful systems suggest that there are times when we need to approach several of the issues of systems engineering by trying to “think outside the box.” Often, this simply implies that, from time to time, it is necessary to question conventional wisdom. Many have reported that they try doing exactly that, but that most of the time, the conventional wisdom prevails. On the other hand, when new approaches are accepted, and prove to be better, we are all encouraged to think even harder about more productive solutions. In many ways, that’s how we make progress—lots of folks trying new ways (in the face of the naysayers) and making them work. To make these notions more concrete, we look below at a half dozen declarations of what might be called “inside the box” thinking in some aspects of systems engineering. 26.1 INSIDE THE BOX 1: BUILD SYSTEMS SO AS TO MAXIMALLY INTEGRATE ALL STOVEPIPES Many managers in the federal government arena come into leadership positions with responsibility for large systems that are mainly composed of stovepipes. In a rather plausible way that has a lot of appeal, they then declare that the ﬁrst priority is to integrate all the stovepipes. The organization then follows that lead, perhaps not aware of the difﬁculties that might lie ahead. The problem that may be lurking is simply that the stovepipes may not be “integrable” within any reasonable time and cost boundaries. Most of the stovepipes in question were not designed to be integrated with the other stovepipes. So why expect that this is an approach that is actually achievable. Is there another more plausible approach? It is suggested here that the “out of the box” approach simply be determined as follows: integrate those stovepipes for which it is cost-effective to do so; otherwise, do not try to crunch systems together that don’t go together. Why abandon our overall sensible approach to build and deploy systems on the basis of their cost-effectiveness? 26.2 INSIDE THE BOX 2: IT’S NOT POSSIBLE TO MAKE CHANGES SO AS TO ACHIEVE MORE THAN MARGINAL IMPROVEMENTS Marginal improvements can be thought of as in the 5-15% range, and according to conventional wisdom, we should accept that type of target and expectation. However, upon more thought, we 26.3. INSIDETHE BOX 3: REQUIREMENTS SHOULD BE CONSIDERED FIXED AND INVIOLATE 105 might ﬁnd that signiﬁcant changes in the process lead naturally to improvements that could be as much as ten times these amounts. What would you say to the approach Federal Express took by way of changing the process? What would you say to the approach Xerox took to constructing a new type of copying machine? What would you say to the business machines (i.e., typewriters, computers) that were built by IBM in terms of improvements in productivity? We build new large systems according to a time-honored set of procedures whereby most of them are designed by means of a “clean sheet of paper” paradigm. What if we were, for certain classes of systems, to try to re-use entire best-of-breed systems. This author set forth such an approach, and showed that improvements in the 2500 percent (!) region were feasible [1]. The world awaits new ideas embedded in new processes, and the two smart graduate students showed us the way with a little system called “Google.” 26.3 INSIDE THE BOX 3: REQUIREMENTS SHOULD BE CONSIDERED FIXED AND INVIOLATE We are very nervous about the notion of changing requirements. Indeed, “creeping” requirements are singled out as one of the reasons we fail in building new systems. However, it makes sense that we should be changing requirements as we learn more and more about a system and what requirements make sense and what do not. If a requirement does not make sense, we should be encouraged to change it. Barry Boehm, one of our software gurus, tells a true story about a 1 second response require- ment that his company could not meet without over-running the system’s original budget of $30 million by an additional $70 million [2]. His company found that by changing the requirement to 4 seconds, which was all right for 90 percent of the cases, the original budget was achievable. That’s the way to treat requirements. How sensitive are schedules and budgets to changes in requirements? How much do we actually need the more stringent requirement in an operational setting? 26.4 INSIDE THE BOX 4: THERE IS NO SILVER BULLET THAT CAN FIX A POORLY PERFORMING ACQUISITION SYSTEM We have been very concerned about our acquisition system, especially in the Department of Defense. Back in 2006, we did a deep special study of this system, the result of which was the so-called DAPA (Defense Acquisition Performance Assessment) report [3]. This report examined 42 issues and deﬁned a set of recommendations in six categories. In September of 2010, Defense Secretary Gates set forth some 23 changes that were needed in the DoD [4]. Questions: Were the DAPA report recommendations implemented? Will the SecDef Gates changes be implemented? The inside the box perspective says that there is no silver bullet that will lead to a reformation of our acquisition system. Yet, in reference to the overall problem, a clear-headed thinker by the name of Norman Augustine gave us the silver bullet when he said [5]: 106 26. THINKING OUTSIDE THE BOX “the difﬁculty resides in having the will to do anything about these problems” It is clear that we know what the problems are, and we also know what the plausible solutions are. As Augustine has said, do we have the will to actually make the necessary changes? That’s the silver bullet. Inside the Box 5: Big systems are hard to build, so as our systems get larger, we should expect more and more failures This inside the box proposition can be translated into: let’s lower our expectations as we attempt to build larger systems. Why not rather set out to (a) build the smarter “learning organization” [6], (b) accept the principles of continuous improvement and six sigma, and then (c) have fewer failures as we move on down the road? That’s what progress is all about, and that’s what we should be planning for as well as achieving in the real world. Inside the Box 6: Try as we may, we will never get away from major patterns of falling behind in cost, schedule and performance Yes, these do seem to be today’s patterns - many programs falling behind, almost at the outset, in one or more of these critical dimensions. Is there another way? The answer is yes, but it likely lies “outside the box”. What are its governing principles? The answers seem to lie in the direction of (a) incentivizing to “tell the truth”, and (b) providing appropriate penalties when agreed-upon goals are not met. Can we change our approach to a “getting ahead of the power curve” mentality? The technical domain is not the problem. The problem lies in the management domain, and in taking a closer look at Augustine’s wise words, as stated above. 26.5 NINE SUGGESTIONS FOR THINKING OUTSIDE THE BOX In 2005, this author published a book that set forth nine perspectives for “thinking outside the box” [7]. A very short overview of these perspectives completes this chapter. 1. Broaden and Generalize Open your ﬁeld of view to admit new strategies and possible solutions. A narrow view will limit your perspective and creativity. 2. Crossover Build a system for one customer and then sell it to many customers. It’s reuse taken to its natural edges, and gaining as much leverage as possible. 3. Question Conventional Wisdom Conventional wisdom changes with the times, so try getting a bit ahead of the pack. If you have a new idea, press it into service. 4. Back of the Envelope A new solution usually does not require the longest equation ever written. Give your intuitive side a chance to converse with your experienced side to produce a new answer on one sheet of paper. REFERENCES 107 5. Expand the Dimensions Problems as well as solutions have many dimensions. Here’s a case whereby just recognizing the dimensions allows a solution to step forward. 6. Obversity The negative side of a positive proposition is what you’re searching for. Why? It may cast a new light on what makes sense and what may not. 7. Remove Constraints Often, perceived constraints turn out to not be real constraints. Remove them, one by one, and a new solution may then become obvious. 8. Thinking With Pictures We know that visual perception is a cognitive activity. Collect, draw and view the pictures to allow the right insights to come forth. 9. Systems Approach There are some seven to ten elements of the systems approach (see chapter two). Try as many as you need to ﬁnd the right solution. Keep the alternatives on the table to help with the process. REFERENCES [1] Eisner, H., (1995), Reengineering the Software Acquisition Process Using Developer-Off-the- Shelf Systems (DOTSS), IEEE International Conference on Systems, Man and Cybernetics, Vancouver, British Columbia, Canada, October 22–25; see also reference [7] 105 [2] Boehm, B., (2002), “Unifying Software Engineering and Systems Engineering”, Computer Magazine, (March), pp. 114–116. 105 [3] “Defense Acquisition Performance Assessment”, DAPA Report, U. S. Department of Defense (DoD), January 2006, Washington, DC. 105 [4] Carter, A., “Memorandum for Acquisition Professionals”, DUSD (A, T & L), September 14, 2010, Department of Defense (DoD), Washington, DC. 105 [5] Eisner, H., Essentials of Project and Systems Engineering Management, 2008, John Wiley, page 415. 105 108 REFERENCES [6] Senge, P., The Fifth Discipline – The Art & Practice of the Learning Organization, Double- day/Currency, 1990. 106 [7] Eisner, H., Managing Complex Systems – Thinking Outside the Box, John Wiley, 2005. 106, 107 C H A P T E R 27 Ten Failure Factors 109 This is a book about attempting to build successful systems. We have seen, from various sections in several chapters, that this is not a simple thing to do. There are many hurdles, obstacles and potholes that lay ahead as one seeks a success pathway. And we would be remiss here not to try to cite some of the ways that managers and programs have basically failed, the notion being that we should try to keep away from these actions and scenarios. 27.1 ONE—UNREALISTIC SCHEDULES Many of the “failure stories” report that this and that program is months, or even years, behind the original schedule. How can this be? Are we literally that bad at the age-old art, and science, of scheduling? The fact is that we know how to schedule and can do so in great detail and with great precision. However, schedule problems still arise because we have a tendency to accept unrealistic schedules. The pressure to do so can be intense, and it is difﬁcult to say no to your boss who says—“The schedule came to us from on high and it is our job to deliver to that schedule. If you can’t do it, let me know now and I’ll ﬁnd someone (other than you) who can!”. So your dilemma is clear. If you say no, the path to promotion may be blocked forever. If you say yes, and then fail, you’re then a bad manager who couldn’t step up to a challenge. Is there another way? Is there a different “solution”? This author believes there is. The essence of it lies in de-scoping the system, thereby deﬁning what you truly believe can actually be delivered to the unrealistic schedule. The de-scoped system is then fully documented along with a cover letter saying: “This is the system I’ve signed up to deliver within the given schedule”. The usual question at that point is then—“OK, what will it take to deliver the original system, not a de-scoped system?” Then you need to be prepared to reveal your fully studied plan for a new and realistic schedule. The two alternatives, and the two schedules, are at that point very clear, and you are off the horns of the dilemma. 27.2 TWO—UNREALISTIC BUDGETS As you might expect, the countermeasure here is much the same as that for the unrealistic schedule. Typically, one can save money by de-scoping and relaxing some of the more difﬁcult and stringent system requirements. Typically, one can save money by “simplifying” the design to a sturdy but not as far-reaching approach. These are the preferred answers. And behind them is the ultimate question— 110 27. TEN FAILURE FACTORS what will it take, by way of budgeted dollars, to meet the original requirements? Be prepared to reveal your well thought-out answer to that question, as well. 27.3 THREE—TOO MANY RISKS IN THE PERFORMANCE DIMENSION The three classical risk areas for systems include (1) schedule risk, (2) cost risk, and (3) performance risk. If a system is pushing the state-of-the-art in terms of required performance, we too often and rather cavalierly accept performance risk without the necessary challenges and without the analysis of what it really takes to reduce the risk. The probability of success takes a nosedive as more performance risks are not dealt with. There is considerable evidence that we have tried to ﬁll the gap with “immature” technology. That has basically not worked. So where might a potential answer lie? In this regard, it would seem that E. Rechtin pointed us on the right direction. In his well deﬁned heuristics [1], he made it clear that after all his years at building and evaluating systems, a viable strategy, in many situations, was still the K.I.S.S. approach. 27.4 FOUR—LOTS OF RISK ANALYSIS, NOT ENOUGH RISK MITIGATION While we’re on the subject of risk, we need to re-emphasize that knowing about a problem, in great detail, is not the same as actually ﬁxing the problem. If risk analysis is to have an appropriate payoff, we must do it early and often, always with an eye toward true mitigation. That can mean changing our design (heaven forbid) backtracking for a while and running new tests that were not originally planned. We do not wish to have risks disappear, we make them disappear. Our level of understanding and commitment to risk mitigation is always enhanced by even a quick review of the “Challenger” incident. This was the well-publicized “O”-ring problem that led to a space shuttle mission failure in January of 1986. None of the seven person crew survived, and this major failure was soon investigated by the Rogers Commission. Apparently, many knew about the risk attendant to the O-ring design, but the culture and decision-making processes did not lead to appropriate before-the-fact action. So the bottom line is the following: it’s not what you know about high risks, it’s what you do about what you know. 27.5 FIVE—LIP SERVICE TO “THE LEARNING ORGANIZATION” The PM (Project Manager) and the CSE (Chief Systems Engineer) are not supposed to carry the organization of which they are a part on their backs. Although their efforts are often Superman-like, we cannot count on it. The organization is supposed to help, support, and facilitate. And when it does not, potential successes can be turned into failures. 27.6. SIX—POOR REQUIREMENTS ENGINEERING 111 Very clear guidance has been given to us by Peter Senge in his “The Fifth Discipline” [2]. In that exposition, he highlighted ﬁve critical disciplines (listed below) and also called for building and sustaining a “learning” organization. 1. Building a Shared Vision 2. Personal Mastery 3. Mental Models 4. Team Learning 5. Systems Thinking (The Fifth Discipline) Table 1—Senge’s Five Disciplines [2] A learning organization tends to not repeat errors and mistakes, and it constantly moves in a “continuous improvement” direction. The learning organization tends to keep away from failure scenarios by its very nature. 27.6 SIX—POOR REQUIREMENTS ENGINEERING Almost every list of “problems” in building systems has this item on the list. Perhaps the simplest way to describe a major part of the problem is to say that (a) we do not know, well enough, how to write an exemplary set of requirements at the beginning of a program, and (b) we do not know, well enough, how to improve poor requirements, or just plain get rid of them. The latter is probably more signiﬁcant, and it implies a well deﬁned and accepted way of changing requirements when it makes good sense to do so. Poor requirements should not be set in stone but rather should be subject to challenge, negotiations, trade-off analysis and change. New ways of advancing this notion need to be worked on and used to improve a situation that has been in need of a new approach for many years. 27.7 SEVEN—FAILURE TO BUY INTO EVOLUTIONARY DEVELOPMENT We have basically accepted the notion of evolutionary development as the appropriate way to build large-scale systems. But still there are many systems that are being constructed on the rejected “grand design” (some say grandiose) idea. Yes, we need to have an overall design concept for the whole system. But no, we don’t have to build and acquire the system as if it’s all or nothing. The evolutionary (some say incremental) approach is the right answer, and the increments need to be useful, functional, and acceptable as separate elements (or subsystems) of the overall system. The documented acquisition plan for all large systems must pass this elemental approach. 112 27. TEN FAILURE FACTORS 27.8 EIGHT—INSUFFICIENT COMMUNICATIONS AND TEAMWORK The failure of many projects can be traceable, ultimately, to poor communications. Each project needs to work on and establish the best communications that are possible under the circumstances. And it starts with regular and well designed project meetings chaired by the PM who understands how to build the appropriate communications discipline. This, as it turns out, is also a key link in establishing a true team. Although we know the importance of Integrated Product Teams (IPTs), we still have a long way to go in actually achieving the same. Formal and informal training would also help. 27.9 NINE—SLIPPAGE IN THE PRACTICES OF SYSTEMS ENGINEERING Although what it takes to establish a solid systems engineering program for the building of systems is well known and well documented, there remains considerable slippage between what we need and what we have. Some aspects of systems engineering need to be tailored to the situation at hand, and many organizations do not know how to do that in an agile way. And some organizations simply do not have the appropriate and integrated mix of domain knowledge and systems engineering expertise. On this overall point, we can consider the following ﬁve systems engineering issues that were deﬁned by the NDIA (National Defense Industrial Association [3]): 1. Lack of awareness of the importance of systems engineering. 2. Inadequate qualiﬁed resources. 3. Insufﬁcient tools and environments for systems engineering execution. 4. Inadequate requirements engineering. 5. Poor initial program formulation. This is but one of many sources that lead us to a deeper understanding of what might need to be improved in order to build successful systems. 27.10 TEN—WE KNOW WHAT TO DO; WHY WON’T WE DO IT? Many study groups, from the Defense Science Board to various industry associations such as the NDIA as cited above, have issued reports on the problems we have in building large systems. In essentially all of these reports, there is a long list of what to do to ﬁx these problems. So—in a very real sense—we know what the problems are, and we know how to ﬁx them. So what then is the problem? As eloquently stated by one of our best systems engineers and executives, Norman Augustine [4], the problem lies in our failure to have to will to take the needed actions, in the real world. REFERENCES 113 REFERENCES [1] Rechtin, E., System Architecting, Prentice-Hall, 1991. 110 [2] Senge, P., The Fifth Discipline – The Art & Practice of the Learning Organization, Double- day/Currency, 1990. 111 [3] www.ndia.org 112 [4] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd edition, John Wiley, page 415. 113 114 C H A P T E R 28 A Success Audit The sub-title of this book is “Building Successful Systems.” So now is the time to summarize the key factors of success in building systems, using the overall disciplines of systems engineering and project management. This will be approached by a “success audit,” using a series of questions, which follow: Are you- 1. Using the systems approach? The elements of the systems approach were discussed very early in this book. Each and every one of them is important in terms of the overall goal of building a successful system. 2. Considering an appropriate set of alternatives? This notion must be called out separately even though it is one of the elements of the systems approach. Mature development teams are always aware of the need to look at other possibilities. Failure to do so opens the door to one or more of your competitors. 3. Doing the risk analyses and mitigation actions that are called for? This cites both the analyses and the follow-up actions. Many programs fail since they do not give priority to the actions that might be required to mitigate high risk scenarios. 4. Not accepting low probability of success scenarios and constraints? (i.e., impossible schedules, budgets and technical performance goals)? If your success probabilities were 0.8 each for cost, schedule and performance, then the likeli- hood that you would fail in at least one of these areas (assuming independence) is around ﬁfty percent. That’s still not good enough. The three success probabilities need to increase if you are looking for overall success (which you are). 5. Challenging high risk requirements? If you are really committed to success, you must say “no” to high risk areas that become system requirements. Look for ways to back up on these requirements. 6. Looking at sensible ways to simplify? This book suggests that trying to simplify (remember the KISS notion) is a positive attribute even as systems are being put forth that have higher and higher performance levels. Can your team ﬁnd the simpler, more elegant, solution? Is it looking for it? 115 7. Using the appropriate architecting process and validating the results? There are several architecting processes that you can choose from. A recommended process is suggested here, but “hybrid” approaches are also available. Pick the one that best ﬁts your program needs, and ﬁgure out how to validate the answers. Ways to accomplish the latter include modeling and simulation. 8. Able to conﬁrm the cost-effectiveness of your preferred architecture? As reiterated several times, the basis for selecting a preferred architecture is its cost- effectiveness, as compared with alternatives. Further, we have speciﬁc ways that we use to compute the effectiveness, as well as the costs, of the various alternatives. It is generally not a good idea to suddenly change the basis for selection. 9. Conﬁrming that you have a “robust” design? A key feature of a robust design is that the system be able to carry out its primary mission despite the existence of various failures in the system. A robust system is also a “slow die” system. In general, we should not allow a single point failure to bring down the entire system. 10. Assuring the system’s interoperability (internal and external)? All systems have internal as well as external interfaces, by design. A critical part of both types of interfaces is interoperability. We should also be better at measuring the degree or level of interoperability that we have achieved, as compared with our goal in this respect. 11. Establishing the maturity of the selected technologies? Using technology in a system when that technology is not fully mature is a clear risk. It is necessary to conﬁrm that our selections of technologies are sound in terms of capabilities (they satisfy the requirements) as well as availability (they are there when we need them). In short, the selected technologies need to be “demonstrated.” 12. Using the evolutionary development approach? This approach means that we are able to construct parts of the system and bring them into operation, while keeping other parts on track for a later implementation. It is a “chunking” approach that has proven to be successful, especially for large and complex systems. 13. Challenging unrealistic stovepipe integration notions? In general, we are not striving to maximize the number of stovepipes that are integrated. Rather, we are trying to ﬁnd cost-effective solutions to the problem at hand. If this means very little stovepipe integration, so be it. 14. Assuring the technical competence of every member of your team? 116 28. A SUCCESS AUDIT You need to have a contribution from every member of the team, which, in turn, means that they need to have the skills in order to make that contribution. To have otherwise, jeopardizes the success of the project and the system. 15. Able to conﬁrm that you have a highly functional and communicative team? Having skilled personnel is a necessary, but not a sufﬁcient condition for success. These folks need to be molded into a highly functional team, which depends upon attitude and high levels of honest informative communications. Divisive team members should not be tolerated. 16. Assuring that you have the appropriate project support from your company or organization? This includes such items as support from the IT people, contracts, accounting and the one of most importance, your management chain. 17. Mobilizing an excellent test and evaluation (T & E) capability? Test and evaluation represents the sign-off milestone for the system. Great T & E people are worth their weight in gold. Get them going as early as possible. 18. Assuring the support of a mature veriﬁcation and validation (V & V) group? Having this support can set the stage for a successful T & E as well asbuilding incremental conﬁdence in the system and its performance against requirements. 19. Using “thinking outside the box” principles? Nine ideas for thinking outside the box have been presented here. Are you able to use some of them? Which ones, and in what context? 20. Invoking project management principles in a rigorous manner? This refers to all aspects of the classical tasks of project management—planning, organizing, directing and controlling. 21. Able to use appropriate “progress tracking” systems? We are always measuring the progress we are making against our plans, even as our plans are being updated. These tracking systems need to provide timely and accurate information. 22. Obtaining inputs from the key members of your team, and using them in making decisions (e.g., multiple independent estimates on cost and schedule)? 23. Maintaining appropriate contingencies and reserves? These generally take the form of budget dollars as well as schedule. Success often depends upon having some types of reserves for problems that were not foreseen. 24. Living up to each and every one of your commitments? The project/systems engineering team, including of course its leadership, needs to maintain the position that all commitments are real, and the team will, in fact, do what it has said it would do. This “attitude” is part of a success scenario. 25. Building and maintaining a constructive relationship with your customer? Even though this is the last question on our list, we must not and will not forget our customer. This is not to be an adversarial relationship. Rather, it’s one in which both you and your customer, with honesty and trust, solve the many problems attendant to building today’s large-scale high-tech systems. If we wish to try going a step further with the above 25 questions, assign a number to each in terms of your experience with a speciﬁc program. Here are some numbers to use: 117 4 = a strong “yes.” 3 = mostly/often. 2 = under consideration. 1 = mostly “no.” 0 = not at all/off the screen. Now add all your assigned numbers. If you get less than 75 there is trouble ahead, depending upon which questions got the lowest score. Now look at the questions that got “1” or “0” and see what you might want to do about them. Success in building large-scale systems requires paying attention, every day, to the types of questions posed here. There is no single “silver bullet;” the closest thing to it is having the will and determination to do what is necessary over a long period of time. 118 C H A P T E R 29 Standards Systems engineering has several standards that have contributed to its development and understand- ing. In this chapter, we are able to brieﬂy examine three standards that apply speciﬁcally to systems engineering and two that apply to software engineering. Other documents are cited, as well, that relate to the ﬁeld’s overall body of knowledge (BoK). 29.1 MILITARY STANDARD 499B A convenient starting point for examining standards in systems engineering is the well-known “499B”[1]. This document goes back to the year 1971 and sets forth some of the important early concepts of systems engineering. Among these is what they called the overall systems engineering process, characterized by the diagram below (Figure 29.1). Requirements(cid:3)Analysis(cid:3) System(cid:3)Analysis(cid:3)and(cid:3)(cid:3)(cid:3) Control(cid:3) Functional(cid:3)Analysis/Allocation(cid:3) Synthesis(cid:3) Figure 29.1: Four Key Elements of Systems Engineering [1]. The above chart focuses upon four key elements of systems engineering, namely: 1. Requirements Analysis. 2. Functional Analysis/Allocation. 3. Synthesis. 4. Systems Analysis and Control. Upon more detailed scrutiny, we see these elements as central to system architecting rather than representing the overall systems engineering process. However, the clear articulation of these “top four” notions advanced the thinking in the overall systems engineering community. Another important aspect of 499B was its deﬁnition of the SEMP—the Systems Engineering Management Plan. The overall SEMP, as therein deﬁned, contained the following key topics: 29.2. IEEE P1200 119 1. Systems Engineering Process. 2. Systems Analysis and Control. - Systems Analysis. - Technical Performance Measurement. - Technical Reviews. 3. Technology Transition. 4. Technical Integration Teams. Even today, there is much wisdom in paying special attention to these aspects of systems engineering. Of special note is the critical need for performance measurement, technology, and teams.These needs remain true today, in a quite fundamental way. 29.2 IEEE P1200 This IEEE standard directly focuses upon systems engineering [2]. In doing so, it accepted the above four elements from 499B (Figure 29.1) and added a ﬁfth element, namely, veriﬁcation and validation. The fact that the IEEE decided to include systems engineering within its ﬁeld of view helped to support the notion that today’s engineers, whatever their specialty discipline, needed to learn about and be able to apply the principles of systems engineering. 29.3 EIA 632 This standard deals with “processes for engineering a system” [3]. The nature of the standard is revealed by its 13 processes, aligned into ﬁve categories, as below (Table 29.1). We note the emphasis on “process,” and the idea that the entire scope of systems engineering can be addressed by means of the 13 deﬁned processes. 29.4 ISO/IEC 15288 This is an especially important standard that deals with systems engineering in the context of system life cycle processes [4]. The key word, again, is “process.” This standard deﬁnes some 25 processes that fall into four categories, namely, agreements, enterprises, projects, and technical matters. This standard has been widely accepted and served as the basis for an important update of the INCOSE 120 29. STANDARDS Table 29.1: Categories and Processes in EIA 632 Standard [3]. A. Acquisition and Supply 1. Supply Process 2. Acquisition Process B. Technical Management 3. Planning Process 4. Assessment Process 5. Control Process C. System Design 6. Requirements Deﬁnition Process 7. Solution Deﬁnition Process D. Product Realization 8. Implementation Process 9. Transition to Use Process E. Technical Evaluation 10. Systems Analysis Process 11. Requirements Validation Process 12. System Veriﬁcation Process 13. End Products Validation Process systems engineering handbook.This update, in turn, plays a central role in the INCOSE certiﬁcation of systems engineers. In other words, to be certiﬁed by INCOSE, it is important that the candidate know and understand their handbook. The full details, including processes, cannot be included in this document. The reader is encouraged to look into the matter further through either INCOSE or the ISO/IEC representatives. 29.5 IEEE/EIA 12207 This is a software standard that is based upon life cycle processes in three domains: (1) primary areas, (2) supporting areas, and (3) organizational areas [5]. A total of some seventeen processes cover all these areas. The processes that are part of the primary area include the following: (1) acquisition, (2) supply, (3) development, (4) operation, and (5) maintenance. Even though we are dealing with software here, we notice some similarities to the 632 systems engineering standard brieﬂy cited above. 29.6 IEEE P1471 This software standard moves directly into the matter of software architectures and descriptions thereof [6]. The standard sets forth a recommended practice for architectural description (AD), REFERENCES 121 and it acknowledges that there is not a reliable consensus on the precise meaning of a software architecture. At the same time, it states that architectural descriptions, or views, are very important as we proceed with our software designs and implementations. A rather complete list of the uses of ADs is provided. Standards in systems and software engineering are extremely useful in terms of developing common understandings and trying to embrace best practices. The standards cited in this short chapter give us some sense of what has been documented, and also what directions have been established as we move forward in these important ﬁelds. REFERENCES [1] “Engineering Management,” Military Standard 499B (1971), Department of Defense (DoD), Washington, DC. 118 [2] IEEE P1200, “Standard for Systems Engineering,” April 7, 1994, IEEE, 445 Hoes Way, Piscataway, New Jersey. 119 [3] “Processes for Engineering a System,” EIA Standard 632 (1998), Washington, DC. 119, 120 [4] ISO/IEC 15288, “Systems Engineering – System Life Cycle Processes,” 2003. 119 [5] IEEE/EIA 12207, “Software Life Cycle Processes,” April 1998, IEEE, 445 Hoes Way, Pis- cataway, New Jersey. 120 [6] IEEE P1471, “Recommended Practice for Architectural Description” (AD), December 1999, IEEE, 445 Hoes Way, Piscataway, New Jersey. 120 122 References This bibliography cites a number of important books in the ﬁelds of systems and software engineering. In general, papers are cited at the end of each of the relevant chapters. The books are in alphabetic order with respect to the ﬁrst-named author. REFERENCES [1] Ahern, D., A. Clouse and R. Turner, CMMI Distilled, Addison-Wesley, 2001. [2] Augustine, N., Augustine’s Laws, 6th edition, AIAA, Reston, VA, 1982. [3] Beam, W., Systems Engineering, McGraw-Hill, 1990. [4] Bertalanffy, L. von, General System Theory, George Braziller, 1968. [5] Boardman, J. and B. Sauser, Systems Thinking: Coping with 21st Century Problems, CRC Press, 2008. [6] Boehm, B., Software Engineering Economics, Prentice-Hall, 1981. [7] Boehm, B. et. al., Software Cost Estimation with COCOMO II, Prentice-Hall, 2000. [8] Blanchard, B., Systems Engineering Management, John Wiley, 1998. [9] Blanchard, B. and W. Fabrycky, Systems Engineering and Analysis, 5th edition, Prentice-Hall, 2011. [10] Buede, D., The Engineering Design of Systems, John Wiley, 2000. [11] Cleland, D. and L. Ireland, Project Management, 5th edition, McGraw-Hill, 2007. [12] Eisner, H., Essentials of Project and Systems Engineering Management, 3rd edition, John Wiley, 2008. [13] Eisner, H., Managing Complex Systems – Thinking Outside the Box, John Wiley, 2005. [14] Eisner, H., Computer-Aided Systems Engineering, Prentice-Hall, 1988. [15] Eisner, H., Reengineering Yourself and Your Company, Artech House, 2000. [16] Forrester, J., System Dynamics, Pegasus Communications, 1968. [17] Forsberg, K., H. Mooz and H. Cotterman, Visualizing Project Management, John Wiley, 2000. [18] Friedenthal, S., A. Moore and R. Steiner, A Practical Guide to SysML: The Systems Modeling Language, Elsevier, 2008. [19] Gibson, J., W. Scherer and W. Gibson, How To Do Systems Analysis, John Wiley, 2007. [20] Goode, H. and R. Machol, System Engineering, McGraw-Hill, 1957. REFERENCES 123 [21] Hall, C., The Age of Synthesis, Peter Lang, 1995. [22] Kerzner, H., Project Management, John Wiley, 2009. [23] Keszbom, D., D. Schilling and K. Edward, Dynamic Project Management, John Wiley, 1989. [24] Kossiakoff, A. and W. Sweet, Systems Engineering Principles and Practice, John Wiley, 2003. [25] Laszlo, The Systems View of the World, George Braziller, 1972. [26] Meadows, D., Thinking in Systems, Chelsea Green Publishing, 2008. [27] Martin, James N., Systems Engineering Guidebook, CRC Press, 1997. [28] “NASA Systems Engineering Handbook,” NASA/SP-2007–6105 Rev. 1, NASA Headquar- ters, Washington, DC, December 2007. [29] Parnell,G., P. Driscoll and H. Henderson, Decision Making on Systems Engineering and Man- agement, John Wiley, 2008. [30] Rechtin, E., System Architecting – Creating and Building Complex Systems, Prentice-Hall, 1991. [31] Rechtin, E. and M. Maier, The Art of Systems Architecting, CRC Press, 1997. [32] Rechtin, E., Systems Architecting of Organizations, CRC Press, 2000. [33] Sage, A. and J. Palmer, Systems and Software Engineering, John Wiley, 1990. [34] Sage, A., Systems Management for Information Technology and Systems Engineering, John Wiley, 1995. [35] Sage, A., Introduction to Systems Engineering, John Wiley, 2000. [36] Sage, A. and J. Armstrong, Introduction to Systems Engineering, John Wiley, 2000. [37] Sage, A. and W. Rouse, Handbook of Systems Engineering and Management, John Wiley, 1999. [38] Senge, P., The Fifth Discipline – The Art & Practice of the Learning Organization, Double- day/Currency, 1990. 124 REFERENCES [39] “Systems Engineering Handbook,” vers. 3.2, International Council on Systems Engineering (INCOSE), 2010. [40] Wasson, C., Systems Analysis, Design and Development, John Wiley, 2006. [41] Weinberg, G., Rethinking Systems Analysis and Design, Dorset House, 1988. [42] Westerman, H. R., Systems Engineering Principles and Practice, Artech House, 2001. [43] Wymore, A. W., Model-Based Systems Engineering, CRC Press, 1993. Author’s Biography 125 HOWARD EISNER Howard Eisner came to The George Washington University (GWU) as a full professor in 1989 after thirty years as an ex- ecutive and research engineer with ORI, Inc. and the Atlantic Research Corporation (ARC). In addition to these positions, he served as president of two systems engineering companies, the In- tercon Systems Corporation and the Atlantic Research Services Company. Dr. Eisner has written four books that relate directly to systems engineering, its management, and connected disciplines. He was trained as an engineer and spent much of his career in the command, control, communications and intelligence arena. He is a Life Fellow of the IEEE (Institute of Electrical and Electronics Engineers) and a Fellow of IN- COSE (International Council on Systems Engineering) and The New York Academy of Sciences. He is also a member of Tau Beta Pi, Eta Kappa Nu, Sigma Xi and Omega Rho, various engineering and research honor societies. In 1994 he was given the Outstanding Achievement Award from the GWU Engineering Alumni. He holds BEE, MS and Doctor of Science degrees from the City College of New York, Columbia University, and The George Washington University, respectively.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6812861.pdf&bkn=6812860&pdfType=book	MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 Project Management for Engineering Design Copyright © 2007 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Project Management for Engineering Design Charles Lessard and Joseph Lessard www.morganclaypool.com ISBN-10: 1598291742 paperback ISBN-13: 9781598291742 paperback ISBN-10: 1598291750 ebook ISBN-13: 9781598291759 ebook DOI 10.2200/S00075ED1V01Y200612ENG002 A Publication in the Morgan & Claypool Publishers Series SYNTHESIS LECTURES ON ENGINEERING #2 Lecture #2 Series ISSN: 1559-811X Series ISSN: 1559-8128 print electronic First Edition 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 Project Management for Engineering Design Charles Lessard Texas A&M University Joseph Lessard Globeleq Inc. SYNTHESIS LECTURES ON ENGINEERING #2 M&C M o r g a n & C l a y p o o l P u b l i s h e r s MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 iv ABSTRACT This lecture book is an introduction to project management. It will be of use for engineering students working on project design in all engineering disciplines and will also be of high value to practicing engineers in the work force. Few engineering programs prepare students in methods of project design and conﬁguration management used within industry and government. This book emphasizes teams throughout and includes coverage of an introduction to project management, project deﬁnition, researching intellectual property (patent search), project scope, idealizing & conceptualizing a design, converting product requirements to engineering speciﬁcations, project integration, project communications management, and conducting design reviews. The overall objectives of the book are for the readers to understand and manage their project by employing the good engineering practice used by medical and other industries in design and development of medical devices, engineered products and systems. The goal is for the engineer and student to work well on large projects requiring a team environment, and to effectively communicate technical matters in both written documents and oral presentations. KEYWORDS Engineering Design, Teams, Conﬂict Resolution, Decision Making, Project Management, Time Management, Cost Management, Risk Management, Earned Value Analysis. MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 v Contents 1. 2. 3. 4. Introduction to Engineering Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Deﬁning the Project or Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Design Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Project Management Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Project Management Knowledge Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1 Project Life Cycles and Project Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 2.3 Product Life Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Organizational Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Project Management Job Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Project Integration Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Project Plan Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1 Project Plan Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 3.3 Project Controlling Process and Change Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Change Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.5 Conﬁguration Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.6 Need for Top Management Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Project Scope Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Project Scope Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1 4.2 Selecting Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 Weighted Scoring Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4 Project Charters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.5 Work Breakdown Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.6 Approaches to Developing Work Breakdown Structures (WBSs) . . . . . . . . . . . . 28 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 vi PROJECT MANAGEMENT FOR ENGINEERING DESIGN 5. 6. 7. 8. Personal and Project Time Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Personal Time Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.1 “Work Smarter, Not Harder” [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.2 Project Time Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3 Project Time Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.4 Project Network Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.5 5.6 Precedence Diagramming Method (PDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.7 Estimation of Activity Times (Duration) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Schedule Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.8 5.9 Critical Path Method (CPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.10 Program Evaluation and Review Technique (PERT) . . . . . . . . . . . . . . . . . . . . . . . 36 5.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Project Cost Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.1 Project Cost Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.2 Resource Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.3 Cost Estimating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 6.4 Cost Estimation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Problems in Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.5 6.6 Cost Budgeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.7 Guidelines for Preparing Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.8 Cost Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 Earned Value Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 7.1 Work Breakdown Structure (WBS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 7.2 Calculating Earned Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 7.3 Earned Value Management System (EVMS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.4 Tools and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.5 Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 Project Quality Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 8.1 Project Quality Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.2 Quality Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.3 Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 8.4 Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 CONTENTS vii 8.5 8.4.1 Pareto Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 8.4.2 Quality Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Statistical Sampling and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . 53 8.4.3 8.4.4 Basic Statistical Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 8.4.5 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Improving Project Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 8.5.1 Maturity Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 8.6 Cost of Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 International Organization for Standardization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 8.7 8.8 Good Manufacturing Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 8.9 Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 9. 9.3 Project Procurement Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Project Procurement Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 9.1 Procurement Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 9.2 9.2.1 Types of Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Solicitation Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 9.3.1 Statement of Work (SOW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Solicitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 9.4 9.5 Source Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 9.6 Contract Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 9.7 Contract Closeout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 10. Project Human Resource Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 10.1 Managing People . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 10.2 Improving Effectiveness: Covey’s Seven Habits. . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 10.2.1 The Seven Habits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 10.2.2 Personality and Behavioral Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 10.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 11. Project Communications Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 11.1 Project Communications Management Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 11.2 Communications Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 11.3 Information Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 11.4 Span of Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 viii PROJECT MANAGEMENT FOR ENGINEERING DESIGN 11.5 Performance Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 11.5.1 Template for Weekly Progress Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 12. Project Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 12.1 Project Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 12.2 Types of Project Risks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 12.3 Risk Quantiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 12.4 Risk Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 12.5 Causes of Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 12.6 Risk Management Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 12.7 Risk Response Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 12.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 13. Project Closeout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 13.1 Closing Processes and Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 13.1.1 Administrative Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 13.1.2 Approval Veriﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 13.1.3 Procurement Contract Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 13.2 Outcomes Assessment Meeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 13.3 Outcomes Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 13.4 Transition Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 13.5 Project Documents to be Archived . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 13.6 Critical Success Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 14. Project Design Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 14.1 Prelude to Conducting a Design Review Meeting . . . . . . . . . . . . . . . . . . . . . . . . . . 89 14.2 Entry Criteria for Design Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 14.3 Conducting the Design Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 14.4 Design Review Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 14.5 Exit Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 15. Making Technical Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 15.1 Group Decision-Making Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 15.1.1 The Rational Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 CONTENTS ix 15.1.2 The Political Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 15.1.3 The Process Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 15.1.4 The Garbage Can Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 15.2 U.S. Navy Executive Decision-Making Framework . . . . . . . . . . . . . . . . . . . . . . . . . 99 15.3 Decision Matrix or Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 15.3.1 Weighted Function Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100 15.3.2 Authors’ Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 15.3.3 Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 15.4 Factor Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 15.5 Grading Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 15.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 16. Management of Team Conﬂict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 16.1 Giving Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 16.2 Conﬂict Resolution Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 16.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Author Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 MOBK076-FM MOBKXXX-Sample.cls April 1, 2007 13:28 book Mobk076 April 2, 2007 18:9 1 C H A P T E R 1 Introduction to Engineering Design The engineering design process is similar to problem-solving processes taught in engineering colleges. Most commercial products begin by identifying the commercial market needs of some novel “ideas,” which may impact some commercial market. Hence, the ﬁrst steps in a product design may include 1. novel idea, or potential market needs, 2. forming a team, since most complex problems or products are not developed by a single individual, 3. development of generalized broad product requirements: a. Generally, user requirements may not be technical; e.g., a doctor wants to monitor temperature, or a veterinarian wants to remove purring sound from a stethoscope so he can hear the cat’s heart valve sounds. What are the technical speciﬁcations? 4. deﬁne required input and outputs, 5. deﬁne the product outcome: a. What is it used for, by whom? Inputs? b. How do we measure the desired outcome? c. How do we test the desired outcome? d. What are the criteria for acceptance? TEAMS 1.1 Webster [1] deﬁnes the word “team—a noun” in various ways: 1. Two or more draft animals harnessed to a vehicle or farm implement. 2. A vehicle along with the animal or animals harnessed to it. 3. A group of animals exhibited or performing together. 4. A group of players on the same side in a game. 5. Any group organized to work together. book Mobk076 April 2, 2007 18:9 2 PROJECT MANAGEMENT FOR ENGINEERING DESIGN Engineering has expanded the deﬁnition to “A team is a small group of people with complementary skills who are committed to a common purpose, performance goals, and approach for which they hold themselves mutually accountable” [2]. You might wonder why work in teams? One might cite that “Team skills are valued by industry” or that one person does not have in-depth knowledge in all the disciplines and functions of engineering to design and produce a spacecraft or a space station. It requires a “team” of people with diverse backgrounds in the necessary technical areas to produce the product for space. Simply put, teams need engineers with a broad set of talents, i.e. 1. 2. technical knowledge creativity 3. people skills 4. planning ability 5. management skills. Diverse abilities and diverse ways of thinking and viewing problems is the strength of teams that function well together. Because teams are important in the success of projects, project managers must understand teams and consider ﬁve issues in team building. 1. Interdependence: It is the issue of how each member’s outcomes are determined, at least in part, by the actions of the other members. Functioning independently of one another or competing with your teammates may lead to suboptimal or disastrous outcomes for both the entire team and the project. 2. Goal speciﬁcation: It is very important for team members to have common goals for team achievement, as well as to communicate clearly individual goals that members may have. 3. Cohesiveness: It refers to the attractiveness of the team membership. Teams are cohesive to the extent that membership in them is positively valued, that is, members are drawn toward the team. Patterns of interpersonal attraction within a team are a very prominent concern. Task cohesiveness refers to the way in which skills and abilities of the team members mesh to allow effective performance. 4. Roles and norms: All teams need to develop a set of roles and norms over time. a. Roles: For a student team, the role structure will enable the team to cope more effectively with the requirements of a given task. The roles may be rotated so that all team members experience, and learn from, the various positions held. It is extremely important that the roles are understood and accepted by team members. book Mobk076 April 2, 2007 18:9 INTRODUCTION TO ENGINEERING DESIGN 3 b. Norms: For a student team, norms are the rules governing the behavior of team mem- bers, and include the rewards for behaving in accord with normative requirements, as well as the sanctions for norm violations. It is not uncommon for a set of norms to develop between team members that are never actively discussed. However, it is always better to have interaction rules appear in the form of a written document, such as in a “code of cooperation”: the agreed upon rules governing the behavior of team members, as well as any appropriate rewards and sanctions. The team code of cooperation sets a norm for acceptable behavior for each team member and repre- sents how the team members will interact with one another. It should be developed, adopted, improved, and/or modiﬁed by all team members on a continuous basis; and copies should be easily accessible by team members. 5. Communication: Effective interpersonal communication is vital for the smooth func- tioning of any task team. It is also important for a team to develop an effective com- munication network: who communicates to whom; is there anybody “out of the loop?” Norms will develop by governing communication. Do those norms encourage every- one to participate, or do they allow one or two dominant members to claim all the “air time?” [3]. Key team roles include the following: 1. Meeting coordinator: Coordinates and prepares the agenda (i.e., what needs to be ac- complished, establishes a process, etc.); coordinates time, date, and place of meetings; ensures all necessary resources are available for the meetings; keeper of the code of cooperation (to be discussed); monitors the decision-making process; coordinates the process check. However, this person is not the “boss.” 2. Recorder: The recorder is the person responsible for doing the writing of the team whenever group work is being done, which should maximize participation by the rest of the team, since no one else needs to worry about it. If required, the recorder also ensures that the process(es) being used by the team is (are) documented and/or prepares an “action list” to keep a record of the assigned actions. In addition, the recorder makes sure that copies of their work are provided to the rest of the team. 3. Time keeper: The time keeper has the responsibility of keeping tract of time, as well as keeping the team moving so that they can ﬁnish the task at hand. 4. Encourager/gatekeeper: The encourager/gatekeeper has the task of giving encouragement to all the other team members. The person also has the responsibility of maintaining a balanced level of participation for all the members. They will encourage the silent members and try to hold back the verbose, dominate members. book Mobk076 April 2, 2007 18:9 4 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 5. Devil’s advocate: The devil’s advocate takes a position opposite to that held by the team to ensure that all sides of an issue are considered. This responsibility should be undertaken by all team members [4]. In a learning environment such as student teams, the roles should rotate among team members. In summary, effective teams include the use of roles, the development of a code of cooperation, the use of the check for understanding to make sure everybody is “on the same page,” the development of effective listening skills, the ability to give and take effective constructive feedback, the use of agendas for planning meetings, the use of contact before work to provide time for nontask-related discussions, the deﬁnition of decision-making processes to be included in the agenda, the use of the issue bin to provide time for discussion of items not in the agenda, the use of action lists to keep a record of assigned actions, the use of a process check for continuous improvement, and a commitment from all the members of the team. Once the team is established, the purpose and objectives of the team should be deﬁned and documented. Subsequently, the project must be adequately deﬁned. 1.2 DEFINING THE PROJECT OR PROBLEM One of the most important aspects in product development and engineering design is to ad- equately deﬁne the scope of the problem. Often, the problem is stated initially in terms of vague project requirements. The team must redeﬁne the product requirements in terms of in- puts, output, and appearances, then convert and link requirements to “technical speciﬁcations,” e.g., performance, accuracy, tolerances, etc. One should keep in mind that “all speciﬁcations must be tested.” Additionally, the team must develop and document “pass or fail acceptance criteria” for each speciﬁcation, as well as goals or criteria for success and constraints (part of scope). Typical goals or criteria for success include aesthetics, performance, quality, human factors, costs (“initial capital” and “life cycle” costs), safety, operating environment, interface with other systems, effects on surroundings, logistics, reliability, maintainability (preventive and corrective maintenance), serviceability, and availability. Constraints usually include the following factors: budget, time, personnel, legal, material properties, availability of materials, off-the-shelf purchase versus fabrication/construction, competition, and manufacturability (can it be manufactured?) [5]. BACKGROUND 1.3 Investors or a company marketing survey may have expressed the need for a new or a better product as an idea or in very general terms, but engineers working on the project design require book Mobk076 April 2, 2007 18:9 greater background knowledge. Knowledge in the form of publications on other similar designs that may be found in INTRODUCTION TO ENGINEERING DESIGN 5 1. library literature searches, 2. Web-based searches, or 3. patent searches. Patent searches are a key element in products being designed and developed for the commercial sector, since patent infringement may lead to lawsuits. Without doubt, searches take a lot of time, and results of the searches must be analyzed, documented, and reported in the “back- ground” section of the proposal, such as a small business incentive research (SBIR) proposal. This step also takes a lot of time, often months; it may be continued throughout the product development period. 1.4 DESIGN PHASES Most student teams believe design is a single-step process, which it is not. Designing in industry is a multipass process that includes various phases: the conceptualization phase, feasibility study phase, preliminary design phase, and detailed design phase. In the feasibility study phase, conceptualization and “brainstorming” ideas are roughed out. In searching for a solution, selection of the most feasible ideas for reﬁnement is a team decision. The following heuristics are often applied in the search for a solution: 1. 2. 3. 4. 5. 6. 7. challenge basic assumptions employ analogies identify critical parameters switch functions alter sequence of steps reverse the problem separate or combine functions 8. use vision 9. employ basic engineering principles. In the preliminary design phase, the most promising ideas are explored and analyzed in more detail. Finally, in the detailed prototype design phase, the team develops highly detailed book Mobk076 April 2, 2007 18:9 6 PROJECT MANAGEMENT FOR ENGINEERING DESIGN Feasibility Phase Implementation Phase Design Phase Integration Phase Final Product Alpha Test Phase Beta Test Phase FIGURE 1.1: The design methodology of IWT on “real-world” experience drawings with ﬁnal speciﬁcations prepared for the “best design option.” In all design phases, the following four steps are repeated: 1. 2. analyzing each potential solution, choosing the best results or solutions, 3. documenting the results or solutions, 4. communicating results or solutions to management. A detailed design phase is when companies usually construct or fabricate prototypes. Marketing strategies would be in development in parallel about this time. Once the prototype is ﬁnished, it undergoes “veriﬁcation” or “alpha” testing and evaluation of design speciﬁcations, perfor- mance parameters, safety, etc. The results are compared against the acceptance criteria. If the speciﬁcation fails the acceptance criteria, the prototype may undergo a redesign. If all tests are acceptable, the product may undergo validation or “beta” testing, which means the product will be sent to various users to test the product with noncompany subjects. Innovative Wireless Technologies (IWT) structured their strict design methodology on “real-world” experience (Fig. 1.1). Their feasibility phase includes requirements, project budget, project schedule, and design speciﬁcations. In their design phase, IWT includes technical patent search, functional design specs (FDS), FDS design review, and product veriﬁcation plan. The implementation phase includes prototype development, integration test plan, patent review, factory prototype review, and product launch. The integration phase includes plans and documentation for factory prototype development, integration testing, and environmental testing. In the alpha test phase (veriﬁcation), test engineers conduct alpha testing, preseries production, release the design, and develop the beta test plan. Validation test phase includes book Mobk076 April 2, 2007 18:9 INTRODUCTION TO ENGINEERING DESIGN 7 beta testing, release customer documentation, initial series production, yield analysis, and training [6]. Testing in industry is not the same as a test conducted by a student in academic lab- oratories. The team must develop test plans and test procedures before the breadboard and prototype system is developed and tested. In the veriﬁcation testing, the prototype (hardware and software) is also veriﬁed in an integrated test environment with all necessary test equipment for EMI/EMC and pre-FCC veriﬁcation. SUMMARY 1.5 Project managers and their teams should focus their attention and efforts on meeting project objectives and producing positive results. It is recommended that instead of blaming team members, the focus should be turned to ﬁxing the problem. Project managers should establish regular, effective meetings with agenda and openness. Part of the program managers tasks include nurturing team members, encouraging them to help each other, and to acknowledge in public the individual and group accomplishments. Additional information on teams may be found in [7, 8]. REFERENCES [1] Webster’s New Collegiate Dictionary, G&C Merriam Co., Springﬁeld, MA, 1973. [2] J. R. Katzenbach and D. K. Smith, The Wisdom of Teams. Boston, MA: Harvard Business School Press, 1993. [3] Surviving the Group Project: A Note on Working in Teams http://web.cba.neu.edu/∼ewertheim/teams/ovrvw2.htm, 2005. [Online]. Available: [4] D. A. Nadler, Designing Effective Work Teams. New York: Delta Consulting Group, 1985. [5] G. P. Shea and R. A. Guzzo, “Group effectiveness: What really matters,” Sloan Manage. [6] Rev., vol. 3, pp. 25–31, 1987. Innovative Wireless Technologies http://www.iwtwireless.com, 2004. (IWT) Design Methodology [Online]. Available: [7] V. R. Johnson. (2005, Mar.). Understanding and assessing team dynamics. IEEE-USA Today’s Eng. [Online]. Available: http://www.todaysengineer.org/2005/ Mar/team dynamics.asp. [8] V. R. Johnson. (2004, Nov.). Understanding and assessing team dynamics. IEEE- USA Today’s Eng. [Online]. Available: http://www.todaysengineer.org/2004/Nov/self- assessment.asp. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 9 C H A P T E R 2 Project Management Overview Before diving into project management, let us begin with a simple question. What is a “project”? A project is a temporary endeavor undertaken to accomplish a unique purpose. I have managed projects ranging from simple projects, like the development of an automated EEG analyzer, to complex high dollar value, such as the installation of Spain’s Air Defense System. Yet, regardless of complexity, all projects have similar attributes: 1. Each project has its own “unique purpose.” 2. Projects are “temporary” with time constraints. 3. Projects require resources (manpower, funding, and materials), often from various areas. 4. Commercial projects should, and usually, have a primary sponsor and/or customer. 5. All projects involve uncertainty. 6. Every project is constrained in different ways by its a. scope goals b. time goals c. cost goals. It is the project manager’s responsibility to balance these three competing goals. So, what is project management? Project management is “The application of knowledge, skills, tools, and techniques to project activities in order to meet or exceed stakeholder needs and expectations from a project” [1]. In the deﬁnition of project management, the terminology is often misinterpreted to mean investors with stock in the company or “stockholders”; whereas, “stakeholders” are the people involved in or affected by project activities. Thus, “stakeholders” include the project sponsor and all members of the project team, support staff, customers, users, suppliers, and even opponents to the project. book Mobk076 April 2, 2007 18:9 10 PROJECT MANAGEMENT FOR ENGINEERING DESIGN PROJECT MANAGEMENT KNOWLEDGE AREAS 2.1 Knowledge areas describe the nine key competencies that project managers must develop. There are four core knowledge areas that lead to speciﬁc project objectives (scope, time, cost, and quality). There are also four facilitating knowledge areas that are the means through which the project objectives are achieved (human resources, communication management, risk management, and procurement management). The ﬁnal knowledge area (project integration management) affects and is affected by all of the other eight knowledge areas. Although much of the knowledge needed to manage the projects is unique to project management, nevertheless, project managers must also have knowledge and experience in “general management” and in the application area of the project. Ultimately, project managers must focus on meeting speciﬁc project objectives. This book will develop and elaborate on each of the nine knowledge areas in separate chapters. There are several project management tools and techniques that assist project managers and their teams in various aspects of project management. Some speciﬁc tools include 1. project charter 2. Work breakdown schedule (WBS) or scope 3. Gantt charts, PERT charts, critical path analysis (time) 4. Cost estimates and earned value analysis (cost). Most of these tools are developed with software programs, such as Microsoft Project 2003. So what is the advantage of implementing project management on any project? The advantages that program management offers might include that “Bosses,” customers, and other stakeholders do not like surprises especially, “Bad News Surprises.” Good project management provides assurance and reduces the risk of project failure or large cost overrun. Project man- agement provides the tools and environment to plan, monitor, track, and manage schedules, resources, costs, and quality of the product (project). Project management also provides a his- tory or metrics base for future planning as well as good documentation, which is required by the Food and Drug Administration (FDA) and Good Manufacturing Practice. Perhaps for the students, the greatest advantage is that project team members learn and grow by working in a cross-functional team environment. Some books contend that “modern project management” began with the Manhattan Project, which the U.S. military led to develop the atomic bomb. Yet, some may argue that it was not until systems approach emerged in the 1950s which described a more analytical book Mobk076 April 2, 2007 18:9 approach to management and problem solving that modern project management really began. The systems approach to project management includes three parts: PROJECT MANAGEMENT OVERVIEW 11 1. Systems philosophy: Project managers should view projects and things as systems, inter- acting components working within an environment to fulﬁll some purpose. 2. Systems analysis: Project managers should use a problem-solving approach, which en- gineering students are taught. 3. Systems management: Project managers should address business, technological, and organizational issues before making changes to systems. Project managers need to take a holistic or systems view of a project and understand how it is situated within the larger organization, since projects developed must operate in a broad organizational environment; meaning, “projects cannot be run in isolation.” PROJECT LIFE CYCLES AND PROJECT PHASES 2.2 A project life cycle is a collection of project phases, which vary with the project or industry. Table 2.1 shows some general phases that include concept, development, implementation, and support. PRODUCT LIFE CYCLES 2.3 Products also have life cycles. The systems development life cycle (SDLC) is a framework for describing the phases involved in developing and maintaining information systems. Typical SDLC phases include planning, analysis, design, implementation, and support. There are TABLE 2.1: Phases of the Project Life Cycle PROJECT FEASIBILITY PROJECT ACQUISITION Concept Development Implementation Closeout Management plan Project plan Last work package Completed work Preliminary cost estimates 3-level WBS Budgetary cost Deﬁnitive cost estimates Lessons learned estimates 6+−level WBS Bulk of time spent in Customer acceptance this phase book Mobk076 April 2, 2007 18:9 12 PROJECT MANAGEMENT FOR ENGINEERING DESIGN several SDLC models such as 1. 2. the waterfall model that has well-deﬁned, linear stages of systems development and support, the spiral model which shows that products are developed using an iterative approach rather than a linear approach. In addition, there are the incremental release model and the prototyping model that are used for developing prototypes to clarify the user requirements. Project life cycle applies to all projects, regardless of the products being produced, and product life cycle models vary considerably based on the nature of the product. Most large projects are developed as a series of smaller projects, and then integrated. Project management activities are done through the entire product life cycle phases. A project should successfully pass through each of the project phases in order to continue on to the next phase of the life cycle. To verify that all the requirements of a phase were completed satisfactory, the program manager should conduct project reviews (also called project management review or program management review) at preset project milestones. Management reviews (often called phase exits or kill points) should occur after each phase to evaluate the project’s progress, likely success, and continued compatibility with organizational goals. 2.4 ORGANIZATIONAL STRUCTURES To understand how the various organizational structures and frames can help or impede the program manager in product development, one needs to understand organizations. There are four basic organizational frames: 1. The structural frame that focuses on roles and responsibilities, coordination and control. Organization charts help deﬁne this frame. 2. The political frame that assumes organizations are coalitions composed of varied indi- viduals and interest groups. Conﬂict and power are key issues within this frame. 3. The human resources frame that focuses on providing harmony between needs of the organization and needs of the people. 4. The symbolic frame that focuses on symbols and meanings related to events. In this frame, culture is important. Most managers and people understand what organizational charts are; yet, many new managers try to change organizational structure rather than concentrating on other changes that are book Mobk076 April 2, 2007 18:9 PROJECT MANAGEMENT OVERVIEW 13 really needed. There are three basic organization structures: functional, project, and matrix, as shown in Table 2.2. The ﬁrst column in Table 2.2 lists project characteristics, and their inﬂuence on the project based on the type of organizational structure are compared in the rows. The table also indicates that the project-oriented organizational structure provides the project manager with the highest level of authority, personnel and administrative staff that are assign “full-time” to work on the project, and that his role and title are “full-time” and “project manager,” respectively. Although the organizational structure inﬂuences the project manager’s authority, project managers also need to remember and address the human resources, political, and symbolic frames. Recall that project stakeholders are the people involved in or affected by project activities; hence, project managers must take time to identify, understand, and manage relationships with all project stakeholders. Using the four frames of organizations can help meet stakeholder needs and expectations. PROJECT MANAGEMENT JOB FUNCTIONS 2.5 At this point, you (the reader) may still be asking, “But what does the project manager do?” Most organizations establish job positions with a description of the responsibilities and func- tions of the position. The job description for the position of project manager usually requires that the project manager deﬁne the scope of project, form a team, identify stakeholders, identify decision-makers, and establish escalation procedures should the project encounter major prob- lem requiring a higher level decision. He is also responsible for the development of a detailed task list or work breakdown structures for the project. Additionally, he is responsible for the estimation of the time requirements not only for the project, but also for each task in the work breakdown schedule. The project manager is responsible for the development of initial project management ﬂow chart and identiﬁcation of required resources with budget estimates. He evaluates the project requirements, identiﬁes and evaluates the risks, and is responsible for preparing contingency plans. The program manager must identify interdependencies within and outside of the orga- nization. He is required to identify and track critical milestones, and conduct or participate in project progress and phase reviews. He has the responsibility of securing the needed resources in a timely manner. Additionally, the program manager is responsible for the management of the change control process, which may require establishment of a “change control board” to administer the handling of product conﬁguration and changes to the baseline conﬁgura- tion. The ﬁnal job function of project managers is the collection of information and prepa- ration of project status reports in documents and in presentation at higher level “program reviews” [2]. book Mobk076 April 2, 2007 18:9 14 D E Z I T C E J O R P X I R T A M X I R T A M X I R T A M L A N O I T C N U F S C I T S I R E T C A R A H C G N O R T S D E C N A L A B X I R T A M K A E W T C E J O R P X I R T A M E P Y T L A N O I T A Z I N A G R O s t c e j o r P n o e r u t c u r t S n o i t a z i n a g r O f o s e c n e u ﬂ n I : 2 . 2 E L B A T t s o m l a o t h g i H e t a r e d o M o t w o L l a t o t h g i h o t e t a r e d o m d e t i m L i e n o n r o e l t t i L % 0 0 1 – 5 8 % 5 9 – 0 5 % 0 6 – 5 1 % 5 2 – 0 e n o n y l l a u t r i V d e n g i s s a l e n n o s r e p t c e j o r p o t e m i t - l l u f s ’ n o i t a z i n a g r o k r o w s ’ r e g a n a m t c e j o r P y t i r o h t u a g n i m r o f r e P e m i t - l l u F e m i t - l l u F e m i t - l l u F e m i t - t r a P e m i t - t r a P s ’ r e g a n a m t c e j o r P e l o r , r e g a n a m , r e g a n a m , r e g a n a m , r o t a n i d r o o c , r o t a n i d r o o c m a r g o r p r e g a n a m m a r g o r p r e g a n a m t c e j o r p r e d a e l t c e j o r p r e d a e l t c e j o r p r e d a e l t c e j o r p r o f s ’ r e g a n a m e l o r t c e j o r P t c e j o r P t c e j o r P t c e j o r P t c e j o r P e l t i t n o m m o C e m i t - l l u F e m i t - l l u F e m i t - t r a P e m i t - t r a P e m i t - t r a P t n e m e g a n a m t c e j o r P f f a t s e v i t a r t s i n i m d a book Mobk076 April 2, 2007 18:9 TABLE 2.3: Comparison of Characteristics of Effective and Ineffective Project Managers PROJECT MANAGEMENT OVERVIEW 15 EFFECTIVE PROJECT MANAGER Leadership by example Visionary Technically competent Decisive Good communicator Good motivator Stands up to upper management when necessary Supports team members Encourages new ideas INEFFECTIVE PROJECT MANAGER Sets bad example Not self-assured Lacks technical expertise Indecisive Poor communicator Poor motivator It is strongly suggested by the author that the project managers develop the following skills: 1. Communication skills: listening and persuading. From elementary grades, we were taught how to speak, read, and write, but we were not taught how to listen. Communication theory requires three elements for effective communication: a transmitter (the speaker), a common media (the language), and the receiver (the listener). 2. Organizational skills: planning, goal setting, and analyzing. 3. Team building skills: people skills, empathy, motivation, and esprit de corps. 4. Leadership skills: sets example, energetic, vision (big picture), delegates, and positive. 5. Coping skills: ﬂexibility, creativity, patience, and persistence. 6. Technological skills: technical knowledge, project knowledge, and experience. Table 2.3 compares the most common characteristics found amongst “effective” and “ineffective” project managers. In summary, project management may be viewed as a number of interlinked management processes that include initiating processes, planning processes, executing processes, controlling processes, and closing processes. Table 2.4 shows the relationship between the project manager’s knowledge areas, project processes, and the activities required in project management. From book Mobk076 April 2, 2007 18:9 16 s a e r A e g d e l w o n K d n a , s e i t i v i t c A , s e s s e c o r P t c e j o r P g n o m A s p i h s n o i t a l e R : 4 . 2 E L B A T S E S S E C O R P T C E J O R P - L A I T I N I E G D E L W O N K G N I S O L C G N I L L O R T N O C G N I T U C E X E G N I N N A L P G N I Z I l o r t n o c y t i l a u Q e c n a r u s s a y t i l a u Q g n i n n a l p y t i l a u Q l o r t n o c t s o C e g n a h c l l a r e v O l o r t n o c e g n a h c e p o c S l o r t n o c n o i t a c ﬁ i r e v n o i t u c e x e n a l p t c e j o r P e p o c S n o i t a m i t s e n o i t a r u d t n e m p o l e v e d e l u d e h c S , n o i t i n ﬁ e d y t i v i t c A , g n i c n e u q e s g n i n n a l p e c r u o s e R g n i n n a l p g n i t e g d u b , g n i t a m i t s e t s o C t n e m p o l e v e d n a l p t c e j o r P e p o c S n o i t a i t i n I n o i t a r g e t n I A E R A e p o c S e m T i y t i l a u Q t s o C t n e m p o l e v e d m a e T g n i n n a l p l a n o i t a z i n a g r O s e c r u o s e r n a m u H n o i t a r t s i n i m d A e r u s o l c g n i t r o p e r e c n a m r o f r e P n o i t u b i r t s i d n o i t a m r o f n I t u o e s o l c t c a r t n o C e s n o p s e r k s i R n o i t a r t s i n i m d a t c a r t n o C g n i n n a l p n o i t a t i c i l o S e c r u o s , n o i t a t i c i l o S n o i t c e l e s t n e m e r u c o r P g n i n n a l p l o r t n o c t n e m p o l e v e d e s n o p s e r n o i t i s i u q c a f f a t S n o i t a c i n u m m o C g n i n n a l p , n o i t a c ﬁ i t n e d i k s i R , n o i t a c ﬁ i t n a u q s n o i t a c i n u m m o C k s i R t n e m e r u c o r P book Mobk076 April 2, 2007 18:9 PROJECT MANAGEMENT OVERVIEW 17 the table, one can surmise that the project manager will use all knowledge areas in the planning phase, but must apply integration, scope, quality, communications, and procurement knowledge areas throughout the project processes or “life cycle” [3]. On the other hand, team members will spend the majority of their time in the “execution” phase of the project life cycle. REFERENCES [1] Project Management Body of Knowledge (PMBOK Guide), Program Management Institute, Newtown Square, PA, 1996, p. 6. [2] Building a Foundation for Tomorrow: Skills Standards for Information Technology, Northwest Center for Emerging Technologies, Belleview, WA, 1997. [3] Project Management, Univ. Washington [Online]. Available: http://www.washington. edu/computing/pm, 2003. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 19 C H A P T E R 3 Project Integration Management Project managers that tend to focus on technical or on too many details have trouble keeping in mind and visualizing the “big picture.” As stated in the previous chapter, Project managers must coordinate all of the other knowledge areas throughout a project’s life cycle [1]. Table 2.4 (Chapter 2) shows that project plan development is a part of the “integration” knowledge area that takes place during the project “planning process.” Project plan development entails taking the results of other planning processes and putting them into a consistent, coherent document (the project plan, also referred to as the program manager’s project plan). Integration during the “executing process” entails carrying out the project plan (project plan execution), and during the “controlling process,” the program manager oversees the overall change control process and ensures coordination of changes across the entire project. Interface management involves identifying and managing the points of interaction between various elements of the project. Project managers must establish and maintain good communication and relationships across organizational interfaces. PROJECT PLAN DEVELOPMENT 3.1 A project plan is a document used to coordinate all project planning documents. The main purpose of project plans is to “guide project execution,” and to assist the project manager in leading the project team and assessing project status. Project plans are unique just as projects are unique. The main attributes of project plans are as follows: 1. They should be dynamic. 2. They should be ﬂexible. 3. They should be updated as changes occur. 4. They should ﬁrst and foremost guide project execution. Let us reemphasize the fourth attribute. Project plans are guides that may be changed; they are not rigid regulations or laws. The most common elements of a project management plan include an introduction or an overview of the project, a section describing how the project is organized, a section on book Mobk076 April 2, 2007 18:9 20 PROJECT MANAGEMENT FOR ENGINEERING DESIGN management and technical processes used on the project, and a section describing the work to be done, a section containing the work schedule with details on the “work breakout schedule” (WBS), with budget information. Table 3.1 contains a sample outline for a project management plan (PMP). The introduction section should start with a statement of the problem as the very ﬁrst sentence of the section followed by the rationale for working on the project. The section should contain full sentences and paragraphs on the project overview, background on previous or similar projects, any reference materials, what the expected outputs or deliverables, and a glossary of deﬁnitions and/or acronyms [2]. The project organization section should contain a paragraph describing the process model to be used with justiﬁcation, paragraphs discussing the organizational structure, its boundaries, and interfaces. Project responsibilities should be clearly assigned and described. The section on managerial process should contain paragraphs detailing the managerial objectives, priorities, assumptions, dependencies, and constraints, and the monitoring and controlling mechanisms to be used. In addition, the section should contain detailed descriptions of the stafﬁng plan and of the risk management process. The technical process section should contain detailed information on the method, tools, and techniques in the product development, as well as documentation on hardware and software design, drawings, operation description, and maintenance. The section should discuss project support functions. The last section contains descriptions of the work packages, dependencies, resource requirements with justiﬁcations, budget and resource allocations, and the project schedule. PROJECT PLAN EXECUTION 3.2 Project plan execution involves managing and performing the work described in the project plan. In general, the majority of time and money is usually spent on the execution phase. The application area or the project directly affects project execution, because the products of the project are produced during execution. Project managers will use the following skills during the execution phase: 1. General management skills, which include leadership, communication, and political skills. 2. Product skills and knowledge. In addition, the execution phase requires skills in the use of specialized tools and techniques. Techniques to assist the project manager during project execution include the work authorization system that provides a method for ensuring that qualiﬁed people do work at the right time and in the proper sequence, and conducting “status review meetings” on a regular (weekly or monthly) schedule to exchange project information and evaluate project progress. The authors prefer weekly face-to-face meetings with monthly written status (progress) reports. 21 s n o i t c n u f e l u d e h c s t r o p p u s t c e j o r p n a l p book Mobk076 April 2, 2007 18:9 , S E G A K C A P K R O W , E L U D E H C S L A C I N H C E T L A I R E G A N A M T C E J O R P T E G D U B D N A S S E C O R P S S E C O R P N O I T A Z I N A G R O N O I T C U D O R T N I ) P M P ( n a l P t n e m e g a n a M t c e j o r P a r o f e n i l t u O e l p m a S : 1 . 3 E L B A T ; s t n e m e r i u q e r ; n o i t a t n e m u c e d ; t n e m e g a n a m k s i r ; s e c a f r e t n i d n a ; s l a i r e t a m e c n e r e f e r d n a t e g d u b e r a w t f o s g n i l l o r t n o c ; g n i r o t i n o m s e i t i l i b i s n o p s e r d n a s n o i t i n ﬁ e d e c r u o s e r e r a w d r a h ; s t n i a r t s n o c , s e i c n e d n e p e d , s e i r a d n u o b , s e r u t c u r t s ; P M P f o n o i t u l o v e ; s e i c n e d n e p e d ; s e u q i n h c e t d n a , s n o i t p m u s s a ; s e i t i r o i r p l a n o i t a z i n a g r o ; s e l b a r e v i l e d s c i p o t s e g a k c a p k r o W , s l o o t , d o h t e M d n a s e v i t c e j b o t n e m e g a n a M ; l e d o m s s e c o r P , w e i v r e v o t c e j o r P n o i t c e S ; s n o i t a c o l l a ; n o i t a t n e m u c o d g n ﬁ f a t s ; s m s i n a h c e m s e i t i l i b i s n o p s e r t c e j o r p s m y n o r c a book Mobk076 April 2, 2007 18:9 22 PROJECT MANAGEMENT FOR ENGINEERING DESIGN To assist project managers in managing projects, there are special project management software, e.g., Microsoft Ofﬁce Project. The ﬁnal project process requiring the “integration” knowledge area is the “project controlling process,” which requires the project manager to oversee and control product or project changes. For the medical device industry, FDA requires a paper trail of documents on any changes to a product. 3.3 PROJECT CONTROLLING PROCESS AND CHANGE CONTROL Overall change control involves identifying, evaluating, and managing changes throughout the project life cycle. Three main objectives of change control are to 1. inﬂuence the factors that create changes to ensure they are beneﬁcial, 2. determine that a change has occurred, and 3. manage actual changes when and as they occur. Changes to a project or product may result from the need to take some corrective action, change requests, or from the reviews of status and progress reports. Starting with the established baseline plan or documents, status and progress reports are compared to the baselines. If it is determined that changes have occurred or should (need) to occur, then some corrective action or actions must be taken, which requires updating and documenting the update in the modiﬁed project plans. The update project plans become the current established baseline. The process is not as simple as it may appear, since government regulations mandate a formal “change control system.” CHANGE CONTROL SYSTEM 3.4 A change control system is a formal, documented process that describes when and how the ofﬁcial project documents and work may be changed. The change control system describes who is authorized to make changes and how to make the changes. Thus, the project manager must establish a change control board (CCB); develop a conﬁguration management ofﬁce with personnel and a conﬁguration management plan; and establish a process for communicating changes to all stakeholders. The CCB is a formal group of people responsible for approving or rejecting changes on a project. The CCB provides guidelines for preparing or changing requests, evaluates all requests, and manages the implementation of approved changes. The board should include stakeholders from the entire organization. Since some CCBs only meet occasionally, it may take too long for changes to occur in a timely manner. Therefore, some organizations have policies in place for time-sensitive changes. book Mobk076 April 2, 2007 18:9 The “48-h policy” permits project team members to make decisions, and then they have an additional 48 h to reverse the decision pending senior management approval. PROJECT INTEGRATION MANAGEMENT 23 CONFIGURATION MANAGEMENT 3.5 Conﬁguration management ensures that the products and their descriptions are correct and complete. It concentrates on the management of technology by identifying and controlling the functional and physical design characteristics of products. Conﬁguration management specialists identify and document conﬁguration require- ments, control changes, record and report changes, and audit the products to verify confor- mance to requirements. Because of its importance, the authors suggest that project managers view project management as a process of constant communications and negotiations. Man- agers should plan for change; therefore, establish a formal change control system, including a CCB. The manager should oversee the use of good conﬁguration management with deﬁned procedures for making timely decisions on smaller changes. Managers should not rely solely on verbal communications, but should use written and oral performance reports to help iden- tify and manage change. Project managers should learn to use project management and other software to help manage and communicate changes. 3.6 NEED FOR TOP MANAGEMENT COMMITMENT Several studies cite top management commitment as one of the key factors associated with project success. A study by Pinto and Slevin in 1987 lists the key factors as 1. 2. top management support clear project mission 3. good project schedule/plan 4. good client consultation. Whereas, the Standish Group Study (1995) lists the key factors as 1. 2. executive management support clear statement of requirements 3. proper planning 4. user involvement. Top management can help project managers secure adequate resources, get approval for unique project needs in a timely manner, receive cooperation from people throughout the organization, and learn how to be better leaders. Project managers should meet the need for organizational book Mobk076 April 2, 2007 18:9 24 PROJECT MANAGEMENT FOR ENGINEERING DESIGN standards. Senior management should encourage the use of standard forms and software for project management, the development and use of guidelines for writing project plans or provid- ing status information, and the creation of a project management ofﬁce or center of excellence. It is a well-tried and proven fact that standards and guidelines help project managers to be more effective. REFERENCES [1] Project Integration, Project Management, University of Washington [Online]. Available: http://www.washington.edu/computing/pm/plan/integration.html, 2003. [2] Project Plan, Management, University of Washington [Online]. Available: http://www. washington.edu/computing/pm/plan, 2003. book Mobk076 April 2, 2007 18:9 25 C H A P T E R 4 Project Scope Management Studies in the mid-1990s cite a clear project mission with a clear statement of requirements as being important for project success, e.g., the Keller Graduate School of Management cites proper project deﬁnition and scope as the main reasons of project failure. Deﬁning the project, product, or problem should not be limited to what is to be accomplished, but should also include what will not be accomplished; i.e., setting boundaries as to what the product is expected to do, and what the product is not being designed to do. So what is project scope management? Project scope refers to all the work involved in creating the products of the project and the processes used to create them. It is important that project scope management include the processes involved in deﬁning and controlling “what is” and/or “what is not” included in the project. Therefore, it is essential that the project team and stakeholders must have the same understanding of what products will be produced as a result of the project, and what processes will be used in producing them. PROJECT SCOPE MANAGEMENT PROCESSES 4.1 Recall from Fig. 2.4 of Chapter 2 that project managers will use the project scope knowledge area throughout the project processes. Project initiation process occurs at the beginning of a project or when the project continues from a completed phase to the next phase. The ﬁrst step in initiating the projects is to look at the big picture or strategic plan of an organization. Strategic planning involves determining long-term business objectives, and it is the project managers to make sure those projects support strategic and ﬁnancial business objectives. Many organizations follow a planning process for selecting projects. The ﬁrst step is to develop a strategic plan based on the organization’s overall strategic plan. The second step is to perform a business area analysis, and then potential projects, project scope, beneﬁts, and constraints are deﬁned. The ﬁnal step is to select the most viable projects and assign resources. During the planning process, the project manager develops project scope planning documents to provide the basis for future project decisions. It is during this process that the project manager develops the scope deﬁnition, subdividing the major project deliverables into smaller, book Mobk076 April 2, 2007 18:9 26 PROJECT MANAGEMENT FOR ENGINEERING DESIGN more manageable components. During the executing process, the project scope veriﬁcation documentation are developed and executed in formalizing acceptance of the project scope. Project scope change control documents are developed and used during the controlling process to ensure compliance in controlling changes to project scope. SELECTING PROJECTS 4.2 There are usually more projects than the available time and resources to implement them; therefore, it is important to follow a logical process in selecting projects to work on. Methods for selecting projects to work on include focusing on broad needs, categorizing projects, ﬁnancial methods, and weighted scoring models. It is often difﬁcult to provide strong justiﬁcation for many projects, even though everyone agrees they have a high value. The “focusing on broad organizational needs” approach is based on meeting three important criteria for projects: 1. There must be a need for the project. 2. Funds must be available for the project. 3. There must be a strong will to make the project succeed. The “categorizing projects” approach is based on the following categories: 1. What does the project addresses? a. a problem, b. an opportunity, or c. a directive for higher management. 2. How long it will take to do the project and when it is needed? 3. What is the overall priority of the project within the organization? The “ﬁnancial analysis of projects” approach is based on the premise that ﬁnancial considerations are an important consideration in selecting projects. Three primary methods for determining the projected ﬁnancial value of projects are net present value (NPV) analysis, return on investment (ROI), and payback analysis. NPV analysis is a method of calculating the expected net monetary gain or loss from a project by discounting all the expected future cash inﬂows and outﬂows to the present point in time. If ﬁnancial value is a key criterion, then projects with a positive NPV should be considered: the higher the NPV, the better. ROI is the income divided by investment, as shown in Eq. (4.1): ROI = total discounted beneﬁts − total discounted costs discounted costs (4.1) book Mobk076 April 2, 2007 18:9 PROJECT SCOPE MANAGEMENT 27 Most organizations have a required rate of return or minimum acceptable rate of return on investment for projects; thus, the higher the ROI, the better. Another important ﬁnancial consideration is “payback analysis.” The payback period is the amount of time it will take to recoup, in the form of net cash inﬂows, the net dollars invested in a project. Payback occurs when the cumulative discounted beneﬁts and costs are greater than zero. Many organizations want projects to have a fairly short payback period. 4.3 WEIGHTED SCORING MODEL A weighted scoring model is a tool that provides a systematic process for selecting projects based on many criteria. The ﬁrst step in the weighted scoring model is to identify the criteria important for the project selection process. The second step is to assign weights (percentages) to each criterion so that the total weights add up to 100%. The next step is to assemble an evaluation team, and have each member evaluate and assign scores to each criterion for each project. In the last step, the scores are multiplied by the weights and the resulting products are summed to get the total weighted scores. Projects with higher weighted scores are the best options for selection, since “the higher the weighted score, the better.” PROJECT CHARTERS 4.4 After an organization or the program manager has decided what project to work on, it is important to formalize projects with ofﬁcial documents. A project charter is a document that formally recognizes the existence of a project and provides direction on the project’s objectives and management. It is important to have key project stakeholders and senior leadership (man- agement) sign a project charter to acknowledge the agreement on the need and intent of the project. Either the project charter or the project management plan should contain a formal scope statement. A scope statement is a document used to develop and conﬁrm a common understanding of the project scope, and it should include the following sections: a project justi- ﬁcation, a brief description of the project’s products, a summary of all project deliverables, and a statement of what determines project success (What are the criteria for the project’s success?). 4.5 WORK BREAKDOWN STRUCTURE After completing scope planning, the next step is to further deﬁne the work by breaking it into manageable pieces. Good scope deﬁnition helps improve the accuracy of time, cost, and resource estimates, deﬁnes a baseline for performance measurement and project control, and aids in communicating clear work responsibilities. A WBS is an outcome-oriented analysis of the work involved in a project that deﬁnes the total scope of the project. book Mobk076 April 2, 2007 18:9 28 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 4.1: Example of WBS in Tabular Form 1.0 Concept 1.1 Evaluate current systems 1.2 Deﬁne requirements 1.2.1 Deﬁne user requirements 1.2.2 Deﬁne content requirements 1.2.3 Deﬁne product requirements 1.3 Deﬁne speciﬁc functionality 1.4 Deﬁne risks and risk management approach 1.5 Develop project plan 1.6 Brief web development team 2.0 Product design 3.0 Product development 3.1 Product testing 4.0 Roll out 5.0 Support 6.0 Deliverables It is a foundation document in project management, because it provides the basis for planning and managing project schedules, costs, and changes. An example of a WBS is given in Table 4.1. 4.6 APPROACHES TO DEVELOPING WORK BREAKDOWN STRUCTURES (WBSS) There are four basic approaches to developing WBSs: 1. The use guidelines approach: Some organizations, like the Department of Defense (DOD), provide guidelines for preparing WBSs. 2. The analogy approach: It often helps to review WBSs of similar projects. 3. The top-down approach: Start with the largest items of the project and keep breaking them down. 4. The bottoms-up approach: Start with the detailed tasks and roll them up. Most project managers will use the top-down approach and may continue to break tasks down further as the need arises. book Mobk076 April 2, 2007 18:9 PROJECT SCOPE MANAGEMENT 29 Here are some basic principles for creating WBSs [1]: 1. A unit of work should appear at only one place in the WBS. 2. The work content of a WBS item is the sum of the WBS items below it. 3. A WBS item is the responsibility of only one individual, even though many people may be working on it. 4. The WBS must be consistent with the way in which work is actually going to be performed; it should serve the project team ﬁrst and other purposes only if practical. 5. Project team members should be involved in developing the WBS to ensure consistency and buy-in. 6. Each WBS item must be documented to ensure an accurate understanding of the scope of work included and not included in that item. 7. The WBS must be a ﬂexible tool to accommodate inevitable changes while properly maintaining control of the work content in the project according to the scope statement. It is very difﬁcult to create a good scope statement and WBS for a project, and it is even more difﬁcult to verify the project scope and minimize scope changes. Many projects suffer from what is referred to as “scope creep” and poor scope veriﬁcation. Scope creep occurs when additional requirements (speciﬁcations or conﬁguration changes) are added to the project without going through an ofﬁcial conﬁguration control process. Johnson [2] published a list of the top 10 factors causing project problems. The list is given in Table 4.2. The factors ranked second and third deal with inadequate scope deﬁnition and scope creep, respectively. TABLE 4.2: Top 10 Factors Causing Project Problems FACTOR RANK Lack of user input Incomplete requirements and speciﬁcations Changing requirements and speciﬁcations Lack of executive support Technology incompetence Lack of resources Unrealistic expectations Unclear objectives Unrealistic time frames New technology 1 2 3 4 5 6 7 8 9 10 book Mobk076 April 2, 2007 18:9 30 PROJECT MANAGEMENT FOR ENGINEERING DESIGN The following suggestions are offered for reducing the incomplete and changing require- ments: 1. Develop and follow a requirements management process. 2. Employ techniques such as prototyping, use case modeling, and joint application design to thoroughly understand the user requirements. 3. Put all requirements in writing and create a requirements management database. 4. Use a process for reviewing requested changes from a systems perspective. 5. Provide adequate testing and emphasize completion dates. REFERENCES [1] D. I. Cleland, Project Management: Strategic Design and Implementation. New York: [2] McGraw-Hill, 1994. J. Johnson. (1995, Jan.). CHAOS: The dollar drain of IT project failures. Appl. Dev. Trends [Online]. Available: www.stadishgroup.com/chaos.html. book Mobk076 April 2, 2007 18:9 31 C H A P T E R 5 Personal and Project Time Management PERSONAL TIME MANAGEMENT 5.1 Project time management is similar to personal time management. Not many young individuals (students) are very good at managing; yet it is a skill that once acquired may become a habit. I wrote a small booklet on how to manage one’s time in college [1], which was used by the College of Engineering for freshmen. To compare the similarities between personal time management and project time management, let us start with the former: To accomplish anything, one must ﬁrst have a goal; however, a goal is no more than a dream, unless you plan to accomplish the desired goal! Setting goals should not be taken lightly, since those goals may impact one’s future career and life. Therefore, be careful in determining goals and in planning how to achieve your goals. Start with an outline of what you wish to happen, and be sure to set both short-range goals and long-range goals. Then determine 1. Why are those goals necessary? 2. What are the beneﬁts and consequences of each goal? 3. How can each goal be accomplished? (Planning) In developing goals, be sure to make goals that are realistic, action-oriented, measurable, and include “time limits” for accomplishment of each goal. Last but not least, “prioritize the list of personal goals.” When asked, “What leads to success in achieving personal goals?” The response is, “Planning what needs to be done in order to achieve desired goals, and control, which means using time efﬁciently and effectively.” The next task is to create a general schedule for the week, which includes determining tasks for the week, setting priorities with “due dates,” determining when to devote time to the tasks, and determining the time limits (the amount of time for each task). The ﬁrst step book Mobk076 April 2, 2007 18:9 32 PROJECT MANAGEMENT FOR ENGINEERING DESIGN is to ﬁll in the working information needed for the “worksheet,” then ﬁll in all the “time blocks” scheduled for tasks (classes and labs). Next, ﬁll in the pre-class and post-class (special study) times, and any essential times, e.g., meals, sleep, etc. Is that all? No! There is the task of managing “daily” activities. If a daily planner or organizer is used, it should be reviewed regularly, completed tasks should be crossed out, and tasks that were not completed during the week should be carried over to the next week. The ﬁnal step is “implementation” of the schedule: follow the schedule and do not procrastinate. “WORK SMARTER, NOT HARDER” [1] 5.2 In summary, to successfully manage your personal time, determine requirements for coming week. Set priorities and goals for week. Make a daily “do-list,” and determine daily priority tasks. Review your daily “do-lists” in the morning before work and in the evening. Postpone unnecessary activities/tasks, and do not spread yourself too thin (learn to say, “no!”). When working, do only one task at a time. PROJECT TIME MANAGEMENT 5.3 As noted in personal time management, schedules are important, and it is even more important to project managers, who indicate that delivering projects on time as one of their biggest challenges, since time schedules often have the least amount of ﬂexibility. Unlike ﬁctional movies, time cannot be replayed in real life. Schedule issues are the main reason for delays or conﬂicts on projects, especially during the execution phase of projects. Because of trying to meet some schedule, products are often introduced before all “buds” or problems with the product have been resolved. It is not surprising to read that the average time overrun on project exceeds 200%. Recently, Chip Reid, NBC Nightly News, Washington, DC (June 6, 2006) reported A vital $7 billion program, now approaching $11 billion, with nowhere to go, critics say, but up. A government investigation says the new polar satellite program is more than $3 billion over budget and as much as three years behind schedule. Why? The report blames “poor management oversight” by government agencies [2]. Congressional Hearing [3] on the same project was held on June 8, 2006, and was reported in the New York Times (June 9, 2006) [4]. Additionally, for those who may be interested, refer to the full audit report on the polar satellite audit by the U.S. Department of Commerce, Ofﬁce of Inspector General, May 2006 [5]. book Mobk076 April 2, 2007 18:9 PERSONAL AND PROJECT TIME MANAGEMENT 33 PROJECT TIME MANAGEMENT PROCESSES 5.4 Project time management involves processes required to ensure timely completion of a project. The processes include 1. 2. 3. 4. 5. activity deﬁnition activity sequencing activity duration estimating schedule development schedule control. Project schedules are developed from the basic documents that initiate a project, for example, the project charter includes start and end dates of the project with some budget information, e.g., a budget ceiling of not to exceed some target amount. The scope statement and work breakdown schedule (WBS) help deﬁne what will be done. Activity deﬁnition involves developing a more detailed WBS and supporting explanations to understand all the work to be done; whereas, activity sequencing involves reviewing activities and determining the type of dependencies. Mandatory dependencies are inherent in the nature of the work, which are considered as hard logic; on the other hand, discretionary dependencies are deﬁned by the project team and are considered as soft logic. External dependencies involve relationships between project and nonproject activities. In order to use critical path analysis, program managers must ﬁrst determine dependencies. PROJECT NETWORK DIAGRAMS 5.5 Project network diagrams is one technique for showing activity sequencing. A project network diagram is a schematic display of the logical relationships among project activities and/or sequencing of project activities. In the “arrow diagramming method,” also called activity-on- arrow (AOA) project network diagrams, activities are represented by arrows, nodes or circles are the starting and ending points of activities. Limitation of the arrow diagramming method is that it can only show ﬁnish-to-start dependencies. The steps in creating AOA diagrams are as follows: 1. Find all of the activities that start at the ﬁrst node (node #1). Draw their ﬁnish nodes and draw arrows between node #1 and those ﬁnish nodes. Put the activity letter or name and duration estimate on the associated arrow. 2. Continuing drawing the network diagram, working from left to right. Look for bursts and merges. Bursts occur when a single node is followed by two or more activities. A merge occurs when two or more nodes precede a single node. book Mobk076 April 2, 2007 18:9 34 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 3. Continue drawing the project network diagram until all activities are included on the diagram that have dependencies. 4. As a rule of thumb, all arrowheads should face toward the right, and no arrows should cross on an AOA network diagram. PRECEDENCE DIAGRAMMING METHOD (PDM) 5.6 Instead of using arrows to represent activities, the precedence diagramming method used boxes to represent activities (tasks) and arrows show relationships between activities. Many project managers will use software like Microsoft Project because of its visual approach in showing the different types of dependencies. Figure 5.1 shows how the four types of dependencies are presented in Microsoft Project. ESTIMATION OF ACTIVITY TIMES (DURATION) 5.7 After deﬁning activities and determining their sequence, the next step in time management is to estimate duration time for each activity. It is important to get the individuals who will be doing the actual work to help project managers create the activity estimates, and then have an expert in this area review the results. FIGURE 5.1: Activity or task dependencies. There are four types of activity dependencies: ﬁnish-to- start (FS), start-to-start (SS), ﬁnish-to-ﬁnish (FF), and start-to-ﬁnish (SF) book Mobk076 April 2, 2007 18:9 PERSONAL AND PROJECT TIME MANAGEMENT 35 FIGURE 5.2: Example of a Gantt chart. Note that horizontal bars denote tasks and the arrows show the dependencies between the tasks SCHEDULE DEVELOPMENT 5.8 Schedule development uses results of the other time management processes to determine the start and end dates of the project and its activities. A key challenge of project management is the creation of realistic schedules, and subsequently, to implement and stick to the schedule. The ultimate goal is to create a realistic project schedule that provides a basis for monitoring project progress for the time dimension of the project. Important tools and techniques to assist the project manager include Gantt charts, PERT analysis, and critical path analysis. The Gantt chart was developed in 1917 by Henry Gantt as a tool for scheduling work. The Gantt chart provides a standard format for displaying project schedule information by listing project activities with corresponding start and ﬁnish dates in a calendar format. Figure 5.2 is an example of a Gantt chart. Note that horizontal bars denote tasks, and that the arrows show the dependencies between tasks. Task name and duration are shown in columns 3 and 4, where the start and ﬁnish dates are given in columns 5 and 6. CRITICAL PATH METHOD (CPM) 5.9 The critical path method (CPM) is a project network analysis technique used to predict total project duration. A critical path for a project is the series of activities that determines the earliest time by which the project can be completed and the longest path through the network diagram, which has the least amount of slack time. If any activity on the critical path takes longer than planned, then the project schedule will slip unless corrective action is taken. There are several misconceptions about the critical path. First, the critical path is not the path that book Mobk076 April 2, 2007 18:9 36 PROJECT MANAGEMENT FOR ENGINEERING DESIGN accounts for all the critical activities, since the critical path only accounts for time. Second, there may be more than one critical path in a project, if the lengths of time of more than one path are the same. Finally, the critical path is not ﬁxed or rigid; the critical path can change as the project progresses. It is important for project managers to frequently update the project schedule information, since the critical path may change as actual start and ﬁnish dates are entered. If the project schedule slips, then the project manager will take corrective action by applying one of the techniques for shortening a project schedule. One method in shortening durations of critical tasks is to add more resources (man hours and workers) or change the scope of the task (this may require a scope change or CCB). Another method, called “crashing,” is to compress the schedule as much as possible for the least amount of incremental cost. If it is possible, the project manager may “fast track” tasks by working the tasks in parallel or overlapping them. However, if it is known that the project completion date will slip, project managers must inform stakeholders, company executives, and negotiate with the project sponsor for project time and perhaps cost overrun. 5.10 PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) PERT charts were developed by the Navy in 1958; however, it was not until the 1970s that the military began using project management software. PERT is a network analysis technique used to estimate project duration when there is a high degree of uncertainty about the individual activity duration estimates. PERT uses probabilistic time estimates based on using optimistic, most likely, and pessimistic estimates of activity durations. PERT uses a basic statistical weighted average formula, given by optimistic time + 4 × most likely time + pessimistic time 6 (5.1) 5.11 SUMMARY In summary, there are several hints in controlling changes to the project schedule. Project man- agers should perform reality checks on schedules on a regular basis and allow for contingencies. Few things work exactly as they are planned. Managers should not plan for everyone to work at 100% capacity all the time; we all need some break time. It is highly recommended that program managers hold regularly scheduled progress meetings with stakeholders, and be clear and honest in communicating schedule or project issues. In dealing with people issues, keep in mind that strong (good) leadership helps projects succeed more than all the good Gantt and/or PERT charts. Many project managers misuse project management software tools, because they do not understand important concepts of the tools and/or they have not had good training in book Mobk076 April 2, 2007 18:9 the use of the tools or in leadership. Project managers should have good interpersonal (people) skill and should not rely solely on software tools in managing time. PERSONAL AND PROJECT TIME MANAGEMENT 37 REFERENCES [1] C. Lessard, How to Succeed in Today’s TAMU. McGraw-Hill Primis, 2001, ISBN 0-390- 1-245-8. [2] C. Reid, NOAA Weather Satellite Program, TV Broadcast, NBC Nightly News, Washington, DC, June 6, 2006. [3] NOAA Weather Satellite Program Capitol Hill Hearing Testimony, Federal Document Clearing House, Congressional Quarterly, June 8, 2006. [4] K. Chang, Ofﬁcials Report Progress in Weather Satellite Effort, New York Times, Section A; Column 5; National Desk; The New York Times Company, June 9, 2006, p. 25. [5] Poor Management Oversight and Ineffective Incentives Leave NPOESS Program Well Over Budget and Behind Schedule, U.S. Department of Commerce, Ofﬁce of Inspector General, Audit Report no. OIG-17794-6-0001, May 2006. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 39 C H A P T E R 6 Project Cost Management Why is project cost management so important? Technical projects in the United States have an extremely poor performance record for meeting cost goals with the average cost overrun over 189% of the original estimates and cancellation of technical projects costing the United States over $200 billion in the mid-1990s. So, what is cost and project cost management? It is well known that to produce a product, resources in terms of personnel, materials, and ﬁnances are necessary. Cost is a resource, usually measured in monetary units like dollars, used to achieve a speciﬁc objective or given up in exchange for something. Project cost management includes the processes required to ensure that the project is completed within an approved budget (in monetary units). PROJECT COST MANAGEMENT PROCESSES 6.1 From Table 2.4 in Chapter 2, it is noted that project cost management takes place during the planning and controlling phases of project processes. Project cost management includes the following knowledge areas during the planning process: 1. Resource planning requires the project manager to determine what resources and the amount of resources are necessary for the project. 2. Cost estimation requires the project manager to develop an estimate of the costs for the resources needed to complete a project. 3. Cost budgeting requires allocating the overall cost estimate to each individual work activity in order to establish a baseline for measuring performance. Cost control is the knowledge area that occurs in the controlling process. Cost control requires the project manager to control changes to the project budget. Since most chief operating ofﬁcers (CEOs) and company board members may know a lot more about ﬁnance than do young engineers or project managers, it is highly recommended that one must at least learn to speak their (CEO and company ofﬁcers) language or attend formal book Mobk076 April 2, 2007 18:9 40 PROJECT MANAGEMENT FOR ENGINEERING DESIGN business courses in economics, accounting, and ﬁnance. Here are some simpliﬁed deﬁnitions of ﬁnancial terms: 1. Proﬁts are revenues minus expenses. 2. Project life cycle costing means determining and developing estimates for the cost of a project over its entire life. 3. Cash ﬂow analysis means determining and developing the estimated annual costs and beneﬁts for a project. 4. Beneﬁts and costs can be tangible or intangible, direct or indirect. 5. Sunk cost should not be the criteria in project selection. RESOURCE PLANNING 6.2 Since resource planning may be affected by the nature of the project and/or the organization, project managers should take into consideration the following questions: 1. How difﬁcult will it be to accomplish speciﬁc tasks on the project? 2. What, if anything, is there in the project’s scope statement that may affect resources? 3. What is the organization’s past history in accomplishing similar projects or tasks? 4. Does the organization have in place the people, equipment, and materials that are capable and available for performing the work? 5. If not, can the organization acquire the necessary resources in a timely manner so as not to delay the project or tasks start times. COST ESTIMATING 6.3 Project managers should realize that the important output of project cost management is a good cost estimate; additionally, it is important to develop a cost management plan that describes how cost variances will be managed on the project. To assist project managers in this endeavor, there are several types of tools and three techniques (rough order of magnitude (ROM), budgetary, and deﬁnitive) to help create cost estimates. Table 6.1 may help in determining when each technique may be applied in the development of a project or product. COST ESTIMATION TECHNIQUES 6.4 Cost estimation techniques include the “top-down” or “analogous” approach that depends on using the actual cost of a previous and similar project as the basis for the new estimate. This book Mobk076 April 2, 2007 18:9 PROJECT COST MANAGEMENT 41 TABLE 6.1: Types of Cost Estimates TYPE OF ESTIMATE WHEN? Rough order of Very early in WHY? Rough estimate for ±25% ACCURACY magnitude (ROM) planning phase decision selection Budgetary Deﬁnitive Early in the budget $ into budget plans ±10–20% planning in planning phase Later in the project in execution phase Actual cost; detail for purchasing ±5–10% approach depends on the availability of organization archives (ﬁles) or personnel that were involved in the previous project. The “bottom-up” techniques require project managers or team to arrive at individual work item estimates without previous examples and to sum tasks estimates to obtain a total cost estimate. Additionally, there is the “parametric” technique that uses project characteristics in a mathematical model to estimate costs, e.g., the constructive cost model (COCOMO). The developers of COCOMO contend that parametric model is the only technique that does not suffer from the limits of human decision-making. From experience, computer decision-making is only as good as the programming logic developed by humans. Flights to the moon have shown that the human decision-making could not be replaced by any automated computer program. There are computerized tools, such as spreadsheets, project management software, or other software to help project managers estimate costs. PROBLEMS IN COST ESTIMATION 6.5 As stated previously, project cost estimates are done at various stages of the project. Developing cost estimates for a large project is a complex task requiring a signiﬁcant amount of effort. A potential arises from the lack of experience of individuals attempting to develop project and/or task estimates; if this is the case, the project manager should provide cost estimation training and mentor individuals working on estimations. Another shortcoming is that most individuals have a bias toward underestimation; therefore, outside experts should be contracted to review estimates and ask important questions to make sure estimates are not biased. In many organizations, upper management wants a number for a bid, whether the ﬁnal cost estimate is or is not a real estimate. The authors have experienced companies that have underestimated costs in order to obtain a contract. Project managers must negotiate with project sponsors to create “realistic cost estimates.” book Mobk076 April 2, 2007 18:9 42 PROJECT MANAGEMENT FOR ENGINEERING DESIGN COST BUDGETING 6.6 Cost budget involves allocating the project cost estimate to individual work activities and providing a cost baseline. Most organizations have developed a standardized format to be used in developing a project budget. Deviations from the format may make it difﬁcult to understand, evaluate, and/or compare the budget request with competing applications. The budget should contain justiﬁcation stating why and how funds in each budget category are to be used. Justiﬁcations need not be elaborate, but must present a clear rationale for the use of the requested funds [1]. 6.7 GUIDELINES FOR PREPARING BUDGET Company guidelines are based on management policies found in the respective company’s project manager’s program guide. Guidelines should be followed when preparing the budgets and justiﬁcations. The following sections are generally included in most budgets: A. Personnel (1) Direct labor (salaries): List separately by name and program title for each person to be supported by budget, list annual salary, percent of time, and the number of months to be supported. (2) Beneﬁts: Fringe beneﬁts are to be included in project budget requests, and the fringe beneﬁt rate is to be presented as a part of the budget. (3) Temporary help: Fees for clerical or other staff, who are engaged on a short-term hourly basis, should be projected. List hourly rate and total hours. (4) Consultants: If the name of the consultant is known, show name and title. Indicate fees by the number of days and daily rate. B. Supply and expense (1) General expenses: Include program and ofﬁce-related expenses (e.g., photocopy ex- penses such as paper, copier rental, service contract, etc.). (2) Communications expenses: Include telephone and postage expenses. (3) Publication costs: Include, but do not limit to, newsletters, continuing education calendars, announcements, and educational materials you will publish or cause to be published. (4) Other expenses: Include subscriptions, books, audiovisuals, and miscellaneous ex- penses not covered in any of the above three categories. C. Rental (1) Justiﬁcation is necessary for each rental required to support the project, present monthly cost, and the number of months rented. book Mobk076 April 2, 2007 18:9 PROJECT COST MANAGEMENT 43 D. Meeting expenses (1) Meeting funds may support planning and development of continuing professional education. Allowable costs include, but are not limited to, meeting room rental and room use charges and equipment use charge for meetings. E. Travel (1) Display number of trips, origin and destination, and round trip rate for airfare. Automobile usage should display total mileage and per mile rate. If per diem is requested, show the number of days and per diem rate. F. Equipment 1. If property is to be acquired on this grant, show each item separately, indicating manufacturer or seller of the equipment, brand name, model number, and cost. COST CONTROL 6.8 Project cost control is performed during the controlling phase of the project. As the term cost control implies, it requires the project manager to monitor “cost performance” and to ensure that only appropriate project changes are included in any necessary revision of the “cost baseline.” Should there be any delays in the schedule or changes in conﬁguration, the project manager needs to inform the project stakeholders of “authorized” changes to the project that will affect costs. The “earned value analysis (EVA)” is an important tool used by project managers for cost control. EVA is a project performance measurement technique that integrates scope, time, and cost data [1]. Given the original planned baseline cost plus approved changes, a project manager can determine how well the project is meeting its goals: scope, time, and cost. EVA is explained in greater detail in Chapter 7. REFERENCE [1] Ofﬁce of Management and Budgets. (2006). Preparation and Submission of Budget Estimates, OMB Circular no. A-11 [Online]. Available: http://www.whitehouse.gov/ omb/circulars/a11/current year/guide.pdf book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 45 C H A P T E R 7 Earned Value Analysis Earned value analysis (EVA) is an industry standard method of measuring a project’s progress at any given point of time, forecasting its completion date and ﬁnal cost, and analyzing variances in the schedule and budget as the project proceeds. It compares the planned amount of work with what has actually been completed, to determine if the cost, schedule, and work accomplished are progressing in accordance with the plan. As work is completed, it is considered “earned.” The Ofﬁce of Management and Budget prescribed in Circular A-11, Part 7, that EVA is required on construction projects: Agencies must use a performance-based acquisition management system, based on ANSI/EIA Standard 748, to measure achievement of the cost, schedule and performance goals [1]. EVA is a snapshot in time, which can be used as a management tool as an early warning system to detect deﬁcient or endangered progress. It ensures a clear deﬁnition of work prior to beginning that work. It provides an objective measure of accomplishments, and an early and accurate picture of the project status. It can be as simple as tracking an elemental cost estimate breakdown as a design progresses from concept through to 100% construction documents, or it can be calculated and tracked using a series of mathematical formulae (see below). In either case, it provides a basis for course correction. It answers two key questions: 1. At the end of the project, is it likely that the cost will be less than, equal to, or greater than the original estimate? 2. Will the project likely be completed on time? 7.1 WORK BREAKDOWN STRUCTURE (WBS) EVA works most effectively when it is compartmentalized, i.e., when the project is broken down into an organized work breakdown structure (WBS). The WBS is used as the basic building block for the planning of the project. It is a product-oriented division of project tasks that ensures the entire scope of work is captured, and allows for the integration of technical, schedule, and cost information. It breaks down all the work scope into appropriate elements book Mobk076 April 2, 2007 18:9 46 PROJECT MANAGEMENT FOR ENGINEERING DESIGN for planning, budgeting, scheduling, cost accounting, work authorization, progress measuring, and management control. The two most common WBS systems are the Construction Speci- ﬁcations Institute (CSI) [2] format and the Uniformat II [3]. Often at the preliminary stages of design, the Uniformat II lends a better understanding of the cost centers, and at ﬁnal bid level of documents, often the CSI format is used. The indirect costs of design, oversight, and management must be included in the WBS to reﬂect the full budget. CALCULATING EARNED VALUE 7.2 Earned value management measures progress against a baseline. It involves calculating three key values for each activity in the work breakout schedule (WBS): 1. The planned value (PV), formerly known as the “budgeted cost of work scheduled” (BCWS) or simply called the “budget,” is that portion of the approved cost estimate planned to be spent on the given activity during a given period. 2. The actual cost (AC), formerly known as the “actual cost of work performed” (ACWP) is the total of the costs incurred in accomplishing work on the activity in a given period. Actual cost must correspond to whatever activities or tasks were budgeted for the planned value and the earned value, e.g., all labor, material, equipment, and indirect costs. 3. The earned value (EV), formerly known as the “budget cost of work performed” (BCWP) is the value of the work actually completed. These three values are combined to determine at that point of time whether or not work is being accomplished as planned. The most commonly used measures are the cost variance (CV), which is the difference between EV and AC, and is given by CV = EV − AC (7.1) and the schedule variance (SV), which is the difference between EV and PV or budget, is calculated as SV = EV − PV (7.2) These two values can be converted to efﬁciency indicators to reﬂect the cost and schedule performance of the project. The most commonly used cost-efﬁciency indicator is the cost performance index (CPI), which is the ratio of EV to AC, and is calculated as CPI = EV AC (7.3) book Mobk076 April 2, 2007 18:9 The sum of all individual EV budgets divided by the sum of all individual ACs is known as the cumulative cost performance index (CCPI) and is generally used to forecast the cost to complete a project. The schedule performance index (SPI) is the ratio of EV to PV, and is calculated as EARNED VALUE ANALYSIS 47 SPI = EV PV (7.4) SPI is often used with the CPI to forecast overall project completion estimates. The general rules in interpreting EVA numbers are as follows: 1. Negative numbers for cost and schedule variance indicate problems in those respective areas. 2. A negative SV calculated at a given point of time means the project is behind schedule, while a negative CV means the project is over budget. 3. CPI and SPI less than 100% indicate problems. EARNED VALUE MANAGEMENT SYSTEM (EVMS) 7.3 Section A-11, Part 7, of the ANSI Standard 748 [4] requires an earned value management system (EVMS) to be used to comply with the standard. A list of guidelines is provided that covers areas such as planning, scheduling and budgeting, accounting issues, management reports, and so forth; however, there are no “approved” systems identiﬁed. The basics of any EVMS are 1. 2. 3. a methodical, organized, thorough, and complete WBS, a baseline schedule, a baseline budget, organized into control accounts, 4. measurement of the work by control account (e.g., $, units in place, man hours, etc.). Scheduling the authorized work is no different than in any large construction project—it is a necessary activity for the success of the project. However, in an EVMS, the schedule will integrate all of the technical, cost, and schedule aspects of the work, resulting in the expected sequence of work. Interdependencies are established that result in the total work time and reveal the critical path, which is also the shortest project duration. Within each task, it is then necessary to identify objective interim measures to allow for accurate performance assessment each month. A sufﬁcient number of these interim measures will be deﬁned after the detailed schedule is established to ensure the performance is measured as accurately as possible. book Mobk076 April 2, 2007 18:9 48 PROJECT MANAGEMENT FOR ENGINEERING DESIGN A time-phased budget baseline, at the control account level, must also be established and maintained. The assignment of budgets to work activities or tasks results in a plan against which actual performance can be measured. This is referred to as the performance measurement baseline (PMB), and it should be established as early as possible after a notice to proceed has been issued. The PMB includes direct hours/dollars, direct material dollars, equipment and any other direct costs, and any indirect costs for the agreed scope. The indirect costs associated with design, oversight, and management must also be included. Essentially, the PMB represents the formal plan for the project manager to accomplish all the work required in the time allotted and within the budget provided. ANSI 748 also requires On at least a monthly basis, generate schedule variance data that provide visibility into root causes and establish actions to achieve project completion. The ﬁrst intent if this criterion is to establish the fact that analysis, to remain viable, must be accomplished on a regular, periodic basis. The second intent is to foster analyses and identiﬁcation of root cause and resulting impacts at the control account level. The monthly performance report must include 1. budget, earned value, and actual costs (reconcilable with accounting system), 2. CV, 3. SV, 4. 5. variance at completion (VAR), a variance analysis narrative (root causes, impacts at completion, and management actions). TOOLS AND TECHNIQUES 7.4 Spreadsheets are a common tool for resource planning, cost estimating, cost budgeting, and cost control. Many organizations prefer to use more sophisticated and centralized ﬁnancial applications software for cost information. Additionally, there are several software packages in the market to help the project managers prepare EVA, e.g. 1. Schedulemaker 2. Planisware OPX2 3. Risk Trak 4. Winsight 5. Primavera. book Mobk076 April 2, 2007 18:9 EARNED VALUE ANALYSIS 49 SUMMARY 7.5 Since EVA is an industry standard method of measuring a project’s progress, project managers should be skilled in applying and interpreting EVA values. Project managers should not be afraid of measuring a project’s progress and performance on a regular basis. Team members should be taught to use and report their respective activities performance using the EVA. Information on EVM systems is available at the Web site www.acq.osd.mil/pm. REFERENCES [1] Ofﬁce of Management and Budgets. (2006). Preparation and Submission of Bud- get Estimates, OMB Circular no. A-11 [Online]. Available: http://www.whitehouse. gov/omb/circulars/a11/current year/guide.pdf. [2] Construction Speciﬁcations http://www.csinet.org, 2004. Institute (CSI). WBS Format [Online]. Available: [3] Uniformat II. (1998, May). New building design management tools for project man- agers. Project Manager [Online]. Available: http://www.uniformat.com/building-design- management.html. [4] Earned Value Management Systems, American National Standards Institute (ANSI)/ Electronic Industries Alliance (EIA) Standard 748-1998, May 19, 1998. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 51 C H A P T E R 8 Project Quality Management In the past couple decades, there have appeared many articles in newspapers and on TV related to quality problems in U.S. products; not to mention the numerous jokes around the country about the poor quality of U.S. cars and computer softwares. Since the public seems to accept systems being down occasionally or needing repairs, a basic question is should we accept lower quality from newer products, with more innovation? If so, watch out for those new futuristic cars or airplanes. Quality is deﬁned by the International Organization for Standardization (ISO) as all the characteristics of an entity that bear on its ability to satisfy stated or implied needs. Other organizations deﬁne quality as conformity to requirements in meeting written speciﬁcations and ensuring that a product is ﬁt to use as it was intended. PROJECT QUALITY MANAGEMENT PROCESSES 8.1 Project quality management processes take place during the planning, execution, and control phases of project management, as shown in Chapter 2 (Fig. 2.4). Quality planning process, which takes place during the planning phase, identiﬁes which quality standards are relevant to the project and how to satisfy them. Quality assurance is done throughout the execution phase to evaluate the overall project performance, and to ensure the project (product) satisﬁes the applicable quality standards while identifying ways to improve overall quality. Quality control is accomplished during the controlling phase by monitoring speciﬁc project (product) results to ensure that they comply with the relevant quality standards. The basic requirements or objectives of quality management include 1. the requirement for customer satisfaction, 2. preference for prevention over inspection, and 3. recognizing that management has the responsibility for quality. 8.2 QUALITY PLANNING Project managers should recognize the importance of considering quality in the very early stages of a product design and in communicating important factors that directly contribute to meeting book Mobk076 April 2, 2007 18:9 52 PROJECT MANAGEMENT FOR ENGINEERING DESIGN the customer’s requirements. Often during the feasibility phase, project teams may have to design experiments that can help in identifying which variables have the most inﬂuence on the overall outcome of a process. The project manager should keep in mind that many scope aspects of projects may affect quality, i.e., functionality, features, system outputs, performance, reliability, and maintainability. 8.3 QUALITY ASSURANCE Quality assurance includes all the activities related to satisfying the relevant quality standards for a project; however, another goal of quality assurance is to provide continuous quality improve- ment. For example, benchmarking can be used to generate ideas for quality improvements, and quality audits can help identify lessons learned that may be used to improve performance on current or future projects. 8.4 QUALITY CONTROL Quality control in essences requires testing or monitoring a speciﬁc product to ensure com- pliance with quality standards. The main outputs of quality control include making an ac- ceptance decision on whether the product met required speciﬁcations and standard or it did not. If the product does not meet the quality standards then the product must be re- jected for “rework” and/or the production process must be reviewed and perhaps require adjustments. Some tools and techniques used in quality control include 1. Pareto analysis, 2. statistical sampling, 3. quality control charts, and 4. testing. 8.4.1 Pareto Analysis Pareto analysis involves identifying the principle factors that account for the most quality problems in a system. Pareto analysis is also called the 80–20 rule, which means that 80% of problems are often due to 20% of the causes (factors). To help identify and prioritize problem areas in a system, Pareto diagrams or histograms are used by management personnel. Dr. Joseph Juran expanded the Pareto principle to quality issues, which is also known as the “vital few and the trivial many,” thus implying that the remaining 80% of the causes should not be totally ignored [1]. book Mobk076 April 2, 2007 18:9 PROJECT QUALITY MANAGEMENT 53 TABLE 8.1: Common Certainty Factors DESIRED CERTAINTY (%) CERTAINTY FACTOR 95 90 80 1.960 1.645 1.281 SIGNIFICANCE LEVEL (α) 0.05 0.10 0.20 SAMPLE SIZE (N) 384 68 10 8.4.2 Quality Control Charts Quality control charts graphically display quality data to show the results of a process over time, thus helping to determine if the process is in control or out of control, and to prevent product defects. One of the quality control charts examines the process for nonrandom problems through the application of the “Seven Run Rule,” which states, “If seven data points in a row are all below the mean, above the mean, increasing, or decreasing, then the process needs to be examined for non-random problems.” 8.4.3 Statistical Sampling and Standard Deviation Statistical sampling involves choosing part (N number of samples) of a population of interest for inspection. The size of a sample (N) depends on how representative is the desired certainty. The formula for calculating the sample size is given by Sample size: N = (0.25) (certainty factor / acceptable error: α)2 (8.1) Table 8.1 shows several common certainty factors used in calculating the sample size. It should be noted that the signiﬁcance level or acceptable error (α) is equal to one minus the desired certainty expressed in decimal format: for example, α = 0.05 = 1 − 0.95. Equation (8.2) is an example for calculating the sample size when the desired certainty is 95%: Sample size (N) = (0.25)(1.960/0.05)2 = 384 (8.2) 8.4.4 Basic Statistical Measures Most college students are familiar with basic descriptive statistics, e.g., mean, median, mode, variance, and standard deviation. The standard deviation (σ ) is a measure of how much variation exists in a distribution of data. A small standard deviation means that data are clustered closely around the middle of a distribution and that there is little variability among the data. The standard normal distribution, often referred to by students as the “bell curve,” is symmetrical book Mobk076 April 2, 2007 18:9 54 PROJECT MANAGEMENT FOR ENGINEERING DESIGN FIGURE 8.1: The standard normal distribution about the mean or average value of a population or samples (Fig. 8.1). One should know that within ±1σ , 68.3% of the samples lie within the one standard deviation range, 95.5% of the samples lie within ±2σ , and 99.7% of the samples lie within ±3σ . Quality control personnel use the terminology of “four sigma” (±4σ ) to indicate how good the quality of their product is. Four sigma means that only 0.0063% of the products do not meet the required standards and are therefore rejected. Table 8.2 shows the relationship between sigma and the number of defective units based on 1 billion units. Greenberg and Hemphill [1] in a white paper contend that the main shortcoming of current quality control systems has been their inability to provide effective links to integrate with enterprise management systems. TABLE 8.2: Relationship Between Sigma and The Number of Defective Units SIGNIFICANCE RANGE (±σ ) ±1 ±2 ±3 ±4 ±5 ±6 PAPULATION WITHIN DEFECTIVE UNITS RANGE (%) PER BILLION 68.27 95.45 99.73 99.9937 99.999943 99.9999998 317,300,000 45,400,000 2,700,000 63,000 57 2 book Mobk076 April 2, 2007 18:9 PROJECT QUALITY MANAGEMENT 55 Quality managers have long been utilizing quality control systems, including statistical process control, production part approval process, failure mode effects analysis, gage calibration and document control. But these systems traditionally have been stand-alone applications. Although these individual applications have been touted as complete quality management systems, they cannot meet all quality objectives for data collection and information sharing required for today’s complex manufacturing processes [2]. 8.4.5 Testing Testing is one of the quality management functions that should be done during almost every phase of the product development life cycle; even though some managers prefer to think of testing as a stage that follows at the end of the product development process. Test requirements and test plans are developed in the planning process (Chapter 2, Table 2.4) with the development of the quality plan well before the product is produced. The program manager should make sure that every speciﬁcation is tested and that the criteria for acceptance or rejection (pass or fail) are included in the test plan. One may think that testing is testing, but in the development of a product, there are four basic types of tests. In “unit testing,” every individual component of a product is tested to ensure that the component or unit is free of defects. “Integration testing” groups components and tests the units for functionally. “Integration testing” occurs between unit and system testing or “veriﬁcation testing”; then the entire system as one entity is tested in “system testing.” The last set of tests is the “user acceptance testing” that has end users independently perform “validation tests” prior to accepting the delivered system. IMPROVING PROJECT QUALITY 8.5 A goal of quality assurance is to provide continuous quality improvement. Various suggestions have been offered for improving the quality of projects which include that program managers and organizational leadership should understand the cost of quality, and promote a quality environment and frame of mind. The suggestions include focusing on organizational inﬂuences and workplace factors that may affect product quality. Additionally, project managers should use some kind of maturity model to improve product quality. 8.5.1 Maturity Models Maturity models are frameworks for helping organization improve their processes and systems; yet there are several categories describing the type of project management maturity model. For example, the “ad hoc” maturity model refers to a project management process that may be described as disorganized, and occasionally even chaotic, since the organization has not deﬁned systems and processes, and project success depends on individual effort. Additionally, project book Mobk076 April 2, 2007 18:9 56 PROJECT MANAGEMENT FOR ENGINEERING DESIGN will have a history of chronic cost and schedule problems. With the “abbreviated” maturity model, there are some project management processes and systems in place to track cost, schedule, and scope; however, success of the project is unpredictable with cost and schedule problems becoming the norm. In the “organized” maturity model, there are standardized, documented project management processes and systems that are integrated into the rest of the organization. Project success with the organized type of maturity model is more predictable with improved cost and schedule performance. In the “managed” maturity model, management collects and uses detailed measures of the effectiveness of project management; hence, the project success is more uniform with cost and schedule performance conforming to plan. Lastly, in the “adaptive” maturity model, feedback from the project management process, and from innovative pilot ideas and/or technologies enables continuous improvement to the project processes. Project success is the norm, with continuous improvements in cost and schedule performance. Dr. Joseph Juran, well known as a business and industrial quality “guru” (known worldwide as one of the most important twentieth century thinkers in quality management), wrote several books including the Quality Control Handbook, in which he outlined 10 steps for quality improvement. Juran wrote It is most important that top management be quality-minded. In the absence of sincere manifestation of interest at the top, little will happen below [4]. COST OF QUALITY 8.6 The cost of quality is often misunderstood by those who insist that the cost of quality only includes the cost of conformance or delivering products that meet requirements and ﬁtness for use, since those individuals have not accounted for the cost of nonconformance or taking responsibility for failures or not meeting quality expectations into the cost of quality. When examining the cost categories related to quality, ﬁve types of cost are generally cited: 1. Prevention cost, which includes the cost of planning and executing a project so that it is error-free and/or within an acceptable error range. 2. Appraisal cost, which takes into account the cost of evaluating processes and their outputs to ensure quality. 3. Internal failure cost, which is the cost incurred to correct an identiﬁed defect before the customer receives the product. 4. External failure cost, which relates to all errors not detected and corrected before delivery to the customer. Keep in mind that these costs may include recalls and liability suites. book Mobk076 April 2, 2007 18:9 5. Measurement and test equipment costs, which include the capital cost of equipment used to perform prevention and appraisal activities. PROJECT QUALITY MANAGEMENT 57 8.7 INTERNATIONAL ORGANIZATION FOR STANDARDIZATION The ISO created the Quality Management System (QMS) standards in 1987. Modiﬁed in subsequent years, the ISO 9004:2000 document gives guidelines for performance improvement over and above the basic standard. The QMS is a system that outlines the policies and procedures necessary to improve and control the various processes that will ultimately lead to improved business performance and better quality control in manufacturing. 8.8 GOOD MANUFACTURING PRACTICE According to the current Good Manufacturing Practice (GMP), medical device manufacturers should use good judgment when developing their quality system, and apply those sections of the Food and Drug Administration (FDA) Quality System (QS) Regulation that are applicable to their speciﬁc products and operations, 21 CFR 820.5 of the QS regulation. The regulation makes clear that it is the responsibility of each manufacturer to establish requirements for each type or family of devices that will result in devices that are safe and effective. Additionally, the manufacturer is responsible for establishing methods and procedures to design, produce, and distribute devices that meet the quality system requirements [5, 6]. SUMMARY 8.9 In summary, project quality management processes take place during the planning, execution, and control phases of project management. It is not only important that the project man- ager continuously assess project and product quality, but it is even more important that top management be quality-minded. REFERENCES [1] Juran. Pareto Principle J. M. Dr. Joseph Moses Juran#Pareto principle, 2006. [Online]. Available: http://en.wikipedia.org/wiki/ [2] N. Greenberg and L. Hemphill. A New Approach: Enterprisewide Quality Manage- ment Systems, White Paper, DATANET Quality Systems [Online]. Available: http:// www.winspc.com/whitepapers.htm, 2005. [3] DATANET Quality Systems. Quality Digest Magazine [Online]. Available: http:// [4] www.winspc.com/quality-management-systems.htm, 2005. J. M. wikipedia.org/wiki/Dr. Joseph Moses Juran. Juran. (1945). Quality Control Handbook [Online]. Available: http://en. book Mobk076 April 2, 2007 18:9 58 PROJECT MANAGEMENT FOR ENGINEERING DESIGN [5] Quality Management Wikipedia. The Free Encyclopedia [Online]. Available: http:// en.wikipedia.org/wiki/Quality management, 2006. [6] Quality Management Wikipedia. The Free Encyclopedia [Online]. Available: http:// en.wikipedia.org/wiki/Quality Management System, 2006. book Mobk076 April 2, 2007 18:9 59 C H A P T E R 9 Project Procurement Management So far, Chapters 4 through 8 have covered the four core knowledge areas: scope, time, cost, and quality management, respectively; Chapters 9 through 12 will cover the four facilitat- ing knowledge areas: procurement management, human resources, communication, and risk. This chapter focuses on project procurement management. The term “procurement” generally means acquiring goods and/or services from an outside source; however, other terms such as “purchasing” or “outsourcing” are often used interchangeably to mean procurement. Often an organization will outsource or purchase components or subunits for another source (company) for various reasons, such as possible reduction in ﬁxed and recurrent costs, to increase ac- countability, to provide the ﬂexibility for the organization to focus on its core business, or to gain access to technical skills, expertise, and/or technologies that the organization does not possess [1]. 9.1 PROJECT PROCUREMENT MANAGEMENT PROCESSES The project procurement management processes, as shown in Table 9.1, include the follow- ing: 1. Procurement planning that takes place during the “project planning process” to deter- mine what part or systems to procure and when to make the purchases. 2. 3. 4. 5. Solicitation planning that takes place during the “project planning process” to document product requirements (materials, parts, components, etc.) and to identify potential sources (vendors) for procurement of required parts, etc. Solicitation, which usually occurs during the “project executing process” to obtain quotations, bids, offers, or proposals as appropriate from the vendors. Source selection that takes places after solicitation during the “project executing process” to select the best offer for the best product from potential vendors. Involving “contract administration” to manage the contractual relationship with the vendor. Keep in mind that engineers generally are not trained in contractual and legal matters. “Leave contractual matters to qualiﬁed contract administrators!” book Mobk076 April 2, 2007 18:9 60 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 9.1: Project Procurement Processes (Excerpt from Chapter 2, Table 2.4) PROJECT PROCESSES KNOWLEDGE INITIAL- AREA IZING EXECUT- PLANNING ING CONTROL- LING Procurement Procurement Solicitation, planning source selection Solicitation Contract planning administration CLOSING Contract closeout 6. The ﬁnal project procurement process, contract closeout, which usually occurs during the “project closing process” as a formal process at the completion and settlement of the contract. PROCUREMENT PLANNING 9.2 Procurement planning involves identifying which project needs can be best met by using products or services outside the organization. Thus, the project manager and his team must evaluate various alternatives and decide whether to make or buy. “Make-or-buy analysis” is a process used to determine whether a particular product or service should be made inside the organization or purchased from some source outside of the organization. Often, the make-or- buy analysis involves doing some ﬁnancial analysis. Additionally, they must decide on “what,” “how much,” and “when” to procure or purchase. The purchasing decision must include “when” to procure so that the required materials or parts are on hand so as not to cause delays in the project schedule. From experience, I was told by the manufacturer of a part that they had a 52-week backlog; meaning that the project would be delayed about a year if I insisted on that part. The only available option at that time was to redesign the product with an equivalent component. If members of the project team are not familiar with the procurement process, the project manager should seek experts within the organization and/or from consultants outside of the organization that can provide valuable and experienced inputs in procurement decisions. 9.2.1 Types of Contracts There are three basic types of contracts: ﬁxed price, cost reimbursable, and unit price contract [2]: 1. The “ﬁxed price contract,” also referred to as the “lump sum contract,” infers that the contract has a ﬁxed total price for a well-deﬁned product or service. A “ﬁxed price book Mobk076 April 2, 2007 18:9 PROJECT PROCUREMENT MANAGEMENT 61 TABLE 9.2: Contract Types and Associated Risk BUYER RISK TYPE OF CONTRACT VENDOR RISK Low Fixed price Medium low Fixed price incentive (FPI) Medium Cost plus insentive fee (CPIF) Medium high Cost plus ﬁxed fee (CPFF) High Medium high Medium Medium low High Cost plus percentage of costs (CPPC) Low incentive” contract is similar to the ﬁxed price contract with the exception that the buyer will pay some incentive or bonus if the seller performs better than that written into the contract (especially, time; i.e., if the end product is produced and delivered earlier than schedule). 2. The “cost reimbursable contract” involves payment to the seller for direct and indi- rect costs. There are three different types of contracts within the cost reimbursable framework: cost plus incentive fee (CPIF), cost plus ﬁxed fee (CPFF), and cost plus percentage of costs (CPPC): a. With a CPIF contract, the buyer pays the seller for allowable performance costs plus a predetermined fee and an incentive bonus. b. With the CPFF contract, the buyer pays the seller for allowable performance costs plus a ﬁxed fee payment that is usually based on a percentage of estimated costs. c. With the CPPC contract, the buyer pays the seller for allowable performance costs plus a predetermined percentage based on total costs. 3. The unit price contract requires the buyer to pay the seller a predetermined amount per unit of service. All contracts involve some risks for both the vendor (seller) and the buyer. Table 9.2 summarizes the risks associated with each type of contract. Note that the lowest risk associated with the type of contract to the buyer is a ﬁxed priced contract; however, the vendor may not negotiate this type of contract, since the ﬁxed price contract presents the highest risk to the vendor. SOLICITATION PLANNING 9.3 In solicitation planning, several documents must be prepared by the procurement team. The ﬁrst document, called the “request for proposals (RFP),” is used to solicit proposals from book Mobk076 April 2, 2007 18:9 62 PROJECT MANAGEMENT FOR ENGINEERING DESIGN prospective sellers where there are several ways to meet the sellers’ needs. On the other hand, “requests for quotes (RFQ)” are used to solicit quotes for well-deﬁned procurements invita- tions for bid or negotiation in which initial contractor responses are also part of solicitation planning. An RFP usually includes sections on the purpose of the RFP, the organization’s background, requirements, environments, statement of work (SOW) with schedule, and re- quired deliverables with schedule. Almost all mutually binding agreements or contracts in- clude a SOW. Additionally, the contracting ofﬁce will add boilerplate information required by law. 9.3.1 Statement of Work (SOW) The SOW is usually developed by the engineering members of the procurement team. It is a description of the work required for the procurement; hence, a good SOW gives bidders a better understanding of the buyer’s expectations. General format for a SOW include sections on the scope and location of work, period of work to be performed (usually, end dates) with scheduled deliverables. The scope of work should describe in as much detail as possible the exact nature of work to be accomplished by the contractor. Not only should the hardware and software be speciﬁed, but also the required tolerances and/or industry or ISO standards to be met. If the work must be performed in a speciﬁc location, such as a designated standard clean room where employees must perform the work on hardware or a secure location for work, then the environment and location of work must be described in the SOW. Contacts often specify within the SOW when the work is expected to start and end, working hours, number of hours that can be billed per week, where the work must be performed, and related schedule information. Deliverables schedule list speciﬁc deliverables, describe what is to be delivered in detail, and when the deliverables are due. SOLICITATION 9.4 Solicitation is a function that occurs in the executing process, and involves obtaining proposals or bids from prospective sellers in response to an RFP or RFQ. Organizations can advertise to procure goods and services in several ways: advertising to anyone that may be interested via some publication or announcement; for example, government agencies place their solicitation in the commerce daily bulletin or on their respective Web sites. Formal evaluation procedures for selecting vendors should be developed and documented before solicitation. Depending on the price and total spending, some organization may approach several potential vendors for quotations or the purchasing agency may only approach preferred vendors, often referred to book Mobk076 April 2, 2007 18:9 PROJECT PROCUREMENT MANAGEMENT 63 as the “buyers short list”. It is not unusual in large complex procurement to host a bidders’ conference to help clarify the buyer’s expectations, thus reducing the number of nonresponsive responses. Responses to RFPs or RFQs always have a cutoff date, after which time any responses arriving are considered “nonresponsive” and are not evaluated. SOURCE SELECTION 9.5 After receiving bidders’ responses, procurement must assemble a source selection committee. Source selection involves evaluation of bidders’ proposals and selection of the best proposal. From this point on, the purchasing department with their contract specialist (contract admin- istrator) negotiate the contract with terms and conditions, and award the contract. CONTRACT ADMINISTRATION 9.6 Contract administration ensures that the seller’s performance meets the contractual require- ments. All contracts are legal relationships between purchasing organizations and selling or service organizations, so it is important that legal and contracting professionals be involved in writing and administering contracts. Project managers and members of the design team should not make comments that may be misinterpreted as redirection of the contract terms or SOW. On the other hand, those project managers who ignore contractual issues may ﬁnd that those issues result in serious problems. Project managers should be aware that changes to any part of the project including contract changes need to be reviewed, approved, and documented in the same way that the original part of the plan was approved. Evaluation of any changes to the project should include an impact analysis, “How will the change affect the scope, time, cost, and quality of the goods or services being provided?” Along with documenting in writing any changes, project team members must document all important meetings and telephone phone calls that deal with project matters. CONTRACT CLOSEOUT 9.7 The ﬁnal process in project procurement management is the formal closing of contracts. Contract closeout includes veriﬁcation to determine if all work was completed correctly and satisfactorily. If there were any discrepancies or deﬁciencies, those deﬁciencies have to be dealt with either correction or wavering of the deﬁciencies. Contract administration is required to update records of administrative activities to reﬂect ﬁnal contract results and to archive contract information for future use. Usually, procurement audits are performed to identify “lessons learned” in the procurement process. book Mobk076 April 2, 2007 18:9 64 PROJECT MANAGEMENT FOR ENGINEERING DESIGN REFERENCES [1] Procurement, Wikipedia. The Free Encyclopedia [Online]. Available: http://en. [2] wikipedia.org/wiki/Procurement, 2005. J. Bronzino, Assessment and Acquisition, Management of Medical Technology. London: Butterworth–Heinemann, 1992, ch. 4, pp. 111–152. book Mobk076 April 2, 2007 18:9 65 C H A P T E R 10 Project Human Resource Management So, what is project human resource management and why is this area important to project managers? Project human resource management may be deﬁned as the processes of making the most effective use of the people involved with a project. Basically, any human resource management implies having “the right people to the right place at the right time,” which requires organizational planning as to the type of personnel (engineers, support staff, etc.) that must be recruited or reassigned from within the organization and/or hired if the required talents or skills are not within the organization to work on the project. Subsequently, those resources (humans) must be developed or molded into an effective project team [1]. Having served on the Institute of Electrical and Electronic Engineers (IEEE) Workforce Committee and the American Association of Engineers Workforce Commission for a decade, the author can assert, “people determine the success and failure of projects and organizations.” The IEEE and the Bureau of Labor and Statistics have cited for the past decade shortages of trained engineers to ﬁll between one-fourth and one-third of a million jobs openings in engineering, which makes human resource management even more challenging for projects. Many CEOs listed the lack of highly skilled, trained workers as the primary barrier to growth; hence, they lobby the U.S. Congress to increase the annual H1B immigration quota to over one-third of a million foreign immigrant workers. Congress, universities, and many technical societies have wrestled with the problem of “How to increase the U.S. engineering labor pool.” The consensus of the various organizations points to the undesirable stereotyping of engineers as “nerds” as a factor in keeping the U.S. students away from the engineering career ﬁeld. Further stereotyping the noted problems of engineering is hard work requiring higher level math than simple addition and subtraction, long work hours (days), and constantly staying abreast of changes in the ﬁeld. Stereotyping engineering disciplines as male-dominated tends to keep women from entering the engineering career ﬁeld. Problems of shortages and reduced numbers of young engineers entering into the human resource pool means that there is a need for better human resource management within organizations. book Mobk076 April 2, 2007 18:9 66 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 10.1 MANAGING PEOPLE Project managers should have not only some formal training in managing people, but also ﬁeld experience in managing people at work. Important knowledge areas related to project management include 1. motivation 2. 3. inﬂuence and power effectiveness. Maslow developed a theory that people’s behaviors are guided by a sequence of needs, and he argued that humans possess unique qualities that enable them to make independent choices, thus giving them control of their destiny [2]. Maslow’s Hierarchy of Needs starts with the need to satisfy physiological needs as the lowest motivator. One may think of these needs as the survival mode, where satisfying hunger and thirst to survive is the paramount need. From the lowest motivator to the highest, the needs to satisfy are physiological, safety, social, esteem, and self-actualization. Maslow contends that growth motives (being motives) are relatively independent of the environment and are unique to the individual [3]. He states that “The esteem needs usually act as motivators only if the three lower types have been satisﬁed to some degree.” Maslow cautions that true self-esteem is based on real competence and signiﬁcant achievement, rather than on external fame. The highest form of motivation is the need for self-actualization. Herzberg [4] distinguishes between “motivational factors” and “hygiene factors.” Moti- vational factors include achievement, recognition, the work itself, responsibility, advancement, and growth, which produce job satisfaction. Examples of motivation factors include higher salaries, more supervision responsibilities, and a more attractive work environment. On the other hand, hygiene factors cause dissatisfaction if not present, but do not motivate workers to do more. Thamhain and Wilemon [5] list nine ways in which project managers have to inﬂuence projects: these ways or methods include the following: 1. Authority: The project manager’s legitimate hierarchical right to issue orders. 2. Assignment: The project manager’s perceived ability to inﬂuence a worker’s later work assignments. 3. Budget: The project manager’s perceived ability to authorize others to use discretionary funds. 4. Promotion: The project manager’s ability to improve a worker’s position. book Mobk076 April 2, 2007 18:9 PROJECT HUMAN RESOURCE MANAGEMENT 67 5. Money: The project manager’s ability to increase a worker’s pay and beneﬁts. 6. Penalty: The project manager’s perceived ability to dispense or cause punishment. 7. Work challenge: The project manager’s ability to assign work that capitalizes on a worker’s enjoyment of doing a particular task. 8. Expertise: The project manager’s perceived special knowledge that others deem impor- tant. 9. Friendship: The project manager’s ability to establish friendly personal relationships between the project manager and others. One should keep in mind that projects are more likely to succeed when project managers inﬂuence with expertise and work challenges; whereas projects are more likely to fail when project managers rely too heavily on authority, money, and penalty [6]. Power is deﬁned as the potential ability to inﬂuence behavior to get people to do things they would not otherwise do. There are several types of power including legitimate, expert, reward, coercive (with treat of penalty or punishment), and referent (meaning to refer to a decision/problem to someone). IMPROVING EFFECTIVENESS: COVEY’S SEVEN HABITS 10.2 Covey ﬁrst published The Seven Habits of Highly Effective People in 1989 and the 15th anniversary edition in 2004. The book lists seven principles that, if established as habits, Covey contends, are supposed to help a person achieve true interdependent “effectiveness” [7]. 10.2.1 The Seven Habits Covey presents his teachings in a series of habits—a progression from dependence, to indepen- dence, to interdependence. The seven habits are as follows: Habit 1: Be Proactive: Principles of Personal Vision Habit 2: Begin with the End in Mind: Principles of Personal Leadership Habit 3: Put First Things First: Principles of Personal Management Habit 4: Think Win/Win: Principles of Interpersonal Leadership Habit 5: Seek First to Understand, Then to be Understood: Principles of Empathetic Com- munication Habit 6: Synergize: Principles of Creative Communication Habit 7: Sharpen the Saw: Principles of Balanced Self-Renewal book Mobk076 April 2, 2007 18:9 68 PROJECT MANAGEMENT FOR ENGINEERING DESIGN Expansion of Covey’s habits are quoted from the Wikipedia Web site (http://en.wikipedia. org/wiki/Stephen Covey) [8]. 1. Be Proactive. Here, Covey emphasizes the original sense of the term “proactive” as coined by Victor Frank. Being “proactive” means taking responsibility for everything in life, rather than blaming other people and circumstances for obstacles or problems. Initiative and taking action will then follow (the authors of this book also extend the meaning to include thinking of potential problem areas before they occur and planning alternative solutions prior to the occurrence of the bad event.) [8]. 2. Begin with the End in Mind, which deals with setting long-term goals based on “true- north principles.” Covey recommends formulating a “personal mission statement” to document one’s perception of one’s own purpose in life. He sees visualization as an important tool to develop this. He also deals with organizational mission statements, which he claims to be more effective if developed and supported by all members of an organization, rather than being prescribed [8]. 3. Put “First Things First”. Covey describes a framework for prioritizing work that is aimed at long-term goals, at the expense of tasks that appear to be urgent, but are in fact less important. Delegation is presented as an important part of time management. Successful delegation, according to Covey, focuses on results and benchmarks that are to be agreed in advance, rather than on prescribing detailed work plans [8]. 4. Think Win/Win describes an attitude whereby mutually beneﬁcial solutions are sought, that satisfy the needs of oneself as well as others, or, in the case of a conﬂict, both parties involved [8]. 5. Seek First to Understand, then to be Understood. Covey warns that giving out advice before having empathetically understood a person and their situation will likely result in that advice being rejected. Thoroughly listening to another person’s concerns instead of reading out your own autobiography is purported to increase the chance of establishing a working communication [8]. Good project managers are empathic listeners; they listen with the intent to understand. Before one can communicate with others, a rapport with the other individual should be established; e.g., a social gathering or a meal so as to get to know the other person on a nonbusiness, more personal manner. Some times mirroring is a technique to help establish rapport. Project managers need to develop empathic listening and other people’s skills to improve relationships with users and other stakeholders. 6. Synergize describes a way of working in teams. Apply effective problem solving. Apply collaborative decision making. Value differences. Build on divergent strengths. book Mobk076 April 2, 2007 18:9 PROJECT HUMAN RESOURCE MANAGEMENT 69 Leverage creative collaboration. Embrace and leverage innovation. It is put forth that, when this is pursued as a habit, the result of the teamwork will exceed the sum of what each of the members could have achieved on their own. The whole is greater than the sum of its parts [8]. 7. Sharpen the saw focuses on balanced self-renewal. Regaining what Covey calls “pro- ductive capacity” by engaging in carefully selected recreational activities [8]. 10.2.2 Personality and Behavioral Tools There are several personality and behavioral tools that help human resource managers, and could help project managers in developing an effective working team. The Meyers–Briggs type indicator (MBTI) is a popular tool for determining personality preferences and helping teammates understand each other. The MBTI has four dimensions in which individuals are classiﬁed as either an extrovert (E) or introvert (I), as sensation (S) or intuition (N), as thinking (T) or feeling (F), and as using judgment (J) or perception (P). Most professionals seem to fall within the category of intuition and thinking (NTs) or as being rationals. Based on the work by Charles Marston (1928), the Texas A&M University Employee Assistance Program Ofﬁce developed a Behavior Proﬁle tool, which they called “DISC” [9]. The acronym DISC stands for 1. dominance, which pertains to how individuals respond to problems or challenges, 2. 3. 4. inﬂuence, which is deﬁned as how individuals inﬂuence contacts with others by chang- ing their point of view to your point of the individual, steadiness, which deals with consistency on how individuals respond to the pace of the environment, compliance, which addresses the issue of constraints or how individuals respond to rules and procedures set by others. The DISC sectors denoting behavioral quadrants are shown in Fig. 10.1 [9]. The DISC behavior proﬁles with comments are shown in Fig. 10.2. Compliance Dominance Steadiness Influence FIGURE 10.1: DISC. Quadrants show the dominant behavior proﬁle book Mobk076 April 2, 2007 18:9 70 PROJECT MANAGEMENT FOR ENGINEERING DESIGN Precise Accurate Concern for Quality Critical Listener Non-verbal C Product oriented Slow to change Self-disciplined Pessimistic S Accommodating Dislikes Confrontation Persistent Controls Emotion Creative Slow Start/Fast Finish Fear Criticism Fear Being Taken Fear Loss Of Security Fear Social Rejection Good Supporter Team Player Persistent Cooperative Competitive Confrontational Direct Results-Oriented Sense of Urgency Change Agent D Process Oriented Quick to change Independent Optimistic I High Trust Level Not Fearful of Change Verbal Skills Projects Self- Confidence FIGURE 10.2: Behavior Proﬁle tool, called the “DISC” [9] 10.3 SUMMARY Repeating the advice given in Chapter 1, project managers and their teams should focus their primary attention and efforts on meeting project objectives and producing positive results. It is recommended that instead of blaming team members, the focus should be turned to ﬁxing the problem. Project managers should establish regular, effective meetings with agenda and openness. Part of the program managers tasks include nurturing team members, encouraging them to help each other, and to acknowledge in public individual and group accomplishments. Project managers should remember to have a team-based reward and recognition systems, since such consideration of others can promote teamwork. Also give some thought on rewarding teams for achieving speciﬁc goals. Additionally, project managers should allow time for team members to mentor and help each other meet project goals and develop interpersonal skills. REFERENCES [1] Resource Assessment, Program Management, University of Washington [Online]. Available: http://www.washington.edu/computing/pm/plan/resource.html, 2005. [2] A. H. Maslow (2003). Self-actualization theory (II). An Introduction to Theories of Per- sonality (6th ed.), R. B. Ewen, Ed. Houston, TX: Questia Media America, Inc. [Online]. ch. 10. Available: www.questia.com. [3] A. H. Maslow, Motivation and Personality, 2nd ed. New York: Harper and Row, 1970. book Mobk076 April 2, 2007 18:9 [4] F. Herzberg, B. Mausner, and B. B. Snyderman, The Motivation to Work, 2nd ed. New PROJECT HUMAN RESOURCE MANAGEMENT 71 York: Wiley, 1959. [5] H. Thamhain and D. L. Wilemon, “One more time: How do you motivate employees?,” Harvard Business Rev., pp. 51–62, 1968. [6] B. Nath. CSS, University of Melbourne [Online]. Available: http://www.cs.mu.oz. au/443/slides/443Lec12.pdf. [7] S. R. Covey. (1989 and 2004). The Seven Habits of Highly Effective People (Paper- back Publication, ISBN 0-671-70863-5) [Online]. Available: http://en.wikipedia.org/ wiki/The Seven Habits of Highly Effective People. [8] The 7 Habits of Highly Effective People [Online]. Available: http://en.wikipedia. org/wiki/Stephen Covey, 2005. [9] DISC Behavior Proﬁle, Texas A&M University Employee Assistance Program Ofﬁce, Texas A&M University, College Station, TX, 1997. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 73 C H A P T E R 11 Project Communications Management It is interesting to note that our society and culture do not portray engineers as good commu- nicators. Both the New York Times and the Washington DC have printed front page articles on the poor communications skills of engineers. Without a doubt, history has shown that engi- neers must be able to communicate effectively to succeed in their positions, since strong verbal skills are a key factor in career advancement for engineering professionals. The IEEE USA Professional Activities has published newsletter with the fact that being technically qualiﬁed is insufﬁcient to maintain employment, the engineer and specially engineering managers must possess interpersonal and communications skills. Project managers are taught that one of the greatest threats to many projects is a failure to communicate. 11.1 PROJECT COMMUNICATIONS MANAGEMENT PROCESSES As shown in Table 11.1, the project communications management processes occur throughout the project development phases, from planning through closing. During the project planning phase, the planning teams must determine the information and communications needs of the stakeholders, then develop and document a communications plan. During the project executing process, information on the project is collected and distributed; making sure that the necessary or needed information is made available to stakeholders in a timely manner. In the controlling process of the project, performance information are collected, analyzed, and disseminated in performance reports. Administrative closure, which occurs during the closing process, consists of generating, gathering, and disseminating information to formalize phase or project completion. 11.2 COMMUNICATIONS PLANNING The communications management plan is a document that guides project communications. As an aid in communications planning, the project manager should create a stakeholder analysis book Mobk076 April 2, 2007 18:9 74 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 11.1: Project Communications Management Processes KNOWLEDGE INITIAL- AREA IZING Communications EXECUT- CONTROL- PLANNING ING LING CLOSING Communi- cations planning Information Performance Administrative reporting distribution closure TABLE 11.2: Example of Stakeholder Analysis for Project Communications STAKEHOLDER DOCUMENT FORMAT CONTACT PERSON DUE Customer Monthly status E-mail and List name and management report hard copy phone number First of month for project communications. It should go unsaid that every project should include some type of communications management plan. Communications management plans usually contain 1. 2. 3. 4. 5. 6. a description of a collection and ﬁling structure for gathering and storing various types of information, a distribution structure describing what information goes to whom, when, and how, a format for communicating key project information; formats facilitate a better under- standing of the communications, a project schedule for producing the information, access methods for obtaining desired information, a method for updating the communications management plans as the project progresses and develops, 7. and last but not least, a stakeholder communications analysis [1]. Table 11.2 is a short example of stakeholder communications analysis format. The table rows would describe the required documents, format, and due date for each stakeholder. INFORMATION DISTRIBUTION 11.3 Getting the right information to the right people at the right time and in a useful format is just as important as developing the information in the ﬁrst place. Project managers should consider book Mobk076 April 2, 2007 18:9 PROJECT COMMUNICATIONS MANAGEMENT 75 the importance of using current electronic communication technologies to enhance informa- tion distribution, as well as considering different formal and informal methods for distributing information. Project teams should know and understand the organization’s communications infrastructure, which are a set of tools, techniques, and principles that provide a foundation for the effective transfer of information. The tools may include e-mail, project management soft- ware, groupware, fax machines, telephones, teleconferencing systems, document management systems, and word processors. The techniques may include reporting guidelines and templates, meeting ground rules and procedures, decision-making processes, problem-solving approaches, and conﬂicting resolution and negotiation techniques. Additionally, the principles foundation for the effective transfer of information should include an agreed upon work ethic and the use of free, honest, and open dialog. 11.4 SPAN OF CONTROL Most managers know how difﬁcult it is to control a large group of individuals. Training in military leadership and experiences in managing projects have taught the authors that for good management of people, the span of control lie between the minimum of 5 and the maximum of 12 individuals. Managing more than 12 requires the manager to delegate the responsibilities and authority (full power) to submanagers, so they may be in full control of their responsible areas. 11.5 PERFORMANCE REPORTING Performance reporting keeps higher level management and stakeholders informed about how resources are being used to achieve project objectives. “Status” reports describe where the project stands at a speciﬁc point in time, whereas “progress” reports describe what the project team has accomplished during a certain period of time. Performance reporting should include earned value analysis (EVA) and project forecasting to predict what the project status and/or progress will be in the future based on past information and trends analysis. Project managers should hold status review meetings often (weekly or monthly) and include performance reporting (EVA) in all reports. The ﬁnal process in communication management occurs during the project closure phase, and is referred to as administrative closure, which produces the following documentation: 1. project archives 2. 3. formal acceptance lessons learned. In summary, a template for a team’s “weekly progress report” is given. book Mobk076 April 2, 2007 18:9 76 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 11.5.1 Template for Weekly Progress Report 1. Accomplishments for past week (include appropriate dates): a. Detailed description of accomplishments. Who did the work? Relate accomplish- ments to project’s Gantt chart by task number (refer to task number). b. If any issues were resolved from a previous report, list them as accomplishments. c. Write in full English sentences/paragraphs, not just bullets. 2. Plans for coming week (include appropriate dates): a. Detailed description of planned work task items to be accomplished in the next week. b. Again, who is going to do the work and relate to the project’s Gantt chart by task? c. Describe any other unplanned items to accomplish, which are not on the Gantt tasks. d. Write in full English sentences/paragraphs, not just bullets. 3. Issues: a. Discuss issues (problems encountered) that surfaced or are still important. b. If problem encountered, discuss impact on schedule (time line), funding/cost, and proposed possible remedy (how does the team plan to get back on schedule?). c. Managers do not like surprises, so be sure to discuss issues in detail. 4. Project changes (date and description): a. List any approved or requested changes to the project. b. Include the date of the change and a detailed description with the reason (why?). c. Include proposed changes to a new Gant chart and schedule. 5. Attachments: a. Previous Gant Chart (before Update); Previous Budget (before Update), b. Updated Gant Chart (Time Line Update); Updated Budget, c. Excel Chart of Time Sheet (Hours worked). REFERENCE [1] Communication Plan, Project Management, University of Washington [Online]. Available: http://www.washington.edu/computing/pm/plan/communication.html, 2002. book Mobk076 April 2, 2007 18:9 77 C H A P T E R 12 Project Risk Management Risk is deﬁned in the dictionary [1] as, “The possibility of loss or injury” and often expressed in terms of severity and probability. However, Project Risk Management is deﬁned as the art and science of identifying, assigning, and responding to risk throughout the life of a project and in the best interests of meeting project objectives. Project risk involves understanding potential problems that might occur on the project and how those problems could impede project success. Risk management is often overlooked on projects by executive managers, but it can help project managers improve project success by helping select good projects, determining project scope, and developing realistic estimates. Thus, risk management may be considered as a form of an investment or insurance. Government organizations deﬁne the terms in a slightly different manner. For example: 1. Hazard is deﬁned as a condition with the potential to cause personal injury or death, property damage, or degradation of performance. 2. Risk is an expression of possible loss in terms of severity and probability. 3. Severity is the worst credible consequence that can occur as a result of a hazard. 4. Probability is the likelihood that a hazard will result in a mishap or loss. 5. Risk Assessment is the process of detecting hazards and assessing associated risks. 6. Control is a method for reducing risk for an identiﬁed hazard by lowering the probability of occurrence, decreasing potential severity, or both. Risk management in the Department of Defense is referred to as Operations Risk management and is deﬁned as the process of dealing with risks associated with daily operations, which includes risk assessment, risk decision-making, and implementation of effective risk controls [2]. 12.1 PROJECT RISK MANAGEMENT Project Risk Management is the process of identifying, assigning, and responding to risks asso- ciated with a project, rather than operations. One may question why organizations would want book Mobk076 April 2, 2007 18:9 78 PROJECT MANAGEMENT FOR ENGINEERING DESIGN to venture into a risky project, and the response would be because the opportunities outweighed the risk. So, “What is Project Risk Management?” The goal of project risk management is to minimize potential risks while maximizing potential opportunities. Major risk management processes include: 1. Risk identiﬁcation, which is the process of determining risks that are likely to affect a project. 2. Risk quantiﬁcation, which requires evaluating risks to assess the range of possible project outcomes. 3. Risk response development, which includes taking steps to enhance opportunities and developing responses to each threat. 4. Risk response control is the process of responding to risks over the course of the project. Risk identiﬁcation is the process of understanding what potential unsatisfactory outcomes are associated with a particular project. 12.2 TYPES OF PROJECT RISKS There are three types of risks associated with commercial ventures in developing a new product; market risk, ﬁnancial risk, and technology risk. Market risk is associated with determining if the new product will be useful to the organization or marketable to others and if users will accept and use the product or service? Financial risk is associated with determining if the organization can afford to undertake the project and determining if this project is the best way to use the company’s ﬁnancial resources. Technology risk is associated with determining if the project is technically feasible and if the technology could become obsolete before a useful product can be produced? Table 12.1 is a short list of the potential risk conditions that are associated with each of the knowledge areas. 12.3 RISK QUANTIFICATION Risk quantiﬁcation or risk analysis is the process of evaluating risks to assess the range of possible project outcomes. The ﬁrst step in the risk analysis process is to determine the risk probability of occurrence and its impact (consequences) to the project if the risk does occur. Risk quantiﬁcation techniques include expected monetary value analysis (EVA), calculation of risk factors, PERT estimations, simulations, and expert judgment. Risk simulation uses a representation or model of a system to analyze the expected behavior or performance of the system. The Monte Carlo analysis simulates a model’s outcome many times in order to provide book Mobk076 April 2, 2007 18:9 PROJECT RISK MANAGEMENT 79 TABLE 12.1: Potential Risk Conditions Associated with Knowledge Areas KNOWLEDGE AREAS RISK CONDITIONS Integration Inadequate planning; poor resource allocation; Scope Time Cost Quality poor integration management; lack of postproject review Poor deﬁnition of scope or work packages; incomplete deﬁnition of quality managements; inadequate scope control Errors in estimating time or resource availability; poor allocation and management of ﬂoat; early release of competitive products Estimating errors; inadequate productivity, cost, change, or contingency control; poor maintenance, security, purchasing, etc. Poor attitude toward quality; substandard design/materials/workmanship; inadequate quality assurance program Human resources Poor conﬂict management; poor project Communications Risk organization and deﬁnition of responsibilities; absence of leadership Carelessness in planning or communicating; lack of consultation with key stakeholders Ignoring risk; unclear assignment of risk; poor insurance management Procurement Unenforceable conditions or contract clauses; adversarial relation a statistical distribution of the calculated results. Some organizations rely on the experience of experts to help identify potential project risks. If the organization uses a number of experts, then the Delphi method is used to derive a consensus among a panel of experts in deriving predictions about future developments [3]. book Mobk076 April 2, 2007 18:9 80 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 12.4 RISK RESPONSES When faced with a hazard or potential risk, individuals and organizations will respond in one of three ways. 1. Risk avoidance response tries to eliminate a speciﬁc threat or risk, by eliminating its causes. The approach may take a lot of time, since to ﬁnd the cause will require an in-depth look at the process with a detailed analysis. The cause should subsequently be ﬁxed. Dorfman [4] deﬁnes avoidance as not performing an activity that could carry risk. Avoidance may seem the answer to all risks, but avoiding risks also means losing out on the potential gain that accepting (retaining) the risk may have allowed. Not entering a business to avoid the risk of loss also avoids the possibility of earning proﬁts. 2. Risk acceptance response means accepting the consequences should a risk occur. 3. Risk mitigation response attempts to reduce the impact of a risk event by reducing the probability of its occurrence. 12.5 CAUSES OF RISK It would seem to some individuals that risk avoidance should be the only response to a hazard or a risk; so, let us examine the causes. Change is considered the “Mother” of Risk, meaning that changes in any project will increase the risk and in some cases signiﬁcantly. To change, one can add development of new technology, complexity of the system, resource constraints, organizational constraints, speed or tempo of work, environmental inﬂuences, work requiring high energy levels, and human nature [2]. The changes are not given in any order, but keep in mind that two or more causes may combine or result in one occurrence of a hazard or a risk. Table 12.2 shows strategies used by organizations to mitigate the various types of risks. To read the table, start with a type of risk, then read the optional mitigation strategies in that vertical column. 12.6 RISK MANAGEMENT PLANS Project managers should develop three different risk management plans. The “Risk Manage- ment Plan” documents the procedures for managing risk throughout the project, but the project manager should also develop “Contingency Plans” that predeﬁne actions the project team will take if an identiﬁed risk event occurs. Additionally, the project manager should have “Contin- gency Reserves,” which are provisions held by the project sponsor for possible changes in project scope or quality that can be used to mitigate cost and/or schedule risk. Always plan ahead, be book Mobk076 April 2, 2007 18:9 PROJECT RISK MANAGEMENT 81 TABLE 12.2: Risk Mitigation Strategies for Technical, Cost, and Schedule Risks TECHNICAL RISKS COST RISKS SCHEDULE RISKS Emphasize team support and avoid stand-alone project structure Increase the frequency Increase the frequency of project monitoring of project monitoring Increase project manager Use WBS and PERT/CPM Use WBS and PERT/CPM authority Improve problem handling and communication Improve communication, Select the most project goals understanding, and team support experienced project manager Increase the frequency Increase project manager of project monitoring authority Use WBS and PERT/CPM proactive in risk management. Questions that need to be addressed in a Risk Management Plan include: 1. Why is it important to take or not take this risk in relation to the project objectives? 2. What speciﬁcally is the risk and what are the risk mitigation deliverables? 3. How is the risk going to be mitigated? 4. What risk mitigation approach should be used? 5. Who are the individuals responsible for implementing the risk management plan? 6. When will the milestones associated with the mitigation approach occur? 7. How much resources are required to mitigate risk [5], [6] ? 12.7 RISK RESPONSE CONTROL Risk response control involves executing the risk management processes and the risk manage- ment plan to respond to risk events. Risks must be monitored based on deﬁned milestones and decisions made regarding risks and mitigation strategies. If there are no contingency plans in place, then workarounds or unplanned responses to risk events are necessary. A tool for maintaining an awareness of risk throughout the life of a project is the tracking of the project’s Top 10 risk items. The list of the Top 10 project risk items should be reviewed periodically and modiﬁed as the risk ranks change. Hence, a listing of the current ranking, previous ranking, book Mobk076 April 2, 2007 18:9 82 PROJECT MANAGEMENT FOR ENGINEERING DESIGN number of times the risk appears on the list over a period of time, and a summary of progress made in resolving the risk item should be developed. Project managers may use Project Risk Management software (databases or spreadsheets) to assist in keeping track of risks and quan- tifying risks. There are several more sophisticated risk management software available in the market that may help the project manager in developing models and/or simulations to analyze and respond to various project risks. 12.8 SUMMARY The Risk Management Processes include identifying the risk or hazard, assessing or analyzing all risks and/or hazards, making risk response decisions, implementing controls to mitigate the risk, and supervising or overseeing the implementation of the responses or corrective actions. Unlike crisis management, good project risk management often goes unnoticed, because well- run projects appear to be almost effortless, but, in reality, a lot of work has gone into running the project well. Hence, project managers should strive to make their jobs look easy; thus, reﬂecting the results of well-run projects. REFERENCES [1] Risk Management. Wikipedia. Encyclopedia. Available: http://en.wikipedia.org, 2005. [2] D. Faherty, “U.S. Navy, operations risk management,” presented at the 2nd Workshop on Risk Analysis and Safety Performance Measurements in Aviation, FAA, Atlantic City, NJ, Aug. 2000. [3] RISK + C/S Solutions Newsletter. Available: http://www.cssi.com/ [4] M. S. Dorfman, Introduction to Risk Management and Insurance, 6th ed. Englewood Cliffs, NJ: Prentice-Hall, 1997, ISBN 0-13-752106-5. [5] B. C. Chadbourne, “To the heart of risk management: Teaching project teams to com- bat risk,” in Proc. 30th Annu. Project Manage. Inst. Semin. Symp., Philadelphia, PA, Oct. 10–16, 1999. [6] A. Jaafari, “Management of risks, uncertainties, and opportunities on projects: Time for a fundamental shift,” Int. J. Project Manage., vol. 19, no. 2, pp. 89–101, Feb. 2001. doi:10.1016/S0263-7863(99)00047-2 book Mobk076 April 2, 2007 18:9 83 C H A P T E R 13 Project Closeout Project Closeout is the last major stage of a project’s life cycle and is completed when all deﬁned project tasks and milestones have been completed, and the customer has accepted the project’s deliverables. So, what is involved in closing projects [1]? Project Closeout includes the following actions: 1. First and foremost is the gaining of stakeholder acceptance of the ﬁnal product, 2. Veriﬁcation of formal acceptance by stakeholders and steering committee, 3. Bringing the project and all its phases to an orderly end, 4. Verify that all of the deliverables have been completed and delivered, 5. Completing a Project Audit (usually internal audit), 6. Redistributing resources; i.e., staff, facilities, equipment, and automated systems, 7. Closing out all ﬁnancial issues such as labor charge codes and contract closure, 8. Documenting the successes, problems, and issues experienced during the project, 9. Documenting “Lessons Learned,” 10. Producing an Outcomes Assessment Report, 11. Completing, collecting, and archiving Project Records, 12. And ﬁnally, it is recommended that the Project Team celebrate project success. 13.1 CLOSING PROCESSES AND OUTPUTS Most of the closing processes involve the communications and procurement knowledge areas as shown in Fig. 13.1. The process of “Administrative Closure” involves collecting project records, verifying and documenting project results to formalize acceptance of the products produced, analyzing whether the project was successful and effective, ensuring products meet speciﬁcations, and archiving project information for future use. Table 13.1 Column 3, row 2, shows the outputs that are the result of the administrative closure. book Mobk076 April 2, 2007 18:9 84 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 13.1: Closing Processes and Outputs KNOWLEDGE AREA PROCESS OUTPUTS Communications Administrative closure Procurement Contract Close-out 1. Project archives 2. Formal acceptance 3. Lessons learned 1. Contract ﬁles 2. Formal acceptance 3. Formal closure 13.1.1 Administrative Closure The issue of primary importance with project closure is the acceptance of the product or project deliverables by the customer for which they were created [2]. During the administrative closure, the project manager should conduct a formal “Final Acceptance Meeting.” The best way is to convene a ﬁnal meeting with stakeholders to review the product delivered against the baseline requirements and speciﬁcations. It is always a good policy to make the stakeholders aware of the baseline deviations, with justiﬁcations for the deviations, and of future action plans to correct or to waive the deviations. Deviations from the established baseline should be documented and approved at the committee for subsequent signatures by responsible executive managers of the organization. Open Action Items or program level issues can be ofﬁcially closed or reassigned to the support organization. Drawing the stakeholders together in a single meeting helps avoid clearing up open issues on an individual basis. 13.1.2 Approval Veriﬁcation Approval is veriﬁed via the signature of a project closure document by the stakeholders who signed the original project baseline documentation (i.e., the Project Plan). Acceptance document should be customized to the particular project to include: 1. Pertinent deliverables, 2. Key features, and 3. Information about ﬁnal product delivery. 13.1.3 Procurement Contract Closure Contract closure is the process of terminating contracts with outside organizations or businesses. Contracts may be for providing technical support, consulting, or any services. Contracts are usually brought to closure upon contract completion, early termination for cause, such as, failure book Mobk076 April 2, 2007 18:9 to perform. Closing a contract usually requires assistance from the Contracts Administrator, since close attention must be paid to ensure all obligations of the contract have been met or formally waived and to prevent any liability for the organization. Normally, procurement will conduct the “Final Contract Review Meeting.” Project managers should make a checklist of all items that must be addressed during contract closure, such as: PROJECT CLOSEOUT 85 1. Review contract and related documents, 2. Validate that the contractor has met all of its contractual requirements, 3. Document any contractor variances, 4. Resolve contractor variances and issues, 5. Validate that the organization has met all of its contractual requirements, 6. Document organization’s variances and issues, 7. Resolve Agency organization’s variances 8. Ensure that all vendor responsibilities have been transferred to the organization or another vendor, 9. Terminate current contract, and 10. Verify that all contractual obligations have been met or formally waived. 13.2 OUTCOMES ASSESSMENT MEETING “Another meeting,” you ask? Well, so far, only two have been covered. Do not be surprised if there are more. In conducting “Outcomes Assessment Meetings,” project managers provide a forum for discussing the various aspects of the project with the primary focus on project successes, problems, and issues, “Lessons Learned,” and recommendations for future process improvements. Program managers should use the information and documentation from the “Final System Acceptance Meeting” as a basis for the Outcomes Assessment Meeting discus- sions. Outcomes Assessment Meetings are usually attended by the project manager as chairman or moderator, all members of the Project Team, along with representation from Stakeholders, Executive Management, Maintenance, and Operations Staff [3]. It is always wise to include some oversight members that are external to the project and even the organization. Typical questions that should be addressed in the Outcomes Assessment meeting include the following: 1. To what extent did the delivered product meet the speciﬁed requirements and goals of the project? 2. Was the customer satisﬁed with the end product? book Mobk076 April 2, 2007 18:9 86 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 3. Were cost budgets met? 4. Was the schedule met? 5. Were risks identiﬁed and mitigated? 6. Did the project management methodology work? 7. What could be done to improve the process? 13.3 OUTCOMES ASSESSMENT REPORT After the meeting, the project manager and project team must generate an Outcomes As- sessment Report that documents the successes and failures of the project. The Outcomes Assessment Report provides an historical record of the planned and actual budget and schedule. The report should include description with rationale of selected metrics that were collected on the project and were based on documented procedures. The report should also contain recommendations for future projects of similar size and scope [4]. Outcome Assessment Reports should contain the following information: 1. Project sign-off, 2. Stafﬁng and skills, 3. Project organizational structure, 4. Schedule management, 5. Cost management, 6. Risk management, 7. Quality management, 8. Conﬁguration management, 9. Customer expectations management, 10. Lessons learned, and 11. Recommendations for process improvement. 13.4 TRANSITION PLANNING Before projects are closed, it is important for organizations to plan for and execute a smooth transition of the project into the normal operations of the company. Most projects produce re- sults (resources) that are integrated into the existing organizational structure, some may require modiﬁcation of the organizational structures, whereas, some other projects are terminated before completion. Additionally, the organization must develop a plan on how to redistribute resources; i.e., project team members, support staff, materials, facilities, equipment, and automated book Mobk076 April 2, 2007 18:9 systems, before projects are closed or cancelled. The Project Manager is responsible for turning over to the operations and maintenance organizations all documentation that has anything to do with the product including design documents, schematics, and technical manuals. PROJECT CLOSEOUT 87 13.5 PROJECT DOCUMENTS TO BE ARCHIVED Some of the typical project documents to be archived include: 1. Project Business Case, 2. Project Plan, including Project Charter, Project Scope Statement, Risk Assessment, Risk Mitigation, 3. Management Plan, Communications Plan, Quality Assurance Plan, etc., 4. Financial Records, 5. All correspondence on project matters, 6. Meeting Notes, 7. Status/Progress Reports, 8. Procurements and Contract File, 9. Test Plans and Results, 10. Technical Documents, 11. Files, Programs, Tools, etc., placed under Conﬁguration Management, and 12. All other documents and information pertaining to the project. 13.6 CRITICAL SUCCESS FACTORS The most critical factors used to measure project closeout success are ﬁrst and foremost ac- ceptance by the end-user, followed by having achieved the business objectives and anticipated beneﬁts. Next factors are the achievement of project objectives and knowledge transfer. The ﬁnal factor is archiving of all project materials. 13.7 SUMMARY Generally, Project Closeouts include the following key elements: 1. Veriﬁcation of formal acceptance by Stakeholders and Steering Committee, 2. Redistributing resources; i.e., staff, facilities, equipment, and automated systems, 3. Closing out any ﬁnancial issues such as labor charge codes and contract closure, 4. Documenting the successes, problems, and issues of the project, 5. Documenting “Lessons Learned,” book Mobk076 April 2, 2007 18:9 88 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 6. Producing an Outcomes Assessment Report, 7. Completing, collecting, and archiving project records, and 8. Celebrating Project Success: “End it with a Bang!” REFERENCES [1] Project Close Out Check List. Project Management. University of Washington, [Online]. Available: http://www.washington.edu/computing/pm/end/ Seattle, WA. closeout.html, 2002. [2] Close the Project. Project Management. University of Washington, Seattle, WA. [Online]. Available: http://www.washington.edu/computing/pm/end, 2002. [3] Close/Audit Phase. Trainers Direct. [Online]. Available: http://www.trainersdirect.com/ resources/Project%20Management/CloseoutPhase.htm, 2005. [4] Project Closeout Report. Document 06-114. (2006, Apr.). History. Texas Depart- ment of Information Resources, Austin, TX. [Online]. Available: http://www.dir. state.tx.us/pubs/pfr/06-114/instruction.pdf. book Mobk076 April 2, 2007 18:9 89 C H A P T E R 14 Project Design Reviews Part of this chapter is based on excerpts from a slide presentation given at the Naval Air Warfare Center in 2000. Why should companies conduct design review? The main reason may be that design reviews are required by some “Regulation” in all government departments or agencies dealing with commercial or military products, e.g., Food and Drug Administration, Federal Aviation Administration, Department of Commerce, National Institute of Standards and Technology, or Department of Defense Regulations. Following the regulation, guidelines are of interest to those companies or industries that propose to enter the U.S. commercial market. Not following the regulations could result in product “Liability” issues. Most court rulings are based on the engineering practice of following “Good Common Practice” (standards and regulations) and abiding by professional ethical codes that hold the “Health and Welfare of the Public” as paramount. The purpose of including this chapter is to provide students and new employees the guidance necessary in the preparation and conduct of Preliminary Design Reviews (PDR) and Critical Design Reviews (CDR). 14.1 PRELUDE TO CONDUCTING A DESIGN REVIEW MEETING The primary objective in conducting design review processes is to ensure that the design ful- ﬁlls the performance requirements. In conducting design reviews, the program manager or his designated chairperson must ﬁrst identify the design review objectives, list the entry and exit requirements for design reviews, and state the responsibilities for the committee conducting design reviews. The Design Review Committee Chairperson must form the committee with project team members, stakeholders, sponsors, technical area experts, and independent mem- bers; and coordinate availability to ensure participation by essential members in the Design Review. Additionally, a “Meeting Agenda” is prepared, coordinated with the committee mem- bers, and subsequently accepted prior to the meeting. Before entering into the design review, the chairperson must ensure that committee members have necessary documents, such as: 1. Requirements Traceability to Speciﬁcations Matrix, which is sufﬁcient for the prelim- inary design review. 2. Math Model Report, which is sufﬁcient for the preliminary design review. book Mobk076 April 2, 2007 18:9 90 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 3. Any design documents; i.e., AutoCAD drawings, circuit drawings, or layouts. 4. Risk assessments and risk mitigation plans that are to be formally addressed. When asked, “Is there a format or any one format for the design review?” The response is, “Not Really, because design reviews are carried out at various intervals (phases) during the development of a product.” Hence, the design reviews may address speciﬁc points or all of the major concerns in a phase. Table 14.1 contains an example of a design review agenda. During a test phase prior to any tests being conducted, the project manager may conduct a review of the test plan, testing procedures, and verify availability of test personnel and that all necessary test equipment are in place, functioning, and calibrated to some standards lab with current calibration stickers. After the tests are conducted and analyzed, the project manager would conduct another review of the test results, listing all deﬁciencies, and perhaps formulate options for correction of the deﬁciencies. 14.2 ENTRY CRITERIA FOR DESIGN REVIEW Entry Criteria are the minimum essential items necessary to enter into a design review. If the design review is not a preliminary review, then one of the most important criteria for entry is that there are “No outstanding prereview action items.” The project manager or the review committee chairperson should deﬁne the design baseline and provide the framework for the design review; including speciﬁc items in the Breakout of Tasks Work (WBS), requirements traceability matrix, speciﬁcations, and items describing the design. Prior to the design review meeting, the chairperson should submit the meeting agenda with speciﬁed items to members for review giving ample time for members to make corrections or comments. The Requirements Traceability Matrix (RTM) provides the information-linking require- ments to all of the design documentation, and is the tool that enables a company to verify that all of the design requirements are being addressed. If the product includes software, then the Soft- ware Design Documentation should adequately disclose software design approach information. Typical software design documents include: 1. Math calculations and Model simulation reports, 2. Software Design Description, requirements, and speciﬁcations, 3. Interface Design Description, requirements/speciﬁcations, and 4. Database Design Description, 5. Software Test Plans, and 6. All Software Development Folders (ﬂow charts, source code listings, etc.). book Mobk076 April 2, 2007 18:9 PROJECT DESIGN REVIEWS 91 TABLE 14.1: Example of a Design Review Agenda (Preliminary Design Review) c(cid:1)2002 DRM Associates REVIEW TOPIC Project Deﬁnition (cid:1) Customer changes to the program since last review (if any) REQUIRED OUTPUTS Program/Team Charter Program Requirements/Deliverables Concept Approach Changes Since Last Review (if any) (cid:1) Changes to customer requirements & speciﬁcations since last review (if any) (cid:1) Speciﬁcation issues (if any) (cid:1) Changes to system architecture and concept approach for the system (if any) (cid:1) Changes to product concept design (if any) Product Design Review of design concept for each product (cid:1) (cid:1) (cid:1) Budget & Schedule Changes Product Speciﬁcations Concept Design Component Drawings/CAD Models Assembly Drawings/CAD Models Product structure walk-through Schematic/Net List Schematic and functional design review (if applicable) PCB Layout Product Bill of Material (cid:1) Assembly drawing/model review (cid:1) Component drawing/model review (cid:1) Part speciﬁcations, signiﬁcant character- istics, and tolerances (cid:1) Design for manufacturability, design for assembly, and mistake-prooﬁng review (cid:1) Design and drawing/modeling standards compliance (cid:1) Technical issues and risks (continued) book Mobk076 April 2, 2007 18:9 92 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 14.1: (continued) REVIEW TOPIC REQUIRED OUTPUTS Product Testing and Veriﬁcation (cid:1) Test requirements and plan (cid:1) Test results (cid:1) Issues in meeting speciﬁcations Preliminary Process Design Test Requirements Test Plan Test Results Build Report (cid:1) Process approach and operation ﬂow Process Flow Diagram (cid:1) Feedback from engineering model build (cid:1) Tooling, ﬁxture, production equipment, and test equipment requirements (cid:1) Tooling and ﬁxture design (cid:1) Tooling, ﬁxture, production equipment, and test equipment cost estimates/quotes Tooling and Fixture Design Tooling & Fixture Cost Estimates Quality Planning (cid:1) Quality issues on similar components and countermeasures taken Design FMEA Process FMEA (cid:1) Design FMEA, reliability issues, and Control Plan mitigation steps (cid:1) Process FMEA, reliability issues, and mitigation steps (cid:1) Control Plan for design validation build Supplier Sourcing and Status Supplier Plan (cid:1) (cid:1) (cid:1) Supplier selection and capability for each component Production, capability, quality, lead-time, and cost issues for each supplier and component Inbound packaging requirements or speciﬁcations book Mobk076 April 2, 2007 18:9 PROJECT DESIGN REVIEWS 93 TABLE 14.1: (continued) REVIEW TOPIC Product Cost and Proﬁtability (cid:1) Current cost estimate compared with target cost (cid:1) Product proﬁtability Program Plan and Management (cid:1) (cid:1) (cid:1) (cid:1) Project plan Schedule issues Resource issues Process deviations REQUIRED OUTPUTS Target Cost Worksheet Project Plan Project Budget Review of Issues and Follow-up Actions Open Issues List Permissions to use the tables were granted by DRM Associates, November 8, 2006. Note the tables were primarily designed for the automotive industry; however, the tables contain general information that can be tailored to speciﬁc design reviews. Hardware Design Documentation should adequately disclose all hardware design infor- mation. Typical hardware design documents include: 1. Theoretical math calculations, Models, and/or Simulation Reports, 2. Hardware requirements and speciﬁcation, 3. Hardware Interface requirements and speciﬁcation, 4. Circuit and/or AutoCAD drawings with parts listings, 5. Hardware Test Plans and Test Results Documents, and 6. Training Plan and Training Manuals. 7. Additionally, Risk Assessments and Mitigation Plans must be formally addressed within the design documentation. 14.3 CONDUCTING THE DESIGN REVIEW Normally, the Design Review Chairperson is responsible for conducting the design review; however, for student design, the Team Chairperson is responsible for conducting the design book Mobk076 April 2, 2007 18:9 94 PROJECT MANAGEMENT FOR ENGINEERING DESIGN review. In most organizations, it is essential that customer representatives and users participate in design reviews; however, for student teams, it is essential that the industry sponsors partici- pate in the review. For either commercial companies or student teams, it is essential to include a representation from appropriate specialties; e.g., hardware, systems, software, human factors integration, facilities engineering, etc. It is recommended that student teams hold their review at the sponsor’s facility. Chairpersons should make sure that all participants have ample oppor- tunity to address questions, issues, and concerns. Typically, the design reviews take the form of formal presentations by the design team to the full Review Committee. The presentations should begin with a brief overview of the overall program (scope, deliverables, and milestone schedules) to set the stage for the design briefs and an overall systems perspective reﬂecting the major subsystems and how they interface to comprise the total system. The brieﬁng format should reveal the following: 1. Identiﬁcation of each requirement referenced to the appropriate speciﬁcation paragraph and/or work task. 2. The design approach for preliminary design review (PDR) or detailed design review (CDR) for each requirement. Illustrations should be included wherever feasible. 3. Risk assessment for each requirement and the risk mitigation techniques employed to manage the risk. 4. Risk management plan including who is responsible for carrying out the risk mitigation strategies. 5. Safety and Human factors. 14.4 DESIGN REVIEW OUTPUT At the conclusion of the design review, minutes of the meeting or a Summary Report of the meeting must be generated. Documents to be submitted with the Summary Report include all the design documents used during the course of the design review. As a minimum, the following documents should be attached or forwarded with the report: 1. Contractor’s Proposal or copy of signed contract, 2. SOW (Tasking with Gantt Chart), 3. Speciﬁcations, 4. Requirements Traceability Matrix (RTM), 5. All Circuit, AutoCAD Drawings, 6. All Design Documents, and 7. Requests for Action (RFA). book Mobk076 April 2, 2007 18:9 PROJECT DESIGN REVIEWS 95 Requests for Action (RFA) are formal forms generated to document questions, issues, and concerns that surface during the design review. It is essential that suspense dates and responsi- bilities for resolving the RFAs be assigned before completion of the design review. The student design teams must be provided some form of RFA as shown in the Appendix of the Design Review Report. 14.5 EXIT CRITERIA Exit criteria are the minimum essential items necessary to successfully complete a design review before proceeding into the next phase. Therefore, project managers should review items speciﬁed in the statement of work, the speciﬁcations, and the requisite items describing the design have been successful resolved and all action items are closed. They should also ensure acceptance of required items and acceptance of the design review minutes. Is it over now? It is not over until management has made the determination from the Exit Documents as to whether or not the program/project/design is ready to proceed into the next phase based upon successful completion of the exit criteria (Signatures are required). REFERENCES [1] Technical Design Reviews, Naval Air Warfare Center, Training Systems Division, 2002. [2] DRM Associates. (2002). Example of a Design Review Agenda (Preliminary Design Review) [Online]. Available: http://www.npd-solutions.com/designreview.html book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 97 C H A P T E R 15 Making Technical Decisions This chapter is added to this book on project management to help student teams learn to make rational informed decisions during their senior design projects. Even though everyone makes daily decisions, not many of those decisions are associated with project management and technical matters. The psychology of decision-making varies among individuals. Comedians poke fun at the decision process between men and women when they draw analogies to shopping differences. Women spend hours in a store buying one item, because they search for all sorts of alternatives with the lowest price being one of the factors; whereas, men go in, see what they came for, get it, and they are out of there in a couple of minutes. Comedians propose that the basis for the difference in decision behavioral patterns goes way back to our cave dwelling ancestors when women would go “berry picking” and they were very picky about their berries. This one is good, no good, ok, bad; hence cavewomen would spend hours picking berries. Cave men, on the other hand, were hunters. “There is the rabbit, kill it!” Off goes the arrow; “got it, now time to go home and eat! Ugh!” Truly, this caveman approach is not the way of modern decision-making with today’s technological advances. Webster’s dictionary [1] deﬁnes “Decision” as the act of making up one’s mind; the result or conclusion arrived at by deciding. “Decision-Making” is deﬁned in Webster’s dictionary as the process by which decisions are made. The Center for the Study of Work Teams (CSWT) at the University of North Texas [2] deﬁned “Group Decision-Making” as the process of arriving at a judgment based upon information and the feedback of multiple individuals. 15.1 GROUP DECISION-MAKING PROCESS Various organizations use different Decision-Making Models to establish a systematic means of developing effective group decision-making. Since a multiplicity of models exists, only the four basic “Group Decision-Making Models” will be discussed: 1. Rational Model, 2. Political Model, 3. Process Model, and 4. Garbage Can Model. book Mobk076 April 2, 2007 18:9 98 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 15.1.1 The Rational Model The Rational Model is based on an economic view of decision-making and grounded on goals/objectives, alternatives, consequences, beneﬁts or opportunities, and optimization. The Rational Model assumes that complete information regarding the decision to be made is available; thus, decision-makers consistently assess advantages and disadvantages of alternatives with goals and objectives in mind. Additionally, they will evaluate the consequences of selecting or not selecting each alternative. Finally, the alternative that provides the maximum utility (i.e., the optimal choice) will be selected as the best choice or solution. The rational model is often used as the baseline against which other models are compared. With the Rational Model, decisions are made deductively by determining goals and objectives to be obtained, evaluating the potential alternatives based on the information at hand and choosing the optimal alternative. The advantage of the Rational Model is that it uses a logical and sequential approach. The disadvantage of the model is that it assumes no intrinsic biases to the decision-making process. 15.1.2 The Political Model With the Political Model, groups or individuals do not decide through rational choice with regard to objectives; instead, the decision-makers are motivated by and act on their own needs and perceptions. The model involves bargaining among the decision-makers as each one tries to get his/her perspective to be the one of choice and does not involve or require making full information available. The only advantage of the Political Model is that it emulates how the real world operates (i.e., bargaining related to personal agendas). The greatest disadvantage of the model is that the best solution or decision may not be selected; for example, decision-making in the “U.S. CONGRESS” is based along party or constituency lines rather than on rational goal-oriented or technical merits [2]. 15.1.3 The Process Model Process Model decisions are based on standard operating procedures, or pre-established guide- lines within the organization in which conformity to past and present organizational rules and standards is an integral part. Conformity relates to the fact that reasoning for the deci- sion is based on the predetermined guidelines: REGULATIONS! Again, large government organizations too often tend to quote regulations [2]. 15.1.4 The Garbage Can Model The last decision model is the Garbage Can Model, which is used to make judgment or decisions on tasks within organizations where the technologies are not clear. In the Garbage Can Model, book Mobk076 April 2, 2007 18:9 MAKING TECHNICAL DECISIONS 99 the involvement of participants as well as the amount of time and effort given to the decision process ﬂuctuates such that choices are usually inconsistent and not well deﬁned. However, the model provides a real-world representation of the nonrational manner in which decisions are often made by individuals and within some organizations. “Ad Hoc” decisions made by “Flying by the seat of the pants!” are not the most efﬁcient means of making a decision. Let us hope that student design teams avoid and never use this model in making technical (engineering) decisions [2]. 15.2 U.S. NAVY EXECUTIVE DECISION-MAKING FRAMEWORK The U.S. Navy includes deﬁnition, analysis, decision, reconciliation, and execution phases in their Decision-Making Framework [3]. The deﬁnition phase requires describing in detail the following: 1. Problem Statement, 2. Decision Objectives, 3. Context, 4. Boundaries or Limits, and 5. Analytic Objectives. The analysis phase requires development of decision criteria based on examining the validity, reliability, practicality of the solution, the uncertainty and risks, the analytical method, sensitivity analysis, the decision model, and alternatives. The decision phase requires taking time to review the entire decision process for timing, any spillover effects, organizational issues, political issues, evaluating the internal decision, and performing a reality check on the process and solution. The reconciliation phase may be thought of as “Smoothing rufﬂed feathers,” that is removing all negative effects on participants. One may also consider this phase as conﬂict resolution among participants. What strategies or techniques to use in conﬂict resolution, i.e., win–win compromise with mutual gains or zero-sum on the scorecards? The last phase is execution of the decision. Implementation of any decision or solution requires planning on how to carry out the decision and verifying that the decision is being carried out correctly. The plan must detail who (Which individual or organization is responsible for implementing the decision?), how (How is the decision to be executed?), and what controls? The execution of the decision is not simply, “Here is a memo, go do it!” Implementation of the decision should be “veriﬁed” by those making and issuing the implementation plans or directives. Veriﬁcation requires measurement of some metric, some feedback mechanism on the progress; i.e., EVA, QA, etc., and a mechanism for adjustments to the implementation. book Mobk076 April 2, 2007 18:9 100 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 15.3 DECISION MATRIX OR UTILITY FUNCTION Lessard [4] and Bronzino [5] used a method for making technical decisions based on the Rational Model, but is referred to in various terms, i.e., Decision Matrix [6], Weighted Function Evaluation [5], and Utility Function [4]. 15.3.1 Weighted Function Evaluation Weighted function evaluation requires assigning a weighing factor to denote the relative impor- tance of each of the desired attributes; usually, 0–10. In collaboration with the other evaluators, it determines how well each device meets each attribute with individually assigned scores (be- tween 0 and 10), and then multiplies the scores by the respective weighing factor to determine a weighted score for each attribute for each device. The total weighted scores (Averaged for multievaluators.) are used to determine the overall rating for each device. The technical deci- sion uses these ratings to determine the relative ability of each device in meeting the speciﬁed requirements [4]. 15.3.2 Authors’ Recommendations The authors recommend that student teams use the “Utility Function Method” for evaluation and decision-making. Teams should start by evaluating product objectives and user require- ments, and translate requirements into engineering system or device speciﬁcations. Lastly, apply the “Utility Function” in making technical or engineering decisions. 15.3.3 Utility Function The Utility Function is a quantitative methodology appropriate to assess the relative merits of the available methods, systems, or devices. The ﬁrst step is to determine essential variables and their respective weights. Variables are deﬁned as those factors necessary to evaluate with some ﬁgure of merit the most useful system. A limitation of the utility function analysis is that the outcome of the evaluation may not be the same for other applications, e.g., purchasing a medical device for use in a medical evacuation aircraft or a large well-equipped hospital. Some consider the fact that the function may neither be unique nor does the function include all possible variables as a limitation. The fact is that very seldom are all the critical factors known and included. The selection of factors is a commonsense approach in which it is necessary to evaluate the importance of what is being measured; e.g., in the determination of vital life signs. How the measurement is obtained is not as important as the need to evaluate how accurate the system may measure an essential vital sign. The next step is to prioritize or assign Weighting Factors by order of importance. book Mobk076 April 2, 2007 18:9 MAKING TECHNICAL DECISIONS 101 15.4 FACTOR WEIGHTS Factor weights are the coefﬁcients or multiplying factors by which the variables (factors) are multiplied. The magnitudes or values assigned to the factor weights are not unique. One method of obtaining the weights is to conduct a survey by having a large number of engineers or specialists in the area assign values based on some guidelines and criteria. Surveys require an extended period of time to collect and analyze. One should always question, “How dependable and reliable will the ﬁnal results be?” The answer is that the results will depend on how well the selection of factors and assignment of weights describe or represent the usefulness of the criteria for the speciﬁed conditions. 15.5 GRADING SCALE The next step is to select a scale for the factor weights, for example, one may use a scale from 5 to 0 in three discrete levels to represent: 1. Most desirable (5 points), 2. Acceptable (3 or 2 points), or 3. Unacceptable (1 or 0 points). A scale may be doubled for the very important factors; thus, the factors were given weights based on their relative importance; for example: It is determined that the types of electrodes used are very important and are weighted 10 points with three levels and points: 1. Noncontact—10 points. 2. Noninvasive without media—5 points. 3. Noninvasive with media (i.e., gel)—0 point. In evaluating, the relative merit and/or utility value of each candidate system is calculated after considering all the factors in the model [Eq. (15.1)]: (cid:1) = yn ai j xi (15.1) where xi is the ith factor, ai j is the weight of the ith factor with j degrees, and yn is the utility value of the nth system. Since the factors are descriptors, ai j xi is not a product, but rather a designation of points that are summed to yield a utility value. book Mobk076 April 2, 2007 18:9 102 PROJECT MANAGEMENT FOR ENGINEERING DESIGN 15.6 SUMMARY In making technical decisions, teams should evaluate objectives and user or system requirements. Then, convert requirements into engineering speciﬁcations of a system or device. Be sure to use the Utility Function Method for evaluation of alternatives leading to a rational, systematic “Group Decision” based on the average of individual analyses. REFERENCES [1] Webster’s New Collegiate Dictionary. Springﬁeld, MA: G. & C. Merriam, 1973. [2] Center for the Study of Work Teams, Group Decision Making Within the Organization: Can Models Help? Denton, TX: University of North Texas, 1996. [3] US Navy Command and Staff School. (1987). Navy Web Site. [Online]. [4] C. S. Lessard and W. C. Wong, “Evaluation of noninvasive measurement methods and systems for application in vital signs detection,” USAFSAM-TR-85-44-PT-1, 1983. J. Bronzino, Management of Medical Technology. London, U.K.: Butterworth, 1992. [5] [6] Executive Decision. New York: McGraw-Hill, 1964 book Mobk076 April 2, 2007 18:9 103 C H A P T E R 16 Management of Team Conﬂict This chapter is presented in part from an article by Vern R. Johnson in the IEEE-USA Today’s Engineer with the permission of the IEEE-USA Publishing [1]. Conﬂict is deﬁned in Webster’s dictionary [2] as a noun meaning argument, dispute, or controversy; and, conﬂict is also deﬁned as a verb meaning to disagree, to differ, to vary, or to disturb. Disagreements and conﬂicts are often described as the heat generated by change. Some individuals claim they can “feel” when conﬂict exists; whereas, others believe the conﬂicts “. . . are unavoidable.” Nevertheless, “A Conﬂict will arise!” whenever individuals disagree in a heated verbal exchange about what direction to take when changes occur or are necessary. Usually, changes due to business directions, customers, and technology within a project may require realigning strategies and goals around the new direction with team members’ agreement or compromise about the realignment [1]. Three basic causes of conﬂict include [1]: 1. Information: Refers to the conﬂict that is based on incorrect information or the lack of information. For example, if someone does not know when or where the team is to meet and does not attend the meeting, that individual’s absence will limit the team’s progress and may create “Conﬂict” between members. 2. Goals/Roles: Refers to the conﬂict that will arise if some team members do not under- stand the team’s task, or if members do not know speciﬁcally what their assignments are, those members cannot align themselves with the project or the team. 3. Values: Refers to the conﬂict that will be present if team members do not share values relative to the task and the approach used in the tasks. The ability of individuals and/or teams to accomplish tasks has been correlated directly with the team’s ability to handle conﬂict. Since it is well known that conﬂict interferes with team productivity, when a team experiences conﬂict, it is essential that its members resolve the conﬂict before moving forward [1]. book Mobk076 April 2, 2007 18:9 104 PROJECT MANAGEMENT FOR ENGINEERING DESIGN TABLE 16.1: Communication Model [1] INDIVIDUAL A INDIVIDUAL B 1 2 3 4 5 6 Data Interpret Feelings Needed action Listen Listen Listen Listen Listen Listen Echo Decide Often, what appears to be a conﬂict may simply be a misunderstanding. One approach to determine if a conﬂict exists is to use the communication model in Table 16.1. Individual A does the following four things while Individual B listens [1]: 1. Give the data as an objective statement, without making a judgment or offering feelings. For example, “I see that you . . . ” or “I noticed that . . . .” 2. Make an interpretation. Individual A shares his/her judgment of what the data means. “I interpret this to mean . . . .” 3. Identify the feelings that result from interpretation. There are always “feelings”; i.e., variations of anger, sorrow, joy, or fear associated with conﬂict. The individual A should make a simple statement that recognizes those feelings, such as, “I feel . . . about it” or “. . . and it makes me angry.” 4. State the need to be ﬁlled or the required action. For example, “I would like you to . . . ,” or “I want you to . . . as a demonstration that you are still part of the team.” Then, individual A should stop talking and listen while individual B responds (steps 5 and 6). 5. Echo the expected action. Individual B should parrot back what was just heard to validate understanding of the message. For example, “I see that you are angry and you don’t think I care,” or “You want me to . . . as a demonstration that I am part of the team.” 6. Decide what you are willing to do about person A’s concern and respond accordingly; e.g., “To prove myself, I will . . . ,” or “I had no idea you would interpret my actions that way. In the future, I will . . . .” book Mobk076 April 2, 2007 18:9 MANAGEMENT OF TEAM CONFLICT 105 If individual B’s answer is, “I will cooperate with your request,” then the situation resolves itself. However, if individual B’s answer is, “I will ignore your need or requested action,” then there is a conﬂict that must be resolved before individuals A and B can move forward and be productive. Without a doubt, most individuals prefer to give advice or feedback, than to take or receive feedback. However, sometimes it may be necessary to notify team members that some of their actions are not acceptable, often resulting from oversight regarding ground rules, shared responsibilities, or personal behaviors. Being invited to examine your behavior is receiving a “wake-up call” from one’s peers that may be an emotional, awkward, or uninvited experience. It is critical that the person who approaches a team member to give appropriate feedback knows how to give feedback without antagonizing the team member or members. Therefore, it is important for both the individual giving feedback and the individual receiving feedback to express appropriate attitudes during any discussion [1]. 16.1 GIVING FEEDBACK In giving feedback, make the meeting cordial and individuals should give appropriate feedback in a simple, straightforward way, but with some degree of care. It is not a time for team members to gang up on the person or to express a litany of concerns. However, do not withhold concerns until they have become overwhelming, because the sooner the problems are approached, the easier it will be to resolve them. The focus should be on the individual’s behaviors and the results of those behaviors, or on the technical merits of an approach, rather than on the individual’s personality. Cite a speciﬁc situation as an example of unacceptable behavior and describe the change that may need to be made; however, when expressing concerns, avoid giving advice and then allow time for the individual to respond [1]. It is just as important for people receiving corrective feedback to know how to respond. Here are some basic guidelines for receiving feedback. Since there is a problem and one needs to understand the basic problem, therefore, listen with an open mind. Make sure to understand what teammates are saying, therefore, do not hesitate to ask questions for clariﬁcation if necessary. Do not overreact, or agree with, or reject the confrontation, the initial objective this time is to gather information. Express appreciation for the information, since teammates are taking a risk by trying to help [1]. 16.2 CONFLICT RESOLUTION METHODS There are four conﬂict resolution methods [1]: 1. Avoidance: Avoidance is the general method used when it has been determined that the relationship is not important enough to save. For example, “I can’t handle this. I’m book Mobk076 April 2, 2007 18:9 106 PROJECT MANAGEMENT FOR ENGINEERING DESIGN out of here.” or, “The cost of complying with your request is just too high. Let’s call the whole thing off.” 2. Exercise power: When power is exercised, an individual takes an assertive position based on power or position; e.g., “I am in control.” or “I am the boss.” 3. Who is right? This method requires a third party to mediate the conﬂict. If the conﬂict is based on ﬂawed information or confusion over goals or roles, it may help to go to an expert or consult a reference book to ﬁnd an acceptable solution. 4. Interest-based. When a conﬂict exists between individuals, each takes a position, they anchor themselves to their positions, and they become entrenched with a barrier be- tween them. What should a project manager do when there appear to be conﬂicts among team members? First, ﬁnd out “why” the individuals took the position they did. What is behind it? From the answers, determine what interest the individuals have in common. The objective is to have the individuals concentrate on the common interest rather than on their differences. Common interests can lead to compromise, which, in turn, helps those in conﬂict to relax from their entrenched positions [1]. 16.3 SUMMARY A simple three-step process that should be used by the project manager includes: 1. Achieve contact a. Validate the feelings of other people. b. Learn why they have taken a position. c. Understand them. 2. Boil down the problem a. Ask clarifying questions about the issues that appear to exist. b. Prioritize these issues. 3. Choice making a. Attempt to identify alternatives that can be chosen to provide an appropriate com- promise. b. Protect the common interest. All members must take responsibility for implementation, and once implemented, the conﬂict will recede. If accountability for implementation is not veriﬁed, the conﬂict can return book Mobk076 April 2, 2007 18:9 without warning. As a ﬁnal note, after a conﬂict is resolved, it is amazing how effective a “Thank You” is at bringing goodwill back into the relationship [1]. MANAGEMENT OF TEAM CONFLICT 107 REFERENCES [1] V. R. Johnson. (2005, Jan.) Managing conﬂict in a small team setting. IEEE-USA Today’s Eng. [Online]. Copyright IEEE 2006. Available: http://www.todaysengineer. org/2005/Jan/conﬂict.asp. [2] Webster’s New Collegiate Dictionary. Springﬁeld, MA: G. & C. Merriam, 1973. book Mobk076 April 2, 2007 18:9 book Mobk076 April 2, 2007 18:9 109 Author Biography Charles S. Lessard, Ph.D., Lt Colonel, United States Air Force (Retired), is an Associate Pro- fessor in the Department of Biomedical Engineering at Texas A&M University. His areas of specialization include Physiological Signal Processing, Design of Virtual Medical Instrumenta- tion, Noninvasive Physiological Measurements, Vital Signs, Nystagmus, Sleep & Performance Decrement, Spatial Disorientation, G-induced Loss of Consciousness G-LOC). Neural Net- work Analysis. Dr. Lessard received a B.S. in Electrical Engineering from Texas A&M (1958) a M.S. from the U.S. Air Force Institute of Technology (1965), and Ph.D. from Marquette University (1972). As an ofﬁcer in the U.S. Air Force, Lessard was a pilot of F86L Interceptors and B-52G Strategic Bombers. He also served as Research Scientist and Chief of Biomedical Engineering Research for the Aerospace Medical Division of the School of Aerospace Medicine, at Brooks Air Force Base, Texas. In this capacity he planned and directed efforts in biomedical projects associated with the Manned Orbiting Laboratory Program (MOL), developed medical instrumentation (EEG Analyzer), conducted research on computer on the analysis of sleep brainwaves and cardiac signals, and the effects of zero-gravity (0-G) on the cardiac response during valsalva maneuvers. U.S. Air Force Medical Research Laboratories, Wright-Patterson AFB, Lessard with Biocybernetics Wing Engineering and worked on neural networks, self- organizing controls (SOC), and remotely piloted vehicles. He was the Field Ofﬁce Director. Program Manager, with the Electronics Systems Division of the Air Force Systems Command during the installation and testing of Spain’s Automated Air Defense System as a part of the Treaty of Friendship and Cooperation between the US and Spain. Dr. Lessard retired from the U.S. Air Force in 1981 after serving as the Deputy Director Bioengineering and Biodynamic Division at Aerospace Medical Research Laboratory (AMRL), Wright-Patterson Air Forces. He began his academic career with Texas A&M University in 1981. His program management experiences are applied in his two Senior Design Courses. Charles Lessard was a Senior Scientist for Veridian Inc. at Brooks Air Force and lead sci- entist for KRUG Life Sciences, Inc. in the psychological and neurophysiological manifestations of spatial orientation, mechanisms of spatial orientation in and countermeasures against spatial disorientation. Additionally, he was responsible for developing and conducting research in spa- tial disorientation and high acceleration (Gz forces) induced loss of consciousness (G-LOC). He was a science and engineering expert for the USAF, Air Force Research Laboratories and book Mobk076 April 2, 2007 18:9 110 Wyle Laboratories, Inc. on joint military (Air Force and Navy) G-LOC studies performing analysis of physiological data, i.e., Auditory Evoked Responses (AER), electroencephalograms (EEG), electrocardiograms (ECG), electro-oculograms (EOG), Oxygen saturation (SaO2), and Tracking Tasks Performance data. Joseph P. Lessard, is the Vice President of Americas for Globeleq, Inc. Globeleq Inc. is a global owner and operator of power assets focused on the emerging markets. He is responsible for all business development activities in Latin America and the Caribbean. Mr. Lessard received a B.S. in Electrical Engineering in 1987 and an M.B.A. in 1994 from Texas A&M. As an ofﬁcer in the U.S. Navy, Mr. Lessard trained in nuclear power and served on the ballistic missile submarine USS Alabama. Mr. Lessard entered the private power industry in 1994 as a project manager for the Coastal Power Company. The following year he was named Regional Managing Director with responsibility for business activities in Southeast Asia. In 1997, Mr. Lessard shifted his attention to the U.S. power market as Managing Director of the Northeast United States. He had proﬁt and loss responsibility for three power plants and led a successful acquisition of a fourth power plant. Mr. Lessard left Coastal Power Company in 1999 to form Hart Energy International, a start-up power company focused on the aggregation of power asset investments in Latin America. Hart Energy’s successful direction of two acquisitions – EGE Haina in the Dominican Republic and Entergy’s Latin American portfolio – led to the launch of Globeleq, Inc. in June 2002. At Globeleq, Mr. Lessard has led the company’s efforts in Latin America including the acquisition of a 200MW hydroelectric company, the divestiture of two non-strategic assets, the development of a greenﬁeld thermal power plant, and the placement of two local bond issues. He is currently directing three greenﬁeld development projects in Guatemala, Panama and Peru.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6812953.pdf&bkn=6812952&pdfType=book	Series ISSN: 1939-5221 Series ISSN: 1939-5221 Series ISSN: 1939-5221 SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING MATLAB for Engineering and the MATLAB for Engineering and the MATLAB for Engineering and the Life Sciences Life Sciences Life Sciences Joseph V. Tranquillo, Bucknell University Joseph V. Tranquillo, Bucknell University Joseph V. Tranquillo, Bucknell University In recent years, the life sciences have embraced simulation as an important tool in biomedical research. In recent years, the life sciences have embraced simulation as an important tool in biomedical research. In recent years, the life sciences have embraced simulation as an important tool in biomedical research. Engineers are also using simulation as a powerful step in the design process. In both arenas, Matlab has Engineers are also using simulation as a powerful step in the design process. In both arenas, Matlab has Engineers are also using simulation as a powerful step in the design process. In both arenas, Matlab has become the gold standard. It is easy to learn, ﬂexible, and has a large and growing userbase. MATLAB become the gold standard. It is easy to learn, ﬂexible, and has a large and growing userbase. MATLAB become the gold standard. It is easy to learn, ﬂexible, and has a large and growing userbase. MATLAB for Engineering and the Life Sciences is a self-guided tour of the basic functionality of Matlab along for Engineering and the Life Sciences is a self-guided tour of the basic functionality of Matlab along for Engineering and the Life Sciences is a self-guided tour of the basic functionality of Matlab along with the functions that are most commonly used in biomedical engineering and other life sciences. with the functions that are most commonly used in biomedical engineering and other life sciences. with the functions that are most commonly used in biomedical engineering and other life sciences. Although the text is written for undergraduates, graduate students and academics, those in industry may Although the text is written for undergraduates, graduate students and academics, those in industry may Although the text is written for undergraduates, graduate students and academics, those in industry may also ﬁnd value in learning Matlab through biologically inspired examples. For instructors, the book is also ﬁnd value in learning Matlab through biologically inspired examples. For instructors, the book is also ﬁnd value in learning Matlab through biologically inspired examples. For instructors, the book is intended to take the emphasis off of learning syntax so that the course can focus more on algorithmic intended to take the emphasis off of learning syntax so that the course can focus more on algorithmic intended to take the emphasis off of learning syntax so that the course can focus more on algorithmic thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra class, there are short introductions to many of these concepts. Following a short history of computing, class, there are short introductions to many of these concepts. Following a short history of computing, class, there are short introductions to many of these concepts. Following a short history of computing, the Matlab environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector the Matlab environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector the Matlab environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector operations. The core programming elements of Matlab are introduced in three successive chapters on operations. The core programming elements of Matlab are introduced in three successive chapters on operations. The core programming elements of Matlab are introduced in three successive chapters on scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output of data, create professional quality graphics and ﬁnd and use Matlab toolboxes. Throughout, biomedical of data, create professional quality graphics and ﬁnd and use Matlab toolboxes. Throughout, biomedical of data, create professional quality graphics and ﬁnd and use Matlab toolboxes. Throughout, biomedical examples are used to illustrate Matlab’s capabilities. examples are used to illustrate Matlab’s capabilities. examples are used to illustrate Matlab’s capabilities. About SYNTHESIs About SYNTHESIs About SYNTHESIs This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development provide concise, original presentations of important research and development provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com visit www.morganclaypool.com visit www.morganclaypool.com Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers & & & ISBN: 978-1-60845-710-6 ISBN: 978-1-60845-710-6 ISBN: 978-1-60845-710-6 90000 90000 90000 w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m 9 781608 457106 9 781608 457106 9 781608 457106 T R A N Q U I L L O T T R R A A N N Q Q U U I I L L L L O O M M M A A A T T T L L L A A A B B B F F F O O O R R R E E E N N N G G G I I I N N N E E E E E E R R R I I I N N N G G G A A A N N N D D D T T T H H H E E E L L L I I I F F F E E E S S S C C C I I I E E E N N N C C C E E E S S S M M M o o o r r r g g g a a a n n n & & & C C C l l l a a a y y y p p p o o o o o o l l l CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers & & & MATLAB for MATLAB for MATLAB for Engineering and Engineering and Engineering and the Life Sciences the Life Sciences the Life Sciences Joseph V. Tranquillo Joseph V. Tranquillo Joseph V. Tranquillo SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING MATLAB for Engineering and the Life Sciences Synthesis Lectures on Engineering MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 iii Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2011 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo www.morganclaypool.com ISBN: 9781608457106 paperback ISBN: 9781608457113 ebook DOI 10.2200/S00375ED1V01Y201107ENG015 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #15 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo Bucknell University SYNTHESIS LECTURES ON ENGINEERING #15 CM& Morgan & cLaypool publishers ABSTRACT In recent years, the life sciences have embraced simulation as an important tool in biomedical research. Engineers are also using simulation as a powerful step in the design process. In both arenas, Matlab has become the gold standard. It is easy to learn, ﬂexible, and has a large and growing userbase. MATLAB for Engineering and the Life Sciences is a self-guided tour of the basic functionality of Matlab along with the functions that are most commonly used in biomedical engineering and other life sciences. Although the text is written for undergraduates, graduate students and academics, those in industry may also ﬁnd value in learning Matlab through biologically inspired examples. For instructors, the book is intended to take the emphasis off of learning syntax so that the course can focus more on algorithmic thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra class, there are short introductions to many of these concepts. Following a short history of computing, the Matlab environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector operations. The core programming elements of Matlab are introduced in three successive chapters on scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output of data, create professional quality graphics and ﬁnd and use Matlab toolboxes. Throughout, biomedical examples are used to illustrate Matlab’s capabilities. KEYWORDS computing, MATLAB, matrix, vector, loops, scripting, conditional logic, biological computing, programming, simulation Contents vii 1 2 3 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A Short History of Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2.1 The Pre-history of Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2.2 The Early History of Digital Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.3 Modern Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 A History of Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Why Matlab? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Matlab Programming Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 The Matlab Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 The Diary Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 An Introduction to Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Basic Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.1 Priority of Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.2 Reissuing Previous Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.3 Built-in Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.4 Finding Unknown Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 The Logistic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Clearing Variables and Quitting Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Vectors in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.1 Creating Vectors in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.2 Creating Regular Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.3 Special Vectors and Memory Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 viii 4 5 Vector Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Strings as Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Saving Your Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.5 3.6 Graphical Representation of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.6.1 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.7 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 4.1 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Creating a Matrix and Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.1 Simpliﬁed Methods of Creating Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.2 Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Indexing a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.1 Higher Dimensional Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Simple Matrix Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Visualizing a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.5.1 Spy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.5.2 Imagesc and Print . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.6 More Complex Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6.1 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6.2 Cell Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4 4.5 4.7 Matrix – Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.3 5.1 5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Basic Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2.1 Vector Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2.2 Vector Transpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2.3 Vector - Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Basic Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3.1 Simple Matrix Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.4 Matrix-Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.4.1 Outer Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.4.2 Matrix Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.5 Other Linear Algebra Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.6 Matrix Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.7 6 Scripts and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 ix 6.1 6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.3 Good Programming Habits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.3.1 Comments and Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.3.2 Catching Errors and Displaying Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 6.4 6.5 Script Example - The Random Walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.5.1 Input-Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.5.2 Inline Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.5.3 The Matlab Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.5.4 Function Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.6 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.7 6.8 6.9 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.7.1 input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.7.2 ginput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Function Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.1 7.2 7.3 7.4 7.5 7.6 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 The For Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.2.1 For Loops Over Non-Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 7.2.2 Variable Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 7.2.3 For Loops Over an Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 7.2.4 Storing Results in a Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Euler Integration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 7.3.1 Numerical Integration of Protein Expression . . . . . . . . . . . . . . . . . . . . . . . . 58 The Logistic Equation Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 The While Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.6.1 Looping over Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.6.2 Parameter Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 x 8 Conditional Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.1 8.2 8.3 8.4 8.5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Logical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8.2.1 Random Booleans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.2.2 Logical Operations on Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.2.3 Logic and the Find Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 If, elseif and else . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.3.1 The Integrate and Fire Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.3.2 Catching Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.3.3 Function Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.3.4 While Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.3.5 Steady-State of Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.3.6 Breaking a Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 8.3.7 Killing Runaway Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Switch Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 9 Data In, Data Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9.1 Built In Readers and Writers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9.2 9.3 Writing Arrays and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 9.3.1 Diffusion Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 9.3.2 Excitable Membrane Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Reading in Arrays and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 9.4.1 Irregular Text Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Reading and Writing Movies and Sounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 9.5.1 Sounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 9.5.2 Reading in Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Binary Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 9.6.1 Writing Binary Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 9.6.2 Reading Binary Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 9.6.3 Headers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 9.5 9.6 9.7 10 Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 10.1 xi 10.2 Displaying 2D Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 10.2.1 Figure Numbers and Saving Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 10.2.2 Velocity Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 10.2.3 Log and Semi-Log Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 10.2.4 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 10.2.5 Other 2D Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 10.2.6 Subplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 10.3 Figure Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 10.3.1 The Hierarchy of Figure Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 10.3.2 Generating Publication Quality Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 10.4 Displaying 3D Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 10.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 11.1 11.2 11 Toolboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Statistical Analysis and Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 11.2.1 Data Fits to Nonlinear Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 11.2.2 Interpolation and Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 11.3 Differential and Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 11.3.1 Integrals and Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Signal Processing Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 11.4 Imaging Processing Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 11.5 11.6 Symbolic Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 11.7 Additional Toolboxes and Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 11.7.1 Matlab Central and Other Online Help . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Preface In 2004, Joel Cohen published a paper in the Public Library of Science (PLoS) Biology, titled “Mathematics is Biology’s Next Microscope, only Better; Biology is Mathematics’ Next Physics, Only Better”. The premise of the article was that in the near future there will be an explosion in both math and biology as the two develop a similar synergistic relationship to the one that exists between math and physics. The article goes on to hint that the computer will play a very large role in this revolution, pushing mathematicians to confront the complexity and unpredictable nature of biology, and pushing biologists to become more comfortable with the rigor of mathematics. To quote directly, The four main points of the applied mathematical landscape are data structures, algorithms, theories and models (including all pure mathematics), and computers and software. Data structures are ways to organize data, such as the matrix used above to describe the biological landscape. Algorithms are procedures for manipulating symbols. Some algorithms are used to analyze data, others to analyze models. Theories and models, including the theories of pure mathematics, are used to analyze both data and ideas. Mathematics and mathematical theories provide a testing ground for ideas in which the strength of competing theories can be measured. Computers and software are an important, and frequently the most visible, vertex of the applied mathematical landscape. If you are going to work in the life sciences in the coming decades, it will be necessary for you to master the rigor of algorithmic thinking, ways of storing and manipulating data, and the simulation of biological models. Engineers have been using simulation as a tool for many decades. It has been incorporated into nearly every phase of the design process and is a core tool of engineering science. As such, an amazing array of specialized computing languages have cropped up, each tailored to particular needs. As learning to program can be a signiﬁcant investment, you many wonder which tool you should learn. It should be a tool that is easy to learn and useful right away. A good ﬁrst language should introduce you to the main elements of every programming language so that you can easily learn a more speciﬁc language later. It should also be a language with a large enough userbase that you can share code and algorithms. As evidenced by the number of courses taught at the undergraduate level, Matlab ﬁts the bill on all counts. No one source could possibly do justice to the enormous capabilities of Matlab. You can think of this text as the survival version of Matlab. As such, it is written to be a breadth-ﬁrst xiv PREFACE approach, from which the reader can jump off to other sources to go into more depth. Given the outstanding world-wide support for Matlab, after reading this text, you should be able to ﬁnd what you need online. For the student, it is important to understand that coding is like learning to ride a bike - you can only learn through concentrated, hands-on experience. And, like learning to ride one bike will make learning to ride another bike easier, once you learn how to program in Matlab, it will be much easier to pick up another programming language. A common problem with learning a language from a programming manual is that the language is divorced from actual problems. In this text, an effort was made to tie programming techniques and concepts to biomedical or biological applications. As such, there is a bias toward simulating classic models from theoretical biology and biophysics. At the end of most chapters are a series of exercises. It is important to complete them because it is here that additional Matlab commands and concepts are introduced. You will also ﬁnd that you will be typing in much of the code that appears in the text by hand. There is a reason why it is important to type in the code yourself - in doing so, you will have time to question the purpose of the line. For the instructor, the intent of this text is to take the emphasis off of learning the syntax of Matlab so that your class and lab time can focus on algorithmic thinking, mathematical routines, and other higher-level topics that are difﬁcult to learn from a text. A command line approach is used rather than to rely on Matlab’s many built-in graphical user interfaces because the command line is backward compatible and will work on different computing architectures. The author has written a conference proceeding for the American Society of Engineering Education (2011), “A Semester- Long Student-Driven Computational Project” (download from www.asee.org or contact the author at [email protected]), that details how the text was incorporated into a course. In particular, the paper advocates the idea of “Coding to Think”, the engineering science equivalent of “Writing to Think”. The article also contains a template for a semester-long project, ideas for games that can teach algorithmic thinking as well as a number of references to other computing education papers. important groups. This text would not have been possible without the support of several First, I would like to thank the Biomedical Engineering Department at Bucknell University, most especially the Class of 2012 who used the ﬁrst version of this text. Second, I would like to thank a number of faculty colleagues, most especially Jim Maneval, Ryan Snyder, Jim Baish, Donna Ebenstein and Josh Steinhurst, for their helpful conversation and comments. Last, I wish to thank my family for their patience and for keeping me focused on what is really important in life. Joseph V. Tranquillo Lewisburg, Pennsylvania C H A P T E R 1 Introduction 1 1.1 INTRODUCTION Learning to program can be compared to learning to ride a bike - you can’t really learn it from a book, but once you do learn you will never forget how. The reason is that learning to program is really learning a thought process. This text is not meant to be a supplement for a rigorous approach to Matlab. It is meant to explain why Matlab is an important tool to learn as an undergraduate and to highlight the portions of Matlab that are used on a daily basis. Unfortunately, you will not ﬁnd the coolest, fanciest or even the best parts of Matlab here, but rather a biased view of the most useful parts. You can think of this as survival Matlab. 1.2 A SHORT HISTORY OF COMPUTING Matlab is in some sense a blip in the overall history of computing. To provide some context, below is an abbreviated history of computing. 1.2.1 THE PRE-HISTORY OF COMPUTING Any history of computing must start with the logic of Aristotle. He was responsible for what in computing has become known as conditional logic (what Aristotle called a Syllogism and later was called deductive reasoning). For example, “If all men are mortal and Socrates is a man, then Socrates is mortal”. Aristotle went on to categorize various types of conditionals, including the logical ideas of AND, OR and NOT. The next great computational hurdle occurred with the publication of An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities in 1854 by George Boole. In that work, Boole laid out a method of transforming Aristotle’s logical statements into formal mathematical calculus. The key insight was that just as there are formal operations that work on numbers, e.g., addition and division, there also exist formal operations that work on logical statements. More work by Boole and Augustus De Morgan advocated the position that logical human thought was simply computation following mathematical rules, and that a machine could in principle perform the same functions. 2 1. INTRODUCTION An attempt to build such a machine was carried out by Charles Babbage, an English math- ematician and mechanical engineer, even before Boole had published his work. Babbage laid out plans for what was called a analytical engine, a mechanical device that would realize the type of general computing outlined by Boole. As in most practical applications of theory, there were a number of technical obstacles to overcome. Perhaps the greatest was that Babbage could not secure funding to build his device. It was in fact never built until the London Science Museum used Babbage’s original plans to make a perfectly working analytical engine in 1991. What is amazing is that Babbage foresaw the type of architecture that would be necessary to make a working computer, including a CPU with some sort of programming language, a data bus, memory and even a type of printer and screen to visualize outputs. As luck would have it the daughter of Lord Byron, Ada Lovelace, helped to translate Bab- bage’s work into French. In her translation, she added in many of her own ideas which came to the attention of Babbage. As a result of those notes, Babbage realized that for his general computing device (hardware) to perform speciﬁc functions, a programming language (software) would be necessary. While Babbage focused on the mechanics of the device, Lovelace began to write the ﬁrst computer algorithms. The ﬁrst computer program ever written was by Ada and computed Bernoulli numbers. It is amazing that she was writing algorithms for a machine that didn’t even exist! One of Lovelace’s major advancements was to show how data and the computer instructions for operating on that data could be saved in the same memory. She also was the ﬁrst to recognize that a computer could do more than act as a fancy calculator. While computing is now often regarded as a practical pursuit, there are some who have gone down the more philosophical road outlined by Aristotle and Boole. For example, Steven Wolfram, the creator of Mathematica, published a book called A New Kind of Science in 2002 that advocated the idea that all of reality (including time and space) are the result of a giant algorithm. Others in the artiﬁcial intelligence and cognitive science ﬁelds have used the computer as a metaphor (either for or against) the human mind as nothing but a very good computer. There is now even a ﬁeld called experimental mathematics which attempts to prove true mathematical statements with a new criteria for proof that uses numerical approximations on a computer. 1.2.2 THE EARLY HISTORY OF DIGITAL COMPUTING The history of digital computing in the form we know it today began with a series of seminal papers in the 1930s by Kurt Godel, Alonzo Church, Emil Post and Alan Turing. All helped to put down a mathematical formulation for what it means to compute something. With an eye toward practical applications, they also outlined how it might be possible to build a device that could perform automatic computations. In a convergence of ideas, all of their proposals were found to be equivalent ways of computing. 1.2. A SHORT HISTORY OF COMPUTING 3 The difference between the 20th century and 19th century approaches to computing was that the 20th century approach was based upon electricity, not mechanics. As such, switching between states was faster and more functions could be performed in a given amount of time. With the advent of World War II, both the Americans and English attempted to use computers to perform tasks such as computing navigation instructions for ships and trajectories of ballistics. In one of the most celebrated moments in computing history, an algorithm developed by Alan Turing cracked the German Enigma cipher, enabling the English to have detailed knowledge of German plans. These ﬁrst computers used vacuum tubes as the way to transition between states. In 1947, Bell Labs created the ﬁrst transistor, a tiny electrical switch that relied on quantum mechanics. The development, and subsequent miniaturization of the transistor, decreased the power and size of the computer hardware, while at the same time increasing switching speed. The trend to make transistors smaller and more efﬁcient has continued to push the entire electronics industry to greater and greater feats of engineering. Following the hardware/software split of Babbage and Lovelace, some worked on comput- ing hardware while others worked on developing algorithms. It was during 1940-1960 that many of the most important computer algorithms were developed, including the Monte Carlo method ( John von Neumann, Stan Ulam and Nick Metropolis), the simplex method of linear programming (George Dantzig), the Householder matrix decomposition (Alston Householder), the quicksort method of sorting (Tony Hoare) and Fast Fourier Transform ( James Cooley and John Tukey). In the early history of computing, programmers were forced to speak the same language as the computers (1s and 0s). This was very tedious and soon was replaced with a somewhat more convenient type of programming language called assembly. Assembly languages allow programmers to avoid using 1s and 0s but programming was still very cryptic. In 1957, John Backus led a team at IBM to create FORTRAN, the ﬁrst high-level programming language. It introduced plain English keywords into programming, e.g., if, while, for and read, that made code easier to write, read and share. Other high-level languages followed, such as LISP, COBOL, ALGOL and C. The major advantage of these high level languages was that they were not speciﬁc to particular computer hardware. As such, users could share programs more easily. The breakthrough made by Backus and his team was to create a compiler. The purpose of a compiler is to make the translation from the human text to an executable, the particular language of 1s and 0s that can be read by that particular computer. It is important to realize that while the text of the program is not unique, the compiler and the executable is unique to a computer’s type of hardware. For example, if C code is compiled on a PC, it will run on the PC but not on a MAC. The actual code, however, could be written and tested on either machine. 4 1. INTRODUCTION 1.2.3 MODERN COMPUTING While there was a clear dividing line between the pre-history of computing and early computing, no one event signaled the modern era of computing. In fact, there were several events, most of which enabled non-computer users to begin using a computer. Below we discuss a few of the more recent advances which are part of modern computing. In the early days of computing, only one program was allowed to run on the hardware at a time. With the advent of operating systems, computers gained the ability to multitask. An operating system is a master program that directs which programs can run and for how long. To be clear, the computer is still doing one thing at a time, but now it can switch back and forth between tasks. If the switching is fast enough, it can give the user the illusion that the computer is multitasking. This is the reason why you can surf the web, listen to music and work on your Matlab homework all at the same time. The three most common operating systems are Microsoft Windows, Mac OS and various favors of UNIX (including Linux). The machine language of 1s and 0s is sometimes called the ﬁrst generation of computing languages. Assembly and high-level languages are the second and third generation. The theme is that each generation built upon the generations that came before. As such, there are two new types of languages that can be called the fourth generation of programming. They are the interpreted and object-oriented languages. Interpreted languages can be contrasted with compiled languages. In a compiled language, an executable is created by the user that will only run on a particular computer. If the user wants to modify their code or move it to another type of computer, they must create a new executable. To overcome these limitations, the user could use an interpreted language. Here the computer has a program called an interpreter which will read the lines of text one by one and transform them into 1s and 0s on-the-ﬂy. This has several advantages. First, the user now can modify code and run it without needing to compile the code. Second, it is possible to move code from one type of machine to another as long as both have the right interpreter. The disadvantage of an interpreter is that it has more overhead in terms of memory and operations, and so an interpreted program will run much slower than a compiled program. Examples of interpreted languages are Perl, Python and Matlab. Object-oriented languages focus on allowing data to be handled in a more natural way. It is often the case that what we call data is not simply one number, but it is a series of objects. These objects may be numbers, text or other values. As a medical example, imagine that we wish to create a database of patient records. In an object oriented language we would create a data structure (called a class) which contains all of the information for a generic patient. Then for each individual patient we would create a particular instance of the class with the appropriate attributes. Although object-oriented programming can be traced back to the 1960s, the ideas did not propagate out of the database and artiﬁcial intelligence communities until the 1980s. Now, nearly every programming language has some support for object oriented programming. 1.3. A HISTORY OF MATLAB 5 The advent of the personal computer occurred in the 1980s, followed quickly afterward by the laptop revolution. Prior to that time, most computer users required access to a shared computer mainframe. You would submit your job into a queue and then wait until it was your turn. Unfortunately, you had no way to test your program on your own. It might be the case that you made a very small error in your program and had to wait for the output to ﬁnd out where you went wrong. And then after you had corrected your error, you would still need to resubmit your job to the queue. The personal computer changed all of that, but it also had another side effect. Personal computing opened up an enormous business niche because, where before there were only a few computer users at university and government labs, now nearly everyone owned a computer. The last modern change to computing has been the creation of networks of computers. The ﬁrst and widest reaching is also the most obvious - the internet. One way to think of the internet is as a giant computer that connects people through the computers they use. It has given rise to ideas such as cloud computing and dynamic web pages. Another version of network computing is parallel computing and distributed computing. Both are used to solve very big or very hard problems with many computers at once. Although there is not a clear dividing line between the two, usually parallel computing is when processors communicate on some dedicated network, while distributed processing uses a non-dedicated network, such as the internet. 1.3 A HISTORY OF MATLAB In the previous section, high-level computer languages and algorithm development were discussed. One problem was that many algorithms were written but all in different languages and for different computers. The US government recognized this problem and so Argonne National Labs took up the task of writing a standard set of numerical algorithms that would be freely available (and still are at www.netlib.org). They were the BLAS (Basic Linear Algebra Subroutines), LINPACK (Linear Algebra Subroutines for Vector-Matrix Operations), EISPACK (To compute eigenvalues and eigenvectors) and other general purpose libraries of algorithms. Cleve Moler was one of the programmers who helped write the LINPACK and EISPACK libraries. He later went on to teach at the University of New Mexico. While there, he realized that the Argonne libraries were cumbersome for those not already ﬁrmly grounded in scientiﬁc computing. Moler recognized in 1983 that the libraries could reach a much wider audience if a nicer interface was written. And so he created Matlab, the “MATrix LABoratory” in 1983 using FORTRAN. The ﬁrst version was in fact used by Moler to teach undergraduates the basics of programming. Over the next two years, Moler visited a number of universities. At each university he would give a talk and leave a copy of Matlab installed on the university computer system. The new program quickly became a sort of “cult” phenomenon on campuses around the US. In 1984, Jack Little and Steve Bangert were so impressed with the new programming envi- ronment that they rewrote many of the Matlab functions in C allowing it to run on the new 6 1. INTRODUCTION IBM PC. They also added some built in functions that allowed Matlab to have its own native programming language, better graphics and a Matlab interpreter. Initially, this version was free, but Moler, Little and Bangert soon banded together to formed Mathworks. At the end of 1984 they sold their ﬁrst product to Professor Nick Trefethen at MIT. In the intervening years, Matlab has become the standard for engineering computing, with millions of users around the world. While the original version of Matlab had only 80 built-in functions, it now has thousands, written not only by Mathworks employees, but by users. Mathworks itself has undergone a transformation from selling the standard Matlab distribution, to a variety of toolboxes that are of interest to particular disciplines. It also has the capability (like Maple and Mathematica) to perform symbolic logic and contains a system simulation program called Simulink. 1.4 WHY MATLAB? At various times during my career I have been asked why I have chosen Matlab as a programming language. And throughout my career I have given various answers ranging from “it is what I know best” to “it does what I want”. What is important is that both answers are probably not your answers right now, and they may never be. Below are some reasons why you should take learning Matlab seriously. First, engineers often need to perform tedious calculation tasks over and over again. The calculations might range from something simple, e.g., taking the average of a list of numbers, to something more complex, e.g., simulating how an ecosystem will react to the introduction of a non-native species. Here most any type of computing language can help. But, some languages are easier to learn and others are more ﬂexible. Unfortunately it seems to be the trend that the most powerful languages are also the most difﬁcult to learn. Matlab strikes a good balance between being easily learned and ﬂexible. For example, Matlab is an interpreted language (see the advantages above) but also can be compiled (see the advantages above). Second, engineers often make ﬁgures to represent large quantities of data. Matlab is one of the few programming languages that has graphics capabilities built-in. It is important to say a word here about Excel. It may be very tempting to default to Excel. After all, it can perform calculations and does have graphics capabilities. The problem is that unless you are willing to learn Visual Basic and write macros, Excel is very limited in its computational abilities. Furthermore, Visual Basic tends to be more difﬁcult to learn than Matlab. Matlab also wins out in that it was designed for engineers, whereas Excel was not. As such, Matlab is a common programming language spoken by nearly all engineers, regardless of their training. Third, because there is a large community of Matlab users, there are many great Matlab books and online resources. It is often the case that a problem you must solve has already been solved by another Matlab user and they have posted their code online at Matlab Central (http://www.mathworks.com/matlabcentral/). There is no claim that Matlab is the “best”. If you are looking to write a database, perform language high-end scientiﬁc computing on huge supercomputers, or do any type of natural processing, some other language may be what you want. But as a language that is easy to learn, designed for engineers, and the common computing language of engineering, you can’t do better than Matlab. 1.4. WHY MATLAB? 7 C H A P T E R 2 9 Matlab Programming Environment 2.1 INTRODUCTION The purpose of this chapter is to introduce you to the basic functions and environment of Matlab. Most every other capability within Matlab is built from these basic concepts, so it is important to have a good understanding of what follows. 2.2 THE MATLAB ENVIRONMENT Although Matlab goes by one name, it is in reality a full service computational engine composed of many integrated parts. There is the core of the program that contains the most basic operations. These functions are often very deeply compiled and cannot be changed. There are graphical libraries that allow users to create plots and images as well as graphical user interfaces for interacting with programs. Users can create their own functions or take advantage of the additional libraries contained in toolboxes. Luckily, Matlab provides an environment, shown in Figure 2.1, that ties everything together. At the very top of the window there are a series of toolbars. It is here that you may obtain useful information, such as the built-in help. Below the toolbar is a large window that is mostly blank. It contains what is known as a command prompt, designated by >>. It is to the command prompt that you will type commands that will be executed by Matlab. In the top right there is a Workspace window that lists all of the variables that you currently have in memory. In the bottom right there is a Command History window that lists commands that have been is- sued to the command line. On the left side is a list of all of the ﬁles in your current working directory. Matlab has many tricks that involve the graphical interface. Versions of Matlab, however, do vary, and Matlab is not the same on every computing architecture. To allow the most ﬂexibility, we will use the common element of all Matlab environments; the command line. 2.3 THE DIARY COMMAND In the following sections, you will be asked to enter commands on the command line and then observe the results. As a portion of your assignment (and other assignments to follow), you will 10 2. MATLAB PROGRAMMING ENVIRONMENT Command Prompt Figure 2.1: The Matlab Command Window demonstrate that you have followed the tutorial below by keeping a record of your commands. Matlab has a command called diary that will create a text ﬁle containing a record of your commands. Throughout this text, italics are used to indicate a built-in Matlab function. To begin, create a folder on your desktop and then navigate your current path (at the top of the toolbar) to the folder. Next, enter the following at the command prompt >> diary Problem1.diary This command will record all subsequent commands into a ﬁle called “Problem1.diary”. As outlined in a separate document, all diary ﬁles should end with “.diary”. After you issue the command, you should see the ﬁle in the Current Directory window. When you wish to turn off the diary command you can enter >> diary off You should wait to turn off the diary until after you have ﬁnished the exercises below. 2.4 AN INTRODUCTION TO SCALARS In the following section, we will go on a self-guided tour of some basic Matlab functions. To begin, type the following at the command prompt. 2.4. AN INTRODUCTION TO SCALARS 11 >> r = 5; Notice that the variable r now appears in the workspace window. Now type in the following command which is similar to the above but without the semicolon >> a = 25 You should see that the Matlab command line echos back what you typed, verifying that the variable a is set to a value of 25. This is your ﬁrst introduction to a feature of Matlab. Adding a semicolon to a line will suppress any output to the command line, while no semicolon will print out the value of the variable. Next type the following on the command line >> whos The whos command will print out all of the variables in your workspace to the command line. You should notice that there is additional information given. For example, you will see in the row corresponding to the variable a Name a Size 1x1 Bytes Class Attributes 8 double Here we can see that a is of size 1×1, meaning that it is a scalar. Later we will discuss variables of other sizes, e.g., vectors and matrices. We also can see that a is stored in 8 bytes as a double class. There are in fact a number of different types of data which can be stored in Matlab. For example, to learn more about the data type single you can type the following on the command line. >> help single First, you should note that we used a new command, help. This is very useful when you know the name of a command but do not know how to use it. By typing “help single”, you learn that the command single will convert a variable to type “single”. You will also see in the second line how to use the command, e.g., Y = SINGLE(X), along with what options are available. Try typing >> b = single(a) You should also note that Matlab is sensitive to case >> r = 3; >> R = 11; will create two different variables, r and R. There are a few things to note about this command. First, Matlab’s help uses all capitals to designate functions, e.g., Y=SINGLE(X), but they are not entered this way on the command line. Second, anything to the right of the equal sign in parentheses is consider an input. Anything to the left of the equal sign is considered an output. There are some functions that take more than one 12 2. MATLAB PROGRAMMING ENVIRONMENT input and can send out multiple outputs. Lastly, if you now type ‘whos’ on the command line, you will see that ‘a’ is a double (8 bytes), but ‘b’ is a single (4 bytes). As an exercise, investigate the sin and log commands. Does sin accept inputs in degrees or radians? Does log take the natural log or the log base ten? Note that both commands have some related functions listed under “See also”. 2.5 BASIC ARITHMETIC Matlab has all of the functions of your calculator (and many more as you will see in future chapters). In this section, we will investigate some of the basic functions that are most likely present on your calculator. We can add two numbers >> 4+5 or multiply numbers >> 56 and Matlab supports subtraction >> 4-5 and division >> 5/6 2.5.1 PRIORITY OF COMMANDS One problem with basic arithmetic is that it is not always clear what order the operations should be performed in. For example, try entering >> 4+56 It should be clear from the result that the multiplication was performed ﬁrst and then the addition. This is because in Matlab multiplication has a higher precedence than addition. But what if we wanted to perform the addition ﬁrst and then the multiplication? In this case, we can use parentheses to make the order clear >> (4+5)6 Although Matlab has a built in ordering of preference, it is generally helpful for debugging to use parenthesis to make the intended ordering more clear. 2.5.2 REISSUING PREVIOUS COMMANDS There are many times in Matlab when you may wish to either repeat a command over again, or enter a command that is similar to one previously issued. Matlab has three nice features that can save you some typing time. First, in the example above, you may wish to reissue the command 4 + 5 ∗ 6. If you double click on this command in the Command History window (lower right), it will copy and 2.5. BASIC ARITHMETIC 13 paste the command and execute it for you on the command line. Although this may not seem like a great savings in time, in the future you may have issued so many commands that the one you want is not easy to ﬁnd. The second helpful feature is the up and down arrows. Try using the up arrow and you will ﬁnd that Matlab will move through previous commands. If you hit the enter key, the current command will be executed again. Likewise, you can use the down arrow key if you have moved past a command. The third feature is known as completion. If you start typing a command and then hit the up arrow, it will ﬁnd the last time you typed a command that began that way. As an example, in an earlier exercise you set the variable r to a value of 5. If you wish to change that value, you could use the arrow key. But, a faster way is to begin entering the command >> r = and then hit the up arrow. You could then change r to 4 and hit enter to update the value. 2.5.3 BUILT-IN CONSTANTS Let us assume for the moment that r is actually the radius of a circle and we would like to ﬁnd the circumference, e.g., 2π r. In Matlab, we could deﬁne a constant with the value of π and then perform the multiplication. Matlab, however, already has built in a number of predeﬁned constants, such as pi for π . On the command line enter >> Circ = 2pir; Because the semicolon was used, Matlab did not print out the result to the command line. It did, however, store the value in the variable Circ. To see the value, simply type ‘Circ’ on the command line and press enter. If you wanted to ﬁnd the area, e.g., πr 2, try typing >> Area = pir ˆ 2 √ Note that the symbol ∧ is for any root. So if you wanted to ﬁnd the value of 3 6.4, you would enter >> 6.4 ˆ (1/3) Note that parentheses were used to indicate the desired order of precedence. The symbol ∧ can also be useful for specifying large and small numbers, for example >> 10 ˆ -6 >> 10 ˆ 8 A second very common constant is the imaginary number i. >> c = 4 + 3i In this example, the variable c is a complex number. You can verify this by issuing the whos command. You can also view the help for the following constants within Matlab, inf, nan. 2.5.4 FINDING UNKNOWN COMMANDS Because Matlab commands are not on buttons you can see (like on your calculator), it can sometimes be difﬁcult to know the name of what you want. To this purpose, Matlab has a function called lookfor that will search all of the help ﬁles for your entry. For example, if you know that you would like to ﬁnd the hyperbolic tangent function but don’t know its name in Matlab, try typing 14 2. MATLAB PROGRAMMING ENVIRONMENT >> lookfor tangent You will get a list of the functions that use the word “tangent” in their help ﬁles. Although the list may be long, you can scan it and ﬁnd that tanh is the function you want. 2.6 THE LOGISTIC EQUATION One of the more famous equations in mathematics is the logistic equation. The connection to biomedical research is that the logistic equation was created to study the growth of a population of reproducing species. The catch is that most environments can only sustain so many individuals (usually because of some ﬁnite resource like food). So, after an initial explosion in growth, the population size will settle down to some reasonable number. This equation is sometimes used as a simple model of bacterial infection. The logistic equation can be written in the form of a difference equation zn+1 = rzn[1 − zn] (2.1) where zn is the current value of z, zn+1 is the next value of z and r is a constant. It is important to realize that the logistic equation is scaled, e.g., normalized, so that the maximum population is 1. Using what you already know, set r = 1.5 and the initial population value to z = 0.5, e.g., half of the maximum. Then issue the following command >> z = rz(1-z) Because the variable z appears on the left and right side of the equation, it is important to understand how Matlab processes a command of this type. Remember that anything to the right is an input and anything to the left is an output. So, the old value of z is used on the right side, e.g., zn, but then that value of z is overwritten in memory to form the output, e.g., zn+1. The reason for writing out commands in this way is that we can issue it once and then use the up arrow to keep issuing it again and again. What is happening here is that you are using the current value to ﬁnd the next value. You should try this to see what happens to the value of z (you should see it decrease, headed for 0.0). We will return to this example in future chapters to show how using some simple programming we can make this type of iterative operation much more efﬁcient. To give a bit of a ﬂavor for some strange things that can happen using the Logistic equa- tion, try repeating the above (remember to reset the initial value of z to 0.5 for each trial) but with the following values for r r = 3.2 r = 3.45 r = 3.6 2.7. CLEARING VARIABLES AND QUITTING MATLAB 15 At this point, you should turn off the diary command (“diary off ”). Then using a text edi- tor, you can open the diary ﬁle. At the end of the text ﬁle, you must write a brief description of what you found for the different values of r. What would this mean for a real population of bacteria? 2.7 CLEARING VARIABLES AND QUITTING MATLAB A useful (but also very dangerous) command is clear. If you issue the following to the command line >> clear everything in Matlab’s memory will be erased. There are times when this is very useful, but it should be used carefully. An alternative is to only clear speciﬁc variables, for example >> a = 34.5; >> b = 27.4; >> whos >> clear a >> whos Note that in this example we only cleared the variable a. Matlab is very simple to quit. Simply type quit on the command line. It is important to know that when Matlab is quit, all variables that were created will be lost. 2.8 EXAMPLES Each chapter will contain a series of problems that will help you strengthen your understanding of the material presented. For all problems below, you should begin a diary entry, complete the problem and then end the diary entry. 1. As problem 1 was following along with the chapter, your ﬁrst exercise is simply to rename your diary ﬁle “Problem1.diary”. 2. Use the lookfor command to ﬁnd the name of Matlab’s function for taking the exponential of a number. Then use the help function to ﬁnd out how it works. Then demonstrate that you can ﬁnd the value of e3.4. Do the same for the operation of a factorial and then report the value for 18! 3. Create two complex variables g = 25 + 2i and h = 1 − 4i and then multiply them in Matlab and store the result in a variable k. Demonstrate that you can use the real and imag commands in Matlab to ﬁnd the real and complex parts of k. 4. When a ﬂuid is placed in a thin tube, it will rise up that tube, against gravity, due to capillary forces (what causes dyed water to be sucked up the xylem of a celery stalk). It can be calculated 16 2. MATLAB PROGRAMMING ENVIRONMENT analytically how high a liquid would rise (h) in a tube due to the capillary effect h = 2σ cos(φ) rρg (2.2) where σ = 0.0728J /m2 is the surface tension, φ = 0.35 radians is the contact angle, r = 0.001m is the tube radius, ρ = 1000kg/m3 is the ﬂuid density and g = 9.8m/s2 is the force of gravity. Using these values, compute the rise of the ﬂuid. First, declare all of the variables and then ﬁnd the answer using an equation with only variable names and the constant 2. Then change r = 0.002m and recompute the rise. C H A P T E R 3 Vectors 17 3.1 INTRODUCTION In this chapter and the next, we will discuss the core of what makes Matlab special - the ability to efﬁciently operate on vectors and matrices. Although Matlab has come a long way since its humble beginnings, vectors and matrices remain the core of nearly everything that happens in Matlab. You will want to turn on the diary, as your ﬁrst exercise is to follow along with the tutorial below. 3.2 VECTORS IN MATLAB Whereas previous chapters considered single numbers, called scalars, vectors are a fancy name for a list. It could be a to-do list, a list of fruits, or for most scientiﬁc and engineering applications, some sort of numerical data. 3.2.1 CREATING VECTORS IN MATLAB >> a = [1 1 2 3 5 8 13]; >> whos This command will simply list the number of elements in a and their type. We can perform operations on the vector a. Matlab has many built-in functions. Some work on scalars, as in the previous chapter, but others work on vectors. For example, >> b = sum(a); will sum up all of the values of a and report the outcome in b. In this example, we turned a vector, a, into a scalar, b. A similar command, prod, will return the product of all values in a vector. Another useful function is the length command which gives the number of elements in a vector >> NumElements = length(a) Matlab also can perform operations that transform one vector into another vector. For example, in the previous chapter, you learned that the hyperbolic tangent function is tanh. If you enter on the command line >> b = tanh(a) b will be a vector that contains the hyperbolic tangent of each entry of a. 18 3. VECTORS 3.2.2 CREATING REGULAR VECTORS You could simply enter in each value of a vector, as shown above. Sometimes, however, you may want to create a vector with a more regular pattern. For example, >> c = 1:21; will create a vector, c, that has 21 entries, where each entry is one bigger than the last, e.g., a list from 1 to 21. You can verify this by typing c on the command line and pressing enter (without a semi-colon). What is more, you can use another feature of the colon notion to skip values. For example, >> d = 1:2:21 will generate a vector, d, that starts at 1 and then skips every other number until reaching 21. You should verify this by entering d on the command line. The colon notion is always start:skip:stop, and can be very useful for creating patterned vectors. For example, you might want to have all numbers that are multiples of 10 (skip) between 50 (start) and 200 (stop) >> e = 50:10:200; 3.2.3 SPECIAL VECTORS AND MEMORY ALLOCATION Many other programming languages, especially those that are compiled, require that the user specify up front exactly what variables will be used throughout the program. What is required is memory to be reserved for storage. The big advantage of allocating memory up front is that it is easier to write (and read) to a vector if it is all in the same place in the computer’s memory. As an interpreted language, Matlab does not require you to specify variables up front. This can be a very nice feature, but it can also cause Matlab to operate slowly at times. To overcome this limitation, Matlab will allow the user to allocate space for a vector. The most usual way to do so is using the zeros command >> f = zeros(25,1); that will create a vector, f , with zeros in all 25 locations. A second useful feature of Matlab is the ones function >> g = ones(45,1); that will create a vector of length 45 where every entry is a 1. The ones command is useful for the following >> h = 0.255ones(18,1) In your diary, explain the output of the command above. 3.3 VECTOR INDICES You can think of a vector as a series of bins, one for each element. What makes vectors powerful is that it is not only the value that is saved but also a type of address, called an index. For example, if we would like to get the fourth entry of a, e.g., the value 3, we can get only that value by typing 3.3. VECTOR INDICES 19 >> a(4) What is more, Matlab uses the same colon notion explained above to index vectors. For example, >> a(3:5) will return the values of a at indices 3,4 and 5. So the output will be a subset of the entire array, here the values 2, 3 and 5. Also as above, the colon notion can be used to skip values. For example, >> a(1:2:7) will start with the ﬁrst value and then skip every other value until getting to the 7th value. So the output will be 1, 2, 5, and 13. This type of regular skipping can be very useful in large vectors, for example, if you wanted only every 10th value. There is an additional function in Matlab that can be very useful. >> a(end) will return the very last value of the vector. The advantage here is that you can use end with the colon notion >> a(1:2:end) >> a(1:2:end-1) Explain in your diary why the two commands above give different answers. A hint is that end-1 is the second to last entry of the vector a. When dealing with very large vectors, it can be helpful to use the ﬁnd command in Matlab. For example, >> j = find(a==8) In this statement, we are using ﬁnd to search the vector a for the value 8. If a value of 8 is found, ﬁnd will return the index where the value was found. In this case, j =6, because the value 8 is in the 6th location of the vector a. In the future, you will learn about conditional statements which will allow you to ﬁnd entries that are, for example, greater than some number. One last example will demonstrate the power of indexing in Matlab. Imagine that you would like to enter some values into the vector f , which was created above. More speciﬁcally you would like to place the values 3, 25.7 and 91.6 in the 4th, 9th and 25th locations of f . You could enter the following commands >> indices = [4 9 25]; >> values = [3 25.7 91.6]; >> f(indices) = values; >> f 20 3. VECTORS 3.4 STRINGS AS VECTORS In Matlab, a vector can be composed of any type of data. For example, vectors could have complex values, e.g., contain real and imaginary parts, integers or even characters. In Matlab, a vector of characters is called a string. >> s = 'Matlab is Great!'; s is a vector of characters, or a string. Note that strings in Matlab are enclosed in single quotes. You can verify that this is indeed stored in the same way as a usual vector by entering >> s(3) >> s(10:end) Strings stored as a vector of characters can be very important in cases such as creating ﬁle names. Let us assume that you have a series of 100 ﬁles that contain data on patients 1 through 200. A common operation might be to open up each ﬁle to search for some important characteristic, e.g., blood pressure. Although you will learn how to perform the details of a this task in later chapters, a ﬁrst step is generating each unique ﬁlename. Rather than entering all 200 in by hand, we can specify a variable >> x = 1:2:200; >> ThisPatient = x(29); >> PatientFilename = ['Patient' num2str(ThisPatient) 'Data.dat']; You will want to begin by understanding the ﬁrst two lines. First, a vector is created that ranges from 1 to 200, skipping every other number. Then we will pick off the number in the 29th spot and store it in a scalar called T hisP atient. In the last line, we build up a vector of characters by starting with the string “Patient”. The num2str command is used because we can not mix different data types within a single vector. So, the numerical value of T hisP atient must be converted to a string. You should see the help ﬁle for num2str for more information. Lastly, we add “Data.dat” onto the end of the ﬁle. You should verify that your commands have worked by typing in >> PatientFilename 3.5 SAVING YOUR WORKSPACE There are times when it is helpful to save all of the data in Matlab’s memory. For example, there are some large projects where you may want to quickly be able to pick up where you left off. >> save MyFirstMatlabWorkspace The save command will save all of the variables in your workspace to a ﬁle called “MyFirstMatlab- Workspace.mat” in your current working directory. The “.mat” ﬁle extension indicates a Matlab data ﬁle. The advantage of a Matlab data ﬁle is that it will work on any version of Matlab - PC, MAC or UNIX. To return the variable to the Matlab memory >> clear >> whos >> load MyFirstMatlabWorkspace 3.6. GRAPHICAL REPRESENTATION OF VECTORS 21 Note that the load command would work even if you had quit Matlab and then wanted to reload the variables in your workspace. You may have noticed that the save command saves your entire workspace. If you are only interested in the two vectors a and f , you can enter >> save MySecondMatlabWorkspace a f You will be using the save in some of your homework exercises. 3.6 GRAPHICAL REPRESENTATION OF VECTORS With short vectors, such as those created so far, it is possible to view our data on the command line (by simply leaving off a semi-colon). But when vectors become long, it can be very useful to take advantage of the graphic capabilities of Matlab. Consider the following commands. >> x = 0:0.01:10; >> y = sin(x); >> length(y) The ﬁrst command creates a vector, x that starts at 0 and ends at 10, but in increments of 0.01, creating a vector with 1001 entries. The second line creates a vector, y that applies the sine function to the vector x. Therefore, y will also have 1001 entries. To plot the two vectors against one another >> plot(x,y) It is also possible to plot a vector with specifying an x-axis vector >> plot(y) where it is assumed that the x-axis is incremented by one for each value of y. In future chapters, we will focus more on how to ﬁne tune Matlab’s graphics. 3.6.1 POLYNOMIALS Matlab stores a number of useful structures as vectors. For example, polynomials can be manipulated as a vector of coefﬁcients. The polynomial x3 + 2x2 − 4x + 8 (3.1) can be represented in Matlab as >> u = poly([1 2 -4 8]); which will give the coefﬁcients of the polynomial with the roots 1, 2, -4, and 8. Note that a third order polynomial must contain four entries. A zero entry may also be used as a place holder. So >> w = poly([-1 0 -1 4]); represents − x3 − x + 4 (3.2) Finding the zeros crossings, e.g., roots, of a polynomial is useful in a number of situations. For second order equations, it is simple to use the quadratic equation. For higher order polynomials, it becomes practical to use a numerical method, e.g., Newton’s Method. Matlab has a built-in root ﬁnder called roots. 22 3. VECTORS >> roots(u) >> roots(w) Note how, in the last command, Matlab will report complex numbers. 3.7 EXERCISES 1. Turn in the diary of your commands for this chapter. You must also include the two “.mat” ﬁles you created in Section 3.5 and answer the questions in Sections 3.2.3 and 3.3. 2. Sine waves are used in many life science and engineering applications to drive everything from the varying magnetic ﬁelds of MRI machines to the supply of nutrients to tissue being grown in a bioreactor. For this problem, you must show your commands in a diary. The general equation for a sine wave is y = A · sin [2πωt + φ] (3.3) where A is the amplitude, ω is the frequency in Hertz (1/seconds) and φ is an angle in radians. First create a vector for time (t) that starts at 0, ends at 5 and skips in increments of 0.001. Next, deﬁne A = 1, ω = 2H z and φ = π. Using the parameters and time vector, create a vector y and then plot t against y. In the next part of this problem, you will create a second sine wave (in a variable z) z = A · sin [2πωt + φ] (3.4) with A = 0.5, ω = 1H z and φ = π/2. Note that you can use the same time vector to create z. You will next plot z against t, but on the same ﬁgure as your previous sine wave. To plot two data sets on the same ﬁgure, you must use the hold on command. In general, plotting two data sets will be achieved by >> plot(t,y) >> hold on >> plot(t,z) 3. One important use for computing is to test out algorithms that will ﬁnd some important characteristic of a data set, e.g., frequency spectrum, time to reach a maximum. The problem with biological data is that it often contains noise. Therefore, many algorithms designed to be used on biological data must work even in the presence of noise. Matlab has a built in command, rand, that can be used to generate random numbers. For example, >> r = rand(1000,1); 3.7. EXERCISES 23 will create 1000 random numbers between 0 and 1. Use the help function (hint: look at the examples in the help ﬁle) to create 2000 random numbers that range between -1 and 2 and store them in a variable, RandomNumbers. It may be helpful to plot RandomNumbers to check that you have created what you intended. Use the save command to save the numbers into a ﬁle, “RandomNumbers.mat”. 4. A Holter Monitor is a device that is used to continuously record ECG, even when the patient may be at home. It is often the case that a patient will allow the device to record for some period of time and then upload the data (using the internet or a phone line) back to the physician. Create a character string, called F irstName, with your ﬁrst name. Create a character string, called LastN ame, with your last name. Then create a ﬁlename (another string) with the following format LastName,FirstName-HolterMonitor6.2.2011.dat In this way, the physician will know exactly what data he/she is looking at. Enter your com- mands for creating the ﬁlename in a diary ﬁle. C H A P T E R 4 Matrices 25 4.1 INTRODUCTION While vectors are useful for storing lists, matrices are good for storing lists of lists. As such, you can think of a matrix as a group of vectors. Although the data can be of any type, e.g., doubles, characters, integers, all of the vectors that make up a matrix must have the same length. 4.2 CREATING A MATRIX AND INDEXING Creating a matrix in Matlab is not all that different from creating a vector. For example, to create the matrix ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 4 8 1 2 3 5 6 0 4 6 7 0 3 12 7 8 2 5 0 4 you would enter >> A = [1 2 3 4 5; 0 4 6 8 6; 7 0 3 12 7; 2 5 0 4 8]; >> whos You should see that matrix A has the dimensions 4×5 and consists of doubles (Matlab’s default format). Rows are separated by semi-colons. It is also convention that matrices in Matlab use capital letters, while scalars and vectors are lower case. This is not necessary but can help distinguish between the two types of data. There are some occasions when you may want to know the dimension of a matrix. Similar to the length command for vectors, you can use the size command for matrices >> [NumRows NumCol] = size(A); where the variables N umRows and NumCol will contain the number of rows and columns of the matrix. 4.2.1 SIMPLIFIED METHODS OF CREATING MATRICES There are several additional ways that a matrix could be created. >> B = zeros(5,6); 26 4. MATRICES will create a matrix with 5 rows and 6 columns where all the entries are zeros. This is a generalization of the zeros command and is a good way to allocate memory for a matrix. Similarly, >> C = ones(4,3); will create a 4×3 matrix of ones. Again, as in the vector version of the ones command, we can scale the entire matrix. >> C = 23ones(4,3); A very common matrix to create is one that has values only along a diagonal, and zeros everywhere else. For example, >> diagvector = ones(7,1); >> D = diag(diagvector) The ﬁrst command creates a vector of ones that is of length 7. Then this vector is placed on the diagonal of the matrix D. In using the diag command, Matlab automatically ﬁlls in the necessary zeros. In fact, the example above is a matrix that is used very often in linear algebra called the Identity Matrix. Matlab has a command, eye, which creates any N ×N identity matrix. The diag function, however, can be used to do much more. Try to interpret the following sequence of commands >> DiagVector = [1 2 3 4 5 6]; >> UpDiagVector = [7 8 9 10 11]; >> DownDiagVector = [12 13 14 15 16]; >> E = diag(DiagVector) + diag(UpDiagVector,1) + diag(DownDiagVector,-1) Notice how the diag command can be used to put values above (indicated with a 1) or below (indicated with a -1) the diagonal, but that the vector used must be the proper length. For example, in a 6×6 matrix, you would place a vector of length 5 above or below the diagonal. If at some later time you wanted to add another diagonal 2 off the main diagonal, >> E = E + diag([17 18 19 20], 2) There are also some occasions where you may want to create a random matrix. >> F = rand(5,6); creates a 5×6 matrix with random values that range between 0 and 1. 4.2.2 SPARSE MATRICES So far we have created matrices that have speciﬁed every value in the matrix, even if they have a value of zero. But zeros take up space in memory. Matlab has a way to compress a matrix in such a way that any zeros are not stored. This is especially useful for very large matrices that contain mostly zeros. In scientiﬁc computing these type of matrices are known as sparse. >> G = sparse(E); >> whos You should notice that the matrix G is now a sparse matrix and takes up fewer bytes in memory than the original matrix E. In small matrices the savings is usually not worth it. But, try issuing the following commands and observe the difference in memory used by matrices H and J . 4.3. INDEXING A MATRIX 27 >> H = diag(ones(500,1)); >> J = sparse(H); >> whos 4.3 INDEXING A MATRIX Values can be read from a matrix in much the same way as they are read from a vector. For example, >> E(1,2) will retrieve the value of 7 in the ﬁrst row and second column. Try getting the value of 15 in the ﬁfth row and ﬁfth column. You can also get entire columns or rows from a matrix using the colon notation. >> E(2,:) will get the entire second row of E. >> ColThree = E(:,3) will get the entire third column of E and store it in a vector called ColT hree. What is more, we can get any submatrix of a larger matrix. >> SubMatrixOfE = E(2:5,3:6) will get from row 2 to row 6 between columns 3 and 6. Note that this submatrix will be a 4×4 matrix of its own. How might you get the bottom right 3×3 submatrix? Note that you can even use the end command introduced in the previous chapter. 4.3.1 HIGHER DIMENSIONAL MATRICES Although Matlab is designed to handle two-dimensional matrices, there is some support for higher dimensional matrices. >> P = zeros(2,3,5); >> Q = rand(3,4,5); >> whos You can read from higher dimensional matrices in the same way as other matrices >> R = Q(1,2:3,2:4) >> whos 4.4 SIMPLE MATRIX ROUTINES There are a number of matrix routines that can be useful in real problems. First, there are occasions where we may want to transform a matrix into a vector using the reshape command >> k = reshape(E,36,1) Here the vector k contains the same values as the matrix E, where each of the columns have been stacked on top of one another. But we can use reshape to do some other interesting things as well. 28 4. MATRICES >> L = reshape(E,9,4) changes the 6×6 E matrix into a 9×4 matrix, again wrapping through the columns. Another command that can be useful is the squeeze command. You may have noticed that the R matrix above is a 1×2×3 which is really a 2×3 matrix. To have Matlab compress any dimensions of 1 >> S = squeeze(R) >> whos 4.5 VISUALIZING A MATRIX 4.5.1 SPY It is often useful to be able to visualize the entries of a matrix. For example, >> A = diag(ones(100,1))+diag(-3ones(99,1),1)+diag(25ones(99,1),-1); First make sure that you understand how this matrix was built up using diag and ones commands. In some applications it is useful to know where any non-zero entries exist in the matrix. >> spy(A) will bring up a graph showing the location of all non-zero entries. At the bottom of the graph you will also ﬁnd the number of non-zero entries in the matrix. In the toolbar (at the top of the graph) you will see a small magnifying glass with a ‘+’ sign. Click on this symbol and select an area that contains some dots. You can use this zoom function on any type of plot within Matlab. To zoom back to the original view simply double click anywhere on the plot. Note that next to the positive magnifying glass is a negative magnifying class which can be used to zoom out. 4.5.2 IMAGESC AND PRINT There are many situations where a matrix will be used to store data. In these situations, we might want to view all of the data at once. >> B = rand(100,100); >> B(25:50,50:75) = 1.5; >> imagesc(B) >> colorbar creates a random 100×100 matrix (with values ranging from 0 to 1, representing some data we have collected from an experiment). The second command ﬁlls a block of the matrix with the value 1.5. The next two commands create a color plot of the values in B and then adds a color bar. There are times when it is helpful to create a jpeg of an image so it can be imported into other applications, e.g., PowerPoint, Word. The Matlab print command can be used to create an external ﬁle 4.6. MORE COMPLEX DATA STRUCTURES 29 >> print('-djpeg','MyFirstImageFile.jpeg'); If you look at the help ﬁle for print you will notice that the ﬁrst entry speciﬁes the ﬁle type (in this case a jpeg). You should notice that there are many other types of image ﬁles that you could create. The second entry speciﬁes the name of the ﬁle. You should try to open “MyFirstImageFile.jpeg” to be sure it has been created properly. 4.6 MORE COMPLEX DATA STRUCTURES Standard matrices and vectors must contain all of the same type of data. For example, we may have an entire vector of characters or an entire matrix of integers. Although there are cases where we want to mix types of data, matrices and vectors will not help us. But what if we want to have data for a patient that contains a combination of names and medications (strings), heart rate and blood pressure (doubles) and number of times a nurse has checked in today (integer). Matlab does have two ways to handle this sort of problem. 4.6.1 STRUCTURES The idea of a structure is that data types can be mixed, but then referenced easily. Enter the following commands >> P(1).Name = 'John Doe'; >> P(1).HeartRate = 70.5; >> P(1).Bloodpressure = [120 80]; >> P(1).Medication = 'Penicillin'; >> P(1).TimesChecked = int16(4); >> who >> P Above we have created a data structure, P , for the patient “John Doe”. You will note that P is now of type struct and that when you type P on the command line it will tell you which data are in P . To retrieve a value from P >> P(1).Name >> P(1).Bloodpressure You may wonder why we needed to reference the ﬁrst value of P , e.g., P(1). The reason is that now we can easily enter another patient >> P(2).Name = 'Jane Doe'; >> P(2).HeartRate = 91.3; >> P(2).Bloodpressure = [150 100]; >> P(2).Medication = 'Coffee'; >> P(2).TimesChecked = int16(2); >> who >> P 30 4. MATRICES It should be noted that you can have ﬁelds within ﬁelds too >> P(2).Family.Father = 'Jerry Doe'; >> P(2).Family.Mother = 'Julia Doe'; >> P >> P.Family 4.6.2 CELL ARRAYS While a structure must be referenced by a known name, a cell is simply a matrix of other data structures, where the data structures do not need to match. >> T = {rand(3,3), 5.3,'BMEG 220'; int16(27),˜[24.5 37.8],'Matlab'}; >> who >> T Here T is a matrix, but each element can take the form of any other data structure. For example, >> T{1,3} will retrieve the text string in the ﬁrst column and third row. Notice that for cells you index using brackets, not parentheses. How can you retrieve the 3×3 random matrix? How about the value 27? One last example will demonstrate the power of cells. >> U = {T 5; 'Computing' [39.2 47]}; >> U{1,1} >> U{1,1}{2,3} Here the cell array U has been embedded within it another cell array T . The second command retrieves the T cell and the third command will retrieve a speciﬁc entry within T . You should save only U and P in a Matlab ﬁle called “MatrixStructures.mat”. For help on saving a Matlab data ﬁle, see the previous chapter. 4.7 EXERCISES 1. Turn in the diary for this chapter along with the image ﬁle created in Section 4.5.2 and .mat ﬁle in Section 4.6.2. 2. Matrices can be a very good way to visualize distributions in space. For example, in modeling the spread of a disease throughout a population, it is important to know who is infected, who is immune and who is susceptible to infection. Let us assign anyone infected a value of 1, anyone immune a value of 2 and anyone susceptible a value of 3. We can visualize what is happening at a particular time with a 2D plot, where each coordinate represents a portion of a college campus. Start by creating a 40×40 matrix that contains all 3’s (hint: use the ones command). Next, create two small regions of infections, one bounded by x=3, x=7, y=8, y=11, and another 4.7. EXERCISES 31 bounded by x=35, x=39, y=27, y=32. Next, create a line of immunization (students vaccinated) that ranges from x=2 to x=38 and y=20. Use the imagesc and print commands to visualize the distribution of infected and not infected students and then print the image to a jpeg. You should include a colorbar. 3. A matrix can be very useful for storing the structure of a network. In biological applications, a network may be the connections between cardiac or neural cells, the interactions between different genes or even the relationships between species in an ecosystem. Typically, each “player” (also called an “agent” or “unit”) is assigned an integer that is in the range 1 to N (where N is the total number of players in the network). Each row of our matrix will correspond to a player. For example, row one is dedicated to player 1, row two is dedicated to player 2 and so on. In each row (corresponding to the current player) we place a 1 in the location of any player with whom it can interact. For example, if row 8 is [001000100001] (4.1) it means that player 8 has some direct relationship with players 3, 7 and 12. This type of matrix is called an adjacency matrix. A very common and simple type of network structure is a one-dimensional ring. In a ring, each player is connected to the player before and after. For example, player 4 would be connected to players 3 and 5. Because of the ring structure, player 1 is also connected to the very last player, completing the ring. Create an adjacency matrix, A, that describes a ring with 10 players. Remember that player 1 is connected to player 10 (and vice-versa), completing the ring. You should ﬁrst write out the matrix by hand so you understand the basic structure. One method of creating the matrix would then be to simply program in the entire matrix by hand. For this exercise you must use the diag command to create the matrix. Note that you may need to add in a few extra commands (using what you know about indexing a matrix) to complete the loop. You should be able to create the entire matrix in 3 commands which you show in a diary ﬁle. Because the matrix is mostly made of zeros, create a new sparse matrix, B. Then save A and B into a “.mat” ﬁle. Lastly, use the spy command on matrix B (note that spy works on sparse matrices too). Save the ﬁgure in a jpeg ﬁle. 4. Bacteria, and other micro-organisms, navigate throughout space using a variety of sensors. For example, they may simultaneously detect pH, glucose concentration gradient, light direction and temperature. To move in a particular direction a bacterium must decide which stimulus to move toward (or away from), but it may sometimes have conﬂicting “motivations”, e.g., moving 32 4. MATRICES toward warmth may move it away from glucose. To model a large population of bacteria we would need to keep track of the state of each bacteria. Let’s assume that pH is a number, glucose concentration gradient is a 2×2 matrix (deﬁnes 2 unit vectors), light direction is three numbers (angles in degrees) and temperature is a qualitative string (hot, just right and cold). In this exercise, you will create a Matlab structure, Bac to store the data for 3 bacteria. The names of the structures should be, pH , Glucose, Light and T emp. You should be able to index data using Bac(1), Bac(2) and Bac(3). For example, Bac(1).pH should return a single number, Bac(2).T emp should return a string, and Bac(3).Glucose should return a matrix. You can make up any values you want for the entries for each bacteria. What is important is the makeup of the structure. When you are ﬁnished, save only the Bacteria Structure, Bac, into a “.mat” ﬁle. C H A P T E R 5 33 Matrix – Vector Operations 5.1 INTRODUCTION The original intent of Matlab was to provide an all purpose platform for performing operations on matrices and vectors. Although Matlab has progressed much farther since these early ambitions, matrix-vector operations are still the core of the environment. In this chapter, we explore the basic functions Matlab has for performing operations on matrices and vectors. This text is not meant to teach you about linear algebra. But there is a small amount of lin- ear algebra that is necessary to understand before we move on to Matlab’s matrix-vector operations. Perhaps the most important concept, is multiplication of a matrix and a vector. To demonstrate the concept, we will work with a 3×3 matrix and a 3×1 vector. ⎡ ⎣ a d g h b c e f i ⎤ ⎡ ⎦ ⎣ A B C ⎤ ⎡ ⎦ = ⎣ ⎤ ⎦ ? ? ? To perform this multiplication we ﬁrst multiply the values across the top row of the matrix by the values down the vector. The result will be a ∗ A + b ∗ B + c ∗ C (5.1) This term will form the ﬁrst value in the resulting vector ⎡ ⎣ a d g h b c e f i ⎤ ⎡ ⎦ ⎣ A B C ⎤ ⎡ ⎦ = ⎣ aA + bB + cC ? ? ⎤ ⎦ We then move down one row of the matrix and multiply again by the elements in the vector ⎡ ⎣ a d g h b c e f i ⎤ ⎡ ⎦ ⎣ A B C ⎤ ⎡ ⎦ = ⎣ aA + bB + cC dA + eB + fC ? ⎤ ⎦ and again for the last row of the matrix 34 5. MATRIX – VECTOR OPERATIONS ⎡ ⎣ a d g h b c e f i ⎤ ⎡ ⎦ ⎣ A B C ⎤ ⎡ ⎦ = ⎣ aA + bB + cC dA + eB + fC gA + hB + iC ⎤ ⎦ Note that the mechanics of matrix-vector multiplication is to go across the rows of the matrix and down the column of the vector. To make the above more concrete, try to follow the example below ⎡ ⎣ 1 2 3 4 5 6 7 8 9 ⎤ ⎡ ⎦ ⎣ 10 11 12 ⎤ ⎡ ⎦ = ⎣ 110 + 211 + 312 410 + 511 + 612 710 + 811 + 912 ⎤ ⎡ ⎦ = ⎣ ⎤ ⎦ 68 167 266 Two points are important about matrix-vector multiplication. First, the number of columns in the matrix must be the same as the number of rows in the vector. Otherwise, the multiplication of matrix rows against the vector column will not work out right. The implication is that we need a matrix that is N × M and a vector that is Mx1 where M and N are any integers. Second, it is often a convention to use bold capital letters to denote matrices and bold lower case letters for vectors. We can therefore rewrite a matrix-vector multiplication as Ax = b (5.2) where A is the matrix, x is the vector and b is the result of the multiplication. 5.2 BASIC VECTOR OPERATIONS We have already explored a few operations on vectors. For example, in Chapter 3 we use the sum command. There are a number of additional commands that work on vectors. For a small sample, try issuing the commands below. You may also want to view the help ﬁles for these commands to better understand how they work. >> v = [8 -1 3 -12 37 54.3]; >> mean(v) >> std(v) >> sort(v) >> sin(v) >> log(v) >> max(v) >> min(v) >> i = find(v==-12) It is important to note that some of the above commands will output only a single number, while others will apply a function to each element of the vector. 5.2.1 VECTOR ARITHMETIC There are a number of very simple arithmetic operations which work on vectors. The most simple is to multiply all values by some constant value. For example, 5.2. BASIC VECTOR OPERATIONS 35 >> y = [1 3 5 7]; >> x = 2y Note that the * in Matlab denotes multiplication. You can also add a constant value to all elements of a vector. >> z = y + 2 You should try subtracting (use “-” symbol) a constant or dividing (use “/” symbol) by a constant. 5.2.2 VECTOR TRANSPOSE Above we created a vector y that has the dimensions 1×4. The problem is that we might eventually want to multiply a matrix by this vector and it is in the wrong format. To transform y into a 4×1 vector we can simply use the transpose command. >> w = y’ >> whos 5.2.3 VECTOR - VECTOR OPERATIONS Matlab can also perform operations on two vectors. Try the four operations below and do not worry if you get errors. >> l = [1 4 9 10]; >> m = [-1 35 2 0.5]; >> m-l >> m+l >> m/l >> ml You will notice that the operations of addition and subtraction act the way you would expect. The division and multiplication, however, do not do what we expect. For the division we would expect to simply divide each element of vector m by each element of vector l and return a vector of the results. Instead, a single number was returned. In the multiplication example, Matlab would not even perform the operation. To understand the problem we will present two different scenarios. First, (cid:8) 1 4 9 10 ⎤ (cid:8) ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎣ (cid:9) −1 35 2 0.5 1-1 + 435 + 92 + 100.5 (cid:9) Here we are simply using the type of multiplication used in the ﬁrst section of this chapter for matrices and vectors. The only exception is that we are multiplying a 1×4 matrix by a 4×1 vector. The result is a 1X1 scalar. To perform this operation in Matlab 36 5. MATRIX – VECTOR OPERATIONS >> ml’ Here the transpose command was used to turn the 1×4 l vector into a 4×1 vector. In fact, this type of vector-vector multiplication has the name of “dot product” or “inner product” in linear algebra. Matlab has a command, dot for taking dot products between two vectors, regardless of their dimensions. The dot product, however, was not what we originally intended. What we expected was to multiply each of the elements of m by each of the elements of l and then place them in a new vector. To make this operation distinct from the dot product, Matlab has a special command. >> m.l will perform the desired operation.The “.” command is shorthand for an operation that is performed on each element. Try the following to see how element division works. >> m./l This still leaves us with why the division command in the original example yielded any answer at all. The answer is that “/” means something in Matlab that relates to matrix-vector division. It will be discussed below. 5.3 BASIC MATRIX OPERATIONS Many of the basic commands we have already discussed work on matrices. First, we will use a built-in command to generate a matrix >> B = magic(4) %You may want to look at the help for 'magic' First, you should notice that % is a special symbol that denotes a comment in Matlab. So, any text that appears after % will not be sent to Matlab. Below, comments will be used to help you understand the commands. You do not need to enter comments on your command line. You may also have noticed in some of the help ﬁles that many commands that work on scalars also work on vectors and matrices. For example, >> sum(B) >> sum(B,2) >> mean(B) >> min(B) >> max(B) >> min(min(B)) >> exp(B) >> [i j] = find(B==10) % sum across the rows % sum down the columns % mean down the rows % minimum down the rows % maximum down the rows % find the absolute minimum of B % take the exponential of each element of B % find row (i) and column (j) of value 10 This is a strength of Matlab - most operations are deﬁned for scalars, vectors and matrices. By default, Matlab assumes that all operations on a matrix will be performed on the rows. The “sum(B)” 5.3. BASIC MATRIX OPERATIONS 37 command thus returns a vector that is the sum of each row. But the sum command can total up columns instead by “sum(B,2)”. You may also have noticed that you can embed commands within one another. For example, “min(min(B))” will ﬁrst create a vector with the minimum value for each row (with the inner min command), but then take the minimum of that vector (with the outer min commands). The result will be the minimum value in the entire matrix. 5.3.1 SIMPLE MATRIX FUNCTIONS One of the simplest matrix functions is the transpose >> B’ The meaning of a matrix transpose is that the ﬁrst row becomes the ﬁrst column. The second row becomes the second column and so on. Although the example above is a 4×4 (or square matrix) it should be easy to check that the transpose of a N × M matrix is a M × N matrix. Like vectors, we can perform basic arithmetic operations on matrices. >> C = [1 2 3; 4 5 6; 7 8 9]; >> D = [-3 -2 -1; -6 -5 -4; -9 -8 -7]; >> C-D >> C+D >> C.D >> C./D >> C.ˆ3 % subtract the elements of D from C % add the elements of C and D % multiply the elements of C and D % divide the elements of C by the elements of D % cube each element in C Each of the operations above is performed element-wise (because + and - are that way naturally, and we used “.”, “./” and “.∧”). It is possible, however, to multiply one matrix by another matrix. % perform a full matrix multiply >> CD where the pattern used for matrix-vector multiplication is used to create the entries of a new matrix. For example, ⎡ ⎣ C11 C12 C13 C21 C22 C23 C31 C32 C33 ⎤ ⎡ ⎦ ⎣ D11 D12 D13 D21 D22 D23 D31 D32 D33 ⎤ ⎦ = ⎡ ⎣ C11D11 + C12D21 + C13D31 C11D12 + C12D22 + C13D32 C11D13 + C12D23 + C13D33 C21D11 + C22D21 + C23D31 C21D12 + C22D22 + C23D32 C21D13 + C22D23 + C23D33 C31D11 + C32D21 + C33D31 C31D12 + C32D22 + C33D32 C31D13 + C32D23 + C33D33 ⎤ ⎦ Again, multiplications is carried out by moving across the rows of the ﬁrst matrix and down the columns of the second matrix. Another way to think about matrix-matrix multiplication is that if we want to know the entry at any row and column of the resulting matrix, we sim- ply take the dot product of that row of the ﬁrst matrix (C) with the column of the second matrix (D). 38 5. MATRIX – VECTOR OPERATIONS Using the idea of matrix-matrix multiplication we can also perform matrix exponentiation >> Cˆ4 which is the same as the matrix multiplication CCCC. 5.4 MATRIX-VECTOR OPERATIONS As the core of Matlab is vector and matrix operations, it is not surprising that there are many functions for such operations. Below we explore only a few of the most important. 5.4.1 OUTER PRODUCTS The inner product is an operation on two vectors that results in a scalar. The outer product is an operation on two vectors that results in a matrix. The key to understanding the difference is in the dimensions of the two vectors. ⎤ ⎥ ⎥ ⎦ (cid:8) ⎡ ⎢ ⎢ ⎣ a b c d (cid:9) = s t ⎡ ⎢ ⎢ ⎣ a ∗ s b ∗ s c ∗ s d ∗ s a ∗ t b ∗ t c ∗ t d ∗ t ⎤ ⎥ ⎥ ⎦ You should note that this operation is the same as the matrix-matrix multiplication but now with two vectors. In general, the outer product of a Nx1 vector and 1×M vector is a N ×M matrix. 5.4.2 MATRIX INVERSE Earlier we introduced the matrix-vector equation Ax = b (5.3) Many problems in engineering can be put in these terms, where we know A and b and would like to ﬁnd x. Using some ideas from linear algebra, we could rearrange our equation. A (A −1(Ax) = A −1A)x = A (I)x = A x = A Ax = b −1b −1b −1b −1b (5.4) (5.5) (5.6) (5.7) (5.8) where A −1 is called the inverse of A. By deﬁnition 5.5. OTHER LINEAR ALGEBRA FUNCTIONS 39 −1A = I A (5.9) where I is the identity matrix, e.g., ones along the diagonal and zeros elsewhere. There are two problems with inverses. The ﬁrst is mathematical and that is that not every matrix has an inverse. The criterion to have an inverse is that the matrix must be square, e.g., same number of rows and columns, and must have a determinate (det command in Matlab) that is non-zero. A matrix with these properties is called invertible or non-singular. A matrix that doesn’t have an inverse is called singular. Second is a more practical concern. Even for a matrix −1 given A. Matlab has that is invertible, there are a number of numerical methods for ﬁnding A a command (inv) for just this sort of operation, but due to the limits of numerical accuracy, it sometimes will not be able to return an inverse. >> A = [3 2 -5; 1 -3 2; 5 -1 4]; >> det(A); >> Ainverse = inv(A); %Check to make sure an inverse will work Now if we deﬁne a vector b we can try to solve for x >> b = [12; -13; 10]; Note that b is a 3×1 vector. This situation corresponds to the following set of linear equations. ⎡ ⎤ ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ ⎣ 3 1 −3 5 −1 2 −5 2 4 x1 x2 x3 ⎦ ⎣ ⎦ = ⎣ 3x1 + 2x2 − 5x3 1x1 − 3x2 + 2x3 5x1 − 1x2 + 4x3 ⎦ = ⎣ ⎦ 12 −13 10 Where the vector x is what we want to solve for. In Matlab there are two ways to solve for x. The ﬁrst is to compute the inverse and then solve. >> x = Ainverseb The second reveals the special role played by the \ symbol in Matlab >> x = A\b And you can verify that x really is the solution by >> Ax It is important to note that Matlab uses different numerical methods when the inverse is taken directly and when the \ symbol is used. The \ symbol is nearly always better for both accuracy and time. 5.5 OTHER LINEAR ALGEBRA FUNCTIONS Some other commands that have a direct tie to linear algebra are rank, trace, det (determinate) and eig (eigenvalues and eigenvectors). 40 5. MATRIX – VECTOR OPERATIONS >> Rand = rand(5,5); >> rank(Rand) >> trace (Rand) >> [V,D] = eig(Rand) >> det(Rand) You may wish to view the help for these functions or consult a linear algebra text book. 5.6 MATRIX CONDITION There are some instances when a set of equations are encountered, which in theory have a solution, but it is difﬁcult to compute an inverse numerically. Consider the following system of equations: a + b = 2 a + (1 + (cid:7))b = 3 (5.10) (5.11) where (cid:7) is some small number. We can solve this equation by subtracting Equation 5.11 from Equation 5.10. The result is b = 3 (cid:7) (5.12) so the smaller (cid:7) the larger b will be, and with it, a will become large and negative. Matlab typically does not do well when numbers become too small or too large. We can recast our problem in Ax = b form (cid:10) 1 1 1 1 + (cid:7) (cid:11) (cid:10) (cid:11) (cid:10) = (cid:11) 2 3 a b Note that there is nothing special about x or b, but A is where the problem lies. The idea of matrix condition is a way to quantify how much numerical error will be associated with inverting a particular matrix. The Matlab condition command is cond. To expose this problem in Matlab, try the following commands, where (cid:7) = 1−20 >> A = [1 1; 1 1+1e-20]; >> inv(A) >> cond(A) Although in theory, you should be able to take the inverse of A, Matlab will give an error that the matrix is singular to working precision. 5.7 EXERCISES 1. Turn in the diary for this chapter. 5.7. EXERCISES 41 2. Create a random 25×1 vector, r, using the rand command. Sort this vector using the sort command in DESCENDING order. Turn in your sorted vector in a “.mat” ﬁle. 3. Nearly every ECG device has an automated heart beat detector (detects the peak of the R- wave), and can count the number of beats since turning on the device. The problem is that it requires these counts to be turned into heart rate changes over time. The data is stored in a vector, with each entry as the number of beats per minute, but where the counting of beats from the beginning did not stop at the end of each minute. Below is data from the ﬁrst 7 minutes of recording. (cid:8) a = 0 64 137 188 260 328 397 464 (cid:9) Use the diff command to take the difference between each value. Note that the length of the difference is one less than the length of the original vector. Find the average heart rate over these 7 minutes. Show your commands in a diary ﬁle. 4. The Nernst Equation is used to compute the voltage across a cellular membrane given a difference in ionic concentration Ek = RT F ln (cid:11) (cid:10) [K]e [K]i (5.13) where Ek is the Nernst Potential in mV , R is the Ideal Gas constant (1.98 cal K·mol ), F is Faraday’s constant (96480 C mol ) and [K]i and [K]e are the concentrations of intracellular and extracellular Potassium in mM respectively. While working in a lab you recognize that in performing repeated cellular experiments, you must know the value of the Potassium Nernst potent. In the experiment, you can control the temperature and the extracellular concentration of Potassium. To avoid needing to compute the Nernst Potential each time, you decide to create a lookup table, i.e., a matrix, containing the Nernst Potentials, thus avoiding the need to perform a new calculation for every experiment. Begin by typing in the following commands >> Temp = [280:5:320]; >> Ke = [0.5:1:29.5]; >> R = 1.98; >> F = 96480; >> Ki = 140; 42 5. MATRIX – VECTOR OPERATIONS You then recognize that you can form Ek from two vectors A = RT F B = ln (cid:11) (cid:10) [K]e [K]i Ek = A ∗ B where AB is an outer product. Note that you will need to use the log command in Matlab and make sure that your vectors are the appropriate dimensions for an outer product. Store your result in the matrix Ek as a “.mat” ﬁle 5. As a biomedical engineer you may be interested in designing a bioreactor for cell culture. A typical chemical formula for aerobic growth of a microorganisms is C2H5OH + aO2 + bNH3 → cCH1.7H0.15O0.4 + dH2O + eCO2 where term CH1.7H0.15O0.4 represents metabolism of the microorganism. The ratio of moles of CO2 produced per mole of O2 consumed is called the respiratory quotient, RQ, which can be determined experimentally. Given this ratio we have 4 constants, a-d that are unknown. We can perform a mass balance on each of the four key elements Carbon : 2 Hydrogen : 6 + 3b Oxygen : 1 + 2a N itrogen : b = c + (RQ)a = 1.7c + 2d = 0.4c + d + 2(RQ)a = 0.15c in matrix notation ⎡ ⎢ ⎢ ⎣ 0 −3 0 RQ 0 −2 0 − 1 0.15 1 0 1.7 2 0.4 1 0 ⎤ ⎡ ⎥ ⎥ ⎦ ⎢ ⎢ ⎣ a b c d ⎤ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 2 6 1 − 2RQ 0 Let RQ = 0.8 and then ﬁnd the vector [a b c d] using Matlab’s matrix solve. Turn in a diary and “.mat” ﬁle with the ﬁnal vector. C H A P T E R 6 43 Scripts and Functions INTRODUCTION 6.1 In this chapter, we will learn about two related ideas that allow Matlab to be a very powerful all- purpose engineering application. The ﬁrst is the idea of a script and the second is the concept of a function. It will often be the case, that future homework problems will require you to write either a script or a function. SCRIPTS 6.2 You may have found in previous sections that you would often type in a number of statements on the command line in some sequence. For example, imagine trying to set up the following matrix. ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 0 1 2 0 0 4 6 8 0 0 3 12 4 0 0 0 0 0 0 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ 0 0 0 8 10 One strategy would be to enter the entire matrix on one line. A second, more reasonable strategy may be to recognize that you might create a few diagonal vectors using the diag command. The problem is that you will need to issue a sequence of statements to the command line in the right order. For a 5×5 matrix, this may not be all that bad, but imagine if this were a 200×200 matrix. To make matters even more difﬁcult, there are many computer algorithms that would require thousands of lines to be typed in one by one. One mistake might mean reentering all commands from the beginning. To overcome this problem, Matlab makes it possible to create a script - a text ﬁle that con- tains all of the commands to be entered in sequence. We will use the matrix above to motivate the creation of our ﬁrst script. >> edit MyFirstScript The edit command in Matlab opens up the Matlab text editor. The second argument is the name of a ﬁle where the script will be saved. In fact, the ﬁle will be called ‘MyFirstScript.m’ where the ‘.m’ designates that the ﬁle is a Matlab script. It is important to know that any text editor will do (a script ﬁle is simply a text ﬁle), but Matlab’s editor has some built in functions that can help you check for errors. Enter the following commands into the script ﬁle 44 6. SCRIPTS AND FUNCTIONS DiagVec = [1 4 3 4 10]; UpDiagVec = [2 6 12 8]; A = diag(DiagVec) + diag(UpDiagVec,1); A(2,4) = 8; %Create Diagonal Vector %Create Upper Diagonal Vector %Create Matrix %Add in one more value in the second row, fourth column Note that you can include % followed by comments. Matlab will not execute anything on the line that follows a %. Now save the ﬁle and close the editor. You should see the ﬁle MyFirstScript.m in your folder directory window. To issue the commands in your script to the Matlab command line, you simply enter >> MyFirstScript >> whos >> A Matlab will literally enter the commands one at a time in sequence. This method of computing is called interpreted programming or scripting and is the default in Matlab. You should notice that from this point onward, any command that contains >> is meant to be entered on the command line. If no >> is included, it means you should include the command in a script. 6.3 GOOD PROGRAMMING HABITS It was mentioned above that some programs could contain thousands (maybe even millions) of lines of code. In such a long program, it would be very easy to become lost. Below we will discuss some ways to make your code more easy to read. 6.3.1 COMMENTS AND VARIABLES The ﬁrst script created above was relatively simple and an experienced Matlab programmer could easily decode its intent. As you become more versed in Matlab, your scripts will become more complex and much more difﬁcult to understand. Comments are the key to explaining complex code. Imagine two scenarios when you are including comments: 1) If you handed your code to another Matlab programmer, could they follow what you were trying to do? 2) If you came across your own code ﬁve years from now, would you remember what you were doing and why? There are some standard ways of commenting that can be very helpful. First is to include a purpose at the top of your script. It is helpful to include in this statement a date or version number. In this way, if you create a newer version you will not confuse the two. If you are writing code which may someday be shared with another programmer, you should include your name as the author. Second, it is very helpful to add comments to any variables you deﬁne, along with units and a brief note on the relationship to your problem. For example, if you are solving a circuit problem, you may initialize a vector, v, at the top of your script that will contain a vector of voltages at each node >> v = zeros(4,1); %Voltage vector at nodes in mV 6.4. SCRIPT EXAMPLE - THE RANDOM WALK 45 Third, there are often blocks of code (ranging from a few lines to hundreds) which together perform some subprocess of the entire script. In these cases, it is helpful to have a header at the beginning of each block of code that explains the lines below. For example, the matrix, A above may have been created as the resistance between nodes, i.e., the coefﬁcients of simultaneous equations. Furthermore, you should include the following line to “MyFirstScript.m”. %%--------------Create Coefficient Matrix for Circuit--------------- The double percent sign is a feature of Matlab 7 or later and allows what is know as Cell Mode. In Cell Mode, regions of code will be blocked together and easy to identify as a functional unit in the code. Fourth, there may be Matlab commands which require some explanation (you do not need to enter the command below) A(g(l),h(m)) = sum(min(B(g(i)-10:g(i)+10,B(h(i)-10:h(i)+10))))); Although a command such as the one above may make sense at the time, it has so many embedded functions and indices that it will be difﬁcult to understand what is going on. A comment can help in these cases. Lastly, it is often helpful to use indentation to make the beginning and end of a functional block of code. This concept will become more clear in Chapter 7. 6.3.2 CATCHING ERRORS AND DISPLAYING TEXT There are two commands in Matlab that can allow you to be alerted to errors and display information. Open up the ﬁle “MyFirstScript.m” and add the following line between the third and fourth line disp('Diagonals created, now entering off diagonal entries'); In more advanced programs you may also want to be able to report out any errors. To view how this will work, enter the following on the last line of your ﬁrst script error('Check to make sure matrix is non-singular first!'); Try running the script with these two additions and observe the results. You may want to view the help ﬁles to understand more about the features of disp and error. Do not be alarmed when the error command sends a text to your screen in red. The difference between disp and error is that disp will simply send text to the command line and continue on with your script. On the other hand, error will display text in red and then terminate your program. 6.4 SCRIPT EXAMPLE - THE RANDOM WALK A bacteria placed in a uniform concentration of nutrients will follow what is known as a random walk. There has been much written on random walks, in ﬁelds as diverse as thermodynamics, 46 6. SCRIPTS AND FUNCTIONS economics and history. In a biological context, a random walk can be thought of as a search process, e.g., for food, light or a potential mate, when there are no outside cues. To program a random walk, open a script ﬁle called “RandomWalk.m” and enter the initial x − y position on the ﬁrst line. C = [1,1]; %Initial Coordinate Next, we deﬁne a random distance to move in the x and y directions Move = randn(1,2); % get next move and, lastly, move to a new spot C = [C; C+Move]; % make next move relative to current position The line above requires some explanation. In the ﬁrst line of our script we created a vector [1 1]. In the second line we created a direction vector, [NextCx NextCy]. In the third line, we are turning C into a matrix. The ﬁrst row of the matrix will contain the ﬁrst x-y coordinate and the second row will contain the second x-y coordinate (C+Move). To make another move Move = randn(1,2); C = [C; C(end,:)+Move]; % make next move relative to current position % get next move Here the general idea is the same as above, we are adding a third location to the bottom of the matrix C, which is now 3×2. The seemingly strange indexing (C(end, :)) is to keep the dimensions uniform. Remember that Move is a 1×2 vector and can only be added to another 1×2 vector, in this case the current last row of C. Try running your script to be sure that it works. Then try adding 8 more lines of the Move and C commands to your script. At the bottom of your script include the following line plot(C(:,1),C(:,2)) %Plot the random path traversed You should see that the x-y position of your bacteria has been printed out. An enormous advantage of a script is that you can run your script again very easily without needing to reenter each command one at a time. And due to the nature of a random walk, you should get a different result each time. 6.5 FUNCTIONS In 1962, Herbert Simon, a pioneer in the ﬁeld of artiﬁcial intelligence and winner of the Nobel Prize in Economics, wrote an article called, “The Architecture of Complexity”. In it was a parable of a watchmaker who is interrupted every few minutes to answer the phone. In frustration the watchmaker develops a solution - make a number of very simple parts that take less time to create, then assemble these simpler parts together into the watch. In this way, if interrupted, the watchmaker will know where to pick up after an interruption. Simon’s conclusion was that any system that is sufﬁciently complex will only become so, and continue to function, if it is arranged in some sort of hierarchy. Simple operations are put together to make more complex functions and so on up the hierarchy. 6.5. FUNCTIONS 47 The computational equivalent of building a hierarchy is to split up a long and complex pro- gramming assignment into smaller functions (also sometimes called subroutines). The simpler functions can then be combined together to perform the more complex task. The reason for programming this way is four-fold. First, and already mentioned above, is clarity. Imagine that you write a long section of code, leave it for a year and then come back to it. Will you know where you left off? This has echos of the watchmaker parable above. A function can help make clear what has and has not already been ﬁnished. Second, it is much easier to ﬁx small sections of code as you go. This is the idea of debugging, a topic that will be discussed at the end of this chapter. Third is reuse of code. There are often times when a particular function will be used more than once in a single programming assignment. And there are many instances where a particular function may be used again in a completely separate assignment. For example, a function that builds an adjacency matrix is a task that might be reused by programs for cardiac, neural, gene, social and ecological networks. Fourth is collaboration. Functions allow teams of programmers to coordinate their work to solve very large problems. 6.5.1 INPUT-OUTPUT The coordination that would be required to collaborate is contained largely in how a function will transform inputs into outputs. Below is the general form that would allow a function to be called from the Matlab command line OUTPUTS = FunctionName(INPUTS); It may come as no surprise that many of the operations you have been using in Matlab are really just functions that are part of the Matlab distribution. To view how a built-in function is written in Matlab, use the type command >> type mean which will display the actual Matlab code that is executed when you use the mean command. You should ﬁrst notice that the ﬁrst line of mean contains a function declaration with the following form function y = mean(x,dim) The key word function tells Matlab the following ﬁle will be a function with the form OUTPUTS = FunctionName(INPUTS). It is important that your “FunctionName” is also the name of the script ﬁle you created. In our example, the text ﬁle that contains the mean function is called “mean.m”. Therefore, if you create a function called “SquareTwoNumbers”, your text ﬁle would have the name “SquareTwoNumbers.m” and would have a ﬁrst line of [xsquared,ysquared] = SquareTwoNumbers(x,y). Following the function declaration for mean is a long section of code that is commented (%) out. This is in fact the help for the mean command. One very nice feature of Matlab is that 48 6. SCRIPTS AND FUNCTIONS the code and help information are all in the same ﬁle. When you write a function, it is good programming form to always include a help section. And you should follow the convention used in Matlab of explaining the format for the inputs (are they scalars, vectors or matrices?) and outputs. It is also helpful to have a few brief words on how the function works. You should note that not all built-in Matlab functions are “.m” ﬁles. >> type sum will return “sum is a built-in function”. There are a number of core Matlab functions that have been compiled. The reason to compile a function (as opposed to running it as an interpreted script) is that it will run much faster. Although we will not discuss them here, Matlab has a way of deeply compiling your own functions. You can ﬁnd out more about this by typing “help mex”. 6.5.2 INLINE FUNCTIONS Matlab does allow users to create what are called inline functions. These are functions that appear in the same text ﬁle. Although they can be very useful in some situations, we will not discuss them here. 6.5.3 THE MATLAB PATH You have already seen that Matlab has built-in functions, some compiled and some as scripts. But all of these scripts are stored in directories and chances are very good that you are not in those directories. Matlab needs to know how to ﬁnd “mean.m” when you use that particular function. For this reason, Matlab contains a list of directories to search for “mean.m”. You can see this list by typing in >> path The advantage of the path is that you do not need to tell Matlab where to look for built-in functions. The disadvantage is that if you write a new function, and are not in the directory that contains your new function, Matlab will not know where to look for it. There are two potential solutions. First, you could simply move into the directory that contains your function. For simple programming exercises this is your easiest solution. In a large programming assignment, however, you may wish to have several directories to help organize your functions. In this case, you will need to add a search path to Matlab. You can view the help for path to see examples for your particular operating system. You may also use the addpath command. One additional consideration when naming functions is that Matlab already has a number of functions. If you name your new function the same as a built-in function, Matlab may become confused as to which function to use. It is a good idea to use unique names for your functions. 6.6. DEBUGGING 49 6.5.4 FUNCTION SIZE So how big should your function be? The answer will depend upon the nature of your problem. In general, a function is meant to achieve one task. It should be something that a user could pick up and have a good idea of how it will work. On the other hand, the task should not be trivial. The balance of these two will change as you become a better programmer. For now, you should focus on writing short, simple functions and nest them in a hierarchy - i.e., use simple functions to build functions of medium complexity and then use the medium complexity functions to create more complex functions, and so on. 6.6 DEBUGGING In writing both scripts and functions it is very helpful to have some techniques for debugging your code. First, Matlab does have a built in debugging tool. Although we will not discuss the debugging tool here, you can ﬁnd out more information by viewing the help for the debug command. Second, trying to write all of your code at once may help you organize your ideas, but you should not expect it to run properly. Rather it is good programming practice to write your code in small sections, testing them out as you go. In this way, you can add a line or two to your program and then test them out to be sure they work. If there is an error, you will know that it has occurred in those lines. Third, you can take the semi-colon off of any line in a Matlab script and the output will be sent to the command-line as the script runs. The advantage is that you can check to make sure that scalars, vectors or matrices look right. The one danger in this method of debugging is that you might overload the command line, e.g., sending a 1000×1000 matrix to the command line is not a good idea. Rather, you may create a new variable that will give you the information you need to know. For example, to perform a quick check on a 1000×1000 matrix you might simply include the following line [N, M] = size(A) which will allow you to see the size of your matrix on the command line. Alternatively, it might be the sum or spy command that you may want to use to help you debug. When it comes to writing functions, it is often a good idea to write your desired function as a script ﬁrst. In this way, you can simply put the inputs and outputs at the top of the ﬁle and change them by hand. Once you become conﬁdent that your code is working the way you intended, you can turn it into a function. 6.7 USER INPUT Earlier it was mentioned that a good Matlab function has deﬁned inputs and outputs. In a large program, one function may call another, which called another, and so the output of one function may become the input to another function. But often, we also want our program to be interactive, meaning that the user can change inputs that impact the ﬂow of the program. 50 6. SCRIPTS AND FUNCTIONS 6.7.1 INPUT There are times when you may wish to allow the user to enter some input to a script or function. The input may be to make a decision about how to proceed, e.g., perform algorithm 1 or algorithm 2, change a parameter value, e.g., coefﬁcient or an initial condition, or even terminate the program. The command in Matlab to use in these instances is input. result = input('The rate constant is-->'); When placed in a script (or function), the text “The rate constant is –>” will be displayed on the command line. Matlab will then wait for the user to enter a command. Once the user enters a number and presses enter, that number will be stored in the variable result and will then be available to the rest of the script. The input command can be used to return any Matlab data type. 6.7.2 GINPUT You will create a new script that contain the following commands. Name your script ﬁle “MySec- ondScript”. First, create the matrix A in Matlab and then use the imagesc command to visualize it in a ﬁgure. ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ A = 6 1 2 0 0 4 6 8 2 0 3 12 4 8 2 0 0 7 0 5 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ 1 0 2 8 10 Next, you should also add a color bar using the colorbar command. On the next line you should include the following line [x, y] = ginput(2); The meaning of the line above is to bring up a cursor which you can move around with your mouse. When you click your right mouse button, the x-y, coordinate of that ﬁrst click will be stored in the value x and y. But the argument to ginput is a 2, meaning that the command will wait for 2 clicks of the mouse. Save and run your script and then try clicking two different points on your ﬁgure. View the 2×1 vectors x and y to verify that they have selected the coordinates of your mouse clicks. 6.8 FUNCTION EXAMPLE The random walk script created above was able to simulate the random movement of a bacterium.The script was limited in at least two ways. First, there was no way for the user to specify parameters from the outside. Second, two lines were repeated over and over again. In a preview of the next chapter, we will begin by tackling this second problem. Open up a script called “RandomWalkReprise.m” and enter 6.8. FUNCTION EXAMPLE 51 figure(1) hold on C = [1,1]; for i=1:10 %Initial Coordinate Move = randn(1,2); C = [C; C(end,:)+Move]; % make next move relative to current position plot(C(end-1:end,1),C(end-1:end,2)); pause(1) % get next move end plot(C(:,1),C(:,2)) The ﬁrst two lines create a blank ﬁgure and then make sure that every future plot command will be sent to Figure 1. The next line creates the initial coordinate. The following line contains what is known as a for loop. You will learn much more about loops in the next chapter. For now, all you need to know is that Matlab will execute the commands between the for and end ten times, e.g., 1:10. The ﬁrst two lines inside the for loop are familiar. The plot command should also be familiar, but you should make sure that you understand the indexing (hint: we are drawing a line from the previous point to the current point each time through the loop). The last line in the for loop will pause for one second to give you a chance to see what is happening. Run the script and observe the results. Now that the script is working, we can begin to make it more general. Copy RandomWalkReprise.m to RandomWalkReprise2.m and modify the new script to match the code below Initialx = [2,1]; NumLoops = 50; pausetime = 0.2; %Initial coordiate %Number of steps to take %Duration of pause figure(2) hold on C = Initialx; for i=1:NumLoops %Change to not confuse with previous script %Initial Coordinate Move = randn(1,2); C = [C; C(end,:)+Move]; % make next move relative to current position plot(C(end-1:end,1),C(end-1:end,2)); pause(pausetime) % get next move end plot(C(:,1),C(:,2)) In this version of the script, all of the values which we want to be user deﬁned have been placed at the top of the script. The last step is to turn I nitialx, NumLoops and pausetime into inputs to a function, called “RandomWalk”, with the matrix C as the output 52 6. SCRIPTS AND FUNCTIONS function C = RandomWalker(Initialx, NumLoops, pausetime) figure(2) hold on C = Initialx; for i=1:NumLoops %Initial Coordinate %Change to not confuse with previous script Move = randn(1,2); C = [C; C(end,:)+Move]; % make next move relative to current position plot(C(end-1:end,1),C(end-1:end,2)); pause(pausetime) % get next move end Then on the command line try >> clear >> C = RandomWalker([3,4], 400, 0.01); >> whos The last important note about functions is that when they are completed, Matlab’s memory will contain only the inputs and outputs. For example, Move is a variable that is used only internal to the function and therefore does not show up in Matlab’s memory after the function has completed. 6.9 EXERCISES 1. Turn in the “.m” ﬁles MyFirstScript.m, MySecondScript.m, RandomWalk.m, Ran- domWalkReprise.m, RandomWalkReprise2.m and RandomWalker.m. 2. Epidemics occur when an infection appears seemingly out of nowhere, spreads throughout a population, sometimes disappearing just as suddenly. The Kermack-McKendrick model describes the number of susceptible, xn, the number of infected, yn, and the number of removals (quarantined, immunized), zn. For a constant population we can assume xn + yn + zn = N. Once N is set, we therefore only need to know two of the variables to know the remaining variable. The dynamics of Kermack-McKendrick model are xn+1 = xne−ayn yn+1 = (1 − e−ayn)xn + byn (6.1) (6.2) where e can be represented by the exp function in Matlab, a and b are constants. First, create a script called ‘KMmodelScript’ that has the following lines at the top a = 0.02; b = 0.0; xn = 25; yn = 5; 6.9. EXERCISES 53 Then add two more lines xn1 = ? yn1 = ? where you ﬁll in ? with the Kermack-McKendrick model. You must turn in this script. Next, create a function called “KMmodel” that will take as inputs a, b, xn and yn and output xn+1 and yn+1. You then must create a script called ’KMmodelFunctionTest’ that contains the following lines a = 0.02; b = 0.0; xn = 25; yn = 5; [xn1,yn1] = KMmodel(a,b,xn,yn); Turn in KMmodel.m and KMmodelFunctionTest.m. 3. One way to model the dynamics of a population of a particular species is to think of it as a series of generational groups, for example, infants, juveniles, mature and post-reproduction. In all cases, as the years go by, some animals will move from one category to another, some will die, others will be born as infants. We can deﬁne a vector xn = ⎤ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎣ xn inf ant xn j uvenile xn mature xn old Then we can hypothesize that there is a matrix, A, which will transform xn to xn+1 xn+1 = Axn (6.3) Such a matrix is called a stage structure matrix. From 1973 to 1987 Brault and Caswell studied killer whale populations and developed the following A matrix ⎡ ⎢ ⎢ ⎣ A = 0 0.0043 0.1132 0.9775 0.9111 0 0.0736 0.9534 0 0 0 0.0452 0.9804 ⎤ ⎥ ⎥ ⎦ 0 0 0 Moving the current population forward one year therefore requires multiplication by A. Mov- ing the population forward by two years requires two multiplications by A 54 6. SCRIPTS AND FUNCTIONS or xn+1 = Axn xn+2 = Axn+1 xn+2 = AAxn xn+2 = A2xn (6.4) (6.5) (6.6) (6.7) (6.8) Therefore, if we want to predict the population at any year in the future we can use the idea of matrix exponentiation xn+2 = AAxn xn+y = Ayxn (6.9) (6.10) (6.11) where the exponent y is the years in the future. Write a function (“PopulationStage”) that will take in any current population vector x, a stage structure matrix A and predict the population at any given year y. Write a script to test your new function with the A as deﬁned above and a current population vector x = [10, 60, 110, 70]. Show that you can predict the population 50 years into the future. C H A P T E R 7 Loops 55 7.1 INTRODUCTION One of the prime purposes of using a computer is to automate a task that would be very tedious to perform by hand (either with pencil and paper or on a calculator). The usual implication is that some task is to be performed over and over again in some systematic way. This chapter will be concerned with the programming concept of a loop, a feature that is at the heart of nearly every computer algorithm. Perhaps the most important concept to understand about loops is the least intuitive; how to get them to stop. In fact, the method of stopping a loop is often how they are classiﬁed. In this chapter, we will explore the for loop in detail and wait until the next chapter to explore the while loop. 7.2 THE FOR LOOP There are often algorithms where you know ahead of time exactly how many times an operation must be performed before stopping the loop. For example, if we must perform some data analysis and know that there are 1037 points, there should be some way to move from point 1 (perform the analysis) to point 2 (perform the analysis) to point 3, and so on. In Matlab, and nearly all other programming languages, this type of operation is performed by a for loop. In Matlab, the most basic type of for loop is the following (do not enter the following commands) for i = 1:200 COMMANDS HERE end There are four parts to any for loop. The ﬁrst is a variable (in this case, i) that will be used to keep track of the number of times through the loop. The second is the values the variable i will take on as it repeats. In our example, i will start by taking the value 1, then 2, then 3 and so on until reaching 200. Third is to place a bound on what will be looped over, denoted in Matlab by the keyword end. Fourth are the commands that will be executed (there can be as many as needed) between the for and the end lines. Note that this is a good example of us- ing indentation to make clear where the loop starts and ends, as well as the commands to be executed. To better understand how loops work, analyze the following code. 56 7. LOOPS x = 1; for i = 1:5 x = x + 1; end In this code, the variable x will start at a value of 1. Then the loop will begin with i = 1. On the ﬁrst pass through the loop, x will be increased by 1 (e.g., x = 2). On the second pass through the loop, (i = 2) x will be increased again by 1, e.g., x = 3, and so on until i = 5. It should be noted that there is no reason why you must start a loop at 1. The following will all yield valid loops (do not enter on the command line, simply view the lines below): for i = 89:108 for i = -27:38 for i = 234:20 for i = 23.5:57.5 You should see that you can start at any number (positive, negative or even a non-integer) and then loop up or down. 7.2.1 FOR LOOPS OVER NON-INTEGERS You probably noticed that the colon notation was used to specify that Matlab should loop from some number to another number in increments of 1. There are often cases where we would like to increment by some other value. For example, imagine that you would like to assign a value at points along a line of length 1cm every 0.01cm. dx = 0.01 for x = 0:dx:1 v = xˆ3 + xˆ2 + 3 end Upon executing the commands, you should see the values of v on the command line. 7.2.2 VARIABLE CODING Above we deﬁned a variable dx to specify how much to increment each time through the loop. There is no need to do this, e.g., for x = 0:0.01:1 would have worked, but it demonstrates the good programming practice of variable coding as opposed to hard coding. In hard coding, we simply write out all of the numbers in our program, e.g., type in 0.01 for dx everywhere in the code. In soft coding, we deﬁne a variable, e.g., dx, and then use that variable throughout the program. There are two reasons why it is good practice to use variable coding. First, by deﬁning a variable dx, we can signal that there is some actual meaning (here a spatial size) to the variable. Second, if at any point in time you would like to change dx, you can make the change in one place, eliminating the need to search for all places where a step size is needed. 7.2.3 FOR LOOPS OVER AN ARRAY A second trick that is often helpful is to loop over some array that has already been created 7.2. THE FOR LOOP 57 >> a = [2 50 34.5 27 91]; >> for i = 1:length(a) >> >>end 2a(i)+100 %Any command here that requires a(i) Here a vector a is created before the loop. The goal is to progress through the entire vector one element at a time, e.g., a(i), performing operations on that element. Note that, in this case, the variable i is playing two roles. It is the loop variable, but it is also the index to the vector, s. This is one of the most powerful aspects of having a loop variable. 7.2.4 STORING RESULTS IN A VECTOR There are two problems with the above script. First, sending the output to the command line makes it difﬁcult to interpret trends in the results. Second, we do not have any record of the resulting calculation. To ﬁx both problems, we can use the loop variable i. Enter the following into a script. % spatial step in cm % create space vector dx = 0.01; space = 0:dx:2; %Allocate memory for a Concentration vector Concentration = zeros(length(space),1); for i = 1:length(space) %Any command here that requires a(i) Concentration(i) = space(i)ˆ2; end plot(space,Concentration) In this example, a space vector is created. Then the a vector Concentration is built up one element at a time by looping over the entire space vector. The catch is that the space vector is also used to create the Concentration vector. As shown in the plot, the above commands create a concentration gradient in space. A careful reader may realize that the above section of code could have been created much more efﬁciently without any loops, by using a simple element-wise vector multiply dx = 0.01; space = 0:dx:2; Concentration= space.ˆ2; plot(space,Concentration) % spatial step in cm % create space vector % simple element-wise operation 58 7. LOOPS In fact, if faced with this type of problem you should choose the above solution, as loops are generally much slower than matrix-vector operations. There are, however, many instances where a problem can not be decomposed into matrix-vector operations. One such case is when you must know one result to compute another result, as in the Kermack-McKendrick difference equation in the previous chapter. A second example is the numerical integration of a differential equation. 7.3 EULER INTEGRATION METHOD Great emphasis is often placed on solving differential equations, meaning that a closed form analytical solution can be written down. The vast majority of differential equations, however, can not be solved analytically. This is especially true for biological systems, where the equations that govern how quantities change are almost always non-linear. In cases where a differen- tial equation can not be solved analytically, we can approximate a solution numerically. There are a number of numerical integration methods, but the simplest to understand is the Euler Method. At the heart of the Euler Method is knowing where you are (current state) and where you ˙V t . We are headed (slope). In Figure 7.1, we deﬁne the current state as V t and the current slope as can then approximate the slope as If we now pick a (cid:8)t we can predict where V will be at time = t + (cid:8)t dV dt = ˙V t = (cid:8)V t (cid:8)t V t+(cid:8)t = V t + (cid:8)V V t+(cid:8)t = V t + (cid:8)t · ˙V t (7.1) (7.2) (7.3) Note that on the left-hand side is the prediction at time = t + (cid:8)t and on the right-hand side are all terms at time = t. In the ﬁgure, the predicted V t+(cid:8)t is not the exact solution, i.e., it does not fall on the solid line. But, as (cid:8)t is made small, the approximation will become better and better. The generic approach of moving step-by-step through a differential equation is called nu- merical integration. The ability to integrate a differential equation (even a non-linear one) is a very important role for computer programming. And the Euler Method will work even if the independent variable is something other than time. You should also note that there are many more numerical integration methods that we will touch upon in future chapters. 7.3.1 NUMERICAL INTEGRATION OF PROTEIN EXPRESSION To demonstrate how the Euler Method works in a real situation, we will integrate the differential equation for protein expression. 7.3. EULER INTEGRATION METHOD 59 . Vt t+Δt V ΔV Vt Δt Figure 7.1: Demonstration of Euler Method. The dotted line indicates the slope of V at time t. The solid line indicates an analytical solution. dY dt f (X) = = f (x) − αY βX K n + Xn (7.4) (7.5) The differential equation above explains how a protein X can promote the upregulation of a gene that produces protein Y . The term −αY expresses how over time the concentration of Y will fall due to protein degradation and cell division. The constant term α describes the rate at which this loss of Y will occur. The term f (X) governs the upregulation of Y , e.g., increase in concentration of Y , and is dependent upon the concentration of X. The form of f (X) can vary, but we have chosen to use the Hill equation for a promotor protein. The Hill equation has three variables. K is the activation coefﬁcient and governs how much of X must be present to cause Y to be expressed half as much as the maximum expression rate. β is the maximum expression, and the ex- ponent n governs how quickly a promotor can switch from on to off as a function of X concentration. Using some fancy analytical technique, we may be able to solve the equation analytically, but the Euler method and some basic programming skills will allow us to investigate the meaning of the parameters much more easily. alpha = 1.0; %Degradation of Y 60 7. LOOPS beta = 1000.0; K = 20; n = 3; %Hill Maximal Expression Level %Hill Half-Maximal Activation %Hill Exponent %Create time vector dt = 0.01; EndTime = 20; time = 0:dt:EndTime; %Find Rate of Y production given concentration of X %Concentration of Promotor x x = 10; fx = betax/(Kˆn+xˆn); %rate of Y production %Initialize Y concentration vector Y = zeros(length(time),1); Y(1) = 0.0; %set to 0 but could be changed %Loop over time using Euler Method for i = 2:length(time) Y(i) = Y(i-1) + dt(fx-alphaY(i-1)); end %Plot out expression of Y over time plot(time,Y); Running the script above should result in a plot of the time course of Y expression. You will revisit this example in an exercise below, so save your script as “ProteinExpressionScript.m”. 7.4 THE LOGISTIC EQUATION REVISITED In Section 2.6, the logistic equation was described as zn+1 = rzn[1 − zn] (7.6) where zn is the current value of z, zn+1 is the next value of z and r is a constant. For example, we will set r = 3.2 and the initial population value to z = 0.5, e.g., half of the maximum. In our previous use of the logistic equation, we simply reentered the command over and over again. Now with scripting and loops, we can automate the process. Enter the following commands into a script called “Logistic.m”. r = 3.2; Initialz = 0.5; %constant for logistic equation %initial condition N = 100; z = zeros(N,1); z(1) = Initialz; for i=2:N 7.5. THE WHILE LOOP 61 %number of iterations to perform %Create vector to store z %Set first value to initial z(i) = rz(i-1)(1-z(i-1)); %Start at 2 because we already z(1) %calculate next value end plot(z) The script above will iterate through the logistic equation 100 times and then plot the results. 7.5 THE WHILE LOOP There are times when it is not possible to know exactly how many times a loop should be performed. It is still very important, however, to have some way to stop the loop from iterating forever. In these types of situations, you may use a while loop. Because while loops require checking a logical condition, e.g., is some variable larger than some other variable, we will not discuss while loops until the next chapter. 7.6 NESTED LOOPS Loops are assigned a variable for two purposes. The ﬁrst is so that the variable can be used to perform some useful function, e.g., as an index to an array or matrix. The second is because loops may exist within other loops, and we need variables to make it clear where in the iteration sequence we are. Do not enter the commands below. for i=1:N for j=1:M COMMANDS HERE end end In the template code above i is set to 1, then j is looped from 1 to M. Then i is set to 2 and j is again looped from 1 to M and so on until i = N. You are certainly not limited to two nested loops, and you can mix and match for and while loops as needed. Below we discuss two situations where this type of nested loop structure can be very useful. 7.6.1 LOOPING OVER MATRICES There are situations where it may be helpful to move systematically through a matrix. For example, consider that a bacterium is capable of swimming up a sucrose gradient to reach a plentiful supply of nutrients. If we were to simulate a bacterium swimming in such an environment, one of our ﬁrst 62 7. LOOPS steps would be to create a concentration gradient. Let us assume that we will create a gradient that is low in the middle of a 200×200 grid and increases as we radiate outward from the center. The problem is that we can not simply issue a few diag (or other Matlab) commands to create our matrix. We must move through each point on the grid and compute its distance from the center. C = zeros(200,200); CenterPoint = [100 100]; dx = 0.01; %[xcoordinate ycoordinate] %spatial step size %compute real physical location of center CenterLocation = CenterPointdx; a = 2.5; %scale factor for distance-concentration for i = 1:200 for j = 1:200 %x loop %y loop %x location %y location XL = dxi; YL = dxj; DistanceFromCenter = sqrt((XL-CenterLocation(1))ˆ2+ ... (YL-CenterLocation(2))ˆ2); C(i,j) = aDistanceFromCenter; end end imagesc(C); colorbar In the line that created DistanceF romCenter we used another feature of Matlab. There are some cases where a line must be very long, and therefore can be difﬁcult to read. The “...” means to continue the command onto the next line. It is important to note that we could have easily created a more general script by not as- suming the grid would be 200 x 200. We also have the ﬂexibility to make the center point anywhere on the grid we would like. Set CenterP oint to [50, 75] and create a ﬁgure called “SucroseGradient.jpeg” showing the result. Can you see how you might turn a script such as the one above into a general function? Can you also see how you could create three nested loops to create a 3D gradient? There are other situations where you may need to use nested loops to move through a data structure, but you should use it only as a last resort. If you can ﬁnd a way to perform an operation without loops, it will generally execute much faster. 7.6.2 PARAMETER VARIATION In Section 7.4, a function was created to iterate through the logistic equation. In this section we will explore how the dynamics of the logistic equation change as the parameter r is varied. Copy the ﬁle “Logistic.m” to a new script called “LogisticBifurcation.m”. r = [2:0.001:4]; % create vector with r values 7.6. NESTED LOOPS 63 figure(1) hold on for j = 1:length(r) Initialz = 0.5; N = 1000; z = zeros(N,1); z(1) = Initialz; for i=2:N % loop over the r vector %CHANGED TO 1000 %calculate next value of x using current r value z(i) = r(j)z(i-1)(1-z(i-1)); end %create a vector with all values of r(j) rvec = r(j)ones(500,1); %only use the last 500 values of z truncatedz = z(501:end); %plot points, but do not connect lines plot(rvec,truncatedz,'.'); end %End r loop In the script above, one loop is used to systematically change r and a second loop is used to perform the iteration of the logistic equation. You should notice that some of the skills learned in the sections above have been used here, for example, creating the r vector ﬁrst and then looping through it with the loop variable j . You should also notice that we created two temporary variables, rvec and truncatedx, for the purposes of removing any of the initial dynamics (transients) of the logistic iteration. Here we are only interested in the long-term behavior. Save your bifurcation plot in a ﬁgure called “LogisticBif.jpeg”. We can now turn to the meaning of the plot. On the x-axis, is the parameter r that we var- ied from experiment to experiment. On the y-axis we have done something a bit unusual - 64 7. LOOPS we have plotted the entire time series on top of one another. To gain insight into the logistic behavior at a particular value of r, we can simply draw a vertical line upward to see where it intersects values for z. If z has reached a steady-state, it will appear as only one point because every point is the same. On the other hand, if z oscillates between two values, our vertical line will intersect at 2 points. You should notice in your plot that as r is increased, we move from steady-state to oscillating between 2 z values, to oscillating between 4 z values, to 8 z values and so on. There are two points about the plot you have created that are important in many biological systems. The ﬁrst is that as r is changed, the system moves from one type of behavior to another, e.g., from steady-state to oscillating. What is most striking is that the transition is abrupt and occurs at a particular value of r. These types of abrupt transitions are called bifurcations and are found in many biological systems. The parameter r is called the bifurcation parameter. In the logistic equation, there is only one parameter, r, that needs to be varied to drive the system through a bifurcation. In many biomedical problems, however, it is some combination of variables that will move the system through a bifurcation. Systems with bifurcations are excellent candidates for parametric studies and highlight one of the strengths of using computation to study biological systems. The second important point is that for some values of r, the behavior of the logistic equa- tion becomes chaotic. It is easy to see from the plot that as r is increased, the period of oscillation doubles, then doubles again, then again, and so on. The meaning is that the time series will visit ﬁrst 1, then 2, then 4, then 8, and then 16 unique values of z. This doubling continues until the period is inﬁnite. The meaning of an inﬁnite number of possible values for z is that there is no longer any deﬁned period, e.g., the behavior never repeats. The logistic equation demon- strates one of the most studied pathways to a chaotic system - a series of period doubling bifurcations. Now that you have a bifurcation map and understand its meaning, you should copy “Logis- tic.m” to “LogisticTest.m” and then try different values of r. You should be able to predict when r will result in steady-state, periodic or chaotic behavior from the bifurcation plot. Create a plot of a chaotic time series of the logistic equation and save it in a ﬁgure called “LogisticChaos.jpeg”. 7.7 EXERCISES 1. Turn in “Logistic.m”, “LogisticBifurcation”, “ProteinExpressionScript.m”, “LogisticBif.jpeg”, “SucroseGradient.jpeg”,“LogisticChaos.jpeg”. 2. In Section 7.3.1, you created a script to compute expression of protein Y over time as a function of a promotor protein X. In this exercise, you will modify you script to evaluate how Y expression changes as X is changed. To do so, you will treat X as a parameter that will vary from 0 to 50 in increments of 1. The goal is to record the steady-state, e.g., t → inf, value of Y . Below is a portion of a script that should help you organize your script, “Assignment6-Problem2.m”. 7.7. EXERCISES 65 figure(1) hold on %Find Rate of Y production given concentration of X x = [0:1:50]; SteadyStateY = zeros(length(x),1); for j = 1:length(x) fx = betax(j)/(Kˆn+x(j)ˆn); %rate of Y production %PLACE APPROPRIATE COMMANDS HERE %Plot out expression of Y over time plot(time,Y); pause(0.2) SteadyStateY(j) = Y(end); end figure(2) plot(x,SteadyStateY); In Figure 1, we will plot the time courses of Y for each value of x. The pause command is used to clarify the trends as x is increased. In Figure 2, we are plotting only the very last (steady-state) value for Y as a function of x. 3. Many biological systems can not be characterized by a single differential equation. In these cases, we can think of the system as a set of coupled differential equations. For example, dx dt dy dt dz dt = f (x, y, z) = g(x, y, z) = h(x, y, z) (7.7) (7.8) (7.9) (7.10) notice that functions f , g and h are functions of all three variables, i.e., the equations are coupled. Also notice that f , g and h could take any form and will mostly likely not be linear. For example, the FitzHugh-Nagumo model of a neuron is = V − V 3 3 = a ∗ (V + b − cW ) − W + I dV dt dW dt (7.11) (7.12) 66 7. LOOPS where V is the cell membrane potential, W is a recovery variable and I is a stimulus current. We will assume the constants are a = 0.08, b = 0.7 and c = 0.8. Because these equations are non-linear, we cannot transform them to the form d dt x = Ax (7.13) and therefore need to use a numerical integration technique. You can assume that the initial values for V and W are both 0. Integrate the equations using the Euler Method with a (cid:8)t = 0.01 from time = 0 to time = 500. You should create a script called, “FHN.m” that will allow you to change parameters. At the end of the script, you should plot the membrane voltage, V , versus time. The parameter to vary is the stimulus current I . First try, I = 0. Next try I = 1.0. Hint: You should see two very different behaviors. The stimulus current is in fact a bifurcation parameter of the system. Find the value of I at which the bifurcation occurs. Place this value in a comment at the bottom of your script “FHN.m”. C H A P T E R 8 Conditional Logic 67 8.1 INTRODUCTION Conditional logic is the use of true and false statements in programming. When given a statement it will either deﬁnitely be true or deﬁnitely be false. In computing terms, we can assign a “1” to any statement that is true and a “0” to any statement which is false. The two types of states, true or false, also goes by the name of Boolean logic. The purpose of using Boolean logic is that it can be used to alter the ﬂow of a program. Here we introduce idea of the state of the program, which is simply the values of all of the variables up to that point that are available in memory. Using this state, we can send the program down different pathways. Therefore, conditional logic allows a programmer to write a much more sophisticated and ﬂexible program. 8.2 LOGICAL OPERATORS To begin understanding how logical operators work, enter the following commands. >> a = 5; >> b = -1; >> c = 0; >> d = 3; >> e = 3; You can now think of the state as the variables a − e in memory. Next enter the following commands one at a time to the command line. For more help, you may wish to type “help relop”. >> logical(a) >> logical(c) >> a==b >> b˜=c >> d>e >> d>=e >> d!=b >> d<a %true (1) because a has a value other than 0 %false (0) because c has a numerical value of 0 %false because a is not equal to b %true because b is not equal to c %false because d is equal to d %true because d is equal to e %true because d is not equal to b %true vecause d is less than a And, logical statements can be combined together using && (logical AND) and \|\| (logical OR) 68 8. CONDITIONAL LOGIC >> (a==b)\|\|(d==e) >> (a==b)&&(d==e) >> (a >= d)&&(c) %True because d is equal to e %False because a is not equal to b %false because c is logically 0 8.2.1 RANDOM BOOLEANS Logical operations can be used to create a number of interesting data structures. One that has been studied extensively by mathematicians, and has applications in systems biology, is a description of a randomly connected network. In Chapter 4, we created an adjacency matrix for a ring. Using logical operations, we can create the adjacency matrix for randomly connected nodes. %Number of Nodes >>N = 100; >>Temp = rand(N,N); %Temp filled with numbers between 0 and 1 >>A = Temp>0.5; >>spy(A) %Any value >0.5 becomes 1, any value < 0.5 becomes 0 Because of the random distribution between 0 and 1, and the value 0.5, the matrix will be half ﬁlled of 0s, with the other half ﬁlled with 1s. Remembering that a 1 indicates a connection; this means that each node is connected to, on average, half of the other nodes. To change the number of connections, all that is necessary is to change the line “A = Temp>0.5”. 8.2.2 LOGICAL OPERATIONS ON STRINGS A second situation where logical operations can be helpful is in checking if two character strings are the same. For example, such an operation may be very useful in searching or sorting the patient database created in Section 4.6.1. Matlab has a number of commands speciﬁcally for >>PatientName1 = 'John Doe'; >>PatientName2 = 'Jane Doe'; >>strcmp(PatientName1,PatientName2) >>strcmp(PatientName1,'John Doe'); For more logical operations on strings, view the help for strcmp. 8.2.3 LOGIC AND THE FIND COMMAND In an exercise in Chapter 5, you created a vector that contained the ﬁrst 7 minutes of heart rate recordings. >>HeartRateData = [0 64 137 188 260 328 397 464]; Now you would like to ﬁnd the minutes when the heart rate went above 70. >> highHRminute = find(diff(HeartRateData)>70) In one command, using some logic and the diff and ﬁnd commands, we can identify the minutes where the heart rate when above 70. 8.3 IF, ELSEIF AND ELSE Logical commands can be used to control the ﬂow of a program using the if, elseif and else structures in Matlab. Do not enter the commands below. 8.3. IF, ELSEIF AND ELSE 69 x = 2; if (x>1) COMMANDS HERE FOR x GREATER THAN 1 elseif (x==1) COMMANDS HERE FOR x EQUAL TO 1 else end COMMANDS HERE FOR x LESS THAN 1 In this template, code we would issue the commands in “COMMANDS HERE FOR x GREATER THAN 1”, because x = 2. It is important to note that there can be any number of commands. 8.3.1 THE INTEGRATE AND FIRE NEURON One of the most simplistic models of an excitable cell, e.g., neuron and muscle, is known as the integrate and ﬁre model. The model has two phases: 1) a period where it will integrate any electrical input and charge up the cell membrane, and 2) a period when the cell produces a spike in membrane potential and then resets back to rest. During the charging phase, we can have the cell obey a simple differential equation for an RC circuit. dV dt = I − V R · C (8.1) where R and C are the membrane resistance and capacitance. I is the current entering the cell. By looking at the equation, if I is a constant current input, V (t) will rise up to some steady-state value (exactly like the charging of an RC circuit). To switch to the second phase, we must deﬁne a threshold voltage, Vt . When the cell membrane voltage reaches Vt , the program will stop using the differential equation and then do two things. First, a “spike” will be issued. The meaning of the spike is to set V to some constant value Vpeak for only that time step. Second, on the following time step, V will be reset back to an initial value of 0. After the reset, the cell membrane is ready to be charged again. These ideas can be captured in the following code called, “IAF.m”. dt = 0.01; EndTime = 50.0; time = 0:dt:EndTime; Vt = 5; R = 1; C = 2; % Threshold voltage % Set to 1 for simplicity % set to 2 for simplicity 70 8. CONDITIONAL LOGIC I = 3; Vpeak = 100; % set membrane voltage of spikes V = zeros(length(time),1); V(1) = 0; for i=2:length(time) if (V(i-1)>Vt) V(i-1) = Vpeak; V(i) = 0; else end end V(i) = V(i-1) + dt(I-V(i-1)/(RC)); plot(time,V); You should notice in your plot that the membrane charges to V = 5, generates a spike and then returns to 0. Upon returning to zero, it will begin charging again. The lines if (V(i-1)>Vt) V(i-1) = Vpeak; V(i) = 0; else require some explanation because a trick was used here. At a particular iteration through the loop, the loop variable has the value of i. When we perform the logical statement V (i − 1) > Vt , we are really checking if the previous value was above threshold. If the statement is true we want the previous value to instead be replaced with a spike, thus the statement V (i − 1) = Vpeak. Then we want the current value of V to be reset (V(i)=0). This appears strange because we are going back to a previous value of V and then changing it. There are other ways to write this section of code, but this is much more efﬁcient. As a test of your script, you should slowly increase I , observing how the pattern of spikes changes. You should notice that as I increases, the rate of ﬁring increases. This is exactly what occurs in most neurons in the brain. If you then decrease I below some level, no ﬁring will occur at all. This behavior is also observed in neurons. 8.3.2 CATCHING ERRORS In Section 6.3.2, we learned how to create an error in Matlab, which will display red text and terminate the script. The combination of error and if-else logic can be used to catch problems in a function and report the problem to the user. For example, 8.3. IF, ELSEIF AND ELSE 71 x = 1; a = 5; if (a>0) b=a/x; else end error('Divide by Negative Number Not Allowed'); 8.3.3 FUNCTION FLEXIBILITY You may have noticed that some Matlab functions can take a number of different arguments. For example, you can call the function mean in two different ways. >> mean(A); >> mean(A,2); Inside the function (mean.m), the program must ﬁrst determine if there are 1 or 2 input arguments. At that point, it will determine how to proceed. In every function, there is a built-in variable that is deﬁned nargin (look at the help for nargin for other useful function commands) that contains the number of input arguments. You should try type mean.m to see how the function was written to take into account the two different ways of called mean. 8.3.4 WHILE LOOPS In the previous chapter, the while loop was introduced as a way to begin an iteration without knowing exactly how many times it should cycle through. As pointed out, however, every loop must have some way to terminate. In the case of the while loop, we will continue to iterate until some logical condition is met counter = 1; while (counter<=25) counter = counter+1 end In the above code, we set counter equal to 1. On the ﬁrst time through the while loop, we check if counter is less than or equal to 25. If it is, then we proceed through the next iteration. But, within each iteration, counter is being incremented by 1. Again, at the beginning of each iteration, the condition counter <= 25 is checked. When counter becomes 26, the condition is not met and the while loop terminates. 8.3.5 STEADY-STATE OF DIFFERENTIAL EQUATIONS The above section demonstrated how a while loop uses logical statements to terminate a loop. It should be noted that any logical statement can be used, and that the loop will terminate when the statement becomes false. To demonstrate a more practical reason to use a while loop we will 72 8. CONDITIONAL LOGIC consider iterating through the Kermack and KcKendrick differential equation model for the spread of a disease. dI dt = −βSI dS dt = βSI − γ I dR dt = γ I (8.2) (8.3) (8.4) where S is the population of Susceptible, I is the population of infected and R is the population of recovered. β is a constant that reﬂects the number of susceptible that become infected each time step. γ is a constant that reﬂects the number of infected which recover each time step. The script, “SIR.m” below, uses a while loop to check when the variable S does not change. dt = 0.01; change = 0.001; %how to define stop condition beta = 0.003; gamma = 0.01; %initial values S = [0 100]; I = [0 2]; R = [0 0]; i = 2; while (abs(S(i-1)-S(i))>change) i = i+1; S(i) = S(i-1) + dt(-betaS(i-1)I(i-1)); I(i) = I(i-1) + dt(betaS(i-1)I(i-1)-gammaI(i-1)); R(i) = R(i-1) + dt(gammaI(i-1)); end figure(1) hold on time = dt[1:length(S)]; plot(time,S) plot(time,I,'k'); plot(time,R,'r'); The reason for the while loop only becomes apparent as the values for β and α are changed. First, change “ﬁgure(1)” to “ﬁgure(2)” so that you can view both ﬁgures side-by-side. Then change β = 0.3 and rerun “SIR.m”. You should notice that the time on the y-axis is drastically different in the two ﬁgures. If we used a for loop, we would not know ahead of time how many iterations to execute before S reached a constant value. But, with a while loop, we can explicitly check when S reaches a steady-state. 8.4. SWITCH STATEMENTS 73 8.3.6 BREAKING A LOOP A for loop should be used when it is known how many times an operation should be performed. A while loop should be used when an operation should be repeated until some condition is met. There are times, however, when a loop is necessary that does not ﬁt easily into either of these predetermined types. To help gain more ﬂexibility, Matlab has a break command. Note that the break command typically would be placed inside of an if statement within a loop. counter = 1; for i=1:100 counter = counter+1; if(counter>=76) break; end end counter The code above will terminate the loop early when counter reaches 76. 8.3.7 KILLING RUNAWAY JOBS Matlab can sometimes get carried away with an operation, usually if a command in the loop uses too much memory or a loop becomes inﬁnite. In these instances, it is helpful to be able to kill whatever Matlab is doing. Although any work that has been performed will be destroyed, you may ﬁnd that it is useful in some cases. To suspend a process, press Control C. 8.4 SWITCH STATEMENTS The if, elseif, else format is very good to use if you need to direct your program in only a few directions. Here you can imagine the ﬂow of your program proceeding down a main trunk and then reaching a branch point. If there are only two or three branches, you can easily use if-else statements. If the branch that occurs in the code must go in more than three directions, there is another type of logical structure that can be very helpful - the switch structure. Let us assume that you wish to study how neurons might synchronize to one another, and how hypersynchronization may lead to epilepsy. You have the dynamics of the individual neurons already coded, probably in the form of a difference or differential equation. Now you want to test out 74 8. CONDITIONAL LOGIC how different networks of neurons might synchronize. The task of the study is to determine if some networks are easier (or harder) to synchronize. For this study, you will need to create a variety of different networks. You would like to try a one-dimensional ring (see Chapter 4), a two-dimensional grid with Von Neumann connections, randomly connected neurons (see Section 8.2.1) and what is known as a small world network. Here you could deﬁne a variable NetworkT ype that contains a character string. Then you could include a switch statement that will send the code in different directions, depending upon the variable NetworkT ype. You do not need to enter the commands below. NetworkType = '2DGrid'; switch(NetworkType) case {’1DRing’} N = input('Enter Size of Ring:'); Network = %Create Ring Network Adjacency Matrix Here case {’2DGrid’} [Nx,Ny] = input('Enter number of rows and columns'); Network = %Create 2D Diffusion-type Adjacency Matrix Here case {’Random’} N = input('Enter number of random points:'); Network = %Create Random 2D Adjacency Matrix Here case{’SmallWorld’} N = input('Enter number of nodes in small world'); Network = %Create Small World Network Here otherwise disp('Please Enter a Valid Network Type'); end spy(Network) In this instance, you used a character string as the variable that controls switching. But, you could use any data type in Matlab. You could also go back to this code at some later time and easily add another type of network, e.g., A Moore Neighborhood for the 2D grid. 8.5 EXERCISES 1. Turn in “IAF.m”, “SIR.m”. 2. A great deal of study has gone into how patterns are generated in nature, for example, the spots on a leopard, stripes on a Zebra or more intricate patterns on some sea shells. It would be tempting to attribute these patterns to genetics, but experiments have shown that the patterns are very sensitive to environmental conditions present at speciﬁc stages of development. For example, a mollusk that is placed in a colder environment may display a very different pattern. As such, theoretical biologists proposed that the genetics lay down some very simple rules that in slightly different situations can lead to drastically different patterns. 8.5. EXERCISES 75 One of the simplest pattern generating mechanisms was discovered in the early 1980s by Steven Wolfram. It is a subclass of mathematical systems called cellular automata. Imagine a one-dimensional line composed of a number of individual elements. Each element can be either on (logical 1) or off (logical 0). We can then make a second one-dimensional line below the ﬁrst line. But, we can make the on and off pattern of this second line dependent upon what is on or off in the ﬁrst line. Then we can add a third line, with values depen- dent upon the second line. We can continue this pattern indeﬁnitely. In this case, the ﬁrst line is like a boundary condition, and then we simply follow some rules to continue adding lines. Figure 8.1 shows the Wolfram rules that look to only three elements of the previous line: the element directly above you, the element above and to the left, and the element above and to the right. You should note that, in the ﬁgure, the 8 combinations in the top row are the only possible combinations of three elements. These combinations are always given in the same order. The rule shown is [ 0 1 1 0 1 1 1 0], which completely speciﬁes the result for all possible combinations of the three values in the previous one-dimensional line. A bit of calculation will show that there are 256 (28) possible rules. Wolfram explored all 256 and showed that some are boring, some interesting, and others are very unexpected. Below is code, which you should enter into a script called, “WolframCA.m”, that implements the [0 1 1 0 1 1 1 0] rule. L = 300; T = 300; %length of one dimensional line %number of one dimensional lines to add A = zeros(T,L); A(1,L) = 1; %Initialize A matrix to store CA %Initial Condition for i = 2:T for j = 2:L-1 %Don’t loop over the two end points l=A(i-1,j-1); m=A(i-1,j); r=A(i-1,j+1); %left at previous time %this node at previous time %right at previous time % Use logic to go through all 8 cases if (l && m && r) A(i,j) = 0; end 76 8. CONDITIONAL LOGIC if (l && m && ˜r) A(i,j) = 1; end if (l && ˜m && r) A(i,j) = 1; end if (l && ˜m && ˜r) A(i,j) = 0; end if (˜l && m && r) A(i,j) = 1; end if (˜l && m && ˜r) A(i,j) = 1; end if (˜l && ˜m && r) A(i,j) = 1; end if(˜l && ˜m && ˜r) A(i,j) = 0; end end end colormap(gray(2)); image(2-A); Explore different rules by changing the values for A(i, j ) = terms. You should note that even one change can completely alter the patterns generated. At the bottom of your script, you must report (in comments) the types of behavior you observed. 8.5. EXERCISES 77 Figure 8.1: Example of Wolfram Cellular Automaton Rules. C H A P T E R 9 Data In, Data Out 79 9.1 INTRODUCTION In previous sections, it was shown how, using the save and load commands, we could easily store and then restore anything in Matlab’s memory. But, most powerful programming languages have some mechanism for reading in data from other applications, as well as some way to write data out that can be read by other applications. For example, you may wish to create geometries (adjacency matrices) or initial conditions in Matlab, but then send these ﬁles to another program that will run on a supercomputer, i.e., on many computers in parallel. In this way, you could run an enormous biomedical simulation with millions (or maybe even billions of points) in a compiled, i.e., faster than matlab, program. Alternatively, you may receive data from a large simulation and need to read data into matlab to analyze it. In this chapter, you will learn how to read in and write out data to and from matlab. 9.2 BUILT IN READERS AND WRITERS The problem with the “.mat” ﬁle format is that you cannot open the ﬁle in anything other than matlab. Matlab has a number of functions that allow for ﬁles to be read and written in other formats. For example, there are two commands, xlsread and xlswrite, that allow matlab to share ﬁles with Excel. A = rand(20,30); xlswrite('FirstExcelExample.xls',A); There are many options to use with xlswrite, and you should view them if you need to perform a more sophisticated function. Matlab also has a method of reading from an excel ﬁle. [Numeric,Txt,Raw]=xlsread('FirstExcelExample.xls'); It should be noted that for communication with external programs, it is important to have the proper version of matlab. It is possible that your version may not support all of the input and output formats explained in this chapter. An even more basic ﬁle is known as a ﬂat text ﬁle. Here the data is simply arranged in a text ﬁle in columns and rows. Enter the following numbers into a ﬁle called “MyFirstTextFile.txt”. 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 80 9. DATA IN, DATA OUT To load the following into matlab you would type [B] = load('MyFirstTextFile.txt'); In the ﬁle above, matlab used spaces (or tabs) to make clear where the breaks are between numbers. Here the spaces (or tabs) were used as deliminators. A deliminator is simply any character that separates other characters. For many reasons, it may have been more clear for the ﬁle to have had the format 1:2:3:4:5 6:7:8:9:10 11:12:13:14:15 where “:” is being used as a deliminator. Matlab has a variety of commands for reading (dlmread and textscan) and writing (dlmwrite) these types of ﬁles. For a more complete list of all the types of ﬁle formats supported in matlab, view the help for ﬁleformats. 9.3 WRITING ARRAYS AND VECTORS In the above example, we created a relatively small matrix (A) that could easily be stored in memory. Then we could simply send the entire matrix to a ﬁle. In the context of a simulation, however, we might be generating the values as we progress throughout a simulation, and we generally do not need to know all values at all times. In these situations, there is no need to store all of the data in memory. Rather, we can send the data to a ﬁle on the hard drive as it is generated. We will now take a bit of a detour to create a simulation that generates more data than can be stored in memory, and therefore requires the creation of an external data ﬁle. 9.3.1 DIFFUSION MATRICES To demonstrate a very generic situation where writing to a ﬁle is very helpful, we will examine an important concept in the movement of any group of particles that is conserved as it ﬂows through a two-dimensional grid. The particles could be ions, animals of a species, a volume of ﬂuid, or even something less tangible such as heat energy. The key is that given a type of particle, q, we can deﬁne a ﬂow rate, dq dt . In electrical circuits the conserved quantity is charge (q) and the ﬂow is current, I . I = dq dt (9.1) Because the particles (charge ions in this case) must be conserved, we can total up all of the charge entering a point and all the charge leaving a point, and they must be equal. Iin = Iout 0 = Iin − Iout (9.2) (9.3) 9.3. WRITING ARRAYS AND VECTORS 81 Figure 9.1: Two dimensional resistor grid, showing the neighbors of a generic node i Figure 9.1 shows a small portion of a large two-dimensional grid. Each point in the grid is connected to its left, right, up and down neighbors and may share charge with only those nodes. Therefore, current may ﬂow left, right, up or down through some resistance, and if we total up the currents entering and leaving any node, they should sum to zero. Given the directions of our arrows, which are arbitrary but should be consistent for every node, we can derive I1 + I2 − I3 − I4 = 0 (9.4) Using Ohm’s Law, we can reexpress the above equation in terms of the voltages at the neighboring nodes (V ) and resistances between nodes (R) Vi−1 − Vi R − Vi Vi−Ny + R Vi−1 − 2Vi + Vi+1 R Vi−Ny − Vi − Vi+1 R Vi−Ny Vi − Vi+Ny R − − 2Vi + Vi+Ny + + Vi−1 − 4Vi + Vi+1 + Vi+Ny R R = 0 = 0 = 0 (9.5) (9.6) (9.7) where subscripts denote the node numbers. We have used i as the node number to indicate that our analysis will work for any node in the grid. The left and right neighbors therefore have subscripts i − 1 and i + 1. The node numbers for the up and down neighbors are offset by the number of nodes in each row of the grid. If we were to write out an equation for each node in the grid, we would have a very similar form to the equation above. The node itself would have a coefﬁcient of −4/R, and the neighbors 82 9. DATA IN, DATA OUT would each have coefﬁcients of 1/R. The nodes at the corners and at edges will have slightly different equations, but they could easily be derived by the same conservation of current laws. In fact, the voltages and coefﬁcients can be decoupled and take the form of Dv (9.8) where D contains the coefﬁcients and v contains a vector of the voltages. Nearly all physical quantities have some sort of conservation law, and therefore our analysis applies to much more than electronic circuits. The code below creates a diffusion matrix, T , for a grid that is M × N. You should save the ﬁle as “FHNPropagate.m”. The code is admittedly long. You may wish to read the text after the code to gain some overall understanding of how it works. Then, as you write each line, you should be thinking about how it ﬁts into the overall context of the code. M = 5; N = 5; %Number of row %Number of columns T = zeros(NM,NM); for i = 1:M for j=1:N %Loop over rows %Loop over columns %Computer node number assumed numbering %starts going across rows Node = (i-1)N+j; %All Interior Nodes if ((i>1) && (j>1) &&(i<M) &&(j<N)) T(Node,Node-1) = 1; T(Node,Node+1) = 1; T(Node,Node+N) = 1; T(Node,Node-N) = 1; T(Node,Node) = -1.0sum(T(Node,:)); end %Top Boundary if(i==1) if (j==1) %Upper left corner T(Node,Node+1) = 2; T(Node,Node+N) = 2; T(Node,Node) = -1.0sum(T(Node,:)); 9.3. WRITING ARRAYS AND VECTORS 83 elseif(j==N) %Upper right corner T(Node,Node-1) = 2; T(Node,Node+N) = 2; T(Node,Node) = -1.0sum(T(Node,:)); else %Top edge T(Node,Node+1) = 2; T(Node,Node-1) = 1; T(Node,Node+N) = 1; T(Node,Node) = -1.0sum(T(Node,:)); end end %Bottom Boundary if (i==M) if(j==1) %Lower left corner T(Node,Node+1) = 2; T(Node,Node-N) = 2; T(Node,Node) = -1.0sum(T(Node,:)); %Lower right corner elseif(j==N) T(Node,Node-1) = 2; T(Node,Node-N) = 2; T(Node,Node) = -1.0sum(T(Node,:)); else %bottom edge T(Node,Node-1) = 1; T(Node,Node+1) = 1; T(Node,Node-N) = 2; T(Node,Node) = -1.0sum(T(Node,:)); end end %Left Boundary if((j==1)&&(i˜=1)&&(i˜=M)) T(Node,Node+1) = 2; T(Node,Node-N) = 1; T(Node,Node+N) = 1; T(Node,Node) = -1.0sum(T(Node,:)); end 84 9. DATA IN, DATA OUT %RightBoundary if((j==N)&&(i˜=1)&&(i˜=M)) T(Node,Node-1) = 2; T(Node,Node+N) = 1; T(Node,Node-N) = 1; T(Node,Node) = -1.0sum(T(Node,:)); end end end spy(T) There are a few points that are important to note. First, we have created a 5×5 grid in this example but could easily change M and N. Second, the numbering of nodes is to start with 1 and move across a row until reaching Node = 5. Then the numbering starts up again on the next row and continues until N ode = 10. Although there are nested loops (loop over rows and then columns), we can, for any i and j , compute the node number (stored in Node). It then makes it much easier to reference any other node to the current node. For example, the node to the left will be Node − 1, the node to the right will be Node + 1, the node above would be Node + N and the node below will be N ode − N . Inside the loops are a series of if statements that handle interior, edge and corner nodes. Although we will not go into the theoretical rationale, it is convention for the coefﬁcient to be “2” when a neighbor does not have a pair. What we mean by a pair is best illustrated by an example. For nodes on the left edge, there is no connection between Node and Node − 1 (because it is on the other side of the grid). In this case, we then make Node + 1 count twice. You may notice that the ﬁrst if statement handles all of the interior nodes, while all the other if statements handle the edge and corner nodes. The last command (spy(T )) will allow you to visualize the entries. You should note that a diffusion matrix is a special type of adjacency matrix. The last point is that from the spy command, T is sparse and all entries are along 5 diago- nal lines. For this reason, the above code could have been greatly condensed, i.e., optimized, by removing the if commands and replacing them with the appropriate diag commands. The code was created as above for illustration purposes. A further reduction in memory could be achieved by using the sparse command, as introduced in Section 4.2.2. 9.3.2 EXCITABLE MEMBRANE PROPAGATION The heart is often thought of as a mechanical pump. But the control and coordination of the pump is largely achieved through electrical communication between neighboring cells. In fact, we can use a diffusion matrix to explain how ionic currents are shared between cells. In this section, we will com- bine the diffusion matrix above and the excitable FitzHugh-Nagumo model introduced in Chapter 7. You should add the following lines to “FHNPropagate.m”. 9.3. WRITING ARRAYS AND VECTORS 85 dt = 0.01; EndTime = 500; time = 0:dt:EndTime; a = 0.08; b = 0.7; c = 0.8; I = zeros(MN,1); I(1) = 0.6; %Simulus Current Vector %Stimulate only Node 1 V = zeros(MN,1); W = zeros(MN,1); VOld = zeros(MN,1); WOld = zeros(MN,1); %Set up Vector to hold V %Set up Vector to hold W %Set up Vector to hold V %Set up Vector to hold W fid = fopen('FHNProp.txt','w'); for i=2:length(time) V = VOld + dt.(VOld-(VOld.ˆ3)/3-WOld+I - TV); W = WOld + dt.(a.(VOld+b-c.WOld)); fprintf(fid,'%f\t',time(i)); for k = 1:MN %Print out time %loop over V values fprintf(fid,'%f\t',V(k)); end fprintf(fid,'\n'); %Go to next line VOld = V; WOld = W; end fclose(fid); You should run the code above. After completion, you should see a ﬁle “FHNProp.txt” in your directory. We will ﬁrst discuss how this implementation of the FitzHugh-Nagomo model is different from the one in Chapter 7. The major difference is that rather than simulate one FitzHugh-Nagomo cell we are simulating one at every grid point ,e.g., N × M = 25. For this reason, we have assigned each cell a number, corresponding to the Node number discussed above. 86 9. DATA IN, DATA OUT In numbering each cell, we can create a vector V and vector W that hold the values at all 25 cells at any one time. You will also note that we created two additional vectors, V Old and W Old, which are temporary vectors that will be used in calculations. Within the time loop, we now perform an update on the differential equations for V and W for all 25 nodes in one step. This is an excellent example of how Matlab’s matrix and vector operations can help make code easier to write, read and run more efﬁciently. You should note that the left side contains all V -terms and the right side contains all V Old-terms. This is done so that we do not mix up previous and current values. For example, we want to use the same V Old in the updating of V as we use in the updating of W . You will also note that a new term, −T ∗ V has appeared in the up- date for V .This is a vector that describes the current entering (or leaving) nodes from their neighbors. You should note that the methods used above could be used to describe nearly any interact- ing nodes, described by any adjacency matrix. In this way, we can decouple the dynamics at any node from the way nodes are connected together in a network. We are not saving the value of V in memory at every node at every time step. Rather, we are generating a new value of V and then sending it to a ﬁle using the fprintf command. First, before the time loop begins, we open a ﬁle using the open command. The input to the command is the ﬁlename with the option “w”, meaning that this ﬁles is being opened for writing. Within the loop, the fprintf command is used to send data to the ﬁle, and then after the loop is over, the ﬁle is closed using the fclose command. The variable f id is called a ﬁle identiﬁer. This ﬁle identiﬁer can become very important if more than one ﬁle is open at any one time, as it will make clear which data is going to which ﬁle. The fprintf command has a very particular format. The ﬁrst input is the ﬁle identiﬁer. The second input is the format of the text that will be sent to the data ﬁle. The third input is the value of any variables. You should view the help for fprintf for details. In the example above, before the k-loop, the value for time is printed. The format is “%f\t”, meaning that a numerical double, %f will be printed, followed by a tab (\t). The third option is what places the value of time into the place of %f. The loop moves though the V vector, printing a particular value of V followed by a tab. After the loop is printed, a return character,\n, is printed Therefore, on each iteration through the time loop, a new line is created in the open ﬁle that contains all of the values of V , separated by tabs. The command fprintf is the most general and powerful way to print out data, but there are other commands, e.g., sprintf, that can be useful and more efﬁcient. 9.4 READING IN ARRAYS AND VECTORS The load command introduced earlier can be used to read in saved matlab work spaces. It can also be used to read in text ﬁles that were created in text format. 9.5. READING AND WRITING MOVIES AND SOUNDS 87 Y = load('FHNProp.txt'); will load the entire data ﬁle “FHNProp.txt” into the matrix Y . We could then plot values against one another. For example, plot(Y(:,1),Y(:,2)) will plot the time vector, Y(:,1), against the ﬁrst node, Y(:,2). The load command is very limited and if a more complex text ﬁle must be loaded in, e.g., a delimitated text ﬁle, the textscan is the command to use. 9.4.1 IRREGULAR TEXT FILES In some situations, a ﬁle does not have a regular layout. Enter the following into a text ﬁle, called “IrregularText.txt”, using a text editor or Matlab’s editor. FHN Parameters 0.01 500 0.08 0.7 0.8 0.6 To read in the text above, enter the following code into a script called “IrregularTextReader.m” fid = fopen('IrregularText.txt',’r’); FirstLine = fscanf(fid,'%s %s',2); Temp = fscanf(fid,'%f %d',2); dt = Temp(1); TimeSteps = Temp(2); Temp = fscanf(fid,'%f %f %f',3); a = Temp(1); b = Temp(2); c = Temp(3); I = fscanf(fid,'%f',1); fclose(fid) The fscanf command will read one line at a time in the format speciﬁed. You should view the help ﬁle for more details. 9.5 READING AND WRITING MOVIES AND SOUNDS Movies are simply a series of images played in sequence. In previous chapters, we have created a simple type of movie using a loop and the pause command. But, matlab also has support for creating 88 9. DATA IN, DATA OUT standalone movies that can be run outside of matlab, i.e., in a presentation. To demonstrate the ability to create movies, we will create a script that simulates John Conway’s Game of Life. The game of life is played on a grid where each element in the grid has eight neighbors, the usual up, down, left and right, but also the four diagonals. Each element can be on (1) or off (0) at any one time. We begin with an initial condition (pattern of 1s and 0s on the grid). Then to get to the next time step, we apply two simple rules to each element. If an element is on and either 2 or 3 of the neighbors are also on, that element will be on the next step. Otherwise, the node is turned off. If an element is off but exactly 3 of its neighbors are on, it will be on the next step. Otherwise, the node remains off on the next step. Conway’s rules are called the game of life because we can think of the rules as correspond- ing to some real situations. If a node is “alive”, it could die by two different mechanisms. First, it could die of “loneliness” if not enough of its neighbors are on. Second, it could die if it is crowded out. It will only survive if 2 or 3 of its neighbors are on (not lonely but not overcrowded either). On the other hand, 3 neighbors can “reproduce” and give rise to a new alive element. Below is code which will play the Game of Life on a 50×50 grid for 100 iterations. The initial condition is set up such that activity will not simply die out. There are many other patterns that could be created, and you could experiment with different initial conditions as an exercise. Below is a script called “GameOfLife.m”. % GameOfLife.m - Conway’s Game of Life %Set up Parameters of Simulation Dim=50; T = 100; Delay = 0.1; %Initial Conditions GRID = zeros(Dim,Dim); GRID(10,10:11)=1; GRID(11,11)=1; GRID(11,15:17)=1; GRID(9,16)=1; %the world is round up=[2:Dim 1]; down=[Dim 1:Dim-1]; for i=1:T %Establish pattern 1 counting up %Establish pattern 2 counting down neighbours=GRID(up,:)+GRID(down,:)+GRID(:,up)+GRID(:,down)+... 9.5. READING AND WRITING MOVIES AND SOUNDS 89 GRID(up,up)+GRID(up,down)+GRID(down,up)+GRID(down,down); GRID = (neighbours==3) \| (GRID & neighbours==2); imagesc(GRID); M(i,:) = getframe; %M(i) = getframe; pause(Delay); end %May be need for some Matlab versions The purpose of the script above is to demonstrate how to capture the dynamics in a movie. You will notice that after the imagesc command displays GRI D there is a command M(i) = getf rame. The getframe command will store the current ﬁgure in a special movie frame structure. If you run the script and type whos, you will notice that a very large structure, M, has been created. To play the movie in matlab >> movie(M) You can view the movie command to see other options for how you can play back the movie you have created. The movie command, however, will only work within matlab. To export the movie so it can be played outside of matlab >> movie2avi(M,'CATestMovie.avi'); which will create an “avi” ﬁle that can be played with many external movie players, including inside a power point presentation. Depending upon how matlab was set up, you may get a warning when you issue this command. You should still see the ﬁle “CATestMovie.avi” in your directory. Try to play it using RealPlayer or Windows Media Player. You should view the help for the movie2avi command to learn how to change options such as frame rate, compression and quality. There is also an “mpeg” writer that can be downloaded from the Mathworks website. 9.5.1 SOUNDS Matlab also has support for recording, e.g., wavwrite, wavrecord, and playing, e.g., sound, waveplay, wavered, and wave. To test your system, try entering >> load handel >> sound(y,Fs); To learn more about the support for movies and other audio/visual commands, view the help for audiovideo. 9.5.2 READING IN IMAGES You have already learned how to write images out using the print command. Matlab also has commands for reading in images. First, we will create a “jpeg” image from one of Matlab’s built in images. 90 9. DATA IN, DATA OUT >> load cape >> imagesc(X) >> colormap(map) >> print('-djpeg','CapeCod.jpeg'); >> close all You should note that the command close all will close all open ﬁgures. To load in the jpeg you created >> A = imread('CapeCod.jpeg','jpeg'); >> imagesc(A) The imread command can be used to load many different types of image ﬁles into a matrix. Once in Matlab’s memory, the image can be displayed in the same way as any other matrix. 9.6 BINARY FILES It is very simple to write out data to a text ﬁle using fprintf or other such commands. The problem is that the size of the text ﬁle can become very large because when a number, for example “0.0012345” is sent to the ﬁle, it is typically stored as a character string. Then when it is read back in, it is converted back to a numerical value. The problem should become apparent if you issue the following commands >> a = ' 0.00123456789'; >> b = 0.00123456789; >> whos %character string %numerical value Storing as a character requires 26 Bytes where as a ﬂoating point number requires only 8. So, there can be a very large savings in hard drive space if numbers are stored as numbers. This format is typically called binary because the numbers are stored in machine language (1s and 0s). 9.6.1 WRITING BINARY FILES To read and write in binary requires a few different commands in matlab, for example fwrite. Copy “FHNPropagate.m” to “FHNPropagateBinaryOutput.m”. Then change the line ﬁd = fopen(‘FHNProp.txt’,‘w’); to fidb = fopen('FHNProp.bin','wb'); The option “wb” speciﬁes that the ﬁle is writable and binary. Next replace fprintf(fid,'%f\t',time(i)); for k = 1:MN %Print out time %loop over V values fprintf(fid,'%f\t',V(k)); end fprintf(fid,’\n’); with fwrite(fidb,V,’double’); %Go to next line 9.6. BINARY FILES 91 Lastly, change fclose(ﬁd); to fclose(fidb); If you run “FHNPropagateBinaryOutput.m” a ﬁle, “FHNProp.bin” will be created. In addition to the ﬁle being somewhat smaller, you will note that there is the added beneﬁt to writing out the data in binary - you no longer need the k loop. Rather, you can simply have matlab send the entire vector V to the ﬁle. 9.6.2 READING BINARY FILES load and other commands will read in ﬁles saved in text format. Matlab also has commands to read in binary ﬁles. We will not expand upon these commands here, but you can analyze the following commands that read in a particular time step of “FHNProp.bin”. TimeStep = 200; fid = fopen('FHNProp.bin','rb'); %Move from the beginning of the file to the timestep fseek(fid,TimeStep8MN,-1); %Read in one time step worth of data in double format Data = fread(fid,MN,'double'); %Reshape Data to be an MxN matrix Data = reshape(Data,M,N); %display the image at timestep 200 imagesc(Data) fclose(fid) Of course, it is possible to read in the entire data ﬁle, by placing the commands above in a loop that iterates through T imeStep. 9.6.3 HEADERS Nearly all ﬁles will be stored in one of two ways - text or binary. The key is to understand the format so that you can write a script to read the data. The format should be contained within the documentation for the program. A good ﬁle format will contain what is known as a header. In the header is important information, which would be helpful for reading in data. For example, in our previous example of storing binary data, it would be helpful to know the dimensions M and N, number of timesteps and the type of data. It would therefore have been helpful to ﬁrst print out a text line at the top of the binary data ﬁle. 1000 500 200 double BINARY DATA 92 9. DATA IN, DATA OUT The above ﬁle header would let a user know that the following binary data is 200, 1000×500 blocks of data that have the double format. In read or writing a header, you will mix Matlab’s text and binary reading capabilities. 9.7 EXERCISES 1. Turn in “FirstExcelExample.xls”, “FHNPropagate.m”, “IrregularText.txt”, “IrregularTex- tReader.m”, “GameOfLife.m”, “CATestMovie.avi”, “FHNPropagateBinaryOutput.m”. 2. Create a function that will compute the Fibonacci series starting with any two numbers. Remember that the series is deﬁned by Fn = Fn−1 + Fn−2 (9.9) Your function should be of the form function [Series]=FSeries(Num1,Num2,NumIterations); 3. Create a script,“WriteOutFibonacci.m” that generates a ﬁle with the following format Fibonacci Series Starting with Num1 and ending with Num2 NumIterations BINARY DATA HERE Num1, Num2 and NumIterations should be numerical values. Note that to create the text strings you may need to use the num2str command learned in Section 3.4. Note that in your script you must pick values for Num1, Num2 and NumIterations, then call the F Series function to generate the vector Series. Then you can generate the header and write Series as binary data. Note that you should have Num1 and Num2 be some value other than 1, and NumIterations should be at least 100. 4. Create a function, “ReadInFibonacci” that will read in any ﬁle generated by “WriteOutFi- bonacci.m”. The function should be of the form function [Series]=ReadInFibonacci(filename); C H A P T E R 10 Graphics 93 10.1 INTRODUCTION Built-in graphics is one of the key features of Matlab. In previous chapters, the plot and imagesc commands were introduced as ways of graphically displaying data. In this chapter, we will introduce more graphical options as well as explain some of the tools in Matlab for ﬁne tuning graphics. 10.2 DISPLAYING 2D DATA Two dimensional data is very often a simple line plot of an independent variable versus a dependent variable. For example, Schnakenberger (1979) gives a set of differential equations that describes an oscillating chemical reaction dx dt dy dt = x2y − x = a − x2y (10.1) (10.2) where x and y are the chemicals and a is a constant parameter. The two equations above are non- linear, and so we could use the Euler Method to solve them. An alternative is to use a graphical non-linear dynamics technique where we plot all of the values for x and y that cause dx = 0. In dt other words, we wish to plot the function 0 = x2y − x (10.3) on an x-y axis for the ﬁrst equation. We can do the same for the second differential equation. After a bit of algebra, we ﬁnd that we must plot the following two functions y = 1 x y = a x2 (10.4) (10.5) In non-linear dynamics, these two curves are called nullclines. y = 1 set of points where dx dt make these plots, we can issue the following commands = 0, and y = a x2 is the nullcline of y, e.g., the set of points where dx x is the nullcline of x, e.g., the = 0. To dt a = 1; x = -0.5:0.01:0.5; %define a range for x 94 10. GRAPHICS yxnull = 1./x; yynull = a./(x.ˆ2); plot(x,yxnull,'r'); hold on plot(x,yynull,'g'); %create x nullcline %create y nullcline %plot x null in red %plot y null in green You should ﬁrst notice that the colors of the plots can be changed using an option to the plot command (view the help for plot for more color options). There are a few issues with the plot that is generated. First, there is a problem with the scales of the plots because some parts go to inﬁnity. To rescale the axes, the following commands can be used >> axis([-0.5 0.25 -10 100]) where the axis takes a vector that has the form [xmin, xmax, ymin, ymax]. You can therefore zoom in to any portion of your data to take a closer look. There are times when you must distinguish your plot in some way other than to use colors. The plot command has a number of options for that as well. a = 1; x = -0.5:0.01:0.5; yxnull = 1./x; yynull = a./(x.ˆ2); plot(x,yxnull,'k'); hold on plot(x,yynull,'k-.'); axis([-0.5 0.5 -10 100]) %Make solid line %Make dash-dot line Now both plots are in black, but the y nullcline is a solid line, and the x nullcline is a dash-dot line. You should view the help for plot to see the other options. It is also important to add appropriate axis labels and a title for your graph by issuing the following commands xlabel('x variable'); ylabel('y variable'); title('X and Y Nullclines for Schnakenberger (1979) Model'); There are times when it is useful to add grid lines grid on We will discuss in a future section how to have more control over the scale of the grid. To turn off a grid you can simply execute grid off You can do the same with the upper and right bounding boxes on the plots using the command box. By default Matlab has the box on, so box off will create a plot with the usual x-y axes. You may also want to adjust the aspect ratio of your plot, e.g., relative lengths of the x-y axes. For example, axis square will create equal equal sizes for the x and y axes. See the axis command for more options. 10.2. DISPLAYING 2D DATA 95 10.2.1 FIGURE NUMBERS AND SAVING FIGURES You may have noticed that if you simply issue a plot command, Matlab will automatically start with “Figure 1”. If another plot command is issued, it will simply write over Figure 1. To start a new ﬁgure >> figure(2) A second problem is that we may want to create a ﬁgure but then add to it later. To illustrate how this can be accomplished, we will the examine the Hindmarsh Rose model for cortical neurons. dx dt = −ax3 + bx2 + y − z + I0 = −dx2 − y + c dy dt = rsx − rz − rsx1 dz dt (10.6) (10.7) (10.8) where the values of a, b, c, d, r, s and x1 are constants and I0 is an externally applied current. We will assume that r is small and so z adapts slowly enough that we can treat it as a constant, e.g., z = 0. Furthermore, we can assume there is no external stimulus, e.g., I0 = 0. Therefore, our set of equations becomes dx dt = −ax3 + bx2 + y dy dt = −dx2 − y + c and we can then plot x and y nullclines using the following equations 0 = −ax3 + bx2 + y 0 = −dx2 − y + c and therefore we must plot the functions y = ax3 − bx2 y = −dx2 + c (10.9) (10.10) (10.11) (10.12) (10.13) (10.14) (10.15) (10.16) (10.17) So we do not conﬂict with what has already been plotted in Figure 1; type the following into a script called “HMRModel.m”. 96 10. GRAPHICS figure(2) which will open up a new (and blank) ﬁgure. Then type the following commands into the script a = 0.3; b = 2.5; c = -1.; d = 1.0; x = -5:0.01:10; yxnull = a.x.ˆ3 - b.x.ˆ2; yynull = -d.x.ˆ2 + c; plot(x,yxnull,'k'); hold on plot(x,yynull,'k-.'); xlabel('x variable') ylabel('y variable'); title('X and Y Nullclines for Hindmarsh-Rose Model') axis([-5 10 -70 10]) %define a range for x %create x nullcline %create y nullcline You should note that, unlike the previous model, in the Hindmarsh-Rose model, there are three points where the nullclines intersect. The meaning of these intersections is that both dx = 0 and dt dy = 0, and therefore the x − y values for these intersections are equilibrium points. We do not dt know from the plot if they are stable or unstable, but from the plot, we do know that they exist even without solving the equations numerically. To ﬁnish off our plot, it would be good to add a legend. Add the following command to the end of your script. legend('x nullcline','y nullcline'); The last step is to save your plot in a ﬁle on your hard drive. In previous sections, you created a “jpeg” ﬁle using the print command. You could easily change the options to create other ﬁle formats. But, Matlab has its own special ﬁle format (“.ﬁg”) for images. saveas(gcf,'HMR.fig'); The saveas command will save the current ﬁgure (speciﬁed by gcf, meaning “get current ﬁgure”) into a ﬁle “HMR.ﬁg”. You should then close your ﬁgure. But you have saved all of the information in “HMR.ﬁg”. To bring the ﬁgure back into the Matlab environment open 'HMR.fig' will reopen the ﬁgure. You will see in later sections that you can continue to modify the ﬁgure. In this way, you can save work on any graphic and then reopen it at a later time. 10.2.2 VELOCITY MAPS Non-linear differential equations, such at the Hindmarsh-Rose model may be solved numerically using integration methods such as the Euler Method. An alternative was provided by plotting the nullclines in state space. But, there is another way to gain a more intuitive understanding of the dynamics of differential equations. 10.2. DISPLAYING 2D DATA 97 a = 0.3; b = 2.5; c = -1.; d = 1.0; [X,Y] = meshgrid(-5:10,-70:10:10); xvec = -a.X.ˆ3 + b.X.ˆ2 + Y; yvec = -d.X.ˆ2 -Y + c; quiver(X,Y,xvec,yvec,0.3); %Make a grid over x and y %create x vector %create y vector %Plot Velocity Vector Field The command quiver generates an arrow at each point in the grid speciﬁed by X and Y that has a length of xvec in the x direction and yvec in the y direction. The extra value of 0.3 simply scales the vectors. The command meshgrid simply creates the X and Y matrices. The meaning of a velocity map is that if we start the system, i.e., initial condition, at any x-y point, the system will follow the velocity vectors. In fact, the length of the vectors even gives us some indication of how fast the system will move from one point to another. For this reason, velocity maps are sometimes called ﬂow maps - we can think of an initial condition ﬂowing around the state space. 10.2.3 LOG AND SEMI-LOG PLOTS In 1935, George Zipf, a linguistics professor at Harvard, made an incredible claim. If you analyze a large volume written in English and keep track of the words used, a pattern emerges. We can rank the word used most often as 1, second as 2, third as 3 and so on. We can then count the number of times each word is used. If we plot the word rank, x, against the number of times used, f (x), the data surprisingly ﬁts f (x) = ax−k (10.18) where a and k are constants that can be determined from experimental data. What is more, Zipf and others found that it was not only English that followed this pattern, but nearly all other languages. US City populations were found to follow the same equation. So was the distribution of wealth in many different economies. The size of rivers, newspaper distributions, and even computer memory were found to follow the same trend. Another name for Zipf ’s Law is a Power Law. It was only a matter of time before biologists began to test if Zipf ’s Law applied to living systems. 98 10. GRAPHICS Let us assume that we would like to plot a function that represents the ranking of the size of bloods vessel (cm) in the brain a = 2; k = 1.4; x = logspace(1,3,100); fx = a.x.ˆ(-k); figure(1) plot(x,fx) figure(2) loglog(x,fx) The command logspace generates 100 points between 101 and 103.The command loglog plots log(f x) against log(x). You can verify that the log-log plot should be a straight line with a bit of analysis. Matlab also has support for semi-log plots in the commands semiology and semiology. 10.2.4 IMAGES In an earlier section, the commands imagesc and colorbar were introduced. There are some additional commands that can allow for more ﬂexibility. %minimum value %maximum value minc = -2; maxc = 5; %random numbers between minc and maxc X = minc + (maxc-minc).rand(100,100); X(50,50) = 100; %make one value very large imagesc(X) colorbar The problem with these commands is that all of the values are between -2 and 5, except for the one value in the center. When imagesc is used, it automatically scales all of the values. To ﬁx this problem, add the following command to the end of the script above caxis([-2 5]) The last command, caxis, will rescale the color map from -2 to 5. The value of 100 will be treated as a value of 5, i.e., it will appear red. In our examples so far, we have used the default colormap. You should view the help for col- ormap and then issue the commands below to gain some idea of the types of colormaps that are available. load flujet imagesc(X) colormap(winter) 10.2. DISPLAYING 2D DATA 99 and load spine image(X) colormap bone 10.2.5 OTHER 2D PLOTS Matlab has support for a wide range of other two-dimensional plots. Below we explore only a few. Enter the commands below to view each type of graphic. You can always view the help to learn more about any of the functions introduced below. >> pie([2 4 9 10],{'Mutation 1','Mutation 2','Mutation 3','Mutation 4'}); >> pie3([2 4 9 10],{'Mutation 1','Mutation 2','Mutation 3','Mutation 4'}); >> load carsmall >> boxplot(MPG, Origin) %Loads in premade data on cars % Note the error bars Sometimes we also wish to display discrete data, i.e., points are not connected together with lines. >> x = 0:0.01:1; %Generate x vector %Generate sinusoid with random noise >> y = 5sin(2pi.x) + rand(length(x),1); >> stairs(y) >> stem(y) At other times, you may wish to create a histogram that shows the frequencies of different types of events. Below is code to generate a random 1000 x 1000 adjacency matrix where each node is connected to 10% of the network. >> A = rand(1000,1000); >> A = A<0.1; >> NumConnections = sum(A,2); >> hist(NumConnections,20) %CHECK THIS The histogram shows how most nodes are connected to 10% of nodes (100 other nodes), but because it is random, there is a distribution. Lastly, Matlab will allow you to create bar charts that graphically compare many different types of data. B = rand(10,5); bar(B) xlabel('Gene Mutation') ylabel('Frequency') legend('American','Canadian','Mexican','English','German') The chart above may have been a comparison of the frequency of 10 different gene mutations in 5 different populations. 100 10. GRAPHICS 10.2.6 SUBPLOTS There are occasions when it is convenient to display several plots side-by-side. In these instances, you will want to use the subplot command. %Generate x vector x = 0:0.01:1; %Generate 4 noisy sinusoids y1 = 5sin(2pi.x) + rand(1,length(x)); y2 = 5sin(22pi.x) + rand(1,length(x)); y3 = 5sin(32pi.x) + rand(1,length(x)); y4 = 5sin(42pi.x) + rand(1,length(x)); figure(1) subplot(2,2,1) plot(x,y1) subplot(2,2,2) plot(x,y2) subplot(2,2,3) plot(x,y3) subplot(2,2,4) plot(x,y4) The help for the subplot command has more information about how to create more complex multi- panel ﬁgures. 10.3 FIGURE HANDLES In previous sections, we generated a number of plots and learned to alter some aspects of the ﬁgure. To gain more ﬂexibility over the appearance of ﬁgures, Matlab allows the user to output a ﬁgure handle. First, we must clear everything in memory and close all ﬁgures. clear all close all %clears everything in matlab’s memory %closes all open figures Next, we will create a ﬁgure that contains a sinusoid x = 0:0.001:1; h = plot(x,sin(2pix)); where h is the ﬁgure handle. get(h) The command get will display all of the options in the ﬁgure handle. To get a particular option, you can issue get(h,'LineStyle') We will not discuss all of the options, but there are some that are useful to know how to change. To change an option, you can use the set command set(h,'LineWidth',3); which will change the line width from the default of 0.5 to 3 (make the line thicker). 10.3. FIGURE HANDLES 101 10.3.1 THE HIERARCHY OF FIGURE HANDLES In the above section, we only showed some of the basics of getting and setting ﬁgure options. But the ﬁgure you created contains much more information. The highest level handle is gcf which is equal to 1. gcf get(gcf) is a command that will show all of the main ﬁgure options. But in these ﬁgure options are Children, other handles to various parts of the ﬁgure. For example, if we want the handle to the axis AxisHandle = get(gcf,'Children') The axis is given a special handle in Matlab called gca. If you type gca on the command line if should give you the same answer. The axis handle has its own Children that contain the plot you created. PlotHandle = get(AxisHandle,'Children') h get(gca,'Children') and you can verify that all three commands should give the same ﬁgure handle. This may all be a bit confusing, but it allows the user to keep track of the various parts of complex plots, e.g., subplots. For example, we can now set the line width of out plot with set(h,'LineWidth',3); Alternatively, we could have issued set(PlotHandel,'LineWidth',3); Now we can add a second plot hold on g = plot(x,sin(1.52pix),'r'); We have explicitly created a ﬁgure handle (g) to make it easier to change this plot. But try the following command l = get(gca,'Children'); You should notice that now there are two ﬁle handles, and we could treat each differently. In fact, l(1) is our most recently created ﬁgure handle and l(2) is our previous handle. So, if we wanted to view the options for our recently created ﬁgure, we could type 102 10. GRAPHICS get(g) or get(l(1)) Now let’s suppose we wish to change the line thickness and the line type from solid to dash-dot. set(l(1),'LineWidth',3) set(l(1),'LineStyle','-.'); Figure handles can become very complex, but you should remember that they are nested in hierarchies with gcf at the top and gca one step down. 10.3.2 GENERATING PUBLICATION QUALITY FIGURES Given the ﬂexibility in how aspects of ﬁgures can be changed, it should not come as a surprise that many engineers and scientists create images for their journals and other technical writings in Matlab. Below is a template that demonstrates how to generate a publication quality ﬁgure. Brain waves are often thought of as being composed of multiple frequency bands. For ex- ample, Delta waves range from 0-4Hz, Theta waves range from 4-7Hz, Alpha waves range from 8-12Hz, Beta waves range from 12-30Hz and Gamma waves are about 30Hz. The Electroen- cephalogram (EEG) can be scored by a clinical neurologist based upon the strength, i.e., amplitude, of the frequencies present. In fact, they can get an accurate picture of the state of the patient (awake, sleeping, dreaming, thinking), just by looking at the EEG. Below is a section of code that will create a theoretical EEG. Following the creation of the code are a series of commands that change shapes, sizes, colors and even the aspect ratio of the ﬁgure. The last line creates an encapsulated postscript ﬁle with high resolution (600 dots per square inch). x = 0:0.001:2; %Create EEG signal from various sinusoids %Amplitudes reflect signal contribution EEG = 1sin(22pix); EEG = EEG + 1sin(62pix); EEG = EEG + 1sin(102pix); EEG = EEG + 4sin(202pix); EEG = EEG + 2sin(502pix); %2Hz Delta %6Hz Theta %10Hz Alpha %20Hz Beta %50Hz Gamma h = plot(x,EEG,'k'); xlabel('Time (s)','FontSize',20) ylabel('EEG (microV)','FontSize',20,'Rotation',90) axis([0 2 -8 8]) set(gca,'Box','off') set(gca,'TickDir','Out') set(gca,'XTick',[0:0.25:2]) set(gca,'YTick',[-8:4:8]) set(gca,'FontSize',20) set(gca,'LineWidth',2) 10.4. DISPLAYING 3D DATA 103 set(gcf,'Color','white') set(gcf,'Position',[400 400 800 400]) set(gcf,'PaperPosition',[4 4 8 4]) print('-depsc','FrequencyAnalysis.eps','-r600'); You should also note that Matlab allows for inline text, arrows and other simple ﬁgures to be added to the plot. These functions, however, are often better to include in power point or another graphics package. 10.4 DISPLAYING 3D DATA There are occasions where it is helpful to visualize data in three dimensions. Matlab has a number of commands designed for 3D plots. Below are some lines which demonstrate some of Matlab’s capabilities figure(1) t = 0:pi/50:10pi; plot3(sin(t),cos(t),t) xlabel('sin(t)') ylabel('cos(t)') zlabel('t') You can actively move around these data by clicking the rotation tool on the toolbar (next to the hand tool). Try holding down the left mouse button and then dragging. This should rotate the ﬁgure. figure(2) [X,Y,Z] = peaks(30); surfc(X,Y,Z) figure(3) contour(Z) figure(4) mesh(X,Y,Z) You should view the help for these functions to learn about additional 3D plotting functions. You may also wish to explore the help for view, a command that allows the user to set the three-dimensional view point. 104 10. GRAPHICS 10.5 EXERCISES 1. Turn in “HMRModel.m”, “HMR.ﬁg”, “FrequencyAnalysis.eps”. 2. A common device used to grow cells and bacteria is a chemostat. The idea is that as cells metabolize they require a constant supply of nutrients but also need some way to eliminate waste products. A Chemostat is a chamber that has a constant inﬂux of nutrients, while at the same time having a constant efﬂux of solution in the chamber. In such a situation, we can imagine keeping track of both the cell population (N) and the concentration of the nutrient (P ). Below are two differential equations that describe this situation. (cid:12) = N KmaxC Kn + C (cid:12) dN dt (Co − C) − αN (cid:13) − F N V (cid:13) KmaxC Kn + C dC dt = F V (10.19) (10.20) where Co is the concentration of the supply, V is the volume of the growth chamber, F is the input and output ﬂow rate, α is a yield constant, Kmax is the maximum growth rate of cells and Kn is a half maximum growth rate relative to concentration. The two equations above can be rearranged using some algebra to ﬁnd equations for the N and C nullclines. F V Kn C = Kmax − F V N = F (Co − C) (Kn + C) V αKmax (10.21) (10.22) Therefore, the N nullcline is a quadratic and the C nullcline is a simple line. Create a script that will plot both nullclines in a N-C phase space. The following code will create the nullclines for speciﬁc values of the constants alpha = 3.0; F = 1.0; V = 1.0; Kmax = 6; Kn = 50.0; Co = 200.0; %Yield Constant %in and out flow of Chemostat %Chemostat Volume %Maximum Growth Rate %Half Max of Growth Rate %Concentration of Supply N = 0:0.1:1000; C = 0:0.1:200; Cvec = (F/V).Kn./(Kmax-(F/V)); Nvec = F.(Co-C).(Kn+C)./(ValphaKmax); %For N Nullcline %For C Nullcline 10.5. EXERCISES 105 figure(1) plot(N,Cvec) hold on plot(Nvec,C) Create an image called “ChemostatNullclines.jpeg” that is of publication quality. You should use your best judgment and what you have learned in this chapter as a guide. C H A P T E R 11 Toolboxes 107 11.1 INTRODUCTION As mentioned in chapter 1, Matlab is a number of environments all rolled into one. As originally envisioned it is a programming environment, scripting language and a graphics package. Since the early days of Matlab, however, many outside of Mathworks have contributed. Often these new contributors are a group of researchers or industrial scientists writing a series of Matlab scripts (“.m” ﬁles) that perform related functions.These suites of functions, after an evaluation process, sometimes become part of Matlab. Matlab calls these packages toolboxes and allows users to purchase them as products separate from the standard Matlab distribution. To check the packages in your version of Matlab >> ver will display the current version of Matlab and any installed toolboxes. There are hundreds of Matlab toolboxes that can be purchased. Some researchers also offer their own Matlab toolboxes free of charge, although with no guarantees of proper functionality or optimization from Mathworks. There are three ways to get help for toolboxes. First, Matlab has a website at www.mathworks.com for each toolbox under the Support tab. The website gives a brief overview of the functionality of the toolbox along with any new versions. Second, Matlab maintains a user’s guide that can be either downloaded as a pdf or viewed online. It is here that all of the functions (“.m” ﬁles) will be listed along with how to call them. This feature is nice because it allows a user to read a manual before purchasing the toolbox. You can also ﬁnd examples of how to use the toolbox and demonstrations. Once a toolbox is installed, the third option is to view the built-in help. >> help will display the high-level help that is available in Matlab. Of these functions, some are the help for the toolboxes listed in ver. For example, >> help symbolic will display the help for the Symbolic Math Toolbox. In this chapter, we only cover a few of the toolboxes which are of most interest to Biomed- ical Engineers and are readily available at most institutions. 108 11. TOOLBOXES 11.2 STATISTICAL ANALYSIS AND CURVE FITTING Much of this text has focused on the simulation of mathematical models. But much biological and biomedical research exists in the experimental realm. Here Matlab can be useful in the analysis of data, speciﬁcally to perform statistical analysis and best ﬁts. The Matlab statistics toolbox contains functions for descriptive statistics for vectors and matrices of data, e.g., skewness for Skew, cov for covariance, as well as sophisticated random number and probability distribution generators. It also contains linear, e.g., anova1 and anova2 for one and two way analysis of variance, lscov for least- squares, and non-linear, e.g., nlinﬁt) data ﬁtting.There are even commands to help design experiments and specialized graphic utilities. See >> help stats for more information. 11.2.1 DATA FITS TO NONLINEAR FUNCTION It is often the case that an engineer or scientist will collect a series of discrete data points and then need to move from the data to an analytical model, e.g., mathematical function. Typically, an experimentalist will collect data as a series of points as a function of some independent variable that can either be controlled or observed, e.g., time, space, concentration, current. For example, the impedance of a biological material is the resistance (R) to current (I ) as a function of the frequency (ω) of a sinusoidal forcing function. The experiment would send in an alternating current with a particular frequency ω and then record the amplitude of the resulting voltage (also a sinewave). The experimenter would then record the peak-to-peak amplitude of the voltage sinewave as a function of the frequency. >> omega = [0:10:100]; >> SineWaveAmplitude = [2 5 10 37 59 41 12 4 3 1 0.1]; >> plot(omega,SineWaveAmplitude,''); >> hold on %frequency in Hz %You will add to this plot later Rearranging Ohm’s Law (V = I R) to R = V I and assuming I is held constant, the measurement of V is proportional to the impedance, R. From the data, it is then clear that this material will pass current best at low and high frequencies, i.e., the impedance is highest around 40Hz. In many biological applications, to begin creating a model, we need to ﬁt a function to re- sults of an experiment. In the experiment above, we may guess that the data is best ﬁt to a bell-shaped curve, known as a Gaussian Function. G = √ A 2πσ 2 − (x−μ)2 2σ 2 e (11.1) What we need to estimate are the parameters μ (mean), σ (standard deviation) and A (area under the curve). To perform this ﬁt we will use the nonlinear least-squares ﬁt, nlinﬁt, function in Matlab. The function has the following command line call 11.2. STATISTICAL ANALYSIS AND CURVE FITTING 109 Beta = nlinfit(x,y,Model,beta0); where x and y are the independent and dependent variables of the real data. beta0 is the initial guess for the parameters and Model is the name of a function that contains the guessed function. You should note that the Model function and parameters, beta0, must match. The function returns the best ﬁt, Beta, for the parameters. For initial guesses, we can assume the mean is at 40. We can also guess that our standard deviation is approximately 15. Lastly, area we can estimate as 1000. >> beta0 = [40 15 1000]; The last step is creating the function to pass to nlinﬁt. Open up a script called “Gauss.m” and enter the following function [G] = Gauss(beta,x); mu = beta(1); variance = beta(2)ˆ2; area = beta(3); %define mean %define area %define standard deviation G = (area/sqrt(2pivariance)).exp(-((x-mu).ˆ2)./(2variance)); To test this function >> x = 0:1:100; >> G = Gauss(beta0,x); >> plot(x,G,'r') We are now ready to tune the parameters >> Beta = nlinfit(SineWaveAmplitude,omega,@Gauss,beta0); >> Beta You should note that the @ symbol is used to reference a function. After many iterations, you will have a best ﬁt to the Gaussian parameters contained within Beta. You can then check the ﬁt >> NewG = Gauss(Beta,x); >> plot(x,NewG,'g'); You should view the help for nlinﬁt to see how to measure the quality of the ﬁt, as well as how to bound certain parameters such as the maximum number of iterations to take in searching for a best ﬁt. Some other common functions to ﬁt are linear and exponentially increasing or decreasing. There are two other functions that deserve mention in the context of biomedical engineering because they appear often. The ﬁrst is the monotonically increasing or decreasing sigmoid. S = 1 1 + eax (11.2) 110 11. TOOLBOXES where x is the independent variable. The sign of a (+ or -) will determine whether the function increases or decreases and the magnitude of a will determine the rate of increase or decrease. You may wish to generate a few lines of Matlab code to plot the sigmoid function - it should be “S” shaped. A more general form of the Sigmoid function is the Boltzmann distribution B = 1 1 + e(x−xo)/k (11.3) where k is the inverse of a, and therefore controls the slope and increasing or decreasing trend. You may have noticed that the sigmoid was centered around zero. The term xo is an offset and controls what is known as the half-max crossing point and will therefore translate the sigmoid. Note that both functions range from 0 to 1, making scaling to ﬁt experimental data a simple task. Note that Matlab also has a series of commands for ﬁtting data to surfaces. The idea is the same, but now there are two independent variables and one dependent variable (often thought of as the height of the surface). 11.2.2 INTERPOLATION AND SPLINES Two very useful operations that follow directly from curve ﬁtting are interpolation and extrapolation. In the impedance example above, we may wish to estimate the voltage output every 1Hz even though you only measured it every 10Hz. The function interp1 will allow you to interpolate values. %frequency in Hz >> figure(2) >> omega = [0:10:100]; >> SineWaveAmplitude = [2 5 10 37 59 41 12 4 3 1 0.1]; >> plot(omega,SineWaveAmplitude,''); >> DesiredOmega = [0:1:100]; >> NewV = interp1(omega,SineWaveAmplitude,DesiredOmega); >> hold on >> plot(DesiredOmega,NewV,'r'); The inputs to interp1 are the original independent and dependent variables, along with the desired independent variable. The output, NewV , is the new vector of voltages that correspond to DesiredOmega. Finally, we plot the interpolated data over the original data. With no options interp1 will default to a “linear” interpolation, meaning that all data points in SineW aveAmplitude will be connected by straight lines. Interpolation can become much more sophisticated by using higher order ﬁts between data points. The most important options for interp1 are “spline” and “cubic”. For example, >> NewVSpline=interp1(omega,SineWaveAmplitude,DesiredOmega,'spline'); >> plot(DesiredOmega,NewVSpline,'g'); You should note that a spline is simply a local polynomial ﬁt to data. In other words, a low order polynomial is ﬁt to only a few local points. A different ﬁt is then created for other local points. 11.3. DIFFERENTIAL AND INTEGRAL EQUATIONS 111 You should be very careful not to confuse NewV with real measured experimental data or the analytical function, created above. To get an analytical function we must assume a form for the equation and then ﬁt the parameters using a best ﬁt. This ﬁt was performed on the entire data set. With N ewV the interpolation was created without assuming any function, only very simple functions, e.g., polynomials, that span a few points between neighboring points. In our example, we used all evenly spaced data points, but this does not need to be the case. In other words, the independent variables omega and DesiredOmega could have been an irregularly spaced vector. You should view the help for interp1 for more details. You can also view the functions interp2, interp3 and interpn which perform 2, 3 and N dimensional interpolation. The spline toolbox also has tools for extrapolation, conﬁdence intervals, tools to remove outliers and ﬁtting to surfaces. You should type >> help splines for more information. 11.3 DIFFERENTIAL AND INTEGRAL EQUATIONS In Section 7.3, we introduced Euler’s Method for the numerical integration of a differential equa- tion. And an example in chapter 7 demonstrated how to use Euler’s Method for multiple coupled differential equations. Although the Euler Method is easy to understand and program, it is limited in that it is only ﬁrst order accurate. The idea of the order of the method is one that comes up in many numerical methods, and it signiﬁes how well of an approximation the method will yield. In the case of differential equations, we can write the solution to a differential equation as a Taylor series. Then the order of the numerical integration technique is given as the number of terms in the Taylor series that are included in the approximation. In the case of Euler, only the ﬁrst term is included. There are other numerical integration methods that use many more orders to improve accuracy. The most popular are a series of methods with any desired order known as the Runga-Kutta method. Although, in principle, the order can be increased to obtain more and more accurate solu- tions, the computational cost (memory and time) increases as order increases. For most applications, the 4-5 order is where the gain in numerical accuracy balances out the computational cost. To show how the built-in solvers can be used, we will solve the same FitzHugh-Nagumo 112 11. TOOLBOXES model of a neuron as in chapter 7 = V − V 3 3 = a ∗ (V + b − cW ) − W + I dV dt dW dt (11.4) (11.5) where V is the cell membrane potential, W is a recovery variable and I is a stimulus current. We will assume the constants are a = 0.08, b = 0.7 and c = 0.8. We will use the ode45 solver that has the following command line call [t,y]=ode45(odefun,tspan,y0); where odef un is a function that will evaluate the derivatives given the variables in the vector y. y0 are the initial conditions and tspan is a vector with two elements, [T 0, Tf inal]. First, open a Matlab function “FHNFunction.m” and enter the following text function dy = FHNFunction(t,y) a = 0.08; b = 0.7; c = 0.8; I = 0.556; V = y(1); W = y(2); %Simulus Current dy = zeros(2,1); dy(1) = V-(Vˆ3)/3-W+I; dy(2) = a(V+b-cW); In this function, all that is reported is how to compute the right-hand term in the differential equations. This is done because there is no assumption made about how the time step ((cid:8)t) will be picked or how the solution will be advanced forward. Next, enter the following on the command line. >> tspan = [0 100]; >> y0 = [0 0]; >> [t,y]=ode45(@FHNFunction,tspan,y0); >> plot(t,y); You should note that the output t contains a vector of the times and y contains both the V and W vectors. One reason to use one of Matlab’s built-in solvers is that they very often have what are known as adaptive time steppers. To view how Matlab has changed (cid:8)t during the simulation >> plot(diff(t)); 11.3. DIFFERENTIAL AND INTEGRAL EQUATIONS 113 You should note that unlike the Euler method used in chapter 7, the time step changes. In general, (cid:8)t becomes large when the solution is not changing much and becomes small when the solution is changing rapidly. The help for ode45 contains a list of the other solvers that can be used, functions for evalu- ating the accuracy of the solution (e.g., deval ) as well as some demonstrations. You should also note that there is a partial differential equation toolbox for handling cases where dynamics are occurring in both time and space. 11.3.1 INTEGRALS AND QUADRATURE Finding the area under a curve can often yield valuable insight into a biological problem. For example, we may need to ﬁnd the area under a curve to compute total charge as a current that ﬂows over time Q = (cid:14) t2 t1 I (t)dt or mechanical work as the integral of force applied over some distance. W = (cid:14) x2 x1 F (x)dx (11.6) (11.7) The problem is that rather than have the analytic functions I (t) or F (x), we have discrete points in the vectors I or F . There are various methods for numerically computing areas under curves formed by discrete points, and they all fall under the general category of Quadrature. For example, >> x = 0:0.01:1; >> y1 = 20exp(x); >> y2 = 10rand(length(x),1); >> Int1 = trapz(x,y1); >> Int2 = trapz(x,y2); And it is a simple matter to then get the area between the two curves as >> Int1-Int2 The above example uses the trapezoidal approximation. Matlab has many other quadrature methods, each with their advantages and disadvantages. As with most numerical methods, there is a trade off between accuracy on the one hand and computing cost on the other. Some quadrature methods can be found in the command quad. You should note that you can also evaluate double (quad2d ) and triple (triplequad ) integrals. 114 11. TOOLBOXES 11.4 SIGNAL PROCESSING TOOLBOX Biological signals are often noise, low in amplitude and composed of many superimposed streams of information. Signal processing is what is necessary to isolate features of interest. For example, when analyzing an EEG signal from the scalp, it may be important to determine the relative contribution of a particular frequency band to the signal. Alternatively, it may be important to look for what is known as a complex - a series of spikes and waves that are signatures of speciﬁc events in the brain. Using these two types of information, a clinical neurologist can gain a great deal of information about the healthy or abnormal function of a patient’s brain. The type of operation to perform is nearly always some sort of ﬁlter, and these are typically either in the time or frequency domain. In the time domain, the two most useful are moving averages and correlations. Moving averages are important because a serious problem with most experimental data is that it is noisy. The result is that an upward or downward trend can often be lost when curve ﬁtting or looking for trends. One often used solution is to smooth the data before ﬁtting to a function. The key is to average nearby points, but the weighting of those points may vary. >> w1 = hamming(64); >> wvtool(w1) >> Sig = rand(1000,1); >> SigWin = conv(Sig,w1,'same'); will create and then display the Hamming Window with 64 samples. The idea is that this window will be moved over the entire dataset, and each new point will then be a weighted average of the 64 points around it. Then the window is moved one step forward the averaging occurs again. For example, >> t = 0:0.01:1; >> Sig = sin(2pit); >> Sig = Sig + rand(1,length(t)); >> plot(t,Sig); >> hold on >> SigWin = conv(Sig,w1,'same'); >> plot(t,SigWin,'r'); %noisy sinusoid %smoothed sinusoid Note that the general shape of the sine wave has been recovered, but the amplitude is off. More processing would be needed to correct this. Also note that the convolving function (conv) was used to apply the ﬁlter to all points. Other useful windows can be found in the help for window. Another very common operation is to gain some quantitative measure of how similar two signals are to one another. Here we are looking for correlations. Matlab has a number of functions, e.g., conv, cov, corrcoef, for performing these types of operations. The theory behind these operations will not be covered here, but you can view the help within Matlab and online for more information. 11.5. IMAGING PROCESSING TOOLBOX 115 In the frequency domain, we typically think of designing a ﬁlter that will eliminate some frequencies but keep others. For example, a bandpass frequency ﬁlter may be needed to analyze the results of fatigue testing on a muscle, but a low pass ﬁlter may be desirable for isolating low frequencies in an EEG. To gain more appreciation for the options in the signal processing tool box, you should open up an internet browser and navigate to www.mathworks.com. Click on Products and Services and then on Product List. You should see a full list of the Matlab toolboxes. Scroll down to the Signal Processing Toolbox and click on the link. On the left-hand menu, you will ﬁnd a link to Demos and Webinars. You should watch the short Introduction demo. On the left-hand side, you will also ﬁnd a description of the toolbox along with a complete list of all of the functions. You should note that nearly all toolboxes in Matlab have good tutorials to help you get started. 11.5 IMAGING PROCESSING TOOLBOX Biomedical engineers often generate images or display their data as images. In both cases, the raw images, like biological signals, are typically noisy and low contrast. The image processing toolbox contains algorithms for bringing features of interest to the forefront. There are also times when a user may be looking for correlations between different parts of an image, for example to track a cell as it crawls across a series of images that comprise a movie (known as image registration). Again, the image processing toolbox contains routines for just such a task. Another important feature of the image processing toolbox is edge detection. Below is a very brief demonstration. >> IMAGE = imread('circuit.tif'); >> figure(1); imshow(IMAGE); >> IMAGE2 = edge(IMAGE,'prewitt'); >> figure(2); imshow(IMAGE2); >> IMAGE3 = edge(IMAGE,'canny'); >> figure(3); imshow(IMAGE3); The above lines highlight three commands. The ﬁrst is imread which is a general purpose reader for many different image formats. Second is imshow which is a general function for displaying grayscale images. Last is the edge command which ﬁnds edges of an image in the regions where there is a large contrast in grayscale. edge contains many different methods and options, and you may want to view the help ﬁle. There are a number of other helpful commands, such as imresize, imrotate, imcrop and im- transform as well as a number of sample images to test image processing algorithms, e.g., “board.tif ”, “trees.tif ”,“cameraman.tif ”. You may wish to view some of the built-in demonstrations that will give you some sense of the power of the image processing toolbox. >> iptdemos 116 11. TOOLBOXES 11.6 SYMBOLIC SOLVER Thus far, we have focused on programming techniques and toolboxes which perform numerical approximations. Matlab also has a toolbox for performing symbolic math, allowing for direct analytical solutions. The functions in the Symbolic Toolbox are very similar to two other well- known symbolic math processors, Mathematica (Wolfram Research) and Maple (MapleSoft). It should be noted that Mathematica and Maple both allow algorithmic computing and graphics, similar to the commands in the ﬁrst 10 chapters, but their focus is on symbolic math. Matlab, on the other hand, is designed for numerical approximations and has the symbolic toolbox as an addition. In keeping with the theme of only showing the surface level of each toolbox, we will show a few examples where the Symbolic Toolbox can be useful. An important distinction between Symbolic and Algorithm solutions must be made ﬁrst. Consider the following equations that describe a compartment model of a drug in the body. dB dt = −koA dA dt = koA − k1B dE dt = k1B (11.8) (11.9) (11.10) where A is concentration at the absorption site, B is the concentration in the body and E is the concentration being eliminated. We have already learned a variety of ways to solve this problem given the initial conditions A(0) = Ao, B(0) = 0 and E(0) = 0. These range from creating a matrix, to ﬁnding eigenvalues to solving the equations numerically using the toolboxes described above. In all cases, Matlab is using some form of a numerical method, e.g., a matrix solve, numerical integration. Below are the commands for solving the equations above >> % To be entered on the same line >> [A,B,E]=dsolve('DA=-k0A','DB=k0A-k1B','DE =k1B', >> 'A(0)=A0','B(0)=0','E(0)=0'); >> A = simplify(A); >> B = simplify(B); >> E = simplify(E); Note that the solution is not a vector of values, but rather an equation. This is what makes symbolic math different from numerical methods. The symbolic math toolbox can also perform differentiation (diff) and integration (int). It may seem strange that the diff command could either be used to ﬁnd the difference between elements in a vector or perform symbolic differentiation. This is an example where Matlab has what is called overload methods. If you type >> help diff 11.7. ADDITIONAL TOOLBOXES AND RESOURCES 117 you will notice that at the bottom of the help is a section on Overload Methods, and one of the listed methods is sym/diff. If you click on this link, you will be taken to the help for the symbolic differentiation. This still does not explain how Matlab seems to know which version of diff to use. The an- swer is in the values that are passed in. You should note that both commands take one variable, but the numerical diff takes a vector whereas the symbolic diff takes a function. >> x = sym('x'); % create a variable called x >> t = sym('t'); % create a variable called t %analytic result >> diff(sin(xˆ2)) %evaluate analytic result >> diff(tˆ6,6) The same logic applies to int, which can be used either in a numerical or analytic way in Matlab. You should note that the sym command was used to create a symbolic variable. You should view the Matlab memory to verify that x and t are in fact of the variable class “symbolic”. Likewise, you may want to force one function to be substituted into another using the sub command. Above a series of differential equations were solved, but a more simple solve is for simulta- neous algebraic equations >> [x,y] = solve('xˆ2 + xy + y = 3','xˆ2 - 4x + 3 = 0') You can even perform more advanced analytical processes such as a Taylor series expansion. 11.7 ADDITIONAL TOOLBOXES AND RESOURCES There are a wide range of additional toolboxes available through Matlab. Below are some that have direct ties to biology and biomedical engineering. 1. Simulink is a graphical programming interface for simulating systems. It consists of a series of graphical blocks that can be connected by “wires”. In this way, the ﬂow of the program is visibly apparent and does not require the writing of a script. 2. Graphical User Interfaces (GUIs) allow a user to interact with programs (similar to those described in Section 6.7), but in a custom designed window. Many of the same web-like inputs are supported, including radio buttons and text boxes, but Matlab also supports sliders, dials and the ability to embed custom graphics into the window, e.g., two and three-dimensional plots, subplots. GUIs are a very powerful way to make a complex program more user friendly. For more information, there are a number of good web resources as well as a built-in GUI creator called guide. 3. Neural Networks are an abstraction of how real neurons connect to one another and perform pattern recognition functions on data. They typically need to be trained on some data set, 118 11. TOOLBOXES where the answer is known. Parameters of the network are adjusted to give the minimum error between the actual output of the network and the desired output of the network. In this way, neural networks are very similar to ﬁlters, but they are adaptable and tunable. 4. Genetic Algorithms are an abstraction of how evolution is thought to use random variation, mutation, selection and mating to produce good (ﬁt in the language of genetic algorithms) solutions to a problem. For some problems, the possible solution is not obvious. Even worse, because there may be many parameters involved, it would take an enormous amount of time to perform a parametric study. In these situations, we can generate a random sampling of possible solutions that must compete with one another for some resource. The most ﬁt solutions will outcompete the less ﬁt. These most ﬁt solutions will have the opportunity to “breed” with other ﬁt solutions in the hope of creating an even more ﬁt solution. Superimposed on these dynamics may also be mutation, which will widen the exploration of the solution space. 5. Control Systems is a diverse ﬁeld that spans many engineering disciplines and is largely about the idea of self-regulation and system characterization. In biological systems, this is similar to the idea of homeostatis and there is an entire ﬁeld called systems physiology that studies biological function from a quantitative, systems point of view. Likewise, a biomedical engineer often must create devices that compensate for some poorly functioning part of the body. The control systems toolbox contains basic routines for simulating and characterizing systems as well as special graphics routines. 6. SimBiology is a graphical interface for modeling systems in biology and pharmacokinetics. It is similar in many ways to Simulink and also provides the user with some unique solvers and analysis tools. 7. MEX, short for Matlab executable, allows users to write a function in a compiled language, e.g., C, C++, FORTRAN, and then use that function in Matlab. MEX code is not written in Matlab and therefore requires a user to have knowledge of another computing language. MEX functions are very useful when an algorithm cannot make good use of matrix-vector operations, i.e., it contains many loops. These functions will appear as built-in functions in Matlab - recall an attempt in an earlier chapter to viewing the “.m” ﬁle for sum. 8. The Matlab Compiler allows a user to compile their Matlab code. There are at least two reasons to compile code. First is to speed up simulation time. Remember that Matlab is an interpreted scripting language, meaning that it is ﬂexible but slow. Compiling could greatly increase the speed of the code. Second is if you wish to share the function of your code, without sharing the code itself. This can be useful if you work for a company and do not wish to share the algorithms that are used. 9. Mathworks recently added a Parallel Computing toolbox to allow users with networked computers to break up a large computational task into smaller tasks that can then be sent to individual computers. It should be noted that some algorithms lend themselves to easy adaptation to parallel computing, whereas others do not. 11.7. ADDITIONAL TOOLBOXES AND RESOURCES 119 11.7.1 MATLAB CENTRAL AND OTHER ONLINE HELP There are a number of other very helpful online resources. The most important is MatlabCen- tral, a place for Matlab users to ask for help, post help and post new code. It is located at http://www.mathworks.com/matlabcentral/ and should be the ﬁrst place you look if you have an algorithm to write. It is accepted practice in the coding world to use the code of others and to cite them appropriately. You may also ﬁnd code by using a search engine to ﬁnd the websites of others. Both can be excellent sources of code, but you should remember that Mathworks does not verify the code from outside parties. Author’s Biography 121 JOSEPH V. TRANQUILLO Joseph Tranquillo is an associate professor of biomedical engineering at Bucknell University where he has been a faculty member since 2005. He received his Doctor of Philosophy degree in biomedical engineering from Duke University (Durham, NC) and Bachelor of Science degree in engineering from Trinity College (Hartford, CT). His teaching interests are in biomedical signals and systems, neural and cardiac electrophys- iology, and medical device design. Nationally Joe has published or presented over 40 peer reviewed or invited works in the ﬁeld of engineering education. He was the founder and inaugural chair of the Undergraduate Research Track at the Biomedical Engineering Society (BMES) conference, co-organized the Biomedical Engineering Body-Of-Knowledge Summit and currently serves on the board of the Biomedical Engineering Division of the American Society of Engineering Education (ASEE). He is the winner of the 2010 National ASEE Biomedical Engineering Teaching Award. His technical research interests are in non-linear dynamics in the heart and brain. He has over 50 publications and presentations, and he has authored a textbook, Quantitative Neurophys- iology. He is a member of the Biomedical Engineering Society, IEEE Engineering in Medicine and Biology Society, American Physical Society and is an elected member of Sigma Xi and Heart Rhythm. When not teaching or doing research, he enjoys improvisational dance and music, running trail marathons, backpacking, brewing Belgian beers, and raising his two children Laura and Paul.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8379400.pdf&bkn=8379399&pdfType=book	Series ISSN 1939-5221 Strategic Cost Fundamentals for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese, West Virginia University (Emeritus) This book is designed to introduce designers, engineers, technologists, estimators, project managers, and financial analysts as well as students in engineering and business to strategic cost tools for project cost evaluations. The three main sections are as follows. (1) Cost Relationships, Financial Statements, and Performance Measures–This section describes the relationships between cash flows and profits; the relationships between financial statements and the Purcell Diagram; and the issues of cost estimating, time-based breakeven analysis and time-based earned schedule. (2) Tools for Economic Evaluations– This section considers the basic mathematical relations used behind the economic equations and factors; discrete and continuous interest; depreciation terms and methods; and the Present Value of Principal Approach for evaluating loans. (3) Methods for Project Evaluation and Risk Analysis–This section considers payback periods, present worth analysis, return on investment, internal rate of return, benefit/ cost ratios and positive-negative project balances; risk techniques of sensitivity analysis, optimistic- pessimistic analysis, discrete probability examples, and continuous probability models using the normal and triangular distributions. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com Synthesis Lectures provide concise original presentations of important store.morganclaypool.com Strategic Cost Fundamentals for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese C R E E S E S T R A T E G I C C O S T F U N D A M E N T A L S M O R G A N & C L A Y P O O L Strategic Cost Fundamentals for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Strategic Cost Fundamentals: for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese 2018 Empowering Professional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimizaton, Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 iii Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 iv Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 v Copyright © 2018 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Strategic Cost Fundamentals: for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese www.morganclaypool.com ISBN: 9781681733524 ISBN: 9781681733531 ISBN: 9781681733548 paperback ebook hardcover DOI 10.2200/S00846ED1V01Y201804ENG032 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Series ISSN Print 1939-5221 Electronic 1939-523X Strategic Cost Fundamentals for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese SYNTHESIS LECTURES ON ENGINEERING #32 CM&cLaypoolMorganpublishers&ABSTRACT This book is designed to introduce designers, engineers, technologists, estimators, project man- agers, and ﬁnancial analysts as well as students in engineering and business to strategic cost tools for project cost evaluations. The three main sections are as follows. (1) Cost Relationships, Financial Statements, and Performance Measures—This section describes the relationships be- tween cash ﬂows and proﬁts; the relationships between ﬁnancial statements and the Purcell Di- agram; and the issues of cost estimating, time-based breakeven analysis and time-based earned schedule. (2) Tools for Economic Evaluations—This section considers the basic mathematical relations used behind the economic equations and factors; discrete and continuous interest; de- preciation terms and methods; and the Present Value of Principal Approach for evaluating loans. (3) Methods for Project Evaluation and Risk Analysis—This section considers payback peri- ods, present worth analysis, return on investment, internal rate of return, beneﬁt/cost ratios and positive-negative project balances; risk techniques of sensitivity analysis, optimistic-pessimistic analysis, discrete probability examples, and continuous probability models using the normal and triangular distributions. KEYWORDS risk analysis, project evaluation, loans, Purcell diagram, engineering economic ex- pressions, breakeven analysis, cost estimating and proﬁt calculations, depreciation methods, earned value management Contents ix 1 2 3 PART I Cost Relationships, Financial Statements, and Performance Measures . . . . . . . . . . . . . . . . . . . . . . 1 Fundamental Terms and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Basic Relationships between Cash Flows, Proﬁts, Depreciation, and Taxes . . . 3 1.2 1.3 Cash Flow and Proﬁt Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Cash Flow Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Financial Statements and the Purcell Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 2.2 Financial Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 The Purcell Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6 Costs and Cost Estimating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Cost Components for Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.1 Basic Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Traditional and ABC Overhead Allocation Methods . . . . . . . . . . . . . . 28 3.2.3 Proﬁt Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Cost Estimation Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6 x 4 Breakeven Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Breakeven Model Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Breakeven Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.1 Categories and Typical Examples for the Production Quantity-Based System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.2 Categories and Typical Examples for the Production Time-Based System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Production Quantity-Based Breakeven Example . . . . . . . . . . . . . . . . . . . . . . . 46 Production Time-Based Breakeven Example . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Earned Value Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Earned Value Management Performance Parameters . . . . . . . . . . . . . . . . . . . . 59 Example Problem Using Traditional Earned Value Management . . . . . . . . . . 62 Example Problem Using Earned Schedule in Earned Value Management . . . 63 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 PART II Tools for Economic Evaluations . . . . . . . . . . . 75 6 Fundamental Deﬁnitions, Terms, and Concepts for Technical Economic Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.1 6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Fundamental Terms Related to Interest Calculations . . . . . . . . . . . . . . . . . . . . 77 6.2.1 Interest and Interest Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Actual, Compound, Nominal, and Eﬀective Annual Interest Rates . . . . . . . . 81 6.3 Factors in Determining Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.4 6.5 Inﬂation-Free Interest Rates, Constant Currency, and Actual Currency . . . . . 83 6.6 Currency Exchange Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 xi 6.7 6.8 6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7 8 Basic Mathematical Relationships for Economic Calculations . . . . . . . . . . . . . 87 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.1 7.2 Sums of Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.3 Geometric Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Inﬁnite Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.6 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.7 Basic Economic Factors and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8.1 8.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Single Payment Discrete Interest Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8.2.1 Discrete Interest Future Worth Factor (F=P; i; n) . . . . . . . . . . . . . . . . . 94 8.2.2 Discrete Interest Future Worth Example . . . . . . . . . . . . . . . . . . . . . . . . 95 8.2.3 Discrete Interest Present Worth Factor .P =F; i; n/ . . . . . . . . . . . . . . . . 95 8.2.4 Discrete Present Worth Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 8.3 Uniform Series Payments Discrete Interest Factors . . . . . . . . . . . . . . . . . . . . . 96 8.3.1 Uniform Series Discrete Interest Future Worth Factor .F=A; i; n/ . . . . 97 8.3.2 Uniform Series Discrete Interest Future Worth Example . . . . . . . . . . . 98 8.3.3 Sinking Fund Discrete Interest Factor .A=F; i; n/ . . . . . . . . . . . . . . . . . 98 8.3.4 Sinking Fund Discrete Interest Factor Example . . . . . . . . . . . . . . . . . . 99 8.3.5 Uniform Series Discrete Interest Present Worth Factor .P =A; i; n/ . . . 99 8.3.6 Uniform Series Discrete Interest Present Worth Example . . . . . . . . . 100 8.3.7 Capital Recovery Discrete Interest Factor .A=P; i; n/ . . . . . . . . . . . . . 101 8.3.8 Capital Recovery Discrete Interest Factor Example . . . . . . . . . . . . . . 101 Single Payment Continuous Interest Factors . . . . . . . . . . . . . . . . . . . . . . . . . 102 8.4.1 Continuous Interest Future Worth Single Payment Factor 8.4 .F=P; r; n/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 8.4.2 Continuous Interest Future Worth Single Payment Example . . . . . . . 103 8.4.3 Continuous Interest Present Worth Single Payment Factor .P =F; r; n/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 8.4.4 Continuous Interest Present Worth Single Payment Example . . . . . . 104 8.5 Uniform Series Payments Continuous Interest Factors . . . . . . . . . . . . . . . . . 104 xii 8.5.1 Uniform Series Continuous Interest Factors–Future Worth, Sinking Fund, Present Worth, and Capital Recovery . . . . . . . . . . . . . 104 8.5.2 Uniform Series Continuous Interest Future Worth .F=A; r; n/ Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 8.5.3 Uniform Series Continuous Interest Sinking Fund .A=F; r; n/ Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 8.5.4 Uniform Series Continuous Interest Present Worth .P =A; r; n/ Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8.5.5 Uniform Series Continuous Interest Capital Recovery Factor .A=P; r; n/ Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 8.6 8.7 8.8 9 Gradient Economic Factors and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 9.6 9.5 9.1 9.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Standard Uniform Gradient Discrete Interest . . . . . . . . . . . . . . . . . . . . . . . . 113 9.2.1 Standard Uniform Gradient Discrete Interest Example . . . . . . . . . . . 116 9.3 Uniform Ramp Gradient Discrete Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 9.3.1 Uniform Ramp Gradient Discrete Interest Example . . . . . . . . . . . . . . 119 9.4 Geometric Gradient Discrete Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 9.4.1 Geometric Gradient Discrete Interest Example . . . . . . . . . . . . . . . . . 123 Escalation Gradient Discrete Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 9.5.1 Escalation Gradient Discrete Interest Example . . . . . . . . . . . . . . . . . . 126 Standard Uniform Gradient Continuous Interest Formulas . . . . . . . . . . . . . . 129 9.6.1 Standard Uniform Gradient Continuous Interest Example . . . . . . . . 129 Ramp Uniform Gradient Continuous Interest Formulas . . . . . . . . . . . . . . . . 131 9.7.1 Uniform Ramp Gradient Continuous Interest Example . . . . . . . . . . . 132 9.8 Geometric Gradient Continuous Interest Formulas . . . . . . . . . . . . . . . . . . . . 133 9.8.1 Geometric Gradient Continuous Interest Example . . . . . . . . . . . . . . 134 Escalation Gradient Continuous Compounding Formulas . . . . . . . . . . . . . . 135 9.9.1 Escalation Gradient Continuous Interest Example . . . . . . . . . . . . . . . 136 9.10 Summary of Gradient Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 9.12 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 9.9 9.7 xiii 10 Depreciation Terms, Methods, and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.1.1 Cash Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 10.2 Depreciation Terms and Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 10.2.1 Depreciation Classes of Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 10.2.2 Recovery Period and Depreciation Life . . . . . . . . . . . . . . . . . . . . . . . . 147 10.2.3 Depreciation Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 10.3 Traditional Methods of Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 10.3.1 Straight Line Depreciation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 10.3.2 Declining Balance Depreciation Method . . . . . . . . . . . . . . . . . . . . . . . 151 10.3.3 Depreciation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 10.4 The MACRS Depreciation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 10.4.1 MACRS-GDS Recovery Periods and Property Classes . . . . . . . . . . . 154 10.4.2 MACRS-ADS Recovery Periods and Property Classes . . . . . . . . . . . 155 10.4.3 MACRS-GDS Mid-Year Recovery Periods . . . . . . . . . . . . . . . . . . . . 156 10.4.4 MACRS-ADS Mid-Year Recovery Periods . . . . . . . . . . . . . . . . . . . . . 156 10.5 Other Depreciation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 10.5.1 Section 179 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 10.5.2 Production-Based Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 10.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 10.8 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 11 The Impact of Loans upon Cash Flows, Taxes, and Proﬁts . . . . . . . . . . . . . . . . 167 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 11.2 The Present Value of Principal Approach for Determining the Principal and Interest Components of a Loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 11.3 Example Problem of Loan Problem Using Present Value of Principal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 11.4 Loans with Cash Flows, Depreciation, Proﬁts, and Taxes . . . . . . . . . . . . . . . 169 11.5 Example Problems of Loans with Cash Flows, Depreciation, Taxes, and Proﬁts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 11.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 11.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 11.8 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 xiv PART III Methods for Project Evaluation and Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 12 Basic Project Evaluation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.2 Payback Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 12.2.1 Traditional Payback Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 12.2.2 Discounted Payback Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 12.3 Time Value of Money Analysis for Project Proﬁt Evaluation . . . . . . . . . . . . 186 12.3.1 Present Worth Analysis of Proﬁts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 12.3.2 Future Worth and Average Annual Worth of Proﬁts . . . . . . . . . . . . . 187 12.4 Return of Original Investment (ROI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 12.4.1 ROI – Not Discounted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 12.4.2 ROI – Discounted (ROI-D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.4.3 ROI Annual Worth – AW (ROI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.4.4 ROI Annual Worth (Base Time) – AW-b (ROI) . . . . . . . . . . . . . . . . 189 12.5 Return on Average Investment (RAI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.5.1 RAI – Not Discounted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 12.5.2 RAI – Discounted (RAI-D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 12.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 12.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 12.8 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 13 Advanced Project Evaluation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 13.2 Internal Rate of Return (IRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 13.3 Modiﬁed Internal Rate of Return (MIRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 13.4 Beneﬁt/Cost Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 13.4.1 Conventional Beneﬁt/Cost Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 13.4.2 Traﬃc Intersection Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 13.5 Modiﬁed Beneﬁt/Cost Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 13.6 Positive and Negative Project Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 13.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 13.6.2 Project A Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 13.6.3 Project Z Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 13.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 13.9 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 14 Introduction to Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 xv 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 14.1.1 Risk vs. Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 14.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 14.2.1 Innovative 3D Rapid Prototyping and Tooling Center Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 14.2.2 Selling Price Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 14.2.3 Processing Capacity Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 14.2.4 Tax Rate Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 14.2.5 Investment Life Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 14.2.6 Required Rate of Return Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 14.2.7 Total Cost Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 14.3 Optimistic-Pessimistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 14.3.1 Innovative 3D Rapid Prototyping and Tooling Center Investor Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 14.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 14.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 14.6 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 15 Risk Analysis with Probability Considerations . . . . . . . . . . . . . . . . . . . . . . . . . 227 15.1 Probability Methods and Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 15.2 Discrete Probability Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 15.2.1 Donnie the Dealmaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 15.2.2 The Innovative 3D Rapid Prototyping and Tooling Center . . . . . . . . 230 15.3 Continuous Probability Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 15.3.1 Normal Distribution Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 15.3.2 Triangular Distribution Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 15.4 Risk Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 15.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 15.6 Evaluative Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 A Discrete and Continuous Compounding Factors . . . . . . . . . . . . . . . . . . . . . . . 247 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 PART I Cost Relationships, Financial Statements, and Performance Measures C H A P T E R 1 3 Fundamental Terms and Concepts 1.1 INTRODUCTION Strategic cost management includes economic analysis (engineering economics) as well as cost estimating (cost engineering), project management, and ﬁnancial analysis. Cash ﬂows and prof- its are the two major strategic cost measures for evaluating the success of an enterprise and taxes, loans, and depreciation have major inﬂuences upon the cash ﬂows and proﬁts. Positive cash ﬂows are necessary for the success of an enterprise and is similar to the need of water to keep a plant alive. Positive proﬁts are the rewards of the enterprise and are similar to the fruit of the plant. If there are no positive cash ﬂows, the enterprise will fail similar to a plant without water and die. If the enterprise does not produce positive proﬁts, the enterprise fails as the investors will not support it and plants that do not produce will also be left to die. Equipment is needed to produce products and the cost of the equipment must be recovered and that is done through the concept of depreciation. Depreciation amounts are spread over the predicted economic life of the investment and diﬀerent approaches for determining the depreciation amounts can be used. Equipment purchases often require loans to assist in the purchase of equipment and the loan interest is a depreciable expense. Taxes are assessed in a variety of manners, such as on property values or on the amount of proﬁts earned, and are used to provide services for the community where the facility is located. Taxes and depreciation are considered as expenses similar to the raw materials, labor, energy, and other items utilized to produce the products that are sold to produce the proﬁts and positive cash ﬂows. 1.2 BASIC RELATIONSHIPS BETWEEN CASH FLOWS, PROFITS, DEPRECIATION, AND TAXES Cash ﬂows represent the net monetary units, such as Dollars, Pounds, Euros, Yen, Won, Bit- coins, Pesos, or other currency ﬂowing into and out of a business ﬁnancial venture and it is desired to have a positive net cash ﬂow. It represents the funds available for expenses and busi- ness enterprises must have an adequacy of funds to pay for their expenses. Companies with negative net cash ﬂows will not survive very long, whereas companies with negative proﬁts may survive for several years if they have positive cash ﬂows. 4 1. FUNDAMENTAL TERMS AND CONCEPTS Net Cash Flow is the diﬀerence between total cash receipts (inﬂows) and total cash dis- bursements (outﬂows) for a given period of time such as a month, quarter, or year. They repre- sent the funds available to pay for expenses and savings for major future investments rather than borrowing funds. Proﬁts represent the net revenues minus the expenses and companies must be proﬁtable to survive in the long-term. Short-term periods of losses often occur during the start-up of businesses or during periods of economic recession, but long-term losses are not sustainable for an enterprise. Net Proﬁts are also referred to as Earnings and thus Net Proﬁts per Share is the same as Earnings per Share. The following relations are utilizing the basic expressions without adjustments. More items can be considered, but these are the primary relationships. Gross Proﬁts Net Proﬁts Taxes D Net Proﬁts D Tax Rate .1 D (cid:0) Revenues D (cid:0) Gross Proﬁts Costs (cid:0) Taxes (cid:0) Gross Proﬁts (cid:2) Tax Rate/ Cash Flows Revenues Depreciation Gross Proﬁts .1 (cid:2) (cid:0) Tax Rate/ D (cid:2) Costs (cid:0) Costs .Revenues Taxes Tax Rate.Revenues (cid:0) (cid:0) (cid:0) Revenues .1 (cid:0) Tax Rate/ Costs (cid:0) .Revenues (cid:0) (cid:2) Costs (cid:0) (cid:0) D D D Depreciation/ Costs Depreciation/ (cid:0) (cid:0) Depreciation/ Cash Flows Cash Flows or (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) Cash Flows Net Proﬁts D this can also be written as: Net Proﬁts D Cash Flows Depreciation Depreciation C (cid:0) Note that the tax rate is expressed as a decimal in the formulas, thus a 10% tax rate is expressed in decimal form as 0.10. It can be noted from Equations (1.8) and (1.9) that depreci- ation has a positive eﬀect on cash ﬂows and a negative eﬀect upon net proﬁts. A decision must be made to select either cash ﬂows or net proﬁts as the primary objective of the corporation and thus one must also focus on the depreciation methods typically used. There are two major depreciation methods utilized which are the straight line method which gives equal amounts of depreciation per year over the life of the investment or the Modi- ﬁed Accelerated Cost Recovery System (MACRS)—referred to as accelerated depreciation method in this chapter) which gives higher depreciation amounts in the early years of the investment life and lower amounts in the later years of the investment. There is an apparent dilemma as ac- celerated depreciation would initially give higher cash ﬂows and lower net proﬁts than straight line depreciation and that would not please stockholders and investors. So the business commu- nity has decided to use both methods; they use accelerated depreciation methods to determine Depreciation (1.7) C (1.8) (1.9) 1.3. CASH FLOW AND PROFIT EXAMPLE 5 the taxes they report to the government and use the straight line depreciation method to report proﬁts to the stockholders and investors. Thus, the reported proﬁts to stockholders and investors are not the actual proﬁts, but are inﬂated by the diﬀerences in the depreciation methods used. The diﬀerence in the depreciation methods adjusted by the tax rate is reported as deferred taxes in the report to the stockholders, but the diﬀerence in the net proﬁts is usually not presented in the stockholders’ report. The purpose of the accelerated depreciation method was to encourage companies to make investments to modernize and improve their production processes. Since accelerated depreciation improved the cash ﬂows and a straight line was used to report prof- its to the stockholders, the decision was made to focus upon cash ﬂows rather than proﬁts in evaluating projects and/or investment alternatives. A second advantage of the focus on cash ﬂows is that in many cases only cost data is available and the prices for the selling of the products is not known, so the alternatives being investigated can be compared on a minimum cost basis rather than a maximum proﬁt basis, but care must be taken in this type of analysis. 1.3 CASH FLOW AND PROFIT EXAMPLE An example illustration will be presented to show the diﬀerences in cash ﬂows and proﬁts using straight line depreciation and accelerated depreciation methods. The data presented in Table 1.1 is used in the formulas presented. Table 1.1: Cash ﬂow and depreciation data for example problem The ﬁrst analysis will be using the accelerated depreciation method, which is what it will be using to report to the government, and it will be assumed that the company has 10,000 shares of stock. Gross Proﬁts Gross Proﬁts Revenues (cid:0) $1;000; 000 D D (cid:0) Costs (cid:0) $775;000 Depreciation $50;000 (cid:0) (1.1) $175;000 D ItemAmount ($)Amount (%)Revenue1,000,000Costs775,000Tax Rate (%)25Depreciable Investment250,000Depreciation—Straight Line25,00010Depreciation—Accelerated (MACRS)50,000206 1. FUNDAMENTAL TERMS AND CONCEPTS Taxes Taxes D D Tax Rate 0:25 (cid:2) $175;000 (cid:2) Gross Proﬁts $43;750 D (1.3) Net Proﬁts Net Proﬁts D D Gross Proﬁts .1 $175;000 (cid:0) Taxes 0:25/ (cid:2) (cid:0) Gross Proﬁts $131;250 .1 (cid:2) (cid:0) D D Tax Rate/ (1.2) The earnings per share would be: Earnings/share $131;250=10;000 shares D 13:125 $=share. D Cash Flows Cash Flows D D Revenues (cid:0) $1;000;000 Costs Taxes (cid:0) $775;000 (cid:0) $43;750 (cid:0) D $181;250 or Cash Flows Cash Flows D Net Proﬁts $131;250 C $50;000 Depreciation $181;250 C The second analysis will be using the straight line depreciation method, which will be reported to its stockholders, and it will also be assumed that the company has 10,000 shares of stock. D D Gross Proﬁts Gross Proﬁts D D Revenues (cid:0) $1;000;000 Costs (cid:0) $775;000 Depreciation $25;000 (cid:0) (cid:0) $200;000 D Taxes Taxes D D Tax Rate 0:25 (cid:2) $200;000 (cid:2) Gross Proﬁts $50;000 D Net Proﬁts Net Proﬁts D D Gross Proﬁts .1 $200;000 (cid:0) Taxes 0:25/ (cid:2) (cid:0) Gross Proﬁts (cid:2) $150;000 instead of 131;250 Tax Rate/ .1 (cid:0) The earnings per share would be: Earnings/share (EPS) D $150;000=10;000 shares 15:00 $=share instead of 13.125 $/share. D D D (1.5) (1.9) (1.1) (1.3) (1.2) The diﬀerence in (EPS) 15:00 $=share (cid:0) D 13:125 $=share D 1:875 $=share 1.3. CASH FLOW AND PROFIT EXAMPLE 7 Cash Flows Cash Flows D D or Revenues (cid:0) $1;000;000 Costs Taxes (cid:0) $775;000 (cid:0) $50;000 (cid:0) D $175;000 Cash Flows Cash Flows D D Net Proﬁts $150;000 C Depreciation C $25;000 $175;000 D Note that the diﬀerence in taxes which is called deferred taxes is: Deferred Taxes Deferred Taxes D D Straight Line Taxes $43;750 $50;000 (cid:0) Accelerated Taxes $6;250 (cid:0) D (1.5) (1.9) (1.10) The deferred taxes can be determined by the product of the depreciation diﬀerences times the tax rate: Deferred Taxes Deferred Taxes D D .Accelerated Depreciation (cid:0) Straight Line Depreciation/ (cid:2) .Tax Rate/ (1.11) .$50;000 $25;000/ .0:25/ (cid:2) D $6;250 (cid:0) Cash Flow .CF/ Diﬀerence Cash Flow (CF) Diﬀerence D D (cid:0) $181;250 $175;000 $6;250 D (cid:0) Accelerated Depreciation CF Straight Line Depreciation CF (1.12) The earnings per share diﬀerence can be determined can be determined by: Earnings/Share(Diﬀerence) .1 Tax Rate/ D (cid:0) ..Accelerated Depreciation-Straight Line Depreciation/=.Number of Shares/ (cid:2) (1.13) Earnings/Share(Diﬀerence) 1:875 $=share D .1 (cid:0) D 0:25/ (cid:2) .$50;000 (cid:0) $25;000/=10;000 In summary, the accelerated depreciation results in lower taxes paid and higher cash ﬂows than the straight line depreciation method, but it also results in lower proﬁts and lower share earnings. Thus, they use the accelerated depreciation method for reporting to the government and the straight line depreciation method for reporting to shareholders. Although this practice is legal, it does raise concerns about it being ethical. 8 1. FUNDAMENTAL TERMS AND CONCEPTS In some instances, a company may have one project with negative cash ﬂows but a net positive cash ﬂow overall. This can occur when a company has several projects and a start-up project may be negative in its initial stages and other projects in the company may have positive cash ﬂows resulting in a net positive cash ﬂow. Construction projects often take long time periods and they are not paid until certain goals have been reached and thus may have negative cash ﬂows until they are paid. A longer working capital cycle often results in negative cash ﬂows for short periods. For example, when a housing developer builds a home, the developer does not recover the expenses until the home is sold and has a negative cash ﬂow until payment is received for the home. Hence, a reasonable amount of positive cash ﬂows from operations is signiﬁcant for three reasons [1]. 1. Healthy cash ﬂows can help a company meet its funding requirements internally rather than borrowing in a high cost environment; but for major capital expenditures borrowing is often necessary and advantageous for the company. 2. Having cash available permits the making of purchases more quickly and often at lower costs. 3. A company’s ability to manage its debts indicates the eﬃciency and strength of the business to its customers, stockholders, and employees. 1.4 CASH FLOW DIAGRAMS Cash ﬂow diagrams are diagrams of the revenues and expenses over time. The abscissa (x-axis) represents time and the time between periods, which is usually constant such as one year, whereas the ordinate (y-axis) represents the amount of cash ﬂow and is usually diﬀerent for each time period. Cash ﬂows are assumed to occur at the end of the period. There are three primary types of cash ﬂow diagrams: (1) the basic cash ﬂow diagram where the net cash revenues and net cash expenses are both shown; (2) the net cash ﬂow diagram where the net incomes per period and net expenses per period are combined into a net overall cash ﬂow per period; and (3) the cumulative cash ﬂow diagram where the cumulative of the net cash ﬂows are plotted. The most common diagram is the net cash ﬂow diagram and the second most utilized is the cumulative cash ﬂow diagram to illustrate the breakeven time. Since the cash ﬂows are considered to occur at the end of the period, the time values on the diagram represent the end of the period. One should always make a cash ﬂow diagram when possible in solving problems and in most cases the ﬂows will be diﬀerent for the various time periods. We will consider an example with an initial investment of $10 which results in a net revenue stream of $6 for each time period (which could be the sum of two or more individual revenue streams) and a net expense stream of $3 over 5 time periods. Figure 1.1 shows the basic cash ﬂow diagram, with the investment (an expense) occurring at time zero and the net revenues (positive) and net expenses (negative) for each period of the study. 1.5. SUMMARY 9 Figure 1.1: Basic cash ﬂow diagram showing net revenue and net expense cash ﬂows for each time period. Figure 1.2 shows the net cash ﬂows, the diﬀerence between the net revenues and net expenses. It is used as the starting point for calculations; somewhat like the use of the free-body diagram for solving in statics courses. Figure 1.2: Net cash ﬂow diagram showing net cash ﬂows for each time period. Figure 1.3 shows the cumulative cash ﬂows which gives an indication as to when the product will become proﬁtable, which is 4 years in this problem. If the cash ﬂows were uniform over the project period, the result could be and is often interpreted as being 3.33 years. However, the cash ﬂows are considered to occur at the end of the period and 4 years should be used if one does not know that the cash ﬂows are uniform over the project period. Since all cash ﬂows are assumed to be at the end of the period, the initial investment occurs at time zero, which is the end of Period 0 and it is also the start of Period 1. Similarly, the end of Period 1 is also the start of Period 2. As we get into more complex examples, the cash ﬂow per period will tend to be diﬀerent for each period and the cash ﬂow diagram helps in properly formulating the problem. Some of the other items that will be considered are accounts payable, accounts receivable, inventory changes, and etc., so some of the formulas presented must be adjusted for these items. 1.5 SUMMARY Cash ﬂows and proﬁts are the two primary measures of corporate projects, but cash ﬂow is the measure that is utilized for evaluating projects as positive cash ﬂows are critical and proﬁts are a 66666301012345Time 3333Revenues +Funds ($)Expenses —Revenues +Funds ($)Expenses —3333301012345Time 10 1. FUNDAMENTAL TERMS AND CONCEPTS Figure 1.3: Cumulative cash ﬂow diagram showing cumulative cash ﬂow over each time period which indicates project becomes positive between the end of time period 3 and the end of time period 4. component of the cash ﬂows. Proﬁts using accelerated depreciation are lower than the straight line depreciation, so accelerated depreciation is used for determining taxes and straight line depreciation is used for reporting to stockholders. The three cash ﬂow diagrams were presented and the net cash ﬂow diagram is used for most economic evaluations and the cumulative cash ﬂow diagram is used for payback period calculations. 1.6 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, 2nd ed., New Academic Science Ltd., page 3, 2012. 8 1.7 EVALUATIVE QUESTIONS 1. Which depreciation method, accelerated or straight line, gives lower amounts of depreci- ation during the last stages of the project life? 2. Depreciation is considered to be what type of item and what is the main purpose of de- preciation? 3. Use the information in Table 1.2 to determine the items listed below for the Accelerated Depreciation Method and for the Straight Line Depreciation Method. The company has 20,000 shares of stock. 3.1 Use the Accelerated Depreciation method and determine: (a) Gross Proﬁts (b) Net Proﬁts Revenues +Funds ($)Expenses —7412010123455Time Table 1.2: Cash ﬂow and depreciation data for problem 3 1.7. EVALUATIVE QUESTIONS 11 (c) Taxes (d) Cash Flows (e) Net Proﬁts/share 3.2 Use the Straight Line Depreciation method and determine: (a) Gross Proﬁts (b) Net Proﬁts (c) Taxes (d) Cash Flows (e) Net Proﬁts/share 3.3 Determine the amount of deferred taxes and the diﬀerence in the net proﬁts/share and the diﬀerence in cash ﬂows between the Accelerated Depreciation and Straight Line Depreciation methods. 3.4 An error was made in determining the costs and instead of $800,000 they were $940,000. What does this diﬀerence make in the results? Calculate the Cash Flows and Net Proﬁts/Share using both depreciation methods and compare the results. 4. Use the information in Table 1.3 to determine the items listed below for the Accelerated Depreciation Method and for the Straight Line Depreciation Method. The company has 20,000 shares of stock. 4.1 Use the Accelerated Depreciation method and determine: (a) Gross Proﬁts (b) Net Proﬁts (c) Taxes (d) Cash Flows (e) Net Proﬁts/share ItemAmount ($)Amount (%)Revenue1,000,000Costs800,000Tax Rate (%)40Depreciable Investment400,000Depreciation—Straight Line40,00010Depreciation—Accelerated (MACRS)80,0002012 1. FUNDAMENTAL TERMS AND CONCEPTS Table 1.3: Cash ﬂow and depreciation data for problem 4. 4.2 Use the Straight Line Depreciation method and determine: (a) Gross Proﬁts (b) Net Proﬁts (c) Taxes (d) Cash Flows (e) Net Proﬁts/share 4.3 Determine the amount of deferred taxes and the diﬀerence in the net proﬁts/share and the diﬀerence in cash ﬂows between the Accelerated and Straight Line Depreciation methods. 5. The large companies use accelerated depreciation when reporting to the government and straight line depreciation when reporting to stockholders. 5.1 This is legal, but is it ethical? Give your reasons for supporting your answer. 5.2 Should a law be made to permit the same depreciation method to both the stock- holders and the government? Give your reasons for supporting your answer. 6. A company made an investment of $1,200,000 for a machine to manufacture a new prod- uct. The sale of the product produced is expected to provide a uniform annual revenue of $500,000 for 6 years. The annual operating, material, and maintenance expenses are $250,000 and the salvage value of the machine at the end of the 6 years is $400,000. Draw the cash ﬂow diagram, the net cash ﬂow diagram, and the cumulative cash ﬂow diagram. What is the breakeven payback period? 7. Explain the diﬀerence between cash ﬂows and proﬁts with respect to depreciation. 8. (a) Given the following data in Table 1.4, create the basic cash ﬂow diagram, the net cash ﬂow diagram, and the cumulative cash ﬂow diagram. ItemAmount ($)Amount (%)Revenue1,000,000Costs800,000Tax Rate (%)20Depreciable Investment500,000Depreciation—Straight Line50,00010Depreciation—Accelerated (MACRS)100,000201.7. EVALUATIVE QUESTIONS 13 (b) When is the breakeven or payback period? (1) Assume end-of-year payments. (2) Assume uniform payments throughout the year. (c) What is the total proﬁt for the project? Table 1.4: Data for problem 8 PeriodInvestmentRevenueExpenses0181 546761223614477125610Totals186036C H A P T E R 2 15 Financial Statements and the Purcell Diagram 2.1 INTRODUCTION Financial statements are critical in measuring the performance of an enterprise, and the two primary ﬁnancial statements used are the Income Statement and the Balance Sheet. The Purcell Diagram [1, 2], developed by W.R. Purcell, integrates these two ﬁnancial statements into a cash ﬂow diagram. It indicates the overall cash ﬂows for a company and illustrates the major components. This is critical for ﬁnancial analysts and it assists engineers in understanding the importance of cash ﬂows in the company picture and explains why project evaluations require a cash ﬂow analysis. 2.2 FINANCIAL STATEMENTS The primary ﬁnancial statements used for reporting are the Income Statement and the Balance Sheet. The items such as long-term debt and short-term debt are not included to keep the problem easy to visualize and to reduce the complexity as they are diﬃcult to add to the basic Purcell Diagram. The income statement summarizes the revenues (sales), the major expenses (costs), the depreciation, the taxes, and the proﬁts. Some items have been added to the expenses on the basic income statement to provide more detail on the total expenses. In the high technology society, more money is being spent on Research and Development (R&D) than in the past and these costs are signiﬁcant. For example, as automobiles are switching from gasoline (fossil fuels) engines to electric motor engines, the development of these electrical engine systems are being done currently and the advanced models must undergo testing for performance and safety issues before they can be marketed. This R&D must be expensed during the development stage and the proﬁts will occur only when the new technology is successfully marketed and those proﬁts will be used to support future R&D developments. More advanced production equipment is being purchased to reduce labor and material costs and thus depreciation expenses will grow. In addition to the federal government taxes, other taxes and fees have been increasing and are added as a separate item. As labor costs are higher in the U.S., the top management costs have also increased signiﬁcantly in salaries and stock options and the legal and computer security 16 2. FINANCIAL STATEMENTS AND THE PURCELL DIAGRAM costs have also increased greatly due to cybersecurity threats. The example income statement for Shawnee Corporation with some of these components is presented in Table 2.1. Table 2.1: Income statement for Shawnee Corporation in 2020 The balance sheet indicates the ﬁnancial positions of the company at the beginning and at the end of the accounting period to show the progress during the year. The basic equation of the balance sheet is that: The relationship between cash ﬂows and proﬁts developed in Chapter 1 was: Assets D Liabilities C Equities Cash Flows Net Proﬁts C D Depreciation (2.1) (2.2) The more inclusive relationship between cash ﬂows and proﬁts is written as indicated by Equa- tion (2.3) as: Cash Flows Net Proﬁts C D Depreciation C Adjustments (2.3) The adjustments to the cash ﬂows are the accounts receivable, accounts payable, new equipment purchases, dividends paid, stock sales, and inventory changes and other items not included in the proﬁt calculations. These adjustments can have a major impact on the cash ﬂows and are considered in this chapter, but the long-term debt, short-term debt, principal, and in- terest payments are not included at this level of development. However, these can be included in the analysis in more advanced models. The balance sheet for Shawnee Corporation is shown in Table 2.2. Income StatementShawnee Corporation 2020 (End-of-Year)Sales620ExpensesCost of Goods Sold290Management Costs40R&D Expenses60Sales Expense70Other Taxes & Fees20Depreciation40520Proﬁ t Before Tax100Taxes (Tax Rate 25%) 25Net Proﬁt 75Table 2.2: Balance sheet for Shawnee Corporation in 2020 2.3. THE PURCELL DIAGRAM 17 2.3 THE PURCELL DIAGRAM The Purcell Diagram gives the cash ﬂows in a combined format of the Income Statement and the Balance Sheet [3]. The Purcell Diagram combines the information of the Income Statement and the Balance sheet into a single representation of the cash ﬂows. The primary advantage of the Purcell Diagram is that it shows how the cash is ﬂowing through the company and is more dynamic than the balance sheet and income statement. The Purcell diagram also uses more detailed data, such as the Purchased Equipment ($50), Stock Sales ($5), and Dividends Paid ($10), and illustrates more details of the owner’s equity. The Purcell Diagram shown in Figure 2.1 gives the cash ﬂows in a much easier format than the balance sheet and is recommended for use. If one rewrites Equation (2.3) to determine the end-of-period cash ﬂows, one has: Cash Flows Net Proﬁts Depreciation Adjustments D C Cash Flows (end) Cash Flows (start) C Net Proﬁts D (cid:0) Depreciation Adjustments C C (2.3) or Cash Flows (end) Cash Flows (start) Net Proﬁts C C Depreciation C D Adjustments (2.4) From Tables 2.1, 2.2, and Figure 2.1, one can calculate the ending cash ﬂows as: Balance SheetShawnee Corporation (Year 2020)StartEndStartEnd2020202020202020AssetsLiabilities & Equities Current Assets Current LiabilitiesCash260290Accounts Payable0 20Accounts Receivables040InventoriesFinished Goods5025Work-in-Progress4580Raw Materials 3030Fixed AssetsOwner’s EquityPlant & Equipment100110Common Stock48555548557548557518 2. FINANCIAL STATEMENTS AND THE PURCELL DIAGRAM Figure 2.1: Purcell diagram for Shawnee Corporation in 2020. CustomersTotalCostsEmployeesSuppliersManagementR&D ExpensesSales ExpensesOwner’s Equity485/555Dividends Paidto StockholdersStock SalesFees & Other TaxersGovernment Income TaxesCash260/290Finished Goods50/25WIP45/80Raw Materials30/30Fixed Assets100/110AccountsReceivable0/40NetEquityChange70ValueCreatedAccountsPayable0/20620 SalesDepreciation40Net Proﬁts75Net Proﬁts+75Purchased Equipment505802602801902020+70+5-10304029060702025407060702025510Cash Flows (end) D Cash Flows (start) Net Proﬁts D C 260 { { (cid:0) (cid:0) 50 C 75 C Purchased Equipment C C 5 Dividends Paid C Total Inventory Increase ( 2.4. SUMMARY 19 Adjustments Depreciation 40 C Stock Sales C 25 35 0) C C (cid:0) Accounts Payable Accounts Receivable } (cid:0) 10 (cid:0) (cid:0) 40 } (cid:0) 75 40 50 5 10 10 20 40 C (cid:0) 115 (cash ﬂow change via proﬁts and depreciation) C C (cid:0) (cid:0) (cid:0) 85 (total adjustments) (cid:0) (cid:0) C 10 20 C 260 260 290 C C (cid:0) D D D Cash Flows (end) Note that the capital equipment is not listed as an expense item on the Income Statement and appears only on the Purcell diagram. Capital equipment must be depreciated over the life of the equipment and the depreciation is listed as an expense on the Income Statement. However, it does aﬀect the cash ﬂows and is presented as one of the adjustments to the cash ﬂows. It is included in the ﬁxed assets as the increase in the ﬁxed assets represents the diﬀerence between the purchased equipment (an increase in assets) and the depreciation (a decrease in the assets). This can also be used in another manner for calculating the ending value of a particular activity. The ending values need to be calculated and the general equation used is: Ending Value D Starting Value C Inputs to Activity (cid:0) Outputs of Activity (2.5) If one examines the cash ﬂow activity in the Purcell Diagram, it is noted that: 290.end/ D 260.start/ C 580.receipts from customers/ 555.outgoing funds/ 5.stock sales/ C (cid:0) Equation (2.5) can be used to determine all the ending values for the balance sheet and Purcell Diagram. The Purcell diagram shows the inputs and outputs for the various activities. The Purcell diagram is an excellent tool in complementing the Income Statement and the Balance Sheet. 2.4 SUMMARY The Purcell diagram ties together the Income Statement and Balance Sheet to illustrate how the cash ﬂows through the ﬁnancial institution. It shows why cash ﬂows are important and how they are related to proﬁts, owner’s equity, ﬁxed assets, and the other key ﬁnancial items for monitoring the performance of the ﬁnancial institution. The focus of most of the remaining chapters will be 20 2. FINANCIAL STATEMENTS AND THE PURCELL DIAGRAM on the cash ﬂow calculations and the Purcell Diagram indicates how they relate to the ﬁnancial statements of the Balance Sheet and Income Statement. 2.5 REFERENCES [1] Purcell, W. R., Understanding a Company’s Finances—A Graphical Approach, Houghton Miﬄin Company, Boston, 1981. 15 [2] Purcell, W. R., Understanding a Company’s Finances: Look at Financial Reports, see a Finan- cial Picture of the Business, July 25, 2009, Kindle eBook. 15 [3] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, 2nd ed., New Academic Science Ltd., 2012. 17 2.6 EVALUATIVE QUESTIONS 1. Use the Income Statement and the Balance Sheet in Tables 2.3 and 2.4 to complete the Purcell Diagram for the Financial Flows for the Shawnee Corporation in Figure 2.2. The equipment purchased during the year was 70 and the labor was the same as 2020. Fill in the blanks in Table 2.4 and in the Purcell Diagram of Figure 2.2. Table 2.3: Income statement for Shawnee Corporation for 2021 Income StatementShawnee Corporation 2021 (End-of-Year)Sales655ExpensesCost of Goods Sold285Management Costs40R&D Expenses60Sales Expense70Other Taxes & Fees20Depreciation60535Proﬁ t Before Tax120Taxes (Tax Rate 25%) 30Net Proﬁ t902.6. EVALUATIVE QUESTIONS 21 Figure 2.2: Purcell diagram for Shawnee Corporation in 2021. CustomersTotalCostsEmployeesSuppliersManagementR&D ExpensesSales ExpensesOwner’s Equity575/655Dividends Paidto StockholdersStock SalesFees & Other TaxersGovernment Income TaxesCash290/___(2)Finished Goods25/30WIP80/___(8)285COGS200Raw Materials30/50Fixed Assets110/120AccountsReceivable40/60NetEquityChange____ValueCreatedAccountsPayable20/30655 SalesDepreciation___(15)Net Proﬁts(13)___Net Proﬁts+90Purchased Equipment___(5)___(1)___(6)___(7)___(9)___(3)___(4)(10)___20(12)+___+10-2030406070204070607020(11)___(14)___102022 2. FINANCIAL STATEMENTS AND THE PURCELL DIAGRAM Table 2.4: Balance sheet for Shawnee Corporation for 2021 2. Use the information in Tables 2.5 and 2.6 with the additional information and complete the Purcell Diagram in Figure 2.3. The additional information given is for calculating some of the adjustment terms in Equations (2.3) and (2.4). Additional information for 2024 is: Stock Sales Dividends Paid Labor Used 20 Cash Received from Customers 20 Raw Materials to WIP WIP to Finished Goods 780 240 325 For Raw Materials For WIP For Finished Goods Supplier Services Equipment Purchased 40 35 55 90 Raw Materials for Prod. 200 WIP Services 45 Money Paid to Suppliers 325 Balance SheetShawnee Corporation (Year 2021)StartEndStartEnd2021202120212021AssetsLiabilities & Equities Current Assets Current LiabilitiesCash290 (1)Accounts Payable2030Accounts Receivables4060InventoriesFinished Goods2530Work-in-Progress8085Raw Materials 3040Fixed AssetsOwner’s EquityPlant & Equipment110 (2)Common Stock (4) (5)575 (3) 575 (6)2.6. EVALUATIVE QUESTIONS 23 Figure 2.3: Purcell diagram for NAC Corporation in 2024. CustomersTotalCostsEmployeesSuppliersManagementR&D ExpensesSales ExpensesOwner’s Equity___/___Dividends Paidto StockholdersStock SalesFees & Other TaxersGovernment Income TaxesCash___/___Finished Goods___/___WIP___/______Raw Materials___/___Fixed Assets___/___AccountsReceivable___/___NetEquityChange____ValueCreatedAccountsPayable___/______ SalesDepreciation___Net Proﬁts___Net Proﬁts+___Purchased Equipment_________Stock Sales_____________________+___+___-_____________________________________________24 2. FINANCIAL STATEMENTS AND THE PURCELL DIAGRAM Table 2.5: Income statement for NAC Corporation for 2024 Table 2.6: Balance sheet for NAC Corporation for 2024 Income StatementNAC Corporation 2024 (End-of-Year)Sales800ExpensesCost of Goods Sold400Management Costs40R&D Expenses60Sales Expense70Other Taxes & Fees30Depreciation80680Proﬁ t Before Tax120Taxes (Tax Rate 25%) 30Net Proﬁ t90Balance SheetNAC Corporation (Year 2024)StartEndStartEnd2024202420242024AssetsLiabilities & Equities Current Assets Current LiabilitiesCash320415Accounts Payable010Accounts Receivables020InventoriesFinished Goods4020Work-in-Progress9085Raw Materials 4040Fixed AssetsOwner’s EquityPlant & Equipment100110Common Stock590680590690 590 690C H A P T E R 3 25 Costs and Cost Estimating 3.1 INTRODUCTION Costs, interest payments, and cost estimating have been in existence since the ﬁrst merchants started buying and selling products. The focus in business today tends to be on proﬁts and cash ﬂows, but the primary component in determining the amount of proﬁts or cash ﬂows are the expenses or costs. Some Biblical verses related to interest and cost estimating are presented to indicate that the issues of interest and cost estimating have existed for a long time; the vs. are paraphrased as: 1. Deuteronomy 23: 19–20 You must charge no interest on a loan made to your brother. On a loan to a foreigner, you must charge interest… 2. Luke 14:28 For which of you, wanting to build a tower, does not ﬁrst sit down to determine the cost, to see if he has enough to complete it? Although most religions now tend to charge interest to all people, a few coun- tries/communities still tend to charge interest only to foreigners. Although costs, cost estimat- ing, and interest payments are not new and have been in existence since pre-Biblical times, the methods for evaluating them have changed considerably over the centuries. Two terms that are related and represent the before and after of a project/product are cost estimating and cost accounting. Cost estimating is done to determine if a project/product is feasible and cost accounting is to determine the actual costs of the project/product for evaluating the proﬁts and determining the accuracy of the cost estimate. These two deﬁnitions are from AACE International Recommended Practice No. 10S-90, Cost Engineering Terminology [1], as revised October 30, 2017. Cost Estimating: Cost estimating is the predictive process used to quantify, cost, and price the resources required by the scope of an investment option, activity, or project. Cost estimating is a process used to predict uncertain future costs. In that regard, a goal of cost estimating is to minimize the uncertainty of the estimate given the level and quality of scope deﬁnition. The outcome of cost estimating ideally includes both an expected cost and a probabilistic cost dis- tribution. As a predictive process, historical reference cost data (where applicable) improve the reliability of cost estimating. Cost estimating, by providing the basis for budgets, also shares a goal with cost control of maximizing the probability of the actual cost outcome being the same as predicted (November 2012). 26 3. COSTS AND COST ESTIMATING Cost Accounting: The historical reporting of actual and/or committed disbursements (costs and expenditures) on a project. Costs are denoted and segregated within cost codes that are deﬁned in a chart of accounts. In project control practice, cost accounting provides the mea- sure of cost commitment and/or expenditure that can be compared to the measure of physical completion (or earned value) of an account ( January 2003). The calculation of proﬁts requires the determination of both revenues and expenses/costs. The expenses/costs represent the majority of the items on the Balance Sheet and management has more control over the expenses/costs than on the revenues items. The revenues have more outside factors aﬀecting their control, such as customer demands, competition, and general eco- nomic prosperity. Cash ﬂows are closely related to proﬁts and both are essential in determining the success of a company. To illustrate the inﬂuence of costs upon proﬁts, Table 3.1 compares the eﬀect of a 10% change in increased price, increased sales volume, and cost reductions upon the gross proﬁts [2]. It indicates that the price increase is the best option, but it is only slightly better than the 10% cost reduction. It is much more likely for companies to achieve a cost reduction of 10% than an increase of selling price of 10%. With this given scenario, the 10% price increase results in a 125% increase in total proﬁts and a 10% cost reduction results in 115% increase in proﬁts. This is why companies focus on cost reductions when trying to increase proﬁts as they have more control on costs whereas price increases are diﬃcult to achieve in a competitive market. When there is a monopoly, outrageous price increases can occur, which has occurred in the medical industry when only one supplier exists and when one has her/his life involved. This is, however, is an exception to usual business practices, but it illustrates that unethical practices are often not illegal. There are three basic approaches to cost estimating which are: Top-Down Estimating, Bottom-Up Estimating, and Combined Top-Down and Bottom-Up Estimating. There are other approaches to cost estimating, but these are the primary approaches utilized. Each of the approaches will be illustrated by examples, but the traditional method of cost estimating has been the bottom-up approach. In the bottom-up estimating approach the complete details of the production process are known and cost for each step of the process can be estimated. The cost of all the steps of the process are estimated and the total cost of all the steps is the estimate for the product or project. This is done by most companies when the new products are similar to existing products and relatively small changes occur in the processes and the estimates tend to be accurate. Greater changes in the new product or process tend to result in more error in the estimate accuracy as items may be omitted in the estimate or more corrections will be needed in the manufacturing process. A foundry producing cast iron six-cylinder engine blocks could use that as the basis for making an estimate for a cast iron four-cylinder or an eight-cylinder engine block as most of the steps in the process would be similar. However, the changing from a six-cylinder cast iron Table 3.1: Gross proﬁt improvement analysis for a two product system [2] 3.1. INTRODUCTION 27 Current Practice10% Price Increase10% Sales Increases10% Cost ReductionTotal Cost + Proﬁ tProduct AProduct BTotal8020100882211088221108020100Variable CostsProduct AProduct B5712571262.713.251.210.8Fixed CostsProduct AProduct B19419419417.13.6Total CostProduct AProduct B7616761681.717.268.414.4Gross Proﬁ tProduct AProduct BTotal448126186.34.811.111.65.617.2Proﬁ t IncreaseAmountProduct AProduct BTotalBaseCase82102.30.83.17.61.69.2Proﬁ t IncreasePercentProduct A (%)Product B (%)Total PercentBaseCase2005012557.52038.81904011528 3. COSTS AND COST ESTIMATING engine to a six-cylinder aluminum would be more diﬃcult as the process steps diﬀerences would be greater. The traditional top-down estimating approach is usually based on Cost-Estimating Re- lationships (CERs) using primary cost drivers as the actual process steps and design details may not be known. These tend to focus on products with signiﬁcant changes in design and where the manufacturing steps and sequence are not known. This often occurs for new military equipment to be manufactured and performance goals are speciﬁed, but the detailed product design has not been completed. A second approach to top-down estimating is Target Costing, which is done in industries which purchase many of the components for their product. In the automobile industry, the manufacturers must estimate the total cost of the model to assure that it will be competitive in the market place. The automobile manufacturers produce the main components such as the engine, power train, frame, and skin, but usually have suppliers produce the tires, wheels, seats, wiring harnesses, glass, audio, etc. They need to set targets for these supplier components so that they can meet their total cost target to be competitive in the market place. The third cost approach is a combination of top-down and bottom-up costing. This is done for projects of long duration, such as the production of an aircraft carrier. It takes several years to make the product, such as 10 years, and technology will change signiﬁcantly over that time. The basic ship building costs can be estimated by bottom-up costing, but the cost for the electronics such as radar systems and defensive systems that will not be designed until several years in the future and thus these costs cannot be determined by bottom-up costing approaches, but will need CERs to estimate the costs. 3.2 COST COMPONENTS FOR ESTIMATES 3.2.1 BASIC COMPONENTS There are numerous cost components and they will vary by industry, company and product and thus only a sample of the items commonly used in manufacturing are presented in Table 3.2. Other companies, such as ﬁnancial services, food services, medical services, hotel and motel industries, and travel services will have similar components, perhaps with diﬀerent names. In activities such as R&D, the expenses of the R&D can be determined by direct cost methods, but they must be allocated as an overhead to current products to recover the overhead costs. 3.2.2 TRADITIONAL AND ABC OVERHEAD ALLOCATION METHODS The overhead costs are replacing direct labor costs as the largest cost component because direct labor costs have decreased through automation replacing labor and a large increase has occurred in overhead cost components such as R&D, legal, safety, and administrative management costs. The material cost proportion can vary considerably depending up the amount of purchased ma- terials involved. In the automotive manufacturing business, most auto companies purchase the Table 3.2: Cost components for estimating in manufacturing 3.2. COST COMPONENTS FOR ESTIMATES 29 A. Pre-production Costs (often in Corporate Overhead and not as separate costs)1. Research & Development2. Engineering Design3. Process Engineering Design (Tooling)B. Production Costs (Direct)4. Direct Materials5. Direct Labor6. Other Direct Costsi. Toolingii. Processing7. Contingency/Riski. Product-Engineering Design Changesii. Process-Tool ChangesC. Overhead Costs (Indirect)8. Overhead Costsi. Shop (Including Indirect Materials & Labor)ii. Plantiii. Corporateiv. Sales9. Adjustments to Costsi. Quantity Adjustmentsii. Surchargesa. Special Testingb. Special DeliveryD. Total Costs10. Total Costs = ∑1 through 9 + TaxesE. Proﬁ t11. Proﬁ t (Mark-up) + Tax Estimate on Proﬁ tF. Selling Price12. Selling Price Selling Price = Total Costs + Proﬁ t + Estimated Proﬁ t Tax30 3. COSTS AND COST ESTIMATING glass, the interior seats, the tires, the head and tail light assemblies, the electrical harnesses, etc., so the total material costs are high as the purchased materials are the ﬁnished products of the suppliers. In companies that produce the glass for the auto windows, the raw materials are a relatively small portion of the total costs, but the processing costs are very high. One approximate method for determining the selling price based on the material cost was the 1-3-9 rule of Rondeau [3]. The 1 represented the material cost (or 1.2 including scrap and tooling), the 3 representing the manufacturing cost, and the selling price represented by the 9. Thus, for a product that used materials of $3, the manufacturing cost would be $9 and the selling price would be $27. The manufacturing cost includes factory overhead including factory admin- istration, product scheduling, quality control, material handling, shipping and receiving, as well as direct labor. The selling price includes the administrative overhead, the R&D, information systems and security (ISS), legal overheads, product testing, sales and marketing expenses, taxes, and a mark-up of 10–25%. The ratio can be developed for speciﬁc companies or industries, but the total overheads and other expenses are typically much greater than the manufacturing costs. There are two major approaches to estimating of overhead costs. The traditional approach uses one or more of the direct costs to estimate the overhead cost, such as direct labor dollars, direct labor hours, or total direct costs. The Activity Based Costing (ABC) uses the measurement of a major activity for a department, such as purchasing orders, and determines a unit cost for that activity which can be assigned to a speciﬁc department or product. The determination of speciﬁc activities for administration, R&D, sales, and marketing are diﬃcult to develop and this has been a problem with the traditional ABC. The traditional allocation of overhead was based upon the amount of direct labor used in the production, which could be measured in either hours or dollars. This was fairly accurate when direct labor was largest cost component as in the early 1900s, but over the last 75 years companies have modernized equipment and used more automated material handling and robotics to reduce the amount of direct labor cost has been reduced from 40–60% of the total costs to 10–30%. New costs such as ISS, computer maintenance, and enhanced legal and safety expenses have increased over the years so labor is no longer the dominant cost as the total support costs far exceed the labor costs. Today direct labor costs are only 10–30% of the total costs and overhead rates based only upon direct labor would result in percentages from 300–500%. In many cases, these overheads are not even closely related to the amount of direct labor and this results in poor overhead allocations. This has resulted in other variables and/or additional variables being utilized to estimate the overhead costs. Direct costs, such as material cost, can be assigned easily to the products, but the support costs often have little direct connection to the various individual products. ABC takes the cost of the overhead activity and divides by the performance measure for that activity to determine the rate. The overhead charge to the consuming department is the product of the rate determined and the amount of the activity consumed by the department. For example, the purchasing department is a service activity and its expenses are overhead. Thus, the 3.2. COST COMPONENTS FOR ESTIMATES 31 expenses of the department divided by the number of purchase orders processed would be the rate and the production department would be charged by the product of the number of purchase orders submitted times the rate. This led to several problems in determining rates as one purchase order may contain only one item and another purchase order would contain numerous items. Also, many of the purchase orders were for other support groups and could not be related to speciﬁc products. The newer approach is to develop rates based on the time for the activity and this has been used in both ABC and traditional overhead determination. Time is what is being consumed and the speciﬁc time values closely related to production are the direct labor time and the time machines are being used for production. The use of time has changed the traditional ABC to Time-Based ABC with the use of activities being related to time. The overhead costs are a much larger component of the total cost and they are diﬀerent in their support of the product, so diﬀerent measures are needed and they can be measured in units, such as units of production or in time units such as machine hours, direct labor hours, or the sum of machine and labor hours. Eventually the overheads need to be assigned to speciﬁc products to determine the product cost and a selling price for recovering the costs and providing an acceptable proﬁt. An example is presented in Table 3.3 of a metal casting facility which is a supplier to the automotive industry. The traditional ABC will be used for two activities and the administrative and facility overheads will be determined by using the traditional direct labor hours, the machine hours and the sum of the direct labor and machine hours. There are four products—pistons, crankshafts, axles, and exhaust manifolds—and the unit selling price, unit direct material costs, direct labor hours, and machine hours, as well as the ABC data for purchase orders and material handling are presented. The machine hours are used for both the depreciation unit and utility unit charge determinations. The quantities, selling prices, and direct costs are known, and the problem is to determine how to allocate the factory and administrative overhead expenses of $900,000 and the other overheads of $652,000 to determine the individual product proﬁt/loss. The ABC method utilizes two drivers in the determination of the overhead and they were: Number of Production Orders and Number of Moves. The Number of Machine Hours would be considered as a driver in either the ABC or Traditional Method. The Number of Machine Hours and the Number of Labor Hours are used for direct costs as they can be directly associated with a product. The data of Tables 3.3 and 3.4 are used to determine the unit cost values for the four products. 32 3. COSTS AND COST ESTIMATING Table 3.3: Cost data for overhead evaluations for an automotive metal casting facility Table 3.4: Unit cost determination Casting Products ProducedOverhead Item/ActivityCost DriverPistonCrank-shaftRearAxelExhaust ManifoldTotal # of ActivityTotal OH Cost - $OH Rate ($/unit)Purchase Orders# ofOrders1203002003801,00056,00056Material Handling# of Moves2003504504001,40056,00040DepreciationExpense# of Machine Hours2,0004,0002,0002,00010,000500,00050Utility Costs# of Machine Hours2,0004,0002,0002,00010,00040,0004Factory Expenses500,000AdministrtiveExpenses400,000Total Expenses1,552,000Casting Products ProducedProduction DataPistonCrank-shaftRearAxelExhaust ManifoldTotal # of ActivityTotal OH Cost - $OH Rate ($/unit)Production Units38,0008,0006,70034,000Selling Price: $/unit101327523Direct Labor: hours1,0005,0002,0005,00013,000520,00040Utility Cost: Machine hours2,0004,0002,0002,00010,00040,0004Direct Unit Costs and Overhead Activities Directly Related to ProductsProduction CostsPistonCrank-shaftRearAxelExhaust ManifoldDirect Materials$/unit4.00032.00019.0006.000Direct Labor$/unit1.05325.00011.9405.882Purchase OH$/unit0.1772.1001.6720.626Material Handling$/unit0.2111.7502.6870.471Depreciation Expenses$/unit2.63225.00014.9252.941Machine Utility$/unit0.2112.0001.1940.235Total Direct Costs$/unit8.28487.85051.41816.155The calculations for the unit costs for the Pistons in Table 3.4 will be illustrated. 3.2. COST COMPONENTS FOR ESTIMATES 33 The Direct Material Cost per unit is given as: DMC D $4:00=unit The Direct Labor Cost per unit is calculated by: DLC D D (direct labor overhead rate (cid:2) piston direct labor hours)/# of pistons produced 40 $=hr (cid:2) 1,000 hrs/38,000 pistons $1.053/unit D The Purchase Order Cost per unit is calculated by: POC D D (# of Piston Purchase Orders (cid:2) Purchase Order OH rate)/# of Pistons produced (120 purchase orders (cid:2) $56/purchase order)/38,000 pistons $0:177=unit D The Material Handling Cost per unit is calculated by: (3.1) (3.2) MHC D D (# of Piston Material Moves (200 Piston Material Moves (cid:2) (cid:2) Material Handling OH rate)/# of pistons produced (3.3) $40/purchase order/38,000 pistons $0:211=unit D The Depreciation Expense Cost per unit can be calculated by: DEC D D (# of Piston Machine Hours (cid:2) Depreciation Expense OH rate)/# of pistons produced (3.4) (2,000 Piston Machine Hours (cid:2) $50/machine hour)/38,000 pistons $2:632 D The Machine Utility Cost per unit is also based upon machine hours and can be calculated by: MUC D D (# of Piston Machine Hours (cid:2) Utility Cost OH rate)/# of pistons produced (3.5) (2,000 Piston Machine Hours (cid:2) $4/machine hour)/38,000 pistons) 0:211 D 34 3. COSTS AND COST ESTIMATING The sum of these costs are presented in Table 3.4 and are the sum of the material cost and the ﬁve calculated overhead costs as: Total Direct Assignable Costs (TDAC) TDAC DMC DLC POC C C C MHC C DEC C MUC (3.6) 4:000 8:284 C 1:053 0:177 C C 0:211 C 2:632 C 0:211 D D D The sum of these direct and overhead costs is $8.284, but this does not include the factory overhead expenses and administrative expenses. The unit costs for the other three products— Crankshaft, Rear Axle, and Exhaust Manifold—can be evaluated in a similar fashion to that presented for the Pistons. The factory and administrative expenses are related to time as many are salaries and beneﬁts and the labor time and/or machine time are logical predictors for allo- cating these overhead expenses. The considerations presented are labor time, machine time, and the combined labor and machine time. Historical data should be used to select the best time base to use to allocate the Factory Overhead, Administrative Overhead, and other overheads such as R&D and Sales and Marketing. These overhead parameters may be diﬀerent for the various overheads, that is Factory Overhead may be related best with direct labor hours while Admin- istrative overhead may best be related to total labor plus machine hours. Table 3.5 presents the allocation of the Factory Overhead and Administrative Overhead ﬁrst as a function of direct labor hours, then with machine hours, and ﬁnally with the sum of labor and machine hours. The factory and administrative overheads will be calculated for direct labor hour basis to illustrate the calculations involved for the Piston. The administrative overhead (PAOH) for the Piston in $/Piston is calculated as: PAOH PAOH D D D Piston Administrative Overhead (Piston DL Hours/Total DL Hours) (cid:2) (Total Administrative Expenses/Total Pistons) .1;000 hrs=13;000 hrs/ .$400;000=38;000/ 0:8097 D (cid:2) The factory overhead (PFOH) for the Piston in $/Piston is calculated as: PFOH PFOH D D D Piston Factory Overhead (Piston DL Hours/Total DL Hours) (cid:2) (Total Factory Expenses/Total Pistons) .1;000 hrs=13;000 hrs/ .$500;000=38;000/ 1:0121 D (cid:2) (3.7) (3.8) Table 3.5: Total product cost using diﬀerent time basis 3.2. COST COMPONENTS FOR ESTIMATES 35 The total unit product cost is: Total Unit Piston Cost (TUPC) Total Direct Assignable Piston Costs (TDAPC) Piston Administrative Piston Factory Overhead (PFOH) (3.9) C D D D Overhead (PAOH) 1:012 0:810 C 8:284 C C 10:106 $=piston Direct Labor Hour Basis for Factory and Administrative Overhead Unit CostsPistonCrank-shaftRear AxelExhaust ManifoldTotal Direct Costs$/unit8.28487.85051.41816.155Factory OH$/unit1.01224.03811.4815.656Adminisstrative OH$/unit0.81019.2319.1854.525Total Product Cost$/unit10.106131.11972.08426.336Selling Price$/unit10.000132.00075.00023.000Product Proﬁ t/Loss$/unit-0.1060.8812.916-3.336Machine Hour OH Basis for Factory and Administrative Overhead Unit CostsPistonCrank-shaftRear AxelExhaust ManifoldTotal Direct Costs$/unit8.28487.85051.41816.155Factory OH$/unit2.63225.00014.9252.941Adminisstrative OH$/unit2.10520.00011.9402.353Total Product Cost$/unit13.021132.85078.28421.449Selling Price$/unit10.000132.00075.00023.000Product Proﬁ t/Loss$/unit-3.021-0.850-3.2841.551Total of Machine plus Labor Hour OH Basis for Factory and Administrative Overhead Unit CostsPistonCrank-shaftRear AxelExhaust ManifoldTotal Direct Costs$/unit8.28487.85051.41816.155Factory OH$/unit1.71624.45712.9794.476Adminisstrative OH$/unit1.37319.56510.3833.581Total Product Cost$/unit11.373131.87274.77924.212Selling Price$/unit10.000132.00075.00023.000Product Proﬁ t/Loss$/unit-1.3730.1280.221-1.21236 3. COSTS AND COST ESTIMATING The total proﬁt would be the unit selling price minus the unit total cost which for the piston is: Total Proﬁt for Piston D Piston Selling Price/unit 10:106 10:000 (cid:0) 0:106 $=piston (loss) Piston Total Cost/unit (3.10) (cid:0) D D (cid:0) This example problem is to show the methodology of the calculations. Note that the two other methods of assigning overheads gave pistons larger losses, the largest loss was $ 3.019 using machine hours as the base for the factory and administration overheads. Pistons would require some precision machining and that would be a cause. This also suggests that the selling price is too low. In the automotive industry, the competition is ﬁerce with the auto companies driving supplier prices down, but they do realize that they need the suppliers because they cannot make all the components at competitive costs. (cid:0) Table 3.5 indicates that the rear axle has the highest proﬁt amount using direct labor hours of $2.916/axle, but when using the machine hour base it has the greatest loss of $ 3.284/axle. This variation indicates why it is important to determine which allocation base is best for allo- cating the factory expense and administrative overheads. One could also use diﬀerent overhead bases, such as using direct labor hours for the factory expense allocation and machine hours for the administrative expense allocation. A previous work [4] has additional examples on overhead allocation. (cid:0) 3.2.3 PROFIT CALCULATIONS If you don’t know the costs, it is diﬃcult to determine a competitive price, and nearly impossible to predict the proﬁtability of the product. Price is based upon cost, but also includes other factors such as market conditions and the value of the product to the customer. Proﬁt should not be a constant percentage or constant amount for all products, but should vary with respect to your ability to produce products. If you are “the best” on certain products, the proﬁt should be greater on those products and lower on those products for which you are not “the best.” There are two methods commonly used to calculate the amount of proﬁt to include in the total cost calculation. The two methods are the percent of cost and the percent of selling price and the diﬀerence is signiﬁcant. An example of a product costing $100 will add 25% mark-up for proﬁt. Percent of Cost Calculations 3.3. COST ESTIMATION ACCURACY 37 C Product cost 0:25 Selling Price Selling Price The proﬁt would be D D D D D C Product Cost $100 $100 $100 $25 $125 $125 $100 C (cid:0) (cid:2) $25 D decimal percent mark-up (3.11) (cid:2) Percent of Selling Price Selling Price Selling Price The proﬁt would be D D D D D decimal percent mark-up) (3.12) (cid:0) 0:25/ (cid:0) Product cost/(1.0 $100=.1:00 $100=.0:75/ $133:33 $133:33 $100 (cid:0) D 33:33 Now since one is making 25% proﬁt, a very good customer wants a 20% discount and the seller would still expect to make a 5% proﬁt. The discount is applied to the selling price, not to the cost. Therefore, using the percent of cost calculations, the discount amount would amount to 20% of $125 which is $25 and thus the seller would have zero proﬁt instead of 5% proﬁt. If one uses the percent of selling price, the discount would be 20% of 133.33 which would be $26.66 and the seller would still have made a proﬁt of $6.66 after the 20% discount, which is 5% of the $133.33. This is why the preferred mark-up approach is to base it upon selling price rather than cost. Proﬁt can also be considered on an after tax basis by including the estimated taxes as part of the selling price. Consider the previous example with a product cost of $100, a desired mark-up of 25% and an expected tax rate of 20%. What should the selling price be to obtain the desired mark-up of 25% after taxes using the Percent of Selling Price Method? The proﬁt after taxes as calculated above would be The total proﬁt needed including the taxes (Gross Proﬁt) The selling price would be The taxes would be 20% of the gross proﬁt 100 The net proﬁt is $141:66 8:33 (cid:0) (cid:0) D D D D D $33:33 $33:33=.1 $100 0:20 C (cid:0) $41:66 41:666 (cid:2) $33:33 0:20/ 41:666 D $141:666 8:33 D D 3.3 COST ESTIMATION ACCURACY The accuracy of estimates will vary considerably depending upon the amount and the accuracy of the information and the degree of complexity, knowledge, and experience of the estima- 38 3. COSTS AND COST ESTIMATING tors. AACE International has developed an estimating system [5] with ﬁve classes. The system presented uses that data, but has modiﬁed it giving two accuracy ranges based on two degrees of Diﬃculty/Complexity expressed as Low and High. The easy estimates (low diﬃculty) will have a higher percentage of the total estimating information required than the diﬃcult, com- plex project estimates (high diﬃculty) and the accuracy ranges of the easy estimates would be smaller. However, the total amount of information required for the easy estimates is much less than the total amount of information required for the complex diﬃcult projects and thus more information is required for complex projects than for the easy projects for all estimate classes. The primary factor is the known amount of information required to produce the product/project vs. the total amount of information required. Table 3.6 presents the expected accuracy range for an estimate based upon the estimate class, the percent of total estimating information required, and the diﬃculty level of the estimate. For example, consider a Class 4 estimate where a sim- ple project may require 10 items of information and a complex project may require 200 items of information. If the simple project has one item of information and the complex project has 16 items of information, the percentages of total information required are 10% for the simple project and only 8% for the complex project. Thus, simple projects have a higher percentage of information required, but the complex projects require more information. If a Class 2 estimate is made for a complex, diﬃcult project and has an estimated value of $3,000,000, what is the expect range of the total project cost? C 15% to For a Class 2 estimate of a project with a high degree of diﬃculty, the estimate range is 20%. That implies the estimate could vary from 85–120% of the project estimate (cid:0) which is a range from $2,550,000–$3,600,000 for a total variation range of $1,050.000. Al- though the percentages of the estimate range seem small, for expensive projects the range is large in terms of dollars and that is why accurate estimates are important. For a Class 2 project 5%, which would result in a range with low diﬃculty, the range of the total project is of $2,850,000–$3,150,000 and a total variation range of $300,000 which is less than 30% of the high diﬃculty project range. 5% to C (cid:0) Cost control is a strategic element in the success of an enterprise. Costs have a major im- pact upon proﬁts and cost is the major item over which management has control in the amount of proﬁts earned. With the reduction in direct labor costs, overhead costs have increased sig- niﬁcantly and are a major element in the total costs and are more diﬃcult to assign to products or projects than direct costs. Accurate estimates are necessary to provide information to deter- mine the potential ﬁnancial success of a product or project. The accuracy for estimates of small, similar products with minor diﬀerences have narrower ranges than complex projects such as the Mars Mission or newly designed complex products or projects. Cost engineers should monitor their estimates to develop an accuracy distribution and range for their estimates which may be diﬀerent than those presented. Table 3.6: Cost estimate accuracy based upon Information Required [5] 3.4. SUMMARY 39 3.4 SUMMARY Costs and cost estimating are extremely important in the determination of cash ﬂows and proﬁts. The two major components are direct costs and overhead costs. The overhead costs have increased greatly due to safety, environmental, legal, and other new costs while the direct labor costs have decreased signiﬁcantly over the past decades as a percentage of the total cost. The approaches to overhead allocation are the traditional methods which utilized percentage relationships of direct costs and the ABC method. The newer approaches are relating the costs to a time basis in both the traditional approach and Time-Based ABC method. If production time can be reduced, the overhead charge per unit will be reduced. The method of determining the product mark-up should be based upon a percentage of the selling price rather than a percentage of the total cost. The estimating class system permits a calculation of the range in the estimate based upon the complexity of the project and the experience of the estimators. Estimate ClassPercent of Total Estimating Information Required (EIR (%)) and Diﬃ culty Level (DL)Typical ApplicationExpected Accuracy Range Based upon Project Diﬃ culty/ComplexityEIR (%)DLAccuracy Range (%)Class 51–10LowScreeningLow-20 – +300–2HighConceptHigh-50 – +100Class 45–20LowBudget Prep.Low-15 – +201–15HighFeasibilityHigh-30 – +50Class 315–50LowBudget ApprovalLow-10 – +1010–40HighBudget PreparationHigh-20 – +30Class 240–80LowControl BudgetLow-5 – +530–70HighBudget ApprovalHigh-15 – +20Class 175–100LowCheck EstimateLow-3 – +370–100HighBid/TenderHigh-10 – +15Table 3.6 is altered slightly from the original publication by AACE International [5]. Th is will reﬂ ect rear-ranging data of the last column to be two rows according to project diﬃ culty/complexity level which originally was:Low-20% – -50%-15% – -30%-10% – -20%-5% – -15%-3% – -10%High +30% – +100%+20% – +70%+10% – +30%+5% – +20%+3% – +15%40 3. COSTS AND COST ESTIMATING 3.5 REFERENCES [1] Cost Engineering Terminology AACE International Recommended Practice No. 10S-90, pages 29, 32, 2017. Copyright© 2017 by AACE International: All rights reserved. (Rec- ommended Practice No. 10S-90, 2017, Cost Engineering Terminology is a free download to the public by visiting web.aacei.org) 25 Reprinted with the permission of AACE International, 1265 Suncrest Towne Centre Dr., Morgantown, WV, 26505, U.S. Phone 304-296-8444. Internet: http://web.aacei.org e-mail mailto:[email protected] [2] Creese, Robert C., Adithan, M., and Pabla, B. S., Estimating and Costing for the Metal Manufacturing Industries, Marcel Dekker, Inc., page 13, 1992. (Reprinted with Permission of Taylor and Francis Group LLC Books.) 26, 27 [3] Rondeau, H. F., The 1-3-9 rule for product cost estimation, Machine Design, pages 50–53, August 1975. 30 [4] Creese, Robert C., Adithan, M., and Pabla, B. S., Estimating and Costing for the Metal Manufacturing Industries, Marcel Dekker, Inc., pages 35–49, 1992. 36 [5] Cost Estimate Classiﬁcation System—As Applied in Engineering, Procurement, and Construc- tion for the Process Industries, AACE International Recommended Practice No. 18R-97, pages 2–3, 2011. 38, 39 Reprinted with the permission of AACE International, 1265 Suncrest Towne Centre Dr., Morgantown, WV, 26505, U.S., Phone 304-296-8444. Internet: http://web.aacei.org e-mail: mailto:[email protected] 3.6 EVALUATIVE QUESTIONS 1. Find two additional references to interest charges or cost estimating before time zero AD. 2. In competitive markets, why is cost control performed more by management than increas- ing prices? 3. What are the major diﬀerences between cost estimating and cost accounting? 4. What are the three basic approaches to cost estimating? 5. Repeat the analysis of Table 3.1 for a 5% increase in price, a 5% increase in sales, and 5% cost reduction. 3.6. EVALUATIVE QUESTIONS 41 6. Determine the new overhead allocations for the Purchase Orders if the total overhead cost for the purchasing department is $60,000 and the orders for the products are: Piston- 300, Crankshaft-500, Rear Axle-100, and Exhaust Manifold-100. Determine the unit purchasing OH cost for each of the four product produced and compare them with those in Table 3.4. The total quantities are the same as those listed in Table 3.4. 7. Determine the unit costs and total unit cost for the crankshaft if 10,000 units were pro- duced (a recording error was made and 10,000 were made instead of 8,000) and compare the results (costs and proﬁts) to the 8,000 total and unit costs of Tables 3.4 and 3.5. Assume all other values remain the same as in Tables 3.3, 3.4, and 3.5. 8. A product has a total cost of $2,000 and the desired proﬁt is 15%. (a) Determine the selling price if the proﬁt percent is based upon the cost. (b) Determine the selling price if the proﬁt percent is based upon the selling price. (c) Determine the selling price if the proﬁt percent is based upon the selling price and the tax rate is 20% and the proﬁt desired is after taxes. 9. A Class 4 estimate is to be prepared for a project estimate of $1,500,000 that is very similar to previous work. What is the estimate range for this project? 10. Company JEN does complex projects and the estimated project cost is $5,000,000 for a Class 1 Estimate. What is the estimate range for this project and what is the minimum percentage of the total estimating information required? C H A P T E R 4 Breakeven Analysis 43 4.1 INTRODUCTION The previous chapter indicated that the best approach for allocating overheads was the time- based system for either the traditional direct cost system or the Time-Based ABC system. Breakeven analysis has traditionally focused upon production quantity-based breakeven anal- ysis and the cost breakeven point. This worked well for marketing, sales, and top-management for planning goals, but it provided little assistance at the plant management level where the production quantity is not a variable, but a quantity speciﬁed by the customer. The plant su- perintendent, production manager, or manufacturing manager can control the time to produce the orders but they cannot control the quantity. Thus, time-based breakeven analysis [1–5] is a concept being considered for use at the operation levels of production. In addition to the two approaches to breakeven analysis, one can also consider diﬀerent breakeven points and these will be presented in detail. The costs will be considered as ﬁxed, variable, and semi-variable, but they will be considered diﬀerently for the two models as an item ﬁxed in one approach may be variable in the other. For example, in the quantity-based system materials would be considered as variable whereas in the time-based system they would be considered as ﬁxed as the quantity is ﬁxed. 4.2 BREAKEVEN MODEL BASICS The basis of the two models is the same equation presented by George Dieter in Volume 20 of the ASM Handbook [6]. The base equation is: Cu D Cm C Cc=n C Cl =pr; (4.1) where Cu Cm Cc Cl n pr D D D D D D unit cost, $/unit unit material cost, $/unit capital cost, $ labor and overhead cost, $/hr production quantity, number of units production rate, units/hr 44 4. BREAKEVEN ANALYSIS If one multiplies Equation (4.1) by the production quantity, n, to obtain the total cost, the equation for total cost (CT ) is: Rewriting this equation with n being emphasized: CT nCm Cc C C D Cl n=pr: CT n (cid:2) D .Cm C Cl =pr/ Cc: C If the production rate is considered to be a constant, the equation would be written as: CT n (cid:2) D .slope constant in $/unit/ intercept ($) C and this is the basis of the production quantity-based approach. The basis of time-based approach is also from Equation (4.2) If one recognizes that: CT nCm Cc C C D Cl n=pr: n=pr nCm D the total production time T and D the total materials cost for the order, Cmt then with slight rearranging Thus, CT T Cl (cid:2) D C .Cmt C Cc/: CT .slope constant in $/unit time/ and this is the basis of the time-based approach. D (cid:2) T intercept ($) C (4.2) (4.3) (4.2) (4.4) 4.3 BREAKEVEN POINTS The four breakeven points are deﬁned so that they can be used in either the time-based system or the quantity-based system. The costs will be deﬁned in three categories as ﬁxed costs, variable costs and as semi-variable costs, but the speciﬁc costs may not be in the same category in the two bases. The typical costs in three categories will be listed for each cost base. 4.3.1 CATEGORIES AND TYPICAL EXAMPLES FOR THE PRODUCTION QUANTITY-BASED SYSTEM In the production quantity-based system the overhead costs are not a separate category and are typically included in the ﬁxed costs or may be assessed to the variable direct labor and/or direct material costs. The production costs will be considered in the three components of ﬁxed costs, variable costs, and semi-variable costs. • Fixed Costs—those costs which are independent of the production quantity required to make the product. The typical examples of ﬁxed costs are property taxes, depreciation, administrative salaries, and plant overhead. The ﬁxed overhead costs are often converted to be components of the direct labor cost. 4.3. BREAKEVEN POINTS 45 • Variable Costs—those costs that are a direct function of production quantity to make the product. Two typical examples of variable costs are direct labor and direct material costs. • Semi-Variable Costs—those costs which are partially ﬁxed and partially variable. Costs such as maintenance expenses and inspection costs frequently are considered as semi- variable costs. 4.3.2 CATEGORIES AND TYPICAL EXAMPLES FOR THE PRODUCTION TIME-BASED SYSTEM These costs are divided into two major groups as production costs and overhead costs. The pro- duction costs are divided into the three groups of ﬁxed costs, variable costs, and semi-variable costs. Since this is a time-based system, the overhead costs can be considered as a separate cat- egory as a variable component. a. Production Costs – Fixed Costs—those costs which are independent of the production time of the prod- uct; these would include the material costs. Since the quantity is ﬁxed, the total ma- terial costs would be ﬁxed. – Variable Costs—those costs which are directly dependent upon the production time of the product; these would include machine time costs, depreciation costs, plant overhead, and direct labor costs. – Semi-variable Costs—those costs which are partially ﬁxed and partially variable; these include maintenance costs and utility costs. b. Overhead Costs – Variable Costs—those costs which are dependent upon time but are not directly at- tributable to a speciﬁc product; these include administrative costs, research and de- velopment costs, etc. Two example problems which have been presented previously [4] will be used to illustrate the types of variables, calculations, results, and interpretation of the results. 46 4. BREAKEVEN ANALYSIS 4.4 PRODUCTION QUANTITY-BASED BREAKEVEN EXAMPLE The production quantity-based method is illustrated ﬁrst as this is the traditional approach to breakeven analysis, but all four breakeven points will be illustrated. This is the same example used at the ASEE [4] conference and one should notice the diﬀerences in the data used for the two approaches. The data for the production quantity-based model is listed in Table 4.1. Table 4.1: Data for production quantity-based breakeven analysis [1, 4] The calculations for the four breakeven points are presented in a general form using the data from Table 4.1. Let x D the units of production. (a) Shutdown Breakeven Level (SD) Semi-variable Costs C Revenues 20x 20x 15x x D D D D D Variable Costs 600 2x 3x C 600 C C 5x 600 40 units Item$/Unit$DecimalSales Revenue20Production CostsFixed CostsVariable CostsSemi-variable Costs322,400600Required Return (Proﬁ t)900Tax Rate (40%)0.40(b) Cost Breakeven Level (C) 4.4. PRODUCTION QUANTITY-BASED BREAKEVEN EXAMPLE 47 Revenues Revenues 20x 20x 15x x D D D D D D Total Costs Variable Costs 600 2x 3x C 3;000 C 5x C 3;000 200 units Semi-variable Costs 2;400 C C C Fixed Costs (c) Required Return Breakeven Level (RR) Revenues Revenues 20x 15x x D D D D D Total Costs 3;000 5x Required Return 900 C C C 5x C 3;900 3;900 260 units (d) Required Return After Taxes Breakeven Level (RRAT) Revenues Revenues Revenues 20x 20x 15x x D D D D D D D Total Costs Required Return After Taxes Taxes on Total Required Return C Total Costs 3;000 5x Required Return After Taxes=.1:0 900=.1 0:4/ Tax Rate/ (cid:0) C C C C (cid:0) 1;500 C C 5x 5x C 4;500 3;000 4;500 300 units Note that to obtain a required return of $900 after taxes that one must earn $1,500 as the 40% taxes would be $600. To obtain the pre-tax required return, one can use the expression: Required Return Including Taxes Required Return After Taxes=.1:0 Tax Rate/ (4.5) (cid:0) D The tax rate is expressed as a decimal. 48 4. BREAKEVEN ANALYSIS Figures 4.1 and 4.2 show the breakeven points of total costs vs. production quantity and unit costs vs. total costs. The results and actions for the various breakeven points are presented in Table 4.2. The Total Cost vs. Production Quantity is the breakeven ﬁgure observed, but the Unit Cost vs. Production Quantity shows the eﬀects of revenue changes upon the various breakeven points more easily than that of Total Costs in Figure 4.1. Figure 4.1: Total revenue and costs for the production-based model [4, 5]. The problem is that the customer usually dictates the level of production and the pro- duction department has little control over the quantity. The unit cost curve indicates what the revenue is required to obtain the desired breakeven points. Total Cost vs. Production QuantityTaxes for Required ReturnTotal RevenueTaxesProﬁtsOverheadCostsManufacturingCostsRRAT(300)RR(260)C(200)SD(40)Required ReturnFixed CostsSemi-variable CostsVariable CostsTotal Revenue ($1000)12108642001002003004005006004.4. PRODUCTION QUANTITY-BASED BREAKEVEN EXAMPLE 49 Figure 4.2: Unit costs vs. production quantity for the production-based model [4, 5]. Unit Cost vs. Production QuantityProduction QuantityTaxesRRAT(300)RR(260)C(200)SD(40)Required ReturnFixed CostsSemi-variable Variable Costs ($/Unit)504540353025201510500804012020016024028032036040050 4. BREAKEVEN ANALYSIS Table 4.2: Shutdown points and actions/implications for production quantity-based model [4] Production Level RangeAction/Implication1. Zero to Shutdown Level (SD) (0–40 units)Do not accept order as all of the out-of-pocket costs (variable and semi-variable costs) will not be recovered.2. Shutdown Level (SD) to Cost Level (C) (40–200 units)Will recover the out-of-pocket costs, but not all of the ﬁ xed costs. Accept only if no better opportunities are available.3. Cost Level (C) to Required Return Level (RR) (200–260 units)Will recover all costs, but will not obtain the desired level of required return. Accept if no better opportunities are available.4. Required Return Level (RR) Level to Required Return After Taxes Level (RRAT) (260–300 units)Have succeeded in making the required return on a pre-tax basis, but not on an after-tax basis. Accept unless better opportunities are available.5. Greater than Required Return After Taxes Level (RRAT) (>300 units)Will recover all costs and exceed required return on an after-tax basis. Accept as this is usually a rare and highly proﬁ table event.4.5. PRODUCTION TIME-BASED BREAKEVEN EXAMPLE 51 4.5 PRODUCTION TIME-BASED BREAKEVEN EXAMPLE The production time-based method is newer and is used as overheads are becoming a major component of costs and is typically based upon time. All four breakeven points will be illustrated and this is the same example used at the ASEE [4] conference. The data for the production quantity-based model is listed in Table 4.3. Table 4.3: Data for production time-based breakeven analysis [1] Notice that the overhead costs are a separate item whereas they were included in the production costs in the quantity-based model. The required return can be used as an hourly rate as illustrated in this example, but it can also be listed as a speciﬁc amount. Let y D production hours and then the breakeven points can be calculated as follows. (a) Shutdown Breakeven Point (SD) Revenues Revenues 13;000 13;000 20y y D D D D D D Production Costs Fixed Costs 18y 2;000 Variable Costs 2y 1;000 C C C 3;000 20y C C 10;000 500 hours Semi-variable Costs C Item$/Hour$DecimalSales Revenue13,000Production (Manufacturing) CostsFixed CostsVariable CostsSemi-variable Costs1822,0001,000Overhead Costs20Required Return (Proﬁ t)10Tax Rate (40%)0.4052 4. BREAKEVEN ANALYSIS (b) Cost Breakeven Point (C) Revenues Revenues 13;000 13;000 40y y D D D D D D Total Costs Production Costs 3;000 20y C 20y C 3;000 40y C C 10;000 250 hours (c) Required Return Breakeven Point (RR) Overhead Costs Revenues Revenues 13;000 50y y D D D D D Total Costs 40y 3;000 C Required Return 10y 3;000 50y C C C 10;000 200 hours (d) Required Return After Taxes Breakeven Point (RRAT) Revenues Revenues Revenues 13;000 56:66y y D D D D D (cid:25) Total Costs Total Costs 40y 3;000 C C Required Return After Taxes C Required Return After Taxes=.1 0:40/ 10y=.1:0 Tax Rate/ (cid:0) Taxes on Total Required Return 3;000 40y 16:66y C C C C (cid:0) 10;000 176 hours .176:47/ Note that to obtain a required return of 10y after taxes one must earn 16:66y as the 40% taxes would be 6:66y. To obtain the pre-tax required return, one can use the expression: Required Return Including Taxes Required Return After Taxes=.1:0 Tax Rate/: (4.5) (cid:0) D The tax rate is expressed as a decimal. 4.5. PRODUCTION TIME-BASED BREAKEVEN EXAMPLE 53 The results and actions for the various breakeven points are presented in Table 4.4. The Total Cost vs. Production Times in Figure 4.3 shows the breakeven points in a manner similar to the production unit costs where the revenue is a horizontal line. The proﬁtability curve in Figure 4.4 highlights that lower production times have a major impact upon proﬁtability. The primary advantage of the proﬁtability plot is that it easily shows the importance of doing things faster and how that improves proﬁtability. This also can be used to estimate the cost of delay upon proﬁtability such as a machine having down-time, delivery delay, weather delay, etc. Table 4.4: Shutdown points and actions/implications for the production time-based model [1, 5] Production Level RangeAction/Implication1. Shutdown Level (SD) or higher (> 500 production hours)Do not accept order as all of the direct pro-duction costs will not be recovered and none of the overhead or return will be recovered.2. Breakeven Cost Level (C) to Shutdown Level (SD) (250–500 production hours)Will recover all of the production costs and some of the overhead costs. None of the re-quired return will be recovered.3. Required Return Level (RR) to Breakeven Cost Level (C) (200–250 production hours)Will recover all costs, but will not obtain the desired level of required return before taxes. Accept unless better opportunities are avail-able.4. Required Return After Taxes Level (RRAT) to Required Return Level (RR) (176–200 production hours)Have succeeded in making the required return on a pre-tax basis, but not on an after-tax basis. Accept unless better opportunities are available.5. Less than Required Return After Taxes Level (RRAT) (< 176 production hours)Will recover all costs and exceed required return on an after-tax basis. Accept as this is usually a highly proﬁ table rare event.54 4. BREAKEVEN ANALYSIS Figure 4.3: Total revenues and costs vs. production time with breakeven points [1, 5]. Total Cost vs. Production TimeProduction Time (hours)Taxes on Required ReturnRevenueOverhead CostsManufacturing CostsRRAT 176RR200C 250SD 500Required ReturnRequired Return($10/hour)Total Revenue and Cost Items504540353025201510501003002005004006007008009004.5. PRODUCTION TIME-BASED BREAKEVEN EXAMPLE 55 Figure 4.4: Proﬁtability vs. production time with breakeven points [1, 5]. Proﬁtability PlotProduction Time (hours)RevenueTaxesNet ProﬁtOverheadCostsManufacturing CostsRRAT 176200 RR 250 C500 SD Required Return($10/hour)Total Revenue ($1,000)14121086420-2-4-6-8-1010050020015035030025040045050055060056 4. BREAKEVEN ANALYSIS SUMMARY 4.6 The traditional breakeven charts usually have only one breakeven point at cost, but three other points can be determined and they are the shut-down point, the breakeven point at required return, and the breakeven point at required return after taxes. The time-based system is being used for allocating overheads and can also be used for determining the four breakeven point using hour units. The plot of total revenue and the various costs vs. production illustrates the breakeven points on the production quantity basis, and the proﬁtability plot of proﬁtability vs. production hours illustrates the breakeven points on the production time basis. 4.7 REFERENCES [1] Creese, Robert C., Time-based breakeven analysis and costing, AACE International Trans- actions, ABC.02, AACE International, Morgantown WV, pp. ABC.02.1–ABC.02.6, 1998. 43, 46, 51, 53, 54, 55 Reprinted with the permission of AACE International, 1265 Suncrest Towne Centre Dr., Morgantown, WV, 26505, Phone 304-296-8444. Internet: http://web.aacei.org [2] Creese, Robert C., AACE.02, Time-based breakeven analysis, Joint Cost Management So- cieties Proceedings, pp. AACE 02.01–AACE 02.07, 1998. [3] Creese, Robert C., A new breakeven analysis uses production versus quantity, Modern Castings, pp. 52–53, March 1996. [4] Creese, Robert C., Time-based versus quantity based breakeven analysis, Proc. of the Amer- ican Society for Education Annual Conference and Exposition, pp. 9.1308.1–9.1308.17, 2004. Selected items are Reprinted with permission of American Society for Engineering Edu- cation. 45, 46, 48, 49, 50, 51 [5] Creese, Robert and Thiruvalam, Kedhar P., Power Point Presentation, “Breakeven Anal- ysis,” prepared in 2009 for presentation at Metal Casting Seminar. 43, 48, 49, 53, 54, 55 [6] Dieter, George E., Costs and related aspects of materials selection, ASM Handbook Volume 20 Materials Selection and Design, ASM International, Metals Park, OH, pp. 248–249. 43 4.8 EVALUATIVE QUESTIONS 1. When plotting the production breakeven charts the ﬁxed costs traditionally were plotted ﬁrst. 4.8. EVALUATIVE QUESTIONS 57 (a) What happens when that is done on the Total Cost vs. Production Quantity graph? (b) What happens if the variable cost is plotted ﬁrst on the Unit Cost vs. Production Quantity graph? 2. What are the four breakeven points if the variable costs are 8 $/unit instead of 3 $/unit in Table 4.1? 3. Plot both the total cost vs. production quantity breakeven chart similar to Figure 4.1 and the unit cost breakeven vs. production quantity chart similar to Figure 4.2 when the vari- able costs are 8 $/unit. 4. What are the four breakeven points if the Required Return in Table 4.1 was $1,200 instead of $900? 5. What are the four breakeven points if the semi-variable costs in Table 4.1 were 7 instead of 2 600? (cid:2) C 900 (cid:2) C 6. What are the four breakeven points for the Production Time-Based Breakeven analysis if the ﬁxed costs in Table 4.3 were $5,000 instead of $2,000? 7. Make the Total Revenues and Costs vs. Production Time results similar to Figure 4.3 and the Proﬁtability vs. Production Time results similar to Figure 4.4 showing the four breakeven points on each of the graphs. 8. The data for a production quantity-based breakeven problem is in Table 4.5. Calculate the following items: (a) Shutdown breakeven point-units (b) Cost breakeven point-units (c) Required return breakeven point-units (d) Required return after taxes breakeven point (e) Draw the Total Revenue and Costs vs. the Production Quantity showing the four breakeven points. 9. The data for a production time-based breakeven problem is in Table 4.6. Calculate the following items: (a) Shutdown breakeven point-units (b) Cost breakeven point-units (c) Required return breakeven point-units (d) Required return after taxes breakeven point (e) Draw the Proﬁtability Plot showing the four breakeven points. 58 4. BREAKEVEN ANALYSIS Table 4.5: Data for production quantity-based breakeven analysis Table 4.6: Data for production time-based breakeven analysis Item$/Unit$DecimalSales Revenue20Production (Manufacturing) CostsFixed CostsVariable CostsSemi-variable Costs323,600900Required Return (Proﬁ t)1,200Tax Rate (20%)0.20Item$/Hour$DecimalSales Revenue13,000Production (Manufacturing) CostsFixed CostsVariable CostsSemi-variable Costs1062 3,000Overhead Costs10Required Return (Proﬁ t)1,200Tax Rate (20%)0.20C H A P T E R 5 59 Earned Value Management 5.1 INTRODUCTION Earned Value Management (EVM) is a tool used to measure project performance with respect to time and cost. It is typically used to measure performance in project work which involves a single highly complex item whereas breakeven analysis is used more frequently in manufacturing and other areas where the output involves a large quantity of a single product or closely related products. EVM focuses on schedule or time, and costs. EVM can be applied to any project such as developing new products, research projects, equipment installation projects, and any project that involves a schedule and costs. Typical EVM projects are large construction projects buildings, highways, bridges, or dams and other very large projects such as aircraft carriers, missions to the moon or Mars, and the development of innovative new products such as the i- Phone or self-driving vehicles. EVM can indicate performance problems such as cost overruns and/or schedule delays during the project to warn management to take action so the project can achieve a successful completion. When the project is large, EVM is used for measuring progress in terms of cost and schedule to speciﬁc milestones of the project. Two sources [1, 2] of the fundamental concepts of EVM are used in the development of the following relationships and equations. The data used is from earlier examples from AACE International [1], which has become a base model for comparing methods for evaluating the traditional EVM approach and the newer time-based EVM approach developed by Lipke [3, 4]. The two approaches will be illustrated to show the diﬀerences as the EVM method shows the schedule variance in terms of hours or dollars and the time-based method calculates the schedule variance in terms of time periods rather than dollars. The diﬀerences can become large at the end of the project when projects have signiﬁcant delays or early completion. 5.2 EARNED VALUE MANAGEMENT PERFORMANCE PARAMETERS Three elements are used to measure project performances in EVM: 1. the Planned Value (PV) of the work scheduled or the Budgeted Cost of Work Scheduled (BCWS); 2. the Earned Value (EV) of the work accomplished or the Budgeted Cost of Work Per- formed (BCWP); and 60 5. EARNED VALUE MANAGEMENT 3. the Actual Cost (AC) of the work accomplished or the Actual Cost of Work Performed (ACWP). The values are traditionally measured in monetary units, such as dollars, or measured in work hours, and sometimes both are used. Work hours are often used at the work site and converted to monetary units at the management level. The earned value is used in both the schedule performance and in the cost performance measurements. The traditional performance measures derived from these elements are the Schedule Vari- ance (SV), the Cost Variance (CV), the Schedule Performance Index (SPI), and the Cost Per- formance Index (CPI), which are presented in the following equation forms. The schedule values will be presented ﬁrst: SV EV (cid:0) D PV; (5.1) where SV EV PV D D D schedule variance earned value planned value: If the schedule variance is positive, the project is ahead of schedule whereas if the schedule variance is negative, the project is behind schedule. This same information can be obtained from the schedule performance index where: SPI D EV=PV; (5.2) where SPI EV PV D D D schedule performance index earned value planned value: A schedule performance index of 1.0 indicates the project is on schedule, a schedule per- formance index greater than 1.0 indicates the project is ahead of schedule, and a schedule per- formance index less than 1.0 indicates the project is behind schedule. The cost performance equations are similar to the schedule performance equations, but use the actual cost and earned value. The equations are: CV EV (cid:0) D AC; (5.3) where CV EV AC D D D cost variance earned value actual cost: 5.2. EARNED VALUE MANAGEMENT PERFORMANCE PARAMETERS 61 If the cost variance is positive, the project is under budget whereas if the cost variance is negative, the project is over budget. This same information can be obtained from the cost performance index where: CPI D EV=AC; (5.4) where CPI EV AC D D D cost performance index earned value actual cost: A cost performance index of 1.0 indicates the project is on budget, a cost performance index greater than 1.0 indicates the project is under budget, and a cost performance index less than 1.0 indicates the project is over budget. These values can be kept on a periodic basis, such as weekly, and on a cumulative basis for monitoring the project performance and direction and can give indications as to what corrective actions need to be taken. Note that Earned Value (EV) is used in both the cost and schedule indices and variances. Another item for consideration is to estimate the completion of the project. The comple- tions can be calculated for the cost completion and the schedule completion. There are various methods, but the one most often used is to consider the work cost in the future will be at the planned rate and this results in: EAC.c/ PV ct .AC (cid:0) C D EV/; (5.5) where EAC.c/ AC EV PV ct D D D estimate at completion-cost D actual cost to date earned value to date planned value for project completion cost: The completion can also be predicted with respect to time as well, using the planned value and is expressed as: EAC.t/ PV ct .PV C (cid:0) D EV/; (5.6) where EAC.t/ PV EV PV ct D D D estimate at completion (time) D planned value to date earned value to date planned value for project completion time: 62 5. EARNED VALUE MANAGEMENT 5.3 EXAMPLE PROBLEM USING TRADITIONAL EARNED VALUE MANAGEMENT An example problem, adopted from the AACEI Skills and Knowledge of Cost Engineering, was expanded and is presented on a project with a delay of one week over the life of the project. The information is presented in Table 5.1. The tables and ﬁgures in this chapter are from the work of Yi Fang which are published in her thesis [5] and also in Cost Engineering [6] and are published with permission of AACE International. To illustrate how the values are calculated, Week 3 will be analyzed in detail for the variances and indexes. The planned time for the project total completion or PV ct is 440 hours. For the period values for week three using Equations (5.1) to (5.4), one obtains: SV.3/ SPI.3/ CV.3/ CPI.3/ D D D D PV EV (cid:0) EV=PV 65 D (cid:0) 65=45 D AC EV (cid:0) EV=AC 65 D (cid:0) 65=62 D 20 D C 1:44 > 1:00 3:0 D C 1:05 > 1:00: 45 D 62 D This indicates that the schedule and cost performance indices were both greater than 1.00 for Week 3 and thus on time and under budget for the week. For the cumulative values, the symbol SV c3 implies the schedule variance for Week 3. The cumulative values for week three are: 110 120 10 SV c3 SPIc3 CV c3 CPIc3 D D D D PV c3 EV c3 (cid:0) EV c3=PV c3 EV c3 (cid:0) EV c3=ACc3 D ACc3 D (cid:0) 110=120 110 (cid:0) D 110=109 D D (cid:0) 0:92 < 1:0 1:0 D C 1:01 > 1:0 D 109 D EAC.c/ PV ct (cid:0) D Percent Completion EAC.t/ PV ct D D (cid:0) CV c3 439 PV ct .EV c3 ACc3/ D 440 (cid:0) .110 D (cid:0) .EV c3=PV ct/ (cid:0) (cid:0) 109/ D 439 D 440 1 (cid:0) D SV c3 450 D PV ct .120 (cid:2) .EV c3 (cid:0) 110/ (cid:0) 450: D PV c3/ 440 D (cid:2) . D 10/ (cid:0) (cid:0) 100 .110=440/ 100 25% (cid:0) D C D This indicates that for the cumulative ﬁrst three weeks, the project is behind schedule, slightly under budget, and expected to be completed at 450 hours based upon schedule perfor- mance (typically used) or at 439 hours based upon cost performance. The project is 25% complete at the end of the third week. If the percent completion is known, it can be used to determine the earned value. That is: Earned Value D .Percent Completion as decimal/ Planned Value: (5.7) (cid:2) 5.4. EXAMPLE PROBLEM USING EARNED SCHEDULE IN EARNED VALUE MANAGEMENT 63 The cumulative PV, AC, and EV values are plotted in Figure 5.1. Note that the period values and cumulative values of the SPI and CPI can be quite diﬀerent, and indicated by the schedule parameters in Table 5.1. One problem with the schedule indices is that the SV tends to 0 and the SPI goes to 1.0 regardless of whether or not the project is delayed. This occurs as the planned and earned values will be equal when the project is completed, regardless if it is early, on time, or late. This has led to a new calculation procedure for the Schedule Variance and the Schedule Performance Index on a time based analysis rather than on a cost-based (or work hour-based) analysis. Figure 5.1: Planned value, earned value, and actual cost [6]. 5.4 EXAMPLE PROBLEM USING EARNED SCHEDULE IN EARNED VALUE MANAGEMENT Lipke [3, 4] introduced the concept of Earned Schedule (ESc) which is similar to the Earned Value, but Earned Schedule is in time units rather than hours or dollars. Fang [5, 6] utilized the concept and applied it to the AACE International data [1] in her M.S. thesis. The earned schedule values are used for cumulative values, not period values. The following calculations are utilizing the data in Table 5.2 which also contains the cumulative values of Table 5.1. The cumulative time values has two PV values for N and N 1. The AT value is usually greater than N , but if a project ﬁnishes ahead of schedule N can equal or be greater than AT. C 5004003002001000CostPeriod (weeks)1234567891011PVACEVPVACEV64 5. EARNED VALUE MANAGEMENT ] 6 , 5 [ t c e j o r p d e y a l e d r o f h c a o r p p a e u l a v d e n r a e r o f a t a d e v i t a l u m u c d n a d o i r e P : 1 . 5 e l b a T Period(Week)(AT)Period ValuesCumulative ValuesPV(BCWS)AC(ACWP)EV(BCWP)SVSPICVCPIPVc(BCWS)ACc(ACWP)EVc(BCWP)SPIcSVcCPIcCVc1301615-150.50-1.00.943016150.50-150.94-1.02453130-150.67-1.00.977547450.60-300.96-2.03456265+201.44+3.01.051201091100.92-101.01+1.04807885+51.06+7.01.092001871950.98-51.04+8.05806670-100.88+4.01.062802532650.95-151.05+12.06505155+51.10+4.01.083303043200.97-101.05+16.0725302501.00-5.00.833553343450.97-101.03+11.08303025-50.83-5.00.833853643700.96-151.02+6.0930333001.00-3.00.914153974000.96-151.01+3.01025282501.00-3.00.894404254250.97-151.000.01101415+15N/A +1.01.074404394401.0001.00+1.05.4. EXAMPLE PROBLEM USING EARNED SCHEDULE IN EARNED VALUE MANAGEMENT 65 The equation for ESc is mathematically expressed as: ESc N D C .EV c (cid:0) PV c.N //=.PV c.N 1/ (cid:0) C PV c.N //; (5.8) where cumulative earned schedule at time period N D period where the cumulative PV is less than the current cumulative EV cumulative earned value at actual time; AT cumulative planned value at period N 1/ cumulative planned value at next period; N D actual time or current time period: 1 C ESc N D EV c.AT/ PV c.N / PV c.N AT D D D C For Period 3 (that is where AT 3 and N 2), D D ES3 2 .110 75/=.120 75/ 2 0:777 2:78 periods (weeks): D C If, at the start of the project, the PV is greater than the EV, then the ES will be less than D D C (cid:0) (cid:0) one and can be calculated by Thus, for Period 1, where AT 1 D ESc D .PV 1 (cid:0) EV 1/=PV 1: (5.9) ES1 .30 (cid:0) D 15/=30 D 0:5 period (week): This calculation can be repeated for the initial periods until ESc exceeds PV 1 and then 1. The schedule variance, based upon time, is Equation (5.9) can be used and this is when N calculated by: D where SV.AT/ ES (cid:0) D AT; (5.10) D SV.AT/ ES D AT D SV.3/ schedule variance based upon time AT earned schedule actual time or current time period 2:78 3:00 (cid:0) D (cid:0) 0:22 periods (weeks) D which implies the project is 0.22 time periods behind schedule at the end of time period 3. The schedule performance index based upon time is: SPI.AT/ ES=AT: D (5.11) If one examines Period 3, then SPI.3/ 2:78=3:0 0:93: D D 66 5. EARNED VALUE MANAGEMENT The ﬁrst cumulative value of PV below EV is when PV 2, thus D 30 and EV D 45 which occurs in period AT EV C N PV c 1/ C D D D D D 2 45 1 30 75 PV c.N and ESc ES.2/ D D N 1 C .EV c .45 PV c.N //=.PV c.N 30/ (cid:0) 30/=.75 1 C (cid:0) (cid:0) D C 1/ (cid:0) C 0:3333 PV c.N // 1:33 periods (weeks): D Thus, the time-based schedule variance using Equation (5.10) is: SV.2/ 1:33 2:00 0:67 periods (weeks). D (cid:0) This implies that the project is 0.67 time periods behind schedule. The schedule performance index based upon time using Equation (5.2) is: D (cid:0) SPI.2/ D ES.2/=AT D 1:33=2:00 0665 D D 0:67: Now examining the data for the last period, that is period 11, note that AT EV .AT/ 11 440: D D The ﬁrst cumulative value of PV below EV .11/ is 415 which occurs in period N 9, thus D N PV C 1/ C D D D 9 415 440 PV C .N and ESc ES D D N 9 C .EV c .440 C (cid:0) PV c.N //=.PV c.N 1/ PV c.N // (cid:0) 415/=.440 415/ (cid:0) D C 9 (cid:0) 1 C D 10 periods (weeks): Thus, the time-based schedule variance using Equation (5.10) is: SV.AT / SV.11/ AT 11 ES 10 (cid:0) (cid:0) D D D (cid:0) 1 periods (weeks). This implies that the project is 1.0 time period behind schedule. The ﬁnal schedule variance is the diﬀerence in time values (AT) when the cumulative planed value (PV c) reaches the project completion time minus the (AT) when the earned value (EV.N 1) ﬁrst reaches the project complete value. The schedule performance index based upon time using Equation (5.11) is: C 5.5. SUMMARY 67 SPI.11/ ES=AT 10=11 0:909 0:91: D D D D The time-based values are the actual values, that is a schedule variance of 1:0 and sched- ule performance index of 0.909 instead of the traditional schedule variance of 0 and SPI of 1.0. Table 5.2 indicates the cumulative-based and cumulative time-based values. The major diﬀer- ences are in the schedule variance and the schedule performance index. The schedule variance is based upon dollars or work hours, whereas the earned schedule is based upon amount of work completed for that particular time period. (cid:0) Figure 5.2 show the comparison of the SPI values based upon the cumulative dollar (or work-hour) base (SPI.$/) vs. the SPI values based upon the cumulative project time (SPI.t/) over the project life for a delayed project. There would also be a diﬀerence if the project was completed early. The diﬀerences are a result of the EVM work hour approach must end with a SPI.$/ at 1.0, regardless of the actual completion time whereas SPI.AT/ is at 0.91. The major diﬀerences between the two SPI indices occur at the end of the project life. The initial diﬀerences are primarily due to the diﬀerence in units; that is dollars vs. the time estimate calculation. The time-based calculation is the relative amount of work earned for the period vs. the amount planned for the period. Table 5.3 is a combination of Tables 5.1 and 5.2 to indicate all the information in a single table. 5.5 SUMMARY The parameters used to measure project performance are the Planned Value, the Earned Value, and the Actual Cost of the work performed. The performance measures evaluated were the schedule variance, the schedule performance index, the cost variance, the cost performance in- dex, the time estimated at completion, the time-based schedule variance, and the time-based schedule performance index. Indices which are greater than unity are favorable (under budget or ahead of schedule) and those less than unity are unfavorable (over budget or behind sched- ule). The traditional schedule variance and schedule performance index calculations give less accurate results near the project completion than the time based schedule variance and schedule performance index. These performance measures are critical for long-term projects success so adjustments can be made to improve project performance during the project execution and to minimize project delays and cost overruns. 68 5. EARNED VALUE MANAGEMENT ] 6 , 5 [ e l u d e h c s d e n r a e r o f s n o i t a l u c l a c d e s a b - e m T i : 2 . 5 e l b a T Period(Week)(AT)Earned Value Cumulative ValuesEarned Schedule Cumulative Time ValuesPV(BCWSAC(ACWP)EV(BCWP)SVcSPIcCVcCPIcNEV(AT)PV(N+1)PV(N)ESSV(AT)SPI(AT)1301615-150.5-10.94N/AN/AN/AN/A0.5-0.50.52754745-300.6-20.9614575301.33-0.670.673120109110-100.9211.012110120752.78-0.220.934200187195-50.9881.0431952001203.94-0.060.985280253265-150.95121.0542652802004.81-0.190.966330304320-100.97161.0553203302805.80-0.200.977355334345-100.97111.0363453553306.60-0.400.948385364370-150.9661.0273703853557.50-0.500.949415397400-150.9631.0184004153858.50-0.500.9410440425425-150.9701.094254404159.40-0.600.941144043944001.011.01044044010.0-1.000.915.5. SUMMARY 69 ] 6 , 5 [ s e u l a v d e s a b - e m i t d n a , s e u l a v e v i t a l u m u c , s e u l a v d o i r e P : 3 . 5 e l b a T Period(Week)(AT)Period ValuesCumulative ValuesCumulative Time-Based ValuesPV(BCWS)AC(ACWP)EV(BCWP)SVSPICVCPIPVc(BCWS)ACc(ACWP)EVc(BCWP)SPIcSVcCPIcCVcNEV(AT)PV(N)PV(N+1)ES(AT)SV(AT)SPI(AT)1301615-150.50-1.00.943016150.50-150.94-1.0NANANANA0.5-0.50.52453130-150.67-1.00.977547450.60-300.96-2.014530751.33-0.670.673456265+201.44+3.01.051201091100.92-101.01+1.02110751202.78-0.220934807885+51.06+7.01.092001871950.98-51.04+8.031951202003.94-0.060.985806670-100.88+4.01.062802532650.95-151.05+12.042652002804.81-0.190.966505155+51.10+4.01.083303043200.97-101.05+16.053202803305.8-0.20.97725302501.00-5.00.833553343450.97-101.03+11.063453303556.6-0.40.948303025-50.83-5.00.833853643700.96-151.02+6.073703553857.5-0.50.94930333001.00-3.00.914153974000.96-151.01+3.084003854158.5-0.50.941025282501.00-3.00.894404254250.97-151.000.094254154409.4-0.60.941101415+15N/A +1.01.074404394401.0001.00+1.01044044010-10.9170 5. EARNED VALUE MANAGEMENT Figure 5.2: Comparison of cost-based SPI.$/ and time-based SPI.t/ [5, 6]. 5.6 REFERENCES [1] AACE International, Skills and Knowledge of Cost Engineering, 5th ed., Chapters 14, 15, 2004. 59, 63 [2] Creese, R. C. and Adithan, M., Earned value management concepts, Strategic Cost Anal- ysis, New Academic Science Limited, Tunbridge Wells, Kent, UK, pp. 13–23, 2012. 59 [3] Lipke, W., A study of the normality of earned value management indicators, Measurable News, pp. 1–16, 2002. 59, 63 [4] Lipke, W., Schedule is diﬀerent, Measurable News, March 2003. 59, 63 [5] Fang, Y., Estimate at Completion for Construction Projects, Master’s Problem Report, Indus- trial and Management Systems Engineering, West Virginia University, 2008. 62, 63, 64, 68, 69, 70 [6] Creese, R. C. and Fang, Yi, Time-based schedule performance index, Cost Engineering, Vol. 53, No. 3, pp. 18–20, March 2010. Reprinted with Permission of AACE Interna- 1.11.00.90.80.70.60.50.4SPISPI ($) vs. SPI (t)Period (weeks)1234567891011PVACEVSPI (t)SPI ($)SPI ($)SPI (t)tional, 1265 Suncrest Towne Centre Drive, Morgantown, WV 26505 Phone (304) 296- 8444. http;//web.aacei.org 62, 63, 64, 68, 69, 70 5.7. EVALUATIVE QUESTIONS 71 5.7 EVALUATIVE QUESTIONS 1. Angel Construction Company was awarded a contract for $2,000,000 to build a cathedral with a budget of 200,000 hours (PV c). Management wants a progress update and the end of week six and the following data had a budget of 200,000 hours (PV c). Management wants a progress update at the end of week six and the following data was obtained. Planned Hours 80,000 Actual Hours Spent 75,000 Percent Completion (based on Earned Hours) 35% (a) How many hours has the project earned? (b) What is the cost variance (hrs)? (c) What is the schedule variance (hrs)? (d) What is the CPI? (e) What is the SPI? (f ) What is the estimated time for completion? (g) What is the estimated cost at completion? 2. Pumpkin Research and Development was awarded a contract for $25,000,000 to build a machine to use supersonic sound waves to remove body fat at a rate of 5 kg/hour. The budget is estimated to take 50,000 hours (PV c). Management wants a progress update and the end of week six and the following data was obtained. Planned Hours 7,000 Actual Hours Spent 8,000 Percent Completion (based on Earned Hours) 20% (a) How many hours has the project earned? (b) What is the cost variance (hrs)? (c) What is the schedule variance (hrs)? (d) What is the CPI? (e) What is the SPI? (f ) What is the estimated time for completion? (g) What is the estimated cost at completion? 72 5. EARNED VALUE MANAGEMENT 3. Use the data of PV; AC, and EV for time periods 6 and 7 in Table 5.1 and calculate the values for SV; SPI; CV, and CPI for the period and cumulative values to three decimals (for non-integer terms) and compare the values with those given in Table 5.1. 4. Calculate the earned value cumulative values of SV c; SPIc, CV c; CPIc, and earned sched- ule cumulative time values of ES; SV.AT/, and SPI.AT/ to three decimals (for non-integer terms) for weeks 6 and 7 and compare the values with those in Table 5.2 for weeks 6 and 7. 5. Change the PV values for Periods 6, 7, and 8 from 50, 25, 30 to 45, 35, 25 and note the diﬀerences in the SV; SPI; CV; CPI, SPIC , SV C , CPIC , CV C , ES, SV.AT/, and SPI.AT/ values from those in Table 5.3 for those three periods. 6. Use the data in Table 5.4 and calculate the period and cumulative values of SV; SPI, CV; CPI, and the time-based values of SV.t/ and SPI.t/ for all the periods for the project manager of the Tibet Construction Company. Plot the SPI.$/ and SPI.t/ values for the project over the ﬁve time periods. Discuss the diﬀerences between the SV c and SV.AT/ and the SPIc and SPI.AT/. 5.7. EVALUATIVE QUESTIONS 73 t c e j o r p n o i t c u r t s n o c l l i m d n i w a n i h C t s e W e h t n o y n a p m o C n o i t c u r t s n o C t e b i T e h t f o a t a d y l k e e W : 4 . 5 e l b a T Period(Week)(AT)Period ValuesCumulative ValuesCumulative Time-Based ValuesPV(BCWS)AC(ACWP)EV(BCWP)SVSPICVCPIPVc(BCWS)ACc(ACWP)EVc(BCWP)SVcSPIcCVcCPIcNPV(N)PV(N+1)EV(AT)ES(AT)SV(AT)SPI(AT)1402520240353534050454404040502520PART II Tools for Economic Evaluations C H A P T E R 6 77 Fundamental Deﬁnitions, Terms, and Concepts for Technical Economic Evaluations 6.1 INTRODUCTION The previous chapters have focused on macro-concepts such as ﬁnancial statements, proﬁts and cash ﬂows, the Purcell Diagram, breakeven analysis, ABC and time-based evaluations, estimat- ing ranges, and accuracies. Now the micro-concepts need to be presented in detail so that the expressions developed and methods applied using these items in the following chapters will be better understood. The primary focus of this chapter will be on interest, the various types of interest, inﬂation, constant and current currency, and exchange rates. This material is available in many references on engineering economy and much of this is based upon materials developed for short courses given in the past [1–3] and a book [4] published based on the materials in these short courses. 6.2 FUNDAMENTAL TERMS RELATED TO INTEREST CALCULATIONS 6.2.1 INTEREST AND INTEREST RATE There are many types of interest and two primary deﬁnitions of interest are the rate charged for the investment of capital and the return rate for the investment of capital. (1) The cost for the use of capital which is also referred to as the time value of money. (This is the view of the borrower who considers it as a cost or rate for the use of the capital borrowed.) (2) The monetary return or rate of return which is necessary to divert money into long-term investments. (This is the view of the lender who considers it as a rate of return on the investment.) 78 6. FUNDAMENTAL DEFINITIONS, TERMS, AND CONCEPTS The interest rate is the ratio of the interest amount accrued in the time period to the amount owed at the start of that period. There are two major types of interest commonly used and they are simple interest and compound interest. Simple Interest Simple interest is the interest rate that determines the interest amount only on the principal amount. Simple interest can be deﬁned as follows. (1) Interest charges are only charged on the principal at the start of the period and not on any additions or deletions made during the period. (2) Interest is calculated only on the investment at the end of the period, but it is not included as part of the investment for the following periods. The interest calculations for simple interest problems are presented by ﬁrst calculating the total amount of interest and then the total amount due at the end of the period which includes the principal. The total interest amount is: niP; I D (6.1) where I i n P total interest amount due interest rate per unit time period .frequently a year/ number of time periods principal amount or initial investment amount at the beginning of the period: D D D D An amount P will be invested for n time periods at an interest rate i and the amount due at the end of the n periods will be the Principal, .P /, and the total amount of Interest (I ). This is usually referred to as the Future Worth (F ) amount or Future worth, thus: F P I C D D P C niP D P .1 C i n/: (6.2) To illustrate the application of the formula, let P n i $500 D 3 D 10% or as a decimal; 0:10: D Thus, the amount paid at the end of three years is calculated as: 0:10 3/ (cid:2) C F 500.1 D D $500 Principal 500.1:3/ D $50 C Interest for D $650 $50 C Interest for First Year Second Year C $50 Interest for Third Year: 6.2. FUNDAMENTAL TERMS RELATED TO INTEREST CALCULATIONS 79 Note that the principal does not change over the n periods and no interest is earned on the accumulated interest. Compound Interest Compound interest is the interest which is most commonly applied. Compound interest is in- terest on the principal amount and the interest on the previous amounts of interest earned. Two deﬁnitions [4] of compound interest are as follows. (1) The type of interest that is periodically added to the amount of principal, investment, or loan so that the subsequent interest rate is based on the cumulative amount of principal plus total interest. (2) The type of interest that is charged on any previous interest earned in any time period as well as on the principal. When considering compound interest calculations, there are two approaches of calculating interest. (1) Discrete Compound Interest Rate is the interest rate is applied at the end of each time period and amount determined is considered only in the following time periods. This is the most common form of compound interest rate application. (2) Continuous Compound Interest Rate is the interest rate is applied continuously during each time period. This is less commonly applied today, but with businesses being open 24-7, it may be applied more in the future. It is often applied on certiﬁcates of deposit. An example of each approach will be presented, starting with the discrete compound rate applications. The following table will illustrate the approach for determining the Future Amount (F ) at the end of n periods starting with the initial Principal Amount (P ). Time Initial Amount Period (Beginning of Period) 1 2 3 P P .1 P .1 4 P .1 C C i/ i/2 i/3 C and in general for any value of n n i/.n P .1 1/ (cid:0) C Interest Amount iP iP .1 iP .1 iP .1 iP .1 C C C C i/ i/2 i/3 i/.n (cid:0) 1/ C C C C C C D D D D D D Total Amount (End of Period) P .1 P .1 P .1 P .1 P .1 C C C C C i/ i/2 i/3 i/4 i/n F D Thus, the expression for discrete compound interest would be: P .1 F D C i/n: (6.3) 80 6. FUNDAMENTAL DEFINITIONS, TERMS, AND CONCEPTS Using the data of the previous simple interest example and now applying the discrete compounding interest formula, let: P n i $500 D 3 D 10% or as a decimal; 0:10 D Time Initial Amount Interest Total Amount Period (Beginning of Period) Amount (End of Period) 1 2 3 500 550 605 50 55 550 605 60.50 665.50. This can be determined by Equation (6.3) as: P .1 F D C i/n D 500.1 C 0:10/3 D $665:50 Note that the total amount is $665.50 for discrete compounding vs. $650. for simple interest. The diﬀerence in total interest or return is $15.50 and which is approximately a 2% diﬀerence over the 3-year period. Continuous compounding is compounding throughout the period and not only at the end of the period. The expression is obtained by letting the number of compounding periods go to inﬁnity and thus the interest is considered as the eﬀective interest over the entire period and r is the nominal interest per year: ieff lim m !1 D (cid:140).1 C r=m/m 1/(cid:141) (cid:0) lim m !1 D h(cid:16)1 C r 1=.m=r/m=r (cid:17) 1i er 1: (cid:0) D (cid:0) (6.4) Thus, for n periods [3] and r 10% interest D P .er 1/n 1 (cid:0) C D D P .ern/ (6.5) n 1(cid:1) 3(cid:1) P (cid:0)ieff C 500 (cid:0)e0:1 (cid:2) $674:93: F F F D D D Equation (6.5) is also the form used for calculating the future worth for continuous com- pounding. Note that over the 3-year period, continuous compounding results in $24.93 (or nearly 4%) more than simple compounding and earns $9.93 more than discrete compounding. The higher the interest rate, the greater the diﬀerences between the amounts of interest calcu- lated by the methods as the calculations are not linear. Also, the more time periods, the greater the diﬀerences between the calculated values. 6.3. ACTUAL, COMPOUND, NOMINAL, AND EFFECTIVE ANNUAL INTEREST RATES 81 6.3 ACTUAL, COMPOUND, NOMINAL, AND EFFECTIVE ANNUAL INTEREST RATES These four diﬀerent interest rates and the diﬀerences between them will be discussed and illus- trations of the diﬀerences will be presented. The actual interest rate (i) represents the interest rate per compounding period. It is the most common of the interest rates used in engineering calculations. The actual interest rates can be expressed in diﬀerent periods, such as: 12% per year —interest would be compounded once per year 6% semi-annually —interest would be compounded 2 times per year 3% per quarter —interest would be compounded 4 times per year 1% per month —interest would be compounded 12 times per year 0.03288% per day —interest would be compounded 365 times per year Nominal interest rate (r) represents the interest rate per year as obtained by multiplying the interest rate per period by the number of compounding periods per year. It is commonly known as the Annual Percentage Rate (APR) which is required for notiﬁcations on some loans. Since the other methods involve compounding more frequently, annual compounding results in the smallest value of the compound interest rates and simple interest is the lowest of all compounding methods. Compound interest rate can be either discrete compounding or continuous compounding. Continuous compounding tends to give the largest amounts of interest. If the compounding period is one year, the continuous compounding rate is known as the annual eﬀective interest rate. If the compounding rate is one year, the actual interest, nominal interest, and discrete compound interest will be the same as there is only one compounding period. Let us consider a comparison of the interest rates for an interest rate of 3% per quarter for four periods. The values would be Actual interest Nominal interest Compound (Discrete) Compound (Continuous) i D 3% 3%/quarter for each quarter 12% 0:1200/yr r 4 1(cid:3) ieff .discrete/ D (cid:0) 100 ieff .continuous/ D (cid:2).1 D (cid:2) (cid:2) D :03/4 C (cid:140)er 1(cid:141) (cid:0) (cid:2)e0:12 (cid:2) 1(cid:3) D 0:03/quarter D 100 12:55% D D 0:1255/yr D The eﬀective interest rate depends upon which of the compounding methods is used and is based upon a one-year period. Now we shall calculate the amounts obtained after 3% per quarter on an initial amount of $1,000 compounded for three years. This results in 12 compounding pe- riods. The calculations that are used are simple interest, compound (discrete) interest, and com- pound (continuous) interest. The actual interest rate is used in the calculation of the compound D D (cid:0) (cid:2) 100 12:75% 0:1275/yr. 82 6. FUNDAMENTAL DEFINITIONS, TERMS, AND CONCEPTS (discrete) multi-period calculations and the nominal period interest used in the calculation of the compound (continuous) multi-period calculations. From Equation (6.2) for simple interest: F P .1 i C (cid:2) n/ D D 1;000.1 12 (cid:2) C 0:03/ D $1;360:00 .Interest total is $360:00/: Using Equation (6.3) for compound (discrete) interest calculations: P .1 F D C i/n D 1;000.1 C 0:03/12 D $1; 425:76: (Interest total is $425.76 and more than 18% greater than simple interest.) Using Equation (6.5) for compound (continuous) interest calculations: D (Interest total is $433.33 which is more than 20% greater than simple interest.) D D F P .ern/ 1;000 (cid:0)e:0:03 12(cid:1) (cid:2) $1;433:33: It is strongly advised to use the actual compounding period (a quarter or 3 months) and the corresponding interest (3%) as the annual interest rate is valid only for annual compounding periods. When other continuous expressions are used which have other factors such as .er 1/ the results would not be correct. (cid:0) The diﬀerence in the values of the two compound interest methods, discrete and con- tinuous compounding, is small compared to their diﬀerences with the simple interest method. The more frequently the compounding, the smaller the diﬀerence between the two compound- ing (discrete and continuous) methods, but the diﬀerences increase as the interest rate increases and/or as the total investment time increases. 6.4 FACTORS IN DETERMINING INTEREST RATES The interest rate considered as a basis for engineering and project calculations is the market interest rate. One interest rate is the prime interest rate, which is available to banks has been as low as 0.25% and is usually between 1% and 2% during normal times. The current rate by banks for deposits is between 0.5–2.0% but has been 3–5% in better economic times. The interest rate for automobile purchases is in the 3–6% range and had been as high as 8–10% range previously. When companies are considering returns on their investments, they typically want 10–20% return on average as some projects may make 30–40% return whereas other projects will lose money. Some of the major factors in considering an interest rate or rate of return are: 1. Administrative Expenses (1–5%); 2. Pure Gain or Proﬁt (3–20%); 3. Risk of Inﬂation (1–200%); and 4. Risk of Loss (1–10%). 6.5. INFLATION-FREE INTEREST RATES, CONSTANT CURRENCY, AND ACTUAL CURRENCY 83 The risk of inﬂation is greater for investments when ﬁnancial strife occurs in countries and prices rise rapidly. Construction projects can have rising labor and material prices and the total costs can go up rapidly. A major problem of inﬂation is that it is hard to predict long term and this has resulted in the use of the inﬂation-free interest rate. 6.5 INFLATION-FREE INTEREST RATES, CONSTANT CURRENCY, AND ACTUAL CURRENCY The interest rates that have been considered have inﬂation as a component in the interest rate. The currency considered is the amount associated with a cash ﬂow at the point of time at which it occurs and this is referred to as actual currency or current currency. The term currency has been used as dollars in the previous examples, but it could be the currency of any country. Constant currency, or dollars, are dollars expressed in terms of the same purchasing power relative to a speciﬁc point in time, usually a base year. They represent the hypothetical purchas- ing power of future receipts and disbursements in terms of the purchasing power at the base year. Constant dollars are referred to as inﬂation free dollars and are often used on construction projects and government projects where the projects have a long life and estimating the inﬂation rates over a long period of time is highly speculative. The relationship between constant and actual currency is: Constant Currency .$/ D (cid:140)Actual Currency at time n .$/(cid:141)=.1 f /n; C (6.6) where f D inﬂation rate (as a decimal) at time period n years in the future. Constant currency is referenced to a base year, which is normally considered time zero or the beginning of the investment. Other names are constant dollars, real currency, inﬂation-free currency, and today’s currency. Constant currency is typically used in construction or govern- ment projects having a project life 10 years or more and involving life cycle costs where the maintenance, repair, and rehabilitation values are diﬃcult to predict that far in the future. For example, the life of a highway bridge can be 100 years and to predict the costs of a bridge deck replacement 20, 40, 60, and 80 years in the future is extremely diﬃcult with any degree of ac- curacy, but the cost of a deck replacement today could be predicted with great accuracy. Thus, using constant currency, the replacement costs would be considered as the same as that of today. The interest rate used for discounting would not include the eﬀects of inﬂation. Although Equation (6.6) assumes the inﬂation will be constant over the n years of the investment, it typically will be changing and either an average value will be assumed or the inﬂation must be adjusted each year and would make the calculations more complex. Actual currency or actual dollars are used in most applications, especially when the project investment life is under 20 years. Other names of actual dollars are nominal currency or current currency. The interest rate used is the eﬀective or market interest which includes the eﬀects of 84 6. FUNDAMENTAL DEFINITIONS, TERMS, AND CONCEPTS inﬂation. For most concerns in manufacturing, commercial, and project with short durations, actual currency or actual dollars are used. The inﬂation-free interest rate, i if , can be determined from the market interest rate and the inﬂation rate by: .1 C i if D where i/ .1 D C or directly by (cid:140).1 i/=.1 C f / (cid:0)1 i if (cid:1) C f /(cid:141) 1; (cid:0) (6.7) C market interest rate (decimal) inﬂation free interest rate (decimal) inﬂation rate (decimal). D i i if f D D For example, if the market interest rate is 7.1% and the inﬂation rate was 2%, what would the inﬂation free interest rate be? Using Equation (6.7), one obtains: i if (cid:140).1 C D 0:071/=.1 0:02/ 1(cid:141) (cid:0) D (cid:140)1:05 1(cid:141) (cid:0) D C 0:05 or 5%: 6.6 CURRENCY EXCHANGE CALCULATIONS The world is an international market and global projects must consider exchange rates involv- ing diﬀerent currencies. A project may be estimated in one currency, but performed in another country with a diﬀerent currency. The ﬂuctuations in currency rates can be large due to diﬀerent inﬂation rates in the two countries. The exchange rate is the amount of one countries currency that would purchase one unit of another country’s currency. For example, if in the year 2015 when one U.S. dollar would purchase approximately 0.80 Euros, a U.S. investor invested $1,000 in Euros. In 2020, the investor decided to convert the Euros back to U.S. dollars and the exchange rate is one U.S. dollar to purchase 0.70 Euros. Consider Currency 1 as the original currency and currency rate in terms of amount of Currency 2 per unit of Currency 1. What did the investor receive? Currency 1 (current value) D Currency 1 (original value) (cid:140)Currency Rate 2 (original)/Currency Rate2 (now)(cid:141): (6.8) (cid:2) Thus, Currency (now) $1;000 (cid:2) D (cid:140).0:8 Euro=$1/=.0:7 Euro=$1(cid:141) $1;000(cid:140)0:8=0:7(cid:141) $1;142:80: D D If in the year 2015 one U.S. dollar purchased approximately 15 Pesos, a U.S. investor purchased $1,500 worth of Pesos. In 2020, the investor decided to convert the Pesos back to U.S. dollars and the exchange rate was 1 U.S. dollar purchased 25 Pesos. What did the investor receive? Currency (now) $1;500 (cid:2) D (cid:140).15 pesos=$1/=.25 pesos=$1/(cid:141) $1; 500(cid:140)15=25(cid:141) $900: D D Thus, the eﬀects of currency exchange rates can be rather large and must be considered in international projects. To reduce the problems, one usually does the cost and budget analysis in currency with the lowest inﬂation rate of the country where the project occurs or in the country where the project is managed and funded. 6.7. SUMMARY 85 6.7 SUMMARY Several types of interest rates have been presented. The interest rate most commonly applied is the market interest rate, but for long-term projects the inﬂation-free interest rate is used. The compound discrete interest rate is most frequently applied in calculations and is the eﬀec- tive interest most considered. However, the actual interest and the nominal interest rates are the basis for determining the eﬀective interest rates for discrete compounding and continuous compounding. The actual dollars and market interest rate are used for most short-term projects whereas the constant currency and inﬂation-free interest rate are used for long-term projects. Currency evaluations are important when the project is being funded in one country and being constructed in another country as the inﬂation rates can be quite diﬀerent. 6.8 REFERENCES [1] Cresse, Robert C. and Kumar, Pradeep, Engineering Economy Basics, 1.5 CEU, p 147, May 18–19, 2000. 77 [2] Cresse, Robert C. and Kumar, Pradeep, Intermediate Engineering Economics, 1.5 CEU, p 147, June 28–29, 2001. [3] Creese, Robert C., Engineering economics for engineers, estimators, managers and project anagers, AACE International Annual Meeting, 1.6 CEU, p. 94, June 28–29, 2008. 77, 80 [4] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, p. 187, 2012. 77, 79 6.9 EVALUATIVE QUESTIONS 1. What is the value of $100,000 invested at 10% simple interest per year for 10 years? 2. What is the value of $100,000 invested at 10% annual discrete compound interest rate per year for 10 years? 3. What is the value of $100,000 invested at 10% annual continuous compound interest per year for 10 years? 86 6. FUNDAMENTAL DEFINITIONS, TERMS, AND CONCEPTS 4. The interest rate is 2% per month and the time period is 1 year. (a) What is the nominal interest rate? (b) What is the discrete eﬀective interest rate? (c) What is the continuous eﬀective interest rate? 5. A person invests $50,000 at 9% simple interest for 4 years. At the end of the 4 years, the entire amount (principal and interest) is invested at 11% discrete compounded annually for 10 years. What is the amount of the investment after 14 years? 6. The inﬂation rate is 4% and the inﬂation free interest rate is 8%, what is the market interest rate? 7. The market interest rate is 20% and the inﬂation rate is 5%, what is the inﬂation free interest rate? 8. If continuous compound interest is used and the nominal rate is 15%, what is the equivalent discrete annual eﬀective interest rate? 9. If the discrete annual eﬀective interest rate is 20%, what is the equivalent nominal rate for the continuous compound interest. 10. If the currency in the country where the project is being constructed (Country C) has an inﬂation rate of 10% and the country where the project is being managed and funded (Country F) has an inﬂation rate 15%, what currency should the funds of the project be kept and why? 11. The $10,000,000 project in Country B is being funded by country A. The exchange rate of Country A is 2 currency units per Country B currency unit. It is projected that the exchange rate for the last half of the project ($5,000,000) will drop and the exchange rate of Country A will drop to 1.5 currency units per Country B currency unit. Which country should the project funded currency be located and why? 12. Canada had an exchange rate of 0.95 Canadian dollars per U.S. dollar in 2015 and a U.S. investor spent $10,000 U.S. dollars to purchase Canadian dollars. How many Canadian dollars did he receive? In 2020 he exchanged those Canadian Dollars for U.S. dollars at the exchange rate of 0.70 Canadian dollars per U.S. dollar. How many U.S. dollars did he receive in 2020? C H A P T E R 7 87 Basic Mathematical Relationships for Economic Calculations INTRODUCTION 7.1 The following chapters will derive and illustrate the fundamental relationships used for eco- nomic evaluations. The derivation of the basic economic formulas are based upon a few algebraic relationships and applying these relationships will make the understanding of the economic for- mulas easier. The mathematics involved in the derivations of the formulas in economics are not complex and some basic references are listed [1, 2] The following sections will focus on the ex- pressions for the sums of numbers, the arithmetical progression, the geometric progression, and the inﬁnite limit expression. SUMS OF NUMBERS 7.2 In evaluating projects one typically examines all the revenues in the future time periods and evaluates them at the beginning of the project to determine the expected cost. Thus, if one wants to determine the total amount or sum S of an amount z each period for n periods, the total would be: S.n/ D nz: zi D (7.1) n X 1 i D Let us suppose that n 5 and z D S.5/ D D D 6, then the sum is 6 5 6 6 C (cid:2) C D 6 6 C 30: 6 C Now let us assume that instead of the period amount remaining constant that it increases by the same amount each period (as in a uniform gradient); that is for the second period it is 2z, for the third period it is 3z, and for the nth period it is nz. This is the basic sum of numbers expression. The total amount S for the n periods would be: S.n/ D n X 1 i D nz D zn.n C 1/=2: (7.2) 88 7. BASIC MATHEMATICAL RELATIONSHIPS FOR ECONOMIC CALCULATIONS Let us suppose the n 5 and z 6 which implies the amount for the second period, 12, and the total amount S for the 5 periods would be: D D S.2/ 6 2 (cid:2) D D S.5/ 6 6 C (cid:2) D D 12 5 (cid:2) C .5 18 C 90 24 C 1/=2 C D 30 90: D The arithmetical progression is a modiﬁcation of the basic sum of numbers where the increment y is diﬀerent than the base amount z. The increment y starts in the second period. The total amount S for the n periods would be: S.n/ D n X 1 i z C n X 2 i D 5, z D 6, and y D nz y D C n.n (cid:0) 1/y=2: (7.3) 3 and the total amount S for the n periods D Let us suppose that n would be: D S.5/ 6 5 9 6 C (cid:2) C C D D 5 12 15 18 60 C 4 C 3=2 (cid:2) (cid:2) D D 30 30 C D 60: 7.3 GEOMETRIC PROGRESSION The expression used in the derivation of discrete interest economic expressions is the geometric progression, commonly called the geometric series, when dealing with discrete interest relation- ships. The discrete relationships are those where there is a discrete payment at a discrete interest rate at a speciﬁc time. This discrete interest rate implies that it is compounded at a ﬁxed time period, whereas a continuous interest implies that it is compounded continuously over time. The case of discrete payments and discrete interest rates is the most common of the economic problems. The basic mathematical relationship for discrete interest problems is the geometric series and for continuous interest problems the inﬁnite limits expression is used. The geometric series expression is: S a C D aR C aR2 aR3 aR4 C C C (cid:1) (cid:1) (cid:1) C aR.n 1/ (cid:0) a (cid:140).Rn D 1/ =.R 1/(cid:141) ; (cid:0) (cid:0) (7.4) where S a R n D D D D sum of the series of n terms constant which occurs in all terms ratio between terms number of terms in the sum (including the initial term without the ratio). Consider the following example where one takes the number 4.a 3 2/ for 3 additional periods .n 4/ and determine the sum. That is: D 4/ and doubles it .R D S.5/ .4 4 C (cid:2) 2/ C D (cid:0)4 (cid:2) C 23(cid:1) 4 8 C C D 16 C 32 D 60: 1 C 22(cid:1) D D (cid:0)4 (cid:2) If one uses the geometric series expression, there are four terms (the initial term and the 3 additional periods), so 7.4. INFINITE LIMIT 89 n R a S.4/ 4 2 4 4 D D D D (cid:2) and thus (cid:2)24 1(cid:3) =(cid:140)2 (cid:0) 1(cid:141) 4 (cid:2) D (cid:0) (cid:140)16 (cid:0) 1(cid:141)=(cid:140)2 1(cid:141) 4 (cid:2) D (cid:0) (cid:140)15(cid:141)=(cid:140)1(cid:141) 60: D This becomes very useful when n is large. In most interest calculations, the ratio is R D i/ which is the periodic compounding amount for compound discrete interest calculations. .1 This will be used in the derivation of the discrete compounding factors in the various economic expressions. C Let us consider the investment of $2,000 per year at an annual interest rate of 1% for 5 years. Thus, a R n S.n/ S.5/ D D D D D D D $2;000 1 i C D 1:01 5 a (cid:140).Rn 1/ =.R (cid:0) $2;000 (cid:2).1:01/5 2;000 (cid:0) 5:101005 (cid:0) (cid:2) $10;202:01: 1/(cid:141) 1(cid:3) =.1:01 1/ (cid:0) D 2;000(cid:140)1:05101 1(cid:141)=(cid:140)1:01 1(cid:141) (cid:0) (cid:0) Thus, the total interest over the 5-year period is $202.01 and the eﬀect of compounding is small, only $2.01 If the interest rate was 3% .R 1:03/, D S.n/ S.5/ D D a (cid:140).Rn 1/ =.R (cid:0) $2;000 (cid:2).1:03/5 (cid:0) (cid:0) 1/(cid:141) 1(cid:3) =.1:03 1/ (cid:0) D 2;000 (cid:2) 5:309136 D $10;618:27: The total interest over the 5-year period is $618.27 and the eﬀect of compounding is $18.27, which is much larger than the $2.01 or even more than 3 times the $2.01 which is $6.03. The higher the interest rate, the greater the eﬀect of compounding and the greater the time period also increases the compounding eﬀect. 7.4 INFINITE LIMIT The inﬁnite limit is used for continuous interest problems, that is when the interest is com- pounded continuously over the periods rather at the end of the discrete time periods. The con- tinuous compounding is also used when continuous cash ﬂows are considered instead of discrete 90 7. BASIC MATHEMATICAL RELATIONSHIPS FOR ECONOMIC CALCULATIONS cash ﬂows. However, continuous cash ﬂow analysis is rarely used and will not be presented in detail. The continuous interest expression is based on: (cid:140)1 Lim k !1 C 1=k(cid:141)k e D D 2:718281834: This can be illustrated by taking values of k such as 1, 2, 3, 100, 1,000, and 10,000 and note that the value approaches the limit of e, which is 2.718 to 3 decimals: Limit (cid:140)1 D C 1=1(cid:141); (cid:20)1 2 (cid:21) 1 2 C ; (cid:140)1 C 1=3(cid:141)3; : : : (cid:140)1 C 1=100(cid:141)100; : : : (cid:140)1 Limit D 2; 2:25; 2:37; 2:704; 1=1000(cid:141)1000; : : : C 1=10000(cid:141)10000 : : : (cid:140)1 C 2:71692; 2:71815: The inﬁnite limit was used in the derivation of continuous compound interest by letting the number of discrete compounding periods go to inﬁnity; that was: ieff ieff D D where r=m/m (cid:140).1 C lim m !1 er (cid:0) 1; 1(cid:141) (cid:0) D lim m !1 h 1 f C 1=.m=r/ r m=r i g 1 (cid:0) D er 1 (cid:0) (7.5) interest rate (eﬀective interest rate on an annual basis) ieff r D D nominal interest rate. One can also express the relationship to determine the nominal interest rate equivalent to the annual eﬀective interest rate as: er (cid:0)ieff 1(cid:1) C D (7.6) or C Equation (7.5) is frequently used to convert discrete compounding factors into continuous compounding factors and Equations (7.6) and (7.7) to determine annual nominal interest r from the continuously compounded interest rate. D r ln (cid:0)ieff 1(cid:1) : (7.7) 7.5 SUMMARY The basic mathematical expressions for sums of numbers, including the basic sum of numbers expression, the arithmetic progression, the geometric progression, and the inﬁnite limit. The ge- ometric series expression will be used in the development of the discrete interest compounding expressions and the inﬁnite limit will be used to convert the discrete interest formulas to contin- uous interest formulas. These expressions are relatively simple and are the basis of the economic expressions presented in the following chapters. 7.6. REFERENCES 91 7.6 REFERENCES [1] Hodgman, Charles D., Ed., Mathematical Tables from Handbook of Chemistry and Physics, 10th ed., Chemical Rubber Publishing Co., Cleveland, OH, pp. 294–296, 1954. 87 [2] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 36–38, 2012. 87 7.7 EVALUATIVE QUESTIONS 1. What is the sum of the numbers from 1 to 10? 2. What is the sum of the numbers from 40 to 50? 3. A gradient of 3 is to be summed over 10 periods and determine the total sum. 4. A cost of $40 per period is for wages. The cost for materials is $5 per period and increases at the rate of $1 per period. What is the total wage cost for 10 periods? What is the total material cost for 10 periods? 5. John earns $5 and the amount is doubled each period for the next 6 periods, what is the sum John will have in his account. 6. Mary earns $10 and the amount is tripled each period for the next 4 periods, what is the sum Mary will have at the end of these 5 periods? 7. Francisco saves $100 per month and his interest rate is 1/2% compounded monthly. What amount will Francisco have at the end of the year? 8. Juanita has invested 10,000 Pesos in a high risk bond which pays 1% compounded monthly which is reinvested automatically. What is the expected value of the bond and total interest at the end of the year? 9. An investment of $2,000 is made and the interest rate is 0.5% per month. At the end of a year, determine the total amount available if: (a) simple interest is used. (b) discrete compound interest is used. (c) continuous compound interest is used. 92 7. BASIC MATHEMATICAL RELATIONSHIPS FOR ECONOMIC CALCULATIONS Also determine (d) the nominal interest rate. (e) the eﬀective discrete compound interest rate. (f ) the eﬀective continuous compound interest rate. 10. An investment of $2,000 is made and the interest rate is 1.5% per month. At the end of a year, determine the total amount available if: (a) simple interest is used. (b) discrete compound interest is used. (c) continuous compound interest is used. Also determine (d) the nominal interest rate. (e) the eﬀective discrete compound interest rate. (f ) the eﬀective continuous compound interest rate. 11. An investment of $2,000 is made and the interest rate is 1.5% per quarter. At the end of a year, determine the total amount available if: (a) simple interest is used. (b) discrete compound interest is used. (c) continuous compound interest is used. Also determine (d) the nominal interest rate. (e) the eﬀective discrete compound interest rate. (f ) the eﬀective continuous compound interest rate. 12. An investment of $2,000 is made and the interest rate is 1.5% per quarter. At the end of ﬁve years, determine the total amount available if: (a) simple interest is used. (b) discrete compound interest is used. (c) continuous compound interest is used. (d) the nominal interest rate. (e) the eﬀective discrete compound interest rate. (f ) the eﬀective continuous compound interest rate. C H A P T E R 8 93 Basic Economic Factors and Equations 8.1 INTRODUCTION There are several expressions utilized in economics to determine the worth of various payments types over time for the evaluation of projects. These are evaluated as Present Worth values, which is the value of the payments at the start or time zero, or Future Worth values, which is the value of the payments at a speciﬁc future time, typically at the end of the project life. The payments can be a single payment or a uniform series of payments. The expressions are generally divided into two categories: the basic expressions and the gradient expressions. The basic expressions will be examined in this chapter and the more complex gradient expressions will be examined in the next chapter. The primary reference for this section is from a previous short course and a previous book [1], but the materials can be found in numerous standard engineering economics textbooks [2, 3] giving slightly diﬀerent approaches and additional problems. Some of the expressions developed is this and the following chapters are available using Excel [4, 5], but one should ﬁrst use and program the expressions before relying on packaged software expressions. The two categories of the basic economic expressions are classiﬁed by the type of payments—the single payment expressions and the uniform payment expressions. There are two single payment expressions and four uniform payment expressions and all six will be presented in this chapter. The expressions will be ﬁrst developed for the discrete compound interest rate and discrete payment case. The developed expressions will then be modiﬁed for the continu- ous compound interest rate with discrete payment case. The highly advanced case of continuous compound interest rate and continuous payments will not be presented as it is currently rarely applied. 8.2 SINGLE PAYMENT DISCRETE INTEREST FACTORS The two single payment cases developed with discrete interest and discrete payments are the future worth expression and the present worth expression. The future worth expression will be presented ﬁrst as it is easier to illustrate. 94 8. BASIC ECONOMIC FACTORS AND EQUATIONS 8.2.1 DISCRETE INTEREST FUTURE WORTH FACTOR (F=P; i; n) The future worth expression converts a present amount to a future worth for a given interest rate and given number of compounding periods. The notation used will be: F P i I n future worth (total amount after n compounding periods) present worth (total amount at time zero, the beginning of the study period) interest rate per compounding period (discrete compound interest) interest earned in compounding period number of compounding periods cash ﬂow is occurring. D D D D D " D A graph indicating where the present worth and future worth are with respect to time D (cid:2) P i appears in Figure 8.1. Figure 8.1: Present and future worth with respect to time. Table 8.1 illustrates the calculations starting with the investment P (Present Worth) at the start of the time period and Future Worth F at the end of the time period. This ﬁgure is similar to that in Chapter 6 to obtain Equation (6.3). In most instances the future worth is greater than the present worth. Thus, from Table 8.1 it can be seen that the value at the end, the Future Worth Equation is: where F P i n F P .1 (cid:2) C D i/n (8.1) future worth (total amount after n compounding periods) present worth (total amount at time zero, the beginning of the study period) interest rate per compounding period (discrete compound interest) number of compounding periods. D D D D The conversion factor to convert the present worth to the future worth is called the single payment future worth discrete compound amount factor is designated as (F=P; i; n), is stated as F given P; i; n, and is equal to .1 i/n. The discrete future worth factor is: C .F=P; i; n/ .1 C D i/n: (8.2) 0 1 2 3 4 5 6 …… (n - 2) (n - 1) nPFTime Table 8.1: Payment illustration for future worth expression derivation 8.2. SINGLE PAYMENT DISCRETE INTEREST FACTORS 95 8.2.2 DISCRETE INTEREST FUTURE WORTH EXAMPLE If a single payment of $100,000 is invested at 15% interest compounded annually, the compound amount at the end of the 4th year would be: F D $10;000.1 0:15/4 C .F=P; i 15%; n 4/ D D D D .1 $10;000 (cid:2) 1:74901 D $17; 490 i/n C .1 C D 0:15/4 D 1:74901 and so F P D (cid:2) .F=P; i 15; n 4/ D D D $10;000 (cid:2) 1:74901 D $17;490: The .F=P; i; n/ factor is given for the formulas in Table 8.2 and the Appendix and one should use the formulas to calculate the values. Students should learn to calculate and program the formulas rather than use tables as many interest rates are not available in the tables. The total interest earned, I (Total), would be the diﬀerence between F and P and would be: I.Total/ F P (cid:0) D D $17;490 (cid:0) $10;000 D $7;490: 8.2.3 DISCRETE INTEREST PRESENT WORTH FACTOR .P =F; i; n/ The present worth expression is the inverse of the future worth expression; that is, the expression is: P D F .1 C n i/(cid:0) F=.1 i/n; C D (8.3) where P D present worth (initial amount at time zero) Time(End of Period)Present Worth (P) at Start of PeriodInterest (I) Earned During PeriodFuture Worth is the Principal + Interest Total at End of Period1P+IP=P × (1 + i)2P × (1 + i)+IP × (1 + i) =P × (1 + i)23P × (1 + i)2+IP × (1 + i)2=P × (1 + i)34P × (1 + i)3+IP × (1 + i)3=P × (1 + i)4…=nP × (1 + i)n-1+IP × (1 + i)n-1=P × (1 + i)n = F96 8. BASIC ECONOMIC FACTORS AND EQUATIONS F i n future worth (total amount after n time periods) discrete interest rate per compounding period number of compounding periods. D D D The conversion factor to convert the future worth to the present worth is called the single payment present worth compound amount factor, is designated as .P =F; i; n/, is stated as P given F , i; n, and is equal to .1 i/n. That is: n or 1=.1 i/(cid:0) C C .P =F; i; n/ .1 C D i/(cid:0) n: (8.4) 8.2.4 DISCRETE PRESENT WORTH EXAMPLE If $10,000 is desired at the end of 4 years and the discrete interest rate is 15% compounded annually, what amount would one need to be deposited initially? P D F=.1 C i/n; P D $10;000=.1 0:15/4 C D $10;000=1:74901 $5;718 D .P =F; i; n/ 1.1 C D n i/(cid:0) D 1=.1 C 0:15/4 D 0:57175 therefore and so P D $10;000 (cid:2) .P =F; i 15; n 4/ D D D $10;000 (cid:2) 0:57175 D $5;717:5 D $5;178: The .P =F; i; n/ factor is listed in Table 8.2 at the end of this chapter and in the Appendix. The present worth analysis is often referred to as “discounting,” that is bringing future values back to the present value. As the sample indicates, the future worth of $10,000 at the end of four years in the future is worth only $5,178 when discounted by 15% per year to the current year. 8.3 UNIFORM SERIES PAYMENTS DISCRETE INTEREST FACTORS The four uniform payment factors with discrete interest payments to be developed are the uni- form series future worth factor .F=A; i; n/, the sinking fund factor .A=F; i; n/, the uniform series present worth factor .P =A; i; n/, and the capital recovery factor .A=P; i; n/. All of these factors involve the payment of an amount A at the end of every period. In the development of the var- ious economic expressions, the assumption is made that the discrete payment is at the end of the payment period, not at the beginning of the payment period. A simple modiﬁcation can be made to convert end of period payments to beginning of the period payments. 8.3. UNIFORM SERIES PAYMENTS DISCRETE INTEREST FACTORS 97 8.3.1 UNIFORM SERIES DISCRETE INTEREST FUTURE WORTH FACTOR .F=A; i; n/ (Also called Discrete Compound Amount Factor.) Payments of the amount A are made at the end of the period for n periods (but that does not include time 0) to determine a total amount F at the end of the last period. The discrete interest rate i will be compounded at the end of each period and the payment sum plus the interest accumulated will result in a future worth of F at the end of the n periods. This includes a period payment A in the ﬁnal period to complete the future worth value of F as the system is based upon end-of-period payments. The geometric series expression is used to develop the formulas. A graphical representation of the payments and future worth appears in Figure 8.2. Figure 8.2: A graphical representation of the payments and future worth. Where A payment each period n, F period, and n future worth (amount at time n), i number of compounding periods. uniform interest rate per compounding D D D D The expression can be derived using the geometric series expression by the payments start- ing from the last period back to the ﬁrst period: A .end of last period/ A.1 i/ A.1 C i/2 C : : : C .1 C C C C i/2 C i/.n 1/(cid:17) (cid:0) A (cid:16)1 .1 i/ C C C .1 A .geometric series/: C (cid:1) (cid:1) (cid:1) C A.1 C i/.n (cid:0) 1/ .end of ﬁrst period/ F D D D .1 D A .r n A (cid:140).1 If one lets r F F D D and thus i/, one has C 1/ =.r i/n (cid:0) (cid:0) C 1/ D (cid:0) 1(cid:141) =(cid:140)i(cid:141) A (cid:140).1 i/n (cid:0) C 1(cid:141) =(cid:140).1 1(cid:141) i/ (cid:0) C D A (cid:140).1 i/n (cid:0) C 1(cid:141) =(cid:140)i(cid:141) A .F=A; i; n/ F D A (cid:140).1 i/n (cid:0) C D 1(cid:141) =(cid:140)i(cid:141) .F=A; i; n/ (cid:140).1 C D i/n (cid:0) 1(cid:141) =(cid:140)i(cid:141): (8.5) (8.6) 0 1 2 3 4 nAAAAAFTime ……98 8. BASIC ECONOMIC FACTORS AND EQUATIONS 8.3.2 UNIFORM SERIES DISCRETE INTEREST FUTURE WORTH EXAMPLE What is the future worth of $1,000 deposited at the end of the year each year for 10 years when the interest is 10%? F D $1;000 (cid:2) $15;937: 0:10/10 (cid:2).1 C 1(cid:3) =(cid:140)0:10(cid:141) $1;000 (cid:2) D (cid:0) (cid:140)1:5937=0:10(cid:141) $1; 000 (cid:2) D (cid:140)15:937(cid:141) D The total amount of interest earned over the 10 years would be: I .total/ D D F n A (cid:0) 15;937 (cid:2) 10 1;000 $5;937: (cid:0) (cid:2) 10%; n D 10(cid:141) The compound amount factor (cid:140)F=A; i 15:937 may be listed in the ta- bles, but if one had an interest rate of 9.8% it would not be available and thus one should be able to use the compound amount factor expression and thus: D D D (cid:140)F=A; i 9:8%; n 10(cid:141) (cid:2).1 C D D D 0:098/10 1(cid:3) =(cid:140)0:098(cid:141) 15:785: D (cid:0) Thus, F A (cid:2) D .F=A; i; n/ $1;000 (cid:2) D (cid:140)F=A; i D 9:8%; n 10(cid:141) D D $1;000 (cid:2) 15:785 D $15;785: 8.3.3 SINKING FUND DISCRETE INTEREST FACTOR .A=F; i; n/ The sinking fund determines the amount of A to obtain a desired amount F in the future. The sinking fund factor involves the same terms as the compound amount factor and the graphical representation of the payments and future worth is the same and is repeated as in Figure 8.3. Figure 8.3: A graphical representation of the payments and future worth. The Sinking Fund Factor is the inverse of the Compound Amount Factor and thus it would be: Therefore, the Sinking Fund Equation is: .A=F; i; n/ D 1=.F=A; i; n/: A F D i= (cid:140).1 (cid:2) f i/n 1(cid:141) g (cid:0) C (8.7) 0 1 2 3 4 nAAAAAFTime ……8.3. UNIFORM SERIES PAYMENTS DISCRETE INTEREST FACTORS 99 .A=F; i; n/ 1= (cid:140).1 i= (cid:140).1 i/n i/n C C (cid:0) (cid:0) D D 1(cid:141) =(cid:140)i(cid:141) 1(cid:141) ; (8.8) and where uniform payment in each period n future worth (amount at time n) interest rate number of compounding periods. A F i n D D D D 8.3.4 SINKING FUND DISCRETE INTEREST FACTOR EXAMPLE Melania wants to have $1,000 at the end of 10 years, so what amount would she have to save at the end of each year if the interest rate over the 10-year period is 15% to obtain the desired $1,000? A D D $1;000 (cid:2)0:15=.1 $1;000 C .0:04925/ 0:15/10 1(cid:3) (cid:0) $49:25: D (cid:2) 10/ Thus, .A=F; i 15%; n 0:04925. D D D $1;000 (cid:2) D (cid:140)0:15=.3:046/(cid:141) Thus, Melania must deposit $49.25 at the end of each year for 10 years to have $1,000 at the end of the ten year period. Her ﬁnal payment at period n is necessary to make the total one thousand dollars. 8.3.5 UNIFORM SERIES DISCRETE INTEREST PRESENT WORTH FACTOR .P =A; i; n/ The uniform series present worth factor is an extension of the present worth expression to have payments in each period and not only in the last period. The uniform series present worth factor is used to convert a uniform series of n payments of the amount A at an interest rate i to a present worth amount P . A graphical represent of the payments and the present worth is presented as in Figure 8.4. Figure 8.4: Payments and the present worth. 0 1 2 3 4 nAAAAAPTime ……100 8. BASIC ECONOMIC FACTORS AND EQUATIONS To determine the present value P , each payment A must be discounted at the interest n for each rate i by the number of periods it occurs in the future. The discount factor is .1 period where n is the speciﬁc period for that particular payment. The expression can be derived using the geometric series expression by: i/(cid:0) C A discounted 1 period A=.1 A=.1 i/ C i/2 A discounted 2 periods i/3 A=.1 A=.1 C (cid:1) (cid:1) (cid:1) C i/4 A discounted n periods i/n A=.1 C C C C C C C (cid:1) (cid:1) (cid:1) C C P P P D D D A=.1 i/ C C h1 1=.1 i/ C C C 1=.1 C i/2 1=.1 i/3 C C C 1=.1 i/4 C C (cid:1) (cid:1) (cid:1) C 1=.1 C i/.n (cid:0) 1/i (cid:140) geometric series (cid:141): Now using the geometric series equation of Equation (7.4) where a A=.1 i/; S P D C D and R .1 D i/(cid:0) i/ one obtains: C S P C 1/ =.R D D 1 or 1=.1 a (cid:140).Rn A=.1 (cid:0) i/ i/ (cid:0) C C (cid:140) 1 f (cid:2) (cid:2) .1 A=.1 A (cid:2) 1/(cid:141) C .1 (cid:0) (cid:140).1=.1 (cid:140) 1 (cid:0) f i/n C g C =.1 i//n i/n (cid:0) =.1 g i/n(cid:141) =(cid:140) C (cid:0) C 1(cid:141) =(cid:140).1=.1 1/(cid:141) i/ 1 (cid:0) C i/n(cid:141) =(cid:140) i(cid:141) f .1 i/ g C =.1 C i/(cid:141) (cid:0) P A (cid:140) .1 f (cid:2) C D i/n 1 g (cid:0) = .i.1 C i/n/(cid:141) ; (8.9) D D where uniform payment each period n present worth (amount at time zero) interest rate number of compounding periods. A P i n D D D D The uniform series present worth factor is thus .P =A; i; n/ (cid:140) .1 f C D i/n 1 g (cid:0) = .i.1 C i/n/(cid:141) : (8.10) 8.3.6 UNIFORM SERIES DISCRETE INTEREST PRESENT WORTH EXAMPLE Barack won a lottery which promised $20,000,000 paid as $1,000,000 at the end of each year for 20 years. If the interest rate is 15%, what is the present worth of the Barack’s lottery winnings? P P D D D D A .P =A; i (cid:2) $1;000;000 $1;000;000 $6;259;300: (cid:2) (cid:2) 15%; n D (cid:2).1:15/20 .6:2593/ 20/ 1(cid:3) = (cid:2)0:15 (cid:2) .1:15/20(cid:3) D (cid:0) 8.3. UNIFORM SERIES PAYMENTS DISCRETE INTEREST FACTORS 101 The total present worth amount of the lottery is less than one-third of the listed $20,000,000 prize amount when the interest rate is 15%. From the calculations, one notes that: .P =A; i 15%; n 20/ D D D 6:2593: 8.3.7 CAPITAL RECOVERY DISCRETE INTEREST FACTOR .A=P; i; n/ The Capital Recovery Discrete Interest Factor is the inverse of the Uniform Series Present Worth Discrete Interest Factor and has the same graphical representation as the Uniform Series Present Worth Factor. It is the amount that one must have initially in order to receive an amount A at the end of each year for n years when the interest rate is i during the n year period (Figure 8.5). Figure 8.5: Uniform series present worth factor. The solution is to determine the amount of the payment A based upon the values of P; i, and n. The Capital Recovery Factor is the inverse of the Uniform Series Present Worth Factor and is: A P D (cid:2) (cid:140).i.1 C i/n/(cid:141) = (cid:140).1 i/n 1(cid:141) : (cid:0) C (8.11) where uniform payment each period n (does not include time zero) present worth (amount at time zero) interest rate number of compounding periods. A P i n D D D D The capital recovery factor is thus: .A=P; i; n/ (cid:140).i.1 C D i/n/(cid:141) = (cid:140).1 i/n 1(cid:141) : (cid:0) C (8.12) 8.3.8 CAPITAL RECOVERY DISCRETE INTEREST FACTOR EXAMPLE Michelle has purchased a new automobile for $50,000 after a down payment of $5,000, that is, the total cost was $55,000. Her loan is for $50,000 for a period of 3 years at an interest rate of 15%/year. She wants to pay oﬀ the loan at the end of 3 years. (a) If annual payments are made, what is the annual payment? A D $50;000 (cid:2) (cid:2)0:15.1:15/3(cid:3) = (cid:2)1:153 1(cid:3) (cid:0) D $50;000 (cid:2) (cid:140)0:437980(cid:141) $21;899 D 0 1 2 3 4 nAAAAAPTime ……102 8. BASIC ECONOMIC FACTORS AND EQUATIONS (b) The total interest paid over the three year period is: I .total/ n A P 3 (cid:2) D (cid:0) (cid:2) D $21;899 (cid:0) $50;000 D $15;697: (c) If monthly payments are made, what is the monthly payment? The interest rate would be 1.25% (15%/12) per month and n 36 A D $50; 000 (cid:2) (cid:2)0:0125.1:0125/36(cid:3) = (cid:2).1:0125/36 (cid:0) $1;754:93: D D 1(cid:3) (d) The total interest paid over the 36 monthly payments would be I .total/ D D n A (cid:2) (cid:0) P $63;177:56 D (cid:0) 36 $1;754;93 $50;000 (cid:2) $50;000 (cid:0) $13;178: D Michelle could save $2,519 in interest by paying monthly instead of yearly. 8.4 SINGLE PAYMENT CONTINUOUS INTEREST FACTORS As indicated in Chapter 7, the eﬀective interest expressions can be expressed in terms of the nominal interest r. Let the eﬀective interest be expressed as i, then the expressions become: and and similarly er i D 1 (cid:0) .1 i/ C D er i/n .1 C D ern: (8.13) (8.14) (8.15) 8.4.1 CONTINUOUS INTEREST FUTURE WORTH SINGLE PAYMENT FACTOR .F=P; r; n/ The discrete future worth equation and discrete future worth factor equations from Section 8.2.2 were: and P .1 F D C i/n .F=P; i; n/ ..1 C D i/n: (8.3) (8.4) The continuous future worth factor and continuous future worth equations using Equa- tion (8.15) and the discrete future worth factor and discrete future worth equations would be: P ern F D (8.16) and where 8.4. SINGLE PAYMENT CONTINUOUS INTEREST FACTORS 103 .F=P; r; n/ ern; D (8.17) F P r n future worth (total amount after n time periods) present worth (initial amount at time zero) continuous interest rate per compounding period number of compounding periods. D D D D 8.4.2 CONTINUOUS INTEREST FUTURE WORTH SINGLE PAYMENT EXAMPLE George has purchased a precious painting for $10,000 and expects it to appreciate in value at a nominal interest rate of 15% per year compounded continuously over the next 4 years. What would be the value of the painting at the end of 4 years that George would be expecting? P ern $10;000 $10; 000 $18;221 (cid:2) (cid:2) F F D D D D 4 (cid:2) e:0:15 1:82212 and .F=P; 15; 4/ e0:15 (cid:2) 4 1:8221: D D If George is correct in his purchase assumptions, he would have a gain of $8,221 on his investment. Note that if discrete compounding was used, his gain would have been $7,490 and if simple interest was used his gain would have been only $6,000. 8.4.3 CONTINUOUS INTEREST PRESENT WORTH SINGLE PAYMENT FACTOR .P =F; r; n/ The discrete present worth factor and discrete present worth equations from Section 8.2.3 were: P D F .1 C n i/(cid:0) and .P =F; i; n/ .1 D C i/(cid:0) n: The continuous present worth factor and continuous present worth equations using Equa- tion (8.15) and the discrete present worth equation and discrete present worth factor equations would be: and rn F e(cid:0) P D .P =F; r; n/ e(cid:0) rn: D (8.18) (8.19) 104 8. BASIC ECONOMIC FACTORS AND EQUATIONS 8.4.4 CONTINUOUS INTEREST PRESENT WORTH SINGLE PAYMENT EXAMPLE Laura wants to have $10,000 for the purchase a new car in 4 years as her current car will be lucky to last that long. Her Aunt Barbara wants to buy a precious book from her. She wants to sell the book at a price that would appreciate to $10,000 at the end of 4 years and has an opportunity to invest in a bank note that would pay 15% interest with continuous compounding over the next 4 years. What is the price she needs to sell her precious book at to have the $10,000 in 4 years? rn F e(cid:0) $10;000e(cid:0) $10;000e(cid:0) $10;000 $5;488:1 (cid:2) P P D D D D D 0:15 4 (cid:2) 0:6 0:54881 and .P =F; r; n/ rn e(cid:0) D D e(cid:0) 0:15 4 (cid:2) D 0:54881: If Laura can persuade Aunt Barbara to pay $5,488 for the book now and invest in the bank note for 4 years, she would have her desired $10,000. Note that if discrete interest was used instead of continuous, she would have needed Aunt Barbara pay $5,718 for the book. 8.5 UNIFORM SERIES PAYMENTS CONTINUOUS INTEREST FACTORS The factors for the uniform series payments continuous interest are more complex than the single payment continuous interest factors, but they can be easily obtianed from the Uniform Series Payments Discrete Interest Factors and they will be illustrated by examples in the following sections. 8.5.1 UNIFORM SERIES CONTINUOUS INTEREST FACTORS–FUTURE WORTH, SINKING FUND, PRESENT WORTH, AND CAPITAL RECOVERY The uniform series discrete future worth factor in Section 8.3.1 was: .F=A; i; n/ (cid:140).1 C D i/n (cid:0) 1(cid:141) =(cid:140)i(cid:141): Using Equations (8.13) and (8.15) and the nominal interest rate r replacing the discrete interest rate i, the uniform series continuous future worth factor becomes: .F=A; r; n/ (cid:140)ern (cid:0) D 1(cid:141) = (cid:140)er 1(cid:141) : (cid:0) (8.20) 8.5. UNIFORM SERIES PAYMENTS CONTINUOUS INTEREST FACTORS 105 The uniform series continuous sinking fund continuous factor (uniform series continuous future worth factor) in Section 8.3.3 was: .A=F; i; n/ (cid:140)i(cid:141)= (cid:140).1 i/n 1(cid:141) : (cid:0) C D Using Equations (8.13) and (8.15) and the nominal interest rate r replacing the discrete interest rate i, the uniform series continuous future worth factor becomes: The uniform series discrete present worth factor in Section 8.3.5 was: .A=F; r; n/ (cid:140)er D (cid:0) 1(cid:141) = (cid:140)ern 1(cid:141) : (cid:0) (8.21) (cid:0) Using Equations (8.13) and (8.15) and the nominal interest rate r replacing the discrete C C D .P =A; i; n/ (cid:140).1 i/n 1(cid:141) = (cid:140)i.1 i/n(cid:141) : interest rate i, the uniform series continuous present worth factor becomes: .P =A; r; n/ (cid:140)ern (cid:0) D 1(cid:141) = (cid:140).er (cid:0) 1/ ern(cid:141) : (8.22) Finally, the uniform series discrete capital recovery factor in Section 8.3.7 was: .A=P; i; n/ (cid:140)i.1 C D i/n(cid:141) = (cid:140).1 i/n 1(cid:141) : (cid:0) C Using Equations (8.8) and (8.11) and the nominal interest rate r replacing the discrete interest rate i, the uniform series continuous present worth factor becomes: .A=P; r; n/ (cid:140).er D (cid:0) 1/ ern(cid:141) = (cid:140)ern 1(cid:141) : (cid:0) (8.23) 8.5.2 UNIFORM SERIES CONTINUOUS INTEREST FUTURE WORTH .F=A; r; n/ EXAMPLE Uncle Bill wants to take a trip to Morgantown, WV from Hope, AK to watch a football game. The bus fare is $400 and he plans to put $100 per month into an account for 6 months (that is 1/2 year). He plans to use the additional monies for his room, meals, and the $85 dollar football ticket. If the account pays continuous annual interest of 6% (which is 1/2% per month), how much money will he have to spend for his room and meals. Using Equation (8.20), the total future amount would be: Therefore, .F=A; r; n/ (cid:140)ern (cid:0) D 1(cid:141) = (cid:140)er 1(cid:141) : (cid:0) 1(cid:141) (cid:0) 1(cid:3) = (cid:2)e0:005 1(cid:3) (cid:0) 1(cid:3) = (cid:2)e0:005 (cid:0) 1(cid:3) (cid:0) 1(cid:141)=(cid:140)1:0050125 (cid:2) (cid:0) 1(cid:141) = (cid:140)er 6 A (cid:140)ern 100 (cid:2)e0:005 100 (cid:2)e0:03 $100(cid:140)1:030454 $100 6:0756 $607:56: (cid:0) (cid:2) (cid:0) F F D D D D D D (8.20) (8.24) 1(cid:141) (cid:0) 106 8. BASIC ECONOMIC FACTORS AND EQUATIONS Note that the low interest rate and short period gives a small amount of interest, only $7.56. Therefore, the money Uncle Bill would have for spending on his room and meals is: $607:56 If one had utilized r 6%/year and n D $400 $85 (cid:0) D $122:56: 1=2 year, then: (cid:0) D F D 100 he0:06 (cid:2) 1=2 1i = (cid:2)e0:06 1(cid:3) (cid:0) D (cid:0) 100(cid:140)0:03045=0:0618(cid:141) 100 (cid:2) D 0:4925 D $49:25; which is wrong. This example intentionally used a low interest rate and short time period to indicate that the length of the compounding period and the nominal interest rate period must be the same, which is one month and the corresponding interest is 0.005% per month. 8.5.3 UNIFORM SERIES CONTINUOUS INTEREST SINKING FUND .A=F; r; n/ EXAMPLE Lady Hillary has an option to buy a business in ﬁve years for $10,000.000. Her account pays a nominal interest rate of 12% per year. She plans to deposit money monthly in the account and wants to know what amount she must pay monthly to achieve the $10,000,000 at the end 1% per of 5 years. For monthly deposits, the interest must be compounded monthly and r month. D Therefore, .A=F; r; n/ (cid:140)er D (cid:0) 1(cid:141) = (cid:140)ern 1(cid:141) : (cid:0) (cid:0) (cid:0) 1(cid:141) 1(cid:141) = (cid:140)ern F (cid:140)er (cid:0) $10;000; 000 (cid:2)e:01 $10;000;000(cid:140)1:010050 $10;000;000(cid:140)1:010050 (cid:0) $10;000;000(cid:140)0:0122247(cid:141) $122;247: 60 1(cid:3) = (cid:2)e:01 1(cid:3) (cid:2) (cid:0) 1(cid:141)= (cid:2)e:01 60 (cid:2) (cid:0) 1(cid:141)=(cid:140)1:8221188 (cid:0) A D D D D D D (8.21) (8.25) 1(cid:3) (cid:0) 1(cid:141) Thus, Lady Hillary must deposit $122,247 at the end of every month to have her $10,000,000. Note that if there was no interest, the monthly payments would be $166,666 in- stead of the $122,247 per month. This example intentionally used a high interest rate and long time period but the length of the compounding period and the nominal interest rate period must be the same. Thus, the 5 years of monthly payments indicates 60 monthly payments and the nominal interest rate per month is 1%. 8.5. UNIFORM SERIES PAYMENTS CONTINUOUS INTEREST FACTORS 107 8.5.4 UNIFORM SERIES CONTINUOUS INTEREST PRESENT WORTH .P =A; r; n/ EXAMPLE Ronnie won the $240,000,000 lottery which will pay $12,000,000 per year for 20 years or he can take a single payment now which is discounted at an annual nominal interest rate of 9% per year. What is the amount that he would receive as a single payment. These would be beginning of year payments, so he would receive the ﬁrst payment at time zero and then 19 more end-of-year payments: Therefore, .P =A; r; n/ (cid:140)ern (cid:0) D 1(cid:141) = (cid:140)ern .er 1/(cid:141) : (cid:0) P D A (cid:140)ern 1(cid:141) = (cid:140)ern .er 1/(cid:141) : (cid:0) (cid:0) (8.22) (8.26) For this problem a payment must be made at time zero and then the following 19 end- of-period payments (which represent the remaining 19 beginning-of-year payments) result in: P A A D D A (cid:140)ern C (cid:140)ern 1 f (cid:0) 1(cid:141) = (cid:140)ern .er 1(cid:141) = (cid:140)ern .er (cid:0) 1/(cid:141) (cid:0) 19 C (cid:2)e0:09 (cid:140)5:52896 (cid:2) (cid:0) (cid:0) 1/(cid:141) (cid:0) g 19 (cid:0)e0:09 1(cid:3) = (cid:2)e0:09 (cid:2) 1(cid:141)=(cid:140)5:52896 (cid:0) .1:09417 (cid:2) 1(cid:1)(cid:3)(cid:9) 1/(cid:141) g (cid:0) P D D D D $12;000;000 (cid:8)1 $12;000;000 1 f $12;000;000 1 f $117;068;160: C C 8:75568 g C Note that the present worth is less than half of the lottery amount when the interest rate is 9% compounded continuously. 8.5.5 UNIFORM SERIES CONTINUOUS INTEREST CAPITAL RECOVERY FACTOR .A=P; r; n/ EXAMPLE Queen Nancy has decided to purchase the Island of Happiness in the Ocean of Calm Waters for 2 billion dollars over 20 years at a 6% annual nominal interest rate compounded continuously. What would her annual end-of-year payments be to repay the 2 billion loan? The factor of .A=P; r; n/ is: Therefore, .A=P; r; n/ (cid:140)ern .er D (cid:0) 1/(cid:141) = (cid:140)ern 1(cid:141) : (cid:0) 1/(cid:141) = (cid:140)ern P (cid:140)ern .er (cid:0) (cid:0) $2;000;000;000 (cid:8)(cid:2)e:0:06 $2;000;000;000 $2;000;000;000 $176;074;944: 1(cid:141) 20 (cid:0)e:0:06 (cid:2) (cid:140)3:320117.1:0618365 f 0:088037472 (cid:0) f g 20 1(cid:1)(cid:3) = (cid:2)e0:06 1(cid:3)(cid:9) (cid:2) 1/(cid:141) = (cid:140)3:3320117 (cid:0) (cid:0) A A D D D D D (8.23) (8.27) 1(cid:141) g (cid:0) 108 8. BASIC ECONOMIC FACTORS AND EQUATIONS The total of the 20 year payments of $176 million will be approximately 3.52 billion which implies that 1.52 billion is paid in interest over the life of the investment which is more than 3/4’s of the original loan value. 8.6 SUMMARY This chapter has used the mathematical relationships of Chapter 7 to develop the discrete interest expressions for the single cash ﬂow present worth and future worth and the discrete interest uniform series expressions for future worth, sinking fund, present worth, and capital recovery. Example problems using each of the formulas were presented. The factors for the discrete interest expressions developed were then converted for the continuous interest expressions. Example problems were presented using the nominal interest and the need to use the nominal interest based on the compounding period used was emphasized. A summary of the formulas is presented in Table 8.2 at the end of this chapter. Table 8.2: Discrete and continuous compounding factors of the basic economic expressions Notation: P = Present Worth A = uniform end-of-period i = discrete interest rate per compounding periodF = Future Worth n = number of compounding periods r = continuous interest rate per compounding periodCompounding FactorsPayment TypeFactor NameFindGivenSymbolFormulaA. Single Payment(discrete interest)Present WorthFuture WorthPFFP(P/F, i, n)(F/P, i, n) (1 + i)-n(1 + i)nB. Uniform Payment or Uniform Series(discrete interest)Sinking FundCapital RecoveryFuture WorthPresent WorthAAFPFPAA(A/F, i, n)(A/P, i, n)(F/A, i, n)(P/A, i, n)i/[(1 + i)n -1][i(1 + i)n]/[(1 + i)n -1][(1 + i)n -1]/i[(1 + i)n -1]/[i[(1 + i)n]C. Single Payment(continuous interest)Present WorthFuture WorthPFFP(P/F, r, n)(F/P, r, n)e-rnernD. Uniform Payment or Uniform Series(continuous interest)Sinking FundCapital RecoveryFuture WorthPresent WorthAAFPFPAA(A/F, r, n)(A/P, r, n)(F/A, r, n)(P/A, r, n)[(er - 1)/(ern - 1)][ern (er - 1)/(ern - 1)][(ern - 1)]/(er - 1)][(ern - 1)/(ern(er - 1))]Note: i = = er -1 and (1+i)n = ern8.7. REFERENCES 109 8.7 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 39–48, 2012. 93, 111 [2] Park, Chan S., Contemporary Engineering Economics, 2nd ed., Addison-Wesley, Menlo Park, CA, p. 803, 1997. 93 [3] Newnan, Donald G., Eschenbach, Ted G., and Lavelle, Jerome P., Engineering Economic Analysis, 11th ed., Oxford University Press, New York, p. 655, 2012. 93 [4] Mehta, Merwan B., Applied Engineering Economics Using Excel, Industrial Press, Inc., South Norwalk, CT, p. 260, 2016. 93 [5] Whitman, David L. and Terry, Ronald E., Fundamentals of Engineering Economics and Decision Analysis, Morgan & Claypool Publishers, San Rafael, CA, p. 219, 2012. 93, 111 8.8 EVALUATIVE QUESTIONS 1. If the time period is 5 years and the interest rate is 10%, calculate the following values: (a) .P =A; i; (b) .F=A; i (c) .A=P; i (d) .A=F; i (e) .P =F; i (f ) .F=P; i 10%; n 10%; n 10%; n 10%; n 10%; n 10%; n 5/ 5/ 5/ 5/ 5/ 5/ D D D D D D D D D D D D 2. If the time period is 5 years and the interest rate is 7.5%, calculate the following values: (a) .P =A; i; (b) .F=A; i (c) .A=P; i (d) .A=F; i (e) .P =F; i (f ) .F=P; i 7:5%; n 7:5%; n 7:5%; n 7:5%; n 7:5%; n 7:5%; n 5/ 5/ 5/ 5/ 5/ 5/ D D D D D D D D D D D D 3. Engineer Jimmy wants to retire in 20 years and would like to have 1 million Euros at that time. If the interest rate is expected to be 5% over the next 20 years, what annual amount would he need to save? 110 8. BASIC ECONOMIC FACTORS AND EQUATIONS 4. Rosalynn has purchased a house with a loan of $500,000 Kroner. If the loan interest rate is 5%, what will be her annual payments over the life of the 20-year loan? 5. Gerald has decided to save for a trip in two years. If the monthly interest rate is 1% and he saves Rs. 2,500/month, how much will he have saved after 2 years? 6. Yi has decided to purchase a new moped and the discrete interest rate is 1/2% per month and the purchase price is 20,000 yuan. The payments will be at the end of the month; what is her expected monthly payment over the 3-year period? 7. Vladimir has purchased a new car and the discrete interest rate is 2% per month and the purchase price is 100,000 rubles. (a) What is the expected monthly payment over a 4-year period? (b) What is the total interest paid over the 4-year period? 8. Marlene won the Irish Sweepstakes of 20 million Irish pounds. The prize is actually 2 mil- lion pounds per year for 10 years. (a) If the payments are 10 beginning-of year payments and the discrete interest rate is 5%, what is the equivalent total amount she would receive if she took a single payment? Note: since payments are end-of-year, she has 9 end-of-year payments plus the initial ﬁrst payment. (b) If the payments are 10 end-of-year payments and the discrete interest rate is 5%, what is the equivalent amount she would receive each year if she converts the payments to beginning-of-year payments. 9. If the time period is 5 years and the nominal continuous interest rate is 10%, calculate the values of the following factors: (a) .P =A; r; (b) .F=A; r (c) .A=P; r (d) .A=F; r (e) .P =F; r (f ) .F=P; r 10%; n 10%; n 10%; n 10%; n 10%; n 10%; n 5/ 5/ 5/ 5/ 5/ 5/ D D D D D D D D D D D D Compare these values with the values in Problem 1. 10. If the time period is 3 months and the nominal continuous annual interest rate is 12%, calculate the values of the following factors: (a) .P =A; r (cid:139); n D D 3/ (b) .F=A; r (c) .A=P; r (d) .A=F; r (e) .P =F; r (f ) .F=P; r 8.8. EVALUATIVE QUESTIONS 111 3/ 3/ 3/ 3/ 3/ D D D D D (cid:139); n (cid:139); n (cid:139); n (cid:139); n (cid:139); n D D D D D 11. Construct a table in a spreadsheet and calculate the expressions for the factors of 10% 100. Compare the values calculated with those in the various ref- .P =F; i; n/, .F=P; i; n/, .P =A; i; n/, .A=P; i; n/, .F=A; i; n/, and .A=F; i; n/ for i 1–60 and n and n erence books [1–5]. D D D 12. Construct a table in a spread sheet and calculate the expressions for the factors of 10% 100. Compare the values calculated with those you calculated for .P =F; r; n/, .F=P; r; n/, .P =A; r; n/, .A=P; r; n/, .F=A; r; n/, and .A=F; r; n/ for r and n Problem 9. 1–60 and n D D D C H A P T E R 9 113 Gradient Economic Factors and Equations 9.1 INTRODUCTION Gradient expressions are more complex than the basic expressions in the previous chapter. The two major classiﬁcations of the gradient expressions are the uniform gradient and the geometric gradient. The uniform gradient is presented in two versions; the standard uniform gradient which starts in second period and the uniform ramp gradient which starts in the ﬁrst period and appears like a ramp or step function. Similarly, the geometric gradient is presented in two versions; the standard geometric gradient in which the gradient does not start until the second period and the escalation gradient in which the gradient part starts in the ﬁrst period. These gradients can be expressed with discrete or continuous interest expressions. Thus, the four gradient expressions will be developed for both the discrete and continuous interest and they are: the standard uniform gradient, the uniform ramp gradient, the geometric gradient, and the escalation gradient. Each of these will be initially described and the details of their derivation will be presented for the discrete interest case and then the expressions will be converted to the continuous interest case for the four systems. Some of these materials were presented in a previous work [1] and the next two references [2, 3] have some of the gradient expressions and present many more examples and problems, but some expressions developed are entirely new. Reference [4] is at a graduate level and uses a diﬀerent approach by using Z-Transforms for some of the expressions developed. The uniform ramp gradient is not presented in most books and the escalation gradient is frequently not considered, but these expressions are quite useful when using the end-of period payments for annual increases starting in the ﬁrst year. 9.2 STANDARD UNIFORM GRADIENT DISCRETE INTEREST The standard uniform gradient can be expressed as a ﬁxed amount which increases by the same amount in each of the following periods. The constant increase is called a uniform gradient appears to look somewhat like a ramp function which is delayed by one period. Most authors indicate that the uniform gradient ﬁrst occurs at the end of the second period as indicated by Figure 9.1. Thus, there is one less payment than there are periods as the ﬁrst gradient payment does not start until period 2; thus, if there is a gradient over a period of ten years, there will only 114 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS be nine payments. The future worth of the gradient can be expressed by Equation (9.1) which starts with last term and proceeds back to the ﬁrst term. The amount of the gradient is G, the interest rate is i, and the number of periods is n and a sketch is shown in Figure 9.1: Figure 9.1: Standard uniform gradient for future worth derivation. F .n (cid:0) D 1/G C 2G.1 .n 2/G.1 (cid:0) i/.n C .year n 3/ (cid:0) C 1/ i/ C G.1 C C i/2 3/G.1 .n (cid:0) i/.n (cid:0) C .year 2/ 2/ C 0 0 C .year 1/ C (cid:0) C (cid:1) (cid:1) (cid:1) C C (cid:1) (cid:1) (cid:1) C .year n/ C (cid:1) (cid:1) (cid:1) .time 0/: C (9.1) If one multiplies Equation (9.1) by .1 i/ and then subtracts Equation (9.1) from that, one obtains Equation (9.2). Rearranging the terms and using the geometric series, the expression then becomes Equation (9.3): C i/F .1 C .n (cid:0) D 1/G.1 2G.1 C F D (cid:1) (cid:1) (cid:1) C .n (cid:0) (cid:1) (cid:1) (cid:1) C 1/G G.1 C .n (cid:0) i/.n (cid:0) C C 2/ (cid:0) .n i/ C i/.n (cid:0) C 2/G.1 2/ 2/G.1 G.1 i/ C C C C i/.n .n i/2 C 1/ (cid:0) 3/G.1 .n (cid:0) i/3 C C (cid:1) (cid:1) (cid:1) 3/G.1 i/2 .n (cid:0) C C 4/G.1 i/3 C C (cid:1) (cid:1) (cid:1) (cid:0) 0 1 2 3 4 nG2G3G(n - 1)GFPeriod (Years) 9.2. STANDARD UNIFORM GRADIENT DISCRETE INTEREST 115 C i/2 C i/.n (cid:0) i/3 G.1 1/ C (9.2) iF .n (cid:0) D (cid:0) 1/G G.1 i/ G.1 C G.1 C G h1 C .1 3/ C i/.n (cid:0) C C i/.n 2/ (cid:0) G.1 C C i/2 i/ C C .1 C .1 i/.n (cid:0) 2/ .1 C .1 i/3 C i/.n (cid:0) C C C C this is the geometric series i/n i/n 1(cid:141) =(cid:140).1 1(cid:141) =(cid:140)i(cid:141) C 1(cid:141) i/ (cid:0) (cid:0) C (cid:1) (cid:1) (cid:1) 1/i (cid:141) C C 1 (cid:0) (cid:0) (cid:0) ni (cid:141) =(cid:140)i(cid:141) g nG D (cid:0) (cid:1) (cid:1) (cid:1) C C .1 nG nG C C (cid:140).1 f C D (cid:0) D (cid:0) G D C (cid:140) G (cid:140).1 G (cid:140).1 i/n : (9.3) Solving for F one obtains the uniform gradient discrete interest expression for the future worth becomes: i/n G (cid:8)(cid:140).1 (cid:0) C G.F=G; i; n/: 1 (cid:0) ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) F D D (9.4) The formula, represented by the factor .F=G; i; n/, is used to convert a discrete interest standard uniform gradient of G to a future worth F and this is what appears in Table 9.1 at the end of this section: C The present worth of the uniform gradient discrete interest can be obtained by: D (cid:0) (cid:0) .F=G; i; n/ (cid:8)(cid:140).1 i/n 1 ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) : F=.1 C i/n i/n D G (cid:8)(cid:140).1 1 i/n (cid:0) ni (cid:141) = (cid:2)i 2.1 C 1 ni (cid:141) = (cid:2)i 2.1 (cid:0) i/n(cid:3)(cid:9) i/n(cid:3)(cid:9) C G (cid:8)(cid:140).1 C (cid:0) G.P =G; i; n/: (cid:0) C P D D D (9.5) (9.6) Thus, the conversion formula to convert a uniform gradient discrete interest to a present worth is: .P =G; i; n/ (cid:8)(cid:140).1 i/n 1 (cid:0) (cid:0) C D ni (cid:141) = (cid:2)i 2.1 i/n(cid:3)(cid:9) : C (9.7) The uniform series of the standard uniform gradient discrete interest can be obtained by i/n (cid:0) 1 F i= (cid:140).1 f G (cid:140).1 C i/n C (cid:0) G .A=G; i; n/: (cid:0) A D D D 1(cid:141) g D G (cid:8)(cid:140).1 ni (cid:141) = (cid:140)i ..1 C i/n i/n ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) .i= (cid:140).1 (cid:2) i/n 1(cid:141)/ (cid:0) C 1 (cid:0) 1/(cid:141) (cid:0) (9.8) C (cid:0) Thus, the conversion formula to convert a standard uniform gradient discrete interest to a uniform series is: .A=G; i; n/ (cid:140).1 C D i/n 1 (cid:0) (cid:0) ni (cid:141) = (cid:140)i ..1 i/n 1/(cid:141) : (cid:0) C (9.9) 116 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS 9.2.1 STANDARD UNIFORM GRADIENT DISCRETE INTEREST EXAMPLE What would be the value of a standard uniform gradient of $200 per year for a period of 10 years. The ﬁrst payment would be at the end of the second year and the last payment at the end of the 10th year. The interest rate is 5% . (a) What is the ﬁnal gradient payment? Payment at 10 year .n 1/ (cid:2) (cid:0) D $200 D $1;800. (b) What is the total payment of the gradient amounts, not including the interest? Total Gradient Payments Made (cid:140)n.n C D 1/=2(cid:141) (Payments occur only in the last 9 periods, so n (cid:2) D $200 .9 (cid:2) D 10=2/ (cid:2) $200 D $9;000. 9.) (c) What is the total value including the compounding of interest at the end of year 10? Total Value is Future Worth if found by using Equation (9.4) which is: ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) 10 G (cid:8)(cid:140).1 D 0:05(cid:3) =.0:05/2 (cid:2) 0:50(cid:141)=.0:0025/ 1 (cid:0) 1 i/n G (cid:8)(cid:140).1 C (cid:0) $200 (cid:2).1:05/10 $200(cid:140)1:62889 (cid:0) $200(cid:140):12889(cid:141)=0:0025 $10;311: (cid:0) 1 (cid:0) (cid:0) F D D D D D i/n (cid:0) C 1(cid:141) =i 2 n=i (cid:9) (cid:0) Note the eﬀect of compounding interest results in a total interest gain of $1,311. The present worth of the gradient can be found directly by Equation (9.6), which is: 1 ni (cid:141) = (cid:2)i 2.1 10 i/n G (cid:8)(cid:140).1 (cid:0) C $200 (cid:2).1:05/10 (cid:2) $200(cid:140):12889(cid:141)=(cid:140)0:0040722(cid:141) $6;330: (cid:0) 1 (cid:0) (cid:0) i/n(cid:3)(cid:9) C 0:05(cid:3) = (cid:2).0:05/2 P D D D D .1:05/10(cid:3) (cid:2) The equivalent annual uniform series payment A can be found by Equation (9.9), which is: ni (cid:141) = (cid:140)i ..1 i/n 1 (cid:0) 1 G (cid:140).1 (cid:0) C $200 (cid:2).1:05/10 (cid:2) $200(cid:140)0:12889(cid:141)=(cid:140)0:031444(cid:141) $819:8: 10 (cid:0) (cid:0) i/n 0:05(cid:3) = (cid:2).0:05/ 1/(cid:141) C (cid:0) A D D D D (cid:0).1:05/10 1(cid:1)(cid:3) (cid:0) (cid:2) 9.3. UNIFORM RAMP GRADIENT DISCRETE INTEREST 117 Thus, it takes $819.8 uniform series payment to be equivalent to a $200 standard uniform gradient over a 10-year period at 5% interest. The equivalent uniform series payments will vary considerably as the time increment changes. The payments have been and usually are considered end-of-period payments. These pay- ments can be converted to beginning-of-period payments by dividing by the annual uni- i/. Thus, the beginning-of-period payments are lower and form series payment A by .1 for the previous end-of-period payment of $819.8 would be $780.7 as the interest rate is 5%. C 9.3 UNIFORM RAMP GRADIENT DISCRETE INTEREST The uniform ramp gradient starts in the ﬁrst period and has the appearance of a ramp starting at zero. The future worth of the gradient can be expressed by Equation (9.10) which starts with last term and proceeds back to the ﬁrst term. The amount of the gradient is G, the interest rate is i, and the number of periods is n. The subscript R is used to distinguish between the standard uniform gradient and the Uniform Ramp Gradient, as shown in Figure 9.2: Figure 9.2: Uniform ramp gradient for future worth derivation. FR .n/G .n C D (cid:0) 1/G.1 .year n/ (cid:1) (cid:1) (cid:1) C C 2G.1 C .year n i/ C i/.n 1/ (cid:0) i/2 1/ (cid:0) C (cid:1) (cid:1) (cid:1) (9.10) C 2/ (cid:0) .n C 2/G.1 (cid:0) G.1 C i/.n C .year 1/: C (cid:1) (cid:1) (cid:1) C If one multiplies Equation (9.10) by .1 i/ and then subtracts Equation (9.10) from that, one obtains Equation (9.2). Rearranging the terms and using the geometric series, the expression C 0 1 2 3 4 n2G1G3G4GnGFRPeriod (Years) 118 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS then becomes Equation (9.3): .1 C i/FR D nG .1 C i/.n 1/G.1 i/3 .n (cid:0) C C 3/G.1 i/4 C C (cid:1) (cid:1) (cid:1) FR D .n/G C i/2 .n (cid:0) C C 3/G.1 i/3 C C (cid:1) (cid:1) (cid:1) (cid:0) 2G .1 (cid:1) (cid:1) (cid:1) C .n (cid:0) (cid:1) (cid:1) (cid:1) C 1/G.1 G.1 C i/2 1/ (cid:0) C C .n (cid:0) C 1/ C C i/.n i/ C i/.n (cid:0) .n (cid:0) G.1 2/G.1 i/n C 2/G.1 i/3 C (cid:1) (cid:1) (cid:1) .1 C C i/3 C (cid:1) (cid:1) (cid:1) iFR .n/G C D (cid:0) G.1 i/ C G .1 G.1 C i/.n (cid:0) C 1/ i/2 G.1 C G .1 C i/n (cid:1) (cid:1) (cid:1) C .1 C i/G h1 nG D (cid:0) C C .1 i/.n C i/ C .1 .1 C 2/ (cid:0) C .1 i/2 C i/.n C 1/i (cid:0) (cid:1) (cid:1) (cid:1) C (cid:140) C C i/G (cid:140).1 C this part is the geometric series i/n i/ i/n C i.n (cid:0) 1/(cid:3) =(cid:140)i(cid:141)(cid:9) : i/G (cid:140).1 1(cid:141) =(cid:140).1 1(cid:141) =(cid:140)i(cid:141) C i/n C C C (cid:0) 1 C 1 .1 .1 (cid:0) (cid:0) C D (cid:0) C nG nG D (cid:0) C G (cid:8)(cid:2).1 D C (cid:141) 1(cid:141) (cid:0) (9.11) (9.12) Solving for F one obtains the uniform ramp gradient discrete interest expression for the future worth becomes: FR D G (cid:8)(cid:2).1 C i/n C 1 1 (cid:0) (cid:0) i.1 C n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) : (9.13) Note that the uniform ramp gradient is similar to the standard uniform gradient with n in the stardard gradient replaced by .n 1/ in the uniform ramp gradient: C F D G (cid:8)(cid:140).1 i/n 1 (cid:0) (cid:0) C ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) : (9.6) The formula, represented by the factor .FR=G; i; n/, is used to convert a standard uniform gradient discrete interest of G to a future worth F and this is what appears in Table 9.1: .FR=G; i; n/ (cid:8)(cid:2).1 C D i/n C 1 1 (cid:0) (cid:0) i.1 C n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) : (9.14) The value for the present worth of the uniform ramp gradient discrete interest can be obtained by converting the future worth to the present worth by: PR D D D C i/n i/n FR=.1 G (cid:2).1 (cid:0) C G .PR=G; i; n/ : D 1 C G (cid:8)(cid:2).1 C i.1 C 1 (cid:0) 1 1 i/n C (cid:0) (cid:0) n/(cid:3) = (cid:2)i 2.1 i.1 n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) .1=.1 C i/n(cid:3) C i/n/ C (9.15) Thus, the conversion formula to convert a uniform ramp gradient discrete interest to a 9.3. UNIFORM RAMP GRADIENT DISCRETE INTEREST 119 present worth is: .PR=G; i; n/ (cid:8)(cid:2).1 i/n C 1 1 i.1 n/(cid:3) = (cid:2)i 2.1 i/n(cid:3)(cid:9) : (cid:0) The value for the uniform series of the uniform ramp gradient discrete interest can be C C C D (cid:0) (9.16) obtained by AR D D D i/n 1 FRi= (cid:140).1 G (cid:2).1 (cid:0) C G .AR=G; i; n/ : C i/n (cid:0) C 1(cid:141) 1 D 1 i/n G (cid:8)(cid:2).1 i.1 C C n/(cid:3) = (cid:140)i ..1 (cid:0) C (cid:0) C 1 (cid:0) i/n i.1 C 1/(cid:141) (cid:0) n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) i= (cid:140).1 i/n (cid:0) C (cid:2) 1(cid:141) (9.17) Thus, the conversion formula to convert a uniform ramp gradient discrete interest to a uniform series is: .AR=G; i; n/ (cid:2).1 C D i/n C 1 1 (cid:0) (cid:0) i.1 C n/(cid:3) = (cid:140)i ..1 i/n 1/(cid:141) : (cid:0) C (9.18) 9.3.1 UNIFORM RAMP GRADIENT DISCRETE INTEREST EXAMPLE What would be the value of a uniform ramp gradient of $200 per year for a period of 10 years. The ﬁrst payment would be at the end of the 1st year and the last payment at the end of the 10th year. The interest rate is 5%. (a) What is the ﬁnal payment? Payment at year 10 .n/ (cid:2) D $200 D $2;000. (b) What is the total payment of the gradient, not including the interest? Total Payments Made (cid:140)n.n 1/=2(cid:141) $200 .10 11=2/ $200 $11;000. D C (cid:2) D (cid:2) (cid:2) D (The payments occur in all 10 periods. The total payments are $2,000 more than the stan- dard uniform gradient, that is: 10 years $200=year (cid:2) (c) What is the total value including the compounding of interest at the end of year 10? $2;000.) D Total Value is Future Worth if found by using Equation (9.13) which is: FR D D D D D i.1 (cid:0) 11 (cid:2) n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) C 0:05(cid:3) =.0:05/2 0:55(cid:141)=.0:0025/ 1 1 (cid:0) 1 i/n G (cid:8)(cid:2).1 C C $200 (cid:2).1:05/11 $200(cid:140)1:71034 (cid:0) $200(cid:140):16034(cid:141)=0:0025 $12; 827: (cid:0) 1 (cid:0) (cid:0) Note the eﬀect of compounding interest results in a total interest gain of $1,827. 120 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS The present worth of the gradient can be found directly by Equation (9.15), which is: PR D D D D 1 i/n 1 (cid:0) (cid:0) i.1 G (cid:2).1 C C $200 (cid:2).1:05/11 (cid:2) $200(cid:140):16034(cid:141)=(cid:140)0:0040722(cid:141) $7;875: 11 (cid:0) (cid:0) 1 n/(cid:3) = (cid:2)i 2.1 C C 0:05(cid:3) = (cid:2).0:05/2 i/n(cid:3) .1:05/10(cid:3) (cid:2) The equivalent annual uniform series payment A can be found by Equation (9.17), which is: AR D D D D 1 i/n 1 (cid:0) (cid:0) i.1 G (cid:2).1 C C $200 (cid:2).1:05/11 (cid:2) $200(cid:140)0:16034(cid:141)=(cid:140)0:031444(cid:141) $1019:8: 11 (cid:0) (cid:0) 1 C n/(cid:3) = (cid:140)i ..1 C 0:05(cid:3) = (cid:2).0:05/ 1/(cid:141) (cid:0) (cid:0).1:05/10 i/n (cid:2) 1(cid:1)(cid:3) (cid:0) Thus, it takes $1019.8 uniform series payment to be equivalent to a $200 uniform ramp gradient over a 10-year period. The equivalent uniform series payments will vary consider- ably as the time increment changes. Note that the amount of the uniform series payment equivalent for the uniform ramp gradient was $200 more than that for the standard uni- A which is how the problem form gradient for this problem. Thus, AR was solved previously by solving the standard gradient and then adding the additional amount. A .Gradient/ C D 9.4 GEOMETRIC GRADIENT DISCRETE INTEREST The geometric gradient does not start until the second period. The present worth of the geo- metric gradient can be expressed by Equation (9.19). The initial amount is A1 starts in period 1 and has the gradient amount g applied each of the follow periods up to the ﬁnal period n. The present worth is obtained by discounting the gradient payments back to time zero. Figure 9.3 is a sketch of the payments for geometric gradient for deriving the present worth factor. Additional i: expressions must be developed when g i and the initial expressions presented are for g D P D A1=.1 i/ C A1 (cid:2).1 C C A1 (cid:2).1 C g/3=.1 C i/4(cid:3) C C (cid:1) (cid:1) (cid:1) C g/=.1 i/2(cid:3) C A1 (cid:2).1 g/2=.1 C g/.n 1/=.1 (cid:0) C A1 h.1 i/3(cid:3) i/ni : C C Rearranging the terms to obtain the value of 1 for the ﬁrst term of the geometric gradient i/, this equation can be reduced and using the geometric series with the ratio of .1 g/=.1 C C C ⁄ (9.19) 9.4. GEOMETRIC GRADIENT DISCRETE INTEREST 121 Figure 9.3: Standard geometric gradient for present worth derivation. to: P P i D g/=.1 C i/ (cid:141) 2 g C (cid:1) (cid:1) (cid:1) C f g/=.1 .1 C n(cid:3) i/ g C C C C C D D D D D (cid:140)A1=.1 (cid:140)A1=.1 (cid:140)A1=.1 (cid:140)A1=.1 A1 (cid:140).1 f (cid:140)1 A1 f i/(cid:141) (cid:2)1 i/(cid:141) C (cid:140) .1 C i/(cid:141) (cid:140).1 g/=.1 f i/(cid:141) (cid:140).1 f g/=.1 C C g/=.1 i/(cid:141)n g/=.1 i/ .1 C C f C geometric series =(cid:140).1 1 C i/(cid:141)n i/(cid:141)n C 1=(cid:140).g (cid:0) i/(cid:141)n=(cid:140).i (cid:0) (cid:0) (cid:0) i/(cid:141) g g g g/(cid:141) : 1 =(cid:140)(cid:140).1 C .1 C g/=.1 D Thus, the geometric gradient present worth factor when i C C (cid:0) (cid:0) g g/=.1 C g/ (cid:0) C 1(cid:141) (cid:0) i/(cid:141)=.1 C .1 i/ C i/(cid:141) C g is: g/(cid:141) : g (cid:0) (9.20) (9.21) ⁄ i/(cid:141)n(cid:141)=(cid:140).i .P =A1; g; i; n/ .1 (cid:140)1 (cid:0) C D f g/=.1 C If i g, the denominator of Equation (9.21) would be zero which is a problem, so when g, Equation (9.19) can be arranged so that the ratio .1 g/=.1 i/ becomes 1 and thus: D i/2(cid:3) C C A1 (cid:2).1 C g/2=.1 C A1 h.1 C g/.n 1/=.1 (cid:0) i/3(cid:3) C i/ni .1 C f g/=.1 C C C C C 2 i/ g C (cid:1) (cid:1) (cid:1) P D D D D D P P A1=.1 i/ C A1 (cid:2).1 g/=.1 A1 (cid:2).1 C g/3=.1 C i/4(cid:3) C (cid:140)A1=.1 C i/(cid:141) (cid:2)1 C .1 C (cid:1) (cid:1) (cid:1) C i/ g/=.1 C .1 C g/=.1 C i/ .n g 1 C 1 1/i (cid:0) C C C (cid:1) (cid:1) (cid:1) C 1(cid:141) C i/(cid:141)(cid:140)1 i/(cid:140)n(cid:141) (cid:1) (cid:1) (cid:1) C f (cid:140)A1=.1 A1=.1 C nA1=.1 C i/: C (9.19) (9.22) 0 1 2 3 4 nA1(1+g)A1A1(1+g)2A1(1+g)3A1(1+g)(n-1)PPeriod (Years) 122 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS Thus, one has a rather simple expression when i worth factor expression becomes: g and the geometric gradient present D D f The value for the future worth of the geometric gradient can be obtained by multiplying D C .P =A1; i g; n/ n=.1 : i/ g (9.23) by .1 C i/n to the present worth of the geometric gradient to obtain: F F D D P .1 A1 C (cid:140).1 f i/n C D i/n A1 (cid:140)1 f .1 .1 (cid:0) C g/n(cid:141) =(cid:140)i (cid:0) C g/=.1 g(cid:141) (cid:0) i/n(cid:141) =(cid:140).i g/(cid:141) g (cid:2) (cid:0) i/n .1 C C : g Thus, the geometric gradient future worth factor is: .F=A1; g; i; n/ (cid:140).1 D f i/n .1 (cid:0) C C g/n(cid:141) =(cid:140)i g(cid:141) : g (cid:0) (9.24) (9.25) If i g, then the future worth factor for the geometric gradient is the present worth factor for the geometric gradient multiplied by .1 i/n which is: D F F D D P .1 C (cid:2)nA1.1 i/n C D i/n C (cid:140).nA1=.1 1(cid:3) : (cid:0) i//(cid:141) .1 (cid:2) C C i/n (9.26) Thus, a simple expression occurs when i factor expression becomes: g and the geometric gradient future worth D .F=A1; i g; n/ (cid:8)n.1 C D D i/n 1(cid:9) : (cid:0) (9.27) The value for the uniform series of the geometric gradient can be obtained by: A A D A1 .F=A1g; i; n/ A1 i/n (cid:2) .1 .A=F; i; n/ g/n(cid:141) =(cid:140)i (cid:140).1 f g (cid:2) f Thus, the geometric gradient uniform series factor is: D C C (cid:0) (cid:0) g(cid:141) i= (cid:140).1 i/n : 1(cid:141) g (cid:0) C (9.28) .A=A1; g; i; n/ (cid:140).1 i/n .1 g/n(cid:141) =(cid:140)i g(cid:141) i= (cid:140).1 i/n (cid:0) g, then the uniform series factor for the geometric gradient is the future worth g (cid:2) f D f C C C (cid:0) (cid:0) : 1(cid:141) g (9.29) If i D factor for the geometric gradient multiplied by (cid:140)i= (cid:140).1 i/n 1(cid:141)(cid:141) which is: A A D D F (cid:140)i= (cid:140).1 (cid:2)niA1.1 C C i/n i/n 1(cid:141)(cid:141) (cid:0) D 1(cid:3) = (cid:140).1 (cid:0) (cid:0)nA1.1 i/n C 1(cid:141) : C (cid:0) C i/n (cid:0) 1(cid:1) (cid:140)i= (cid:140).1 (cid:0) i/n 1(cid:141)(cid:141) (cid:0) C (9.30) Finally, the geometric gradient uniform series factor expression when i .A=A1; i g; n/ (cid:2)ni.1 C D D i/n 1(cid:3) = (cid:140).1 (cid:0) i/n 1(cid:141) : (cid:0) C g becomes: D (9.31) 9.4. GEOMETRIC GRADIENT DISCRETE INTEREST 123 9.4.1 GEOMETRIC GRADIENT DISCRETE INTEREST EXAMPLE What would be the value at the end of 10 years of a geometric gradient of 10% if the initial amount was $200 for a period of 10 years. The ﬁrst payment would be at the end of the ﬁrst year and the last payment at the end of the 10th year. The interest rate is 5%. (a) What is the ﬁnal gradient payment? $200.1 0:10/9 C D $100.2:3574/ $471:5. D (b) What is the total payments (TP) of the gradients not including the interest? TP TP D D D D D C C A1 (cid:0)1 .1 C g/n A1 ..1 g/n A1 ..1 $200 (cid:0)1:110 $3; 187: C (cid:0) C C g/ .1 C 1/ =.1 (cid:0) 1/ =g (cid:0) 1(cid:1) =0:10 g/2 g (cid:0) C (cid:1) (cid:1) (cid:1) C 1/ g/n 1(cid:1) (cid:0) .1 C (9.32) (c) What is the future worth including the compounding of interest? i/n .1 C (cid:0) 0:05/10 :9648478(cid:141)=(cid:140) C g/n(cid:141) =(cid:140)i .1 (cid:0) :05(cid:141) C D (cid:0) (cid:140).1 A1 C f $200 (cid:8)(cid:2).1 $200(cid:140) (cid:0) $3;859: g(cid:141) (cid:0) g 0:10/(cid:3)(cid:9) =(cid:140)0:05 $100.19:2969/ (cid:0) F F D D D D (9.24) 0:10(cid:141) (d) Therefore, the total interest earned over the 10 years would be: (e) What is the present worth of the gradient? TP F (cid:0) D $3;859 (cid:0) $3;187 D $672: (cid:140).1 g/=.1 C (cid:140).1 C 0:10/=.1 i/(cid:141)n(cid:141) =(cid:140).i g/(cid:141) g 0:05/(cid:141)10(cid:3) =(cid:140).0:05 (cid:0) (9.20) 0:10/(cid:141)(cid:9) (cid:0) (cid:0) C 0:59233(cid:141)=(cid:140) :05(cid:141) (cid:0) C P P D D D D (cid:140)1 A1 (cid:0) f $200 (cid:8)(cid:2)1 $200(cid:140) (cid:0) $2;369: (f ) What is the equivalent annual uniform series payment A? 124 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS i/n f (cid:140).1 A1 (cid:0) C $200 (cid:8)(cid:2).1:05/10 (cid:140).19:2970(cid:141) $200 f $307: .1 (cid:0) (cid:2) A D D D D (cid:0) g/n(cid:141) =(cid:140)i g(cid:141) C .1:10/10(cid:3) =.0:05 (cid:140).0:079504(cid:141) g g f (cid:0) i= (cid:140).1 0:10/ C (cid:2) i/n 1(cid:141) g (cid:2)0:05=1:0510 (cid:0) (9.28) 1(cid:3)(cid:9) (cid:0) Note that the geometric gradient usually is smaller than the uniform ramp gradient or the standard uniform gradient as it is a percentage gradient rather than a ﬁxed amount. 9.5 ESCALATION GRADIENT DISCRETE INTEREST Escalation is used in construction projects as the cost of materials and labor are expected to increase over time and this is done with the escalation rate. Since traditional engineering econ- omy expressions use end-of-period payments, the escalation must start in the ﬁrst period. The projects estimates are done long before the project starts and the inﬂation eﬀects will need to be included starting with the ﬁrst period. This is the diﬀerence between escalation and the ge- ometric gradient series which is similar to the diﬀerence needed for the uniform ramp gradient series and the standard uniform gradient. The illustration of the escalation payments and present worth is below and the present worth of the escalation can be expressed by Equation (9.33). The symbol E will be used to indicate escalation, but is used in the same manner as g except it is also in the ﬁrst period. The escalation gradient is illustrated in Figure 9.4. Figure 9.4: Escalation gradient for present worth derivation. 0 1 2 3 4 nA1(1+ᴇ)A1(1+ᴇ)2A1(1+ᴇ)3A1(1+ᴇ)4A1(1+ᴇ)nPPeriod (Years) 9.5. ESCALATION GRADIENT DISCRETE INTEREST 125 PE D D D D A1.1 C A1 (cid:2).1 E/=.1 i/ C E/4=.1 C A1 (cid:2).1 i/4(cid:3) C E/2=.1 i/2(cid:3) A1 (cid:2).1 C A1 (cid:140).1 C E/n=.1 C (cid:140)A1.1 C E/=.1 C .1 C E/=.1 (cid:1) (cid:1) (cid:1) C f C C i/(cid:141) h1 i/ C (cid:140) C E/=.1 E/=.1 C E/=.E i/(cid:141) (cid:2)(cid:140).1 i/(cid:141) (cid:2)(cid:140).1 i/(cid:141) (cid:140)(cid:140).1 C (cid:140)A1.1 (cid:140)A1.1 A1 A1 C (cid:140).1 f (cid:140).1 f C (cid:1) (cid:1) (cid:1) C .1 E/=.1 C i/ C C C n(cid:141) g Geometric Series i/(cid:141)n E/=.1 i/(cid:141)n (cid:0) i/(cid:141)n i/(cid:141)n E/=.1 E/=.1 E/=.1 C C C C C (cid:0) .1 C f C (cid:141) 1(cid:3) =(cid:140).1 1(cid:3) =(cid:140)(cid:140).1 1(cid:141) C i/n(cid:141) C E/=.1 E/3=.1 i/3(cid:3) C i/ 2 g C C (cid:1) (cid:1) (cid:1) E/=.1 C E/ (cid:0) C 1(cid:141) (cid:0) i/(cid:141)=.1 C .1 i/ C i/(cid:141) C (cid:0) C C E/=.E D PE D Equation (9.33) is the expression for the escalation gradient and E is the escalation amount, and the symbol E is used instead of g. The escalation gradient present worth factor to obtain the present worth of an escalation gradient is. i/(cid:141) (cid:140)(cid:140).1 (9.33) C C C 1(cid:141) (cid:0) (cid:0) (cid:0) g g : .PE=A1; E; i; n/ (cid:140).1 D f C E/=.E (cid:0) i/(cid:141)(cid:140).1 C E/=.1 i/(cid:141)n : 1 g (cid:0) C (9.34) If i D E, Equations (9.33) and (9.34) will have denominators that are zero, so the equa- E. This is solved in the same manner as tions must be derived initially using the case where i was done for the standard geometric gradient: D E/2=.1 i/2(cid:3) C C C A1 (cid:2).1 E/3=.1 i/3(cid:3) C C (cid:1) (cid:1) (cid:1) C i/ 1 C C f C E/=.1 2 i/ g C C (cid:1) (cid:1) (cid:1) C .n E/=.1 1/(cid:21) (cid:0) PE D A1.1 E/=.1 C A1 (cid:140).1 i/ C C E/n=.1 (cid:1) (cid:1) (cid:1) C (cid:140)A1.1 C E/=.1 C i/(cid:141) (cid:2)1 A1 (cid:2).1 i/n(cid:141) .1 C D C n.1 C E/.n (cid:0) C 1/=.1 C i/o (cid:1) (cid:1) (cid:1) C (cid:140)A1 (cid:2) nA1: 1(cid:141)(cid:140)1 1 1 1(cid:141) (cid:1) (cid:1) (cid:1) C C D PE D Thus, for this special case; C .PE=A1; i E; n/ n: D D (9.35) (9.36) The equation for the future worth of the escalation gradient can be determined from the present worth equation by: FE D FE D FE D A1 A1 A1 (cid:2) .PE=A1; E; i; n/ (cid:140).1 E/=.E (cid:2) i/(cid:141)(cid:140).1 .F=P; i:n/ (cid:2) f (cid:140).1 f C C E/=.E (cid:0) i/(cid:141) (cid:140).1 C E/n (cid:0) C (cid:0) E/=.1 i/(cid:141)n (cid:0) i/n(cid:141) : g C .1 C 1 .1 C g (cid:2) i/n (9.37) (9.38) (9.39) (9.40) (9.43) (9.44) 126 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS This also results in the factor being: .FE=A1; E; i; n/ D f (cid:140).1 C E, then For the special case where i D E/=.E i/(cid:141) (cid:140).1 E/n .1 i/n(cid:141) : g C (cid:0) C (cid:0) FE D D and thus A1 (cid:2) A1n.1 .PE=A1; i i/n C E; n/ (cid:2) D .F=P; i; n/ .FE=A1i e; n/ n.1 i/n: D The equation for the uniform series of the escalation gradient can be determined from the D C present worth equation by: .A=P; i:n/ AE D AE D AE D A1 A1 A1 (cid:2) .PE=A1; E; i; n/ (cid:140).1 E/=.E (cid:2) i/(cid:141)(cid:140).1 (cid:2) f (cid:140)i.1 C E/=.E (cid:0) i/(cid:141) (cid:140).1 f This also results in the factor C (cid:0) C E/=.1 E/n C .1 i/(cid:141)n 1 g (cid:2) f (cid:0) i/n(cid:141) = (cid:140).1 (cid:140)i..1 i/n C i/n= (cid:140)..1 1(cid:141) : i/n C (cid:0) 1/(cid:141) g (9.41) C (cid:0) C C (cid:0) g E/n .1 (cid:0) C C i/n(cid:141) = (cid:140).1 i/n 1(cid:141) : g (cid:0) C (9.42) E/=.E i/(cid:141) (cid:140).1 (cid:0) E, then .AE=A1; E; i; n/ (cid:140)i.1 D f C For the special case where i AE D D D A1 A1 .P =A1; i E; n/ .A=P; i:n/ (cid:2) ni.1 f C D i/n= (cid:140)..1 (cid:2) i/n C : 1/(cid:141) g (cid:0) And thus, .AE=A1i E; n/ ni.1 D f C D i/n= (cid:140)..1 i/n 1/(cid:141) : g (cid:0) C 9.5.1 ESCALATION GRADIENT DISCRETE INTEREST EXAMPLE What would be the value at the end of 10 years of an escalation gradient of 10% if the initial amount was $200 for a period of 10 years. The ﬁrst payment would be at the end of the ﬁrst year and the last payment at the end of the 10th year. The interest rate is 5%. (a) What is the ﬁnal payment? $200.1 0:10/10 $200.2:5937/ $518:8 $519. C (b) What is the total payments .TP/ of the gradients not including the interest? D D D TPE D D D D D TPE D .1 C C E/ C C E/ (cid:0)1 E/ ..1 A1 (cid:0).1 A1.1 A1.1 A1.1 C C $200.1:1/ (cid:0)1:110 $3;506: E/ ..1 C C C .1 C E/n E/n (cid:0) E/2 E/1 C (cid:1) (cid:1) (cid:1) C .1 C .1 E/n (cid:1) E/n C (cid:1) (cid:1) (cid:1) C E 1/ = .1 C 1/ C (cid:0) (cid:0) 1/ =E (cid:0) 1(cid:1) =0:10 1(cid:1) (cid:0) (9.45) (c) What is the future worth including the compounding of interest? 9.5. ESCALATION GRADIENT DISCRETE INTEREST 127 FE D D D FE D i/(cid:141) (cid:140).1 C E/=.E (cid:0) 0:10/=.0:10 (cid:140).1 A1 f $100(cid:140).1 $200(cid:140)22:0(cid:141)(cid:140)0:964847(cid:141) $4;245: C (cid:0) .1 E/n C 0:05/(cid:141) (cid:8)(cid:2).1 (cid:0) i/n(cid:141) g 0:10/10 C C (9.37) .1 (cid:0) C 0:05/10(cid:3)(cid:9) (d) Therefore, the total interest earned over the 10 years would be: FE (cid:0) TPE D $4245 (cid:0) $3506 D $739 (e) What is the present worth of the escalation gradient? PE D D D D (cid:140).1 A1 C f $200 (cid:8)(cid:140).1 $200 (cid:2) $2;606: E/=.E i/(cid:141)(cid:141) (cid:140)(cid:140).1 E/=.1 (cid:0) 0:10/=.0:10 C 0:05/(cid:141) C .1:1=0; 05/ (cid:0) (cid:140)0:59233(cid:141) i/(cid:141)n C (cid:2)(cid:140).1 (cid:2) C (cid:2) 1(cid:141) (cid:0) g 0:10/=.1 0:5/(cid:141)10 1(cid:3)(cid:9) (cid:0) C (9.33) (f ) What is the equivalent annual escalation payment Ae? (cid:0) C C C i/(cid:141) (cid:140).1 i/(cid:141) (cid:140).1 E/=.E E/=.E (cid:140)i.1 f (cid:140)i.1 f A1 A1 $200(cid:140)0:05.1 (cid:0) $200(cid:140)1:1; 0:964847(cid:141)=(cid:140)0:62889(cid:141) $338: 0:10/=.0:10 C C (cid:0) (cid:0) C .1 i/n(cid:141) = (cid:140).1 i/n(cid:141) = (cid:140).1 E/n E/n .1 C 0:05/(cid:141) (cid:2).1:10/10 (cid:0) C i/n i/n 1(cid:141) g (cid:0) 1(cid:141) (cid:0) .1:05/10(cid:3) = (cid:2).1:05/10 C g (cid:0) (9.41) 1(cid:3) (cid:0) AE D D D D AE D Note that the escalation gradient ($338) is larger than the geometric gradient ($307) as the gradient-escalation starts in the ﬁrst period rather than the second period.This diﬀerence results in the 10% as the escalation gradient has one more escalation. A summary of all the discrete formulas is in Table 9.1. This diﬀerence is not only for AE but also for PE or FE. 128 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS t s e r e t n i e t e r c s i d d n a s t n e m y a p e t e r c s i d — s n o i s s e r p x e c i m o n o c e f o s r o t c a f g n i d n u o p m o c e t e r c s i D : 1 . 9 e l b a T Payment TypeFactor NameFindGivenSymbolFormulaA. Single PaymentPresent WorthPF(P/F, i, n)(1 + i)-nFuture Worth (Compound Amount)FP(F/P, i ,n)(1+i)n B. Uniform PaymentSinking FundAF(A/F, i ,n)i / [(1+ i)n -1] (Uniform Series)Capital RecoveryAP(A/P, i, n)[(i(1+i)n] ] / [ (1+i)n - 1] Compound AmountFA(F/A, i, n)[(1+i)n -1] / iPresent WorthPA(P/A, i, n)[(1+i)n -1] / [i((1+i)n ]C. Uniform Gradient Expression Standard Uniform GradientUniform Gradient Present WorthPG(P/G, i, n)[((1+i)n - 1 -ni) / ( i2 (1+i)n )] Uniform Gradient Future WorthFG(F/G, i, n)[((1+i)n - 1 -ni) / i2 ]Uniform Gradient Uniform SeriesAG(A/G, i ,n)[((1+i)n - 1 -ni) / ((1+i)n -1)] Uniform Ramp GradientUniform Ramp Gradient Present WorthPRG(PR/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i2 (1+i)n )] Uniform Ramp Gradient Future WorthFRG(FR/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i2)] Uniform Ramp Gradient Uniform SeriesARG(AR/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i(1+i)n - 1)] D. Geometric Gradient Expression Geometric GradientGeometric Gradient Present WorthPA1, g(P/A1,g, i, n)[(1-((1+g)n / (1+i)n))/(i-g)]If g=i(P/A1,g=i, n)n/(1+i)Geometric Gradient Future WorthFA1, g(F/A1, g, i, n)[((1+i)n – (1+g)n)]/[i-g]If g=i(F/A1, g=i, n)n(1+i)(n-1)Geometric Gradient Uniform SeriesAA1, g(A/A1, g, i, n)[(i((1+i)n –(1+g)n))/((i-g)((1+i)n-1))]If g=i(A/A1, g=i, n)[ni(1+i)(n-1) ]/ [(1+i)n -1] Escalation GradientEscalation Gradient Present WorthPᴇA1, ᴇ(Pᴇ/A1, ᴇ,i, n)[(1+ᴇ) /(ᴇ - i)] [((1+ᴇ)/(1+i))n -1]If ᴇ=i(Pᴇ/A1, ᴇ=i,n)nEscalation Gradient Future WorthFᴇA1, ᴇ(Fᴇ/A1, ᴇ,i, n)[(1+ᴇ) /(ᴇ - i)] [((1+ᴇ)n - (1+i))n]If ᴇ=i(Fᴇ/A1, ᴇ=i, n)n(1+i)nEscalation Gradient Uniform SeriesAᴇA1, ᴇ(Aᴇ/A1, ᴇ,i, n)[(i(1+ᴇ)/(ᴇ - i))((1+ᴇ)n - (1+i)n)]/[(1+i)n 1]If ᴇ=i(Aᴇ/A1, ᴇ=i,n)ni(1+i)n /[(1+i)n -1]Notation:P=Present Worth; i = eﬀ ective discrete interest rate per period; A=uniform end-of-period payments; n = number of periods;F=Future Worth; g=Geometric Gradient Rate; G=Uniform Gradient Amount; ᴇ = Escalation Gradient Rate;A1 = Initial Geometric Gradient Amount and Initial Escalation Gradient Amount9.6 9.6. STANDARD UNIFORM GRADIENT CONTINUOUS INTEREST FORMULAS 129 STANDARD UNIFORM GRADIENT CONTINUOUS INTEREST FORMULAS The basic relationships between the nominal (r) and market (i) interest will be used to convert the discrete interest formulas to continuous interest formulas similar to that done in Chapter 8. Most books have only small discussions of continuous interest, but Park and Sharp-Bette is a great reference [4]. The relationships used are: (9.46) (9.47) (9.48) (9.49) (9.5) (9.7) (9.9) er i D 1 (cid:0) .1 i/ C D er i/n .1 C D ern ln.1 r D C i/: and and similarly and and The factors for the standard uniform gradient discrete interest were: .F=G; i; n/ .P =G; i; n/ (cid:8)(cid:140).1 (cid:8)(cid:140).1 i/n i/n 1 1 (cid:0) (cid:0) (cid:0) (cid:0) C C D D ni (cid:141) = (cid:2)i 2(cid:3)(cid:9) ni (cid:141) = (cid:2)i 2.1 i/n(cid:3)(cid:9) C .A=G; i; n/ (cid:140).1 D f i/n 1 (cid:0) (cid:0) C ni (cid:141) = (cid:140)i ..1 i/n : 1/(cid:141) g (cid:0) C The conversion of these factors for the standard uniform gradient continuous interest fac- tors result in the following equations: F P A D D D G.F=G; r; n/ G.P =G; r; n/ G.A=G; r; n/ G n(cid:140)ern G n(cid:140)ern (cid:0) (cid:0) G (cid:140)ern f (cid:0) n.er n.er n.er 1 1 1 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) 1/(cid:141) = (cid:140).er 1/(cid:141) = (cid:140).er 1/(cid:141) = (cid:140).er (cid:0) (cid:0) (cid:0) D D D 1/(cid:141)2o 1/(cid:141)2 erno 1/ .ern : 1/(cid:141) g (cid:0) (9.50) (9.51) (9.52) 9.6.1 STANDARD UNIFORM GRADIENT CONTINUOUS INTEREST EXAMPLE The example will be the same as that in Section 9.2.1 to illustrate the diﬀerence between discrete and continuous. What would be the value of a standard uniform gradient (G) of $200 per year for a period of 10 years. The ﬁrst payment would be at the end of the second year and the last payment at the end of the 10th year. The continuous interest rate is 5%. 130 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS (a) What is the ﬁnal payment? Payment at 10 year .n 1/ (cid:2) (cid:0) D $200 D $1;800. (b) What is the total payment of the gradient, not including the interest? Total Payments Made (cid:140)n.n 1/=2(cid:141) $100 .9 (cid:2) D (cid:2) C D 10=2/ 200 (cid:2) D $9;000. (Payments occur only in 9 periods even though there are 10 periods, so n 9.) D (c) What is the total value including the continuous compounding of interest at the end of year 10? Total Value is Future Worth of the standard uniform gradient continuous interest found by using Equation (9.50) which is: F D D D D D D D G .F=G; r G n(cid:140)ern (cid:0) $200 (cid:2)e:05 (cid:2) D 1 (cid:0) 10 5%; n n .er 1 (cid:0) (cid:0) 10/ D 1/(cid:141) = (cid:140).er (cid:0) 10 (cid:0)e0:05 (cid:0) 10.1:05127 1 (cid:0) (cid:0) $200(cid:140)1:64872 $200(cid:140):13601(cid:141)=(cid:140)0:0026287(cid:141) $200(cid:140)51:74(cid:141) $10;348: 1/(cid:141)2o (cid:0) 1(cid:1)(cid:3) = h(cid:0)e0:05 2i 1(cid:1) (cid:0) 1/(cid:141)= (cid:2).1:05127 (cid:0) 1/2(cid:3) (cid:0) This is slightly greater than the discrete interest (10,312) as the equivalent discrete interest would be 5.13% instead of the 5.00% applied in the discrete interest calculations. Note the eﬀect of continuous interest results in a total interest gain of $1,348 which is slightly greater than the discrete case. The present worth of the gradient can be found directly by the factor Equation (9.51), which is: P D D D D D D G.P =G; r 5%; n 10/ D 1 (cid:0) 10 G n(cid:140)ern (cid:0) $200 (cid:2)e:05 (cid:2) D n .er 1/(cid:141) = (cid:140).er 1 (cid:0) (cid:0) (cid:0) 10 (cid:0)e0:05 (cid:0) 10.1:05127 1 $200(cid:140)1:64872 $200(cid:140):13601(cid:141)=(cid:140)0:004334(cid:141) $6;276: (cid:0) (cid:0) 1/(cid:141)2 erno (cid:0) 1(cid:1)(cid:3) = h(cid:0)e0:05 2 1(cid:1) e:05 (cid:2) 10i (cid:0) 1/(cid:141)= (cid:2).1:05127 (cid:0) 1/2 (cid:0) (cid:2) 1:64872(cid:3) 9.7. RAMP UNIFORM GRADIENT CONTINUOUS INTEREST FORMULAS 131 The discrete interest value of the present worth was $6,330 and thus the diﬀerence is rel- atively small. The lower present worth is due to the slightly higher discount rate of the continuous compounding vs. discrete compounding. The equivalent annual uniform series continuous interest payment can be found by Equa- tion (9.52), which is: A D D D D D D 10/ 1/(cid:141) = (cid:140).er (cid:0) 10 (cid:0)e0:05 (cid:0) 10.1:05127 D D 1 (cid:0) 10 5%; n n .er 1 G .A=G; r (cid:140)ern G (cid:0) f $200 (cid:2)e:05 $200(cid:140)1:64872 $200(cid:140):13601(cid:141)=(cid:140)0:0332606(cid:141) $818: (cid:0) (cid:0) (cid:0) (cid:0) 1 (cid:2) 1/ .ern (cid:0) (cid:0) 1(cid:1)(cid:3) = (cid:2)(cid:0)e0:05 1/(cid:141)=(cid:140).1:05127 (cid:0) 1/(cid:141) g 1(cid:1) (cid:0)e:05 (cid:2) 1/ (cid:0) (cid:0) (cid:2) 10 1(cid:1)(cid:3) .1:64872 (cid:0) 1/(cid:141) (cid:0) Thus, it takes $818 uniform series continuous payment to be equivalent to a $200 standard uniform gradient of a 10-year period. The equivalent uniform series payments will vary considerably as the time increment changes. The discrete interest and continuous interest values have only a slight diﬀerence as the interest rate is low and the compounding periods are relatively low. 9.7 RAMP UNIFORM GRADIENT CONTINUOUS INTEREST FORMULAS The discrete interest formulas for uniform ramp gradient from Section 9.3 are presented and then converted into the continuous formulas for the uniform ramp gradient: .FR=G; i; n/ .PR=G; i; n/ .AR=G; i; n/ D D D (cid:8)(cid:2).1 (cid:8)(cid:2).1 (cid:2).1 C C i/n i/n i/n C C C 1 C 1 (cid:0) 1 1 1 (cid:0) i.1 i.1 (cid:0) 1 (cid:0) i.1 (cid:0) (cid:0) C C C n/(cid:3) = (cid:2)i 2(cid:3)(cid:9) n/(cid:3) = (cid:2)i 2.1 n/(cid:3) = (cid:140)i ..1 i/n(cid:3)(cid:9) C i/n (cid:0) C 1/(cid:141) : (9.13) (9.16) (9.18) The conversion of these factors from discrete to continuous interest factors results in the factor: .FR=G; r; n/ .PR=G; r; n/ .AR=G; r; n/ D D D nher.n C 1/ her.n C 1/ 1 .er (cid:0) 1 (cid:0) .er 1/ .1 (cid:0) 1/ .1 n/i = h.er C n/i = h.er 1/2io (cid:0) 1/2 erni (cid:0) (cid:0) (cid:0) C (cid:0) her.n C 1/ .er 1 (cid:0) (cid:0) (cid:0) 1/ .1 C n/i = (cid:140).er 1/ .ern 1/(cid:141) : (cid:0) (cid:0) (9.53) (9.54) (9.55) 132 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS 9.7.1 UNIFORM RAMP GRADIENT CONTINUOUS INTEREST EXAMPLE What would be the value of a uniform ramp gradient continuous interest of $200 per year for a 10-year period with a nominal interest rate of 5%. The ﬁrst payment would be at the end of the ﬁrst year and the last payment at the end of the 10th year. (a) What is the ﬁnal payment? Payment at year 10 .n/ (cid:2) D $200 D $2;000. (b) What is the total payment of the gradient, not including the interest? Total Payments Made (cid:140)n.n 1/=2(cid:141) (cid:2) (The payments occur in all 10 periods.) C D $200 .11 (cid:2) D 10=2/ (cid:2) $200 D $11;000. (c) What is the total value including the compounding of the continuous interest at the end of year 10? Total Value is Future Worth if found by using Equation (9.53) which is: .FR=G; r; n/ FR D D D D D D nher.n C 1/ 1 (cid:0) 1/ (cid:0) 1 1/ G nher.n C (cid:0) $200 he0:05.10 C .er 1/.1 n/i = h.er 1/2io (cid:0) .er C 1/ .1 (cid:0) n/i = h.er (cid:0) (cid:0) 1 (cid:0) (cid:0)e:05 C 1(cid:1) .1 (cid:0) (cid:0) .1:051271 (cid:0) C 1/.11/(cid:141)=.0:0025/ 1/2io (cid:0) 10/i = (cid:0)e0:05 (9.53) 2 1(cid:1) (cid:0) 1 $200(cid:140)1:73325 $200(cid:140):169269(cid:141)=0:002629 $12;877: (cid:0) (cid:0) Note the eﬀect of compounding interest results in a total interest gain of $1,877. The present worth of the gradient can be found directly by using Equation (9.54), which is: .PR=G; r; n/ PR D D D D D 1/.1 1 .er 1/ (cid:140).er.n C G(cid:140).er.n C (cid:0) 1/ (cid:0) 1 (cid:140).e0:05.10 (cid:0) (cid:0) .er (cid:0) 1/ C (cid:0) 1 C 1/.1 C .e0:05 f $200 $200(cid:140)0:16927(cid:141)=(cid:140)0:0043340(cid:141) $7;811: (cid:0) (cid:0) n/(cid:141)=(cid:140).er (cid:0) n/(cid:141)=(cid:140).er 1/.10 (cid:0) 1/2ern(cid:141) 1/2ern(cid:141) 1/(cid:141)=(cid:140).e0:05 (cid:0) C (9.54) 1/2 (cid:0) (cid:2) e0:05 10(cid:141) (cid:2) 9.8. GEOMETRIC GRADIENT CONTINUOUS INTEREST FORMULAS 133 The equivalent annual uniform series payment A can be found by Equation (9.55), which is: .AR=G; i; n/ AR D D D D D h(cid:16)er.n C 1/ 1(cid:17) .er 1/ .1 n/i = (cid:140).er 1/ .ern 1/(cid:141) (9.55) (cid:0) .er C 1/(cid:17) .1 (cid:0) n/i = (cid:140).er (cid:0) 1/ .ern 1/(cid:141) (cid:0) (cid:0) 10/i = C (cid:0) 1/ (cid:0) 1 1/ (cid:0) G h(cid:16)er.n C (cid:0) $200 he0:05.10 1 C = (cid:2)(cid:0)e0:05 (cid:0) (cid:0) 1(cid:1) (cid:0)e0:05 (cid:2) $200(cid:140)0:16927(cid:141)=(cid:140)0:0332607(cid:141) $1;018: (cid:0) (cid:0) (cid:0)e0:05 10 C 1(cid:1) .1 (cid:0) 1(cid:1)(cid:3) (cid:0) Thus, it takes $1,018 uniform series payment to be equivalent to a $200 uniform ramp gra- dient over a 10-year period. The equivalent uniform series payments will vary considerably as the time increment changes. Note that the amount of the uniform series payment equiv- alent for the uniform ramp gradient was $200 more than that for the standard uniform gradient for this problem which was expected. 9.8 GEOMETRIC GRADIENT CONTINUOUS INTEREST FORMULAS D The geometric gradient is often called the exponential gradient, and thus the geometric gradi- ent continuous interest formulas may also be called the exponential gradient continuous interest formulas. The formulas from the discrete interest sections will be converted to continuous in- terest formulas. However, the formulas (9.46)–(9.49) did not include the conversion of g to a continuous expression. The formulas for b r will be left for student development. Similarly, one would need relationships to convert the discrete gradient interest .g/ to a continuous interest rate which will use the symbol .b/. Therefore: and and thus and g eb 1 (cid:0) D g/ .1 C D eb g/n .1 C D ebn ln.1 b D C g/: (9.56) (9.57) (9.58) (9.59) 134 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS The factors for the standard geometric gradient with discrete interest are: .P =A1; g; i; n/ .F=A1; g; i; n/ .A=A1; g; i; n/ D f D f D f (cid:140)1 (cid:140).1 (cid:140).1 (cid:0) C C .1 C i/n i/n g/=.1 i/(cid:141)n(cid:141)=(cid:140).i C g/n(cid:141) =(cid:140)i g/n(cid:141) =(cid:140)i .1 .1 (cid:0) (cid:0) C C (cid:0) g(cid:141) g(cid:141) g/(cid:141) g g g f i= (cid:140).1 i/n 1(cid:141) : g (cid:0) C (9.21) (9.25) (9.29) (cid:0) (cid:0) The conversion of these factors the geometric gradient continuous interest result in the following expressions for the cases where r b: ⁄ (cid:0)ebn= .ern/(cid:1)(cid:3) = h(cid:16)er eb(cid:17)io .P =A1; b; r; n/ .F=A1; b; r; n/ .A=A1; b; r; n/ n(cid:2)1 (cid:0) n(cid:2)(cid:0)ern n(cid:2)(cid:0)ern D D D ebn(cid:1)(cid:3) = h(cid:16)er ebn(cid:1)(cid:3) = h(cid:16)er (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) eb(cid:17)io eb(cid:17)io .er f (cid:0) 1/ = (cid:140)ern : 1(cid:141) g (cid:0) (9.60) (9.61) (9.62) 9.8.1 GEOMETRIC GRADIENT CONTINUOUS INTEREST EXAMPLE What would be the value at the end of 10 years of a geometric continuous gradient of 10%.b D 10%/ if the initial amount was $200 for a period of 10 years. The ﬁrst payment would be at the end of the 1st year and the last payment at the end of the 10th year. The interest rate is 10:52%.) 5%.r 5%/. (Note: if b 10%, then g D D (a) What is the ﬁnal payment? $200e0:10 D 9 (cid:2) D $200.e0:9/ $492. D (b) What is the total payments .TP/ of the gradients not including the interest? (cid:0)e0:1(cid:1) 2 C (cid:1) (cid:1) (cid:1) C (cid:0)e0;1(cid:1) n 1(cid:17) (cid:0) A1 (cid:0)(cid:0)ebn 1(cid:1)(cid:1) = (cid:16)eb 1(cid:17) (cid:0) (cid:0) D TP D D D D A1 (cid:16)1 C A1 (cid:0)ebn (cid:0) $200 (cid:0)e1:0 $3;268: (cid:0)e0:1(cid:1) C 1(cid:1) = (cid:16)eb 1(cid:17) (cid:0) 1(cid:1) = (cid:0)e0:1 1(cid:1) (cid:0) (cid:0) (c) What is the future worth including the compounding of interest? .F=A1; b; r; n/ F D D D D D n(cid:2)(cid:0)ern (cid:0) ebn(cid:1)(cid:3) = h(cid:16)er eb(cid:17)io (cid:0) (9.61) 0:05 A1 .F=A1; b; r; n/ $200 (cid:0)e10 $200. (cid:0) $3;969: (cid:0) (cid:2) e10 0:10(cid:1) = (cid:0)e0:05 (cid:2) 0:05390/ 1:069560/=. (cid:0) e0:10(cid:1) (cid:0) (d) Therefore, the total interest earned over the 10 years would be: TP F (cid:0) D $3;969 (cid:0) 3;268 D $701: 9.9. ESCALATION GRADIENT CONTINUOUS COMPOUNDING FORMULAS 135 (e) What is the present worth? .P =A1; b; r; n/ P D D D D A1 n(cid:2)1 A1 n(cid:2)1 (cid:0)ebn= .ern/(cid:1)(cid:3) = h(cid:16)er (cid:0) (cid:0)ebn= .ern/(cid:1)(cid:3) = h(cid:16)er eb(cid:17)io eb(cid:17)io (cid:0) (cid:0) (cid:0) 0:64872= 0:05390(cid:141) (cid:0) $200(cid:140) (cid:0) $2;407: (f ) What is the equivalent annual uniform series payment A? .A=A1; b; r; n/ A D D D D n(cid:2)(cid:0)ern (cid:0) A1 n(cid:2)(cid:0)ern ebn(cid:1)(cid:3) = her ebio 1/ = (cid:140)ern (cid:0) ebn(cid:1)(cid:3) = her (cid:0) .er f :05390(cid:141)(cid:140)0:05127=0:64872(cid:141) (cid:0) 1/ = (cid:140)ern (cid:0) (cid:0) (cid:0) 1:06956= .er f ebio 1(cid:141) g 1(cid:141) g (cid:0) (cid:140) (cid:0) 200 f 314: (cid:0) (9.60) (9.62) 9.9 ESCALATION GRADIENT CONTINUOUS COMPOUNDING FORMULAS The escalation gradient starts with the gradient in the ﬁrst period whereas the geometric gradient does not start the gradient until the second period. The factors for the discrete interest model will be converted to continuous interest factors. The factors will be developed for the case where r E. The escalation gradient is used primarily in the construction industry and used with constant dollars. The symbol E is used for the escalation gradient and is similar to that of g in the geometric gradient. The factors for the discrete case were: E and it will be left to the students to develop the case where r D ⁄ .PE=A1; E; i; n/ .FE=A1; E; i; n/ .AE=A1; E; i; n/ (cid:8)(cid:140).1 (cid:140).1 D D f D f C C C E/=.E E/=.E (cid:2)(cid:140).1 i/(cid:141) (cid:2) i/(cid:141) (cid:140).1 (cid:0) (cid:0) (cid:0) E/=.1 C E/n E/n (cid:0) C .1 C .1 1(cid:3)(cid:9) (cid:0) i/(cid:141)n i/n(cid:141) g i/n(cid:141) = (cid:140).1 (cid:0) C C C (cid:140)i.1 E/=.E i/(cid:141) (cid:140).1 i/n 1(cid:141) : g (cid:0) C (9.34) (9.38) (9.42) Similarly, one would need relationships to convert the discrete gradient interest .E/ to a continuous interest rate which will use the symbol .c/. Therefore: and E D ec 1 (cid:0) E/ .1 C D ec (9.63) (9.64) 136 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS and thus and E/n .1 C D ecn (9.65) c ln.1 E/: (9.66) C The conversion of these factors to continuous compounding of the interest and the gradi- D ent results in: .PE=A1; c; r; n/ .FE=A1; c; r; n/ .AE=A1; c; r; n/ (cid:140).ec/ = .ec (cid:140).ec/ = .ec (cid:140).er (cid:0) D f D f D f (cid:0) er /(cid:141) er /(cid:141) (cid:2) (cid:0) (cid:2) 1/ .ec/ = .ec (cid:140)(cid:140).ecn/ = .ern/(cid:141) (cid:140).ecn (cid:0) er /(cid:141) ern/(cid:141) g (cid:140).ecn (cid:0) (cid:2) 1(cid:141) g (cid:0) ern/(cid:141) = (cid:140).ern : 1/(cid:141) g (cid:0) (cid:0) (9.67) (9.68) (9.69) 9.9.1 ESCALATION GRADIENT CONTINUOUS INTEREST EXAMPLE What would be the value at the end of 10 years of a escalation gradient of 10%.c 10%/ if the initial amount was $200 for a period of 10 years. The ﬁrst payment would be at the end of 5%/. the ﬁrst year and the last payment at the end of the 10th year. The interest rate is 5%.r (Note: if c 10:517%.) 10%, E D D D (a) What is the ﬁnal payment? $200 e0:10 D 10 (cid:2) $200.2:71828/ $544. D (b) What is the total payments .TP/ of the gradients not including the interest? The expression D is converted from the discrete form to the continuous form. PT E D D D PT E D 1/ =E E/ ..1 E/n C (cid:0) 1/ = .ec A1.1 C A1 .ec/ .ecn (cid:0) (cid:0) $200.1:10517/.2:71828 $3;612: 1/ 1/=.1:10517 1/ (cid:0) (cid:0) (c) What is the future worth including the compounding of interest? .FE=A1; c; r; n/ D f FE D D er /(cid:141) (cid:140).ecn (cid:2) er /(cid:141) (cid:0) (cid:140).ecn (cid:0) (cid:140).ec/ = .ec f (cid:140).ec/ = .ec A1 $200(cid:140).1:10517=.1:10517 $200.1:10517=0:0539/.1:06956/ $4;386: ern/(cid:141) g ern/(cid:141) g 1:05127/(cid:141) (cid:0) (cid:0) (cid:0) (cid:2) D D (d) Therefore, the total interest earned over the 10 years would be: FE (cid:0) PT E D $4;386 (cid:0) $3;612 D $774 .2:71828 (cid:2) (cid:0) 1:648720/ (9.45) (9.68) (e) Determine the present worth 9.10. SUMMARY OF GRADIENT EXPRESSIONS 137 .PE=A1; c; r; n/ D f PE D D er /(cid:141) (cid:2) er /(cid:141) (cid:0) (cid:140).ec/ = .ec f (cid:140).ec/ = .ec A1 $200(cid:140).1:10517=.1:10517 $200(cid:140)13:301(cid:141) $2;660: (cid:0) (cid:2) (cid:140).ecn/ = .ern/ 1(cid:141) g (cid:0) (cid:140).ecn/ = .ern/ (cid:0) 1:05127/(cid:141) (cid:0) D D 1(cid:141) g (cid:140):64872(cid:141) (cid:2) (9.67) (f ) What is the equivalent annual escalation payment Ae? .AE=A1; c; r; n/ er /(cid:141) 1/ .ec/ = .ec (cid:140).er (cid:0) 1/ .ec/ = .ec A1 $200(cid:140)0:05127/.1:10517/=.1:10517 (cid:0) (cid:140).er f (cid:2) er /(cid:141) (cid:140).ecn (cid:0) (cid:0) (cid:2) (cid:0) (cid:140).ecn ern/(cid:141) = (cid:140).ern/ (cid:0) ern/(cid:141) = (cid:140).ern (cid:0) 1:05127/(cid:141) (9.69) 1(cid:141) g 1/(cid:141) g (cid:0) D f AE D D (cid:0) 1:6487/=.0:6487/ (cid:140)1:06958=0:64872(cid:141) (cid:2) (cid:140).2:71828 (cid:2) (cid:0) $200(cid:140)1:05124(cid:141) $347: D D Note that the escalation gradient continuous compounding is larger than the escalation geometric gradient because of the additional gradient period. The continuous compounding formulas are presented in Table 9.2. Note that the values of the escalation geometric continuous compounding gradient are greater than the geometric continuous compounding by the factor b which is the continuous compounding interest rate plus one—that is, A for when c D the geometric gradient is 314 and e0:1 347. 1:10517 and the A for escalation is 1:10517 b by ec 314 D D D (cid:2) 9.10 SUMMARY OF GRADIENT EXPRESSIONS The discrete gradient expressions were derived in the ﬁrst sections using discrete interest com- pounding and the results are summarized in Table 9.1. An example problem was solved in each section to illustrate the application of the formulas. The next four sections derived continuous interest compounding expressions and the results are summarized in Table 9.2. The diﬀerence in the results was relatively small and the continuous interest results tended to be larger for future worth and annual payments. The diﬀerences between the two compounding interest rates will be greater for a greater number of time periods and higher interest rates. This will happen in long range projects where life cycle costs are involved over periods such as 50–100 years in the life of a bridge, highway interchange, or large oﬃce building. The continuous interest is also 138 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS t s e r e t n i s u o u n i t n o c d n a s t n e m y a p e t e r c s i d — s n o i s s e r p x e c i m o n o c e f o s r o t c a f g n i d n u o p m o c s u o u n i t n o C : 2 . 9 e l b a T Payment TypeFactor NameFindGivenSymbolFormulaA. Single Payment Present WorthPF(P/F, r, n)e-rnFuture WorthFP(F/P, r, n)ernB. Uniform Payment (Uniform Series)Sinking FundAF(A/F, r, n)[(er-1)/(ern-1)]Capital RecoveryAP(A/P, r, n)[ern(er-1)/(ern-1)]Future WorthFA(F/A, r, n)[(ern-1)/(er-1)]Present WorthPA(P/A, r, n)[(ern-1)/ (ern(er-1))]C. Uniform Gradient Expressions Standard Uniform GradientUniform Gradient Present WorthPG( P/G, r, n){[(ern-1) - n(er-1)]/[(er-1)2 ern)]}Uniform Gradient Future WorthFG( F/G, r, n){[(ern-1) - n(er-1)]/[(er-1)2 )]}Uniform Gradient Uniform SeriesAG( A/G, r, n){[(ern-1) - n(er-1)]/[(er-1)( ern -1)]}Uniform Ramp GradientUniform Ramp Gradient Present WorthPRG( PR/G, r, n){[(er((n+1)-1) - (n+1)(er-1)]/[(er-1)2(ern)]}Uniform Ramp Gradient Future WorthFRG( FR/G, r, n){[(er((n+1)-1) - (n+1)(er-1)]/[(er-1)2 ]}Uniform Ramp Gradient Uniform SeriesARG( AR/G, r, n){[(er((n+1)-1) - (n+1)(er-1)]/[(er-1)2(er n-1)]}D. Geometric Gradient Expressions Geometric GradientGeometric Gradient Present WorthPA1,b(P/A1 b, r, n) {[1-(ebn/ern)]/[er - eb)]}If b=r(P/A1, b=r, n) n/erGeometric Gradient Future WorthFA1,b(F/A1, b, r, n) {[ern-ebn)]/[er - eb)]}If b=r(F/A1, b=r, n)n/er(n-1)Geometric Gradient Uniform SeriesAA1,b(A/A1, b, r, n) {[ern-ebn)]/[er - eb)]} {[(er -1) / (ern-1)]}If b=r(A/A1, b=r, n) [n{(ern )/(ern-1)] * [(er-1)/(er)]Escalation GradientEscalation Gradient Present WorthPᴇA1,c(Pᴇ/A1, c, r, n) {[((ec)/(ec-er))] * [(ecn - ern)/ern]If c=r(Pᴇ/A1, c=r, n) nEscalation Gradient Future WorthFᴇA1.c(Fᴇ/A1, c, r, n) {[((ec)/(ec-er))] * [(ecn - ern)]If c=r(Fᴇ/A1, c=r, n) nernEscalation Gradient Uniform SeriesAᴇA1,c(Aᴇ/A1, c, r, n) {[((er-1)(ec)/(ec-er)] * [(ecn-ern)/(ern-1)]}If c=r(Aᴇ/A1, c= r, n{[n(er -1)ern/ (ern -1)}Notation:P=Present Worth; i = eﬀ ective discrete interest rate per period; A=uniform end-of-period payments; n = number of periods;F=Future Worth; g=Geometric Gradient Rate; G=Uniform Gradient Amount; ᴇ = Escalation Gradient Rate;A1 = Initial Geometric Gradient Amount and Initial Escalation Gradient Amountused in the evaluation of interest rates on certiﬁcates of deposits in many institutions to show higher return rates. The formulas will be utilized in many of the problems in this chapter. 9.11. REFERENCES 139 9.11 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and En- gineers, New Academic Science Limited, Tunbridge Wells, UK, pp. 25–58, 2012. 113, 142 [2] Park, Chan S., Contemporary Engineering Economics, 2nd ed., Addison-Wesley, Menlo Park, CA, p. 803, 1997. 113 [3] Newnan, Donald G., Eschenbach, Ted G., and Lavelle, Jerome P., Engineering Economic Analysis, 11th ed., Oxford University Press, New York, p. 655, 2012. 113 [4] Park, Chan S. and Sharp-Bette, Gunter P., Advanced Engineering Economics, John Wiley & Sons, Inc., New York, pp. 38–128, 1990. 113, 129, 142 9.12 EVALUATIVE QUESTIONS 1. If the time period is 5 years and the discrete interest rate is 10%, ﬁnd the following values for the uniform gradient: (a) .P =G; i (b) .F=G; i (c) .A=G; i 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D 2. If the time period is 5 years and the discrete interest rate is 10% and the geometric gradient is 5%, ﬁnd the following values: (a) .P =A1; g (b) .F=A1; g (c) .A=A1; g 5%; i 5%; i 5%; i 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D D D D 3. If the time period is 5 years and the interest rate is 10% and the escalation rate is 5%, ﬁnd the following values: (a) .PE =A1; E (b) .FE =A1; E (c) .AE =A1; E 5%; i 5%; i 5%; i 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D D D D 140 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS 4. The cost of materials for a project is $1,000,000 per year for the next 5 years. The interest rate (return rate) is expected to be 15% and the escalation rate is predicted to be 5%. What is the expected present worth of the materials for the project (a) using discrete interest calculations with escalation and (b) using continuous interest and escalation calculations? 5. A contractor is building a high rise apartment which will take 3 years to build. The contrac- tor predicts that the materials will be $3,000,000 per year. Consider these as end-of-year expenses. He expects the materials to escalate by 8% per year. His expected return rate is 20%. (a) What is the present worth of this project to the contractor? (b) What is the Future Worth of the project to the contractor? (c) What is the annual end-of-year payment? (d) If the project was considered as a geometric gradient, what is the annual end-of-year payment? (e) The annual payment for the gradient was a beginning of period payment, what is the amount? 6. If the time period is 5 years and the nominal interest rate is 10%, ﬁnd the following values: (a) .P =F; r 10%; n D 10%; n D 5/ 5/ (b) .F=P; r (c) If F D D D $300, ﬁnd the value of P 7. If the time period is 5 years and the discrete interest rate is 10%, ﬁnd the following values: (a) .P =F; i (b) .F=P; i (c) If P D D 10%; n 10%; n D 5/ 5/ D D $300, ﬁnd the value of F 8. If the time period is 5 years and the nominal interest rate is 10%, ﬁnd the following values: (a) .P =A; r (b) .P =F; r (c) .A=P; r (d) .A=F; r (e) .F=P; r 10%; n 10%; n 10%; n 10%; n 10%; n D D D D D D D D D D 5/ 5/ 5/ 5/ 5/ 5/ (f ) .F=A; r 10%; n D $200, ﬁnd the values of F and P D (g) If A D (h) If P D $200, ﬁnd the values of F and A 9. If the time period is 5 years and the discrete interest rate is 10%, ﬁnd the following values: 9.12. EVALUATIVE QUESTIONS 141 D D D D D 10%; n 10%; n 10%; n 10%; n 10%; n 10%; n D D D D D 5/ 5/ 5/ 5/ 5/ 5/ (a) .P =A; i (b) .P =F; i (c) .A=P; i (d) .A=F; i (e) .F=P; i (f ) .F=A; i (g) If A (h) If P D D D $200, ﬁnd the values of F and P D $200, ﬁnd the values of F and A 10. If the time period is 5 years and the nominal interest rate is 10%, ﬁnd the following uniform gradient factors: (a) .P =G; r (b) .F=G; r (c) .A=G; r 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D 11. If the time period is 5 years and the nominal interest rate is 10%, ﬁnd the following uniform ramp gradient values: (a) .PR=G; r (b) .FR=G; r (c) .AR=G; r 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D 12. If the time period is 5 years and the discrete interest rate is 10% and the geometric gradient g rate is 6%, ﬁnd the following values: (a) .P =A1; g (b) .F=A1; g (c) .A=A1; g (d) If A1 D 6%; i 6%; i 6%; i 10%; n 10%; n 10%; n 5/ 5/ 5/ D D D D D D D D D $200, what are the values for P and F ? 13. If the time period is 5 years and the nominal interest rate is 10% and the geometric gradient b rate is 6%, ﬁnd the following values: (a) .P =A1; b (b) .F=A1; b 6%; r 6%; r 10%; n 10%; n 5/ 5/ D D D D D D 142 9. GRADIENT ECONOMIC FACTORS AND EQUATIONS (c) .A=A1; b 6%; r 10%; n 5/ D D $200, what are the values for P , A, and F ? D (d) If A1 D 14. If the time period is 5 years and the nominal interest rate is 10% and the escalation gradient c rate is 6%, ﬁnd the following values: (a) .PE=A1; c (b) .FE=A1; c 6%; r 6%; r D D D D 10%; n 10%; n (c) .AE=A1; c 6%; r 10%; n D D 5/ 5/ 5/ (d) If A1 D D D $200, what are the values for PE, AE, and FE? D 15. If the time period is 5 years and the nominal interest rate is 10% and the geometric gradient b rate is 10%, ﬁnd the following values: (a) .P =A1; b 10%; r 10%; n D D (b) .F=A1; b 10%; r 10%; n D 5/ 5/ (c) If A1 D D D $200, what are the values for P , A, and F ? D 16. If the time period is 5 years and the nominal interest rate is 10% and the escalation gradient c rate is 10%, ﬁnd the following values: (a) .PE=A1; c (b) .FE=A1; c 10%; r 10%; r D D D D 10%; n 10%; n (c) .AE=A1; c 10%; r 10%; n D D 5/ 5/ 5/ (d) If A1 D D D $200, what are the values for PE, AE, and FE D 17. Show the derivation of the equations for the geometric gradient continuous interest for- mula when the continuous interest rate r and the continuous gradient b are equal. 18. Show the derivation of the equations for the escalation gradient continuous interest for- mula when the continuous interest rate r and the continuous escalation gradient c are equal. 19. Construct a table in a spreadsheet and calculate the expressions for the Uniform Gra- dient and the Uniform Ramp Gradient factors of .P =G; i; n/, .F=G; i; n/, .A=G; i; n/, .PR=G; i; n/, .FR=G; i; n/, and .AR=G; i; n/ for i 100. Compare the values calculated with those in the various reference books [1–4], but it may be diﬃcult as the only ones usually given are .P =G; i; n/ and .A=G; i; n/. 10%, and n 1–60 and n D D D 20. Construct a table in a spreadsheet and calculate the geometric gradient expressions for the 5%, and 100. Compare the values calculated with those calculated for Problem 2. factors of .P =A1; g; i; n/, .F=A1; g; i; n/, and .A=A1; g; i; n/, for i n 1–60 and n 10%, g D D D D 21. Construct a table in a spreadsheet and calculate the escalation gradient expressions for 9.12. EVALUATIVE QUESTIONS 143 the factors of .PE =A1, E; i; n/, .FE =A1, E; i; n/, and .AE =A1; E; i; n/, for i 5%, and n Problem 3. D 100. Compare the values calculated with those calculated for 1–60 and n 10%, E D D D 22. Construct a table in a spreadsheet and calculate the expressions for the Uniform Gradient and the Uniform Ramp Gradient factors with continuous compounding of .P =G; r; n/, 10%, and .F=G; r; n/, .A=G; r; n/, .PR=G; r; n/, .FR=G; r; n/, and .AR=G; r; n/ for r n 100. Compare the values calculated with those in Problem 8. 1–60 and n D D D 23. Construct a table in a spreadsheet and calculate the geometric gradient expressions for the 6%, and 100. Compare the values calculated with those calculated for Prob- factors of .P =A1; b; r; n/, .F=A1; b; r; n/, and .A=A1; b; r; n/, for r n D lem 13. 1–60 and n 10%, b D D D 24. Construct a table in a spreadsheet and calculate the escalation gradient expressions for the factors of .PE =A1; c; r; n/, .FE =A1; c; r; n/, and .AE =A1; c; r; n/, for r 6%, and n D Problem 14. D 100. Compare the values calculated with those calculated for 1–60 and n 10%, c D D C H A P T E R 10 145 Depreciation Terms, Methods, and Systems 10.1 INTRODUCTION Depreciation is one of the most important deductions that businesses make to recover their initial investment in facilities and equipment used to produce their products and to lower their taxes. Every enterprise has some depreciation as facilities such as oﬃces and computers are depreciable assets as well as items such as race horses, breeding cattle, hogs, goats or sheep, amusement parks, manufacturing facilities, and equipment, and almost anything you can think of to produce a product or service is depreciable. Depreciation is the item which causes major corporations to keep two sets of books, one for the government for paying taxes and another for the stockholders to show their earnings and proﬁts. The primary sources of references used for depreciation in this work is Publication 946, How to Depreciate Property, for 2016 Returns [1]. Depreciation is extremely complicated, but the basics presented will meet most of the practical cases that are encountered in preparing estimates for projects and project evaluations. A brief review of some of the terms from Chapter 1 will be repeated as they are critical in the determination of depreciation and its impact upon proﬁts and cash ﬂows. The basic terms are as follows. 1. Revenues Income or money generated from Sales of Products and Services, Royalties, Financial Investments, Gambling/Lottery Winnings, etc. 2. Expenses Income or money consumed in production of Products and Services such as labor, materials, equipment, computers, etc. 3. Depreciation D An annual income tax deduction that allows for the recovery of the cost or other basis of certain property over the time you use the property. It is an allowance for the wear and tear, deterioration or obsolescence of the property. IRS Publication 946 gives details on the calculations for depreciation [2]. 4. Tax Rate D A percentage amount applied to the proﬁts to determine the amount of taxes. The amount of taxes and proﬁts are determined from these terms by the relationships previously presented in Chapter 1: D D 146 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS Taxes Proﬁts D D 10.1.1 CASH FLOWS .Revenues Revenues Expenses Expenses (cid:0) Depreciation/ Taxes: Tax Rate (cid:2) (10.1) (10.2) (cid:0) (cid:0) (cid:0) Cash Flows Before Taxes (CFBT) considers only net cash ﬂows. This analysis is used when taxes cannot be considered and one is considering only the expenses. In general, one can consider: CFBT .Cash Flows Before Taxes/ Revenues (cid:0) D Expenses: (10.3) Cash Flows After Taxes (CFAT), considers taxes as an additional expense and is a more realistic of the actual cash ﬂows. CFAT is typically used rather than CFBT as taxes can be a large item in the cash ﬂows. Taxes are generally calculated based on a percentage of taxable income, and this is generally often represented as 40% in the U.S., but many of the major companies in the U.S. pay no income taxes. Some oil-rich countries in the middle east have zero income taxes whereas in some of the Northern European countries the total taxes reach 70%, but in these countries the people generally are satisﬁed in paying higher taxes as they often provide government pensions and/or healthcare. In Denmark, the tax on a new automobile was 180% and thus one paid 2.8 times the car price to purchase a new car. The income tax rate in the U.S. was as high as 90% in the 1950’s, but was reduced during the last half of the 20th century to under 40% for individuals and corporate taxes were recently reduced to 20%. Although new tax laws were passed in 2017 for 2018, the details have not been available from the Internal Revenue Service. Very high tax rates are often imposed during wars to fund the war eﬀort. The 40% presented in most problems represents an estimate based upon the total of the federal, state and local taxes and although federal taxes are decreasing, it may cause an increase in the state and local taxes. The taxable income is based upon the net cash ﬂows less the depreciation expenses. Thus, the amount allowed for depreciation must be determined to calculate the taxable income and taxes paid: CFAT .Cash Flows After Taxes/ Revenues Expenses Taxes: (cid:0) (cid:0) D (10.4) 10.2 DEPRECIATION TERMS AND DEFINITIONS Depreciation is the systematic allocation of the cost of a capital asset over the recovery period (useful life). IRS Publication 946 [1–11], which can be downloaded from the IRS website at http://www.irs.gov, is the best publication on depreciation for most individuals and is up- dated yearly for the new tax laws. Depreciation can be applied to nearly everything, but one notable exception is land. There are a wide variety of terms applied in depreciation as to de- preciable property, depreciation life, and depreciation techniques. Many counties have diﬀerent methods for depreciation, but the acceptable methods used in the U.S. system of depreciation will be emphasized. 10.2. DEPRECIATION TERMS AND DEFINITIONS 147 10.2.1 DEPRECIATION CLASSES OF PROPERTY The two major classes of depreciable property are tangible property and intangible property. Some examples of each are as follows. A. Tangible Property—property you can see and touch [3] 1. Personal Property—assets such as automobiles, houses, buildings, machines, com- puter equipment, furniture, etc. 2. Real Property—land and buildings erected or agricultural produce growing on the land. The land is not depreciable, but buildings erected on the land are depreciable. B. Intangible Property—property that has value, but cannot be seen or touched [3] 1. Intangible Property—it includes items such as goodwill, computer software, copy- rights, royalty, franchises, patents, trademarks, trade names and permits and licenses. 10.2.2 RECOVERY PERIOD AND DEPRECIATION LIFE Recovery period is the life used for determining the depreciation life for recovery of the asset. However, there can be diﬀerent permissible recovery periods permitted by the tax codes as most companies want rapid recovery periods, but some want long recovery periods as their income increases with increasing asset value and depreciation reduces the asset value. Depreciable items must have a useful life of one year or more, be used in business or used to produce income, and they lose value via obsolescence, wear and tear, or natural causes, and are not inventory, stock in trade, or investment property. There are diﬀerent types of asset life and the major types of asset life for consideration in determining the recovery period and the terms often considered are useful life, physical life economic life, and class life. The key term is the class life and is deﬁned by the Internal Revenue Service (IRS) in the U.S. Class life is the “number of years that establishes the property class and recovery period for most types of property under the General Depreciation Schedule (GDS) and the Alternative Depreciation Schedule (ADS)” [4]. The various assets are assigned a speciﬁc asset class and that asset class will have a recovery period for that class life. The recovery periods used in the Modiﬁed Cost Recovery System-General Depreciation System (MARCS-GDS) for property classes are presented in Table 10.1. The recovery periods have been set into nine classes to make classiﬁcation easier. The property class is the recovery period in years, that is a three-year property class implies that the recovery period is three years. The MACRS-ADS and MACRS-GDS have speciﬁc recovery periods and the recovery period for the MACRS-GDS is usually less than that of the MACRS-ADS. The GDS class life values are generally less than the asset class life period and is the accelerated depreciation life. 148 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS Table 10.1: MACRS-GDS property classes and types of property [4] One major exception is the recovery period for automobiles which is ﬁve years under the ADS and the class life recovery period is only three years. This occurred as loans for new automobiles increased from three years to ﬁve years and the government decided the class life should also increase. The ADS class life values are equal or greater than the asset class life period. The recovery periods are presented in Table 10.2 for several asset classes. Property Class LifeRecovery PeriodExamples of Types of Property3-year propertyTrailer units for over-the-road use; special tools for—manufacture of motor vehicles, fabricated metal products, glass products, and rubber products.5-year propertyAutomobiles, taxis, buses, light trucks, heavy duty trucks; information systems-computers and peripherals; construction; manufacture of apparel; cutting of timber; manufacture of chemicals and allied products; manu-facture of electronic components, products, and systems.7-year propertyEquipment for the manufacture of cement, glass products, primary fer-rous metals, foundry products, fabricated metal products, electrical and non-electrical machinery, motor vehicles, ship and boat building; oﬃ ce furniture and ﬁ xtures. (If no life is established, a product is classiﬁ ed as 7-year property)10-year propertyPetroleum reﬁ ning equipment; equipment for the manufacture of grain and grain mill products; ship and boat building dry docks.15-year propertyPipeline transportation, water transportation, telephone distribution equipment; electrical utility nuclear power plant; municipal wastewater treatment.20-year propertyElectric, gas, water and steam utility services; gas utility production plants; electric utility hydraulic production plants; gas utility distribution plants.25-year propertyWater utilities, municipal sewer.Residential Rental Property 27.5-year Residential Structures (depreciated over 27.5 years).Nonresidential Property 39-yearBuildings (depreciated over 39 years).Table 10.2: Class life and recovery periods for selected asset classes [5] 10.2. DEPRECIATION TERMS AND DEFINITIONS 149 Asset ClassAsset DescriptionClass Life (Years)Recovery Period (Years)General GDSAlternative ADS0.11Oﬃ ce furniture101277770.12Information systems, including computers6550.13Data handling, except computers6560.22Automobile, taxis 3550.23Buses9590.24Heavy general purpose trucks5661.21Cattle, breeding or dairy71.223Racehorse, above 2 yrs. agenone1253756620282810Mining10101071014711714714714715771271271213Oﬀ shore drilling7.557.513.3Petroleum reﬁ ning16101615Construction24.4Manufacture of wood products 1030.1Manufacture of rubber products1430.2Manufacture of plastic products1132.1Manufacture of glass products1433.2Manufacture of primary nonferrous metals 1433.3Manufacture of foundry products1433.4Manufacture of primary steel mill products 1534.0Manufacture of fabricated metal products1235.0Manufacture of electrical machinery and other mechanical products101036.0Manufacture of electronic components, products65636.1Semiconductor manufacture equipment55537.1Manufacture of motor vehicles1237.2Manufacture of aerospace products1039.0Manufacture of athletic, jewelry, and other goods1248.4Satellite space segment property (satellites)85849.4Central steam utility production and distribution49.3Liqueﬁ ed natural gas plant22152251.0Municipal sewer50255080.0Th eme and amusement parks 12.5712.5GDS = General Depreciation System ADS = Alternative Depreciation System 150 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS 10.2.3 DEPRECIATION CONVENTIONS The possible depreciation conventions are full-year, mid-year, mid-quarter, and mid-month. The full-year convention was used previously, but now is no longer in use because all depreciable pur- chases made during the ﬁrst year are not on the ﬁrst day of the year. Thus, mid-year convention is the most used convention as it considers that purchases are made throughout the year. This is used when all purchases are spread out through the year and only one depreciation rate is used for the year. Only mid-year convention will be considered in detail. Mid-year convention increases the number of years for depreciation calculations. Thus, a 5-year mid-year depreciation will have only half of the depreciation in the 1st and 6th years as it assumes the purchases are made throughout the year. If most purchases are made at the end of the year, then the mid-quarter or mid-month conventions would be required. 10.3 TRADITIONAL METHODS OF DEPRECIATION There are numerous methods of depreciation and only a few of the more commonly used meth- ods will be presented in detail. The straight line method is the traditional method which gave a uniform amount of depreciation over the life of the asset. The declining balance method gave a uniform percentage of depreciation over the investment life which gave larger amounts ini- tially, but which has the problem of not going to zero. The MACRS system is a combination of both systems, giving the higher initial amounts of depreciation via the declining balance method initially and then switching to the straight line method to fully depreciate the item. The production-based system is not used in the U.S., but is used in other parts of the world and is based on the amount of use of the facility. There are special depreciation methods, and in the U.S., the method “Section 179” permits expensing the entire purchase in the ﬁrst year, but there are several restrictions. Each of the methods will be present in more detail. The depreciation amounts are used to update the book value of the asset. The book value is the initial invest minus the sum of all the depreciations up to the end of the year under con- sideration. It can be expressed in equation form by: BV k B (cid:0) D Di ; K X 1 i D (10.5) where B Di BV k D D D initial investment amount depreciation in years i book value at end of year k. 10.3. TRADITIONAL METHODS OF DEPRECIATION 151 10.3.1 STRAIGHT LINE DEPRECIATION METHOD The straight line method gives a constant amount of depreciation per year and this is why it was preferred as it is the easiest method. The expression for straight line depreciation is: Dk .B (cid:0) D SV/=N; (10.6) where depreciation amount for all years k.k 1; N / D investment (purchase cost salvage value at end of life of asset at N years (usually taken to be zero) depreciable life of asset, years year of interest. installation costs of asset) C D Dk B SV N k D D D D The salvage value is taken as zero when using the MACRS straight line schemes, and the actual net disposal value would be treated as a capital gain (or loss) when the asset is disposed. Also, the prediction of a salvage value several years in the future is diﬃcult and by taking the value as zero, the salvage monies received could be taken as a capital gain. In some cases, the cost of removal would be greater than any salvage value and would be diﬃcult to predict, but could be considered as a capital loss. One must not list only the purchase price, but also any installation costs such as connecting utilities, preparing foundations and other necessary items to make the purchase operable as the total cost is depreciable. 10.3.2 DECLINING BALANCE DEPRECIATION METHOD The declining balance method is a constant percent of depreciation of the book value. It is a faster depreciation method in the initial years than the straight line method. However, the depreciation amounts decreases in the later years and become less than straight line and the total depreciation never reaches zero. The expression for declining balance depreciation, for full year depreciation, is: Dk .B/ (cid:2) D R.1 (cid:0) R/k 1; (cid:0) (10.7) where year of interest depreciation for year k.k investment (purchase cost depreciation rate depreciable life of asset, years salvage value (the salvage value is not included in the calculations). 1; N / installation costs of asset) 100/ (usually 150% or 200%)/.N D C D (cid:2) D k D Dk B R N SV D D D D If the life is 10 years .N / and the depreciation rate of 200% is used, then R (cid:2) 0:2, where R is a decimal less than 1.0. The rate of 200% implies the value initially 200=.10 D 100/ D 152 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS would be twice that of straight line depreciation and 150% implies that the initial value would be 1.5 times that of straight line method. However, the amount for declining balance method decreases but never becomes zero. This method is not used directly today as a separate depreci- ation method, but it is used in combination with straight line depreciation be presented later as part of the MACRS. Using the mid-year convention, the depreciation rate would be 100% or r 0:10 for the ﬁrst year. For mid-year convention, the declining balance is a more diﬃcult expression: D D1.%/ Dk.%/ R=.100 " 1 R (cid:0) D D The amount of depreciation would be N 2/ (cid:2) D .%/i # : (cid:2) k 1 (cid:0) X 1 i D (10.8) (10.9) Dk.$/ Bk 1 (cid:0) (cid:2) D Dk.%/: (10.10) 10.3.3 DEPRECIATION EXAMPLE What is the depreciation amounts using mid-year convention for an investment of $10,000 with an asset life of 5 years using straight line and double declining balance (200%)? The straight line depreciation would be 1/5 or 20%, that is $2,000. The 200% declining balance would be 2 20 or 40%. With the mid-year convention, the ﬁrst year values and last year values will be half of that calculated. Formulas (10.6) and (10.7) were used to calculate the values with: (cid:2) B N D D 10;000 5 depreciable life of asset, years (however it will take 6 years to fully depreciate the item as only 1/2 of the amount calculated is allocated in the ﬁrst and last years) For example, in year 3 of the DDB, the amount of depreciation would be using Equa- tions (10.8), (10.9), and (10.10): D1.%/ D3.%/ D3.$/ D D D 200=.100 0:40.1 (cid:0) $10;000 5 (cid:2) 0:20 (cid:2) 2/ D 0:32/ (cid:0) .0:192/ D (cid:2) 0:20 0:192 D $1;920: Assume the asset is disposed in the last year. The calculation results are in Table 10.3. SL (Straight Line) DDB (Double Declining Balance) 10.3. TRADITIONAL METHODS OF DEPRECIATION 153 D Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 1=5 20% D ½.0:20 0:20 0:20 0:20 0:20 (cid:2) ½.0:20 10;000/ (cid:2) 10;000 10;000 10;000 10;000 (cid:2) (cid:2) (cid:2) D D D D $2;000 $2;000 $2;000 $2;000 D 10;000/ (cid:2) D D D D D D D $1;000 Year 1 Year 2 2=5 D 40% D ½.0:40 0:40 Year 3 Year 4 0:40 0:40 Year 5 $1;000 Year 6 0:40 (cid:2) 1=2.0:40 D D D D D D 10;000/ $2;000 (cid:2) 8;000 4;800 1;920 1;152 (cid:2) (cid:2) (cid:2) D $3;200 $1;920 $1;152 $691:20 D D D D 691:20/ $207:36 D (cid:2) .20:00%/ .32:00%/ .19:20%/ .11:52%/ .6:912%/ The double-declining balance method is a percentage of the book value, so after the ﬁrst year the amount is 40% of the book value of the previous year. In the ﬁrst and last years, the amount is only ½ as a result of being mid-year convention. However, in the MACRS systems, the switch over in the last years is to straight line and the DDB method is not used. Table 10.3: Straight line and declining balance depreciations and asset book values The initial depreciation is much more rapid with the declining balance in the early years (years 1 and 2 for this example), but it never reaches zero. The MACRS uses declining balance until the amount of depreciation is less than or equal to that of the straight line method for the remaining life. The straight line depreciation is based upon the remaining investment and the remaining life, and the straight line depreciation for year 4 would be the book value divided at the end of year 3 by the remaining life for year 3 which is 2.5 years (for years 4 and 5, and 1/2 year of year 6): SL Depreciation .year 4/ $2;880 .book value at the end of year 3/ D 2:5 .2:5 years remain after year 3/ D $1;152: YearLifeStraight LineDeclining BalanceRemaining ($) at Year EndDepreciationBook Value ($)Depreciation ($)Book Value ($)05010,0000.0010,000.0014½1,0009,0002,000.008,000.0023½2,0007,0003,200.004,800.0032½2,0005,0001,920.002,880.0041½2,0003,0001,152.001,728.005½2,0001,000691.201,036.80601,0000207.36829.44Total10,000 9,170.56154 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS This is the same amount ($1,152) as the declining balance amount for year 4, so the switch to straight line would be made at the end of year 3 on a straight line basis. The original straight line depreciation is no longer used $2,000, but a straight line depreciation over the remaining 2.5 years which is $1,152. Since the straight line method is used, the depreciation for years 4 and 5 will also be $1,152 and year 6 would be for ½ year and thus $576. The total depreciation would be 2;000 3;200 1;920 1;152 1;152 576 C D C C C C 10;000. 10.4 THE MACRS DEPRECIATION SYSTEMS The MACRS are the depreciation systems used for depreciation. The MACRS systems follow the declining balance method with a switch-over to the straight line method. A more detailed explanation of the MACRS systems are in Publication 946. The salvage value in the MACRS system is taken as zero in the calculation of the depreciation amounts. The two MACRS systems are: 1. GDS—General Depreciation System 2. ADS—Alternative Depreciation System 10.4.1 MACRS-GDS RECOVERY PERIODS AND PROPERTY CLASSES The GDS is generally used unless ADS is required by law or if the user wants a slower depreci- ation. The GDS has the faster depreciation schedule as more depreciation occurs in the earlier years than in the ADS. The detailed Recovery Period and Property Classes for the GDS are listed in Table 10.1. The 200% and 150% values refer to the declining balance method percent- age amount used before the switch to the straight line depreciation method. The nine property classes and recovery periods most frequent used [6] are: (1) 3-yr property (200%) (2) 5-yr property (200%) (3) 7-yr property (200%—any property that does not have a class life speciﬁed is considered to have a 7-yr class life.) (4) 10-yr property (200%) (5) 15-yr property (150%) (6) 20-yr property (150%) (7) 25-yr property (150%) (8) Residential Rental Property (27.5-yr, straight line) (9) Non-Residential Real Property (39-yr, straight line) The GDS does permit other systems and they are used in special instances when acceler- ated depreciation is not preferred. Accelerated depreciation leads to lower taxes paid, but also leads to lower proﬁts or even losses which may not be desired. A list of all the possible ADS [6] system is as follows. 1. 200% declining balance for 3-, 5-, 7-, and 10-yr property 10.4. THE MACRS DEPRECIATION SYSTEMS 155 2. 150% declining balance over a GDS recovery period for all property used in farming busi- nesses (except real property) and for all other property in the 15-, 20-, and 25-yr property classes 3. straight line for 3-, 5-, 7-, 10-, 15-, 20-, and 25-yr property as well as the residential rental property and non-residential real property 4. 150% declining balance over an ADS recovery period for property in the 3-, 5-, 7-, and 10-yr property classes. 10.4.2 MACRS-ADS RECOVERY PERIODS AND PROPERTY CLASSES The ADS system almost always results in equal or longer recovery periods than the GDS [6]. For example, the personal property without a speciﬁed class life is 12 years in the ADS system compared to the 7 years in the GDS system. Some of the diﬀerences are the following. 1. See Table 10.2 Class Life Asset Depreciation Range (ADR) System. 2. Any personal property without a class life speciﬁed is 12 years. 3. Any real property without a class life speciﬁed is 40 years. There are certain instances where the ADS must be used instead of the GDS. The ADS is required for the following. 1. Any tangible property predominantly used outside the U.S. 2. Any tax-exempt use property (churches, non-proﬁt organizations, etc.). 3. Any property predominantly used in farming or agricultural business. 4. Any imported property covered by the executive order of the President of the U.S. The primary systems of ADS used in practice are as follows. 1. 150% declining balance over the ADS recovery period. 2. Straight Line over the GDS Recovery Period (farming). 3. Straight Line of the ADS recovery Period. 156 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS 10.4.3 MACRS-GDS MID-YEAR RECOVERY PERIODS The MACRS is a declining balance method with a switchover to straight line [7]. This is the most commonly used system. The MACRS assumes a zero salvage value for all cases. Table 10.4 gives the depreciation percentages for the various mid-year recovery periods for the MARCS- GDS system. Note that there are only certain recovery periods; that is 3, 5, 7, 10, 15, and 20 years and that the totals of the columns are always 100.00. Other conventions are the mid-quarter convention and mid-month convention and must be used for certain investments or other conditions. For example, if 40% or more of the purchases are in one quarter, the mid-quarter convention must be used. The mid-month is primarily for non-residential real property, (e.g., railroad grading or tunnel bore) and residential rental prop- erty. The mid-quarter and ADS tables are in the Publication 946. Only the mid-year convention will be presented in detail. MACRS-GDS Depreciation Example Consider the case of a $10,000 investment, zero salvage value, and determine the MACRS- GDS values for 200% GDS method for 5-yr property. Using the mid-year convention it will take 6 years as the ﬁrst and last years will receive only ½ of a depreciation value calculated for that year. Also, if an asset is sold in a year, only ½ of the depreciation is applied for that year. (cid:2) R D 100/ 200=.5 0:40 that is 40% depreciation per year (Double Declining Balance) D 0:20 or 20%. Note that the 200% declining rate is double and the straight line rate R that of the straight line method at the start. The straight line value changes according to the book value and life remaining values of the previous year. The declining balance depreciation is the 40% of the previous Book Value and is not used after the switch over point when it is less than or equal to the straight line depreciation. The results are in Table 10.5. 1=5 D D If one takes the Amount Used column and divides by 100, note that one obtains the exact same percentages in Table 10.4 for the Double Declining (200%) Balance column for a recovery period of 5 years. Thus, if one takes the values for the ﬁve year recovery in Table 10.5 and uses the percentages as decimals and multiplies by the investment of $10,000, one obtains the MACRS depreciation values in Table 10.5 which is presented in Table 10.6. 10.4.4 MACRS-ADS MID-YEAR RECOVERY PERIODS There are several MACRS-ADS recovery period tables and they are much larger as they have many more periods and the full tables can be seen in Publication 946. A section of two tables will be presented to illustrate the similar construction of the tables using the same mid-year con- ventions. One table illustrate the straight line convention and the other will illustrate the 150% declining balance method. The values presented in these tables then can be used to compare with MACRS-GDS values in Table 10.4. Table 10.7 lists the percentages for the MACRS- ADS mid-year convention for straight line depreciation. Table 10.4: Depreciation percentages for MACRS-GDS mid-year (half-year) recovery peri- ods [7] 10.4. THE MACRS DEPRECIATION SYSTEMS 157 Table 10.8 lists the percentages for the MACRS-ADS mid-year convention for the 150% declining balance depreciation. Tables 10.7 and 10.8 give only a small portion of the values for these ADS values, but in comparison of the 3, 5, and 7 year value of the GDS values in Table 10.4, they are lower in the initial years. It is also interesting to note that the ADS schemes have many more recovery periods than the ADS , such as the 2.5, 3.5, 4, 6, and 7.5 in addition to the 3, 5, and 7 years and this would result in much more record keeping. YearRecovery Period(Double Declining (200%) Balance) (150% Declining Balance) 357101520 133.3320.0014.2910.005.003.750244.4532.0024.4918.009.507.219314.8119.2017.4914.408.556.67747.4111.5212.4911.527.706.177511.528.939.226.935.71365.768.927.376.235.28578.936.555.904.88884.466.555.904.52296.565.914.462106.555.904.461113.285.914.462125.904.461135.914.462145.904.461155.914.462162.954.461174.462184.461194.462204.461212.231Totals100.00100.00100.00100.00100.00100.000158 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS Table 10.5: MACRS depreciation calculations from declining balance and straight line MACRS-ADS Depreciation Example Consider the case of a $10,000 investment, zero salvage value, and determine the MACRS-ADS depreciation values for the straight line and 150% declining balance methods for 5-yr property. The percent rate is determined by: R D 150=.5 100/ (cid:2) D 0:30 D 30%: The result is 30% depreciation rate per year for the 150% Declining Balance MACRS-ADS compared to the 40% depreciation in the MACRS-GDS. The faster depreciation increases cash ﬂows and is advantageous for most companies to use the GDS depreciation. The Straight Line depreciation is even slower than the 150% Declining Balance Method, as shown in Table 10.9. YearLifeDeclining Balance DepreciationStraight Line DepreciationMACRS DepreciationEnd of Year Book ValueRemainingAmount ($)Amount ($)Amount Used ($)(End of Year)End of Year200% of Straight Line Initial AmountUse Remaining Life (SL)(Largest of DDB and SL Methods)0500 010,00014½2,0001,0002,0008,00023½3,2001,7783,2004,80032½ 1,920 1,9201,9202,88041½**1,1521,1521,7285½1,1521,152652606526520First year depreciation is for only 1/2 year in mid-year convention.Straight line is determined by the book value of the previous year divided by the remaining life at the end of the previous year.* Switch-over Point.**** Remaining Declining Balance Depreciation items do not need to be calculated as they will be equal or less than the Straight Line Depreciation.10.4. THE MACRS DEPRECIATION SYSTEMS 159 Table 10.6: MACRS-GDS depreciation calculations Table 10.7: Depreciation percentages for MACRS-ADS straight line depreciation [8] 1234Year[Table 10.4]Recovery Period 5 YearsDepreciation (%)Column 2Expressed as a DecimalMultiplied by $ 10,000[Table 10.5]MACRS-GDS DepreciationAmount in $0--120.002,0002,000232.003,2003,200319.201,9201,920411.521,1521,152511.521,1521,1526 5.76 576 5760Recovery Period in Years-Depreciation Amounts in PercentagesYear2.533.54566.57120.0016.6714.2912.5010.008.337.687.14240.0033.3328.5725.0020.0016.6715.3914.29340.0033.3328.5725.0020.0016.6715.3814.29416.6728.5725.0020.0016.6715.3914.28512.5020.0016.6615.3814.29610.0016.6715.3914.2878.3315.3814.2987.14IRS Publication 946, p. 75160 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS Table 10.8: Depreciation percentages for MACRS-ADS 150% declining balance deprecia- tion [9] Table 10.9: MACRS-ADS 150% declining balance and straight line depreciation calculations with a 5-yr recovery period Recovery Period in Years-Depreciation Amounts in PercentagesYear2.533.54566.57130.025.021.4318.7515.0012.5011.5410.71242.037.533.6730.4725.5021.8820.4119.53328.025.022.4520.3117.8516.4115.7015.03412.522.4520.3116.6614.0613.0912.25510.1616.6614.0613.0912.2568.3314.0613.0912.2577.3313.0812.2586.03IRS Publication 946, p. 8512345150% Declining Balance150% Declining BalanceStraight LineStraight LineYear[Table 10.8]Depreciation (%)(Column2/100)$10,000 =Depreciation Amount ($)[Table 10.7]Depreciation (%)(Column4/100) $10,000 =Depreciation Amount ($)0----115.001,50010.001,000225.502,55020.002,000317.851,78520.002,000416.661,66620.002,000516.661,66620.002,00068.3383310.001,00010.5. OTHER DEPRECIATION METHODS 161 10.5 OTHER DEPRECIATION METHODS There are several other depreciation systems, but two of the most interesting methods are the Section 179 and the Production-Based methods. The Section 179 method is part of the U.S. code and is used to expense rather than depreciate costs. The Production-Based method is based upon the amount of use of the item and is not approved in the U.S. tax code. 10.5.1 SECTION 179 DEPRECIATION This Special Depreciation Method is unique to the U.S. and is intended to give small and medium-size companies a method of more rapid depreciation [10]. The limits that can be ex- pensed change almost yearly with signiﬁcant increases in the amounts. The maximum amount of depreciation that could be allowed for 2010 was $250,000 and it increased yearly to $500,000 in 2016. When the total depreciation amount exceeds $2,010,000, the maximum limit is reduced dollar for dollar. The total amount of depreciation must be less than $2,510,000 during 2016 to use any of Section 179 Depreciation. There are special limitations on passenger automobiles or Sport Utility Vehicles (SUV). Enterprise Zone Businesses can have an increase of $35,000 for the Section 179 limit and have a reduction in the reduced dollar for dollar limit. The asset must be used 100% exclusively for business use. If less than 100%, only that percentage used for business can be used and one must use the GDS system to calculate yearly amounts. Section 179 Depreciation Examples: 1. Farmer Jimmy bought a tractor for $600,000 during the year and that was the only pur- chase he has made. He could have a Section 179 Depreciation of $500,000 and the basis for the remaining depreciation of the tractor would then be $100,000. 2. Farmer Rosalyn bought a small tractor for $120,000 during the year and that was the only purchase she has made. She could have a Section 179 Depreciation of $120,000 and the tractor would be fully depreciated. 3. Donnie Great American Farms bought a tractor for $700,000 during the year and had a to- tal depreciation for all their purchases of $2,410,000 in 2010. Thus, the maximum amount $2,010,000) or that could be used for Section 179 would be $500,000 (cid:0) $100,000. The remaining depreciation for the tractor would be $700,000 $100,000 or $600,000. ($2,410,000 (cid:0) (cid:0) 4. Consultant Betty has purchased a new computer system for $8,000 and that is the sole depreciable item she purchased. Betty uses the computer for business 80% of the time and 20% for personal use. She can take 80% of the $8,000 or $6,400 as a business depreciation expense. 162 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS 10.5.2 PRODUCTION-BASED DEPRECIATION The production-based depreciation method is used where the extent of use of equipment depends on the production quantity or volume of production. The production quantity would be based on the number of units the equipment could produce before it is worn out. The volume of production may be the volume of material extracted from a resource before the resource is depleted of the material. This system is similar to that used in the U.S. for depletion of assets, such as oil, natural gas, and minerals equipment. However, the production-based depreciation system is not accepted by the IRS in the U.S. even though an example appears in Publication 946 [11]. Production-Based Depreciation Examples: 1. A truck has a capacity of hauling 500,000 tons during its lifetime and the initial cost of the truck is $50,000. During the 3rd year, the truck hauls 75,000 tons. The depreciation for the 3rd year would be: Depreciation D .75;000=500;000/ $50;000 (cid:2) D $7;500: 2. A gold mine has an estimated deposit of 500,000 troy ounces of gold and 1,000,000 tons of rock need to be mined to process the gold. The purchase cost of the mine was $3,000,000. A mine drilling machine was purchased for $400,000 to do all the mining as its expect life is also 1,000,000 tons. What would be the drilling machine depreciation if in the ﬁrst year it mined 150,000 tons? Depreciation D .150;000=1;000;000/ $400;000 $60;000 D (cid:2) 3. The expected life of a rolling mill roll unit is 600,000 tons of steel. The unit costs $1,400,000 and the amount rolled in year 2 was 80,000 tons. What would be the depreciation for the second year? Depreciation D .80;000=600;000/ 1;400;000 $186;667 D (cid:2) 10.6 SUMMARY Cash ﬂows and proﬁts are the two major items for the ﬁnancial success of an enterprise, and de- preciation expenses have a major impact upon them. Depreciation is the recovery of expense in the past and cash ﬂows increase as depreciation increases. Thus, accelerated depreciation acceler- ates cash ﬂows into the enterprise. The IRS Publication 946 is a primary guide for depreciation. The declining balance and straight line methods have been combined and are the basis of the MACRS depreciation systems. The Section 179 depreciation system allows small and mid-size companies recover much of their equipment investments under $500,000 in the ﬁrst year. The MACRS depreciation systems and the Section 179 depreciation system represent the majority of depreciation systems used in the U.S. The advantage of the Section 179 depreciation is that you do not need to keep records to determine depreciation over the investment life as you can often fully depreciate the investment in the ﬁrst year. This makes it very attractive for small and mid-size companies. 10.7. REFERENCES 163 10.7 REFERENCES [1] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 114. 145, 146 [2] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 3. 145 [3] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), pp. 110–111. 147 [4] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), pp. 30–31. 147, 148 [5] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), pp. 100–109. 149 [6] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), pp. 29–38. 154, 155 [7] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 71. 156, 157 [8] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 75. 159 [9] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 85. 160 [10] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), pp. 15–23. 161 [11] IRS Publication 946—How to Depreciate Property (for 2016 Returns), Department of the Treasury, Internal Revenue Service, (download at http://www.irs.gov), p. 111. 146, 162 164 10. DEPRECIATION TERMS, METHODS, AND SYSTEMS 10.8 EVALUATIVE QUESTIONS 1. An asset was purchased for $80,000 and it took $20,000 to prepare the site and install the equipment. The asset has a recovery period of 7 years and MACRS-GDS depreciation was used. (a) What is the depreciation amount for the 1st year? (b) What is the book value at the end of the 3rd year? (c) What is the depreciation amount for the 5th year? (d) What is the book value after the 6th year? 2. An asset has value of $100,000 and a recovery period of 3 years. Use MACRS-GDS de- preciation and determine the depreciation amount and book value over the life of the investment. 3. Your company has purchased a large new tractor trailer truck (heavy duty truck). It has a basic cost of $180,000 and with additional options costing $20,000, so the cost basis for depreciation purpose is $200,000. Its market value at the end of 5 years is estimated as $30,000 and will be depreciated under the GDS. (a) What is the cumulative depreciation through the end of the 3rd year? (b) What is the MACRS depreciation in the 4th year? (c) What is the book value at the end of the 2nd year? (d) What is the book value at the end of the 5th year? 4. Your company has purchased a large new tractor trailer truck (heavy-duty truck). It has a basic cost of $180,000 with additional options costing $20,000, so the cost basis for depreciation purpose is $200,000. Its market value at the end of 5 years is estimated as $30,000 and it will be depreciated under the ADS with straight line depreciation. (A heavy-duty truck has life of 6 years under ADS, but assume 5 years for this problem.) (a) What is the cumulative depreciation through the end of the 3rd year? (b) What is the MACRS-ADS depreciation in the 4th year? (c) What is the book value at the end of the 2nd year? (d) What is the book value at the end of the 5th year? 5. You are a private consultant and purchased a new computer valued at $3,000. You decide to use the Section 179 method for the computer you purchased as this is the only equipment purchase for the year. (a) What is the 1st year depreciation amount? (b) What is the 2nd year depreciation amount? 10.8. EVALUATIVE QUESTIONS 165 6. You have started a consultancy company and purchased a new computer system valued at $3,000. You decided to use MACRS-GDS depreciation for the computer. (a) What is the 1st year depreciation amount? (b) What is the 2nd year depreciation amount? 7. A longwall mining machine was purchased for $500,000 and is expected to mine 5,000,000 tons of coal during its life. The machine mined 400,000 tons the 1st year and 700,000 tons the 2nd year. (a) What is the amount of depreciation using the production-based system? Year 1______ Year 2______ (b) If the MARCS-GDS system is used, what would be the depreciation amounts for the ﬁrst two years? What is its recovery period?____ If the GDS system is used, what would be the depreciation amounts for the ﬁrst two years? Year 1_____ Year 2_____ 8. President Trump has decided that he wants to have a 4-year MACRS-GDS depreciation scheme. You, as his chief tax adviser, are to determine the depreciation rates in 24 hours, or be ﬁred. What are the rates for each of the 5 years since mid-year convention is used? 9. Since the 25-year class life is new, the rates are not yet in Publication 946 (2016 Version). Therefore, for the 150% class, calculate what the rates should be for the MACRS-GDS system for a 25-year life. 10. An asset has value of $100,000 and a recovery period of 3 years. Use MACRS-ADS (150%) depreciation and determine the depreciation amount and book value over the life of the investment. Compare results with question 2. C H A P T E R 11 167 The Impact of Loans upon Cash Flows, Taxes, and Proﬁts 11.1 INTRODUCTION The use of loans is frequently necessary to purchase capital equipment including machinery, computers, facilities, materials, and other items necessary to produce products or services re- quired for the enterprise. Loans are important as they impact cash ﬂows, proﬁts, and taxes. The loan is repaid in payments which contain two major components—the principal portion which is the portion used to repay the loan balance and the interest which is the fee for the use of the capital borrowed. The ﬁrst section will be to analyze loans to determine the two components of principal and interest and then focus on how these items impact the cash ﬂows before taxes, taxes, cash ﬂows after taxes, and proﬁts. The loan interest is a depreciable expense and the prin- cipal is not a depreciable expense, but it reduces the cash ﬂows. Therefore, it is critical to know both the principal and the interest portions of a loan. Many general references [1–3] exist on general methods of loans, but only the Principal Present Value Approach will be presented in this chapter with permission of the American Society for Engineering Education [4]. 11.2 THE PRESENT VALUE OF PRINCIPAL APPROACH FOR DETERMINING THE PRINCIPAL AND INTEREST COMPONENTS OF A LOAN A new approach has been developed to determine the amounts of interest and principal of a loan. In the repayment of loans, where the loan payment is usually ﬁxed for each of the payment periods. The individual principal and interest components change each period, with the principal payment increasing each period and the interest portion decreasing each period. However, the present worth of the principal is constant for each period and thus once determined, it permits relatively simple calculations for the two components of principal and interest for each period. The concept that the principal present value is constant gives a better understanding of how loan payments work. This approach is thus called the Present Value of Principal Approach or the Principal Present Worth Approach. To illustrate this process an example will be presented. The nomenclature used is expressed in Table 11.1. 168 11. THE IMPACT OF LOANS UPON CASH FLOWS, TAXES, AND PROFITS Table 11.1: Nomenclature for loan principal and interest components [4] 11.3 EXAMPLE PROBLEM OF LOAN PROBLEM USING PRESENT VALUE OF PRINCIPAL APPROACH Let us consider determining the values of interest and principal payments on a Loan of $10,000 (LV) with an interest rate .i/ of 5% with 10 .n/ yearly end-of-year payments. The initial values are: $10;000 0:05 LV 5% 10: D D P i n D D D The initial calculated values are the loan payment .A/ and the present value of the principal .PVP/: A PVP D D D D LV .A=P; i; n/ (cid:2) $10;000(cid:140)0:05 i (cid:140).A (cid:2) LV/=.1 (cid:0) (cid:2) (cid:140).1;295:05 :05 (cid:0) (cid:2) D LV (cid:2) 1:05/10= i/(cid:141) f 1 i C (cid:2) .1:05/10 LV C D 10;000/=.1 (cid:2) i/n= 1 f (cid:141) g .1 i/n 1 (cid:141) g (cid:0) C $1;295:05 1=..1 D i// (cid:0) i=.1 C :05/(cid:141) (cid:2) $757:19: C C D (11.1) (11.2) i/n 1/(cid:141) (cid:0) SymbolVariable DescriptionFormula for Variable or Type of Unit UsedLV or PLoan value or initial principaliInterest rate (%)Used in decimal formnLoan lifeLife in yearsALoan paymentA = LV[i(1+i)n /{(1+i)n -1}] = LV(A/P,i,n)tTime period of interestt = 1,2,...nPVPPresent value of principal per periodPVP = [(A - iLV)/(1+i)] P(t)Principal per period tP(t) = PVP(1+i)t = PVP(F/P,i,t)I(t)Interest per periodI(t) = A - P(t)PVI(t)Present value of interest per periodPVI(t) = I(t)/(1+i)t = I(t)(F/P,i,n) U(t)Unpaid balance of loan after t periodsU(t) =LV-∑t=1P(t) = LV-(A-iLV)((1+i)t-1)/i) =LV - (A-iLV)(F/A,i,t)IT(t)Total interest paid to period tIT(t) = ∑t=1I(t) = tA-PT(t)=tA -(A-iLV)(F/A,i,t)PT(t)Total principal paid to period tPT(t) = ∑t=1P(t) = LV -U(t) = (A-iLV)(F/A,i,t)ttt11.4. LOANS WITH CASH FLOWS, DEPRECIATION, PROFITS, AND TAXES 169 All remaining calculations are based on these two calculated values—A and PVP—and the input values of LV; i, and n and the time of interest, t: P .t/ I.t/ PVI.t/ U.t/ PT.t/ IT.t/ D D D D D D D t t D X 0 t D t t D X t 0 t D (cid:2) PVP.1 i/t C D PVP.F=P; i; t / A P .t/ (cid:0) I.t /.P =F; i; t / LV.F=P; i; t/ I.t/=..1 C D A.P =F; i; t/ (cid:0) i/t D LV.1 i/t C (cid:0) A(cid:140).1 i/t C (cid:0) 1(cid:141)=i (11.3) (11.4) (11.5) (11.6) P .t/ .A i (cid:0) (cid:2) D LLV /.P =F; i; t/ .A i (cid:0) (cid:2) D LV/ (cid:2) (cid:140)..1 C i/t (cid:0) 1/=i(cid:141) (11.7) I.t/ A (cid:0) D .A A t (cid:2) (cid:0) PT.t / t A .A i (cid:0) (cid:2) (cid:0) (cid:2) D LV/.P =F; i; t/ i (cid:0) (cid:2) LV/ (cid:2) (cid:2)..1 C i/t (cid:0) 1/=i (cid:3) : (11.8) Some interesting information about the totals of the loan components occur. (See Ta- ble 11.2.) The most important item is that the present value of the principal is a constant. Ob- serve that the present value of the interest and the present value of the principal sum to the total initial value of the loan. The total sum of the principal parts of the loan is the expected total value of the initial loan value. These items are not as apparent in the traditional approaches to the evaluations of loans. Calculate the present worth of the interest payments. Since they are not the same, each needs to be calculate individually. Thus, where PWI(total) PWI.1/ C D PWI.2/ C (cid:1) (cid:1) (cid:1) C PWI.10/; PWI.n/ I.1/=.1 0:05/ C C I.2/=.1 C D 0:05/2 C (cid:1) (cid:1) (cid:1) C I.10/=.1: 0:05/10 C 2;428: D As a check on the PVP use, one can consider it to be an escalation gradient (E) of 5% the with and interest rate .i/ of zero and A1 757:19, thus, from Chapter 9: D i/(cid:141)(cid:140).1 (cid:0) C 0:05/=.0:05 FE D D D D E/=.E f C (cid:140).1 A1 $757:19 (cid:8)(cid:2).1 $757:19 f $10;000: C 13:20679 g E/n .1 (cid:0) 0/(cid:141)(cid:140).1 (cid:0) i/n(cid:141) g 0:05/10 C C .1 (cid:0) C 0/10(cid:3)(cid:9) (9.37) 11.4 LOANS WITH CASH FLOWS, DEPRECIATION, PROFITS, AND TAXES The basic relationships between the revenues, expenses, cash ﬂows before taxes, cash ﬂows after taxes, taxes, gross proﬁts, net proﬁts, depreciation, loan interest, and loan principal will be re- 170 11. THE IMPACT OF LOANS UPON CASH FLOWS, TAXES, AND PROFITS Table 11.2: Calculations for example Problem 1 using present value of Principal Approach viewed. The nomenclature for the cash ﬂows is in Table 11.3. The equations for the relationships will be presented and then an example problem will be used. The basic expression for Cash Flows Before Taxes is: CFBT CFBT D D Revenues R LV Loan Value C E: Expenses (cid:0) C (cid:0) The basic expression for Cash Flows with a Loan is: CFAL CFAL D D Cash Flows Before Taxes CFBT LCF: (cid:0) Loan Cash Flow (cid:0) The basic expression for Taxable Income with a Loan is: TI TI D D Cash Flows Before Taxes CFBT D: I (cid:0) (cid:0) Interest Paid (cid:0) (cid:0) Depreciation (11.9) (11.10) (11.11) PeriodInterest per PeriodPrincipal per PeriodPV of Interest per PeriodPV of Principal per PeriodUnpaid BalanceTotal Interest PaidTotal Principal PaidtI(t)P(t)PVI(t)PVPU(t)IT(t)PT(t)00.000.000.000.0010,000.000.000.001500.00795.05476.19757.199,204.95500.00795.052460.25834.80417.46757.198,370.16960.251,629.843418.51876.54361.52757.197,493.621,378.762,506.384374.68920.36308.25757.196,573.251,753.443,426.755328.66966.38257.52757.195,606.872,082.104,393.136280.341,014.70209.20757.194,592.172,362.445,407.837229.611,065.44163.18757.193,526.732,592.056,473.278176.341,118.71119.35757.192,408.022,768.397,591.989120.401,174.6477.61757.191,233.382,888.798,766.621061.671,233.3837.86757.190.002,950.4610,000.00Totals2,950.4610,000.002,428.147,571.8611.4. LOANS WITH CASH FLOWS, DEPRECIATION, PROFITS, AND TAXES 171 Table 11.3: Nomenclature for cash ﬂow analysis with loans and depreciation [4] The Basic Expressions for Taxes Paid are: TP TP TP TP D D D D Taxable Income TI TR (cid:2) Tax Rate (cid:2) (Cash Flows Before Taxes .CFBT TR: D/ I (cid:0) (cid:0) (cid:2) Interest (cid:0) (cid:0) Depreciation) Tax Rate (cid:2) (11.12) (11.13) SymbolVariable DescriptionFormula for Variable or Type of Unit UsedINVInvestment that is depreciableAn expense usually at time zero nDProject life (years)tStudy period yeart = 0,1,2....nPR(t)RevenueE(t)ExpenseExpenses would include initial investmentCFBT(t)Cash ﬂ ows before taxesCFBT(t) = R - E(includes INV) LVLoan amountLV = P (usually at time zero)A(t)Loan paymentA = LV(P/A, i, nL)iLoan interest ratenLLoan life (years)tL = 1,2,....nLLI(t)Loan interest amountLoan interest for each period tPVPPresent value of loan principalPVP=(A - iLV)/(1+i)LCF(t)Loan cash ﬂ owLV(t=0) and A(t=1,2..nL) values thru loan lifeLP(t)Loan principal amountLP(t) = A(t) - LI(t)CFAL(t)Cash ﬂ ows after loanCFAL(t) = CFBT(t) - LCF(t)DR(t)Depreciation rate for year tDepreciation rates for investmentD(t)Depreciation amount for year tD(t) = DR(t)INVTI(t)Taxable incomeTI(t) = CFBT(t) - I(t) - D(t)TRTax rate Usually speciﬁ ed and use decimal formTP(t)Taxes PaidTP(t) = TI(t) TRCFAT(t)Cash ﬂ ows after taxesCFAT(t) = CFAL(t) - TP(t) NP(t)Net proﬁ tsNP(t) = TI(t) - TP(t) = TI(t)(1.0 - TR)CFAT(t)Cash ﬂ ows after taxes(a check)CFAT(t) = NP(t) + D(t) - P(t)172 11. THE IMPACT OF LOANS UPON CASH FLOWS, TAXES, AND PROFITS The net proﬁts can be determined by: or or by NP NP D D NP NP D D Taxable Income TI TR TI (cid:0) TI Taxes .1 (cid:0) (cid:2) D (cid:2) (cid:0) TR/ Cash Flows Before Taxes .CFBT D/ .1 I (cid:0) TR/: (cid:0) (cid:0) (cid:2) (cid:0) Interest Depreciation) (1 (cid:0) (cid:2) Tax Rate) (cid:0) The cash ﬂows after taxes can be determined by: CFAT CFAT CFAT CFAT D D D D Cash Flows After Loan CFAL TP (cid:0) Taxes Paid (cid:0) Net Proﬁts NP D Depreciation C P .t/: Loan Principal (cid:0) C (cid:0) (11.14) (11.15) (11.16) (11.17) 11.5 EXAMPLE PROBLEMS OF LOANS WITH CASH FLOWS, DEPRECIATION, TAXES, AND PROFITS Example Problem A. China Electronics-USA wants to purchase a new set of tooling with a total cost including installation of $50,000. This tooling would have a MACRS-GDS recovery period of 5 years to determine the depreciation percentages and the study period would be for 6 years. A loan for $20,000 would be needed and it is planned to pay the loan oﬀ in 4 years with an interest rate of 10% and the loan payments for each of the 4 years would be $6,309.42. The project is expected to generate a revenue of $30,000 per year and the expected annual costs are $14,000. The desired rate of return for the company is 15%. Although the totals for the CFAT and NP are the same with zero required return considerations, they are quite diﬀerent as to when they occur. They are very diﬀerent when the 15% return is considered. The present worth of the cash ﬂows is only $3,710 whereas the net proﬁts are $13,242 and the payback period is 4 years. The calculations are in Table 11.4. Example Problem B. Use the same information in Problem A but use Section 179 De- preciation instead of the MACRS Depreciation. The diﬀerence between the two depreciation rates for problems A and B is signiﬁcant when the required rates of return are considered. The faster depreciation (Section 179 in this problem) gives higher cash ﬂows and much lower prof- its. Thus, the Section 179 depreciation or other accelerated depreciation would be reported to the government and straight line depreciation would be reported to the stockholders as slower depreciation gives higher proﬁts in the early years. In the ﬁrst year the Section 179 depreciation 11.5. EXAMPLE PROBLEMS OF LOANS WITH CASH FLOWS, DEPRECIATION, TAXES, AND PROFITS 173 n o i t a i c e r p e d S R C A M d n a , s e x a t , s t ﬁ o r p , s w o ﬂ h s a c h t i w n a o L — A m e l b o r P e l p m a x E : 4 . 1 1 e l b a T Year EndRevenueExpenseCash FlowsLoan Cash FlowCash Flow After LoanLoan Interest Depr. RateDepr. AmountTaxable IncomeTaxes PaidCash Flow After TaxCum CFAT(t)Net Proﬁ ts(t)R(t)E(t)CFBT(t)LCF(t)CFAL(t)LI(t)DR(t)D(t)TI(t)TP(t)CFAT(t)∑CFAT(t)NP(t)0050,000-50,00020,000-30,00000000-30,000-30,0000130,00014,00016,000-6,3099,6912,00020.0010,0004,0001,6008,091-21,9092,400230,00014,00016,000-6,3099,6911,56932.0016,000-1,569-62810,318-11,591-941330,00014,00016,000-6,3099,6911,09519.209,6005,3052,1227,569-4,0233,183430,00014,00016,000-6,3099,69157411.525,7609,6663,8675,8241,8015,800530,00014,00016,000016,000011.525,76010,2404,09611,90413,7056,144630,00014,00016,000016,00005.762,88013,1205,24810,75224,4577,872Total180,000134,00046,000-5,23840,7625,23810050,00040,76216,30524,45724,457Present Worth (CFAT-0%) = 24,457Present Worth (CFAT-15%) = 3,710Present Worth (NP-15%) = 13,242174 11. THE IMPACT OF LOANS UPON CASH FLOWS, TAXES, AND PROFITS gave a loss of $21,600 whereas the MARCS gave a proﬁt of $2,400. The present worth of the cash ﬂows increases to $7,298 whereas the present worth of the proﬁts decreases to $7,860 and the payback period is reduced to 3 years. Straight line depreciation would give more proﬁts and lower cash ﬂows as its depreciation rates are slower than the MACRS method. The Section 179 results are in Table 11.5 11.6 SUMMARY This new approach to loan evaluations does not contain terms to powers of .t 1/ that has been required in the previous published approaches for loan calculations. This approach better explains how loans work in that the present worth of the principal is constant for each period t which has not been mentioned or emphasized previously in the literature. 1/ or .t C (cid:0) The eﬀects of loan interest and depreciation upon proﬁts and cash ﬂows is large when there is consideration of required return or the time value of money. The eﬀects of diﬀerent de- preciation methods was illustrated was also illustrated when comparing MACRS vs. Section 179 Depreciation The present worth of Cash Flows After Taxes and Proﬁts will be the same if there is no required return or time value of money consideration, but there are large diﬀerences when the required return is considered. The focus is on cash ﬂows as accelerated depreciation give higher cash ﬂows and lower taxes, but also lower proﬁts. The proﬁts will be reported to the stockholders using straight line depreciation as they will be greater, but an accelerated depreciation will be used to report to the government for taxes. 11.7 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 74–82, 2012. 167 [2] Park, Chan S., Contemporary Engineering Economics, 2nd ed., Addison-Wesley, Menlo Park, CA, p. 803, 1997. [3] Newnan, Donald G., Eschenbach, Ted G., and Lavelle, Jerome P., Engineering Economic Analysis, 11th ed., Oxford University Press, New York, p. 655, 2012. 167 [4] Creese, R. C., Present value analysis of traditional loans, paper presented at ASEE Annual Conference and Exposition, Atlanta, Georgia, pp. 23.981.1–23.981.10, June 2013. https: //peer.asee.org/22366 167, 168, 171 (Materials published with permission of American society) 11.8 EVALUATIVE QUESTIONS 1. A loan for $40,000 is made for a period of 10 years with a 4% interest rate. Determine the loan payments for end-of-period payments, present value of the principal per period, the 11.8. EVALUATIVE QUESTIONS 175 n o i t a i c e r p e d 9 7 1 n o i t c e S d n a s e x a t , s t ﬁ o r p , s w o ﬂ h s a c h t i w n a o L — B m e l b o r P e l p m a x E : 5 . 1 1 e l b a T Year EndRevenueExpenseCash FlowsLoan Cash FlowCash Flow After LoanLoan Interest Depr. RateDepr. AmountTaxable IncomeTaxes PaidCash Flow After TaxCum CFAT(t)Net Proﬁ tsR(t)E(t)CFBT(t)LCF(t)CFAL(t)LI(t)DR(t)D(t)TI(t)TP(t)CFAT(t)∑CFAT(t)NP(t)0050,000-50,00020,000-30,00000000-30,000-30,0000130,00014,00016,000-6,3099,6912,000100.0050,000-36,000-14,40024,091-5,909-21,600230,00014,00016,000-6,3099,6911,5690014,4315,7723,918-1,9918,659330,00014,00016,000-6,3099,6911,0950014,9055,9623,7291,7378,943430,00014,00016,000-6,3099,6915740015,4266,1713,5205,2579,256530,00014,00016,000016,00000016,0006,4009,60014,8579,600630,00014,00016,000016,00000016,0006,4009,60024,4579,600Totals180,000134,00046,000-5,23840,7625,23810050,00040,76216,30524,45724,457Present Worth (CFAT-0%) = 24,457Present Worth (CFAT-15%) = 7,298 = -30,000 + 24,191/(1+.15)1 + 3,918/(1+.15)2 + 3,729/(1+.15)3 + 3,520/(1+.15)4 + 9,600/(1+.15)5 + 9.600/(1+.15)6Present Worth (NP-15%) = 7,860 = 0 - 21,600/(1+.15)1 + 3,918/(1+.15)2 + 8,943/(1+.15)3 + 9,256/(1+.15)4 + 9,600/(1+.15)5 + 9.600/(1+.15)6176 11. THE IMPACT OF LOANS UPON CASH FLOWS, TAXES, AND PROFITS principal payments each period, the interest payments per period, the cumulative principal for each period, the cumulative interest per period, and the unpaid balance at the end of each period. 2. A loan is taken for a ﬂat in the metropolis of Morgantown. The home is priced at $550,000 and the mortgage is for $400,000 at 6% APR for 30 years and the payments are made monthly. (a) What is the mortgage payment? (b) What is the interest on the 125th payment? (c) What is the principal on the 125th payment? (d) What is the total interest paid on the loan during the 30 years? (e) What is the remaining principal amount after the 125th payment is paid? (f ) What is the total interest paid after the 125th payment is paid? 3. Company WV Consolidated has purchased a new 3D printing machine for $300,000 and with a loan $200,000 at 6% interest for 5 years. The annual income (savings) from this machine is expected to be $120,000 and the annual expenses are expected to be $30,000. MACRS-GDS depreciation is used, the 5-year class life is used and the tax rate is 40%. (a) What is the amount of depreciation for the 4th year? (b) What is the book value after the 4th year? (c) What would be the income taxes due for the 4th year assuming this is the only ma- chine? (d) What would be the total cash ﬂows for the 4th year? (e) What would be the net proﬁts for the 4th year? (f ) What are the CFAT (15%) at the end of the project? (g) What is the present worth of the proﬁts at 15% return on the project? 4. Resolve the problem in Section 11.3 and Table 11.2 using an investment of $12,000 instead of $10,000 and calculate the annual payment, the interest per period, the principal per period, the PV of principal per period, the unpaid balance each year, and the cumulative total interest paid and the total principal paid at the end of each period using a 15% interest rate. 5. Resolve the Example Problem A (Table 11.4) of Section 11.5 using an investment of $60,000 instead of $50,000 and a loan for $30,000 instead of $20,000 and calculate all the values in Table 11.4 as well as the Present Worth of the Cash Flows and the Present Worth of the Proﬁts using a Minimum Acceptable Rate of Return (MARR) of 15%. 6. Resolve problem Example Problem A in Table 11.4 using straight line depreciation with the mid-year convention and compare the results with those of Problem A and Problem B. 11.8. EVALUATIVE QUESTIONS 177 PART III Methods for Project Evaluation and Risk Analysis C H A P T E R 12 181 Basic Project Evaluation Techniques 12.1 INTRODUCTION There are several basic methods for evaluating projects and two projects will be presented for comparison by these basic traditional techniques. In some cases the results will be diﬀerent, and the evaluations can be either on cash ﬂows or net proﬁts. The ﬁrst seven techniques are the methods that have been commonly used for project evaluation [1–3] are presented in this chapter and Chapter 13. The commonly used basic techniques for project evaluation presented in this chapter are: 1. Payback Period 2. Discounted Payback Period 3. Present Worth (PW) Analysis 4. Future Worth (FW) Analysis 5. Average Annual Equivalent (Average Annual Cost) 6. Return on Original Investment (ROI) 7. Return on Average Investment (RAI) These techniques will be illustrated with a sample problems utilizing the data in Ta- bles 12.1 and 12.2. The techniques can be used on a cash ﬂow before taxes or a cash ﬂow after taxes basis or on a net proﬁt basis and the results between the two projects will be compared. The analysis, however, should be made on an after tax basis (CFAT) whenever possible as these are the preferred results. Some investors may prefer the proﬁt basis rather than cash ﬂows, but cash ﬂows are typically utilized. In addition, since companies use straight line depreciation in- stead of accelerated depreciation for the stockholders, the stockholders may want to examine the depreciation used for the government taxes for evaluating the actual proﬁts rather than the reported “fake news” proﬁts. There are two projects under consideration by the Jen-Nat company—one project is to invest $50,000 in an additive manufacturing machine to cut tooling costs and lead times for 182 12. BASIC PROJECT EVALUATION TECHNIQUES production. The second project is to invest $50,000 for an improved computer security system to prevent hacking. Only one of the projects can be approved for implementation. The required return is 15% and loans are required for both projects. The additive manufacturing project (referred to as Project A) will allow for the creation of tooling much faster and can be depreciated at the three-year class level. It will require im- proved computer skills by engineering staﬀ to fully beneﬁt the use of the machine and thus will have higher expenses, but the more rapid tooling will generate more revenue. The life of the project would be 5 years and a loan for $20,000 at 10% interest for a 3-year is required. MACRS depreciation would be for a 3-year property. The data for the project is presented in Table 12.1. The improved security system to prevent cybersecurity attacks (referred to as Project B) would provide more security as well as improve computer services. The life of the project is for 6 years and MACRS depreciation would be for a 5-year property. A loan for $20,000 at 10% interest for 4 years can be obtained as the project life is 6 years. The data security system project is presented in Table 12.2. The data in Tables 12.1 and 12.2 includes the loans, the loan interest, the taxable income, the taxes paid, the total cash ﬂows after taxes, the net proﬁts, the total net proﬁts, the discounted cash ﬂows after taxes, and the discounted net proﬁts. The MARR used is 15% for discounting the cash ﬂows and the net proﬁts. The total net proﬁts and the total cash ﬂows after taxes are equal even though the values in the individual periods are quite diﬀerent when no discount rate is used. This is a good check for your calculations. However, the total discounted net proﬁts and the total discounted cash ﬂows after taxes are not equal. This is because the amounts of cash ﬂows and proﬁts are frequently diﬀerent in the same time period. The diﬀerence in amounts per period result in diﬀerent total amounts. Thus, since the discounted proﬁts and discounted cash ﬂows are diﬀerent, one must make a choice in selecting a criteria for the evaluation of a project. If there is a salvage value, it can be treated as a revenue in the last period when the equipment is sold. The various techniques for the evaluation of the projects will be examined using the data of the two example projects. 12.2 PAYBACK PERIOD The payback period is the year when the cumulative cash ﬂows becomes positive. This technique is used for small investments at lower levels of management where decisions are made quickly and when the payback period typically is less than 3 years. It may also have a total initial funding limit, such as $10,000 or $100,000 depending upon the size of the company initial funding limits. This not used when the funding is in the $1,000,000 range or higher as payback period is not the critical issue is large projects. 12.2.1 TRADITIONAL PAYBACK PERIOD The payback period occurs in the year when the cumulative cash ﬂows after taxes becomes pos- itive. The limiting payback period may be as short as 1 year, and more frequently is considered 12.2. PAYBACK PERIOD 183 ) A t c e j o r P ( t c e j o r p g n i r u t c a f u n a m e v i t i d d a f o s w o ﬂ h s a C : 1 . 2 1 e l b a T ) B t c e j o r P ( t c e j o r p y t i r u c e s r e t u p m o c f o s w o ﬂ h s a C : 2 . 2 1 e l b a T End of YearRevenue FlowExpanse FlowCash Flow Before TaxesLoan Cash FlowCash Flow After LoanLoan Interest AmountDepreciationTaxable IncomeTaxes PaidCash Flow After TaxesTotal Cash FlowNet Proﬁ tsTotal Net Proﬁ tsDiscountedCumulativeDiscountedRateAmountNet Proﬁ tsCash FlowCFATNet Proﬁ ts(t)R(t)E(t)CFBT(t)LCF(t)CFAL(t)LI(t)DR(t)D(t) TI(t)TP(t)CFAT(t)∑CFAT(t)NP(t) ∑BO(t) Proﬁ tsFlows-AT∑CFAT(t) ∑NP(t).0050,000-50,00020,000-30,000 0 0 0 0 0-30,000-30,000 0 0 0 -30,000-30,0000150,00030,00020,000-8,04211,9582,00033.3316,665 1,335 53411,424-18,576 801 801 697 9,934 -20,066 697250,00030,00020,000-8,04211,9581,39644.4522,225 -3,621 -1,44813,406 -5,170 -2,172 -1,371-1,64310,137-9,929-946350,00030,00020,000-8,04211,958 73114.81 7,40511,864 4,746 7,212 2,042 7,1185,7474,680 4,742 -5,187 3,734450,00030,00020,000020,000 0 7.41 3,70516,295 6,51813,48215,524 9,777 15,5245,5907,7082,5219,324550,00030,00020,000020,000 0.00 020,000 8,00012,00027,52412,000 27,5245,9665,9668,48715,290Totals250,000200,00050,000-4,12745,8734,12710050,00045,873 18,34927,52427,52415,2908,487End of YearRevenue FlowExpanse FlowCash Flow Before TaxesLoan Cash FlowCash Flow After LoanLoan Interest AmountDepreciationTaxable IncomeTaxes PaidCash Flow After TaxesTotal Cash FlowNet Proﬁ tsTotal Net Proﬁ tsDiscountedCumulativeDiscountedRateAmountNet Proﬁ tsCash FlowCFATNet Proﬁ ts(t)R(t)E(t)CFBT(t)LCF(t)CFAL(t)LI(t)DR(t)D(t) TI(t)TP(t)CFAT(t)∑CFAT(t)NP(t) ∑BO(t) Proﬁ tsFlows-AT∑CFAT(t) ∑NP(t).0050,000-50,00025,000-25,000 0 0 0 0 0 -25,000-25,00000 0-25,000-25,0000130,00012,00018,000-7,88710,1132,50020.0010,000 5,5002,2007,913-17,0873,3003,300 2,870 6,881 -18,119 2,870230,00012,00018,000-7,88710,1131,96132.0016,000 39 15 10,098 -6,989233,323187,635-10,4842,887330,00012,00018,000-7,88710,1131,36919.209,600 7,0312,8127,301 3124,2197,5422,7744,800-5,683 5,661430,00012,00018,000-7,88710,113 71711.525,760 11,5234,609 5,504 5,8166,91414,4563,9533,147-2,5369,614530,00012,00018,000018,00011.525,760 12,2404,896 13,104 18,9207,34421,8003,6516,5153,97913,265630,00012,00018,000018,000 5.762,880 15,1206,04811,952 30,8729,07230,872 3,9225,1679,14617,187Totals180,000122,00058,000-6,54751,4536,547100.0050,00051,453 20,58130,87230,87217,1879,146184 12. BASIC PROJECT EVALUATION TECHNIQUES to be 2 or 3 years. Longer periods are generally not advised as the time value of money is usu- ally not considered. Comparing the two alternatives from the data in Tables 12.1 and 12.2, the traditional payback periods are presented in Table 12.3. Table 12.3: Traditional payback period The payback values as integers assume the year in which the ﬁrst positive value occurs. The periods in parenthesis assume that cash ﬂows are continuous throughout the year and, for Project A, would be calculated using the last negative and ﬁrst positive values as: Project A Payback Payback Period D D D D D year of last negative . (cid:0) C CFAT(negative)/( (cid:0) (CFAT negative) C CFAT Positive)) (12.1) . .5;170//=.. (cid:0) (cid:0) .5;170/=.5;170 . (cid:0) 5;170/ 2;042/ 2;042// C C 2 2 2 C C C 0:72 2:72 years: Although the payback is frequently calculated in fractional years, the basis of cash ﬂow analysis is the payments are at the end of the period and that payments are considered as discrete, not continuous. The payback period should be considered as three years in both cases and another criteria should be used. If only one alternative is being considered, then if payback period is less than or equal to the speciﬁed limit, it should be approved and if more than the speciﬁed limit, it should be rejected. Some problems with the payback period analysis are as follows. 1. No consideration is given to the beneﬁts after the payback period. 2. When comparing two investments, if the alternatives have diﬀerent project life periods, the payback periods would be expected to be diﬀerent. For this example, the projects would be repeated—6 times for Project A and 5 times for Project B to have the same life of 30 years. 3. The magnitude of the cumulative cash ﬂows makes no diﬀerence, only the payback year— unless one is considering uniform continuous payments throughout the year. Since Project A has a shorter payback period in uniform continuous payments throughout the year it would be the preferred project only if uniform continuous payments considerations are Payback MethodProject A (years)Project B (years)CFAT3 years (2.72 Years)3 years (2.96 years)Project Life5 years6 years12.2. PAYBACK PERIOD 185 accepted. Otherwise, Project A and Project B have equal payback periods and another alternative project evaluation technique, such as return on investment, should be considered to diﬀerentiate between the projects if both cannot be approved as both meet the three year limit. Note that discounted net proﬁts would be a poor indicator of project performance as with the accelerated depreciation schemes, the 2nd year usually has much lower proﬁts (and can be negative) than the 1st year which tends to be positive. This is another reason why cash ﬂows are a better measure for project performance than proﬁts. 12.2.2 DISCOUNTED PAYBACK PERIOD A more realistic payback period can be determined by discounting the future cash ﬂows and this is the basis of the Discounted Payback Method. Diﬀerent paybacks consider the cumulative cash ﬂows of the project until a positive cash ﬂow results. The paybacks of interest are the cumulative discounted cash ﬂows before taxes, the cumulative discounted cash ﬂows after loan, and the cumulative the discounted cash ﬂows after taxes. These discounted cash ﬂows are presented in Table 12.4 using a discount rate of 15% for Project A. Table 12.4: Project A payback periods by cumulative discounted cash ﬂows for CFBT, CFAL, and CFAT Note that the discounted payback period of 4 years is the same for all 3 methods as all of them ﬁrst become positive during the 4th year. The discounted payback period has the same problems as the traditional payback period. The discounted payback period typically increases the payback period when uniform continuous cash ﬂows are assumed. When end-of-period cash ﬂows are assumed, it may increase the payback period by one year or more over that of the traditional payback period. This is expected as the future cash ﬂows are mainly positive and YearCash Flows Before TaxesDiscounted CFBT FlowsCumulativeDiscounted CFBT FlowsCash Flows After LoanDiscounted CFAL FlowsCumulative Discounted CFAL FlowsCash Flows After TaxesDiscounted CFAT FlowsCumulative Discounted CFAT Flows0-50,000-50,000-50,000-30,000-30,000-30,000-30,000-30,000-30,000120,00017,391-32,60911,95810,398-19,60211,4249,934-20,066220,00015,123-17,48611,9589,042-10,56013,406,10.137-9.929320,00013,150-4,33611,0587,862-2,6987,2124,742-5,187420,00011,435+7,09920,00011,435+8,73713,4827,708+2,521520,0009,943+17,04220,0009,944+18,68112,0005,966+8,487Total50,00017,04245,97318,68127,5248,487186 12. BASIC PROJECT EVALUATION TECHNIQUES are being reduced by the discounting, so the payback period would tend to increase. The best evaluation technique for determining the payback period is the cumulative discounted cash ﬂows after taxes. 12.3 TIME VALUE OF MONEY ANALYSIS FOR PROJECT PROFIT EVALUATION The time value of money approaches probably the most utilized approaches for project analysis. The present worth, future worth, and average annual worth of the proﬁts and cash ﬂows, such n is to as the CFAL, CFBT, and CFAT, are commonly used. The factor for discount is .1 discount all of the n periods back to time zero to calculate the present worth which can then easily be converted to a future worth or average annual worth. i/(cid:0) C 12.3.1 PRESENT WORTH ANALYSIS OF PROFITS To determine the return on investment the returns use the proﬁts rather than the cash ﬂows. The present worth method discounts all the payments back to time zero. The present worth is the most commonly used method to determine the various cash ﬂows or the proﬁts. For proﬁts and cash ﬂows, one generally wants to maximize the value. The discount factor for discounting n where n is the number of periods the speciﬁc amount is to be discounted and i is is .1 the discounting factor. The present worth for the cash ﬂows of the discounted net proﬁts for Project A can be calculated using the data from Table 12.4 and the results are presented in Table 12.5. i/(cid:0) C The calculation procedure will be illustrated for calculating the present worth of the proﬁts: PW.NP i%/ (cid:0) D NP.0/ .NP.1//=.1 C NP.3/.1 C i=100/3 i=100/1 NP.2/=.1 C NP.n/=.1 i=100/2 C i=100/n C C C (cid:1) (cid:1) (cid:1) C C (12.2) PW.NP 15%/ (cid:0) 0 0 D D C C 697 C 15;290 (cid:0) D C 801=.1 C 9;777=.1 0:15/ 2;172=.1 0:15/2 7;118=.1 (cid:0) 0:15/4 C 12;000=.1 C 0:15/5 0:15/3 C C 1;643 C 4;680 C 5;590 C C C 5;966 (if > 0.0 accept if a single alternative or if it is the greatest of all the alternatives considered). The present worth approach has another major advantage in the it will give identical values when using actual currency or constant currency. One does not need to convert the dollars to constant dollars or use the inﬂation free interest rate for the base calculations. However, to obtain future worth or average annual equivalents, the constant dollars and inﬂation free interest rates must be used. The present worth analysis is the most commonly used method for project 12.3. TIME VALUE OF MONEY ANALYSIS FOR PROJECT PROFIT EVALUATION 187 Table 12.5: Project A discounted proﬁts cash ﬂows calculations data for determining present worth and ROI evaluations. Also note that the discount rate has a major impact upon the proﬁts as shown by reducing the undiscounted proﬁts from $27,524 to the discounted proﬁts of $15,290. 12.3.2 FUTURE WORTH AND AVERAGE ANNUAL WORTH OF PROFITS The results of the calculations for determining the present worth of the various cash ﬂow expressions—CFBT, CFAL, and CFAT—are in Table 12.4. The present worth values can easily be converted to Future Worth Values or Average Annual Values, which is important for com- paring projects which may have a diﬀerent project evaluation periods, or commonly called the project life: P P (cid:2) .1 .F=P; i; n/ i/n .1 C C (cid:2) 15;290 (cid:2) $30;753; 15=100/5 15;290.1:15/5 D (12.3) FW D F F F F D D D D where FW PW F P D D D D future worth present worth. YearNet Proﬁ ts NPDiscounted Net Proﬁ ts (MARR=15%)CumulativeDiscountedNet Proﬁ tsDepreciationof InvestmentBook Value(end-of-year)of InvestmentAverage Mid-Year BookValue of InvestmentDuring the Year0000050,00050.000180169769716,66533,33541,667.52-2,172-1,643-94622,22511,11022,222.537,1184,6803,7347,4053,7057,407.549,7775,5909,3243,70501,852.5512.0005,96615,290000Totals27,52415,29050,00098,150123,150Include initial investment (50,000) which is used to calculate end-of-year book values Mid-Year Book Value = (Previous year book Value + Current year book Value)/2 and Initial Book Value188 12. BASIC PROJECT EVALUATION TECHNIQUES The future worth increases the values and those who are impressed by large numbers like to utilize this method. It is used to indicate future sums such as expected retirement incomes or pension values in the future. The average annual value or average annual equivalent, A, is determined from: AW A A A A D D D D D D D D where P .A=P; i; n/ (cid:2) P ..i=100/ 15;290 $4;561; (cid:2) ..1 (cid:2) .0:15/ C (cid:2) i=100/n/=..1 C ..1:15/5=..1:15/5 i=100/n 1// (cid:0) 1// (cid:0) (12.4) AW PW A P D D D D Average Annual Worth Present Worth. D Average Annual Equivalent The average annual equivalent values can be compared when the projects have diﬀerent project life values and this is the best method for making decisions under those circumstances. If one uses the present worth analysis, one must have the same life and that results in multiple projects. For example, if Project 1 has a life of 4 years and the competing Project 2 has a life of 5 years, then a total life of 20 years would be needed. This results in repeating Project 1 ﬁve times and Project 2 four times to have an equivalent study period of 20 years. One of the evaluative questions requests the calculation of the average annual equivalent for Project B and compare it with Project A. 12.4 RETURN OF ORIGINAL INVESTMENT (ROI) The return on original investment (often called return on investment—ROI) can be considered on a undiscounted (not discounted) or on a discounted basis. The return on investment is the average yearly proﬁt divided by the initial ﬁxed investment. This gives the average of the yearly ROI values. The data being applied is from Table 12.5 12.4.1 ROI – NOT DISCOUNTED The basic form does not include discounting the proﬁts. The formula used to obtain the values on a percentage basis is: ROI D (Average Yearly Proﬁt/Original Fixed Investment) 100: (cid:2) (12.5) For Project A the ROI would be: ROI D f (cid:140).801 2;172 7;118 9;777 (cid:0) C (cid:140).27;524/=5(cid:141)=50;000 C 100 12;000/=5/(cid:141)=50;000 100 g (cid:2) C D f D 11:01%: g (cid:2) 12.5. RETURN ON AVERAGE INVESTMENT (RAI) 189 12.4.2 ROI – DISCOUNTED (ROI-D) The total discounted proﬁts were calculated previously as $15,290 in Table 12.5 and thus the discounted ROI with the MARR of 15% would be: ROI-D D D (Average Yearly Discounted Proﬁt/Original Fixed Investment) 100 (Total discounted Proﬁts/5)/Original Fixed Investment) (cid:2) 100 (cid:2) (12.6) ROI-D D f (cid:140).15;290/=5(cid:141)=50;000 100 D g (cid:2) 6:12%: The ROI not-discounted percentage value is almost twice the percentage of the discounted ROI-D, and thus it is often preferred in the selling of the project. The annual worth of discounted proﬁts with beginning-of-period payments is consistent in the timing of the payments and the investment. The discounted return is lower, but it is the return above the MARR value. 12.4.3 ROI ANNUAL WORTH – AW (ROI) A new measure of the average annual worth of the proﬁts would be with respect to the original investment when the investments lives are diﬀerent or as another general approach to the ROI method. Since the annual worth is discounted, this represents the average return per year over the original investment. In this case: AW (ROI) AW=I D D 4;561=50;000 0:0912 D D 9:12%: (12.7) 12.4.4 ROI ANNUAL WORTH (BASE TIME) – AW-B (ROI) Since the annual worth payments are end of periods and the investment occurs at time zero, the annual worth payments should be made beginning-of-period payments. This put both the annual worth payments and the original investment being considered at the same time (base time) for evaluating the return. Thus, for evaluating it at time zero, the annual worth payments must be moved to the beginning and is: AW-b (ROI) (cid:140)AW=..1 C (cid:140)4;561=..1 D D C i//(cid:141) I / (cid:2) 0:15/(cid:141) 50;000/ 0:0793 D D 7:93%: (cid:2) (12.8) This rate [AW-b (ROI)] will be higher than the ROI-discounted as payments. All payments in the ROI discounted are taken at time zero whereas the AW-b (ROI) are considered yearly in the future at the beginning of the year. 12.5 RETURN ON AVERAGE INVESTMENT (RAI) Since the original ﬁxed investment is being depreciated over the investment period, the average investment over the investment life is thought to give a more reasonable representation of the 190 12. BASIC PROJECT EVALUATION TECHNIQUES investment amount. Both the actual investments and the discounted investments can be utilized in the calculations and each will be presented separately using the data in Table 12.5. The average investment is usually considered as the end-of-year book value, but it also can be considered as the average book value of the investment. Both calculations will be presented, with the end-of year book value ﬁrst followed by the average book value. 12.5.1 RAI – NOT DISCOUNTED The return on average investment (RAI) is the percentage relationship on the average annual proﬁt to the average outstanding investment. The general formula used is: RAI D where (Average Yearly Proﬁt/Average Outstanding Fixed Investment) 100; (cid:2) (12.9) Return on Average Investment using End-of-Year Book Values D RAI Average Yearly Proﬁt Average Outstanding Fixed Investment D D Values/Total Project Life. Total Net Proﬁt/Total Project Life Total End-of-Year Book Therefore, using the values in Table 12.5: RAI D D .27;524=5/=.98;150=5/ 28:04%: 100 (cid:2) This is a rather large return compared to the ROI and is not representative of most opera- tions. The sum of the end-of-year book values are less than the total investment, so an extremely large value is obtained. To obtain a better representation of the book value during the year, the mid-year book values are used which can be obtained by: Mid-Year Book Value D (Previous year book Value C Current year book Value)=2: (12.10) If the average mid-year book value is utilized, then the RAI values are somewhat more reasonable, but are still high. The revised form of Equation (12.7) is: RAI-M D (Average Yearly Proﬁt/Average Mid-Year Book Value of Fixed Investment) 100; (cid:2) (12.11) where Return on Average Investment using Mid-Year Book Value RAI-M D Average Yearly Proﬁt Average Mid-Year Book Value of Fixed Investment Total Net Proﬁts/Total Project Life D Total of Average Mid-Year Book Values of Investment/Total Project Life. D Therefore, using the values of Table 12.5: 12.5. RETURN ON AVERAGE INVESTMENT (RAI) 191 RAI-M D D .27;524=5/=.123;150=5/ 22:35%: 100 (cid:2) The 22.35% is still a high return on investment, but that is expected when the investment portion of the calculation is reduced. The next consideration will be to consider the reduction of the proﬁts by discounting. 12.5.2 RAI – DISCOUNTED (RAI-D) The discounted return on average investment (RAI-Discounted) is the percentage relationship on the average annual discounted proﬁts to the average outstanding investment. The general formula used is: RAI-D D (Average Yearly Discounted Proﬁt/Average Outstanding Fixed Investment) 100; (cid:2) (12.12) where Return on Average Investment using Discounted Proﬁts D RAI-D Average Yearly Discounted Proﬁt Average Outstanding Fixed Investment D D Values/Total Project Life. Total Net Discounted Proﬁt/Total Project Life Total End-of-Year Book Therefore, using the values in Table 12.5: RAI-D D D .15;290=5/=.98;150=5/ 15:58%: 100 (cid:2) The discounted proﬁts are the present worth of the proﬁts and the RAI-D is much lower than the undiscounted RAI. If the average book value is utilized, then the RAI-D values are somewhat more reason- able. The revised form of Equation (12.12) is: RAI-DM D (Average Yearly Discounted Proﬁt/Average Mid-Year Book Value of Fixed Investment) 100; (cid:2) (12.13) where RAI-DM D Return on Average Investment using Discounted Proﬁts and Mid-Year Book Values Average Yearly Proﬁt D Total Net Proﬁts/Total Project Life 192 12. BASIC PROJECT EVALUATION TECHNIQUES Average Mid-Year Book Value of Fixed Investment Total of Average Mid-Year Book Values of Investment/Total Project Life D Therefore, using the values of Table 12.5: RAI-DM D D .15;290=5/=.123;150=5/ 12:42%: 100 (cid:2) In the selection of a return on investment method, it is important to select one method and use it consistently. In selecting a method, it should be one that tends to best match your actual returns on investment. The study period should be over the economic life of the investment or when the book value ﬁrst reaches zero or the expected salvage value. In general, the ROI values seem more reasonable as the book values decline more rapidly than the actual value of the equipment. Note that automobiles are fully depreciated in 5 years, but there are millions of cars on the road that are older than 5 years. However, the operating expenses of the automobile increase as they age. 12.6 SUMMARY Several alternatives have been presented for evaluating projects. The best method presented thus far is probably the present worth method when projects have equivalent project lives, but the average annual worth is best when projects have diﬀerent lives or when considering ROI analysis. The present worth method also has the advantage that it would result in the same results if used for constant dollars (inﬂation-free dollars) and inﬂation-free interest rates as well as actual dollars market rates including inﬂation. The payback period method is based on the fact that earlier payback periods are usually better than later payback periods and would tend to reduce the risk of the project failing. This will also be shown by the project balance method illustrated in Chapter 13. The average annual worth method is the best when comparing projects which have dif- ferent project study periods. The present worth method would be used to calculate the values which would be converted to average annual worth values for comparison in the selection of the best method. The return on original investment is the used frequently as it does not depend on the discount rate of the returns or book values and reasonable values are obtained. The rate of return methods provide alternative methods for project evaluation that can supplement the present worth overall approach. The present worth method has a pre-selected return for evaluation and does not determine the return automatically and all projects in compa- nies do not have the same required return level. Projects critical to the survival of the enterprise may have lower return requirements than non-critical projects. The ROI is a more used performance measure than the RAI methods, and the ROI-D better indicates if the required return is made on the original investment. The AW (ROI) method and beginning of period method, AW-b (ROI), appears best for evaluating ROI investments when the alternatives have diﬀerent study periods. The AW-b (ROI) has both the AW payments and investment evaluated at the same time (beginning-of-period). 12.7. REFERENCES 193 12.7 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 83–108, 2012. 181 [2] Gelhausen, Marvin, Managing Editor, Certiﬁcation Study Guide, 2nd ed., revised, AACE International, Inc, Morgantown, WV, pp. 17-1-6, 2003. [3] Heinze, Kurt, Cost Analysis of Capital Projects, Marcel Dekker, Inc., New York, pp. 115– 119, 1996. 181 [4] Humphreys, Kenneth K., Jelen’s Cost and Optimization Engineering, McGraw-Hill, Inc., New York, pp. 103–110, 1991. 12.8 EVALUATIVE QUESTIONS 1. Prepare an equivalent Table 12.4 for Project B Payback Periods by Cumulative Discounted Cash Flows for CFBT, CFAL, and CFAT and determine the Project B Payback Periods by Cumulative Discounted Cash Flows for the CFBT, CFAL, and CFAT approaches. Are they diﬀerent? 2. Determine the future worth value and average annual equivalents for Project B. Compare the values with Project A to make a selection. 3. Determine the end-of-year book values for Project A and Project B for each year over the life of the project. 4. Prepare a table similar to that of Table 12.5 for Project B. Then determine the discounted and non-discounted values of ROI and RAI; that is: (a) ROI (b) ROI-D (c) RAI (d) RAI-M (e) RAI-D (f ) RAI-DM (g) AW (ROI) (h) AW-b (ROI) 194 12. BASIC PROJECT EVALUATION TECHNIQUES Include initial investment (50,000) which is used to calculate end-of-year book values. ** Mid-Year Book Value Initial Book Value. D (Previous year book Value C Current year book Value)/2 and 5. Solve Project A using the MACRS-ADS straight line depreciation method (same number of years) and compare the results with the MACRS-GDS solution. Compare the payback periods the PW values of the proﬁts and cash ﬂows at 0% and 15% return. 6. Solve Project A using Section 179 depreciation method and compare the results with the MACRS solution. Compare the payback periods the PW values of the proﬁts and cash ﬂows in the 1st year and for the total project duration. Determine the various discounted and non-discounted values of ROI and RAI for the two methods; that is: (a) ROI (b) ROI-D (c) RAI (d) RAI-M (e) RAI-D (f ) RAI-DM (g) AW (ROI) (h) AW-b (ROI) 7. An investment of $80,000 is made for a 3D-printing machine. It is expected to generate an annual revenue of $40,000 with annual expenses of $15,000. The project life is 8 years and the equipment has a class life of 5 years and MACRS depreciation is used. The 3D-printing machine will have a salvage value estimated at $5,000 when the project is complete at the end of the 8th year. The equipment has a class life of 5 years, MACRS depreciation will be used and the income taxes are 35% The required return is 10% and assume the capital gains tax is the same as the income tax. A loan for $20,000 is needed and the interest rate is 15%. Answer the following questions using the data from Table 12.6. (a) (i) Determine the Payback Period in years. (ii) Determine the Discounted Payback Period in years. (b) Determine the Present Worth of the project CFAT. (c) Determine the Average Annual Worth of the Project CFAT. (d) Determine the Returns on Investment—ROI and ROI-D, AW (ROI), and AW-b (ROI). (e) Determine the Returns on Average Investment—RAI, RAI-D, RAI-M, and RAI- DM. 12.8. EVALUATIVE QUESTIONS 195 7 m e l b o r P r o f a t a D : 6 . 2 1 e l b a T RevenueInvestmentExpensesLoanAfter LoanLoanDepreciationTaxable IncomeTaxes PaidNet Proﬁ tsCFATCumDiscCumYearRIECFBTCash FlowCFALInterest%AmountCFATCFATDiscFAT0080,00080,000-80,00020,000-60,000000000-60,000-60,000(60,000)(60,000)140,00015,00025,000-8,76016,2403,0002016,0006,0002,1003,90014,140-45,86012,855(47,145)240,00015,00025,000-8,76016,2402,1363225,600-2,736-958-1,77817,198-28,66114,213(32,932)340,00015,00025,000-8,76016,2401,14319.215,3608,4972,9745,52313,266-15,3959,967(22,965)440,00015,00025,00025,00011.529,21615,7845,52410,26019,4764,08013,302(9,662)540,00015,00025,00025,00011.529,21615,7845,52410,26019,47623,55612,0932,430640,00015,00025,00025,0005.764,60820,3927,13713,25517,86341,41910,08312,513740,00015,00025,00025,000025,0008,75016,25016,25057,6698,33920,852840,00015,00025,00025,000025,0008,75016,25016,25073,9197,58128.43395,00005,0005,000005,0001,7503,2503,25077,1691,51629,949Total325,000200,000125,000(6,279)118,7216,27910080,000118,72141,55277,16977,16929,949C H A P T E R 13 197 Advanced Project Evaluation Techniques 13.1 INTRODUCTION The project evaluation techniques are mainly used to evaluate single projects on an accept-reject basis and are diﬃcult for selecting the best of several of several projects when investing funds are limited. The techniques are the internal rate of return, the modiﬁed internal rate of return, bene- ﬁt/cost ratio analysis, and project balance. These comparisons can be added to your spreadsheets in evaluating projects. General references [1–3] for this section have guided the arrangement of these topics. The Internal Rate of Return (IRR) method determines the actual rate of return of the project and one can select the project with the highest rate of return. It was diﬃcult to calculate the IRR before computers as it required several trial calculations, but with computers repeated calculations are performed very rapidly and this technique now more frequently applied. The Modiﬁed Internal Rate of Return (MIRR) method, also referred to as the External Rate of Return (ERR) method, was used to closely approximate the IRR and was much easier to calculate as it could be performed in a single calculation. It utilizes the future worth of the beneﬁts divided by the present worth of the costs to determine the MIRR, but the ease in now calculating the IRR has reduced the importance of the MIRR. The Beneﬁt/Cost (B/C) ratio method involves the similar calculations as the present worth method, but often involves other factors such as safety issues, environmental issues, and eco- nomic development factors which often are not considered in traditional present worth analysis. It is, however, another view of the present worth method by rearranging its components to measure the ratio of the beneﬁts to the costs The Project Balance (PB) method considers the value of the cash ﬂow by escalating the initial cash ﬂow (which usually are negative) through the period and adding the cash ﬂow earned during the period at the end of the period. The ﬁnal project balance and the end of the study period should be positive for the project to be acceptable and the area of the negative balances compared to the area of the positive balances give an indication of the risk of the project. Projects with no positive areas or small positive areas would be considered as risky projects. This is a more conservative approach than the other evaluation methods. 198 13. ADVANCED PROJECT EVALUATION TECHNIQUES 13.2 INTERNAL RATE OF RETURN (IRR) The IRR is compared to the ﬁrm’s MARR and if the IRR is greater than the MARR, the project is acceptable. One advantage is that the IRR can be compared to projects that have a diﬀerent project life and/or a diﬀerent investment amount. The IRR method calculates the speciﬁc rate of return that makes the present worth of the project cash ﬂows equal to zero. Typically, the present worth of the cash ﬂows is positive at a zero rate of return and is reduced as the rate of return increases and when it becomes zero, then the project would earn the desired rate of return. The example Project A from Chapter 12 will be used as an example for calculations and the data is repeated in Table 13.1. The additive manufacturing project will allow the creation of tooling much faster and can be depreciated at the three year level. The investment is $50,000 and the required return is 15%. It will require improved computer skills by engineering staﬀ to fully beneﬁt the use of the machine and thus will have higher expenses, but the more rapid tooling will generate more revenue. The life of the project would be 5 years and a loan for $20,000 at 10% interest is needed to assist in the initial ﬁnancing. The present worth of the of the project cash ﬂows with the 15% required return is $8,487. The return rate will be increased until the present worth of the project cash ﬂows becomes zero and values are listed in Table 13.2. These calculations are now performed easily with spreadsheets and the IRR is 26.4% and are illustrated in Figure 13.1 This is the anticipated return that the project will bring. Thus, by comparing the IRR’s, the project with the highest IRR would be preferred and the eﬀects of project life and investment are considered. Discounting of net proﬁt cash ﬂows does not work for IRR evaluations as it would be positive even at 100% IRR. This is another reason why cash ﬂows are preferred over proﬁts for project evaluation analysis. The primary disadvantage is that trial and error is typically used, but this is no longer a serious problem as it can be done automatically by the computer. There may be cases where there is more than one IRR, but the ﬁrst one, which would be the lowest, is usually the one desired. The MIRR has only one value, so it was used as a check as an estimate of the IRR, but it is now rarely used as the actual IRR can be calculated directly with little diﬃculty. 13.3 MODIFIED INTERNAL RATE OF RETURN (MIRR) The MIRR was used to estimate the IRR and has only one rate of return without the possibility of multiple rates of return. However, it is only an approximate value of the IRR but will be close and if multiple values of the IRR occur, the one nearest to the MIRR would be the correct one to select. The MIRR method takes the future worth of the of the net positive cash ﬂows and the present worth of the net negative cash ﬂows to determine the MIRR and can be expressed as: MIRR/n .1 C Future Worth of positive cash ﬂows at MARR Present Worth of negative cash ﬂows at MARR : D (13.1) 13.3. MODIFIED INTERNAL RATE OF RETURN (MIRR) 199 ) A t c e j o r P ( t c e j o r p g n i r u t c a f u n a m e v i t i d d a f o s w o ﬂ h s a C : 1 . 3 1 e l b a T End of YearRevenue FlowExpanse FlowCash Flow Before TaxesLoan Cash FlowCash Flow After LoanLoan Interest AmountDepreciationTaxable IncomeTaxes PaidCash Flow After TaxesTotal Cash FlowNet Proﬁ tsTotal Net Proﬁ tsDiscountedCumulativeDiscountedRateAmountNet Proﬁ tsCash FlowCFATNet Proﬁ ts(t)R(t)E(t)CFBT(t)LCF(t)CFAL(t)LI(t)DR(t)D(t) TI(t)TP(t)CFAT(t)∑CFAT(t)NP(t) ∑BO(t) Proﬁ tsFlows-AT∑CFAT(t) ∑NP(t).0050,000-50,00020,000-30,000 0 0 0 0 0-30,000-30,000 0 0 0 -30,000-30,0000150,00030,00020,000-8,04211,9582,00033.3316,665 1,335 53411,424-18,576 801 801 697 9,934 -20,066 697250,00030,00020,000-8,04211,9581,39644.4522,225 -3,621 -1,44813,406 -5,170 -2,172 -1,371-1,64310,137-9,929-946350,00030,00020,000-8,04211,958 73114.81 7,40511,864 4,746 7,212 2,042 7,1185,7474,680 4,742 -5,187 3,734450,00030,00020,000020,000 0 7.41 3,70516,295 6,51813,48215,524 9,777 15,5245,5907,7082,5219,324550,00030,00020,000020,000 0.00 020,000 8,00012,00027,52412,000 27,5245,9665,9668,48715,290Totals250,000200,00050,000-4,12745,8734,12710050,00045,873 18,34927,52427,52415,2908,487200 13. ADVANCED PROJECT EVALUATION TECHNIQUES Table 13.2: Internal rate of return calculations Figure 13.1: Present worth vs. rate of return to determine IRR. Estimated IRR (%)Cash Flows After Taxes027,524 15 8,48720 4,23725 86626 24426.4 130,00025,00020,00015,00010,0005,0000Present Worth ($)051015202530Rate of Return (%)Present Worth vs. Rate of ReturnTable 13.3: Positive future worth and negative present worth for calculating MIRR 13.4. BENEFIT/COST RATIO 201 Using the data of Table 13.3 in Equation (13.1) for the MIRR one obtains: 0:15/4 C C 13;406.1 0:15/3 C C 7;212.1 30;000 C 0:15/2 13;482.1 0:15/ C C 12;000 C .1 MIRR/5 C 11;424.1 D .1 .1 C MIRR/5 MIRR/ D C MIRR D 20:9%: D 2:58039 1:2089 Note that the MIRR (20.9%) is greater than the MARR (15%), but not near to the actual IRR (26.4%) for this case. This is because the MIRR used the MARR to calculate the values and then it should be recalculated using the MIRR value and calculate a new MIRR. The MIRR is now rarely used as it is relatively easy to directly calculate the IRR. 13.4 BENEFIT/COST RATIO B/C analysis utilizes the present worth procedure to determine the beneﬁts and costs. There are two versions of the analysis—the conventional B/C ratio and the modiﬁed beneﬁt cost M (B/C) ratio. The conventional ratio utilizes the total beneﬁts and total costs as the ratio components whereas the M (B/C) utilizes the net beneﬁts and total investment costs as the ra- tio. The M (B/C) will give higher values of the ratio, but the decision as to whether the process is acceptable will be the same. YearPositive Cash FlowsFuture Worth of Positive Cash FlowsNegative Cash FlowsPresent Worth of Negative Cash Flows030,00030,000111,42419,981213,40620,38937,2129,538413,48215,504512,00012,000Totals57,52477,41230,00030,000202 13. ADVANCED PROJECT EVALUATION TECHNIQUES 13.4.1 CONVENTIONAL BENEFIT/COST RATIO The B/C ratio is an extension of the present worth method as it uses the present worth value of the beneﬁts compared to the present worth value of the costs. When the present worth of the beneﬁts exceeds the present worth of the costs, the ratio of beneﬁts to costs exceeds unity (1.0), and the project is considered acceptable. This is the same as the total present worth being greater than zero which is the criteria for an acceptable project by present worth analysis. This approach is frequently used for evaluation of government projects and other projects where the beneﬁts and costs include the potential eﬀects upon society, safety, and the environment, which are diﬃcult to measure directly as well as the direct beneﬁts and costs. The saving of lives, fewer accidents, etc. are considered as beneﬁts and the costs for implementing them are considered as costs. The problem also requires the value of saving a life and administrations who prefer to avoid safety and environmental projects use a low value of a “life” and administrations who want to implement safety and environmental measures use a higher value of “life.” The ratio is also dependent upon the rate of return and, in general, the higher the required rate of return, the less likely for the approval of the project as most beneﬁts occur in the future, and higher MARR values decrease the present worth of the future beneﬁts. The acceptance of a project by present worth analysis requires that the project value is positive, that is: For B/C analysis, the project is separated into beneﬁts (positive values) and costs (negative val- ues), and this results in Equation (13.2) being rewritten as: PW (project value) 0: (cid:21) (13.2) That is the approach of present worth analysis and the approach of B/C analysis is: PW (beneﬁts) PW (costs) 0: (cid:21) (cid:0) (cid:21) Now dividing PW (Beneﬁts) by the PW (costs), one obtains the relationship for B/C ratio anal- ysis: PW (beneﬁts) PW (costs): PW (beneﬁts)=PW (costs) 1: (cid:21) (13.3) Equation (13.3) illustrates the standard version of the B/C ratio. An example of the B/C ratio from the data in Table 13.1 using the CFAT values with no rate of return, what is the B/C ratio for the cash ﬂows after taxes for Project A? (The values are listed in Table 13.3.) The B/C ratio using a zero discount rate starts with the present worth of the beneﬁts (positive cash ﬂows) in the cash ﬂow after taxes which is: PW (Beneﬁts) 11;424 13;406 7;212 C C C D 13;482 C 12;000 D 57;524: Present worth of the costs (negative cash ﬂows) in the cash ﬂow after tax costs is: PW (Costs) 30;000: D 13.4. BENEFIT/COST RATIO 203 Beneﬁt-Cost Ratio D Therefore, at a zero rate of return, the beneﬁt/cost ratio exceeds one and the project is D D PW (Beneﬁts)/PW (Costs) 57,524/30,000 1:92 > 1:0. acceptable. If the MARR is 15%, the B/C ratio can be determined using the data of Table 13.1. The present worth of the discounted beneﬁts (positive cash ﬂows) in the cash ﬂow after taxes is: PW (Beneﬁts) 9;934 10;137 4;742 C C 7;708 C 5;966 D C D 38;487: The present worth of the costs (negative cash ﬂows) in the cash ﬂow after tax costs is: PW (Costs) 30;000: D Beneﬁt-Cost Ratio Thus, the eﬀect of a high MARR will generally greatly reduce the B/C ratio and could make it negative and the project unacceptable. PW (Beneﬁts)/PW (Costs) 38,487/30,000 1:28 > 1:0. D D D When comparing alternatives, the study period must be the same when using present worth values. The alternative with the highest beneﬁt/cost ratio that is greater than 1.0 is the best acceptable alternative project. If the project all have negative B/C ratios the one closest to 1.0 is the best if a project must be selected; but it does have a negative present worth. If discounted values are used and the ratio is greater than 1.0, the project will also meet the MARR requirements. If the projects have unequal lives, then the B/C should be calculated on an annual worth basis. In comparing alternatives, projects with large investments may have a higher present worth value than a lower investment project, but the B/C ratio may favor the lower present worth project. 13.4.2 TRAFFIC INTERSECTION EVALUATION This is a diﬀerent version of the problem presented in Strategic Cost Analysis [4]. This problem considers a traﬃc light vs. a traﬃc circle proposed for a dangerous intersection. In the past 3 years an average of 2 fatalities and 6 major accidents have occurred. The installation of the traﬃc light signal will cost $500,000, the traﬃc circle will cost $4,000,000. The annual maintenance for the traﬃc circle will be $10,000 and the annual maintenance of the signal will be $20,000. The safety engineers expect the fatalities using the traﬃc light to be reduced by 20% and the serious injuries to be reduced by 40%. They also predict that the traﬃc circle will reduce fatalities will be reduced by 80% and serious injuries reduced by 50%. The cost of a fatality is estimated at $5,000,000 and a serious injury at $200,000. The discount rate for such projects is 5% (funded by bonds) and the project life is estimated to be 25 years for both alternatives. What is the B/C ratio for each of the alternatives. 204 13. ADVANCED PROJECT EVALUATION TECHNIQUES Present Worth Values are: Traﬃc Light Study Costs Investment PW (Annual Maintenance) $20,000 (cid:140).1:05/25 (cid:0) D $20,000 .P =A; i 5%; n 25/ D 1(cid:141)=(cid:140)0:05.1:05/25(cid:141) D D $20,000 (14.094) D Total Costs Beneﬁts PW (Fatality Savings) .P =A; i 5%; n D 25/ D D PW (Injury Saving) .P =A; i 5%; n D D 25/ (cid:2) 80,000 D D (0.20) 5,000,000 (cid:2) $1,000,000 D (0.40) (cid:2) 200,000 14.094 14.094 (cid:2) Total Beneﬁts Beneﬁt/Cost Ratio D Traﬃc Circle Study Costs 15,221,520/781,890 19.47. D Investment PW (Annual Maintenance) $20,000 (cid:140).1:05/25 (cid:0) D $10,000 .P =A; i 5%; n 25/ D 1(cid:141)=(cid:140)0:05.1:05/25(cid:141) D D $10,000 (14.094) D Total Costs Beneﬁts PW (Fatality Savings) .P =A; i 5%; n D 25/ D D PW (Injury Saving) .P =A; i 5%; n D D D (0.80) 5,000,000) (cid:2) $4,000,000 D (0.50) (cid:2) 200,000 14.094 D 25/ (cid:2) 100,000 14.094 (cid:2) Total Beneﬁts $500,000 $281,880 $781,890 $14,094,000 $1,127,520 $15,221,520 $4,000,000 $140,940 $4,140,940 $56,376,000 $1,409,400 $57,785,400 D D D D D D D D D D D D Beneﬁt/Cost Ratio 57,785,400/4,140,940 13.95. The present worth of both proposals are much greater than 1.0, but the traﬃc light is preferred as its B/C ratio is the largest of the two. However, if one compares the projects on a present worth basis, the traﬃc circle would be preferred. D D 13.5 MODIFIED BENEFIT/COST RATIO The M B/C considers the net beneﬁts divided by the total investment costs. The net beneﬁts are the present worth of all the annual beneﬁts minus the present worth of all the annual operating costs and cost term is only the present worth of all the investment costs, which usually occur at 13.5. MODIFIED BENEFIT/COST RATIO 205 time zero but may also be in other periods for large construction projects. This method results in a higher ratio value, but generally does not alter the preference between the alternatives. If the projects have identical project lives, the present worth approach values can be used, but if the project lives are diﬀerent the average annual values should be use. The values will be higher than the conventional B/C ratio, but the relationship with respect to 1 as to being greater or less than one will not change. It results in a higher B/C number, which makes the project appear better. The investment costs may occur over more than time zero and it would include the present worth of all investment costs: Modiﬁed Beneﬁt/Cost (Beneﬁts (cid:0) D Operating Costs)/Total Investment Costs. (13.4) If one takes the data for the Traﬃc Light vs. Traﬃc Circle problem, one has the following. Traﬃc Light Study Costs Investment PW (Annual Maintenance) $20,000 (cid:140).1:05/25 (cid:0) D Beneﬁts $20,000 .P =A; i 5%; n 25/ D 1(cid:141)=(cid:140)0:05.1:05/25(cid:141) D D $20,000(14.094) D Total Costs PW (Fatality Savings) .P =A; i 5%; n D 25/ D D PW (Injury Saving) .P =A; i 5%; n D D 25/ (cid:2) 80,000 D D (0.20) 5,000,000 (cid:2) $1,000,000 D (0.40) (cid:2) 200,000 14.094 14.094 (cid:2) Total Beneﬁts Modiﬁed Beneﬁt/Cost Ratio 29.88. 14,939,641/500,000 D (15,221,520 (cid:0) 281,890)/500,000 D D Traﬃc Circle Study Costs Investment PW (Annual Maintenance) $20,000 (cid:140).1:05/25 (cid:0) D $10,000 .P =A; i 5%; n 25/ D 1(cid:141)=(cid:140)0:05.1:05/25(cid:141) D D $10,000(14.094) D Total Costs $500,000 $281,880 $781,880 $14,094,000 $1,127,520 $15,221,520 $4,000,000 $140,940 $4,140,940 D D D D D D D D D 206 13. ADVANCED PROJECT EVALUATION TECHNIQUES Beneﬁts (cid:2) D PW (Fatality Savings) .P =A; i 5%; n D 25/ D D PW (Injury Saving) .P =A; i 5%; n D D (0.80) 5,000,000 (cid:2) $4,000,000 D (0.50) (cid:2) 200,000 14.09 D 25/ (cid:2) 100,000 14.094 (cid:2) Total Beneﬁts $56,376,000 $1,409,400 $57,785,400 D D D 14.41. D Modiﬁed Beneﬁt/Cost Ratio (57,785,400 (cid:0) 140,940)/4,000,000 D (57,664,460/4,000,000) Both ratios increased, but the traﬃc light ratio increased more and has the highest ratio. The modiﬁed B/C ratio will always give a higher value, but it will not change the alternative selection. The higher value may cause people think it is better, but the changes in the numerator and denominator are the same and since the numerator is always larger for the ratio to be greater than one, the ratio will increase under the M B/C ratio. The calculations could also be performed on an annual worth cost basis by converting the investment costs to an annual worth (AW) by using .A=P; i; n/ and using the original costs and will be illustrated for the traﬃc light. Traﬃc Light Study Costs AW (Annual Investment) $500,000 .A=P; i 500,000 ..0:05.1 $500,000 (0.070952) D C D D D AW (Annual Maintenance) 5%; n 25/ D 0:05/25/=..1 0:05/25 1/ (cid:0) C $20,000 D Total Annual Costs Beneﬁts AW (Fatality Savings) AW (Injury Saving) D (0.20) D (0.40) (cid:2) 5,000,000 (cid:2) 200,000 Total Annual Beneﬁts $35,476 $20,000 $55,476 $1,000,000 $80,000 $1,080,000 D D D D D D ($1,080.000 Modiﬁed Beneﬁt/Cost 20,000)/($35,476 ) The M B/C is the same whether on a present worth basis or on an annual cost basis. In many instances there are several annual costs and it is easier to use the annual cost basis. If one uses annual costs, one must convert the initial investment cost to an annual investment cost. 29.88 (Annual Costs). D D (cid:0) 13.6 POSITIVE AND NEGATIVE PROJECT BALANCES 13.6. POSITIVE AND NEGATIVE PROJECT BALANCES 207 13.6.1 INTRODUCTION A Project Balance (PB) determines the project balance at the end of each period. It usually starts with a negative balance, which is a result of the initial investment. An excellent reference for project balances is that by Chan and Sharp-Bette [2]. The balances are summed and the positive future balances reduce the initial negative investment. It is a future worth approach being accumulated from the starting period to the end of the project. The balance lasts through the period and then the next value is added at the end of the period. Each period, usually a year, changes at the end of the period and the last period has no area. This procedure permits one to select between projects which may have similar present worth evaluations. Those projects which have large positive cash ﬂows in the initial periods will have a higher project balance. This method is to be used for comparing projects which have the same study period. The ratio of the negative area balance to the positive area balance is an indication of the risk of the project as the higher the ratio, the higher the risk. 13.6.2 PROJECT A EXAMPLE PROBLEM If one takes Project A, from Table 13.1 the future worth of the project would be: FW.CFAT/ 15%/ (cid:0) 30;000.1:15/5 7;212.1 11;424.1 0:15/4 13;406.1 0:15/3 D C D (cid:0) C 0:15/2 C 19;980 C 13;482.1 C 0:15/ C 12;000 C C 20;389 C 9:538 C 15;504 C C C 60;341 C 12;000 D $17;070 (if > 0.0 accept if single alternative or if greatest value among alternatives) and PW.CFAT 15%/ (cid:0) D 17;170=.1:15/5 8;487: D The project balance approach calculates the project balance at the end of each year and time zero is also included. The future worth of the initial period balance is added to end period balance to create the initial period balance for the next period. The balance is added to the previous balance to determine the end of the current years cumulative cash balance. The last value of the cumulative balance is identical to the future worth of the cash ﬂows for the project. The area represented for the current project balance times the period length, which is one for all periods. The last value which has a zero length as it is the end of the project and does not contribute to the area balance, but is part of the cumulative balance. The results for Project A are shown in Table 13.4 and Figure 13.2 and the large negative areas represent an indication of the risk of the project. 208 13. ADVANCED PROJECT EVALUATION TECHNIQUES Table 13.4: Project balance Project A calculations for cumulative balances and area balances Figure 13.2: Project balance diagram for Project A example problem. $74;097 and the positive area is The total negative area of the project is $4,409 so the (cid:0) project is a somewhat “risky” project. The payback year using the Project Balance method would not occur until the end-of-period 4 and the discounted cash ﬂows also would be in the 4th year, but the undiscounted total cash ﬂow analysis would be the end-of-period 3. In general, the project balance method is more negative as the initial cash ﬂow is throughout the study period and then increased by the MARR. Projects with longer study periods should have lower ratios of negative area/positive area than projects of shorter study periods. C Project Balance (PB) for Project ACumulative BalanceArea CalculationArea Balance(-) Balance(+) BalanceNegative AreaPositive AreaPB0 = -30,000-30,000-30,000 1 -30,000 PB1 = -30,000(1 + 0.15) + 11,424 -23,076-23,076 1 -23,076PB2 = -23,076(1 + 0.15) + 13,406 -13,131- 13,131 1 -13,131PB3 = -13,131(1 + 0.15) + 7,212 - 7,889- 7,889 1- 7,889PB4 = - 7,889(1 + 0.15) + 13,482+ 4,409 + 4,409 1+ 4,409 PB5 = 4,409(1+ 0.15) +12,000+ 17,070 +17,070 00Total-74,096+ 4,409 Note that the ﬁ nal positive project balance is the same as the future worth of the project.012345-30,000-23,076-13,132- 7,889+ 4,40917,070Period (years)PositiveProject BalanceNegativeThe ratio of Negative Area to the Positive Area is: 13.6. POSITIVE AND NEGATIVE PROJECT BALANCES 209 Negative Area/Positive Area 74;097=4;409 16:81: D D 13.6.3 PROJECT Z EXAMPLE PROBLEM Project (Z) with an initial cost of $30,000 and a set of annual net cash ﬂow after taxes for 5 years to be $25,000, and $ 34,147. $15,000, $10,000, $8,000, (cid:0) The return rate is 15% and the present worth would be: C C C C PW.CFAT 15%/ (cid:0) 30;000 15;000=.1 D (cid:0) C D (cid:0) D 30;000 $8;487: 10;000=.1 0:15/3 C C 8:696 C 6;049 C (cid:0) (cid:0) 0:15/ 8;000=.1 C 25;000=.1 C 0:15/4 14;294 C 9;863 C C 0:15/2 34;147=.1 16;077 C C 0:15/5 C This present worth is identical to Project A as calculated in Table 13.1. The project balance, however, is diﬀerent as shown by Table 13.5 and Figure 13.3. The future worth would also be the same at $17,070. Table 13.5: Project balance Project Z calculations for cumulative balances and area balances The negative project balance for Project Z, at $167,175, is much more negative than $73,766. and indicates a higher risk (more than double) the project balance for Project A, at involved with Project Z. Although the present worth values are the same over the same project lives, the risk for loss is much greater for Project Z than for Project A. There is a positive cu- mulative balance for Project A at the end-of-period 4, but the Project Z becomes positive only at the end of the project in period 5. Since there is no positive are for Project Z, the ratio of (cid:0) (cid:0) Project Balance (PB) for Project ACumulative BalanceArea CalculationArea Balance(-) Balance(+) BalanceNegative AreaPositive AreaPB0 = -30,000-30,000-30,000 1 -30,000 PB1 = -30,000(1 + 0.15) + 10,000 -44,500-44,450 1 -44,450PB2 = -44,500(1 + 0.15) + 8,000 -43,175-43,175 1 -43,175PB3 = -43,175(1 + 0.15) + 15,000 -34,651-34,651 1- 34,651PB4 = - 34,651(1 + 0.15) + 25,000-14,849 -14,849 1- 14,849 PB5 = - 14,849(1+ 0.15) +34,147+ 17,071 + 17,071 00Total-167,175 210 13. ADVANCED PROJECT EVALUATION TECHNIQUES the negative area to positive area would be inﬁnity and this indicates a highly risky project as a positive cumulative balance ﬁrst occurs at the end of the last period. Figure 13.3: Project balance diagram for Project Z example problem. 13.7 SUMMARY Five additional methods for the evaluation of projects have been presented—the internal rate of return (IRR), the modiﬁed internal rate of return (MIRR), the beneﬁt/cost ratio (B/C), the modiﬁed beneﬁt cost ratio (M B/C), and the project balance approach (PB). The IRR determines the rate of return at which the present worth becomes zero using a trial and error approach. The MIRR was an estimate of the IRR and will be greater than the MARR, but less than the IRR and is being replaced by directly calculating the IRR. The B/C ratio is the ratio of the positive cash ﬂows to the total of the negative cash ﬂows and the investment. The M B/C ratio considers the ratio of the net beneﬁts (positive cash ﬂows minus the negative cash ﬂows) to the investment and will result in a higher ratio value, but generally will not change the selection between projects with the same study period. The project balance approach is used to compare acceptable projects with present worth that are similar to look at the risk with respect when the positive cash ﬂows occur. It is based upon future worth calculations of projects with equivalent future worth values and equal project lives, and projects with the greater net negative cash ﬂow areas are the more risky projects. Projects with short study periods, large investments, and high MARR values will have large negative areas even though large revenues may occur in the latter project periods. 012345-30,000-44,500-43,175- 34,651- 14,849+ 17,170Period (years)Positive+Project BalanceNegative-13.8. REFERENCES 211 13.8 REFERENCES [1] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 83–108, 2012. 197 [2] Park, Chan S. and Sharp-Bette, Gunter P., Advanced Engineering Economics, John Wiley & Sons, Inc., New York, pp. 207–209, 231–236, and 246–253, 1990. 207 [3] Newnan, Donald G., Eschenbach, Ted G., and Lavelle, Jerome P., Engineering Economic Analysis, 11th ed., Oxford University Press, New York, p. 655, 2012. 197 [4] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 95–105, 2012. 203 13.9 EVALUATIVE QUESTIONS 1. Two alternative public works projects to prevent ﬂooding by hurricanes are under con- sideration. If the MARR is 4%, which of the projects should be selected? Use both the conventional and modiﬁed B/C ratios. Capital Investment for Dams and Pumps Project HC Project LC $7,500,000 $9,000,000 Annual Operations and Maintenance $250,000 $200,000 Annual Beneﬁt Useful Project Life (years) $400,000 $300,000 60 45 2. Calculate the B/C ratio and the M B/C ratio for the traﬃc circle and traﬃc light using annual worth values. Also determine the PW values for both the traﬃc light and traﬃc circle. 3. Use a value of $7,000,000 for a saved life and calculate the new B/C ratio for the traﬃc circle and traﬃc light. 4. An investment of $800,000 was made for a new process which is expected to generate an annual revenue of $350,000 with annual expenses of $100,000 for 7 years before being replaced. The equipment has a MACRS-GDS of 5 years and the MARR is 15% and the data is in Table 13.6. You may want to add additional columns to determine the answers. (a) Determine the Internal Rate of Return (IRR). (b) Determine the MIRR. (c) Determine the B/C ratio on a before tax and depreciation basis (only revenues, ex- penses, and investment). 212 13. ADVANCED PROJECT EVALUATION TECHNIQUES 4 m e l b o r P r o f a t a D : 6 . 3 1 e l b a T YearNetDepreciationTaxableTaxesNetCumulativeDiscountedCumulativeDiscountedRevenuesExpensesCFBTPercentAmountIncomePaidProﬁ tsCFATCFATCFATCFAT00800,000-800,00000000-800,000-800,000-800,000-800,0001350,000100,000250,00020.00160,00090,00036,00054,000214,000-586,000186,087-613,9132350,000100,000250,00032,00256,000-6,000-2,400-3,600252,400-333,600190,851-423,0623350,000100,000250,00019.20153,60096,40038,56057,840211,440-122,160139,025-284,0374350,000100,000250,00011.5292,160157,84063,13694,704186,86464,704106,840-177,1975350,000100,000250,00011.5292,160157,48063,13694,704186,864251,56892,904-84,2936350,000100,000250,0005.7646,080203,92082,568122,352168,432420,00072,818-11,4757350,000100,000250,00000250,000100,000150,000150,000570,00056,39144,916Totals2,450,0001,500,000950,000100800,000950,000380,000570,000570,00044,91613.9. EVALUATIVE QUESTIONS 213 (d) Determine the M B/C ratio on a before tax basis and depreciation basis. (e) Calculate the FW of the CFAT. (f ) Prepare a Project Balance Diagram on the CFAT and determine the total negative area and the total positive areas. (g) Determine the book value of the equipment over the project life, starting at year zero. (h) What is the payback period using CFAT and with using discounted CFAT? (i) Calculate the ROI and ROI-D, AW (ROI), and AW-b (ROI). 5. Rework Problem 4 using straight line depreciation (MACRS-ADS) for 5 years with mid- year depreciation. 6. Rework Problem 4 using a MARR of 5% instead of 15%. 7. Make a project balance diagram for Problem 4. Calculate the future worth of the project and use that as a check for your calculations. C H A P T E R 14 215 Introduction to Risk Analysis 14.1 INTRODUCTION The basic methods of risk analysis involve varying selected input parameters of the model to determine their eﬀect upon the cash ﬂows. The probabilistic methods for estimating risk analysis are more advanced and presented in the following chapter. The positive and negative project balances of the previous chapter can also be used for an approximate conservative estimate of project risk and more realistic methods will be presented. The projects considered involve data for future events such as revenues, expenses, depreci- ation rates and methods, taxes, and a desired rate of return. The values used are the best estimates that are available when the project study is made and the future is full of uncertainty. The longer the project, the higher degree of uncertainty in the future data. In the previous chapters the data were point estimates of the variables that were assumed known with certainty, but one should consider variation to determine which of the variables are most critical and the sensitivity of the parameter to change. In this chapter, discrete changes will be considered to estimate the variation to estimate project risk. 14.1.1 RISK VS. UNCERTAINTY Risk refers to situations which can be described by some outcomes whose probabilities can be es- timated. These probabilities can be discrete or continuous and the distributions, and parameters are assumed to be known. Uncertainty implies the probabilities, distributions, and/or parameters are not known. The techniques for considering decisions under conditions of uncertainty are more advanced than the scope of this book. More detailed discussions on the diﬀerences between risk and uncertainty are presented in the reference [1]. Thus, the focus in this and the following chapter will be risk analysis [2] but the variability in the risk analysis is often called the uncertainty of the project. Two basic approaches for considering risk presented in this chapter are: 1. Sensitivity Analysis and 2. Optimistic-Pessimistic Analysis (Scenario Analysis) These two techniques will be illustrated by several examples to emphasize the methodology for obtaining results. The results are used to illustrate the eﬀect of variation of the input variables upon the output. 216 14. INTRODUCTION TO RISK ANALYSIS 14.2 SENSITIVITY ANALYSIS Sensitivity analysis is an approach for examining the impact of change of selected critical param- eters in the estimate. The present worth method is frequently used to evaluate the percentage change in one variable while the other variables remain ﬁxed. The variables which will be ex- amined for change are selling price, capacity utilization, investment life, return rate, and total cost changes for an example problem concerning a 3D rapid prototyping project for tooling production. 14.2.1 INNOVATIVE 3D RAPID PROTOTYPING AND TOOLING CENTER EXAMPLE PROBLEM A group of investors are planning to start a 3D rapid prototyping and tooling center to provide tooling and prototypes for the various manufacturing companies in Manufacturing Valley. The plant initial investment will be $30 million with $10 million for the physical plant construction and $20 million for installation and equipment. The plant will have 50 engineers and technicians with an average salary of $60,000/year and a management and sales force of 6 employees with an average salary of $80,000/year. The process uses a wire feed which is melted by a laser source. The planned processing capacity is 100 kg of wire per hour with an eﬀective product yield of 80% and the other 20% represents scrap and test specimens. The maximum capacity would be 125 kg per hour. The life of the facility is estimated to be 10 years for investment recovery. The operating costs are estimated at $20/hour, the annual equipment investment is $1 million, the annual depreciation at $2 million, and the total taxes are estimated at 25%. The plant operation is 24 hours/day and for 340 days per year and 25 days for shutdowns and holidays and the annual utility costs are $200,000. The sales revenue is expected to be $40/kg of product sold and the wire cost is expected to be $10/kg used. The data for analysis is in Table 14.1. The present worth of the investment at the 15% MARR, that is PWI.15%/: PWI.15%/ $ $ $ (cid:0) (cid:0) C D D D 30;000;000 30;000;000 12;428;900: $8;454;000 $8;454;000 (cid:140)P =A; i 5:0188 (cid:2) (cid:2) 15; n 10(cid:141) D D C C The calculated IRR of 25.21% is greater than 15% MARR and the project is approved for further study. The next steps are to investigate the sensitivity of the PWI.15%/ to changes in selling price, capacity utilization, tax rate, investment life, return rate, and total cost changes. 14.2.2 SELLING PRICE SENSITIVITY The selling price (SP) will be evaluated at a 20% decrease, 10% decrease, zero change, 10% increase, and 20% increase which will result in the selling price levels of 32, 36, 40, 44, and Table 14.1: Innovative 3D rapid prototyping and tooling center 14.2. SENSITIVITY ANALYSIS 217 48 $/kg. The expression for revenue becomes: Revenues D 652;800 652;800 (cid:2) selling price (SP) SP: D Then the present worth of the investment at a 15% MARR, that is PWI.15%/: (cid:2) PWI.15%/ D Expenses) (1 (cid:2) (cid:0) (cid:0) Taxrate (decimal)) Investment .P =A; i D 30;000;000 (cid:2) (Revenues 10/ C 15; n D .652;800 30;000;000 2;457;204 C C SP (cid:2) (cid:0) D (cid:0) D (cid:0) D 2;457;204 85;859;244: SP (cid:0) SP (cid:2) (cid:2) (cid:0) 14;840;000/ 55;859;244 .1 (cid:2) (cid:0) 0:25/ (cid:2) 5:0188 (14.1) (14.2) Land and Building Construction = $10,000,000Equipment and Controls= $20,000,000Total Investment= $30,000,000Annual RevenuesProduct Sales340 days/yr 24 hr/day * 100 kg/hr * 0.8 kg product/kg wire used$ 40/kg= $26,112,000Annual ExpensesLaborEngineers and Technicians50 Employees @ $60,000= $3,000,000Management and Sales6 Employees @ $80,000= $480,000Operating CostsMaterials 340 days/yr24 hr/day100 kg/hr110 $/kg= $8,160,000Annual Utility Costs= $200,000Yearly New Equipment Investment= $1,000,000Annual Depreciation Expenses= $2,000,000Total Annual Expense $14,840,000Gross Proﬁ t11,272,000Taxes @25%2,818,000Net Proﬁ ts 8,454,000218 14. INTRODUCTION TO RISK ANALYSIS Solving for various costs and the results are in Table 14.2. Table 14.2: Selling price sensitivity Thus, one observes that the operation is very sensitive to selling price, as a 10% change has approximately a $10 million change in the present worth of the investment. 14.2.3 PROCESSING CAPACITY SENSITIVITY The processing capacity (PC) will be evaluated similarly to that of the selling price, but both the revenues and the expenses have components related to the processing capacity. The relation for the revenues will be: Revenues 340 24 PC 0:8 40 (cid:2) D (cid:2) (cid:2) (cid:2) D 261;120 PC: (cid:2) (14.3) The relation for the material expenses will be similar and is Material Expenses 340 24 PC 1 (cid:2) (cid:2) 10 D (cid:2) (cid:2) D 81;600 PC: (cid:2) This will change the total expense expression to: Expenses 81;600 81;600 PC PC (cid:2) (cid:2) C C D D .14;840;000 6;680;000 (cid:0) 6;680;000/: PW.15%/ D Investment .P =A; i (Revenues 10/ C 15; n (cid:2) D 30;000;000 D .261;120 Expenses) .1 (cid:2) (cid:0) (cid:0) Taxrate(decimal)/ PC (cid:2) (cid:0) .81;600 PC (cid:2) C 6;680;000// D (cid:0) (cid:2) D (cid:0) .1 0:25/ 5:0188 (cid:0) C (cid:2) C 30;000;000 .675;731 P C (cid:2) 25;144;188/ (cid:0) 675;731 PC 55;144;188: (cid:2) Solving for various capacity levels, the results are in Table 14.3. D (cid:0) (14.4) (14.5) Sales Price($/kg)Sales PriceChange (%)PWI (15%)($)32-20-7,228,70036-102,600,10040012,428,90044+1022,257,70048+2032,086,500Table 14.3: Process capacity sensitivity 14.2. SENSITIVITY ANALYSIS 219 The present worth is also very sensitive to the processing capacity (PC) as a 10% change results in a nearly $7 million change. It is not as sensitive as the selling price, but it would be a critical parameter to monitor. 14.2.4 TAX RATE SENSITIVITY The eﬀect of tax rates (TR) receives considerable attention in the political world and the TR being considered range from 20–40%, and that range will be considered. This results to changes 60%. The values for the revenues and expenses before of taxes would be for the base case: 20%, base case 40%, and 20%, C C C (cid:0) Revenues Expenses D D $26;112;000 $14;840;000: PW.15%/ 30;000;000 .P =A; i D 30;000;000 30;000;000 D (cid:0) (cid:2) D (cid:0) D (cid:0) C C .26;112;000 C 0:15; n 10/ D .11;272;000/ 56;571;914 (cid:2) 14;840;000/ .1 (cid:2) (cid:0) TR/ (cid:0) (cid:2) .1 ..1 (cid:0) 5:0188 TR/ (cid:0) TR/: (cid:2) (14.6) Solving for the eﬀects of taxes on the PW.15%/ results are in Table 14.4. Even though the tax rate has changed considerably both as the amount applied and the percentage increase, the project still has a positive present worth, PW.15%/, which is greater than 10% of the initial investment. Since the percentage changes are larger than the other com- parisons, they cannot be compared directly, but the changes are smaller than one normally would expect. This indicates that the eﬀects of sales and operations management performance have a much greater eﬀect upon the project present worth than the tax rate. Processing Capacity(kg/hr)Processing Capacity Change (%)PW (15%)($)80-20-1,005,70090-105,671,600100012,428,900110+1019,186,200120+2025,943,500220 14. INTRODUCTION TO RISK ANALYSIS Table 14.4: Tax rate sensitivity 14.2.5 INVESTMENT LIFE SENSITIVITY The investment life (IL) of the facility will aﬀect the (cid:140)P =A; i; n(cid:141) term in the PW.15%/ expression. The various investment lives considered will be 8, 9, 10, 11, and 12 years. The expression would be: PW.15%/ 30;000;000 .P =A; i D 30;000;000 .P =A; i D 30;000;000 D (cid:0) (cid:2) D (cid:0) (cid:2) D (cid:0) .26;112;000 14;840;000/ (cid:0) C 0:15; n C 0:15; n D .11;272;000/ 8; 9; 10; 11; 12/ ..0:75/ (cid:2) 8; 9; 10; 11; 12/ D 8;454;000/ C .1 (cid:2) (cid:0) 0:25/ .P =A; i 0:15; n D D (cid:2) 8; 9; 10; 11; 12/: (14.7) Using this expression and varying the investment life from 8–12 years with the results in Ta- ble 14.5. Table 14.5: Investment life sensitivity Tax Rate Applied (%)Tax Rate Change (%)PWI (15%) ($)20-2015,257,50025012,428,90030+209,600,30035+406,771,70040+603,943,100Investment Life (IL)(years)Percent Change (%)P/A,i = 0.15n = ILPW (15%)($)8-204.49728,016,3009-104.771610,339,1001005.018812,428,90011105.233714,245,70012205.420615,825,800One notices that the operations sensitivity to investment life to a 10% change in invest- ment life changes the present worth, PW.15%/, by roughly 2 million dollars compared to the much greater 7 and 10 million dollar changes by sales price and processing capacity changes. 14.2. SENSITIVITY ANALYSIS 221 14.2.6 REQUIRED RATE OF RETURN SENSITIVITY The MARR of the facility will aﬀect the (cid:140)P =A; i; n(cid:141) term in the PW (MARR)) expression. The various required return values considered will be 12, 13.5, 15, 16.5, and 18% which represent changes of 20% of the initial MARR. The expression would be: 10, and 10, 0, 20, (cid:0) (cid:0) PW.15%/ C C 30;000;000 .P =A; i D 30;000;000 .P =A; i D 30;000;000 .P =A; i D D (cid:0) (cid:2) D (cid:0) (cid:2) D (cid:0) (cid:2) .26;112;000 14;840;000/ .1 (cid:2) (cid:0) C 0:12; 0:135; 0:15; 0:165; 0:18; n (cid:0) 10/ 0:25/ D .11;272;000/ ..0:75/ C 0:12; 0:135; 0:15; 0:165; 0:18; n (cid:2) 8;454;000/ C 0:12; 0:135; 0:15; 0:165; 0:18; n 10/ 10/: D D (14.8) Using this expression and varying the MARR from 12–18% with the results in Table 14.6. Table 14.6: MARR sensitivity The magnitude of the PW change in the MARR is similar to that of the investment life, but as the MARR requirement increases the PW decreased. The change per increase was less than 2 million per 10% change which is similar to the changes in investment life, but in the opposite directions. 14.2.7 TOTAL COST SENSITIVITY The total cost (TC) can often change faster than the revenues, so an examination of similar changes in the total costs as was done for changes in the total revenues will be presented. An adjustment factor (AF) will be used on the expenses to have the same percentage changes as MARR (i)Percent(%)Percent Change of MARRP/A,i = MARRn = 10PW (MARR(i))($)12-205.650216,513,90013.5-105.319514,971,1001505.018812,428,90016.5104.744610,110,80018204.49417,993,100222 14. INTRODUCTION TO RISK ANALYSIS occurred in the revenue increases. The cost adjustment factors (AF) will be: 0.80, 0.90, 1.0, 1.1, and 1.2: PWI.15%/ D (Revenues-Expenses Investment .P =A; i D 30;000;000 (cid:2) C 15; n 10/ D .26;112;000 D (cid:0) D (cid:0) C C 30;000;000 .26;112;000 AF) .1 (cid:2) (cid:0) (cid:2) Taxrate(decimal) 14;840;000 14;840;000 AF/ AF/ (cid:2) (cid:2) (cid:2) (cid:2) (cid:0) (cid:0) .1 0:25/ (cid:0) 3:7641: (cid:2) 5:0188 (14.9) Using this expression and the AF values of 0.80, 0.90, 1.0, 1.1, and 1.2, the present worth results are in Table 14.7. Table 14.7: Total cost sensitivity The lower the cost adjustment factor, the higher the present worth. The changes as a result of the changes in total costs are large, but not as large as the sales revenue or the process capacity changes. But it is an area that management primarily controls at the operations area, rather than at the marketing and sales areas, and is the one that production management should focus on. 14.3 OPTIMISTIC-PESSIMISTIC ANALYSIS Optimistic-Pessimistic Analysis is used to evaluate variation in one or more variables and three diﬀerent levels of variation for each of the variable(s). Three cases are usually considered for each variable and they are: a “worst-case” (Pessimistic or P ), “most-likely case” (Most Likely or ML), and “best-case” (optimistic or O). Often more than one variable is analyzed in the study. The worst case is one which the results would be lower in less than 5 (or 10)% of the cases and the best case would be exceeded in only 5 (or 10)% of the cases. This is a simple and eﬀective method for analyzing the eﬀect of two variables. More variables can be considered, but the tables would be considerably more complex. Cost Adjustment Factor (AF)Percent Change in AF (%)PW (15%)($)0.8-2023,600,8000.9-1018,014,6001.0012,428,9001.1106,843,0001.2201,257,10014.3. OPTIMISTIC-PESSIMISTIC ANALYSIS 223 14.3.1 INNOVATIVE 3D RAPID PROTOTYPING AND TOOLING CENTER INVESTOR CONCERNS The investors for the rapid prototyping and tooling center had two major concerns after making the sensitivity analysis of the variables. The investors were concerned with the revenues and the investment life as computerized equipment can become obsolete rapidly as noted by the rapid changes in smartphone capabilities. The following three scenarios were developed for the desired rate of return of 15% after taxes for the two variables of Net Revenues and Investment Life. The investment life values were changed to 6 years and 14 years as the depreciation issues under accelerated depreciation would be over in 6 years and major replacements would deﬁnitely be required after 14 years. Table 14.8: Innovative rapid prototyping and tooling center analysis The present worth of three scenarios of the nine total scenarios were evaluated as: PW (cid:0) O.15%/ PW (cid:0) ML.15%/ PW (cid:0) P .15%/ 30 30 30 30 30 30 D (cid:0) D (cid:0) D (cid:0) D (cid:0) D (cid:0) D (cid:0) C C C C C C 12:40(cid:140)P =A; i 12:40(cid:140)5:7245(cid:141) D 15; n 14(cid:141) D 41:0 D 15; n 8:45(cid:140)P =A; i 8:45(cid:140)5:0188(cid:141) 4:54(cid:140)P =A; i 4:54(cid:140)3:7845(cid:141) D D D 10(cid:141) D 12:4 15; n 6(cid:141) D 12:8: D (cid:0) Table 14.9 contains the results of all nine scenarios and the reader should check the other calculated values in the solution matrix. These three scenarios give an simple average of $11.0 million and a range of $53.8 million. The question is which of the two variables is the critical variable, revenue, or investment life. This analysis indicates that the low revenues are the primary cause and not the short life. Only when the revenues are low does the project lose money, and it does so at all three lives considered. This indicates to management that revenues are key and perhaps should be re-examined. The overall average is $11.0 million on equal weight basis compared to the most likely value of 12.4. Optimistic (O)ScenariosMost-Likely (ML)Pessimistic (P)Capital Investment (Million $ Units)303030Investment Life (yrs)14106Net Annual Revenues (Million $ Units)12.408.454.54224 14. INTRODUCTION TO RISK ANALYSIS Table 14.9: Innovative rapid prototyping and tooling center analysis solution matrix 14.4 SUMMARY Two commonly used methods are applied for estimating variability and risk are sensitivity anal- ysis and optimistic-pessimistic analysis to indicate which are the critical variables and which are the non-critical variables. These methods utilize the present worth approach and probabilities are not considered. Sensitivity analysis takes only one variable for consideration at a time, but it is straight forward process. The optimistic-pessimistic analysis considers two variables at a time and often indicates which of the two variables is more critical easier than the individual variable analysis. The consideration of three variables is much more diﬃcult than two variables in the optimistic-pessimistic analysis. 14.5 REFERENCES [1] Garvey, Paul R., Probability Methods for Cost Uncertainty Analysis, Marcel Dekker, Inc, New York, p. 27 and p. 338, 2000. 215 [2] Creese, Robert C. and Adithan, M., Strategic Cost Analysis for Project Managers and Engi- neers, New Academic Science Limited, Tunbridge Wells, UK, pp. 109–114, 2012. 215 14.6 EVALUATIVE QUESTIONS 1. The salaries were too low in the data of Table 14.1 and the engineers and technicians were increased to $80,000 and the management and sales were increased to $100,000. The tax rate was decreased to 20%. Since cash ﬂows were was very sensitive to selling price, calculate the present worth of the cash ﬂows and determine the sensitivity of it similar to that of Table 14.2. 2. Two projects are being considered, one with high risk (risky) with a higher investment but higher returns and a more conservative project (traditional). Should the risky project be selected? Investment Life (years)61014NetRevenues(Million $ Units)$12.4016.932.241.0$ 8.452.012.418.4$ 4.54-12.8-7.2-4.014.6. EVALUATIVE QUESTIONS 225 Project Challenge Net Investment ($) Total Revenues Total Costs Net Revenues ($) MARR (%) Project Life T (Traditional Project) R (Risky Project) 150,000 80,000 20,000 60,000 15 4 225,000 110,000 20,000 90,000 15 4 (a) Using PW analysis, which is the better project? Note that the net investment is 50% higher as well as the net revenues. What are the average annual worth of the invest- ments? (b) Let the investment life of the traditional project be 5 years instead of 4? How does that alter the selection? Use average annual worth techniques for consideration. (c) Use the investment live of 4 years for both projects, but the risky project must earn 20% MARR and the traditional project remains at 15%. (d) What is the B/C ratio for the two projects over 4 years? (Evaluate the risky project at both MARR values.) 3. Project ABC has a high risk has a high investment but higher returns. Should it be selected with the new data? Project ABC Net Investment ($) Total Revenues ($) Total Costs ($) Net Revenues ($) MARR (%) Project Life (years) R (Risky Project) 225,000 90,000 25,000 65,000 15 5 (a) Should it be selected? (b) Do a sensitivity analysis by varying the project life for 3, 4, 5, 6, and 7 years. What is the trend? (c) Do a sensitivity analysis by varying the MARR from 5, 10, 15, 20, and 25%. What is the trend? (d) What is the rate of return at which the project has a zero present worth value? What is this rate of return named? 226 14. INTRODUCTION TO RISK ANALYSIS (e) What is the discounted and non-discounted B/C ratio for the initial project? (f ) What is the ROI and ROI-D for the project. (assume total costs includes all expenses including depreciation and taxes)? 4. Calculate the six scenarios that were that were not done for the results in Table 14.9. Give the equations, the values used, and the results for six scenarios. 5. The investors were concerned about with the net revenues and the investment life in new process. The following three scenarios were developed for the desired rate of return of 15% after taxes for the 2 variables of net revenues and investment life. The investment life values were changed to 3, 5, and 7 years as the project is risky. Project Challenge Data Capital Investment (Million $ Units) Investment Life (years) Net Annual Revenues (Million $ Units) Scenarios Optimistic Most-Likely Pessimistic (O) 40 7 21 (ML) 40 5 18 (P) 40 3 15 (a) Determine the present worth of the nine possibilities and form a solution matrix. Discuss which of the variables you consider to be most important for this problem. (b) Calculate the ROI for the three scenarios: optimistic, most-likely, and pessimistic. (c) Calculate the ROI for the 3 scenarios using the investment live of 7 years for all three. C H A P T E R 15 227 Risk Analysis with Probability Considerations 15.1 PROBABILITY METHODS AND TERMINOLOGY The traditional risk methods of the previous chapter gave point estimates values for the project of interest, but little indication of the potential range of the results or the probability of a loss on the project. This added information is helpful in making decisions about the selection of a particular project. This chapter will present an introduction to probability considerations in the evaluation of projects, but other references are listed for a more detailed coverage of the topic [1, 2]. The key terms are random variables and probability distributions. A random variable can take on several values which can have a probability that can be determined by the probability distribution for that variable. The random variable can have either discrete values predicted by discrete probability distribution (also called discrete probability density function) or continu- ous values predicted by a continuous probability distribution (or continuous probability density function). In discrete distributions there are a ﬁnite number of values and each value as a distinct probability associated with it. With continuous distributions, the set of variables is not count- able and the probability density function does not produce a probability value at a point as in the discrete distribution, but a probability range for between two points which are designated as the lower point, L, and the higher or upper point, U . The key measures of probability distributions are the mean or “expected value” and the “variance” and “standard deviation” which are used to indicate mean and the possible variation of the mean and the data set. The standard deviation is the square root of the variance and is more commonly used to describe the variation about the mean. The formula for the expected value for the discrete probability distribution, which involves a summation is: E.x/ (cid:22) D D N X 1 i D pi xi (discrete case), (15.1) where E.x/ (cid:22) i N D D expected value of the variable or mean x D symbol for mean number of outcomes of variable x in discrete case total number of outcomes and N is the last outcome D 228 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS pi D probability of speciﬁc ith outcome occurring. The formula for the variance of the discrete probability distribution is: Var.X/ (cid:27) 2 D D i N D X 1 i D (cid:22)(cid:141)2pi (cid:140)xi (cid:0) (cid:140)x2 i (cid:0) 2(cid:22)xi C (cid:22)2(cid:141)pi (cid:27) 2 (cid:27) 2 (cid:27) 2 (cid:27) 2 (cid:27) 2 D D D D D where N i D X 1 i D i N D X 1 i D i N D X i 1 D E.x2/ E.x2/ (cid:140)x2 i (cid:141)pi 2(cid:22) (cid:0) i N D X 1 i D xi pi (cid:22)2 C pi i N D X 1 i D x2 i (cid:0) 2(cid:22) (cid:22)i (cid:2) C (cid:22)2 1 (cid:2) (cid:22)2 (cid:140)E.x/(cid:141)2; (cid:0) (cid:0) (15.2) (cid:27) 2 D (cid:27) D E.x/ (cid:22) D E.x2/ i N pi D D D symbol for the variance, which is the square of the standard deviation symbol for the standard deviation expected value of the variable or mean x which is (cid:22) D symbol for the mean D expected value of the square of the variable x an outcome of variable x in the discrete case total number of outcomes and N is the last outcome probability of speciﬁc ith outcome occurring. For continuous probability density functions (PDFs), the probability of an event x be- tween the lower limit of L and the upper limit U is given by: P .L < x < U / U Z D L f .x/dx: (15.3) When the lower and upper limits are the total range of the distribution of the distribution, Highest Value) will be 1.0. When the values are less than the value of P (Lowest Value the total range, the probability will be less than 1.0. (cid:20) (cid:20) x The formula for the expected value for the distribution between the, that is the mean (cid:22), for the continuous PDF, which involves an integral, is: E.x/ (cid:22) D U Z D L x (cid:2) f .x/dx; (15.4) where 15.2. DISCRETE PROBABILITY EXAMPLES 229 E.x/ (cid:22) D f .x/ U L D D expected value of the variable or mean x D symbol for mean continuous probability distribution function of variable x D upper limit of continuous probability distribution of variable x lower limit of continuous probability distribution of variable x. The formula for the variance of the continuous probability distribution, which also involves an integral, is: Var.X / D U Z L (cid:140)x (cid:0) E.x/(cid:141)2f .x/dx (continuous case) (cid:27) 2 D U (cid:27) 2 Z D L x2f .x/dx (cid:140)E.X/(cid:141)2: (cid:0) This follows the same procedure as in the discrete case except integrals are used instead of sum- mations and results in: (cid:27) 2 E.X 2/ (cid:140)E.X/(cid:141)2: (15.5) (cid:0) Examples will now be presented illustrating the use of discrete probability analysis and D then will follow with some continuous probability examples. 15.2 DISCRETE PROBABILITY EXAMPLES 15.2.1 DONNIE THE DEALMAKER Donnie the Dealmaker has invested in a product where he has arranged for three suppliers and has three major customers. He needs all the suppliers and the customer demand is high, and they are completely independent of each other. The information on the costs, revenues proportion of the total supplied by each supplier, and their cost as well as the proportion of the total sold to each customer is in Table 15.1. This problem follows a procedure illustrated by Garvey [3]. All of the product supplied by the suppliers will be sold to the customers. Table 15.2 shows the revenues, revenue probabilities, costs, cost probabilities, proﬁt amounts proﬁt probabilities, expected proﬁts, and E.x/2. Donnie the Dealmaker wants to know what he will make as a proﬁt and the standard deviation. The total of the expected proﬁt is 11.0 and that is the expected proﬁt with the suppliers and customers and the probabilities with no inventory or shortage problems. The variance and standard deviation can be found using the last two columns of Table 15.2 and Equation (15.2): (cid:27) 2 D D D (cid:140)E.X/(cid:141)2 E.X 2/ 206 (cid:0) (cid:140)11(cid:141)2 (cid:0) 85: 230 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS Table 15.1: Supplier and customer share of product and prices Table 15.2: Revenues, costs, and proﬁts for Donnie the Dealmaker’s product investment The standard deviation is the square root of the variance and is: 851=2 9:22: (cid:27) (cid:27) D D Dealmaker Donnie will make an average of $11 in sales, but the proﬁt on any individual $30 in $10 increments. The probability of a loss occurs on only sale can range from one event which has a 3% probability (0.03 in Table 15.2) of occurring. $10 to C (cid:0) 15.2.2 THE INNOVATIVE 3D RAPID PROTOTYPING AND TOOLING CENTER The Innovative 3-D Rapid Prototyping and Tooling Center example in Sections 14.2.1 and 14.2.3 had the following capacity values and present worth values as presented in Table 15.3. SupplierABCSupplier Share of Product0.20.50.3Supplier Price to Dealmaker304050CustomerXYZCustomer Share of Product0.10.60.3Customer Price Paid to Dealmaker405060Revenue AmountRevenue ProbabilityCost AmountCost ProbabilityProﬁ t AmountProﬁ t ProbabilityExpected Proﬁ tE(X2)400.1300.2100.020.22400.1400.500.050.0000400.1500.3-100.03-0.33500.6300.2200.122.448500.6400.3100.303.030500.6500.500.18600.3300.2300.061.854600.3400.3200.153.060600.3500.5100.090.99Totals1.0011.0206The probabilities for each capacity level are as assigned and thus one can determine the expected value (mean), variance, and standard deviation and then determine the mean value of the present worth: 15.3. CONTINUOUS PROBABILITY MODELS 231 Table 15.3: Innovative 3D rapid prototyping and tooling center data (cid:22) D E.x2/ (cid:27) 2 (cid:27) D D P x Mean E.x/ D P x2 D D Variance (cid:0) Standard Deviation D p.x/ E.x2 (cid:2) D p.x/ (cid:2) 9;760 .E.x//2 D 98 D 9;760 D Square root of variance D (cid:0) 982 9;760 (cid:0) 12:49 9;604 156 D D The expected value (mean) of the processing capacity is 98 kg/hr, which is less than the designed operating capacity of 100, the variance is 156 (kg/hr)2, and the standard deviation is 12.49 kg/hr. The present worth as a function of the processing capacity from ﬁnal version of Equation (14.2) was: The mean of the present worth would be: PW.15%/ 675;731 D PC (cid:2) (cid:0) 55;144;188: (14.2) (cid:22).PW.15%// D D $675;731 $11;077;450: (cid:2) 98 55;144;188 (cid:0) Since the process capacity mean is lower than the base processing capacity value of 100, the present worth value is also lower than its original value of $12,428,900. The standard deviation for the present worth is approximately $8,422,000. 15.3 CONTINUOUS PROBABILITY MODELS As mentioned previously, the probability at a speciﬁc value with a continuous distribution is zero and the probabilities are calculated for a range of values between an lower limit, L and an upper Processing CapacityKg/hrProbability of Event “x”Present Worth(15%)Expected CapacityKg/hrxp(x)PW/103xp(x)x2 * p(x)800.20-1,006161,280900.205,672181,6201000.3012,429303,0001100.2019,186222,4201200.1025,944121,440Totals1.00989,760232 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS limit, U . The probability is the area between the two limits of the PDF. There are numerous continuous probability density functions and only two will be considered which are the normal distribution and the triangular distribution. The normal distribution is the most commonly used distribution of all the probability density functions, but the triangular distribution is commonly used in estimating and in determining ranges of cost data. 15.3.1 NORMAL DISTRIBUTION PROPERTIES The normal distribution is frequently assumed for many problems as the central limit theorem indicates that the means from samples are distributed normally. For example, the cost of an item is the total of three items that are independent random variables, then the distribution of the total cost will be normal even if the independent random variables are not normally distributed. Some of the properties about means and variances of distributions are: E ! X N X 1 i bX2/ D E.aX1 C N X 1 i D ! X Variance E.X1/ C E.X2/ C (cid:1) (cid:1) (cid:1) C E.N / for i 1; 2; : : : N D aE.X1/ bE.X2/ C (15.6) (15.7) Variance .X1/ C Variance .X2/ C (cid:1) (cid:1) (cid:1) C Variance.XN/ (15.8) D D D (cid:27) D standard deviation Square Root (variance) D (cid:140)a2 variance Standard Deviation .aX1 bX1/ (cid:0) The cumulative probability for the variable X to a speciﬁc value c is given by D C C (cid:0) X1 b2 variance X2(cid:141)1=2 (15.9) Probability .X < c/ (cid:136)(cid:140).c (cid:0) D (cid:22)/=(cid:27)(cid:141) D (cid:136).Z/: (15.10) Probability values of (cid:136)(Z) are in Table 15.4. Basic Normal Probability Examples Use Equation (15.10) and Table 15.4 to answer the following questions to gain familiarity in obtaining probability values. Table 15.4 is useful, but the NORMSDIST function in Excel® is much better and it, or other equivalent expressions in other software packages, would be easier and faster than look-up tables. If using electronic spreadsheets it would be useful, easier, and more accurate to use the computer function rather than Table 15.4. A. If the mean of a normal distribution is 20 and the standard deviation is 10, what is the probability that a random variable selected from that distribution is less than zero? Prob.X < 0/ (cid:136)(cid:140).0 (cid:0) D 20/=10(cid:141) (cid:136)(cid:140) (cid:0) D 2:0(cid:141) D 0:023 D 2:3% Table 15.4: Probability values (cid:136).Z/ for the standard normal distribution Z-Values in 0.05 in- crements 15.3. CONTINUOUS PROBABILITY MODELS 233 B. What is the probability that the random variable selected is less than 15? Prob.X < 15/ (cid:136)(cid:140).15 (cid:0) D 20/=10(cid:141) (cid:136)(cid:140) (cid:0) D 0:5(cid:141) D 0:308 D 30:8% C. What is the probability that the random variable selected is greater than or equal to 30? Prob.X 30/ (cid:21) 1 1 (cid:0) (cid:0) D D 0:841 D Prob.X < 30/ 1 (cid:136)(cid:140).30 D 0:159 or 15:9% (cid:0) 20/=10(cid:141) 1 (cid:0) D (cid:136)(cid:140) C 1:0(cid:141) (cid:0) Z -ValueΦ (Z)Z -ValueΦ (Z)Z -ValueΦ (Z)Z -ValueΦ (Z)Z -ValueΦ (Z)Z -ValueΦ (Z)-3.000.001-2.000.023-1.000.1590.000.50010.8412.000.978-2.950.002-1.950.026-0.950.1710.050.5201.050.8532.050.980-2.900.002-1.900.029-0.900.1840.100.5401.100.8642.100.982-2.850.002-1.850.032-0.850.1980.150.5601.150.8752.150.984-2.800.003-1.800.036-0.800.2120.200.5791.200.8852.200.986-2.750.003-1.750.040-0.750.2270.250.5991.250.8942.250.988-2.700.004-1.700.045-0.700.2420.300.6181.300.9032.300.990-2.650.004-1.650.049-0.650.2580.350.6371.350.9112.350.991-2.600.005-1.600.055-0.600.2840.400.6551.400.9192.400.992-2.550.005-1.550.061-0.550.2910.450.6741.450.9262.450.993-2.500.006-1.500.067-0.500.3080.500.6911.500.9332.500.994-2.450.007-1.450.073-0.450.3260.550.7011.550.9392.550.995-2.400.008-1.400.081-0.400.3450.600.7261.600.9452.600.995-2.350.009-1.350.088-0.350.3630.650.7421.650.9512.650.996-2.300.011-1.300.097-0.300.3820.700.7581.700.9552.700.996-2.250.012-1.250.106-0.250.4010.750.7731.750.9602.750.997-2.200.014-1.200.115-0.200.4210.800.7881.800.9642.800.997-2.150.016-1.150.125-0.150.4400.850.8021.850.9682.850.998-2.100.018-1.100.136-0.100.4600.900.8161.900.9712.900.998-2.050.020-1.050.147-0.050.4800.950.8291.950.9742.950.998-2.000.023-1.000.1590.000.5001.000.8412.000.9783.000.999234 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS D. What is the probability that the random variable selected is between 15 and 30? Prob.15 X (cid:20) (cid:20) 30/ D D D Prob.X (cid:136)(cid:140).30 (cid:136). C (cid:0) 1:00/ 30/ (cid:20) (cid:0) 20/=10(cid:141) (cid:136). (cid:0) (cid:0) Prob.X < 15/ (cid:136)(cid:140).15 20/=10(cid:141) (cid:0) 0:50/(cid:141) (cid:0) 0:841 D 0:308 (cid:0) D 0:533 D 53:3% E. If one assumes that Donnie the Dealmaker can assume his data is distributed normally, the probability of a loss would be: Prob.X < 0/ (cid:136)(cid:140).0 11/=9:22(cid:141) (cid:136)(cid:140) D (cid:0) This is very close to the discrete probability of 3.0%. D (cid:0) 1:193(cid:141) (cid:25) 0:027 or 2:7%: This risk of a project is usually considered to be the probability of obtaining a loss, but it can be speciﬁed to be a loss at a speciﬁc required return. Cash Flow Normal Distribution Example Problem The cash ﬂows from a project are presented in Table 15.5. The required rate of return is 15%. What is the present worth of the cash ﬂows on the project with an investment of $40,000, expected mean revenues, and expected standard deviation of the cash ﬂows? What is the prob- ability that the cash ﬂow from the project has a loss? Table 15.5: Cash ﬂow example data The ﬁrst steps are to calculate the mean, variance, and standard deviation of the present worth of the cash ﬂows at the required rate of return. This can be done by: PW.15%/ D (cid:0) 40;000 40;000 15;000(cid:140)P =F; 15; 1(cid:141) 15;000 0:8696 (cid:2) C C C D (cid:0) C 20;000 20;000(cid:140)P =F; 15; 2(cid:141) 20;000(cid:140)P =F; 15; 3(cid:141) 0:7561 (cid:2) C 0:6575 (cid:2) C 20;000 PW.15%/ (cid:22) D D D $1;316: $1;316: YearExpected Cash Flow µ($)Standard Deviationof Cash Flow σVariance of Cash Flow σ20-40,0001,0001,000,000115,0001,5002,250.000220,0002,0004,000,000320,0003,0009,000,000The variance is calculated by: 15.3. CONTINUOUS PROBABILITY MODELS 235 V .PW/ D (cid:27).PW/2 (cid:27).PW/2 (cid:27).PW/ D D D D D .:8696/2 106 (cid:2) (cid:2) C 1;5002 2:2867 C .:7561/2 106 (cid:2) 3:8908 2;0002 C 106 (cid:2) C (cid:2) 12 1 1;0002 (cid:2) 106 (cid:2) 8:8790 C 1:7015 C 106 (cid:2) 103 2:980 (cid:2) 2;980: .:6575/2 3;0002 (cid:2) D (cid:0) P .PW < 0/ (cid:136)(cid:140).0 1;316/=2;980(cid:141) (cid:136)(cid:140) 0:4416(cid:141) (cid:136)(cid:140) 0:45(cid:141) 0:326 0:33 33% This indicates the mean value of the present worth is $1,316, the standard deviation is $2,980 and there is a 33% chance that the project will not make the desired return of 15%; that is, it will have a negative present worth value for the desired MARR 33% of the time. D (cid:0) (cid:25) (cid:0) (cid:25) D D 15.3.2 TRIANGULAR DISTRIBUTION PROPERTIES The triangular distribution is described by a lower limit, the most likely value (which is also called the mode) and an upper limit. Costs of individual items tend to follow the triangular distribution rather than the normal distribution. The equations for the cumulative PDFs, mean, and variance are listed in many sources, such as Wikipedia [4] and Garvey [2]. P .x < M / P .x > M / D D .x 1 L/2=..U (cid:0) .U x/2=..U (cid:0) L/ (cid:0) (cid:0) (cid:2) L/ (cid:0) (cid:2) (cid:0) .U .M L// for L x M M // (cid:0) (cid:20) for M (cid:20) L x (cid:20) (cid:20) where L U M Lower limit Upper limit Most Likely Value, also called Mode D D D (cid:22) (cid:27) 2 D D E.x/ D Var.x/ .L M C .1=18/ D C (cid:2) U /=3 ..M L/ (cid:2) (cid:0) .M (cid:0) U / C .U (cid:0) L/2/ (15.11a) (15.11b) (15.12) (15.13) Basic Triangular Probability Example A variable follows the triangular distribution and has a most likely value of 12 and a lower limit of 7 and a upper limit of 20. What is the mean, standard deviation, the probability that the random variable is less than 10, the probability the random variable is between 8 and 10, and 236 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS the probability the random variable is greater than 18? U /=3 .7 12 20/=3 13 C (cid:2) 7/ ..M .12 (cid:0) (cid:0) (cid:2) D L/ C .M C U / (cid:2) 20/ (cid:0) .20 C 7/2/ C (cid:0) D .U D (cid:0) 7:17 L/2/ E.x/ D Var.x/ .L M C .1=18/ D ..12 .1=18/ (cid:2) .7:17/1=2 .10 D 7/2=..20 (cid:0) 2:68 (cid:22) (cid:27) 2 (cid:27) P .x < 10/ P .8 < x < 10/ P .x < 8/ D D D D D D D 7/ .12 7/ (cid:0) D 0:138 D 13:8% (cid:0) P .x < 10/ (cid:0) (cid:2) P .x < 8/ (cid:0) 7/2=..20 .8 (cid:0) 7/ (cid:2) (cid:0) .12 (cid:0) 7/ D 0:015 D 1:5% Therefore, P .8 < x < 10/ P .X > 18/ D D D P .x < 10/ P .x < 8/ 13:8% (cid:0) P .x < 18/ 1 :038(cid:141) (cid:140)1 (cid:0) D D (cid:0) 0:038 D (cid:140)1 D .20 (cid:0) (cid:0) 3:8%: 1 1 (cid:0) (cid:0) 1:5% D (cid:0) 18/2=..20 12:3% 7/ (cid:2) (cid:0) .20 (cid:0) 12//(cid:141) PERT and the Cooper and Davidson Approach The triangular distribution is often used in cost analysis as individual cost components tend to follow the triangular distribution rather than the normal distribution, but the sum of cost components via the central limit theorem will have a normal distribution. The PERT [5] and Cooper and Davidson [6] approaches use modiﬁed triangular versions with more weight on the mode than on the outside limits. The Program Evaluation and Review Technique (PERT), utilizes the triangular distribution with a high (optimistic), low (pessimistic), and most likely values and that is similar to the Optimistic-Pessimistic Analysis of Chapter 14. PERT was ﬁrst used in the late 1950s in the development of the Polaris nuclear submarine program. As in the use of the Optimistic-Pessimistic Analysis Technique, it is assumed that the high and low values are known (or can be estimated) and are the endpoints of the distribution. The normal distribution with its endpoints of inﬁnity (plus and minus) is not practical in cost analysis situations as negative costs would not be reasonable for a single component. It is very diﬃcult to estimate the end points, and Cooper and Davidson (C&D) have modiﬁed the parameters so the end points are 10% values; that is, the low estimate implies there is only a 10% chance of having a value lower than this estimate and the high estimate implies there is only a 10% chance of having a value higher than this estimate. Using this deﬁnition, their expressions for the mean and standard deviation are: (cid:140)H (cid:140)H (cid:22) (cid:27) D D C (cid:0) 2M L(cid:141)=4 C L(cid:141)=2:65; (15.14) (15.15) where 15.3. CONTINUOUS PROBABILITY MODELS 237 H D L D M D 2:65 D high estimate low estimate most likely value (Mode) value for 80% conﬁdence level. Note that the expression for the mean for the previous problem would be: (cid:140)H (cid:22) D C 2M C L(cid:141)=4 .20 2 (cid:2) C 12 C D 7/=4 D 12:75: This is less than the mean value of 13 for the actual triangular distribution as the mode has a higher weight in the approximation expression. It could be higher or lower if 2M is higher or lower than .H L/. Note that the mode has the same weight as the total of the high and C low estimates in determining the mean. The equations used in PERT are very similar to those of C&D, but they assume the high and low values are the actual high and low values with no probability of being outside the limits and a conﬁdence limit of approximately 100%. The standard deviation equation represents the range divided by 6, which is occasionally used to estimate the standard deviation when the normal distribution is used. Those equations for PERT analysis are: (cid:140)H (cid:140)H (cid:22) (cid:27) D D C (cid:0) 4M C L(cid:141)=6; L(cid:141)=6 (15.16) (15.17) where H L M 6 high estimate low estimate most likely value (Mode) D D D value for 100% conﬁdence level. D Note that the expression for the mean for the previous problem would be: (cid:140)H (cid:22) D C 4M C L(cid:141)=6 .20 4 (cid:2) C 12 C D 7/=6 D 12:50: This is less than the value of 13 for the actual triangular distribution as the median has a higher weight in the approximation expression. It could be higher or lower if 4M is higher or lower than 2 L/. In these formulas the most likely value or mode is used, and if the distribution was normal, the mean and the mode would be equal. Note that the mode has twice the weight of the sum of the high and low estimates in PERT vs. equal weights in the C&D approach. .H C (cid:2) 238 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS Triangular Cash Flow Analysis Using Cooper and Davidson Approach A present worth cash ﬂow analysis, in million dollar units, was performed using the Cooper and Davidson [6] equations using the assumption that there is only a 10% chance that the value will be higher or a 10% chance that it will be lower than the lower limit. This represents a 80% conﬁdence range and the following values were obtained in Table 15.6: Table 15.6: Cash ﬂow analysis data for C&D approach 16:982 C 342:811=2 D D (cid:27) 2 (cid:27) P (cid:140)CF < 0(cid:141) MinCFAT MaxCFAT D 9:75 9:75 D (cid:136)(cid:140).0 D D The range would be (cid:0) 6:792 C 18:51 2:832 D 342:81 9:75/=18:51(cid:141) 18:51=2 18:51=2 (cid:0) 2:65 2:65 (cid:2) (cid:2) (cid:136)(cid:140) 0:526(cid:141) (cid:0) 14:8 34:3: D D (cid:0) D C (cid:0) C 14:8 to 34:3 or 49:1 million dollars. 0:30 D (cid:25) 30% Traditional analysis indicates that the project will make 15 million dollar units using the most likely values. The C&D risk analysis indicates that, due to the variability in the data, the expected value of the CFAT is only 9.75 million because of the range of cash ﬂow components. Also, there is a 10% chance that the project will have a cash ﬂow of a negative 14.8 million or lower. There is also a 10% chance the project will have a cash ﬂow greater than 34.3 million. The relatively high probability of a negative cash ﬂow at approximately 30% would tend to cause rejection of the project. Triangular Cash Flow Analysis Using PERT Approach An analysis using PERT would have a larger range for the higher and lower values as that assumes the lower and upper limits are absolute values; that is there is no chance of higher or lower values. The follow is using estimated values for the higher and lower limits for the 3 standard deviations of the revenues and expenses of 30 and 50% values. These are the upper accuracy range limits for feasibility studies (see Table 15.7). 202 82 470:251=2 C (cid:27) 2 (cid:27) D D 470:25 2:52 21:69 D C D Most LikelyRange (%)Low ValueHigh ValueMean µStandard Deviation σRevenue 150-20/+10120165146.2516.98Expenses60-10/+205472 61.56.79Investment75 -5/+571.2578.75 75.0 2.83Cash Flow+15µ = +9.75σ = 18.51Table 15.7: Cash ﬂow analysis data for PERT approach 15.4. RISK SUMMARY 239 D P (cid:140)CF < 0(cid:141) MinCFAT MaxCFAT D D The range would be 8:0 8:0 0:369(cid:141) (cid:136)(cid:140).0 (cid:0) 6 (cid:2) 6 (cid:2) 8:0=21:69(cid:141) 21:69=2 21:69=2 D (cid:0) D (cid:0) D C C 57:1 to 73:1 or 130:2 million dollars (cid:136)(cid:140) (cid:0) 57:1 73:1 (cid:25) 0:35 35% D (cid:0) Traditional analysis using the most likely values indicates that the project will make the required return plus an additional 15 million dollar units. This PERT risk analysis indicates that, due to the variability in the data, the expected value of the additional CFAT is only 8 million. 57:1 million to a positive 73.1 million. The range is larger The estimate range is from a low of than the C&D analysis as the conﬁdence level would be nearly 100% instead of 80%. The higher probability of a negative cash ﬂow at approximately 35% would tend to cause rejection of the project. The PERT values results in a wider estimate range and higher probability of a negative cash ﬂow. The larger range of the PERT analysis, approximately 130 million dollars, vs. that of the C&D, approximately 50 million dollars, is what had led to the development of the C&D approach. (cid:0) If the exact same ranges were used for the PERT and C&D models, the PERT would have a smaller range as it divides the range by 6 vs. 2.65 for C&D. The PERT method also puts more weight on the mode in calculating the distribution mean. 15.4 RISK SUMMARY The basic risk analysis methods in of Sensitivity Analysis and Optimistic-Pessimistic Analy- sis give a point estimate value, but no indication of the range of possible error. The sensitivity analysis gives an indication of the eﬀect of critical variables upon the engineering economic expression by examining speciﬁc cases to determine which variables are critical for cost con- trol of the process. The optimistic-pessimistic analysis is generally restricted to two variables to determine which variable is more important. The discrete probability analysis requires that the discrete probability density function for each of the possible events be known and when the number of events is numerous, it can be tedious to evaluate. However, the mean can be calculated to determine the expected proﬁt of Most LikelyRange (%)Low ValueHigh ValueMean µStandard Deviation σRevenue 150-50/+307519514520Expenses60-30/+504290 628Investment75 -10/+1067.582.5 75 2.5Cash Flow+15µ = +8.0σ = 21.69240 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS the process and the probability of a loss can be determined by summing the probabilities of those events in which a loss occurs. The continuous probability analysis uses the data and the probability density function for that data set to calculate the mean and standard deviation. The probability of an individual item has zero probability, so an event represents a continuous range of events. The two primary density functions for the analysis of cost data are the triangular distribution and the normal distribution. The normal distribution can be used for analyzing the sum of individual distributions which may not be normal, but will approach the normal distributions via the central limit theorem. The triangular distribution is better for estimating individual revenue and cost components as the most likely value is usually not the mean in cost analysis and the total cost can be estimated with the normal distribution via the central limit theorem. The advantage of probability analysis is that it is able not only to determine a range but also determine the probability of a loss. The PERT method is applied more and has a higher conﬁdence level than the C&D approach but the longer range of PERT tends to lower the estimated mean and results in a higher standard deviation leading to a higher probability of a loss. The variability of the estimate and conﬁdence level of the estimate are important in evaluating the risk of the project. 15.5 REFERENCES [1] Lindgren, B. W. and McElrath, G. W., Introduction to Probability and Statistics, The McMillan Company, New York, p. 277, 1959. 227 [2] Garvey, Paul R., Probability Methods for Cost Uncertainty Analysis, Marcel Dekker, Inc, New York, pp. 109–112, 2000. 227, 235 [3] Garvey, Paul R., Probability Methods for Cost Uncertainty Analysis, Marcel Dekker, Inc, New York, pp. 51–53, 2000. 229 [4] Wikipedia Web Page, (2-17-2018). https://en.wikipedia.org/wiki/Triangular_d istribution 235 [5] Wikipedia Web Page, (2-17-2018). https://en.wikipedia.org/wiki/Program_eval uation_and_review_technique 236 [6] Cooper, D. O. and Davidson, L. B., The parameter method for risk analysis, Chemical Engineering Progress, pp. 73–78, November 1976. 236, 238 15.6 EVALUATIVE QUESTIONS 1. Use the following discrete data matrix, complete the matrix (Table 15.8) and calculate the mean and standard deviation of the Present Worth (15%). 15.6. EVALUATIVE QUESTIONS 241 PW.15%/ 2;457;204 SP.$=kg/ (cid:2) (cid:0) D 85;859;244 Table 15.8: Selling price data matrix 2. Donnie the Dealmaker has a revised set of revenue probabilities. Complete Table 15.9 and answer the following questions. (a) What is the expected proﬁt?. (b) What is the variance of the proﬁt? (c) What is the standard deviation of the proﬁt? (d) What is the range for the possible proﬁt scenarios? (e) What is the actual probability of a loss? (f ) What is the probability of a loss using the normal distribution? 3. The mean of a normal distribution is 1,000 and the standard deviation is 100. (a) What is the probability that a random variable selected from that distribution is less than 700? (b) What is the probability that the random variable selected is less than 900? Sales Price $/KgProbabilityPresent Worth (15%)Expected Selling Price 5/KgE(x2) for VarianceExpected Present Worth (15%)E(x2) for Variance of PW (15%)xp(x)PW/103xp(x)x2 p(x)300.10340.30380.30420.30460.10Totals1.00µ (Selling Price) =_______σ2 (Selling Price) = _______µ (Present Worth (15%)) =_______σ2 (Present Worth (15%)) = _______242 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS Table 15.9: Revenues, costs, and proﬁts for Donnie the Dealmaker’s revised product investment (c) What is the probability that the random variable selected is greater than or equal to 1,200? (d) What is the probability that the random variable is between 900 and 1,100? 4. A variable follows the triangular distribution and has the lower limit of 600, an upper limit of 2,200 and the most likely value of 1,200. (a) What is the mean? (b) What is the standard deviation? (c) What is the probability that the variable is less than 800? (d) What is the probability that the variable is greater than 1,500? (e) What is the probability that the variable is between 800 and 1,500? 5. The cash ﬂows for a project with an initial investment of $20,000 are in Table 15.10. (a) If the MARR is 10%, what is the present worth of the cash ﬂows? (b) What is the variance of the cash ﬂows? (c) What is the standard deviation of the cash ﬂows? (d) What is the probability that the cash ﬂows will be negative? (e) What is the probability that the cash ﬂow is less than 2000? Revenue AmountRevenue ProbabilityCost AmountCost ProbabilityProﬁ t AmountProﬁ t ProbabilityExpected Proﬁ tE(X2)400.3300.2100.060.66400.3400.500.150.00400.3500.3-100.09-0.99500.5300.220 500.5400.310500.5500.50600.2300.230600.2400.320600.2500.510Totals1.00Table 15.10: Cash ﬂows for a project with an initial investment of $20,000 15.6. EVALUATIVE QUESTIONS 243 6. The values in Table 15.11 were obtained is the response to the bids for a contract. The bids are assumed to follow a normal distribution. (a) What is the actual range of the bids? (b) What is the mean value of the bid distribution? (c) What is the standard deviation for the bid distribution? (d) What is the probability that a bid would be less than $350,000? (e) What is the probability that a bid would be greater than $450,000? Table 15.11: Bids for a contract 7. (a) Cost/value engineers were sent back to re-examine a project with the new data pro- vided. (See Table 15.12.) Using the C&D approach, determine the “risk” and would you recommend the project? – What is the mean value? – What is the standard deviation? – What is the probability the cash ﬂow is negative? YearExpected Cash Flow µStandard Deviationof Cash Flow σVariance of Cash Flow σ20-20,00010010,00018,00020040.00029,00030090,000310,000400160,000Bid NumberEstimate (1,000 $ Units)03501420237533905370244 15. RISK ANALYSIS WITH PROBABILITY CONSIDERATIONS – What is the probability that the cash ﬂow is less than 10? – What is the probability the cash ﬂow is less than 20? – Why or why not do you recommend the project? Table 15.12: Cash ﬂow analysis data for C&D approach (b) Using the PERT approach (see Table 15.13), determine the “risk” and would you recommend the project? – What is the mean value? – What is the standard deviation? – What is the probability the cash ﬂow is negative? – What is the probability that the cash ﬂow is less than 10? – What is the probability the cash ﬂow is less than 20? – Why or why not do you recommend the project Table 15.13: Cash ﬂow analysis data for PERT approach 8. The cash ﬂows from a project are presented in Table 15.14. The required rate of return is 10%. What is the present worth of the expected cash ﬂow on the project and what is the probability that the cash ﬂow from the project has a loss? (a) What is the present worth of the expected cash ﬂows at a MARR of 10%? Most LikelyRange (%)Low ValueHigh ValueMean µStandard Deviation σRevenue 140-15/+5Expenses50-10/+15Investment70 -5/+5Cash Flow+20µ = σ = Most LikelyRange (%)Low ValueHigh ValueMean µStandard Deviation σRevenue 140-15/+5Expenses50-10/+15Investment70 -5/+5Cash Flow+20µ = σ = (b) What is the standard deviation of the cash ﬂows for the project? (c) What is the probability the project will have zero cash ﬂows with the MARR of 10%? (d) What is the probability the project will have zero cash ﬂows with the MARR at 20%? 15.6. EVALUATIVE QUESTIONS 245 Table 15.14: Cash ﬂows from a project YearExpected Cash Flow µ($)Standard Deviationof Cash Flow µVariance of Cash Flow µ20-9,000100 10,0001 4,000200 40,0002 4,000400 160,0003 4,000600 360,000A P P E N D I X A 247 Discrete and Continuous Compounding Factors Please see the tables on the pages that follow. 248 A. DISCRETE AND CONTINUOUS COMPOUNDING FACTORS t s e r e t n i e t e r c s i d d n a s t n e m y a p e t e r c s i D — s n o i s s e r p x e c i m o n o c e f o s r o t c a f g n i d n u o p m o c e t e r c s i D : 1 . A e l b a T Payment TypeFactor NameFindGivenSymbolFormulaA. Single PaymentPresent WorthPF(P/F, i, n)(1 + i)-nFuture Worth (Compound Amount)FP(F/P, i ,n)(1+i)n B. Uniform PaymentSinking FundAF(A/F, i ,n)i / [(1+ i)n -1] (Uniform Series)Capital RecoveryAP(A/P, i, n)[(i(1+i)n) ] / [ (1+i)n - 1] Compound AmountFA(F/A, i, n)[(1+i)n -1] / iPresent WorthPA(P/A, i, n)[(1+i)n -1] / [i(1+i)n]C. Uniform Gradient Expression Standard Uniform GradientUniform Gradient Present WorthPG(P/G, i, n)[((1+i)n - 1 -ni) / ( i2 (1+i)n )] Uniform Gradient Future WorthFG(F/G, i, n)[((1+i)n - 1 -ni) / i2 ]Uniform Gradient Uniform SeriesAG(A/G, i ,n)[((1+i)n - 1 -ni) / ((1+i)n -1)] Uniform Ramp GradientUniform Ramp Gradient Present WorthPᴿG(Pᴿ/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i2 (1+i)n )] Uniform Ramp Gradient Future WorthFᴿG(Fᴿ/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i2)] Uniform Ramp Gradient Uniform SeriesAᴿG(Aᴿ/G, i, n)[((1+i)n+1 - 1 –i(n+1)) / ( i(1+i)n - 1)] D. Geometric Gradient Expression Geometric GradientGeometric Gradient Present WorthPA1, g(P/A1,g, i, n)[(1-((1+g)n/(1+i)n))/(i-g)]If g=i(P/A1,g=i, n)n/(1+i)Geometric Gradient Future WorthFA1, g(F/A1, g, i, n)[((1+i)n – (1+g)n)]/[i-g]If g=i(F/A1, g=i, n)n(1+i)(n-1)Geometric Gradient Uniform SeriesAA1, g(A/A1, g, i, n)[(i((1+i)n –(1+g)n))/((i-g)((1+i)n-1))]If g=i(A/A1, g=i, n)[ni(1+i)(n-1)]/ [(1+i)n -1] Escalation GradientEscalation Gradient Present WorthPᴇA1, ᴇ(Pᴇ/A1, ᴇ,i, n)[(1+ᴇ) /(ᴇ - i)] [((1+ᴇ)/(1+i))n -1]If ᴇ=i(Pᴇ/A1, ᴇ=i, n)nEscalation Gradient Future WorthFᴇA1, ᴇ(Fᴇ/A1, ᴇ,i, n)[(1+ᴇ) /(ᴇ - i)] [((1+ᴇ)n - (1+i))n]If ᴇ=i(Fᴇ/A1, ᴇ=i, n)n(1+i)nEscalation Gradient Uniform SeriesAᴇA1, ᴇ(Aᴇ/A1, ᴇ,i, n)[(i(1+ᴇ)/(ᴇ - i))((1+ᴇ)n - (1+i)n)]/[(1+i)n-1]If ᴇ=i(Aᴇ/A1, ᴇ=i,n)ni(1+i)n /[(1+i)n -1]Notation:P=Present Worth; i = eﬀ ective discrete interest rate per period; A=uniform end-of-period payments; n = number of periods;F=Future Worth; g=Geometric Gradient Rate; G=Uniform Gradient Amount; ᴇ = Escalation Gradient Rate;A1 = Initial Geometric Gradient Amount and Initial Escalation Gradient Amountappendix1249 t s e r e t n i s u o u n i t n o c d n a s t n e m y a p e t e r c s i D — s n o i s s e r p x e c i m o n o c e f o s r o t c a f g n i d n u o p m o c s u o u n i t n o C : 2 . A e l b a T Payment TypeFactor NameFindGivenSymbolFormulaA. Single Payment Present WorthPF(P/F, r, n)e-r nFuture WorthFP(F/P, r, n)er nB. Uniform Payment (Uniform Series)Sinking FundAF(A/F, r, n)[(er-1)/(er n-1)]Capital RecoveryAP(A/P, r, n)[er n(er-1)/(er n-1)]Future WorthFA(F/A, r, n)[(er n-1)/(er-1)]Present WorthPA(P/A, r, n)[(er n-1)/ (er n(er-1))]C. Uniform Gradient Expressions Standard Uniform GradientUniform Gradient Present WorthPG( P/G, r, n){[(er n-1) - n(er-1)]/[(er-1)2 er n)]}Uniform Gradient Future WorthFG( F/G, r, n){[(er n-1) - n(er-1)]/[(er-1)2 )]}Uniform Gradient Uniform SeriesAG( A/G, r, n){[(er n-1) - n(er-1)]/[(er-1)( er n -1)]} Uniform Ramp GradientUniform Ramp Gradient Present WorthPᴿG( Pᴿ/G, r, n){[(er((n+1)-1)-(n+1)(er-1)]/[(er-1)2(er n)]}Uniform Ramp Gradient Future WorthFᴿG( Fᴿ/G, r, n){[(er((n+1)-1) - (n+1)(er-1)]/[(er-1)2 ]}Uniform Ramp Gradient Uniform SeriesAᴿG( Aᴿ/G, r, n){[(er((n+1)-1) - (n+1)(er-1)]/[(er-1)2(er n-1)]}D. Geometric Gradient Expressions Geometric GradientGeometric Gradient Present WorthPA1,,b(P/A1, b, r, n) {[1-(ebn/er n)]/[er - eb)]}If b=r(P/A1, b=r, n) n/erGeometric Gradient Future WorthFA1,b(F/A1, b, r, n) {[er n-ebn)]/[er - eb)]}If b=r(F/A1, b=r, n)n/er(n-1)Geometric Gradient Uniform SeriesAA1,b(A/A1, b, r, n) {[er n-ebn)]/[er - eb)]} {[(er -1) / (er n-1)]}If b=r(A/A1, b=r, n) [n{(er n )/(er n-1)] [(er-1)/(er)] Escalation GradientEscalation Gradient Present WorthPᴇA1,c(Pᴇ/A1, c, r, n) {[((ec)/(ec-er))] * [(ecn - er n)/ern]If c=r(Pᴇ/A1, c=r, n) nEscalation Gradient Future WorthFᴇA1.c(Fᴇ/A1, c, r, n) {[((ec)/(ec-er))] * [(ecn - er n)]If c=r(Fᴇ/A1, c=r, n) nernEscalation Gradient Uniform SeriesAᴇA1,c(Aᴇ/A1, c, r, n) {[((er-1)(ec)/(ec-er)] * [(ecn-er n)/(er n-1)]}If c=r(Aᴇ/A1, c= r, n{[n(er -1)er n/ (er n -1)}Notation:P=Present Worth; i = eﬀ ective discrete interest rate per period; A=uniform end-of-period payments; n = number of periods;F=Future Worth; g=Geometric Gradient Rate; G=Uniform Gradient Amount; ᴇ = Escalation Gradient Rate;A1 = Initial Geometric Gradient Amount and Initial Escalation Gradient AmountAuthor’s Biography 251 ROBERT C. CREESE Dr. Robert C. Creese was Professor of Industrial and Management Systems Engineering at West Virginia University and taught courses on Engineering Economy, Advanced Engineering Economics, Cost and Estimating for Manufacturing, Manufacturing Processes, and Advanced Manufacturing Processes. He has previously taught at The Pennsylvania State University (9 years), Grove City College (4 years), Aalborg University in Denmark (3 sabbaticals), and West Virginia University for 35 years. He worked at US Steel for two years as an Industrial Engineer before starting his teaching career. Dr. Creese is a Fellow of the AACE International, received the Charles V. Keane Service Award and Brian D. Dunﬁeld Educational Service Award presented by AACE International, and was treasurer of the Northern West Virginia Section of AACE International for more than 20 years. He is a Life Member of AACE International, ASEE (American Society for Engineer- ing Education), and ASM (American Society for Materials). He also is a member of ICEAA (International Cost Estimating & Analysis Association), AIST (Association for Iron & Steel Technology), AWS (American Welding Society), and AFS (American Foundry Society). He obtained his B.S. in Industrial Engineering from The Pennsylvania State University, his M.S. in Industrial Engineering from the University of California at Berkeley, and his Ph.D. in Metallurgy from The Pennsylvania State University. Dr. Robert C. Creese has authored the book Introduction to Manufacturing Processes and Materials (Marcel Dekker-1999) and co-authored two books Estimating and Costing for the Metal Manufacturing Industries (Marcel Dekker-1992) with Dr. M. Adithan, Professor Emer- itus of VIT University Vellore, India, and Dr. B.S. Pabla of the Technical Teachers’ Training Institute, Chandigarh, India, and Strategic Cost Analysis for Project Managers and Engineers (New Age International Publishers-2010) with Dr. M. Adithan, VIT University, Vellore, India. He has authored/co-authored more than 100 technical papers.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8355744.pdf&bkn=8355743&pdfType=book	Series ISSN 1939-5221 Data Mining and Market Intelligence Implications for Decision Making Mustapha Akinkunmi, American University of Nigeria This book is written to address the issues relating to data gathering, data warehousing, and data analysis, all of which are useful when working with large amounts of data. Using practical examples of market intelligence, this book is designed to inspire and inform readers on how to conduct market intelligence by leveraging data and technology, supporting smart decision making. The book explains some suitable methodologies for data analysis that are based on robust statistical methods. For illustrative purposes, the author uses real-life data for all the examples in this book. In addition, the book discusses the concepts, techniques, and applications of digital media and mobile data mining. Hence, this book is a guide tool for policy makers, academics, and practitioners whose areas of interest are statistical inference, applied statistics, applied mathematics, business mathematics, quantitative techniques, and economic and social statistics. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com store.morganclaypool.com A K I N K U N M I D A T A M N I I N G A N D M A R K E T I N T E L L I G E N C E M O R G A N & C L A Y P O O L Data Mining and Market Intelligence Implications for Decision Making Mustapha Akinkunmi Data Mining and Market Intelligence Implications for Decision Making Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi 2018 Empowering Proessional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimizaton, Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 iii Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 iv Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 v Copyright © 2018 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi www.morganclaypool.com ISBN: 9781681733203 ISBN: 9781681733210 ISBN: 9781681733227 paperback ebook hardcover DOI 10.2200/S00838ED1V01Y201803ENG030 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Series ISSN Print 1939-5221 Electronic 1939-523X Data Mining and Market Intelligence Implications for Decision Making Mustapha Akinkunmi American University of Nigeria SYNTHESIS LECTURES ON ENGINEERING #30 CM&cLaypoolMorganpublishers&ABSTRACT This book is written to address the issues relating to data gathering, data warehousing, and data analysis, all of which are useful when working with large amounts of data. Using practical examples of market intelligence, this book is designed to inspire and inform readers on how to conduct market intelligence by leveraging data and technology, supporting smart decision making. The book explains some suitable methodologies for data analysis that are based on robust statistical methods. For illustrative purposes, the author uses real-life data for all the examples in this book. In addition, the book discusses the concepts, techniques, and applications of digital media and mobile data mining. Hence, this book is a guide tool for policy makers, academics, and practitioners whose areas of interest are statistical inference, applied statistics, applied mathematics, business math- ematics, quantitative techniques, and economic and social statistics. KEYWORDS data mining, decision making, market intelligence, market pooling, survey ix To Dr. Sarah Omotunde Alade, Former Deputy Governor (Economic Policy), Central Bank of Nigeria Contents xi Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1 Introduction to Market Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Understanding the Link Between Marketing Insights and Decision Making . . 1 Transform Data into Insights for Decisions: Segmentation, Positioning, 1.2 Product Development, etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Market Intelligence Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Scientiﬁc Method and Technology of Marketing Research . . . . . . . . . . . . . . . . 3 1.4 1.5 Innovative Solutions to Real-life Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.6 Designing the Research Methodology, Questionnaire, Sampling Plan, and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Turning Data into Strategic Insights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.7 1.8 2 The Market Research Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 The Marketing Research Framework and Process . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Research Problems and Correct Design Techniques . . . . . . . . . . . . . . . . . . . . . 10 2.3 Data Collection Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Generating Marketing Insights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 3 Qualitative Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1 3.2 3.3 Self-administered Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Personal Interview or Face-to-Face Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 xii 4 5 6 7 Quantitative Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.1 Data Preparation and Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 Fundamentals of Quantitative Methods and Their Applications . . . . . . . . . . . 19 4.3 Concept of Distribution Pattern, Central Tendency, and Dispersion . . . . . . . 20 4.3.1 Distribution Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3.2 Measure of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3.3 Measure of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4 Construction of Conﬁdence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4.1 Application of Conﬁdence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5 Other Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5.1 Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5.2 Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6 Hypothesis Testing and Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1 Data Preparation and Evaluation for Quantitative Analysis . . . . . . . . . . . . . . . 39 5.2 Constructing and Testing Data Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.3 Regression Analysis: Concept and Applications (Interpret Data Relationships and Forecasting) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.3.1 Assumptions of Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.3.2 Simple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.3.3 Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.3.4 Assumptions of Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4 Analyzing Survey Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.1 Quantitative Technique of Collecting Survey Data: Consumer Expenditure Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Types of Measurement Scales and Their Applications . . . . . . . . . . . . . . . . . . . 51 Survey Research Rigor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Testing Data Quality: Survey Error Detection Procedures . . . . . . . . . . . . . . . 55 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 6.3 6.4 6.5 Index Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.1 bra Expectation Index: Principles, Techniques, and Applications . . . . . . . . . . 59 7.1.1 Objectives of bra Expectation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 xiii 7.2 7.3 7.4 7.5 7.6 7.1.3 Calculation of bra Expectation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 bra Consumer Conﬁdence Index: Principles, Techniques, and Applications . . 61 7.2.1 Components of braCCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.2.3 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 7.2.4 Index Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 braIndex: Principles, Techniques, and Applications . . . . . . . . . . . . . . . . . . . . . 63 7.3.1 Basic Criteria for Selection of Constituent Stocks . . . . . . . . . . . . . . . . . 63 7.3.2 Technical Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.3.3 Fundamental Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.3.4 Corporate Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 7.3.5 Stock Splits Adjustment Barometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.3.6 Free-ﬂoat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.3.7 Calculation of braIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.3.8 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7.3.9 Measure of braIndex Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.3.10 Index Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 bra Producer Price Index: Principles, Techniques, and Applications . . . . . . . . 75 7.4.1 Uses of braPPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.4.2 Components of braPPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4.3 Scope and Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4.4 Collection of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.4.5 Index Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.4.6 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 bra Bond Index: Principles, Techniques, and Applications . . . . . . . . . . . . . . . 78 7.5.1 Deﬁnition of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.5.2 Basic Criteria for Constituent Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.5.3 Index Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.5.4 Sub-indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.5.5 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 braInﬂation Index: Principles, Techniques, and Applications . . . . . . . . . . . . . 85 7.6.1 Uses of bra Inﬂation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7.6.2 Classiﬁcation of braII Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7.6.3 Period of the Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.6.4 Data Collection, Collation, and Processing . . . . . . . . . . . . . . . . . . . . . . 87 7.6.5 Quality Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.6.6 Index Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 xiv 8 9 7.6.7 bra Inﬂation Indices Publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.6.8 Expenditure Category Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.6.9 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.7 Digital Media Monitoring, Measurement, and Modeling . . . . . . . . . . . . . . . . . 97 8.1 Understandings of Social Media Monitoring, Measurement, and Modeling . 97 Strategic Insight of Social Media Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 98 8.2 Social Media Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 8.3 Social Media Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 8.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 8.5 Causal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9.1 Marketing Mix Modeling: Concept, Principles, Methods, and Applications 109 Eﬀective Communication of Research, Intelligence, and Analytic Insights . 112 9.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 9.3 10 Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 10.1 Concept of Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 10.2 Activities of Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 10.3 Architecture of Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 10.4 Algorithms of Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 10.5 Application of Mobile Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 10.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 A Questionnaires, Items Survey, and Weights of Elementary Items . . . . . . . . . . 121 A.1 Sample of Business Expectation Survey Questionnaire . . . . . . . . . . . . . . . . . 121 A.2 List of Items Survey Monthly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 A.3 Weights of Some Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Foreword xv Data Mining and Market Intelligence: Implications for Decision Making, could not have been writ- ten at a more appropriate and relevant time. Central banking, especially monetary policy, is often regarded as boring and uninspiring; this erroneous conclusion is reached due to the visible out- come of monetary policy committees’ decisions—whether to hold the policy rate steady or raise or drop the benchmark by a few basis points. Thus, the common belief is that there is limited scope for complex decision making and data management techniques in a central bank setting. However, unbeknownst to many, a variety of analytical techniques including data mining and market intelligence—supported by extensive research and consumer polls—are employed by the staﬀ of central banks. This is sometimes bolstered by the input from consultants before ar- riving at various policy options, the consequences of which are subject to extensive deliberations by policy makers. Dr. Mustapha Abiodun Akinkunmi is an expert in macroeconomics and has been con- ducting data mining research through his consulting assignment with the Central Bank of Nige- ria, spanning almost 10 years from March 2008 to December 2017. He has shared his expertise in great detail in this book, particularly regarding technical details including research method- ology, market intelligence, and data collection methods. He exposes readers to qualitative tools and techniques deployed in processing data including hypothesis testing, regression analysis, and other methods. The analysis of survey data using indices, including the author’s customized “bra Bond index,” was also explained in great detail. He provides a comprehensive overview of digital me- dia monitoring, measurement, and modeling, and explains the distinction between digital and social media. Methods of exploring cause and eﬀect relationships—very useful in monitoring the impact of monetary policy decisions—are also thoroughly explored. Mobile data mining, featured in Chapter 10, should be of interest to younger experts. As a member of the central Bank of Nigeria Monetary Policy Committee for 10 years, I greatly appreciate the positive impact of Dr. Akinkunmi’s consulting assignments, and how profoundly his work has assisted us in conducting sound monetary policy in spite of the political and socio-economic constraints of the time. xvi FOREWORD This book is strongly recommended for researchers, statisticians, and policy makers, and can also serve as a textbook to support teaching data mining at universities and colleges. Tunde Lemo, OFR Former Deputy Governor Central Bank of Nigeria xvii Preface This book is written to address the issues relating to data gathering, data warehousing and data analysis. These are useful when working with large amounts of data. Using practical examples of market intelligence, this book is to inspire and inform readers on how to conduct market intelli- gence by leveraging data and technology, supporting smart decision-making. The book explains some suitable methodologies for data analysis that are based on robust statistical methods. For illustrative purposes, the author uses real-life data for all the examples in this book. In addition, the book discusses the concepts, techniques and applications of digital media and mobile data mining. Hence, the book is a guide tool for policy makers, academics and practitioners whose areas of interest are statistical inference, applied statistics, applied mathematics, business mathematics, quantitative techniques and economic and social statistics. Mustapha Akinkunmi March 2018 Acknowledgments xix This book grew out of the decade-long market intelligence assignment undertaken at the Cen- tral Bank of Nigeria (CBN). First, I would like to extend my deepest appreciation to Mr. Bola Onadele (Koko). Without his introduction, I would not have met Dr. Sarah Alade with whom I convinced on my understanding of the methodology of market intelligence, leading to the inception of this book. I was fortunate to have had many excellent contributors in the Mon- etary Policy Department (MPD) of the CBN, especially under the leadership of Mr. Moses Ajayi, Dr. Okorie Uchendu, Dr. Alvan Ikoku, and other senior staﬀ of MPD CBN such as Dr. Ngozi Egbuna, Mr. Ademola Bamidele, Mr. J.S. Akuns, Mr. Lawrence Akinboyo, the late Mr. P.J. Obaseki, and numerous others of MPD CBN, whose questions and comments greatly contributed to the clarity and exposition of this text. I owe a great intellectual debt to Dr. Darryl McLeod of Fordham University, my brilliant former professor, my colleagues at Fordham University—Center of International Policy Studies, Dr. Emre Ozsoz and Dr. Erick Rengifo, and Mr. Daniel Eduardo Butt of Grenoble Ecole de Management. To the founding directors of Brickﬁeld Road Associates Limited (bra), Mr. Wale Edun and Mr. Tunde Folawiyo: I thank you both for your ﬁnancial contribution and encouragement. Additional signiﬁcant contributions were made by my colleagues at bra, Mr. Saheed Bello and Mr. Lanre Sanni. I am exceptionally grateful to these gentlemen. Parts of this book were written while I was teaching at the Economics Department of Montclair State University and State University of New York—FIT during 2017. I would like to extend my appreciation to both institutions for their wonderful, supportive working environ- ments and friendly atmosphere. Mustapha Akinkunmi Chair, Accounting and Finance School of Business and Entrepreneuship American University of Nigeria Yola, Nigeria March 2018 Acronyms xxi American Marketing Association Automated Teller Machine Brickﬁeld Road Associates Consumer Conﬁdence Index Business Expectation Index Brickﬁeld Road Associates Brickﬁeld Road Associates Inﬂation Index Brickﬁeld Road Associates Index Brickﬁeld Road Associates Producer Price Index Central Bank of Nigeria Consumer Expenditure Survey Conﬁdence Interval Consumer Price Index Central Processing Unit Deoxyribonucleic Acid Expectation Index Extract, Transform, and Load Earnings Per Share Foreign Direct Investment Focus Group Discussion Gross Domestic Products Gross National Income Gross Rating Points AMA ATM braCCI BES bra braII braIndex braPPI CBN CES CI CPI CPU DNA EI ETL EPS FDI FGD GDP GNI GRPs xxii ACRONYMS HTTP IIR INFL IPR IQR ITR LBS Hypertext Transfer Protocol Index of Interest Returns Inﬂation Index of Price Returns Interquartile Range Index of Total Returns Location-Based Service MMM Marketing Mix Model NBS NSE POS PSI ROE ROI SOA TRPs WDI XML National Bureau of Statistics Nigerian Stock Exchange Point of Sale Present Situation Index Return on Equity Return on Investment Service-Oriented Architecture Target Rating Points World Database Indicator Extensible Markup Language C H A P T E R 1 1 Introduction to Market Intelligence This introductory chapter will broadly deﬁne issues related to market intelligence. In addition, we identify important market intelligence tools and provide the strategies to eﬀectively utilize these tools in a market intelligence environment. 1.1 UNDERSTANDING THE LINK BETWEEN MARKETING INSIGHTS AND DECISION MAKING It has become easier to access large volumes of data, thanks to the decreasing cost of data stor- age technologies as well as the wide availability of internet connections. However, the pattern of these data still exhibits heterogeneity in the characteristics of origin, content, and represen- tation. It is pertinent to ask whether it is possible to transform raw data into information and knowledge that can be communicated to and explored by decision makers to support and boost their operations. Market intelligence is a set of mathematical models and analytical techniques that utilizes the existing data to provide valuable insights, which can be critical for supporting the decision- making process in both simple and complex market environments. Making decisions is a continuous process in a complex market environment. These deci- sions may be more or less impactful, have short- or long-term implications, and involve mobi- lizing employees at lower or higher levels of an organizational hierarchy. One of fundamental drivers of the performance and competitive strength of any given organization is the capacity to make well-informed decisions both at the organizational and individual level, especially as modern organizational trends move toward empowering employees and devolving the decision- making processes which may normally be performed by supervisors or management. Most people reach a decision by exploring easy and intuitive approaches that consider factors such as experience, knowledge of their domain, and the quality or breadth of information available to them. This technique results in a constant, reactive decision-making approach that may not be suitable to navigate unstable conditions, such as those arising from frequent and rapid ﬂuctuations in the economic environment. When the possible outcomes of a decision are too diﬃcult to explore using an intuitive method, the processes of decision making require more rigorous approaches in terms of analytical 2 1. INTRODUCTION TO MARKET INTELLIGENCE techniques and mathematical models. Quite a number of decision makers have broadly accepted that the competitive advantages of their ﬁrm are supported by eﬀective strategic decision making. 1.2 TRANSFORM DATA INTO INSIGHTS FOR DECISIONS: SEGMENTATION, POSITIONING, PRODUCT DEVELOPMENT, ETC. Marketing research is deﬁned as the discovery and analysis of information in order to better un- derstand the eﬀectiveness of a ﬁrm’s marketing eﬀorts and to support business strategy. Accord- ing to The American Marketing Association (AMA), marketing research connects the supplier, customer, and public to the marketer through information. This information is utilized to iden- tify and deﬁne marketing opportunities and problems, generate, reﬁne, and evaluate marketing actions, monitor marketing performance and enhance the understanding of marketing as a pro- cess. Marketing research provides the information needed to confront these problems, design the techniques of gathering information, manage and implement the data collection process, analyze the results, and communicate the ﬁndings and their implications. By deﬁnition, marketing research must include customer research since customers are the end user of a product. Marketing research is mainly applied to the following: market sizing, market share analysis, product concept testing, pricing strategies, focus groups, brand perception studies, and customer attitude or perception research. The mix of metrics, marketing research, and data mining is crucial to the eﬀective execu- tion of a marketing plan. Therefore, the following steps are employed to integrate these metrics. 1. Identify relevant stakeholders and their interests. 2. Choose appropriate metrics to measure marketing success. 3. Evaluate market opportunities. This step provides an answer to four basic questions: Where are the market opportunities? What are the market segments? What is the size of each segment? How fast does each segment grow? Market opportunity information can be ob- tained using a variety of techniques. One technique is to explore publicly available news and existing internal ﬁrm-level data. Another technique is to use forecasted data on market opportunities by segment. These forecasts entail both opportunity size and growth infor- mation, based on underlying assumptions. In the absence of existing market opportunity information, customized research is needed to obtain information. 4. Conduct competitive analysis. 5. Derive the optimal marketing spending and media mix. Several analytical methods are em- ployed to model optimal marketing spend. Optimization deals with the maximization or minimization of a particular metric. The most common aim of optimization of marketing spending is proﬁt maximization. 1.3. MARKET INTELLIGENCE TOOLS 3 6. Leverage data mining for optimization and get early buy-in and feedback from key stakehold- ers. As marketing research is used as the bedrock of formulating a high-level marketing strategy, the implementation of this strategy through tactics demands robust analytical modeling. Here, data mining adds value by providing a path to achieve the opportunities opened by research. 7. Track and compare of metric goals and results. Managers monitor the actual outcome of their marketing eﬀorts vs. the marketing plan, in order to evaluate the eﬀectiveness of a cam- paign (or lack thereof ) in meeting the ﬁrm’s targets. If their marketing plans appear suc- cessful, managers can implement these successful tactics and strategies in future market- ing eﬀorts. However, if monitoring reveals that a marketing strategy is failing to meet its goals, managers can learn from the inadequacies of past marketing approaches to lessen the probability of failure in the future. It should also be noted that failure to meet the targets identiﬁed by a marketing plan may not be due to poor execution; it is possible that the original marketing strategy was ﬂawed, and used metrics which were unrealistic, methodologically unsound, or not relevant to the ﬁrm’s actual desired outcomes. 8. Incorporate learning into the next round of marketing planning. As noted in point seven above, managers can look at the deviation of actual results from their plan, identify the reasons for these deviations, and incorporate their experiences to reﬁne future marketing plans. 1.3 MARKET INTELLIGENCE TOOLS The key aim of the market intelligence system is to supply decision makers with the relevant tools and techniques that can enhance their ability to make eﬀective and timely decisions. By applying in-depth analytical approaches, decision makers can make better decisions and strate- gize actionable plans to attain their objectives in a more eﬀective way. This analytical approach requires decision makers to clearly deﬁne both the steps for assessing alternative choices as well as the devices needed to regulate the problem under investigation. In addition, full awareness and understanding of the fundamental logic behind the decision-making process relies on thorough examination and thought. The statistical tools, mathematical models, and algorithms made available through a good market intelligence system support strong logical inference and lead to analytically sound con- clusions, while exploring a large number of possible outcomes in a minimal period of time. 1.4 SCIENTIFIC METHOD AND TECHNOLOGY OF MARKETING RESEARCH Quick responses to the actions of competitors and to new market conditions determine the success or even the survival of a company. The urgency of making speedy and eﬀective decisions is intensiﬁed in markets where competition is ferocious and customer needs constantly evolve. 4 1. INTRODUCTION TO MARKET INTELLIGENCE Broadly, the use of market intelligence systems enhances the scientiﬁc and rational tech- niques used to manage the volatility of complex markets. Mathematical models have been ex- plored to capture a real system in other scientiﬁc disciplines like physics, operation research, etc. Chapters 4 and 5 of this book will provide the key mathematical models utilized in market intelligence and decision-making processes, while applications of these models are presented in Chapters 6 and 7. 1.5 INNOVATIVE SOLUTIONS TO REAL-LIFE ISSUES The success of any market intelligence project depends on the following factors. (a) Technologies: The evolution of technology plays a critical role in boosting the develop- ment of market intelligence systems. The downward trend in the cost of hardware and the increasing ubiquity of cheap storage and software technologies means that the use of sophisticated algorithms and statistical techniques is no longer the sole domain of large ﬁrms. In addition, falling technology costs encourage the use of state-of-the-art graphi- cal visualization approaches, increase data storage capacities, and allow an organization to store terabytes of data for market intelligence systems. With the aid of network connectiv- ity, information, and knowledge extracted from market intelligence systems are diﬀused within organizations. The diﬀusion of data analysis tools is determined by the integra- tion pattern of hardware and software bought by diﬀerent suppliers or built internally by a company. (b) Analytics: Mathematical models, as well as analytical methodologies, perform a crucial responsibility of extracting relevant information and knowledge from the available data within and outside an organization. Merely providing a visualization of data is not a suf- ﬁcient platform for facilitating decision making; it is necessary to supplement graphical representations of data with more advanced models of inductive learning and optimiza- tion to bolster the decision-making process. (c) Human resources: The competencies of employees individually and collectively deter- mine the human assets of an organization. Organizational culture consists of the whole knowledge acquired and shared by these employees. One of the major assets of any or- ganization is the ability of its employees to translate acquired information into practical actions. The value of human assets has become increasingly important in modern times; in fast-developing sectors (such as software development and technology), as physical assets required for production become less costly, more accessible, and homogeneous, a ﬁrm’s employees are a source of value that cannot be replicated by competing ﬁrms. As a con- sequence, ﬁrms must focus on developing the decision-making skills of its employees, and hone their ability to perform analysis, interpret ﬁndings, work out creative solutions, and devise eﬀective action plans. An organization tends to form a comparative advantage 1.6. DESIGNING THE RESEARCH METHODOLOGY, QUESTIONNAIRE, SAMPLING PLAN, AND DATA ANALYSIS 5 by employing people with greater mental quickness and willingness to accept changes in decision-making styles, under the assumption that their decision making will be supported by information gleaned from market intelligence systems. 1.6 DESIGNING THE RESEARCH METHODOLOGY, QUESTIONNAIRE, SAMPLING PLAN, AND DATA ANALYSIS The following key features of the market-related rational approach are as follows. • Identify the aims of the analysis as well as the performance measures used to assess alter- native options. • Build mathematical models that appropriately reﬂect the connections among system con- trol variables, parameters, and evaluation metrics. • Evaluate the impact of variations in the control variables and changes in parameters on performance, using what-if analyses. Other advantages of mathematical models include developing a deeper understanding of the phenomena under investigation, enabling knowledge transfer to other individuals, preserving knowledge, and providing ﬂexible approaches to similar problems. Market Intelligence Designs: The design of a market intelligence system entails three key components. (a) Source of data: The ﬁrst step is to gather and integrate the data stored in the various primary and secondary sources. These sources of data may not be homogenous in origin and type. The data sources are mainly from operational systems, complemented by un- structured documents and data received from external providers. Practitioners will face challenges to unify and integrate the diﬀerent data sources. (b) Data warehouses and data marts: Data from diﬀerent sources are stored in databases, and are extracted using transformation tools known as extract, transform, and load (ETL), in order to improve the analysis of market intelligence. These databases are often called data warehouses and data marts. (c) Market intelligence techniques: Involve the use of extracted data to feed mathemati- cal models and analytical approaches used to aid decision making. The most common techniques include multidimensional cube analysis, exploratory data analysis, time series analysis, inductive learning models for data mining, and optimization models. The building blocks of a market intelligence system are depicted in Figure 1.1. 6 1. INTRODUCTION TO MARKET INTELLIGENCE Figure 1.1: Structure of market intelligence system. (Source: Excerpt from Business Intelligence System.) (d) Data exploration: Tools employed in this level are passive, in the sense that decision- makers need to generate hypotheses or deﬁne criteria for extracting data, then utilize the analysis measures to ﬁnd answers and conﬁrm (or disprove) their original insight. For instance, if a practitioner observes low market demand in a particular day, he or she might formulate a hypothesis using extraction and visualization tools, then subject the hypothesis to a statistical test to verify his or her inference is suﬃciently driven by data. Chapter 5 will describe statistical approaches for exploratory data. (e) Data mining: This is an active segment of market intelligence methodologies, and is aimed at extracting information and knowledge from raw data. This entails leveraging mathemat- ical models for pattern recognition, using machine learning and data mining tools. In the data mining phase, the formulation of a hypothesis is not necessary, as the decision maker’s primary purpose during this phase is to expand their knowledge of the data and consider possible paths for exploration. (f ) Optimization: This phase allows decision makers to determine the best solution out of a set of alternative actions. DecisionsOptimizationChoosing the BestAlternativeData MiningModels for Learning from DataData ExplorationStatistical Analysis and VisualizationData Warehouses/Data MartsMultidimensional Cube AnalysisData SourcesOperational Data, Documents, and External Data1.7. TURNING DATA INTO STRATEGIC INSIGHTS 7 (g) Decisions: These are the top of the market intelligence pyramid, where decision makers adopt a particular course of action based on the outcomes of steps a–f. Stated diﬀerently, this represents the concluding segment of the decision-making process. Moving from the bottom to the top of the pyramid requires more sophisticated tools of an active type. This also alters the roles and competencies needed in each phase. At the lower end of the pyramid, information system specialists such as database administrators perform marketing intelligence tasks. Intermediate phases require data analysts and experts in mathematical and statistical modeling in order to execute tasks. Decision makers and managers are mandated to execute tasks at the top of the pyramid. Market intelligence systems troubleshoot the challenges confronting diﬀerent types of agents in a market environment. 1.7 TURNING DATA INTO STRATEGIC INSIGHTS The path of any market intelligence analysis is based on its application domain, characteristics of the decision makers, as well as the available analytical methodologies. An ideal cyclical market intelligence path will have four components, as illustrated in Figure 1.2. Figure 1.2: Market intelligence cyclical path. (a) Analysis: The ﬁrst phase requires accurately identifying the problem at hand. Based on this identiﬁcation, decision makers have to create a mental picture of the problem being analyzed through diagnosing the key drivers that are considered as the most relevant. This phase prompts decision makers to ask several questions and to get quick reactions in an interactive way. EvaluationsInsightsAnalysisDecisions8 1. INTRODUCTION TO MARKET INTELLIGENCE (b) Insight: This second phase is intended to provide a deeper understanding of the existing problem. The information gathered from the analysis phase is transformed into knowledge during the insight phase. The extraction of knowledge happens as a result of the intuition of the decision makers based on experience and the available unstructured information. However, inductive learning models could be relevant in this stage if the data are struc- tured. (c) Decision: This phase converts the knowledge obtained in the second phase into decisions and then into actions. The presence of market intelligence approaches can encourage more rapid execution of the ﬁrst two phases (analysis and insight) in order to make eﬀective and timely decisions that are better suited to the strategic priorities of a given market agent. This contributes to an overall fall in the execution time of the analysis- decision-action— revision cycle, and hence to a decision-making process of better quality. (d) Evaluation: This phase deals with monitoring, performance measurement, and evaluation. In addition, it requires extensive metrics beyond ﬁnancial metrics in order to examine the key performance indicators in diﬀerent market environments. Robust analytical tools for evaluating performance will be described in subsequent chapters. 1.8 EXERCISES 1.1. a. What do you understand by market intelligence? b. Mention and describe the factors that are responsible for a successful market in- telligence. c. How would you relate marketing insight and decision making? 1.2. a. What is marketing research? b. Explain the mix of marketing research and data mining tools used for the eﬀective execution of a marking plan. c. What are the market intelligence tools? 1.3. a. Discuss the components of market intelligence designs. b. With the aid of diagram, describe the structure of market intelligence systems. 1.4. a. Enumerate the components of the market intelligence cyclical path. b. Distinguish between data exploration and data mining. C H A P T E R 2 9 The Market Research Process The main objective of this chapter is to assist practitioners in understanding the steps involved in conducting market research. In this chapter, we will study how information derived from customer feedback reaches producers. Exploiting this information is useful to identify market opportunities, deﬁne or hone competitive advantages, and navigate market challenges. 2.1 THE MARKETING RESEARCH FRAMEWORK AND PROCESS The marketing research process is a procedure that outlines the tasks which must be accom- plished in order to conduct a successful marketing strategy. There are six processes involved in conducting marketing research. These steps are: (i) deﬁnition of the problem, (ii) develop- ment of an approach to the problem, (iii) formulation of research design, (iv) collection of data, (v) preparation of data and data analysis, and (vi) generation of report and presentation. Deﬁnition of the problem: The ﬁrst step to be taken when commencing marketing research is to deﬁne the problem which entails the purpose of the study, relevant information about the study and how to use the information gathered in decision-making processes. This step also involves considering the limitations of decision making at a ﬁrm; therefore, there is a need to discuss potential problems with decision makers and industry experts. Development of an approach to the problem: After deﬁning the problem, the next step is to formulate objective analytical models, research questions, hypotheses testing techniques, and to specify the required information. This process necessitates developing speciﬁc strategies to resolve the components of the research problems deﬁned earlier. Formulation of research design: Research design is a framework for conducting the market- ing research survey. At this stage, the methods of obtaining required information, constructing suitable hypotheses, and designing a questionnaire that will obtain useful data are delineated. The procedure in formulating a rigorous research design includes obtaining secondary data, de- signing a questionnaire, deﬁning an appropriate sampling method, conducting qualitative and quantitative primary research, measuring and scaling variables, and deﬁning which types of anal- ysis will be commensurate with testing the hypothesis. 10 2. THE MARKET RESEARCH PROCESS Collection of data: This entails making decisions regarding the nature of the data and method of collecting the data. After collaborating with decision makers and industry experts, the lead re- searcher will facilitate training for ﬁeld researchers. This training will intimate the ﬁeldworkers with the objective of the study, the challenges in carrying out their duties and possible solu- tions to overcome these challenges. In addition, to improve the quality of data gathering, proper supervision and constant evaluation are both necessary. Preparation of data and data analysis: Data preparation involves discretization, cleaning, in- tegration, transformation, and reduction of data for analytical use. Data analysis processes in- volve the exploration of data through descriptive statistics, graphs, exploring the relationship between variables, and comparing matched groups. Data analysis incorporates a wide variety of techniques; data mining concentrates on modeling and knowledge discovery for predictive rather than descriptive purposes. Generation of report and presentation: This involves the documentation of the whole project in a written form. The report documents the procedure in the ﬁrst ﬁve steps described above in a systematic manner. The results of the project, major ﬁndings, conclusion, and recommendations are part of the report generated. A PowerPoint presentation is encouraged to present salient points and interpretation of results to the decision makers or professionals who are not part of the research project. 2.2 RESEARCH PROBLEMS AND CORRECT DESIGN TECHNIQUES Building a market intelligence system can be conceptually viewed as a project that exhibits the following features: an ultimate objective; expected duration and costs; the usage and coordination of the resources required to carry-out planned activities. The project cycle of a market intelligence system is picturized in Figure 2.1. (a) Analysis: This is the ﬁrst phase of the project in which an organization has to carefully identify its needs. Broadly speaking, this phrase is carried out through interactions with agents engaging in diﬀerent activities with the market. It is very crucial to clearly deﬁne the major objectives and priorities of the project, as well as to estimate the costs and beneﬁts attached to the development of the project. (b) Design: The second phase entails two sub-phases focused on providing a provisional plan of the whole layout as well as the evolution of the project, either near-term or mid-term and future-term. The ﬁrst step during this phase is to assess the existing information in- frastructure, and to investigate the main decision-making processes in order to suﬃciently ascertain information requirements. Based on the traditional approaches of project man- agement, the plan will include identiﬁcation of development phases, priorities, expected 2.3. DATA COLLECTION METHODS 11 Figure 2.1: Phases in the project cycle of a market intelligence system. execution times and projected costs, complemented with stating required roles and re- sources. (c) Planning: This stage demands establishing the characteristics of a suitable market intel- ligence systems in greater detail. In addition, it includes the assessment of existing data and external data in order to design a central data warehouse. At this stage, practitioners also delineate the boundaries of the available data, specify the mathematical models to be employed, ensure that the available data are ﬁt for the deﬁned models, and test how ef- ﬁcient the models are in addressing the objectives of the marketing plan. In conclusion, it is important to make a system prototype at the lowest cost possible and with limited capabilities in order to close the gap between actual needs and project speciﬁcations. (d) Implementation and control: This ﬁnal stage comprises ﬁve major sub-stages. These sub- stages are development of data warehouses; creation of metadata; extraction and transfor- mation of data into the data warehouses; development of application tools for the analyses; and a test-run of the system. 2.3 DATA COLLECTION METHODS This section presents ﬁve commonly used methods of collecting data, including personal inter- views, direct observation, questionnaires, focus group discussions, and documents and records. AnalysisAnalysisIdentiﬁcation ofMarket NeedsDesign - Infrastructure Recognition- Project Macro PlanningPlanning - Detailed projectrequirements (e.g., deﬁnitionof mathematical modelsneeded; developmentof a prototype; identiﬁcationof the data, and deﬁnitionof data warehousesand data marts) Implementation and Control - Development of data warehouses and data marts - Developmet of ETL tools - Development of applications - Development of metadata - Release and testing12 2. THE MARKET RESEARCH PROCESS Personal interview method: This method encourages interaction between an interviewer and respondents regarding a topic of interest. It gives respondents the ability to express his or her perception of a topic, through the perspective of their personal beliefs, values, knowledge, feel- ings, and experiences. Usually, before the interview, the interviewer has prepared the questions he or she intends to ask the respondent. The questions may be easily understood by the respon- dent, or may be ambiguous and require some clariﬁcation on the part of the interviewer. The three types of interview are structured, semi-structured, and unstructured interviews. The struc- tured interview is similar to a questionnaire, where the respondents choose from given options or supply an answer in the case of an open-ended question. Semi-structured interviews allow the interviewer to be ﬂexible in the manner and sequence of posing questions, in order to adapt inquiry to better ﬁt the information they seek, but the questions are still hinged upon a num- ber of central thematic questions. Unstructured interviews are basically open-ended in nature, allowing an interviewer more latitude to improvise and explore diﬀerent topics. However, the more unstructured an interview, the harder it is to standardize or codify responses into data that is conducive to analysis using quantitative or objective analytical methods. Direct observation method: This is a method of data collection where the observer passively participates by recording the behavior of respondents. In most cases, this method is used in be- havioral science to study interactions among groups of people. Direct observation methods often require the recording of participants, such as by using a video camera mounted at a strategic lo- cation to record interactions. This clip of the video can be watched and analyzed by the observer after the scene. However, although the visual or audio data can appear objective, interpreting the underlying motives of participant behavior is performed through the subjective lens of the researcher. Therefore, the best practice is to use other methods in conjunction with direct ob- servation methods in order to achieve greater accuracy, combined with a reﬂexive approach that acknowledges how personal biases can arise when interpreting the behavior of participants. Questionnaire method: A questionnaire is an instrument used in data collection that con- sists of series of questions and other prompts for the purpose of gathering information from the respondent. A ﬁeld worker approaches a respondent to administer the questionnaire. The respondent will be given time to digest and complete the questionnaire. Many people feel more comfortable with this method in comparison to participating in an interview. This approach reduces bias from the researcher, since the same questions are asked of all the respondents. Focus groups discussion: Focus groups discussions usually involve about 6–12 people with similar characteristics or common interests. This involves an in-depth interview accomplished in a group setting to provide feedback on what people think about products or issues, and en- gender a deeper understanding of the topics of interest. The interaction within the group serves as an object of analysis, and participants are often inﬂuenced by the responses of their peers during the course of discussion. There is need for a moderator to anchor the discussion with comments and guidelines, and capture the relevant information from the group. This method is 2.4. GENERATING MARKETING INSIGHTS 13 more economical than the individual interview method, and can often unearth insights which may not otherwise be discovered in an individual interview setting. Power-distance dynamics between the interviewer and interviewee can be bridged, as group participants have the support of peers and can feel more at ease in expressing direct (possibly negative) opinions about a ﬁrm or product vs. expressing opinions in an individual interview setting. Document and records: This entails examining existing data in the form of reports, publi- cations, newsletters, databases, multimedia, formal records, secondary data, etc. This method provides foundational information about a phenomenon, is relatively cheap or accessible, and provides a behind-the-scenes look at a project. Media reports can also help marketing practi- tioners understand current trends in phenomena which are piquing public interest. However, secondary data can suﬀer from shortcomings in that it may not meet the speciﬁc informational needs of an organization, or may be out of date or compiled by an untrustworthy source. 2.4 GENERATING MARKETING INSIGHTS Market intelligence is deﬁned as insights generated from marketing research or data mining. It presents the entire picture of market opportunities and challenges in order to provide maxi- mum value and understanding. To enhance market intelligence, there is need to have integrated database systems that connect together data from sales, marketing, customer, research, opera- tions, and ﬁnance. These disaggregated data should ideally be maintained on the same hardware system. Groth (2000) identiﬁed the common challenges confronting the marketers in the as- pect of data quality. These are redundant data, incorrect or inconsistent data, typos, stale data, variance in deﬁning terms, and missing data. 2.5 EXERCISES 2.1. a. Describe marketing research framework and process. b. Provide a detailed explanation of the project cycle of a market intelligence system. 2.2. a. Discuss the methods of data collection that you are familiar with. b. What are the similarities and dissimilarities between the personal interview method and the questionnaire methods of data collection? 2.3. Describe how data can be collected from a focus group discussion. C H A P T E R 3 15 Qualitative Techniques In the previous section, we discussed the methods of data collection. The goal of this chapter is to elaborate on two qualitative techniques utilized by ﬁeld researchers to gather data from respondents—the self-administered method and the personal interview method. The factors that aﬀect the choice of method include the characteristics of the target population and access to the sample in terms of location, time, and infrastructural availability. 3.1 SELF-ADMINISTERED METHOD This method requires respondents to answer questions independently, without any interference or intervention on the part of the interviewer. The self-administered survey method involves designing a well-structured questionnaire itemized in a chronological order. The questions are concise and unambiguous to avoid misleading or guiding respondents into providing unintended responses. The questionnaire can consist of open-ended or closed-ended responses. An open- ended question allows respondents to provide an answer based on their knowledge or experi- ence about a topic, and can result in responses that can range from a full sentence to multiple paragraphs. Closed-ended questions require respondents to select the most appropriate response from a set list of options provided by the interviewer. These questions can be structured in a mul- tiple choice, yes/no, or Likert scale format, but interviewees can only choose from the responses oﬀered. In order to accommodate the opinion of the respondent, the ﬁeld “Other/specify” can be added to the options, allowing those surveyed to provide their own response. We should bear in mind that in the preparation process we might have deﬁned our target population, segmented by region and also delineated into non-overlapping enumeration areas. A sampling frame that contains the list of sampling units is used to know exactly from whom we are getting the data. In developing our sample frame, a sampling technique might have been adopted depending on the objective of the research. Depending on the requirements or restrictions of the research being performed, the researcher can choose simple random sampling, cluster random sampling, or stratiﬁed random sampling approaches. Responses generated using the self-administered method can be gathered by meeting in- dividuals or groups in person. Alternatively, the researcher can gather responses via post, inter- net or email. After choosing the appropriate method of gathering respondents, a copy of the questionnaire will be distributed to each of the respondents in the sampling frame, and the re- spondents will be given a reasonable time to answer the questions either by ﬁlling or ticking the appropriate answer(s). However, there is the possibility of recording some non-responses. Some 16 3. QUALITATIVE TECHNIQUES respondents may (accidentally or deliberately) fail to answer some of the questions in the survey, or fail to submit a response to a survey in the required time frame. Interviewers or ﬁeld workers will need to examine the data and reach a judgment about whether to revisit respondents or survey more respondents to bridge these gaps in the data. To illustrate a practical example, Brickﬁeld Road Associates Limited (bra) employs a num- ber of ﬁeld workers to carry out a business expectation survey on a monthly basis. The question- naires are given to a list of industry leaders from the major sectors of the economy, allowing them to express their sentiments regarding monetary policy indicators and their future expecta- tions of the Nigerian economy as a whole. Many of the questions contained in the questionnaire are closed-ended, with the exception of a ﬁeld in the questionnaire that allows respondents to elucidate upon the reasons behind their opinions and forecasts. The ﬁrm distributes its question- naire by leveraging its technologies to notify respondents when the questionnaire is available to complete online. bra has developed a mobile app to collect data; this enables the company to check the responses submitted, support its ﬁeld researchers and improve the quality of the data gathered in future surveys. The mobile app includes GPS functionality to capture the time and location of the survey. Non-responses are mitigated by sending reminders to the respondents via text messages, emails, calls and visitation. A sample of the questionnaire used for the bra business expectation survey can be found in the Appendix A. 3.2 PERSONAL INTERVIEW OR FACE-TO-FACE METHOD The personal interview method, also known as the face-to-face method, is a method of data collection where the interviewer goes to the ﬁeld with prepared questions to ask respondents in person. In contrast to self-administered surveys, the personal interview method gives interview- ers the freedom to explore the responses given by survey subjects. The interviewer can do so by asking further questions of respondents, and observing their behavior while oﬀering responses, in order to establish why respondents answered in a particular manner. As noted above, this practice can be performed in person, or via telephony media. The in- terviewer should have an intimate understanding of the purpose of the survey and its content. In a situation where a question seems ambiguous to the interviewee, it is the duty of the interviewer to rephrase the question without losing the contextual meaning of the question. The interviewer should be swift when asking questions and recording the answers provided by respondents. The major advantages of the personal interview method are high response rates and the ability to gather more nuanced, natural responses supplemented by observation of the behavior of the respondents. The face-to-face method also mitigates the problem of non-responses suﬀered by the self-administered method. On the other hand, the disadvantage of using the personal interview method is that it is time consuming and expensive, especially if interviews are to be conducted in person with subjects in a far away or remote location. 3.3 EXERCISES 3.1. What do you understand by the concept of qualitative techniques? 3.2. a. With the aid of examples, describe open-ended questions and closed-ended ques- 3.3. EXERCISES 17 tions. b. What is a sampling frame? 3.3. Explain how technology can assist in the aspect of data collection. 3.4. Describe how to conduct a survey using the personal interview method. 3.5. State the merits and demerits of the personal interview method of data collection. 3.6. Design a well-structured questionnaire that captures the processes, opportunities, and challenges faced by a new business. C H A P T E R 4 19 Quantitative Techniques 4.1 DATA PREPARATION AND DESCRIPTIVE STATISTICS In this chapter, we will examine the deﬁnition of quantitative techniques, diﬀerent types of quantitative techniques, the functions of quantitative techniques, and the application of quan- titative techniques. We will discuss distribution patterns as well as measures of central tendency and dispersion for both grouped and ungrouped data using illustrative examples. Also, we will explain the diﬀerence between point and interval estimates, how to construct conﬁdence inter- vals, and the necessity of performing these tasks. In addition, we will shed light on the other useful descriptive statistics. 4.2 FUNDAMENTALS OF QUANTITATIVE METHODS AND THEIR APPLICATIONS Quantitative techniques can be deﬁned as methods or systematic approaches of solving prob- lems, planning, and making informed decisions using numerical data. With the aid of quanti- tative techniques, decision makers can make optimal decisions in order to achieve set goals and objectives. Quantitative techniques can be classiﬁed into three areas: (i) mathematical quan- titative techniques, (ii) statistical quantitative techniques, and (iii) programming quantitative techniques. We will brieﬂy discuss each classiﬁcation in this order. Mathematical quantitative techniques: These techniques employ the principles of mathe- matics to quantitative data to make smart decisions. These techniques include using calculus, matrix algebra, set theory, and exponential smoothing to assist eﬃcient and accurate decision- making. Statistical quantitative techniques: These techniques involve using statistical methods in data collection, data analysis, and presentation. Statistical tools include probability theory, re- gression analysis, discriminant analysis, time series analysis, panel data analysis, experimental design and statistical quality control, heuristic methods, sequencing and scheduling problems, and other statistical methods. Programming techniques: These techniques involve writing code or designing software pack- ages to build models which are used to aid decision-making processes. This technique is com- monly used in the area of operations research. Programming methods include uses of linear pro- 20 4. QUANTITATIVE TECHNIQUES gramming, game theory, decision theory, inventory theory, and computer simulation, among others. Uses of Quantitative Techniques Quantitative techniques are mostly useful in the following areas: (i) optimal allocation of limited resources; (ii) inventory control; (iii) queuing theory; and (iv) timetabling and scheduling. Limitations of Quantitative Techniques (i) It relies on numerical assumptions. (ii) It involves some complex calculations, models, and equations. (iii) It does not measure intangible factors or variables such as skill or attitude. (iv) It is one of the tools for making decisions, but is not a decision in itself (i.e., quantitative techniques can be used in conjunction with other techniques like qualitative to make a better decision). 4.3 CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 4.3.1 DISTRIBUTION PATTERN A distribution pattern summarizes the characteristics exhibited by a set of observations, repre- sented in graphical terms. For instance, a researcher may have interest in knowing how a given set of data is clustered or spread apart. A simple way of doing this is to plot the observations on a set of axes and see how tightly clustered the observations are distributed across these axes. The relationship among sets of observations can be vividly seen with the aid of chart. These charts include scatter diagrams, bar charts, pie charts, histograms, etc. In some cases, a set of observa- tions may be generated by a probability distribution. The diagrams in Figure 4.1 show features of a number of datasets generated from probability distributions. 4.3.2 MEASURE OF CENTRAL TENDENCY This is the statistical measure that identiﬁes a single value as representative of an entire distribu- tion by identifying the central position within that set of data. The most common measures of central tendency are mean, median, and mode. We will discuss these measures under two cases 4.3. CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 21 Figure 4.1: Datasets generated from probability distributions. 1.210.80.60.40.20-0.20102030405060Uniform (0,1)(b) Uniform distribution with a = 0, b = 11210864200102030405060Binomial (0.05,100)(a) Binomial distribution with p = 0.05, n = 1003210-1-2-3-40102030405060Normal (0,1)(c) Standard normal distribution with mean = 0 and variance = 122 4. QUANTITATIVE TECHNIQUES of grouped and ungrouped data. It is important to note that the mean, median, and mode are equal in a standard normal distribution. Ungrouped Data This is the kind of dataset given as individual data point. In some cases it is not accompanied by a frequency table. (a) Mean: This is one of the most important measures of location; the mean is often also referred to as the average. The mean can be calculated by adding all the observations and (cid:31) and is dividing the result by the total number of observations. The mean is denoted by N n i xi , where xi is value of the ith observation and n mathematically represented as n is the number of observations. (cid:31) N D P (b) Median: The median is the middle value of a given dataset after re-arranging the observa- tions in either ascending or descending order. In case the number of observations is even, the median is calculated by taking the average of the two central values. It is calculated as .n th is the position of the median th, where n is the number of observations and .n 1/ 1/ C 2 C 2 value in a given dataset. (c) Mode: The mode is deﬁned as the most frequent value(s) in a given dataset. It is possible to have two or more values that appear equally most frequently in a dataset. A dataset is mono-modal when a single value appears most in a dataset, and bi-modal when there are two values having the equal highest frequency in a dataset. Example 4.1 Table 4.1 shows the distribution of month-on-change inﬂation (%) in Nigeria in the year 2015. Table 4.1: Distribution of month-on-change inﬂation (%) in Nigeria, 2015 Calculate: (i) mean, (ii) median, and (iii) mode of the distribution. MonthJanFebMarAprMayJunJulAugSepOctNovDecInﬂ ation0.90.71.00.91.11.10.80.60.60.50.81.2Source: NBS4.3. CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 23 Solution (i) (cid:31) N D D (ii) P n i xi n 0:9 C 0:7 1:0 0:9 1:1 1:1 C C C C C 12 0:8 0:6 0:6 C C 0:5 C 0:8 C 1:2 C 0:8: D median 0:9 0:8 C 2 D 0:85: D (iii) Modes are 0.6, 0.8, 0.9 and 1.1. Grouped Data Grouped data is a set of data that are given in intervals. It is normally comes with a frequency table and the interval groupings are equal in most cases. (a) Mean: n i f xi P N ; (cid:31) N D where f is the frequency of the each group or class and N is the total number of observa- tions or sum of the frequencies. (b) Median: This can be calculated as follows: Median Lm C D N 2 (cid:0) Fm CF ! C; where Lm is the lower class boundary of the median class, CF is the cumulative frequency of class preceding median class, Fm is the frequency of the median class, N is the sum of the frequency, and C is the class width. (c) Mode: The mode formula for the grouped data is represented mathematically as Mode Lm D (cid:18) Fm C 2Fm (cid:0) Fb (cid:0) Fa Fb (cid:0) (cid:19) C; where Lm is the lower limit of modal class, Fm is the frequency of the modal class, Fb is the frequency of class before the modal class, Fa is the frequency of class after the modal class, and C is the class width. 24 4. QUANTITATIVE TECHNIQUES Table 4.2: Distribution of score in mathematics examination Example 4.2 One-hundred school students sat a mathematics examination. The distribution of their scores is grouped and presented in the Table 4.2. Calculate the mean, median, and mode of the distribution of score in Mathematics ex- amination. Solution n i f xi P N (i) Mean; (cid:31) N See Table 4.3. D 4500 100 D D 45. Table 4.3: Mean, median, and mode of the distribution of score in mathematics examination (ii) Median Lm C D N 2 (cid:0) Fm CF ! C . Score Interval0-910-1920-2930-3940-4950-5960-6970-7980-8990-99Frequency41071831561252Score IntervalFrequencyClassMid-point(x)FXClass BoundaryCumulative Frequency0-944.518.0-0.5-9.5410-191014.5145.09.5-19.51420-29724.5171.519.5-29.52130-391834.5621.029.5-39.53940-493144.51379.539.5-49.57050-59554.5272.549.5-59.57560-69664.5387.059.5-69.58170-791274.5894.069.5-79.59380-89584.5422.579.5-89.59890-99294.5189.089.5-99.5100Sum 10045004.3. CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 25 To determine the median class: N 2 th D (cid:18) 50 50th, this falls within (40–49) class interval 39 (cid:19) (cid:0) 31 10 (cid:2) D 43:05: 39:5 C (cid:18) Fm Fb (cid:19) C . (iii) Mode Lm (cid:0) Fa The modal class is the same (40–49) class interval 2Fm Fb C D (cid:0) (cid:0) 40 C D (cid:18) 31 2.31/ 18 5 (cid:0) (cid:0) (cid:0) (cid:19) 18 (cid:2) 10 D 43:33: 4.3.3 MEASURE OF DISPERSION In a situation whereby the measure of tendency is not suﬃciently adequate to describe the data, measures of dispersion, or spread be employed. It is possible to have two diﬀerent datasets having the same means, so we can also look at the spread or the variance within the data. Measures of dispersion include: range, interquartile range, standard deviation and variance, among others. In this chapter, we are going to discuss some important measures of dispersion using grouped and ungrouped data. Ungrouped Data (a) Range: This is the diﬀerence between the highest and lowest values in a dataset. (b) Interquartile range: It is the diﬀerence between ﬁrst quartile and the third quartile. The ﬁrst quartile and third quartile are equivalent to the 25th and 75th, percentiles respectively, and are obtained after arranging the dataset in an ascending or descending order. The in- terquartile range describes 50% of the dataset, lying between the 25th and 75th percentile. The ﬁrst and third quarters can be denoted by Q1 and Q3, respectively: Q1 D .n 1/ th C 4 Q3 D 3.n 1/ th C 4 IQR Q3 Q1: D Standard deviation: This is the commonly used measure of dispersion. It describes how obser- vations are from the mean. Standard deviation can be computed by ﬁnding the square root of the sum of squared deviation from the mean divided by the number of observations. It is important to note that there is a slight diﬀerence in how the population and sample standard deviations (cid:0) 26 4. QUANTITATIVE TECHNIQUES are calculated (the sum of squared diﬀerences is divided by n sample standard deviation). (cid:0) 1 in the case of calculating the (a) Standard deviation (b) Standard deviation s n P i D 1 .xi n x/2 (cid:0) N s n P i D x/2 (cid:0) N 1 1 .xi n (cid:0) D D (population) (sample) Variance: This is calculated by squaring the value of standard deviation (a) Variance (b) Variance n P i D n P i D 1 .xi n 1 .xi n (cid:0) x/2 (cid:0) N x/2 (cid:0) N 1 D D (population) (sample) Example 4.3 An investor wants to know how the annual growth (%) in Gross Domestic Products in Africa is dispersed. He selected a random of sample of 13 countries. Table 4.4 presents the data. Table 4.4: Annual growth (%) in gross domestic products in Africa. (Country Codes1). Calculate: (i) range, (ii) interquartile range, (iii) standard deviation, and (iv) variance of the distribution of the annual growth of GDP. Solution (i) Range 9:61 1:26 D (ii) Interquartile range. (cid:0) 8:34. D Arranging the dataset produced Table 4.5. 1Algeria (DZA), Angola (AGO), Central African Republic (CAF), Egypt (EGY), Ethiopia (ETH), Gambia (GMB), Ghana (GHA), Kenya (KEN), Lesotho (LSO), Mali (MLI), Nigeria (NGA), Senegal (SEN), South-Africa (ZAF). CountryCode1DZAAGOCAFEGYETHGMBGHAKENLSOMLINGASENZAFGDP (%)3.763.014.804.209.614.723.925.651.615.962.656.491.26Source: WDI, 20154.3. CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 27 Table 4.5: Dataset Q1 D .13 1/ th C 4 D 3:5th 2:83 D Q3 D 3.13 C 4 1/ th D 10:5th 5:81: D Therefore, IQR 2:98. D (iii) Standard deviation s P n i D D x/2 (cid:0) N 1 1 .xi n (cid:0) P n i xi n D (cid:31) N D 4:43 r .1:26 (cid:0) 4:43/2 C .1:61 (cid:0) 4:43/2 .2:65 C Standard deviation 2:22 D (iv) Variance = 2:222 4:93. D Grouped Data 4:43/2 (cid:0) 13 1 (cid:0) ::: C C .6:49 (cid:0) 4:43/2 .9:61 (cid:0) C 4:43/2 D (a) Range: For grouped data, the range is calculated by subtracting the lower-class boundary of the ﬁrst class from the upper-class boundary of the last class. (b) Interquartile range: This is computed by modifying the median formula: Q1 LQ1 C D Q3 LQ3 C D N CF ! C 4 (cid:0) FQ1 3N 4 (cid:0) FQ3 CF ! C IQR Q3 (cid:0) D Q1; CountryCodeZAFLSONGAAGODZAGHAEGYGMBCAFKENMLISENETHGDP (%)1.261.612.653.013.763.924.204.724.805.655.966.499.6128 4. QUANTITATIVE TECHNIQUES where LQi is the lower limit of quartile class, FQi frequency of the quartile class, CF is the cumulative frequency of class preceding quartile class, N is the sum of the frequency, and C is the class width. (c) Standard deviation: The population standard deviation is denoted by (cid:27) while the sample standard deviation is denoted by s. It can be computed as follows: s P f .x n x/2 (cid:0) N (cid:27) D .population/ s x/2 P f .x n (cid:0) N 1 s D .sample/: (cid:0) (d) Variance: The population parameter and the sample statistic for variance are denoted by (cid:27) 2 and s2, respectively, and are mathematically deﬁned as follows: (cid:27) 2 D P f .x n x/2 (cid:0) N .population/ s2 D P f .x n (cid:0) x/2 (cid:0) N 1 .sample/: Example 4.4 Table 4.6 shows the distribution of the broad money annual growth (%) in the selected 45 African countries. Calculate the: (i) range, (ii) standard deviation, (iii) variance, and (iv) in- terquartile range of the distribution. Table 4.6: Distribution of the broad money annual growth (%) in the selected 45 African coun- tries Solution (i) Range 99:5 0:5/ . (cid:0) (cid:0) D 100 D Class Interval0-910-1920-2930-3940-4950-5960-6970-7980-9890-99Frequency616135220001Source: WDI, 20104.3. CONCEPT OF DISTRIBUTION PATTERN, CENTRAL TENDENCY, AND DISPERSION 29 (ii) Standard deviation P n i f xi N (cid:31) N D 1042:5 D 45 D 23:17 s x/2 P f .x n (cid:0) N 1 (cid:0) 23:17/2 s .4:5 (cid:0) s D D 270:91 .14:5 C (cid:0) 23:17/2 1 45 (cid:0) : : : C C .94:5 (cid:0) 23:17/2 16:46 D (iii) s2 D (iv) IQR Q3 Q1. D (cid:0) To determine the quartile class, we compute (cid:0) 45 quartile falls in (10–19) class interval (see Table 4.7). 4 (cid:1) th 11:25th, this implies that the ﬁrst D Q1 9:5 D (cid:18) 11:25 16 (cid:0) C 6 (cid:19) 10 (cid:2) D 12:78: Table 4.7: Class interval and class boundary Also, the position of third quartile (cid:0) 3 45 4 (cid:1) th (cid:2) 29) class intervals (see Table 4.7): D 33:75th, the third quarter falls within (20– Q3 D 19:5 (cid:18) 33:75 (cid:0) 13 C 22 (cid:19) 10 (cid:2) D 28:54: ClassIntervalFXFXX-mean(X-mean)2F(X-mean)2CFClass Boundary0-964.527-18.67348.442090.676-0.5-9.510-191614.5232-8.6775.111201.78229.5-19.520-291324.5318.51.331.7823.113519.5-29.530-39534.5172.511.33128.44642.224029.5-39.540-49244.58921.33455.11910.224239.5-49.550-59254.510931.33981.781963.564449.5-59.560-69064.5041.331708.440.004459.5-69.570-79074.5051.332635.110.004469.5-79.580-89084.5061.333761.780.004479.5-89.590-99194.594.571.335088.445088.444589.5-99.5Sum451042.51192030 4. QUANTITATIVE TECHNIQUES Therefore, IQR 28:54 (cid:0) D 12:78 D 15:76. 4.4 CONSTRUCTION OF CONFIDENCE INTERVALS In statistics, the primary objective in selecting a random sample from a population is to be able to compute a statistic which closely describes the population parameter. This estimate can be referred as a Point Estimate. It is important to know how accurately the sample statistic represents the population parameter. In order to illustrate this, we can calculate a range of values for the sample, in which we are conﬁdent that the population parameter of interest is contained. In most cases, a statistician would like to compute a 95% conﬁdence interval for his estimation; this is common practice in sciences, social sciences, and education. We refer to this range of values inside which the true population value falls as an Interval Estimate. The threshold of the conﬁdence interval can be amended based on the ﬁeld of study. A biostatistician would prefer to look at 99% conﬁdence interval rather than 95% conﬁdence interval. In the health sector, because we deal with human life, it is expected to be more precise with our estimates to reduce loss of lives, or the release of a drug which could either be ineﬀective or cause adverse side-eﬀects. A 99% conﬁdence limit implies that we are conﬁdent that if we took 100 samples from the population, approximately 99 will be contain the true value of the parameter of interest. A conﬁdence interval can be constructed generally as: point estimate margin of error (cid:6) CI D sample statistic Critical value (cid:2) (cid:6) standard error of estimate: For instance, a conﬁdence interval (C:I) for population mean can be written as: C:I (cid:31) D N (cid:6) tn (cid:0) 1; q (cid:2) s pn : A 100 .1 (cid:0) (cid:11)/ % conﬁdence region for (cid:22) contains: tn (cid:31) N (cid:0) (cid:0) 1; q (cid:2) s pn (cid:20) (cid:22) (cid:31) (cid:20) N C tn (cid:0) 1; q (cid:2) s pn ; where (cid:11) is the level of signiﬁcance, n is the sample size, s is the standard deviation, and t is the critical region from the t-distribution table. x is the mean N Suppose we want to construct a 99% conﬁdence interval for an unknown population mean, then a 99% probability that conﬁdence interval will contain the true population mean could be written as P (cid:20) (cid:31) N tn (cid:0) (cid:0) 1; q (cid:2) s pn (cid:20) (cid:22) (cid:31) (cid:20) N C tn (cid:0) 1; q (cid:2) (cid:21) s pn D 0:99: Example 4.5 Refer to Example 4.4. Construct a 95% conﬁdence interval on the average broad money annual growth (%) in selected African countries. 4.5. OTHER DESCRIPTIVE STATISTICS 31 Solution 45; n D (cid:31) N D 23:17%; s D 16:46; and (cid:11) 0:05 D Since the sample size is large, i.e, n > 30 we will use normal distribution (z) instead of (cid:11)=2, student t-distribution. Under the assumption of two-tail test, we have critical value to be z1 while one-tail test is z1 (cid:11): (cid:0) (cid:0) C:I D 23:17 (cid:0) z0:975 C:I C:I D D 23:17 23:17 1:96 1:96 (cid:0) (cid:0) 16:46 p45 (cid:20) (cid:22) (cid:20) 23:17 16:46 p45 (cid:20) (cid:22) (cid:20) 23:17 16:46 p45 (cid:20) (cid:22) (cid:20) 23:17 C C C (cid:2) (cid:2) (cid:2) z0:975 16:46 p45 (cid:2) 1:96 1:96 16:46 p45 16:46 p45 (cid:2) (cid:2) C:I D 18:36% (cid:22) (cid:20) (cid:20) 27:98%: 4.4.1 APPLICATION OF CONFIDENCE INTERVALS In as much we cannot be speciﬁc about events, one needs to provide a reasonable range for the variable of interest. A simple point estimate is often insuﬃcient for practical needs; a range of possible outcomes within a deﬁned probability is more useful. Conﬁdence intervals can be applied in business, production, healthcare, science, engineering, etc. Governments can apply the concept of conﬁdence intervals in price control; businesses apply its concept in inventory control and sales movement; manufacturing ﬁrms use the concept in the area of quality control; an athlete can use conﬁdence intervals to estimate the average time range of times he or she can complete a race of 100 m. Engineers employ it to determine the range of years for the durability of a bridge or to determine the ranges of conditions between which a certain structure or part operate safely. In addition, understanding conﬁdence intervals helps to determine the quantity of resources required to carry out some speciﬁc tasks and aid overall planning. 4.5 OTHER DESCRIPTIVE STATISTICS Apart from some basic descriptive statistics explained above, there are a few other supplementary statistics that assist us in understanding the nature of how data is dispersed. In the section, we shall elucidate on skewness and kurtosis. 32 4. QUANTITATIVE TECHNIQUES 4.5.1 SKEWNESS Skewness is deﬁned as the measure of symmetry or departure from center in a dataset. A dataset or distribution is said to be symmetric if it has the same features at both right and left from the central point. In a normal distribution, the skewness is zero. It is positively skewed if the value of skewness is positive, this means that it has a long tail at the right side of the ﬁgure implying that there are concentration of the high values in the distribution of the dataset. However, when there is high concentration of low values in a distribution, then there is heavy tail at the left side of the ﬁgure and is it said to be negatively skewed. In a skewed distribution, values of mean, median and mode would not coincide. The value of skewness can be positive or negative or zero. These under-listed conditions could be helpful to determine the nature of the skewness. (a) When the values of mean, median, and mode are equal, there is no skewness. (b) When mean > median > mode, skewness will be positive. (c) When mean < median < mode, skewness will be negative. The skewness can be diagrammatically represented in Figure 4.2. Figure 4.2: The skewness. According to Bulmer (1979) rule of thumb, he suggested that: • If skewness is less than 1 or greater than (cid:0) C 1, the distribution is highly skewed. • If skewness is between erately skewed. 1 and (cid:0) (cid:0) 1=2 or between 1=2 and C C 1, the distribution is mod- • If skewness is between 1=2 and (cid:0) C 1=2, the distribution is approximately symmetric. There are two approaches to calculate the skewness of a dataset, namely: (i) Skewness (Bowley’s Method) where Q1; Q2, and Q3 are lower quartile, median, and upper quartile, respectively. (cid:0) Q1 C Q3 D (cid:0) ; Q1 Q3 2Q2 Negative Skew(large tail to the left)Positive Skew(large tail to the right)(ii) Pearson’s coeﬃcient of skewness 3 .mean-median/ standard deviation ; D (Karl-Pearson’s method) For simplicity, we will illustrate examples in the sub-section with ungrouped data. 4.5. OTHER DESCRIPTIVE STATISTICS 33 Example 4.6 Table 4.8 shows the prices of 25 selected food prices watch by the National Bureau of Statistics (NBS) in the month of August 2017. Table 4.8: Food prices Calculate the skewness using (i) Bowley method, (ii) Karl-Pearson’s coeﬃcient of skew- ness, and (iii) compare the results in (i) and (ii). Solution 599:64; Q1 (cid:31) N D .25 1/ C 4 D Q3 D 3.n C 4 th 1/ 308:77; Q2 D .n 1/ th C 2 D D 349:64; th D 890:83 and s 544:65 D (i) Skewness Q1 D Q3 C Q3 (cid:0) 2Q2 (cid:0) Q1 D 308:77 890:83 349:64 2 (cid:2) 308:77 (cid:0) C 890:83 (cid:0) 0:86. D 3 .599:64 (ii) Pearson’s coeﬃcient of skewness D 3 .mean-median/ standard deviation D 349:64/ (cid:0) 544:65 1:38. D (iii) The results in (i) and (ii) indicated that the distribution of the prices of 25 selected foods are positively skewed. 4.5.2 KURTOSIS Kurtosis can be deﬁned as a measure of the sharpness or shallowness of the peak of a distribution curve. A normal distribution has kurtosis of 3 with excess kurtosis of exactly 0. There are three Item12345678910Price485.1942.92370.25335.711131.381376.85311.20278.70465.34834.74Item11121314151617181920Price946.93158.85192.531629.25310.15345.821070.572361.70226.66349.64Item2122232425Price320.19343.45394.35401.30307.39Source: NBS, August, 201734 4. QUANTITATIVE TECHNIQUES types of kurtosis: mesokurtic, platykurtic, and leptokurtic. A mesokurtic (normal kurtosis) dis- 0), a platykurtic (negative kurtosis) has kurtosis tribution has kurtosis (cid:138) < 3 (i.e., excess kurtosis < 0), and leptokurtic (positive kurtosis) distribution has a kurtosis > 3 (implying excess kurtosis > 0). Figure 4.3 shows the types of the shape of kurtosis. 3 (i.e., excess kurtosis (cid:138) Figure 4.3: Shape types of kurtosis. The moment of coeﬃcient of Kurtosis is denoted by K4, and can be deﬁned mathemati- cally as: and Kurtosis.k4/ m4 m2 2 D x/2 P .x (cid:0) N n m2 D and m4 x/4 P .x (cid:0) N n ; D where m2 and m4 are the second moment (variance) and fourth moment, respectively. The excess kurtosis D Or excess kurtosis k4 K4 3 1/ .n (cid:0) 2/.n (cid:0) .n (cid:0) (cid:0) (population). 3/ ..n 1/ K4 6/. C C D Example 4.7 Refer to data in Example 4.6. Compute the coeﬃcient of kurtosis for the prices of selected foods. Solution 599:64 (cid:31) N D Negative KurtosisPositive KurtosisNormal Distributionx/2 P .x (cid:0) N n .485:19 (cid:0) 599:64/2 : : : C .401:30 (cid:0) 284780:20 (cid:0) C .42:92 25 599:64/2 25 599:64/2 .307:39 C m2 D D D 4.6. EXERCISES 35 : : : 599:64/2 C (cid:0) x/4 P .x (cid:0) N n .485:19 599:64/4 .42:92 (cid:0) C (cid:0) 460719706565:24: m4 D D D 599:64/4 25 : : : C C .307:39 (cid:0) 599:64/4 Therefore, K4 m4 m2 D 2 D 460719706565:24 284780:202 D 5:68, the excess kurtosis is .5:68 3/ (cid:0) D 2:68. We are using sample data, thus, excess kurtosis 22 .26 k4 D The excess kurtosis of 3.59 means the distribution is highly leptokurtic. .n 1/ (cid:0) 2/.n 3/ ..n 1/ K4 3:59. 2:68 6/ 6/ C C D C D (cid:2) 23 24 .n (cid:0) (cid:0) (cid:2) 4.6 EXERCISES 4.1. a. Mention and explain the diﬀerent types of quantitative techniques. b. In what areas are quantitative techniques applicable? c. What are the limitations of using quantitative techniques? 4.2. a. What do you understand by the term “measure of central tendency?” b. Find the mean, median, and mode of the following score of students in mathemat- ics test: 5, 7, 10, 3, 5, 7, 8, 9, 6, 6, 7, 10, 5, 4, 7, 3, 1, 4, 8, 9, 10, 7, 5, 4, 4, 6, 4, 2, 8, 3, 4, 3, 3, 7, 1, 6, 9, 4, 7. 4.3. The age distribution of students that participated in an A-level examination is as follows: 16, 15, 17, 18, 16, 15, 21, 15, 19, 17, 20, 21, 16, 14, 22, 21, 19, 16, 17, 17, 21, 22, 18, 19, 16, 18, 20, 20, 23, 18, 20, 16, 19, 18, 15, 16, 15, 19, 21, 20, 17, 15, 14, 17, 21, 23, 20, 18, 19, 18, 20, 17, 17, 19, 21, 23, 24, 21, 22, 19. Calculate: (i) mean, (ii) median, (iii) mode, (iv) range, (v) interquartile range, and (vi) variance. 36 4. QUANTITATIVE TECHNIQUES Table 4.9: Weekly wages 4.4. The weekly wages of 100 employees in a ﬁrm are given in Table 4.9. Find: a. mean, median, and mode of the distribution of the wages; and b. standard deviation and variance of the wages. 4.5. The annual gross domestic products (GDP) growth (%) of United States from 1961– 2016 is recorded as follows: 2.30, 6.10, 4.40, 5.80, 6.40, 6.50, 2.50, 4.80, 3.10, 3.21, 3.30, 5.26, 5.64, -0.52, -0.20, 5.39, 4.61, 5.56, 3.18, -0.24, 2.59, -1.91, 4.63, 7.26, 4.24, 3.51, 3.46, 4.20, 3.68, 1.92, -0.07, 3.56, 2.75, 4.04, 2.72, 3.80, 4.49, 4.45, 4.69, 4.09, 0.98, 1.79, 2.81, 3.79, 3.35, 2.67, 1.78, -0.29, -2.78, 2.53, 1.60, 2.22, 1.68, 2.37, 2.86, 1.49. Calculate: a. Mean, median, and mode of the annual GDP growth (%). b. Range, interquartile range of the United States annual GDP growth (%). c. Standard deviation and variance of the distribution. 4.6. a. Deﬁne skewness and Kurtosis. b. Refer to the data in question 5. c. Calculate the Pearson’s coeﬃcient of skewness and kurtosis of the United States annual GDP growth (%). Wages ($)Number of Employees1–10311–20521–30631–401541–501851–602561–701371–80981–90491–1002d. Construct a 95% conﬁdence interval for the annual GDP growth rate. 4.7. Table 4.10 shows the distribution of yield strength (MPa) of steel produced at a steel rolling company. Find: 4.6. EXERCISES 37 a. skewness using Bowley’s Method and Pearson’s coeﬃcient of skewness and b. kurtosis of the yield strength (MPa). Table 4.10: Distribution of yield strength (MPa) of steel produced at a steel company Yield Strength (MPa)250–269270–289290–309310–329330–349350–369370–389Frequency19232825353027Yield Strength (MPa)390–409410–429430–449450–469470–489490–509510–529Frequency2114109 5 2 2C H A P T E R 5 39 Hypothesis Testing and Regression Analysis In this chapter, we look at the diﬀerent stages of data preparation involved in quantitative analy- sis. Understanding these processes will help us gather reliable data and reach a valid conclusion. We will discuss types of hypotheses and how they are stated mathematically. Furthermore, we shall discuss hypothesis testing with worked examples. 5.1 DATA PREPARATION AND EVALUATION FOR QUANTITATIVE ANALYSIS Data preparation and evaluation processes involve data validation, editing, coding, assembling, and transformation. In this section, we will discuss these processes of preparing and evaluating data before conducting a rigorous analysis. Data validation: This is a process of checking data for authenticity. This is a way to determine if the survey was carried out correctly and appropriately. This process helps researchers ascer- tain whether interviewers or ﬁeld workers conducted research according to the research plan and objectives. Researchers can aﬃrm that the survey was conducted using the correct target population, in the appropriate location and during an appropriate period. Checking the ques- tionnaires may require the annulment of unacceptable questionnaires. The need to invalidate a questionnaire may arise as a result of a considerable number of incomplete questions, missing pages, or responses gathered from unqualiﬁed respondents who were not appropriate to poll for the purposes of the survey. Data editing: This is a process of checking for errors and biases in the data. Errors can come from the interviewer or the respondent. Data editing veriﬁes response consistency and accuracy, making corrections where necessary. Errors may occur during the completion of a questionnaire; for example, a respondent who graduated from a higher institution at the age of 21 can mistak- enly write 12 as their present age. It is the duty of a quality control manager to edit the data, based on the results gathered from other associated questions. Data editing is necessary before data analysis to remove problems that can lead to invalid analyses and incorrect conclusions (possibly resulting in Type I or Type II errors; see Section 5.2 below). 40 5. HYPOTHESIS TESTING AND REGRESSION ANALYSIS Data coding: The data obtained from the questionnaire are not all numerical in nature. Some- times, responses must be translated into numerical data to allow quantitative analysis. Binary variables (e.g., yes or no, male or female) are usually coded as 1 or 0, or 1 or 2. These dummy variables can be used to capture responses in a numerical fashion. The category variables (nomi- nal or ordinal) are represented by numbers (e.g., 1, 2, 3 , …, n). It is a good practice to assign the highest code number to the most positive response or to the most important end of a scale. Some questionnaires are pre-coded, while some questionnaires are not pre-coded. For a questionnaire that is not pre-coded, it is essential for researcher to code the responses in the questionnaire before quantitative analysis. Data assembling: This is the process of collating all the validated, edited, and coded data together and entering the corresponding values for each of the variables under investigation into the relevant software for analysis. The collated data are presented in a data matrix that has rows and columns. Data assembling can be performed in an Excel spreadsheet and then exported into a statistical software application (such as Stata or R) for analysis. Some statistical software allows the researcher to enter the data directly by selecting the appropriate box in the answer options provided. Some online survey software packages are able to detect invalid responses and inappropriate answers. For instance, if a ﬁeld in the questionnaire requires a numeric answer and the respondent enters an alphanumeric answer, the software will ﬂag the particular question in the questionnaire for the respondent to amend with an appropriate response, and prevent submission of the survey unless all the ﬁelds are completed with valid responses. Data transformation: This involves replacing a particular variable with a function of that vari- able. For instance, we can replace a variable by taking the logarithm of that particular variable or taking the square or square root of a particular variable. Data transformation helps to observe otherwise obscure relationships among variables, especially variables that are not linearly related. It can also assist smoothing or changing the shape of a distribution. 5.2 CONSTRUCTING AND TESTING DATA HYPOTHESES A hypothesis is a statement made through speculating upon the outcome of a research study or experiment. It is often a statement about a population. Generally, a researcher takes a sample from a given population and assesses if the sampled data supports the stated hypothesis about the population. A typical example of hypothesis is to test if the mean of population A is equal to the mean of population B, or to test if the mean of population A is signiﬁcantly diﬀerent from zero. In either case, a sample of data will be taken from the populations to evaluate the claim. The steps for constructing and testing hypotheses are as follows. State the hypotheses: There are two types of hypothesis—the null hypothesis and the alter- native hypothesis. The null hypothesis is the hypothesis under investigation and it is denoted by H0. The alternative hypothesis is the other hypothesis if the null hypothesis is rejected and 5.2. CONSTRUCTING AND TESTING DATA HYPOTHESES 41 it is denoted by H1. The following are the possible example of hypotheses for one-tail test and two-tail test: H0 H0 H0 H0 H0 H0 W W W W W W (cid:22) (cid:22) D D 0 vs. H1 0 vs. H1 (cid:22) > 0 vs. H1 0 vs. H1 (cid:22) (cid:21) (cid:22) < 0 vs. H1 (cid:22) < 0 vs. H1 W W W W W W (cid:22) < 0 (one-tail test) (cid:22) > 0 (one-tail test) 0 (one-tail test) (cid:22) (cid:20) (cid:22) < 0 (one-tail test) 0 (one-tail test) 0 (one-tail test) (cid:22) (cid:22) (cid:21) (cid:21) H0 W (cid:22) D 0 vs. H1 (cid:22) W 6 D 0 (two-tail test): Set the signiﬁcance level .(cid:11)/: There is need to set the level of signiﬁcance before the exper- iment. A Type I error occurs when the null hypothesis is rejected when it is actually true. The probability of committing a Type I error in a test is denoted as P (rejecting H0 H0) = (cid:11) and the signiﬁcance level is usually set at 5%. A Type II error is committed when accepting a null hypothesis which is actually false; this is denoted by (cid:12). Table 5.1 shows the statistical errors. j Table 5.1: Statistical errors Compute a test statistic: A test statistic is used to measure the degree of agreement between the sample data and the null hypothesis. It is a standardized value obtained from the sample data and is used to determine whether to accept or reject the null hypothesis. If the data shows evidence strongly in favor for rejection of the null hypothesis, the absolute value of the test statistic (in the case of F or t tests) becomes large and the p-value becomes small, depending on the alternative hypothesis. A computed test statistic that exceeds the value of the test statistic will result in a p-value below the selected signiﬁcance level. The choice of test statistic depends on the probability model assumed under null hypothesis. The commonly used test statistics include z-statistic, t-statistic, F-statistic, and chi-square statistic. DecisionHo Is Actually TrueFalseReject HoType I error (α)CorrectAccept HoCorrectType II error (β)42 5. HYPOTHESIS TESTING AND REGRESSION ANALYSIS Construct acceptance/rejection regions: The acceptance region consists of values that are consistent with the null hypothesis while the rejection region consists of values that may not occur (or are very unlikely to occur on a frequent basis) if null hypothesis is true. The rejection region is also known as the critical region and the values that contains in the critical region is called the critical values. The critical value is compared with the test statistic to determine whether to reject the null hypothesis. For absolute value of test statistic greater than the critical value, null hypothesis is rejected. The acceptance and rejection regions of a two-tail tests for normal distribution are depicted in Figure 5.1. Figure 5.1: Critical regions for the test of signiﬁcance. Draw a conclusion: The decision rule is to reject the null hypothesis whenever the absolute value of computed statistic is greater than the critical value (table value). Thus, a valid conclusion can be drawn based on the data. 5.3 REGRESSION ANALYSIS: CONCEPT AND APPLICATIONS (INTERPRET DATA RELATIONSHIPS AND FORECASTING) Regression analysis is a statistical technique to analyze quantitative data in order to estimate model parameters and make forecasts. Regression analysis is used to model the relationship between a response variable and one or more explanatory variables. The response variable or dependent variable is denoted by Y , while the independent variable or explanatory variable is denoted by X. A regression model is said to be simple linear regression if it contains one depen- dent variable and one independent variable, and the two variables are linearly related. Thus, the Critical RegionCritical RegionAcceptanceRegion-Zα/2-Zα/2-Z05.3. REGRESSION ANALYSIS: CONCEPT AND APPLICATIONS 43 variation in the dependent variable (Y ) can be explained by the variation in independent variable (X). A multiple regression shows the relationship between one dependent variable (Y ) and more than one independent variable (i.e., X1, X2, …, Xn). In this chapter, we will concentrate on the simple linear regression and multiple regression models. A forecast is a prediction about the future values of data. A regression forecast can be either extrapolation or interpolation. Extrapolation is an estimation of value based on extending a known sequence of values and interpolation is an estimation of value within the sequence of two known values. After modeling the relationship between variables of interest to create a regression model, we can use this model equation to predict the value of the dependent variable given any value of the independent (explanatory) variable. 5.3.1 ASSUMPTIONS OF LINEAR REGRESSION (i) The relationship between the response variable (Y ) and explanatory variable (X) must be linear. (ii) The explanatory variable (X) is non-stochastic (deterministic). (iii) The model residuals (errors) are statistically independent. (iv) The errors are normally distributed with zero mean and a constant standard deviation. 5.3.2 SIMPLE LINEAR REGRESSION The mathematical model for the simple linear regression is given as: Y (cid:12)0 C D (cid:12)1X C "; (5.1) where " is the error term, and (cid:12)0 and (cid:12)1 are the intercept and regression coeﬃcient of X, respectively. This equation mathematically represents the relationship between two variables, for example, the relationship between income and expenditure, advertising spend in a region and sales revenue, years of education and salary, and other uses. This model will give us the best line of ﬁt for the two variables under investigation. Using the ordinary least squares (OLS) method to estimate the model, the regression coeﬃcients can be calculated as follows: (cid:12)1 D n P XY n P X 2 .P X/.P Y / .P X/.P X/ (cid:0) (cid:0) The regression model is ﬁtted as Y (cid:12)0 D N (cid:0) (cid:12)1 N X: Y D O(cid:12)0 C O(cid:12)1X: (5.2) (5.3) (5.4) 44 5. HYPOTHESIS TESTING AND REGRESSION ANALYSIS Example 5.1 Table 5.2 shows the log of ﬁnal consumption expenditure (Y ) and log of Gross Domestic Products (X) in Nigeria between 1981 and 2015. (i) Fit the model by regressing ﬁnal consump- tion expenditure (Y ) on Gross Domestic Products (X) and interpret the result. (ii) Extrapolate the value of log of ﬁnal consumption expenditure when log of Gross Domestic Products is 7.0. Table 5.2: Final consumption expenditure and log Gross Domestic Products Solution (i) n 35, P XY D 5:22 X and N D 4673:12, P X 182:60, P Y D D D 893:94, P X 2 960:90 Y N D 25:54, D (cid:12)1 D 35 .4673:12/ .182:60 893:94/ (cid:0) 35 .960:90/ (cid:2) .182:60/2 (cid:0) 1:1282: D Substitute for the value of (cid:12)1 in (5.3) to solve for (cid:12)0 (cid:12)0 D 25:54 (cid:0) .1:1282 5:22/ (cid:2) D 19:6508: Y Therefore, the model is O 19:65 C D 1:13X. Year1981198219831984198519861987198819891990Y25.3325.2825.1525.0725.1524.9624.7424.8424.8125.00X4.824.814.764.744.824.734.614.694.754.87Year1991199219931994199519961997199819992000Y25.0325.1325.1125.0725.1325.3025.2725.2825.2225.24X4.864.874.894.904.894.944.975.005.005.05Year2001200220032004200520062007200820092010Y25.5625.5725.6925.9226.0125.9026.2626.1826.3626.34X5.105.135.235.525.565.645.705.765.835.91Year20112012201320142015Y26.3226.3126.4726.4726.47X5.956.006.056.116.14Source: WDI5.3. REGRESSION ANALYSIS: CONCEPT AND APPLICATIONS 45 The one percentage change in Gross Domestic Products (X) results in 13 percentage changes in ﬁnal consumption expenditure. This indicates a household spending elastic- ity of 1.13, implying that GDP responds to consumption spending is 1.13. (ii) When X Y 7:0, then O D D 19:65 C 1:13 .7/ D 27:56. 5.3.3 MULTIPLE REGRESSION This is an extension of simple linear regression. In the real world, what determines the value of a particular variable, such as salary, is dictated by more than one explanatory variable, such as years of education, years of experience, geographical location, and even gender or ethnicity. The model that shows the relationship between the response variable (Y ) and a set of explanatory variables (Xi ) is called Multiple Regression. The multiple regression model is of the form: Y (cid:12)0 C D (cid:12)1X1 C (cid:12)2X2 C : : : (cid:12)kXk " C (5.5) where Y is the dependent variable, Xi are the explanatory variables, and (cid:12)i are the coeﬃcients of regression (change in Y per unit change in Xi ). 5.3.4 ASSUMPTIONS OF MULTIPLE REGRESSION (i) The relationship between the dependent variable and the independent variables is linear. (ii) The residuals are normally distributed. (iii) The residuals are homoscedastic, i.e., residuals are uncorrelated. (iv) No multicollinearity, i.e., independent variables are not correlated. For the sake of simplicity, we assumed that we are dealing with one dependent variable and two independent variables. The model can be stated as: Y (cid:12)0 C D (cid:12)1X1 C (cid:12)2X2 ": C The regression coeﬃcients can be deﬁned as: (cid:12)1 D (cid:12)2 D (cid:0)P x2 (cid:0)P x2 (cid:0) 1(cid:1) (cid:0)P x2 2(cid:1) 2(cid:1) .P x1y/ (cid:0)P x2 1(cid:1) .P x2y/ (cid:0)P x2 X1 (cid:12)1 N (cid:0) 1(cid:1) (cid:0)P x2 2(cid:1) X2; (cid:12)2 N (cid:0) Y (cid:12)0 D N (cid:0) .P x1x2/ .P x2y/ .P x1x2/2 (cid:0) .P x1x2/ .P x1y/ .P x1x2/2 (cid:0) (5.6) (5.7) (5.8) (5.9) 46 5. HYPOTHESIS TESTING AND REGRESSION ANALYSIS where P x1y P X1Y D (cid:0) .P X1/.P Y / N X X2Y .P X2/ .P Y / N (cid:0) X x2y X x1x2 D D X X1X2 .P X1/ .P X2/ N (cid:0) .P X1/ .P X1/ N .P X2/ .P X2/ N : (cid:0) (cid:0) X x2 1 D X X1X1 X x2 2 D X X2X2 Example 5.2 Table 5.3 shows the data for Nigeria’s net foreign direct investment inﬂow as percentage of GDP (FDI), real GDP growth rate (GDP), and inﬂation rate (INFL) recorded in 1986–2015. 10 and GDP (i) Regress FDI on INFL and GDP. (ii) What is the value of FDI when INFL D 2:72? D Table 5.3: Data for Nigeria’s net foreign direct investment inﬂow YearFDIINFLGDPYearFDIINFLGDP19860.935.72-8.7520012.7018.874.4119872.5311.29-10.7520023.1712.883.7819881.6354.517.5420032.9614.0310.3519897.7850.476.4720042.1315.0033.7419901.917.3612.7720054.4417.863.4419912.6013.01-0.6220063.348.248.2119923.0644.590.4320073.635.386.8319938.5257.172.0920083.9411.586.27199410.8357.030.9120095.0511.546.9319953.7872.84-0.3120101.6313.727.8419964.5529.274.9920112.1510.844.8919974.308.532.8020121.5312.224.2819983.2810.002.7220131.088.485.3919992.806.620.4720140.828.066.3120002.466.935.3220150.649.022.65Source: WDISolution 5.3. REGRESSION ANALYSIS: CONCEPT AND APPLICATIONS 47 1:93, (cid:12)1 D (cid:0) FDI D (i) To reduce computational eﬀort, the relationship between Nigeria’s net foreign direct in- vestment inﬂow as percentage of GDP (FDI), real GDP growth rate (GDP), and inﬂation rate (INFL) is shown in the E-Views result below (see Table 5.4). As we can see in the result shown below, (cid:12)0 D Thus, the model is estimated as: 0:01, and (cid:12)2 D 1:93 (cid:0) (cid:3) Note that only the constant term and the inﬂation rate are statistically signiﬁcant while GDP is not signiﬁcant in the model. Let us relax the signiﬁcance of variables at this mo- ment and assume that all variables are signiﬁcant. The model can be interpreted as for a unit change in real GDP growth rate, net foreign direct investment inﬂow as percentage of GDP (FDI) decreases by 1%. Also, for a unit change in inﬂation rate, net foreign direct investment inﬂow as percentage of GDP (FDI) increases by 7% while the constant term is 1.93 (i.e., the value of FDI when GDP and INFL at zero). b INFL 0:07. GDP 0:01 0:07 C (cid:3) (ii) FDI 1:93 (cid:0) D 0:01 .2:72/ 0:07 .10/ 2:6 D C Remember that the diﬀerence between the actual value and estimated value is the error; thus the error is 0.68 (see Table 5.4). b 48 5. HYPOTHESIS TESTING AND REGRESSION ANALYSIS Table 5.4: E-Views output 5.4 EXERCISES 5.1. Discuss the data preparation and evaluation processes. 5.2. What is a hypothesis? Give an example of a phenomenon which could be explored using a hypothesis. 5.3. a. What is the diﬀerence between a null and alternative hypothesis? b. State the steps in constructing and testing a hypothesis. 5.4. a. What do you understand by regression analysis? b. State the assumptions of the linear regression model. c. Table 5.5 shows the GDP growth rate (Y ) and inﬂation rate (X) of the U.S. from 1961–2016. Fit the regression model; what is the value of GDP growth rate (%) when inﬂation rate is 3.0%? 5.5. The following data in Table 5.6 shows the monthly revenues (in billions naira) generated from the federal government of Nigeria from Oil (OILR) and non-oil (NONR) sectors between June 2015 and May 2016. E-Views OutputDependent Variable: FDIMethod: Least SquaresDate: 11/23/17 Time: 15:38Sample: 1986 2015Included Observations: 30VariableCoeﬃ cientStandard Errort-StatisticProbabilityCGDPINFL1.932733-0.0078280.0706210.5789590.0488530.0185763.338289-0.1602373.8017950.00250.87390.0007R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog LikelihoodF-statisticProb(F-statistic)0.3531760.3052631.90411697.89273-60.308287.3712090.002790Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionHannan-Quinn criterionDurbin-Watson statistic3.3390002.2844584.2205524.3606724.2653772.043500Table 5.5: GDP growth rate (Y ) and inﬂation rate (X) 5.4. EXERCISES 49 Table 5.6: Monthly revenues a. Plot a scatter diagram of the data. b. Calculate the coeﬃcients of the regression model. c. If the Nigeria oil sector revenue in June 2016 is NGN170.5 billion, what would be the predicted revenue for the non-oil sector? YearYXYearYXYearYXYearYX19612.301.081975-0.209.1319893.684.8320032.812.2719626.101.1219765.395.7419901.925.4020043.792.6819634.401.2119774.616.491991-0.074.2320053.353.3919645.801.3119785.567.6519923.563.0320062.673.2319656.401.6719793.1811.2719932.752.9520071.782.8519666.502.991980-0.2413.5119944.042.612008-0.293.8419672.502.7819812.5910.3219952.722.812009-2.78-0.3619684.804.221982-1.916.1619963.802.9320102.531.6419693.105.4119834.633.2119974..492.3420111.603.1619703.215.9019847.264.3219984.451.5520122.222.0719713.304.2619854.243.5619994.692.1920131.681.4619725.263.3119863.511.8620004.093.3820142.371.6219735.646.2219873.463.7420010.982.8320152.860.121974-0.5211.0419884.204.0120021.791.5920161.491.26Source: WDIMonthJun-15Jul-15Aug-15Sep-15Oct-15Nov-15OILR270.16224.06218.22217.70112.13202.97NONR262.76281.41215.69165.91276.96160.59MonthDec-15Jan-16Feb-16Mar-16Apr-16May-16OILR218.40256.36225.92183.81183.31161.36NONR162.75187.64159.23143.74157.10173.15Source: CBN Statistical BulletinC H A P T E R 6 51 Analyzing Survey Data Analyzing survey data entails processing data, presenting data and drawing valid conclusions from the analysis. In the following example, we are going to use consumer expenditure surveys to illustrate how survey data are collected. We will consider types of measurement and their real-world applications, explore survey research puzzles, obtain strategic insights from survey research, and discuss how to test the quality of data. 6.1 QUANTITATIVE TECHNIQUE OF COLLECTING SURVEY DATA: CONSUMER EXPENDITURE SURVEY Consumer expenditure surveys are conducted to obtain data regarding household income, ex- penditure and the demographic characteristics of consumers. The method of data collection is similar to the personal interview and questionnaire methods described in Section 2.3. In the survey, we are able to discover which are the most frequently purchased items in the market with respect to income group, geographic location, size of the family, and other demographic information. This survey shows the pattern of consumer spending at a particular period of time and provides a continuous trend of information regarding purchasing habits. Consumer expen- diture surveys are also used to determine the relative importance of goods and services in the “basket” of products used to determine the consumer price index (CPI). The bra Inﬂation Index is an independent consumer price index developed by bra to measure the price level movement in Nigerian markets, built upon consumer expenditure surveys. The relative importance of products as part of an entire basket of purchases is used to provide the weightings necessary to calculate the CPI. 6.2 TYPES OF MEASUREMENT SCALES AND THEIR APPLICATIONS The four types of measurement scales include nominal, ordinal, interval, and ratio. Nominal scale: Nominal is a Latin word that means name. Nominal scales are used to classify variables into discrete groups; these groups do not have any inherent numerical association. The variables on a nominal scale are also known as categorical variables. Nominal variables are categorized without any order or sequence. Example of categorical variables are sex, race, eye color, genotype, religion, etc. Nominal variables can be represented in a bar chart, histogram, 52 6. ANALYZING SURVEY DATA or pie chart. Consider Table 6.1 that contains the information on the obtained from a survey of types of houses in a community and presented in a bar chart. Table 6.1: Types of houses in a community Figure 6.1: Frequency of types of houses in a community. Ordinal scale: Ordinal variables are similar to nominal or categorical variables, with the dif- ference that each variable is assigned a numerical value based on a desired ordering. For instance, education level can be categorized into ﬁve categories; primary school leaver, secondary school leaver, college of education graduate, polytechnic graduate, and university graduate. We may want to assign the number 1 to indicate primary school education, 2 to secondary school, 3 to college of education, 4 to polytechnic, and 5 to university. In this case, we can delineate the diﬀerence between one educational level and another based on the order applied; for example, House TypeFrequencyBungalow12Duplex16Cottage2Detached7Flat5Semi-detached6Terrace3BungalowDuplexCottageDetachedFlatSemi-detachedTerrace1216275636.2. TYPES OF MEASUREMENT SCALES AND THEIR APPLICATIONS 53 the gap between primary and secondary school leavers is wider than the gap between polytech- nic and university. However, applying ordinal scales to categorical variables implies that each category is equally spaced. In this example, the gap between primary and secondary education is the same as the gap between high school and university education. This assumption may not hold true, thus care must be taken to justify the ordering of an ordinal scale. Table 6.2 is the new country classiﬁcation by income level. The World Bank classiﬁcation of the thresholds are low-income, lower-middle income, upper-middle income, and high-income countries with un- equal GNI/Capita range. We can assign values to these thresholds as follows: low-income 1; lower-middle income 2; upper-middle income 3; and high-income D 4. D D D Table 6.2: Country classiﬁcation by income level Interval scale: An interval variable is similar to an ordinal variable, the main diﬀerence being that the interval variable contains a range of values that are equally spaced (i.e., the interval variable has values of equal range). Assuming that a teacher conducted a test of 10 marks to 30 pupils in Mathematics class and none of the pupils got zero. We know that the minimum and maximum scores are one and ten marks, respectively. The teacher can classify the test scores into ﬁve distinct groups as follows: 1–2, 3–4, 5–6, 7–8, 9–10. See Table 6.3. Table 6.3: Distribution of test score Ratio scale: A ratio variable has the qualities of nominal, ordinal, and interval variables, and also has an absolute zero that is meaningful. This implies that a meaningful fraction can be constructed with a ratio variable. Ratio scale provides the ultimate-order, interval values, and Th resholdGNI/Capita (current US$)Low-income<1,005Lower-middle income1,006 – 3,955Upper-middle income3,956 – 12,235High-income>12,235Test ScoreFrequency1–223–415–6107–8159–10254 6. ANALYZING SURVEY DATA the ability to calculate ratios since a “true zero” can be deﬁned. For example, we can simply say that the service time is greater than zero, this means that we have conceptualized a zero point in time. A ratio scale allows comparisons to be made easily. For instance, it is possible to say that “the doctor has twice patients in this month than in the previous month.” In a research, it is a good idea to have a higher level of measurement like ratio and interval rather than a lower one like nominal and ordinal. Other example of ratio variables are height, weight, length, gross sales, expenditure, income, etc. A ratio variable can be used as a dependent variable for most of parametric statistical tests such as t-tests, F -tests, correlation, and regression analysis. 6.3 SURVEY RESEARCH RIGOR In order to formulate a survey that achieves results reﬂective of a population while minimizing errors, the researcher must follow rigorous standards of quality, engagement and execution. These three factors are discussed below. (a) Quality of questionnaire: The quality of the questionnaire determines the quality of the data obtained from the survey. It is the aim of the researcher to understand a phenomenon by exploring the underlying reasons for variance in the responses obtained from a survey. If survey questions are poorly worded or ambiguous, this results in respondent errors and adds variance to the results which are not reﬂective of the phenomenon being studied, but are simply a result of poor survey design. Before the questionnaire is set to be administered, a researcher must perform the following task on the questionnaire. (i) Check the correctness of the questions by putting himself and others in position of the respondents to provide answers to the questions. (ii) Ensure that questions are simple, avoiding double-negatives (do you disagree that housing is too expensive?) or double-barreled questions (do you think housing is too expensive and cars are aﬀordable?) (iii) Avoiding leading questions (e.g., “Do you think politicians deserve their pay rises despite the poor performance of the economy and their personal lack of ethics?”) (iv) Make the questions as concise as possible. (v) Constantly edit the questionnaire by removing irrelevant questions or checking for ambiguous meanings. (vi) Accommodate all possible answers, for instance by oﬀering “none of the above” or “other, specify” type responses. (b) Survey engagement: When conducting a survey, it is necessary to ask respondents to sac- riﬁce their time, thus researchers should be conscious of the duration of the survey. To achieve a greater accuracy in our survey, we should mindful of our respondents’ time and set a time limit on our survey, particularly when using online surveys. This will encourage 6.4. TESTING DATA QUALITY: SURVEY ERROR DETECTION PROCEDURES 55 more respondents to participate in our survey. The greater the number of people that par- ticipate in the survey the more the robust the analysis should be (assuming that the correct demographic is being surveyed). It is essential to add “save and continue” buttons to allow a respondent to ﬁnish a survey later; this is especially useful for longer surveys. For online surveys, it is good practice to show a progress bar to indicate the percentage of questions that have been completed by the respondent. More importantly, oﬀering respondents in- centives enhances the quality of data. If incentives are given to respondents, they will be more willing to supply the correct data and express their feeling toward a question, and oﬀering incentives can often lead to a larger number of respondents willing to complete the survey. However, the ability to oﬀer incentives is often dependent on research funding, and may not be cost-eﬀective on a large scale. (c) Eﬀective survey execution: Aside from administering face-to-face surveys or interviews, we can also use other methods to administer our questionnaires. The methods include email, social media, mobile apps, and oﬄine surveys. These methods are eﬀective and eﬃcient for conducting a large sample survey in a limited time interval. In addition, we should test the functionality and responsiveness of the online questionnaire before it is ﬁnally deployed. Communication between the researcher and respondents is crucial before, during and after administering questionnaires. 6.4 TESTING DATA QUALITY: SURVEY ERROR DETECTION PROCEDURES Good quality data should be free of errors. After collecting data from the ﬁeld, it is necessary to perform a routine data check to conﬁrm the authenticity of the data and to check for other errors that may have occurred during the data gathering process. The Consumer Expenditure Survey and Commodity Price Expenditure Survey are con- ducted by bra to track consumer spending patterns. As with any survey, the accuracy of consumer expenditure and commodity price estimates depends on the accuracy of the collected data. The surveys have several procedures already in place to ensure the accuracy of the published results. The following steps are used to cross-check data generated from the ﬁeld. (a) Re-interview respondents. (b) Use computerized checks to verify the logical consistency of responses given by respon- dents. (c) Perform an outlier review of individual survey responses. (d) Perform an outlier review of the summarized expenditure estimates before they are pub- lished. 56 6. ANALYZING SURVEY DATA (e) Use Benford’s Law to determine the distribution of the leading digit of all numbers re- ported on a survey form. Here, we are going to discuss the characteristics, technique and application of Bedford’s law. The kind of data that Benford’s law can be applied to are as follows. (a) Data that has a wide variety in the number of ﬁgures (i.e., data with a large range). (b) The data is right skewed, i.e., the mean is greater than the median, and the distribution has a long right-tail rather than being symmetric. (c) Data with values that are formed by a mathematical combination of numbers from other distributions. (d) Data that has no predeﬁned maximum or minimum value (except a minimum of zero). Benford’s Law involves examining the distribution of the leading (or left-most) digits of all the numbers reported on a survey form. These leading digits have been observed to follow a certain distribution regardless of the nature of the survey. This law is used to detect sources of unusual data, especially in the case that the ﬁeld worker is under suspicion of manipulating data. Benford’s Law states that the proportion of “real world” numbers whose leading digit is 1; 2; 3; : : : ; 9 are approximately log10 (cid:16) d (cid:17), where d is the leading digit of the randomly selected number. For instance, 125,000, 28,013,20 and 72,467,456 have the leading digits of 1, 2, and 7, respectively. D C d d 1 Benford’s law for the prediction of the leading digits (1–9) is tabulated in Table 6.4. Table 6.4: Benford’s Law Comparing the distribution of the leading digits against Benford’s predicted distribution, we identify large variances between the leading digits distribution and Benford’s predicted dis- tribution. Wide margins between the observed and predicted distribution may indicate data tampering or erroneous data gathering processes which could warrant further investigation. Let us consider the hypothetical example, assuming that there were 2,000 respondents in the Consumer Expenditure Survey and the leading digits of their expenditure are classiﬁed as in Table 6.5. From Table 6.5, we can observe that the margin between the percentage of reported ex- penditure with the leading digits 3 and 8 vary signiﬁcantly from the predicted distribution, with absolute diﬀerence of 3.50 and 3.68, respectively. Thus, these expenditure values under a leading digit of 3 and 8 should be scrutinized because they are suspicious. 1st Signiﬁ cant Digit123456789Benford Prediction (%)30.1017.6112.499.697.926.695.805.124.58Table 6.5: Benford’s prediction 6.5. EXERCISES 57 6.5 EXERCISES 6.1. Discuss the purpose(s) of a consumer expenditure survey. 6.2. Describe the four types of measurement scales. 6.3. What are some of the features of a good questionnaire? 6.4. State the procedures used to detect errors in a survey. 6.5. What is Benford’s law, and what are its applications? 6.6. Given the following data obtained from 30 households expenditure ($): 1,500, 1,725, 2,458, 1,620, 2,550, 1,740, 1,420, 2,375, 1,810, 1,450, 1,430, 980, 910, 1,001, 2,000, 1,720, 899, 769, 580, 4,000, 1,665, 3,110, 755, 680, 1,200, 2,500, 590, 880, 1,008, 675. Calculate Benford’s prediction for the data and interpret your results. 6.7. The Statistics department arm of Central Bank of Nigeria conducted an expenditure survey to explore the distribution pattern of people living in the state capital, Abuja. A random sample of 5,000 households are selected and the result of the survey is summa- rized in Table 6.6. a. Compute Benford’s prediction for the distribution of expenditure. b. Do any suspicious values arise from the previous computation? Leading Digit (d)Reported ExpenditureBenford’s Predictionlog10 d + 1 dDiﬀ erenceNumberPercentage160830.4030.100.30235017.5017.61-0.1131808.9912.49-3.5041919.549.69-0.1551567.787.92-0.1461326.626.69-0.0771165.815.800.0181768.805.123.689914.564.58-0.02Total2,00010010058 6. ANALYZING SURVEY DATA Table 6.6: Result of the survey of a random selected 5,000 households Leading Digit123456789Frequency689496126784329545636952965C H A P T E R 7 59 Index Methodology bra develops and maintains a number of indices that measure the performance of the Nigerian economy. In this chapter, we will elucidate on the principles and techniques used to formulate indices by providing the reader with practical examples. These indices include bra Expectation Index, bra Consumer Conﬁdence Index, braIndex, bra Producer Price Index, bra Bond Index, and bra Inﬂation Index. We will discuss each of the indices extensively. 7.1 bra EXPECTATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS bra conducts a monthly business survey which polls respondents across a number of sectors about their expectations for the Nigerian economy during the next one-, three-, and six-month time frames. Our expectation surveys gather the opinions of business leaders and entrepreneurs regarding the performance of key areas such as: employment, prices, bank rates, economic con- ditions, business conditions, cost of production, volume of products, market share, stock level and production, access to credit facilities, ﬁnancial condition, and the success of social or ﬁs- cal policies, among other factors. The survey obtains a cross-section of sentiments from small, medium, and large ﬁrms in the following sectors of the economy: the ﬁnancial sector, manufac- turing sector, hotel sector, petroleum marketing, telecommunication sector, commercial sector, agricultural sector, and construction sector. 7.1.1 OBJECTIVES OF bra EXPECTATION INDEX (i) To survey short run business conditions. (ii) To assist optimal decision making and better planning for economic improvement. (iii) To serve as a leading business cycle indicator. 7.1.2 METHODOLOGY There are two approaches to compute bra Expectation Index, namely—(i) diﬀusion index and (ii) net balance. (a) Diﬀusion index: This is calculated by assigning weights to the percentage of respondents under each response category: positive, negative, and neutral. The index takes the values of 0–100. An index value of 100 indicates that the respondents are unanimously positive 60 7. INDEX METHODOLOGY regarding the economic variable under consideration, or unanimously expect this variable to improve. The index value of zero indicates a unanimously pessimistic response about the key variable, or a unanimous expectation that this variable will deteriorate. For the al- location of weightings to the response options, we will look at the cases when the response options are three and when the response options are four. Case I: Three response options From the survey questions where there are three dif- ferent options provided to the respondents—Positive/Increase, Negative/Decrease, and Neutral/Remain Unchanged. We assigned the weight of 1.0 to the percentage reporting increase, a weight of 0.5 to the percentage reporting decrease and a weight of zero to percentage reporting remain unchanged. Case II: Five response options For the questions where there are ﬁve options are provided—substantially increase, increase, same, decrease, and substantially decrease. The diﬀusion index would weigh the responses 1.0, 0.75, 0.5, 0.25, and 0.0, respectively. (b) Net balance: This is calculated as the percentage of respondents expecting an improve- ment/increase in economy indicator less the percentage expecting a deterioration/decrease in the same economic variable. 7.1.3 CALCULATION OF bra EXPECTATION INDEX bra adopts the formula below to calculate the diﬀusion index for the business expectation survey: Index 1 2 D (cid:8)(cid:0)% reporting increase % reporting decrease(cid:1) 100(cid:9) : C (cid:0) (7.1) The index is read thus. 1. If the index is above 50, it shows that respondents expect conditions to improve. 2. If the index is at 50, it shows that respondent expect conditions to remain unchanged. 3. If the index is below 50, it shows that respondents expect conditions to deteriorate. It is important to keep in mind the current state of what is being measured. To illustrate, if an economy is in a deep recession, current economic conditions will be very unfavorable. If we poll respondents about economic expectations and determine a result above 50, this indicates that our respondents believe there will be some improvement in economic conditions. However, this does not necessarily mean that the economy is expected to achieve positive GDP growth, only that conditions are expected to improve from a deeply negative position to possibly slightly negative (perhaps respondents believe that the economy will contract at a slower pace). See the illustrative example in Table 7.1. 7.2. bra CONSUMER CONFIDENCE INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 61 Table 7.1: Illustrative example 7.2 bra CONSUMER CONFIDENCE INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS The bra Consumer Conﬁdence Index (braCCI) is based on a monthly survey that shows the direction of the economic performance within a short period; it serves as a leading indicator that gives speciﬁc insight of what consumers expect of the economy within the speciﬁed period. The index will be generated on monthly basis from the monthly business expectation survey (BES) conducted by the company’s ﬁeld researchers. The questions selected from the observations made by the respondents to compute the index will remain constant throughout the history of the series. 7.2.1 COMPONENTS OF braCCI The components of braCCI are Present Situation Index (PSI) and Expectation Index. The survey questions have three diﬀerent options responses—Positive, Negative, and Neutral and covers the same sectors covered, as mentioned above. The Present Situation Index is composed of current business conditions, current employ- ment conditions, and general sales conditions. On the other hand, the constituents of expecta- tion index are expected business conditions, employment conditions, general sales conditions, and ﬁrm income expectations predicted for the next six month horizon. 7.2.2 METHODOLOGY bra adopts the average relative approach in the computation of the consumer conﬁdence index; this can be written mathematically as: Relative value .Xi / D (Positive responses)/(Total responses): The relative value is derived for each of the questions; the average relative for the calendar month is then estimated in (7.2) as follows: Average Relative (CCI) 7 1 Xi P N ; D (7.2) PeriodResponses in PercentagesDiﬀ usion IndexIncreaseDecreaseUnchanged1-month751510803-month50050756-month001005062 7. INDEX METHODOLOGY where N represents the total number of variables constituting the component of the questions in the document, while i represents the items in the components. The consumer conﬁdence index is then split into two parts, namely the current month and six-month outlook: Present Situation Index (PSI) P 3 1 Xj nj ; D (7.3) where j represents the items of current month responses in the components and nj is the number of current month variables in the component section of the document. Expectation Index (EI) P 4 1 Xk nk ; D (7.4) where k represents the items of six month responses in the components and nk is the number of six-month variables in the component section of the document. The benchmark for the index as a reference of economic direction is 0.5 (50 index points). 7.2.3 ILLUSTRATIVE EXAMPLE Let us consider that Table 7.2 is the summary of the business expectation survey for 100 respon- dents. Table 7.2: Business expectation survey General Outlook Average Relative Value Average Relative Value Consumer Conﬁdence Index D D .0:70 0:617 0:60 C C 0:50 .0:617 100/ (cid:3) D 0:60 0:70 C C 0:60/=6 61:7 C D Current Month Average Relative Value Average Relative Value D D .0:70 0:633 C 0:50 C 0:70/=3 ResponsePositiveNegativeNeutralRelativeBusiness conditions (current month)7020100.7Business conditions (six month)6020200.6Employment status (current month)5030200.5Employment status (six month)6010300.6Sales status (current month)7020100.7Sales status (six month)6020200.6Firm income realize in the next six (6) month8010100.87.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 63 Present Situation Index .0:63 100/ (cid:3) D 63:3 D Six Month Outlook Average Relative Value Average Relative Value Expectation Index D D .0:65 .0:60 0:65 D 100/ (cid:3) D 65:0 0:60 0:60 C C C 0:8/=4 7.2.4 INDEX MAINTENANCE We keep track of the components of the index and make proper adjustments (expanding the number of components) when appropriate. Constant monitoring and management is set in place for eﬀective maintenance. 7.3 braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS braIndex is a pure market capitalization weighted index. This index is also known as bra50 Index. This equity index is estimated daily, using the total market capitalization of the constituent stocks without adjustment for free ﬂoats. Consistency in adjustment for corporate actions and events as well as stock rotation is a quality control component of the braIndex’s formulation. The braIndex consists of the 50 top-performing stocks on the Nigeria Stock Exchange (NSE). The component stocks are fundamentally sound and technically liquid enough to justify selection. Selected stocks must have proven records of earnings and growing shareholder value in addition to being listed on the exchange for at least ﬁve years. Stocks are placed under rigorous selection screening before they are qualiﬁed to be among the constituent stocks. These selection criteria are: basic criteria, technical criteria, and fundamental criteria. 7.3.1 BASIC CRITERIA FOR SELECTION OF CONSTITUENT STOCKS 1. Any companies selected must be quoted companies on the Nigerian Stock Exchange (NSE). 2. Stocks delisted from the NSE are NOT qualiﬁed. 3. Stocks must be listed on the NSE for a minimum of ﬁve years. 4. Companies that have not held an AGM (Annual General Meetings) in the last ﬁve years or for two consecutive years are not considered. 5. Stocks must have a minimum market capitalization that is equal to or higher than the average of its sector. 6. Any company that did not pay dividends for a minimum of three years, or declared a rights issue or bonus issue for the same number of years, are not considered. 64 7. INDEX METHODOLOGY 7. If any ﬁnancial institutions fall under the marginal banks list of the Central Bank of Nigeria (CBN), such a ﬁnancial institution is disqualiﬁed. 8. Any companies that have not published up-to-date unqualiﬁed ﬁnancial statements as of the time of selection or review are not considered. 9. Any companies that satisfy the above basic criteria will be considered in the calculations of bra equity index. 7.3.2 TECHNICAL CRITERIA 1. Stocks that are not active and traded persistently on the NSE for a minimum of three months without a basic reason are not considered. Component stocks that violate this criterion are removed. 2. Stocks must be traded at an average volume of at least 5,000 shares a day for the last 12-month period preceding the determination date. 3. Stocks experiencing persistent price crashes for three months are not considered. 4. Stocks with a negative 52 week beta vs. the market beta are not considered. 5. Stocks with a negative 52 week beta vs. the industry beta are not considered. 6. P/E growth must also be positive for at least the last two consecutive years. 7.3.3 FUNDAMENTAL SELECTION CRITERIA 1. Earnings Per Share (EPS) must be positive (more than zero) for at least the last two years. 2. Dividends, rights issues, and bonus issues must be positive for at least the last two consec- utive years. 3. Selected companies must have positive revenue reserve/retained earnings for at least the last two consecutive years (out of ﬁve years). 4. Market Capitalization Threshold: Stocks must have a market capitalization that is more than or equal to the industry/sectorial average capitalization. 5. The company must have a positive Return on Equity (ROE) for at least the last two con- secutive years (out of ﬁve years). 6. Price-Earnings Ratio must be positive for at least the last two consecutive years. 7. Growth rate of EPS must be positive for at least the last two consecutive years (out of four years). 8. Sustainable growth rate must be positive for at least the last two years. 7.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 65 7.3.4 CORPORATE EVENT The following are corporate actions that require divisor adjustment. Stock Split A stock split simply involves altering the number of shares outstanding of a listed company and proportionally adjusting the share price to compensate. This exercise in no way aﬀects the intrin- sic value or performance of the stock; the stock split aﬀects the market price of each individual share of stock and not the company’s value. For example, a company may have 1,000 outstanding shares priced at $1,000 each; in a 2-for-1 split, the company now has 2,000 outstanding shares priced at $500 each. Both before and after, the company’s market capitalization is $1,000,000. Some ﬁrms may perform a stock split to make their shares more aﬀordable for smaller investors, as Apple did in 2014 by performing a 7-1 split in 2014 once their shares hit $645. Theory shows that in some cases, this may slightly increase market capitalization after a split as demand for the stock rises due to a large number of small investors buying the stock. The most common splits are 3-for-2, 2-for-1, 5-for-4, 3-for-1, and sometimes 1-for-10. Dividend If the price of a stock is adjusted for a dividend, this will aﬀect the index divisor as well as the index on the day of the adjustment only. The eﬀect is that the index divisor will be lower than 50 for the price average, and immediately after such an adjustment, the divisor will go back to 50, provided there are no other corporate actions. Bonus Issues If the price of a stock is adjusted for a bonus, it will also aﬀect the index divisor as well as the index on the day of adjustment only. The eﬀect on the divisor is the same as that of the dividend adjustment described above. Right Issues If a company declares a rights issue oﬀer, its stock will be subject to a technical suspension during the period the oﬀer is available for the existing shareholders to claim. Therefore, the oﬀered price will be lower than the market determined price. However, right issues will increase the company value, unlike dividend and bonus actions. The eﬀect is diﬀerent from above in that index divisor will be lower than 50 (for the price average for instance) for only the periods the right issues are oﬀered and immediately after the period, the divisor will go back to 50, provided also that there are no other companies taking corporate actions. Note that the adjustment to a divisor will only be done once and is sustained for the entire period of suspension. 66 7. INDEX METHODOLOGY 7.3.5 STOCK SPLITS ADJUSTMENT BAROMETER Ai (cid:2) .i j / ; C i (7.5) where Ai is the volume of issued shares, i is the proportion of share units, and j is the proportion of shares added. 7.3.6 FREE-FLOAT Free-ﬂoat of a company is the proportion of shares held by investors who are likely to be willing to trade. It thus excludes shares held by strategic shareholders. Free-ﬂoat Adjustment The following shareholdings are viewed as strategic in nature and are excluded from index cal- culations. 1. Strategic Holdings: Shares held by strategic shareholding(s) that individually or collec- tively control more than 30% of the shareholdings. 2. Directors’ Holdings: Shares held by director(s) who individually control more than 5% of the shareholdings. 3. Cross-Holdings: Shares held by a Nigerian—listed company which controls more than 5% of the Shareholdings as investments. 4. Lock-Up Shares: Shares held by shareholder(s) who individually or collectivity represent more than 5% of the shareholdings in the company with a publicly disclosed lockup ar- rangement. 5. The free ﬂoat adjustment is built on the proportion (two-thirds) of the existing constituent. Free-ﬂoat Adjustment Formula FAF1 D 100% 2 3 (cid:0) .100% (cid:0) FAF2/ ; (7.6) where FAF1 is the free-ﬂoat of the new constituent stock and FAF2 is the free-ﬂoat of the existing constituent stock. 7.3.7 CALCULATION OF braINDEX The braIndex is calculated on a daily basis with mathematical expression: Current Index P .Pt P .Pt (cid:0) D IS/ (cid:2) IS/ (cid:2) (cid:2) 1 (cid:2) FAF FAF (cid:2) Yesterday’s Closing Index; (7.7) 7.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 67 1/, IS is the issued, where Pt is the current price at day t, Pt and FAF is the free-ﬂoat-adjusted factor; its value falls between 0 and 1, and adjusted every six months. 1 is the closing price at day .t (cid:0) (cid:0) 7.3.8 ILLUSTRATIVE EXAMPLE Base Day Consider seven constituent stocks with the following number of issued shares and closing prices. These stocks are grouped in two sectors. Table 7.3 shows the information about the stocks. Table 7.3: Information about the stocks SectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.20512,400B27,50018.50508,750C14,0009.30130,200D18,00011.40205,2001,356,550IIE10,0008.8088,000F6,00010.2561,500G13,5009.75131,625281,125Total1,637,67568 7. INDEX METHODOLOGY Table 7.4: Day 1 Day 1: Only the prices of shares changedSectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.25514,500B27,50019.15526,625C14,0009.50133,000D18,00011.80212,4001,386,525IIE10,0009.1091,000F6,00010.2561,500G13,5009.72131,220283,720Total1,670,245Index ComputationSectorAggregate Market Capitalization(NGN)Base Day’s IndexDay 1 IndexDay 1Base DayI1,386,5251,356,550100102.21II283,720281,125100100.92Index1,670,2451,637,675100101.997.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 69 Table 7.5: Day 2 Day 2: Stock C traded ex-bonus at the ratio of “1 for 4”SectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.25514,500B27,50019.15526,625C17,5008.00140,000D18,00011.80212,4001,393,525IIE10,0009.1091,000F6,00010.3061,800G13,5009.90133,650286,450Total1,679,975Index computationSectorAggregate Market Capitalization(NGN)Day 1 IndexDay 2 IndexDay 2Day 1I1,393,5251,386,525102.21102.73II286,450283,720100.92101.89Index1,679,9751,670,245101.99102.5870 7. INDEX METHODOLOGY Table 7.6: Day 3 Day 3: Stock E traded ex-right issue at the ratio of “1 for 2” at NGN 5 per shareSectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.25514,500B27,50019.20528,000C17,5008.30145,250D18,00011.60208,8001,396,550IIE15,0008.50127,500F6,00010.3562,100G13,5009.92133,920323,520Total1,720,070Index ComputationSectorAggregate Market Capitalization(NGN)Day 2 IndexDay 3 IndexDay 3Day 2I1,396,5501,393,525102.73102.95II323,520311,450101.89105.84Index1,720,0701,704,975102.58103.497.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 71 Table 7.7: Day 4 Day 4: Replacement of stock F by stock H, supposing stock H is sellling at NGN 10.5 with 7,500 number of issuedSectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.2512,400B27,50019522,500C17,5008.5148,750D18,00011.65209,7001,393,350IIE15,0008.1121,500H7,50010.578,750G13,5009.92133,920334,170Total1,727,520Index ComputationSectorAggregate Market Capitalization(NGN)Day 3 IndexDay 4 IndexDay 4Day 3I1,393,3501,396,550102.95102.71II334,170340,170105.84103.98Index1,727,5201,720,070103.49103.9472 7. INDEX METHODOLOGY Table 7.8: Day 5 Day 5: Suspension of stock B, requires stock B to trade at the last traded priceSectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.35518,700B27,50019522,500C17,5008.55149,625D18,00011.5207,0001,397,825IIE15,0008.15122,250H7,50010.5378,975G13,5009.88133,380334,605Total1,732,430Index ComputationSectorAggregate Market Capitalization(NGN)Day 4 IndexDay 5 IndexDay 5Day 4I1,397,8251,393,350102.71103.04II334,605334,170103.98104.11Index1,732,4301,727,520103.94104.237.3. braINDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 73 Table 7.9: Day 6 Day 6: Resumption of stock BSectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00012.3516,600B27,50018.55510,125C17,5008.7152,250D18,00011.5207,0001,385,975IIE15,0008.19122,850H7,50010.6579,875G13,5009.9133,650336,375Total1,722,350Index ComputationSectorAggregate Market Capitalization(NGN)Day 5 IndexDay 6 IndexDay 6Day 5I1,385,9751,397,825103.04102.17II336,375334,605104.11104.66Index1,722,3501,732,430104.23103.6374 7. INDEX METHODOLOGY Table 7.10: Day 7 Day 7: Dividend on stock ASectorStock NameIssued SharesClosing PriceMarketCapitalization (NGN)Aggregate MarketCapitalization(NGN)IA42,00011.90499,800B27,50018.55510,125C17,5008.70152,250D18,00011.50207,0001,369,175IIE15,0008.19122,850H7,50010.6579,875G13,5009.90133,650336,375Total1,705,550Index ComputationSectorAggregate Market Capitalization(NGN)Day 6 IndexDay 7 IndexDay 7Day 6I1,369,1751,385,975102.17100.93II336,375336,375104.66104.66Index1,705,5501,722,350103.63102.627.4. bra PRODUCER PRICE INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 75 7.3.9 MEASURE OF braINDEX VOLATILITY The bra50Index volatility is calculated on a 30, 60, 90, 180, and 365 days basis with the following mathematical expression: Index Volatility where (cid:22) x (cid:3) D P .x/, P .x/ xi xj D , and x D 7.3.10 INDEX MAINTENANCE D xi D q.x (cid:22)/2 (cid:3) (cid:0) P .x/; (7.8) daily index value. Periodic Rotation: This is required to remove ﬁrms with declining fundamental and technical proﬁles, and replace their shares with those of companies with a rising proﬁle. The periodic review/rotation shall be done every six months to eﬀect change in any of our constituent stocks. Situations that could result in such rotation include a consistent fall in share prices of a stock, delisting of a stock, ﬁrm bankruptcy, and suspension of a stock on the exchange, among others. The automatic detection and rotation of such stock requires daily monitoring of component stocks for these eﬀects. In other words, the database and front-end is designed to capture these eﬀects. In conclusion, the bra team continues to work consistently at evaluating various actions that might aﬀect the indices trend. We are positioned to ensure they are captured in order to maintain the integrity of the index at all times. 7.4 bra PRODUCER PRICE INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS bra Producer Price Index (braPPI) is one of the core short-term business indicators used to measure the economic situation of the country. It is the instrument used to measure the average change in prices of industrial products, which are produced and sold by Nigerian enterprises. This is performed by continuously sampling the prices of groups of items produced and sold on the domestic market. This sample is simply the representation of total industrial production. The braPPI measures price changes from the producer’s perspective, while the braCPI (bra Inﬂation Index) measures price changes from the consumer’s perspective. 7.4.1 USES OF braPPI The main uses of the braPPI are: 1. to serve as a leading indicator of inﬂationary trends in the Nigerian business environment; 2. to serve as deﬂator of national accounting at constant prices; 3. to serve as “escalators” to adjust prices of inputs in long term sales contracts; and 4. as an analytical tool for business owners and researchers. 76 7. INDEX METHODOLOGY 7.4.2 COMPONENTS OF braPPI The indices are calculated for each of these groups: 1. All commodities 2. Fuel 3. Stages of processing 4. Durable and non-durable categories In order to achieve transparency in the report, the durable and non-durable category is sub-divided into 15 sub-groups (aggregates): 1. Farm Products 2. Processed Foods and Feeds 3. Textile Products and Apparel 4. Hides, Skin, Leather, and related Products 5. Fuels, related Products, and Power 6. Chemicals and Allied Products 7. Rubber and Plastic Products 8. Lumber and Wood products 9. Pulp, Paper, and Allied Products 10. Metal and Metal Products 11. Machinery and Equipment 12. Furniture and Household durables 13. Non-metallic Mineral Products 14. Transportation Equipment 15. Miscellaneous Products 7.4.3 SCOPE AND COVERAGE braPPI survey covers many industrial sectors such as manufacturing, mining and quarrying, oil and gas extraction, and gas and steam supply. 7.4. bra PRODUCER PRICE INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 77 7.4.4 COLLECTION OF DATA Data are collected monthly from the companies in each sector using probabilistic sampling tech- niques called stratiﬁed sampling. The questionnaires are designed to capture product character- istics such as: the name of product(s), brand names, product speciﬁcations, units of measure, production cost per product, and producer’s price of selected product(s). There are many methods used when collecting data, varying from one establishment to another. These include: personal visits to the outlet, telephoning, e-mailing, and questionnaires, among others. 7.4.5 INDEX CALCULATION braPPI indices are base weighted (Laspeyres) according to the sales in the base year. After col- lecting price data from the enterprises, elementary indices (price relatives) are calculated for each speciﬁcation (price relative-speciﬁcation price in the current month divided by the weighted with sales structure in the base year). The weight reference period is updated periodically (two years) for adjustment. At the ﬁrst stage of elementary aggregation, individual prices are combined and each price is weighted by the value of production which it represents. In a case where one price from each enterprise is combined to give an elementary aggregate for product P, then the weight would correspond to the share of enterprise production of a particular product P in the entire economy. However, where more than one price for a product is collected from a single enterprise then the price would be weighted using relative production values for the diﬀerent transaction speciﬁcations. Industry indices are obtained by weighting together the product indices relevant for each industry using the values of output of the diﬀerent products for that industry, and not enterprises in the sample alone. As mentioned earlier, the index is calculated according to the Laspeyres’ formula, which is the weighted average of prices, as follows: It D n X 1 i D Wi 0 (cid:19) (cid:18) Pit Pio (cid:2) 100; (7.9) where It is the price index in the current period; Pt is the current price of the product i; and P0 is the price of product i in the reference period and Wio is the weight associated with product i. 7.4.6 ILLUSTRATIVE EXAMPLE Table 7.11 shows the producer’s prices for ﬁve commodities with their associated weights. Q: What is the producer price index for the commodities in 2017 using 2016 as the base year? Solution See Table 7.12. It D n X 1 i D Wi0 (cid:19) (cid:18) Pit Pio (cid:2) 100 D 103:47: 78 7. INDEX METHODOLOGY Table 7.11: Producer’s prices for ﬁve commodities Table 7.12: Price index for 2017 commodities using 2016 as the base year 7.5 bra BOND INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS The FGN Bond Index is a market value-weighted index designed to measure the performance of the Nigerian Investment-grade ﬁxed income market. It is a powerful tool used by investors and ﬁnancial managers to describe the market, and to compare the return on investments. The index is divided into sub-indices based on a variety of maturity classiﬁcations. The index, sub-index returns, and other statistics are calculated at the end of the business day. The constituent bonds undergo a review and rebalancing on a monthly basis. 7.5.1 DEFINITION OF TERMS Announcement date: The date on which changes to the index are published. Blended price: The price calculated from the individual bid prices that bra Limited receives from price providers for Index Bonds as of the close of each business day. For Index Bonds CommodityWo20162017PoPtCommodity A0.3502,5002,500Commodity B0.2857,6207,800Commodity C0.1005,1805,100Commodity D0.2504,5005,000Commodity E0.0153,0003,350Total1.00022,80023,750CommodityWo20162017Wi0 Pit PioPoPtCommodity A0.3502,5002,5000.3500Commodity B0.2857,6207,8000.2917Commodity C0.1005,1805,1000.0985Commodity D0.2504,5005,0000.2778Commodity E0.0153,0003,3500.0168Total1.00022,80023,7501.03477.5. bra BOND INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 79 where three or fewer price providers have submitted pricing information, the blended price is the arithmetic average of the individual bid prices after removing outliers. Business day: Any day that Nigerian bonds are traded, as determined by the Central Bank of Nigeria. Close: The end of a calendar or Business Day for the purpose of calculating Index values and other statistics, currently 04:00PM. Eligible bond: A bond that meets all of the eligibility criteria, based on publicly available information as of the close of the Business Day preceding the Announcement Date, but is not currently an Index Bond. Index bond: A bond that is included in the Index. Par amount: The total par or “face value” amount outstanding of an Index Bond or an Eli- gible Bond as determined by the Index Committee, net of strips, reconstitutions, re-openings, and sinking fund payments. Holdings of the Central Bank of Nigeria are included in the Par Amount. 7.5.2 BASIC CRITERIA FOR CONSTITUENT BONDS A constituent bond must possess the following criteria in the area of: insurance, bond type, coupon frequency, par-amount, and minimum term. (a) Issuance – The constituent bond must be delivered in the domestic market on or before the next rebalancing date. – It must be denominated in local currency (Nigerian-Naira). – It must be intended to be traded by institutional investors. – It must be issued by the Federal Government of Nigeria. (b) Type of bond: The bond must be one of the following types: bullet bond, callable bond, asset-backed security, capital bond, sinking fund bond, extendible bond, ﬁxed-ﬂoater bond, or retractable bond. (c) Coupon frequency: The frequency of coupon payments must be semi-annual. (d) Par amount: The bond must have a minimum par of N 100 Million for inclusion in the constituent bond and a minimum of N 50 Million as of the rebalancing date. (e) Minimum term: The bond must have at least 18 months term-to-maturity as of the next rebalancing date. 80 7. INDEX METHODOLOGY 7.5.3 INDEX CALCULATION A market value is calculated for each Index Bond as of the close on each business day. The market value of an Index Bond on day t is calculated as follows: Vt D Part (cid:18) Pt At C 100 (cid:19) ; where Vt is the market value at day t, Pt is the average price of a bond, At is the accrued interest of index bond at day t, Part is the face value as of the last monthly rebalancing, adjusted for principal repayments and mandatory sinking fund payments up to and including day t. The relative weight of a bond: weightk D Vk Pk Vk : The total return of a bond: Vt It C TRt D Vt 1 (cid:0) ; C C Vt Prt 1 (cid:0) where TRt is the total return, It is the interest payments on day t, Prt is the principal repayments on day t, Vt 1, and Vt is the market value on day t. 1 is the market value on day t In addition, total return is the addition of interest return and price return. The interest (cid:0) (cid:0) returns can be represented mathematically as: Part At 100 (cid:0) (cid:2) IRt D 1 (cid:0) (cid:2) At It 1 C (cid:0) 100 : Part Vt 1 (cid:0) However, the price returns is calculated as: Part (cid:2) PRt D .P t 1/ Pt (cid:0) 100 (cid:0) .100 Pt (cid:0) 100 1/ (cid:0) ; Prt (cid:2) 1 Vt C (cid:0) (7.10) (7.11) where IRt is the interest return on day t, Part is the par amount of bond, At is the accrued interest to the index bond at day t, It is the interest payment on day t, and Part is the face value as of the last monthly rebalancing, adjusted for principal repayments and mandatory sinking fund payments up to and including day t. The unrealized capital gain or loss due to any change in the price: Part .P t 1/ Pt (cid:0) 100 (cid:0) : (7.12) (cid:2) Vt 1 (cid:0) The realized capital gain or loss due to receiving a principal repayment at par rather than at the current price is computed as: Prt (cid:2) .100 Pt (cid:0) 100 1/ (cid:0) Vt 1 (cid:0) (7.13) 7.5. bra BOND INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 81 Part .P t 1/ Pt (cid:0) 100 (cid:0) : (7.14) (cid:2) Vt 1 (cid:0) 7.5.4 SUB-INDICES The three sub-indices are index of the total returns (ITR), index of the interest returns (IIR), and the index of the price returns (IPR). These indices can be computed as follows: ITR D IIR D IPR D TRi t Pi V i t 1 (cid:2) (cid:0) Pi V i 1 t (cid:0) IRi t Pi V i t 1 (cid:2) (cid:0) Pi V i 1 t (cid:0) Pi V i t 1 (cid:2) (cid:0) Pi V i t (cid:0) PRi t ; 1 (7.15) (7.16) (7.17) where TRt is the total return, IRt is the interest return on day t, PRt is the price return on day t, and Vt 1 is the market value on day t 1. (cid:0) Thus, the daily indices value can be computed as follows: (cid:0) ITRt ITRt 1.1 (cid:0) C D TRt / IIRt IIRt 1.1 (cid:0) C D PRt / IPRt IPRt 1.1 (cid:0) C D IRt /: (7.18) (7.19) (7.20) 7.5.5 ILLUSTRATIVE EXAMPLE Consider ﬁve bonds issued by the Nigerian Federal Government. Tables 7.13–7.15 show the transactions made on the two consecutive trading days. From the daily quoted prices, the yields, accrued interests, and market values were calculated. 82 7. INDEX METHODOLOGY ) 8 1 0 2 - n a J - 2 0 ( y a D e s a B : 1 y a D : 3 1 . 7 e l b a T Day 1: Base Day (02-Jan-2018)Issue DateBond NameTenor (yr)Coupon (%)MaturityPar Issue (N’bn)Bid PriceYield (%)Accrued InterestTTM (Yr)Market Value4/12/17Bond A313.79%4/12/2035100.8013.35%10.102.2838,814,236,187.857/27/16Bond B57.95%7/27/2136101.287.53%11.393.5740,562,105,482.563/30/17Bond C710.75%3/30/2415103.2210.04%8.176.2416,707,819,289.325/25/17Bond D1012.25%5/25/272597.9012.63%7.399.4026,322,486,413.046/29/17Bond E2015.00%6/29/372095.4315.76%7.6619.5020,618,786,885.25Total143,025,434,258.017.5. bra BOND INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 83 ) 8 1 0 2 - n a J - 3 0 ( : 2 y a D : 4 1 . 7 e l b a T Day 2: (03-Jan-2018)Issue DateBond NameTenor (yr)Coupon(%)MaturityPar Issue (N’bn)Bid PriceYield (%)Accrued InterestTTM (Yr)4/12/17Bond A313.79%4/12/2035100.8913.30%10.135922.2738,859,072,928.187/27/16Bond B57.95%7/27/2136101.507.46%11.414123.5640,649,082,656.473/30/17Bond C710.75%3/30/2415104.109.85%8.1948346.2416,844,225,027.025/25/17Bond D1012.25%5/25/272598.2512.57%7.4232349.3926,418,308,423.916/29/17Bond E2015.00%6/29/372095.8715.68%7.70491819.5020,714,983,606.56Total143,485,672,642.14(2)Market Value84 7. INDEX METHODOLOGY s n r u t e R : 2 y a D : 5 1 . 7 e l b a T Day 2: ReturnsClassBond Name(3) Interest Return(4) Price Return(5) Total Return(1)(3)(1)(4)(1)(5)Between 1 and 3Bond A0.0003440.0008120.00115513,336,74031,500,00044,836,740.46Between 3 and 5Bond B0.0001920.0019530.0021447,777,17479,200,00086,977,173.995 years and aboveBond C0.0002640.007900.0081644,405,738132,000,000136,405,737.8Bond D0.0003160.0033240.003648,322,01187,500,00095,822,011Bond E0.0003980.0042680.0046658,196,72188,000,00096,196,721.47All Constituent bonds42,038,385418,200,000460,238,384.707.6. braINFLATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 85 For term-to-maturity between 1 and 3 (Bond A), the interest return is calculated as: 35;000;000;000 (cid:2) IRt D 10:13592 35;000;000;000 100 (cid:0) 38;814;236;187:85 10:10 13:30% C 100 (cid:2) 0:000344: D We assumed that there is no principal repayment on Bond A, thus the formula for price return reduced to: PRt D 35;000;000;000 (cid:0) 100 (cid:2) 38;814;236;187:85 .100:89 100:80/ 0:000812 D Furthermore, we can compute the sub-indices as follows: TRt IRt D C PRt D 0:001155: IIR IPR ITR 42038385 D 143;025;434;258:01 D 0:000294 418200000 D 143;025;434;258:01 D 0:002924 460238384:70 D 143;025;434;258:01 D 0:003218: Thus, the daily index values are computed as follows: IIRt 1000 .1 (cid:3) C D 0:00294/ D 1003:22 IPRt 1000 .1 (cid:3) C D 0:002924/ ITRt 1000 .1 (cid:3) C D 0:003218/ 1002:94 1002:92: D D 7.6 braINFLATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS The bra Inﬂation Index (braII) is an independent index that measures the change in the price level of a market basket of consumer goods and services purchased by households in Nigeria. Researchers visit designated markets to collect the prices of goods and services, after which the indices are computed monthly. These indices include the overall index and sub-indices. The percentage change in the consumer price index is used to measure inﬂation. 86 7. INDEX METHODOLOGY 7.6.1 USES OF bra INFLATION INDEX The major uses of the braII are: (i) to measure changes in the purchasing power of money; (ii) to measure price inﬂation witnessed by Nigerians; (iii) to measure changes in living standards; and (iv) to serve as one of the major macro-economic indicators. 7.6.2 CLASSIFICATION OF braII ITEMS The braII is classiﬁed into three constituent items: category items, aggregate items, and ele- mentary items. The following are the 11 category items in braII: (i) alcoholic beverages and tobacco, (ii) clothing and footwear, (iii) communication, (iv) education, (v) energy, (vi) food and non-alcoholic beverages, (vii) housing and household goods and services, (viii) medical and household chemicals products services, (ix) recreation, (x) transportation, and (xi) utilities, other goods, and services. The aggregates items are the aggregation of elementary items unit. The table that shows the category items, aggregate items, and elementary items is found in the Appendix A. The survey identiﬁes all the local governments in each senatorial district, with special attention paid to land mass and population size. Local Governments with the lowest population density were considered as rural and the most densely populated areas were considered urban, while those in between were classiﬁed as rural-urban. More explicitly, based on population density, three local government areas are enumerated from the three senatorial districts considered per state, such that the three local government areas with the highest, medium, and lowest population density are considered. Hence, nine local government areas are considered in total per state, with the exception of Abuja, where all six local government areas in the senatorial district are considered. Thus, in each senatorial district, the survey considers three segregation classes, categorized in descending order from least to most densely populated: • Rural • Rural-urban • Urban As detailed above, the braCPI surveys markets from each local government area with emphasis on one rural and one urban market. Urban markets are markets where transactions take place every day with no speciﬁc market day, while Rural markets are markets that have speciﬁc market days. 7.6. braINFLATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 87 Based on this, nine local government areas are enumerated in each of our representative states (Adamawa, Anambra, Kano, Oyo, Plateau, Rivers, and Lagos) besides Abuja (FCT), where all the six local government areas in the territory are covered. Notably, all the local gov- ernment areas surveyed in each state are spread across the senatorial districts in the state, with two markets sampled in each of the local government areas. The market survey considers 138 markets in total from the above listed states (FCT inclusive). Eighteen markets are considered from each state, with the exception of Abuja, where 12 markets are considered from 6 local governments. 7.6.3 PERIOD OF THE SURVEY The market surveys are conducted between the 2nd and 3rd week of every month. 23 of our staﬀ (CPI ﬁeld enumerators) visit designated markets in the targeted states to obtain information on the recent prices of the items used to track and measure price changes. The ﬁeld enumerators record the prices of over 500 items each month, representing a scientiﬁcally selected sample of the prices paid by consumers for goods. Detailed descriptions of the items survey are provided in the Appendix A.2. 7.6.4 DATA COLLECTION, COLLATION, AND PROCESSING Our data collection units across the nation are staﬀed with three enumerators and one manager per state (one ﬁeld staﬀ person in each senatorial district with an overall manager for the entire state), except for Abuja, which has two enumerators and a manager. During each visit, the ﬁeld enumerator collects price data on a speciﬁc good or service that was precisely deﬁned in our price data sheet. We have employed a somewhat unorthodox methodology in obtaining our prices, such as by purchasing phone credit, maintaining a periodical presence, presenting of our branded shirt, etc. This allowed us to create a relationship with people in each market. The recorded information is sent to the bra server in Lagos through an online data entry and analytics engine (Opera) built for the purpose of collection and analysis of data from the enumerated states. Surveyed prices are controlled by regional managers, who verify the accuracy of the survey prices compared to the last month’s prices and state whether or not the speciﬁc variance selected by the ﬁeld survey enumerator corresponds with the representative characteristics. In case of doubt, the ﬁeld enumerators are contacted to verify prices. In addition, commodity specialists check the data for accuracy and consistency at the bra limited Lagos oﬃce and make any nec- essary corrections or adjustments, which can range from adjustment for a change in the size or quantity of a packaged item to more complex adjustments based upon statistical analysis of the value of an item’s features or quality. Thus, commodity specialists strive to prevent changes in the quality of items from aﬀecting the CPI’s measurement of price change. Processing collected commodity prices involves the following. 88 7. INDEX METHODOLOGY (a) Calculation of the average prices of commodities from diﬀerent locations. More explicitly, the average price of the representative commodity is calculated as a weighted arithmetic mean of prices for locations calculated by simple arithmetic mean. (b) Using the average price to get the index baseline for each commodity. (c) Comparing the current year price of each commodity with a base year price to obtain a relative price. (d) Generating a constant weight from the consumer expenditure survey in the base year. (e) Using Laspeyres formula to calculate an aggregated index for each category. In compliance with the National Bureau of Statistics methodology, the Laspeyres’ formula of constant weights is used for the calculation of the bra inﬂation index, using the prices from November 2009 as the base year prices. 7.6.5 QUALITY ADJUSTMENT The quality adjustment of the price index is performed when a product which is part of the price survey is replaced by another product. The change is due to the absence of the original product in the market or decreased demand for the product. When this occurs, the product representative in the consumer basket is replaced by a similar product or a product in great demand. More frequently, product substitution takes place when the product surveyed ceases to be sold in the market, most likely due to the producer facing liquidation. After ﬁeld staﬀ advise that a product’s disappearance from a market is permanent, the bra oﬃce selects another similar product, complying with the description or survey prices in the market. Steps to perform the adjustment may include the following. (a) Direct adjustment This is often used when dealing with two comparable products. The new item is considered directly comparable, if the following is true. 1. It is produced by the same manufacturer. 2. It is produced from the same materials and has the same or similar technical param- eters which are important for customers (utility value). 3. It has the same measurement unit. 4. It has the same type of packaging. 5. The diﬀerence between the original and the new items are not signiﬁcant and may re- fer to customer taste and personal preferences, such as color, design, shape, decorative elements, etc. 7.6. braINFLATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 89 (b) Overlap imputation method When dealing with two incomparable products or samples, the overlap imputation method is used where the price of both the original (old) and new products are surveyed. In the overlap month, the prices of both products are surveyed. Price development in the ﬁrst month is measured based on the original product, while next month’s price is performed with the new product using its price surveyed in the previous overlap month. The price diﬀerence of the original and new products will not feed into the price index. 7.6.6 INDEX CALCULATION The bra Inﬂation Index is built in two stages. In the ﬁrst stage, prices for over 200 speciﬁc items are averaged to yield a price for the elementary items in the basket. The index for each aggregate item is calculated based on these average prices. This stage is often referred to as “lower-level aggregation” as it involves averaging the most fundamental component of the index—observed price change for speciﬁcally deﬁned consumer goods, services, and products. For example, the prices of approximately ﬁve diﬀerent brands of milk at designated markets in enumerated states are observed every month. Milk is one of the 217 elementary items in the current bra Inﬂation Index market basket structure and is categorized as a canned/packaged foods and other groceries aggregate item (full description of groceries and other groceries). The canned/packaged foods and other groceries index is one of the 10 basic indices of the food and beverages category. Three versions of the bra Inﬂation Index formula are used for the lower-level aggregation in the food basket. Each formula has both strong and weak points, and computations are per- formed with caution. The ﬁxed basket Laspeyres’ method is adopted, and the other two formulae are stated as follows: (i) Laspeyres Index: (ii) Paasche Index: (iii) Fisher Ideal Index: L D n X 1 i D Wi 0 (cid:21) (cid:20) Pit P0t (cid:2) 100 P D n X 1 i D Wit (cid:21) (cid:20) Pit Pio (cid:2) 100 F D pL P ; (cid:2) (7.21) (7.22) (7.23) n where Wi0 is the weight of items at reference period .P i price of items at current and previous periods. D 1 Wi0 D 1/ , and Pit and P0t are the 90 7. INDEX METHODOLOGY 7.6.7 bra INFLATION INDICES PUBLICATION bra limited publishes diﬀerent Consumer Price Inﬂation (CPI) series on a monthly basis. The published series include the following. Composite Inﬂation (Headline Inﬂation) The composite rate of inﬂation consists of changes in the consumer price index including the inﬂuence of changes in the price of food and energy. The mathematical representation of Com- posite Inﬂation is given as: where CPI t is the value of CPI for the current period and CPI t previous period. H D CPI t CPI t (cid:0) CPI t 1 (cid:0) 1 (cid:0) 100; (cid:2) (7.24) 1 is the value of CPI for the (cid:0) Core Inﬂation The core rate of inﬂation consists of changes in the consumer price index without the inﬂuence of changes in the prices of food and energy. The core inﬂation index is made up of the following categories: alcoholic beverages and tobacco, clothing and footwear, health, recreation and cul- ture, education, communication, furnishing household equipment and maintenance, restaurant and hotel, and miscellaneous goods and services: C D cCPI t cCPI t (cid:0) cCPI t 1 (cid:0) 1 (cid:0) 100; (cid:2) where cCPI t is the value of core CPI for the current period and cCPI t for the previous period. (7.25) 1 is the value of core CPI (cid:0) Non-core Inﬂation The non-core inﬂation rate consists of components such as changes in the prices of food and energy. The non-core inﬂation is made up of the following categories: food and non-alcoholic beverages, housing water, electricity, gas and other fuels, and transportation. It is mathematically expressed as: where nCPI t is the value of non-core CPI for the current period and nCPI t non-core CPI for the previous period. N D nCPI t nCPI t (cid:0) nCPI t 1 (cid:0) 1 (cid:0) 100 (cid:2) (7.26) 1 is the value of (cid:0) Food Inﬂation Food inﬂation explains the changes in the consumer price index considering only food items, excluding the inﬂuence of changes in the price of other items. F D fCPI t fCPI t (cid:0) fCPI t 1 (cid:0) 1 (cid:0) (cid:2) 100; (7.27) 7.6. braINFLATION INDEX: PRINCIPLES, TECHNIQUES, AND APPLICATIONS 91 where fCPI t is the value of food CPI for the current period and fCPI t for the previous period. (cid:0) 1 is the value of food CPI The construction of the bra Inﬂation Index begins by selecting a group of goods and ser- vices that are usually bought by the reference population in the index. This collection of goods and services is known as the market basket. The bra inﬂation market basket is developed from detailed expenditure information provided by the households who participate in the Consumer Expenditure Survey (CES). Altogether, 2,280 households provide expenditure information for use in determining the importance or weight of each item in the index structure. This data is also used to select the categories of items from which speciﬁc unique commodity and service items are selected to be priced for the bra Inﬂation Index. The Consumer Expenditure Survey (CES) provides essential inputs required to compile the CPI. The survey has been conducted on a monthly basis since the inception of the contract in order to obtain comprehensive (up-to-date) information about the expenditure patterns of households, and for updating the expenditure weights used in compiling the CPI. Two kinds of information are required for compiling the CPI. First, a “basket” of con- sumer goods and services commonly purchased by households and a weighting system reﬂecting the relative importance of individual items in the basket, in terms of their shares in the overall household expenditure, has to be established. Since consumers spend more on some items than on others, similar price movements in diﬀerent items may have diﬀerent impacts on the overall price change. Second, data on the price movements of various items of goods and services in the basket have to be collected continuously so that movements of market prices can be fully reﬂected in the price indices. However, as advised by the Central Bank, our expenditure pattern used to calculate the bra Inﬂation Index has been back-dated to November 2009, to follow the rebasing of the National Bureau of Statistics (NBS) to 2009. 7.6.8 EXPENDITURE CATEGORY WEIGHT Expenditure weights are used to give proportional emphasis for the price change of one item (or component) in relation to other items (or components) in the bra Inﬂation Index. These weights are derived from the CES. Such expenditure weights allow the bra Inﬂation Index to distinguish between items that are important to consumers and to provide the appropriate weighting for changes in that product’s price, based on its importance. Altogether, 660 households provide expenditure information for use in determining the importance, or weight, of each item in the index structure. Table 7.16 gives the category weight of bra Inﬂation Index. The weights of elementary items is shown in Appendix A.3. 92 7. INDEX METHODOLOGY Table 7.16: Category weight of bra Inﬂation Index 7.6.9 ILLUSTRATIVE EXAMPLE Table 7.17 shows the prices of ﬁve commodities and quantity demanded between 2016 and 2017. Calculate: (i) Lasperyre index, (ii) Paasche index, and (iii) Fisher’s ideal index. Table 7.17: Prices of ﬁve commodities Solution See the solution on Table 7.18. Let us generate our weight since it is not given in the question: (i) Laspeyres Index: Category ItemsWeightAlcoholic beverages and tobacco10.83Clothing and footwear53.39Communication45.56Education36.36Energy48.04Food and non-alcoholic beverages259.01Housing and household goods and services256.06Medical and household chemical products services16.47Recreation8.90Transportation260.92Utilities, other goods, and services4.46Total1,000Commodity20162017PoQoPtQtRice25072556Beans18041953Yams55035803Wheat20021802Plantains15051206Table 7.18: Indexes 7.7. EXERCISES 93 Wi0 D P0Q0 5 P i 1 P0Q0 D L D n X 1 i D Wi 0 (cid:21) (cid:20) Pit P0t (cid:2) 100 D 100:85 (ii) Paasche Index: Wit D P Pt Qt 5 i 1 Pt Qt D P D n X 1 i D Wit (cid:21) (cid:20) Pit Pio (cid:2) 100 D 99:88 (iii) Fisher Ideal Index: pL F D P (cid:2) D p100:85 99:88 (cid:2) D 100:36: 7.7 EXERCISES 7.1. a. What is an expectation index? b. What are the main functions of the expectation index? c. Describe two approaches of business expectation index computation. 7.2. a. What is a consumer conﬁdence index? Items20162017PoQoPtQtWoWi0 Pit P0tWtWit Pit P0tPoQoPtQtRice250725561,7501,5300.3320.33870.3100.3162Beans180419537205850.1370.14800.1190.1284Yams550358031,6501,7400.3130.33020.3530.3718Wheat200218024003600.0760.06830.0730.0657Plantains150513067507200.1420.12330.1460.1167Total1,330211.340205,2705,2651.0001.00851.0000.998894 7. INDEX METHODOLOGY b. What are the components of the bra consumer conﬁdence index? c. Table 7.19 shows the outcome of a business expectation survey polling 1,000 re- spondents. Calculate: (i) consumer conﬁdence index, (ii) present situation index, and (iii) business expectation index. Table 7.19: Outcome of a business expectation survey 7.3. a. What is the bra Inﬂation Index and what are its uses? b. What are the category items of the bra Inﬂation Index? c. Table 7.20 shows the prices and quantities demanded for six commodities and quantities between 2016 and 2017. Calculate: (i) Lasperyre index, (ii) Paasche in- dex, and (iii) Fisher’s ideal index. Table 7.20: Prices and quantities demanded for six commodities 7.4. a. State the basic, fundamental, and technical criteria for selection of constituent stocks. b. Using Table 7.21, ﬁnd the market capitalization for the Agriculture and Banking sectors. IndicatorsPositiveNegativeNeutralBusiness conditions (current month)770230-Business conditions (six months)65025010Employment status (current month)510135355Employment status (six months)9151075Sales status (current month)85411036Sales status (six months)76022020Firm income realize in the next six months80011585Commodity20162017PriceQuantityPriceQuantityA1,150121,23014B7552081515C4801547518D60086208E8501083012F33053208c. Compute the stock index, assuming the agriculture and banking indices were 102.23 and 105.50, respectively, at the close of the previous day. 7.7. EXERCISES 95 Table 7.21: Market capitalization 7.5. a. What is a producer price index? b. What are the uses of the bra producer price index? c. List the components of bra producer price index. 7.6. Refer to Table 7.22 and calculate the Lasperyre’s producer price index for the commodi- ties in 2017 using 2016 as the base year. Table 7.22: Lasperyre’s producer price index (assume all commodities have equal weights) 7.7. a. State the basic criteria for constituent bonds. b. Enumerate the diﬀerent types of bonds. c. Deﬁne the following terms: coupon, face value, and term-to-maturity. SectorStock NameNumber of SharesClose PriceAgricultureI15,0008.20II11,3005.50III8,7505.00BankingIV22,0007.25V20,2208.15VI19,5007.38VII10,6007.30Commodity20162017PoPtA7,5007,575B5,0005,000C3,7504,015D1,8001,900E2,6402,600F3,0003,050C H A P T E R 8 97 Digital Media Monitoring, Measurement, and Modeling This chapter introduces us to the concept of digital media and the distinction between digital media and social media. The chapter concentrates on how to monitor, measure, and model social media. It also covers how social media monitoring reports can be interpreted. The concept of digital and social media is often used interchangeably, but the two terms are diﬀerent in nature. Social media is a subset of digital media, thus all social media strategies are digital, but not all digital media can be categorized as social media. Digital media includes the following channels of communications: mobile messaging, email, website, apps, and social media, among others. However, social media are online communications channels and platforms for community-based input, interaction, content sharing and collaboration. Some notable social media platforms include Facebook, Twitter, Instagram, and LinkedIn. 8.1 UNDERSTANDINGS OF SOCIAL MEDIA MONITORING, MEASUREMENT, AND MODELING Social media monitoring is a process of using tools or software to track, gather, and analyze data from the online activities of social media users to assess consumer perceptions of companies’ brands. Social media monitoring tools include Online Analytics, Buzz Analytics, and Social Media Analytics, among others. To gain a deeper understanding of how consumers feel about a particular product, it can be worth monitoring what users have said about the product on diﬀerent social platforms, including via blogs, micro-blogs, forums, social networking services (LinkedIn, Facebook, etc.), video sharing sites (YouTube), and message/complaint sections of corporate social media pages or corporate websites. To minimize costs, employees can utilize free social media search engines to explore and monitor the feedback of consumers regarding particular products and services. However, free social media search engines have limited functionality and are not comprehensive enough to perform some speciﬁc tasks (e.g., automatic digital storage of clips). Companies with a serious ﬁnancial and reputational interest in monitoring the sentiments expressed by consumers through social media often subscribe to the apps speciﬁcally designed for social media monitoring with comprehensive coverage, features, and functions; some apps designed for this purpose include TweetDeck, CoTweet, and Twitscoop. These tools collate searches from numerous websites and 98 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING present the information gathered from searches through a user interface. This enables ﬁrms to learn the keywords that are trending online and understand consumer sentiments regarding their products, enabling the ﬁrm to take proactive action in identifying developing customer needs. 8.2 STRATEGIC INSIGHT OF SOCIAL MEDIA MONITORING The essence of monitoring social media is to keep ﬁrms apprised of online discussions concerning the products and services the ﬁrm oﬀers. The information gathered from online monitoring tools can aid managers in supporting corporate strategy and achieving the ﬁrm’s marketing goals and objectives. The data and information gathered from online activities can serve as a point of strategic action in the area of marketing, sales, publicity and customer relations. Social media monitoring helps to boost the company’s image and provides an avenue to sensitize potential customers toward other brands in the ﬁrm’s product mix. In marketing, social media monitoring is particularly helpful as it tells a company what is being said about its products. It can also reveal the general geographical location of the company’s primary consumers, allowing better demographic targeting so that the company can best position its products in the market, supported with the appropriate message to aﬀect the purchasing decisions of potential consumers. Also, marketing and sales departments can use the information obtained from the online conversations to correct wrong impressions about the company and its brands and to promote the company’s products. The company can establish its presence online by having a representative to engage in sales activities in online conversations, for example, by maintaining an oﬃcial Facebook or Twitter page through which the representative responds to the queries of social media users. It is particularly important that the company leverage these channels to provide customers with solutions when they encounter a problem with the company’s product or services. The support team monitors every comment about the company’s products to understand the major problems associated with the company’s brands. A company that fails to adequately manage dissatisfaction may be faced with negative social media campaigns, which could become viral and spread beyond the control of the company’s public relations team. 8.3 SOCIAL MEDIA MEASUREMENT While there are many approaches to measure the activities in social media, we will discuss ﬁve important measurements in this section. These measurements include: exposure, engagement, preference, impact, and advocacy. (a) Exposure This metric comprises of the following. (i) Gross Rating Points—this is a measure of the impressions an advertisement promo- tion can achieve. It is calculated as a product of percentage of audience reached, and 8.3. SOCIAL MEDIA MEASUREMENT 99 the number of advertisement impressions; mathematically represented as: GRPs Reach Frequency. (cid:2) D (ii) Target Rating Points (TRPs)—this is similar to GRPs, but instead of calculating a rating based on the population at large, the focus is narrowed to a target audience. (iii) Number of mentions or posts. (iv) Percentage increase in number of likes or follows. (v) Percentage increase in opportunity to view. (vi) Percentage increase in desirable items. (vii) Percentage decrease in undesirable items. (viii) Percentage decrease in cost per thousand impressions. (b) Engagement This involves tracking the number of users that interacted with an advert or item of content. Engagement creates a higher possibility of viewing, liking, sharing, and commenting upon content. Involvement in these activities is crucial in the social process that creates more awareness and popularity, leading to an increase in sales. Social media engagement metrics are: (i) Interaction rate. (ii) Percentage page per visit. (iii) Percentage increase in requests for information. (iv) Percentage increase in return visits and time spent on pages. (v) The time period spent viewing a webpage, posting, or video download. (c) Preference This measures the general inclination a customer has toward a product after visiting social media; this eventually may lead to purchase of the product. The followings are metrics relating to preference: (i) Number of purchase intent. (ii) Number of preference. (iii) Percentage increase in willingness to consider. (iv) Percentage increase in likelihood to recommend. (v) Preference for speciﬁc product. 100 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING (d) Impact This measures how successful a company’s social media/online campaigns have been in reaching an audience, and how eﬃcient the ﬁrm has been in converting interest into sales. Impact may eventually lead to increases in a ﬁrm’s revenue over time as the number of conversions increases. Impact can be measured via the following statistics: (i) Percentage of new visits to the contents. (ii) Number of new subscribers. (iii) Number of referral traﬃc to the content. (iv) Percentage increase in sales. (v) Percentage of coupon downloads. (vi) Percentage increase in coupon redeemed. (vii) Percentage decrease in cost of communication. (viii) Percentage change in issue sentiment. (e) Advocacy This is a measure of support or promotion. Advocacy can be used to measure how satisﬁed consumers were after the purchase of a product or service. When a company builds a strong online following through a successful product oﬀering, it can greatly beneﬁt from word- of-mouth marketing as users recommend products to people in their own social networks. The following metrics are categorized as advocacy measurement in social media: (i) Percentage increase in recommendations. (ii) Percentage increase in satisfactory ratings. (iii) Percentage increase in good reviews. (iv) Percentage increase in the fans/ambassador of brands. 8.4 SOCIAL MEDIA MODELING In this section, we will discuss social media modeling based on centrality analysis, community detection, inﬂuence modeling, and sentiment analysis. A. CENTRALITY ANALYSIS This is a measures how signiﬁcant a node is within a network. Commonly used criteria include degree centrality, eigenvector centrality, closeness centrality, and betweenness centrality. (a) Degree centrality 8.4. SOCIAL MEDIA MODELING 101 This classiﬁes the importance of a node based on the number of links held by each node to other nodes; the higher the number of links, the more important the particular node is likely to be. It is useful to determine the number of inbound links and outbound links. The degree centrality for node in an undirected graph is displayed in Figure 8.1 and it is calculated as: where c is the degree centrality and di is the degree of node ni . c .ni / di ; D Figure 8.1: Degree centrality. (b) Closeness centrality The closeness centrality measures how each one of the nodes close to other nodes. Any central node should have a shortest distance path to reach the remaining nodes. The node with higher closeness centrality value is more important. Closeness centrality is computed as the inverse average geodesic distance of one node to the others. It is mathematically represented as: Cclose .ui / 2 D 4 n 1 (cid:0) 1 n X i j ⁄ 1 3 (cid:0) d (cid:0)ui ; uj (cid:1) ; 5 (8.1) where n denotes the number of nodes and d (cid:0)ui ; uj (cid:1) denotes the geodesic distance be- tween nodes ui ; uj . 102 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING (c) Normalizing degree centrality This involves the process of normalizing by maximum possible degree. The simple nor- malization is calculated as: Cnorm .ni / di (cid:0) ; 1 D n (8.2) where n is the total number of nodes. The normalized by maximum degree is computed as: Cmax .ni / di maxkdk : D (8.3) (d) Eigenvector centrality Having a large number of friends does not guarantee the importance of a node; having a number of important and inﬂuential neighbors makes a node more important in a network. Therefore, eigenvector centrality integrates the importance of neighbors. Eigenvector cen- trality is deﬁned as: Ceig .ni / D 1 (cid:21) n X 1 k D Ak; i Ceig .nk/ ; (8.4) where Ceig nodes and ﬁxed constant, respectively. T (cid:0)Ceig .n1/ ; Ceig .n2/ ; : : : ; Ceig .nn/(cid:1) D Equation (8.3) can be written as: and (cid:21) are the centrality vectors for the D where Ceig stands for eigenvector of adjacency matrix AT and (cid:21) represents the correspond- ing eigenvalue. (cid:21)Ceig AT Ceig; (8.5) (e) Betweenness centrality Betweenness centrality measures the number of times a node serves as bridges between other nodes in a network. It is useful to identify individuals that inﬂuence others in de- cision making. However, this measurement could also be carefully used in the analysis of communication dynamics. A high number of betweenness shows an individual has inﬂu- ence or control over other members of the community. Illustrative Examples 1. Table 8.1 shows the geodesic distance between nodes. What node has the highest closeness centrality? Table 8.1: Pairwise geodesic distance 8.4. SOCIAL MEDIA MODELING 103 Solution Cclose .1/ D 1 1 C C Cclose .2/ D 1 1 C C Cclose .3/ D 1 1 C C Cclose .4/ D 1 2 C C Cclose .5/ D 2 2 C C Cclose .6/ D 2 3 C C 7 1 7 2 7 1 7 1 7 1 7 1 1 2 1 2 1 1 1 1 1 1 1 2 (cid:0) C (cid:0) C (cid:0) C (cid:0) C (cid:0) C (cid:0) C 2 C C 3 D 3 C C 3 D 1 C C 2 D 2 C C 3 D 1 C C 4 D 1 C C 2 D 0:60 0:50 0:86 0:60 0:55 0:55 0:35 Cclose .7/ D 3 3 4 2 D 1 3 7 2 (cid:0) C C Therefore, node 3 has the highest closeness centrality among the seven nodes. C C C 2. Consider Figure 8.2. Determine the most centralized node from the ﬁgure. Node123456710111223210122333110111241210123522110146231210273323420104 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING Figure 8.2: Centralized node. Solution The adjancency matrix 2 6 6 6 6 6 6 6 4 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 3 7 7 7 7 7 7 7 5 A D Then (cid:21)Ceig AT Ceig implies .A (cid:21)I /Ceig 0. D The eigenvalues are 2.94, the corresponding eigenvector of (cid:0) 2:24, 0.67, 0, (cid:0) (cid:0) D 1:37, and 0. The largest eigenvalue is 2.94, with Ceig D 2 6 6 6 6 6 6 6 4 0:30 0:44 0:44 0:48 0:52 0:18 3 7 7 7 7 7 7 7 5 : Therefore, node (e) is the most central. B. COMMUNITY DETECTION In the context of community detection, a community refers to a group or clusters. These are identiﬁable groups that consist of nodes that frequently interact with one another, vs. nodes that do not belong to the same group. The community shares their common interests on social media and most of their interactions center on problem-solving and promotion of content. In other words, a community consists of nodes with common boundaries and attributes. For instance, communities can be regarded as groups of friends attending the same university or friends in the same geographical vicinity. abdfec8.4. SOCIAL MEDIA MODELING 105 C. INFLUENCE MODELING This is used in information diﬀusion and spreading new ideas. In this model, there is an active node that can easily inﬂuence other nodes in making a decision. The two common inﬂuence models are the Linear Threshold Model (LTM) and Independent Cascade Model (ICM). Tang and Liu [2010] cited Granovetter (1978) in stating that an actor would take an action if the number of his friends who have already taken the action exceeds a certain threshold. LTM assumes that node thresholds are generated randomly from a uniform distribution U (cid:140)0; 1(cid:141) before the commencement of diﬀusion process. On the other hand, ICM emphasizes the sender’s view instead of receiver’s view. Let us consider a node (say v) activated at step s; this node has a chance to activate all other nearby nodes with probability p of a successful activation with another closest node u. Then, node u will be active at step s 1 if the activation is completed. See Figures 8.3 and 8.4. C D. SENTIMENT ANALYSIS Sentiment analysis is referred to as opinion mining. It is useful to summarize public opinion regarding certain products, services, or issues on social media. Sentiment analysis helps compa- nies to monitor the popularity of their products, gauge the perception of new products, measure the ﬁrm’s reputation, and support market analysis. Sentiment analysis can also be used to re- view customer feedback on products or services to understand the developing perception of a particular product or service. E. TOPIC AND RELATIONSHIP RECOGNITION Topic recognition is the process of analyzing written information (such as comments, forum discussions, etc.) to know whether the analyzed content can be categorized as a new or existing topic. This is done by mapping a given piece of text to one or more labels. Relationship recog- nition of topics is important when the texts to be analyzed are part of a current discussion, or serve as references between posts or discussions. 106 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING Figure 8.3: Linear threshold model diﬀusion process (green nodes are active, orange nodes are newly activated, and dark nodes are inactive). ABCDHIGFEABCDHIGFEInitial StageStage 1ABCDHIGFEStage 2ABCDHIGFEFinal Stage8.4. SOCIAL MEDIA MODELING 107 Figure 8.4: Independent cascade model diﬀusion process (green nodes are active, orange nodes are newly activated, and dark nodes are inactive and red nodes are not succeed in activation). ABCDHIGFEABCDHIGFEInitial StageStage 1ABCDHIGFEStage 2ABCDHIGFEStage 3108 8. DIGITAL MEDIA MONITORING, MEASUREMENT, AND MODELING 8.5 EXERCISES 8.1. a. What is digital media? b. What is social media monitoring, measurement, and modeling? 8.2. Using Figure 8.5, what is the most central node? Figure 8.5: Determine the central node. 8.3. a. What is community detection? b. Explain sentiment analysis. c. What is topic and relationship recognition? 8.4. The geodesic distance of ﬁve nodes is shown in Table 8.2. Find the highest closeness centrality. Table 8.2: Geodesic distance IIIIIIIVVNode12345101112210122311011412101522110C H A P T E R 9 Causal Methods 109 Causal methods are techniques used to identify the extent and nature of cause-and-eﬀect rela- tionships among variables of interest. Causal methods are used to analyze problems by showing the existing patterns of relationships among variables. The conﬁrmation of cause-and-eﬀect rela- tionships is based on the existence of causal evidence. The major components of causal evidence are brieﬂy explained below. In this case, the eﬀect follows the cause. To illustrate, it would be er- Temporal sequence: roneous to credit an advertising campaign for an increase in sales revenues if the rise in sales had occurred before the advertisement were published. Logically, there should be sales growth after an advertising campaign commences as a result of heightened awareness of a ﬁrm’s product oﬀerings. Concomitant variation: This is logical or systematic variation between two variables of inter- est. The practical example is that if a company does not conduct survey on products, the level of products acceptability would not be known. Non-spurious association: Establishing a true cause-and-eﬀect between two variables as- sumes that no interference arising from other variables exists. For example, a surge in consump- tion of a ﬁrm’s products may be due to macroeconomic or sector-wide eﬀects (variables) rather than the speciﬁc advertising and marketing eﬀorts of the company. 9.1 MARKETING MIX MODELING: CONCEPT, PRINCIPLES, METHODS, AND APPLICATIONS The Marketing Mix Model (MMM) measures the impact of sales on marketing activities. An MMM can help a ﬁrm maximize its future spend and its return on investment (ROI). The MMM measures all possible marketing inputs and detects marketing investments that would yield long-term revenue growth. These are the variables that marketing managers can control to inﬂuence the company’s sales. The term “mix” in the MMM refers to the combination of the classical “4Ps” of marketing—Product, Price, Place, and Promotion (see Figure 9.1). Product stands for the ﬁrm’s products and how they are diﬀerentiated from competing product oﬀerings (high quality, visual appearance, maintenance, and repair). Promotion stands for how the ﬁrm publicizes its products through advertisements, oﬀering coupons, privilege cards, sales displays, trade fairs, and other promotional eﬀorts. Price entails the pricing strate- 110 9. CAUSAL METHODS Figure 9.1: Marketing Mix—the 4Ps. gies relating to a company’s product mix depending on the life cycle of the product oﬀering, product features, perceived utility and competing products. Place stands for product delivery area quantiﬁed by variables such as distribution, availability and convenience. The evolution of the MMM came as a result of the attempt to ﬁnd answers for the many questions relating to the optimal allocation of the marketing budget. These questions are: At what level or combination of these marketing mix variables does the ﬁrm maximize one of the output variables (company’s sales, market share or proﬁt)? How did sales or market share respond to previous levels of or expenditures on these variables? Consequently, researchers provided an- swers to these persistent questions by developing econometric models of market responses to the marketing mix, bearing in mind how to manage available resources (the marketing mix vari- ables) to maximize output variables. The MMM makes use of past data or existing information to make valid conclusions and to develop a better marketing plan or strategy for the future (see Tellis [2011]). In recent times, establishing the most eﬃcient marketing mix has become more complex; in the presence of new marketing strategies and the complexity of computerized data, MMM often uses multiple regression models to forecast the optimal mix of marketing variables. The application of a regression model will help to understand how the independent variables (in- put variables such as advertisement, promotion) can explain the variation in dependent variable ProductWhat products to makeand sellTARGETMARKETPlaceWhere to sell yourprocuctPromotionAdvertising, personal selling, sales promotion,and publicityPriceHow much your productis going to cost9.1. MARKETING MIX MODELING: CONCEPT, PRINCIPLES, METHODS, AND APPLICATIONS 111 (sales). Having developed a regression model to show the relationship that exists among the variables of interest, this model can be used to predict for future values, say the company’s sales over a horizon. The model can also identify which of the independent variables’ coeﬃcients has the strongest eﬀect on consumer intentions to buy, so as best to focus its eﬀorts when tailoring its product mix. The various data that can be used to build the MMM are economic data (interest rate, inﬂation rate, etc.), industry data (pricing, competitive, services), market data (sales, rev- enues, proﬁts, ROI, etc.), and target audience data. Naturally, the robustness of the model relies on the accuracy of the data. The four main steps to take in order to create a robust marketing mix model are shown in Figure 9.2. Figure 9.2: Procedure for creating MMM. A typical simple regression model can be constructed in which the response (dependent) variable is a product’s sales and the independent variable is advertising. The model can be rep- resented mathematically as: Yt (cid:12)0 C D (cid:12)1Xt C "t ; (9.1) where Yt denotes the product’s sales at period t, Xt denotes advertising at period t, (cid:12)0 and (cid:12)1 are the regression coeﬃcients, and "t denotes error terms (assuming "t N.0; 1//. In this section, we will discuss the major types of regression model that can be used the (cid:24) modeling marketing mix. RECOMMENDATIONImplement recommendations basedon the modelsFORECAST OPTIMIZATIONCalculate optimal marketing spend allocation for markets and channels based on diﬀerent scenariosMODEL BUILDING- Explore the collected data - Build the MMM using collected datato identify the major driversDATA COLLECTION- Identify data sources- Collect historical data to builda database112 9. CAUSAL METHODS 1. Multiple Linear Regression This shows a linear relationship between two or more independent variables (price, dig- ital spends, newspaper and magazine spends, TV spends, etc.) and a response vari- able (sales/market share/proﬁt). A multiple linear regression model with k predictors .X1; X2; : : : ; Xk/ and a response can be written in the form: Yt (cid:12)0 C D (cid:12)1X1t C (cid:12)2X2t C : : : C (cid:12)kXkt "t ; C (9.2) where Yt denotes the product’s sales at period t, Xt denotes advertising at period t, (cid:12)i s are the regression coeﬃcients, and "t denotes error terms (assuming "t N.0; 1//. The (cid:12)i s help to measure the eﬀect or contribution of each of the explanatory variables on response. The beta is interpreted as one unit increase in the explanatory variable would increase the response variable by beta units with all other explanatory variables constant. (cid:24) 2. Nonlinear Regression In some cases, the relationship between independent variable(s) and dependent variable are not linear. For instance, some variables may show a linear relationship with sales; this implies that as the independent variables increase, sales are increasing. However, TV GRP does not show a linear relationship with sales, thus increase TV GRPs will increase sales up to a limit. At a certain point in time, for every increase unit in TV GRP would result to less inﬂuence on sales (diminishing marginal returns). In addition, an advertisement will create more awareness to potential customers to a certain extent and boost sales, which in turn reduce the percentage of change in sales as the brand is known to all. As a result, the data is transformed to apply a nonlinear relationship to the linear model. A typical example of a nonlinear regression model is represented below: (cid:12)0X (cid:12)1 1t X (cid:12)2 2t ; Yt D (9.3) where Yt represents the dependent variable at period t, Xit s represent explanatory variables at period t and (cid:12)i s are the regression coeﬃcients. Speciﬁcally, the diminishing eﬀect of past advertisements on present sales shows a non- linear relationship. There exists a small component referred to as lambda that is multiplied with the previous period of GRP value. This can be written mathematically as: Sales D .GRPt /n (cid:21)GRPt 1: (cid:0) C (9.4) 9.2 EFFECTIVE COMMUNICATION OF RESEARCH, INTELLIGENCE, AND ANALYTIC INSIGHTS Research communication can be deﬁned as the process of interpreting or translating complex research ﬁndings into a language, format, and context that non-experts can easily comprehend. 9.2. EFFECTIVE COMMUNICATION OF RESEARCH, INTELLIGENCE, AND ANALYTIC INSIGHTS 113 Figure 9.3: Linear and nonlinear response to advertisement. One of the purposes of conducting market research is to measure customer satisfaction and how to maintain a competitive edge over other brands, while ﬁnding new markets for products or services. Research can provide ﬁrms with the knowledge of whether the resources and ﬁnancial expenditures dedicated to developing a new product or service will yield proﬁt in the future. It is a necessity for researchers to keep a project’s stakeholders informed by communicating its ﬁndings and recommendations to both the decision makers and other stakeholders. Based on these research ﬁndings and recommendations, the decision makers will have to deliberate inten- sively on how to incorporate recommendations into the organizational system for growth. For some research projects, participants and beneﬁciaries can be researchers, policy makers, donors, government agencies, academics, and others. There are many dissemination tools available to researchers, each of which has strengths and weaknesses in reaching its potential audience. These tools can be used to complement one another to produce an eﬀective dissemination package. Types of dissemination tools include research reports, peer-reviewed papers, policy briefs, and press releases. The work contained in one dissemination tool can be modiﬁed or replicated in the development of another tool. Other dissemination channels/tools are interpersonal communication, email messages, websites, mass media, etc. As a practical illustration, after the completion of the monthly market intelligent survey exercise, bra Limited generates a monthly report and presents detailed ﬁndings and recom- mendations to the staﬀ of Central Bank of Nigeria, Abuja. The presentation team consists of representatives from diﬀerent departments that form the organization. In the course of the pre- sentation, questions emerge as a result of the outcomes of the survey, and bra Limited provides answers based on the market information and experiences. In a case where the answers provided are not satisfactory, questions are thrown open to the ﬂoor for further deliberation. A high number of employees in attendance from diﬀerent departments with a wealth of experience in SalesAdvertisingNonlinearResponseLinearResponse114 9. CAUSAL METHODS their area of specializations has helped to generate the research that is used to provide a lasting solutions to the challenges facing the Nigerian economy at large. 9.3 EXERCISES 9.1. What do you understand by causal methods? 9.2. Deﬁne the following: a. Temporal sequence. b. Concomitant variation. c. Non-spurious association. 9.3. a. What is marketing mix model? b. Mention the 4Ps of marketing mix. c. Explain the procedure of creating a marketing mix model. 9.4. Diﬀerentiate between multiple linear regression and nonlinear regression. 9.5. a. What is research communication? b. Describe how can we generate insights from the eﬀective communication of re- search. C H A P T E R 10 115 Mobile Data Mining Modern communication technology has become ubiquitous in everyday life, and as such has generated a huge amount of research interest. Modern smartphones integrate numerous func- tions and allow the converge of numerous forms of media; these features include internet brows- ing, multimedia, gaming, and many others. Nowadays, researchers can make use of mobile phones to collect a wealth of data and useful information. The data can be in form of call logs, message logs, location, application usage, web usage, and sensor data, among other character- istics (see Figure 10.1). Some behavioral analysis such as sentiment analysis, and segmentation analysis can be performed to analyze these activities. Figure 10.1: Diﬀerent kinds of data in mobile phone. 10.1 CONCEPT OF MOBILE DATA MINING Data mining is an analytic process designed to explore patterns or systematic relationships be- tween variables. Data mining provides the link between stored transactions and analytical sys- tems. The essence of mining data is to provide a prediction for future occurrences of the data. Mobile data mining can play signiﬁcant roles of data producer, data analyzer, and client of remote data miners. The ﬁrst task of smartphone data mining is to use the smartphones to cap- ture data from various sources, such as call logs, message logs, locations, etc. Second, the data collected undergoes ETL. This process involves extracting data from diﬀerent sources and con- Sensor DataApplication Usage DataWeb Usage DataLocation DataCall and Message Log Data116 10. MOBILE DATA MINING verting them into a unique format, transforming it into clean data that is suitable for analysis by removing errors, and then loading and storing the clean data into data warehouses for mining. Third, after the data has been warehoused, mining activities (behavior analysis, location-based services) can be conducted. Figure 10.2 demonstrates the process of mobile data mining. Figure 10.2: Mobile data mining process. Behavioral Analysis reveals the social impact of the various activities performed by a mo- bile phone user. This analysis may be based on the social interactions of mobile phone user in a community or in an organization, or it could reveal information about a user’s personality of behavior. The interaction of a user with the mobile phone gives a holistic overview of their habits. For instance, a user may prefer to listen or watch video whenever he or she is on a bus in traﬃc. These activities can be recorded over time and can be used to predict the user’s behavior whenever he or she experiences similar conditions. Location-Based Services (LBS) allow an analyst to predict where the mobile user will visit in the future, considering the past movement history of the mobile phone user. There are three steps for forecasting the location of a mobile phone. Systematic gathering of the movement history of the user, recognition of movement patterns, and prediction of the next location based on pattern observed. In recent technological developments, some application models have been deployed into mobile phones for mining data collected via smart phones. bra develops a mobile application that is used to collate data on business expectation survey and market survey. The mobile application uses the embedded GPS to log the time and location of the survey. This function helps to monitor the activities of the ﬁeldworkers during the period of survey, and also aids in conﬁrming the authenticity of the data collected. The collection of data is done through the mobile phone but the data resides on a database server. The outcome of the survey can be displayed on the phone by invoking the necessary functions integrated in the app. Application DataLocation DataMessage DataSensor DataBehavioralAnalysisLocation-basedAnalysisCall Data Data WarehouseDataMartExtractionTransformationLoading10.2 ACTIVITIES OF MOBILE DATA MINING 10.2. ACTIVITIES OF MOBILE DATA MINING 117 The models in the mobile phone application can run in three diﬀerent schemes. These schemes are mobile interface, On-board CPU and Client server. In the mobile interface scheme, mobile applications provide a user interface, but data mining activities are performed through back- end computational infrastructures. For the on-board CPU scheme, mobile data mining jobs are performed locally using the computational power and structure of the mobile device. Through the client-server arrangement, data mining activities are carried out on both the mobile devices and back-end servers. Communication overheads in mobile interface schemes are high when compared to on- board CPU schemes. The on-board CPU data mining scheme has good data visualization and low dormancy, while the mobile interface system does not have such beneﬁts. However, the issues encountered in using on-board CPU center on limitations concerning battery power, memory, processing and storage. These problems are largely ameliorated in a mobile interface scheme. bra uses technologies based on JAVA 1.7, JAVA Enterprise Edition, MS SQL, JSF, and Structs in the development of the mobile data mining. The diagram in Figure 10.3, shows the Figure 10.3: End-to-end ﬂow. ﬂow of data within the platform to produce various reports. The following are the steps taken to produce reports. 1. Data Entry Clerks collate data of speciﬁc formats based on the various indexes supported by the platform and inputs the “raw data” into the system via various supported channels, web, or mobile. End-to-End FlowEnters data via webor mobileReport generated is stored in thepreferred formatAd-hoc reports can also be generatedAnalysis is run automaticallyon a chosen day of the monthSubmits data for valicationAnalysisTriggerAnalysisDataEntryClerkNoYesIsDataValid?DatabaseforStorageDataSubmission118 10. MOBILE DATA MINING 2. The data are validated by an internal logic built for each data format. The validation ensures the ﬁnal data stored are valid entries matching various stipulated algorithms to ensure the reports that will be generated eventually are of very high integrity. 3. After all data are captured, the “Index Engine System” is executed based on the scheduled period or manually as required. It executes the various process on the data captured to produce the report. 10.3 ARCHITECTURE OF MOBILE DATA MINING In recent times, the Service Oriented Architecture (SOA) model is mainly used to implement distributed systems where applications and components interact each other independently from platforms and language [Kumar and Ramadevi, 2016]. Kumar and Ramadevi state that the most important implementation of the SOA model is web services, because of internet technologies (XML and HTTP) which are globally accepted. web services encompass the integration of dis- tributed applications, processes and data, optimizing the deployment of systems and improving their eﬃciency. The wide use of web services in mobile environments allows the integration of mobile devices with server applications to run on diﬀerent platforms, and allows us to access and distributed services from mobile devices. bra develops mobile data mining architecture based on ﬁve components, namely: data capture, middle ware, data storage, data analysis, and data reporting. The architecture diagram shows the design of the systems/components that form the entire platform. It shows the vari- ous connections between the components that allow the data to be captured, validated, stored, processed, reported, and ﬁnally consumed by the Reporting Analyst. Figure 10.4 shows the ar- chitectural design of mobile data mining. 10.4 ALGORITHMS OF MOBILE DATA MINING Data mining algorithms are heuristic procedures that are used to analyze data by observing the historical pattern or trends in a dataset. It uses the outcome of the analysis to deﬁne the optimal parameters for creating models. Data mining algorithms incorporate statistical and learning algorithms that help to advance the collection and management of data. Data mining can be applied in the area of education, bioinformatics, education, genetics, banking, and electrical power. Mobile data mining uses algorithms of data mining in a mobile computing environment. Figure 10.5 shows the algorithms in the data mining process. 10.5 APPLICATION OF MOBILE DATA MINING Recently, it has become possible for ﬁrms to purchase mobile apps with the capacity of per- forming data mining tasks. This concept of mobile data mining is used across a variety of ﬁelds, for example, to develop body-health monitoring smart phones, vehicle control systems, fraud 10.5. APPLICATION OF MOBILE DATA MINING 119 Figure 10.4: Mobile data mining architecture. Figure 10.5: Data mining algorithms. ArchitectureData CaptureMiddle-wareData StorageData AnalysisData ReportingMobileWebMiddle-wareLoadBalancerDB LoadBalancerIndexAlgorithmEngine1st MWInstance1st DBInstance2nd DBInstanceNth DBInstance2nd MWInstanceNth MWInstanceData Mining AlgorithmsOnline Analytical ProcessQuery ToolsPredictionClassiﬁcationVisualizationDescriptionClusteringAssociationSequentialAnalysisDecisionTreeNeuralNetworkRegressionSQLDiscovery-driven Methods120 10. MOBILE DATA MINING detection software, and wireless security systems. More research should be done to improve the battery life of mobile phones, since data mining through mobile phones requires a lot of processing power that can quickly drain the life of a handset. Innovative applications of data mining have materialized in the following sectors. (a) Healthcare: There is tremendous growth in biomedical research, including in areas such as pharmaceuticals, cancer therapies, and human genome research. Lately, research on DNA has revealed genetic sources for diseases and led to the development of preventive medicines and treatments to manage these diseases. (b) Finance: Financial institutions collect a lot of high-quality and reliable data from cus- tomers using banking services, investment services, and insurance services. This data can be used for a wide variety of purposes, for example, ﬁnancial engineering (i.e., the cre- ation of new asset classes, especially in the ﬁeld of derivatives), credit checking, and fraud detection. (c) Telecommunication: A vast amount of data has been collected from the telecommuni- cation sector, ranging from personal data to the biometry data of individual subscribers. This data can be used to tracking fraudulent activities (including other criminal activities). (d) Retail industry: Data collected on sales, customers’ shopping patterns, and services col- lected through e-commerce site purchases, ATM withdrawals, and POS transactions can yield useful information about consumption behavior. For example, we can identify cus- tomers’ shopping patterns and trends over a period of time. With the aid of data mining, we can have the knowledge of when, where, and how a customer spends their disposable income. This data can be leveraged to improve the quality of customer service to enhance consumer retention and satisfaction, and reduce business costs. 10.6 EXERCISES 10.1. What is mobile data mining? 10.2. With the aid of a diagram, describe the mobile data mining process. 10.3. Discuss the end-to-end ﬂow in producing bra reports. 10.4. With the aid of a diagram, describe mobile data mining architecture. 10.5. a. Explain the function of data mining algorithms. b. Mention areas where mobile data mining may be applicable. A P P E N D I X A 121 Questionnaires, Items Survey, and Weights of Elementary Items A.1 SAMPLE OF BUSINESS EXPECTATION SURVEY QUESTIONNAIRE Business Expectation SurveySector: Manufacturing (Finance)Company InformationPlease provide the following information in Block Letters for veriﬁ cation purposes.Company Name:Principal Activity/Product Line:Division/Department:Company Address & Local Government:Name of Respondent:Position:Phone Number:Email:*All information gathered herein shall be treated strictly conﬁ dential and shall be used for statistical purposes only.Note: Please indicate “Increased” if an increase of at least 5% is expected or has been experienced. Please indicate “Decreased” if a decrease of more than 5% is expected or has been experienced. Otherwise, please indicate “Remain Unchanged”.Kindly indicate by a check mark your answer for each item in this questionnaire unless otherwise speciﬁ ed. If the item is not applicable, please write N.A on its left side. Th ank you!122 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 1. Employment Expectation:What is the Institution’s Employment Expectation for: ___?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment2. Prices ExpectationsWhat is the Inﬂ ation Rate Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentWhat is the Company Product Prices Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentWhat is the Exchange Rate (NGN/USD) Expectation?PeriodAppreciateDepreciateUnknownRemainUnchangedCurrent MonthOne MonthTh ree MonthsSix MonthsCommentA.1. SAMPLE OF BUSINESS EXPECTATION SURVEY QUESTIONNAIRE 123 3. Bank RatesWhat is the general Interest Rate Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentWhat is the Deposit Rate Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment124 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 4. Access to Credit Facilities and Financial ConditionWhat is your company’s Financial Condition?PeriodEasyNormalTightUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentWhat is your company’s Load Credit Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentWhat is your company’s Access to Credit Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentIf opportune, would you like to access Loan Credit?YesNoIf yes, for what purpose?PeriodExpansionStock Raw Material InputAcquisition of AssetsInvestmentCurrent MonthOne MonthTh ree MonthsSix MonthsCommentA.1. SAMPLE OF BUSINESS EXPECTATION SURVEY QUESTIONNAIRE 125 5. Economic and Business ConditionsWhat do you think of the country’s Economic Condition in the next ___?PeriodImproveRemain UnchangedDeteriorateUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentHow will you rate and predict Business Conditions in the next ___?PeriodImproveRemain UnchangedDeteriorateUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment126 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 6. Production Cost ExpectationsWhat is the general Cost of Production Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment7. Market Share ExpectationsWhat is the general Sales Expectation?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment8. Stock Level ExpectationsHow would you rate and predict your company’s Stock (Inventory of Raw Materials)?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentA.1. SAMPLE OF BUSINESS EXPECTATION SURVEY QUESTIONNAIRE 127 9. Capacity Utilization ExpectationsWhat is the Current Capacity Utilization of the production of your ﬁ rm?ResponsesMark (X)At full capacity (100%)Slightly below capacity (80%)Moderately below capacity (60%)Signiﬁ cantly below capacity (40%)At close to zero capacity utilizationCommentWhat is your forecast for the trend of capacity utilization of the production processes at your ﬁ rm?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsComment10. Social and Economic Policy Shocks (Factors Limiting Business Operations)What factors are currently or might likely limit your ability to increase business activity? Please number the factors ranked according to its signiﬁ cance in your production/business activity, “1” being the most signiﬁ cant.NoneAccess to creditForeign competitionDomestic competitionHigh operating costLack of demandShortage of laborHigh staﬀ turnoverDiﬃ cult to collect debtHigh interest rateUnclear economic lawLack of equipmentOthers (please spedify)Please provide details on the top three factors limiting your business activity.Factor 1Factor 2Factor 3128 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS What are the business expectations on the current economic, social, and ﬁ scal issues?PeriodDecreasedRemain UnchangedIncreasedUnknownCurrent MonthOne MonthTh ree MonthsSix MonthsCommentSuggestions, if any, for policy implications:What is the value of the following lending rates:TypeValueInterest RateManagement FeeProcessing FeeOther Fees (if applicable)CommentA.1. SAMPLE OF BUSINESS EXPECTATION SURVEY QUESTIONNAIRE 129 Purchasing Manager’s IndexHow did the quantity of new orders in the current month compare to the quantity of orders in the previous month?% Decreased% Remain Unchanged% Increased% UnknownJuly 2017 IndexAugust Index% ChangeHow did supplier delivery times from the current month compare to the previous month?% Improve% Remain Unchanged%Deteriorate% UnknownJuly 2017 IndexAugust Index% ChangeHow did the volume of production in the current month compare to production level in the previous month?% Decreased% Remain Unchanged% Increased% UnknownJuly 2017 IndexAugust Index% ChangeHow did the quantity of raw materials/WIP inventory from the current month to the quantity of inventory in the previous month?% Decreased% Remain Unchanged% Increased% UnknownJuly 2017 IndexAugust Index% ChangeHow did your ﬁ rm’s employment levels this month compare to the previous month?% Improve% Remain Unchanged%Deteriorate% UnknownJuly 2017 IndexAugust Index% Change130 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS A.2 LIST OF ITEMS SURVEY MONTHLY List of Items Survey MonthlyS/NCategory ItemElementary ItemMeasurement1Food and Non-Alcoholic BeveragesBread SlicedGramsBread UnslicedGramsCake (Ordinary)GramsGramsGramsRound BreadWheat BreadChewing Gum PiecePeppermint1 1 1 1 1 PieceVicks Lemon Plus1 Piece3 Crowns Evaporated Milk 170 g1 TinBlue Band 450 g TinCow and Gate Baby Milk 900 g1 TinSt. Louis Cubed Sugar 500 g1 PackExeter Corned Beef 340 g1 TinGeisha 155 g TinGlucose D 400 g TinGranulated SugarGramsKetchup 450 ml450 mlLocal Coasta BiscuitGramsLocal Cracker BiscuitGramsMacaroni 500 g 1 PacketNan Baby Milk 450 g450 gramsLocal Coasta BiscuitGramsLocal Cracker Biscuit GramsMacaroni 500 g 1 PacketNatural Honey:Local Production1 Beer BottleIndomie Noodles 70 g70 GramsPackaged Wheat FlourKilogramsPeak Evaporated Milk 170 ml1 TinPlantain Chips (Indicate Weight)GramsA.2. LIST OF ITEMS SURVEY MONTHLY 131 List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement1Food and Non-Alcoholic Beverages (continued)Poundo Yam (Indicate Weight)GramsPowdered 3 Crowns MilkGramsPowdered Peak Milk 400 g1 TinQuaker OatsGramsSalt (Indicate Weight)GramsTitus Sardine 125 g 1 TinGolden Penny Semovita 2 kgKilogramsSma Baby Milk 450 g1 TinGolden Penny Spaghetti500 g/0.5 kg500 g/0.5 kgStar Kist Tuna1 TinStrawberry Jam (Indicate Weight)GramsTomato PureeWafersGramsGramsBag Tea-1 Packet of Lipton1 PackBournvita 450 g1 TinNasco Corn Flakes 350 g1 PackCustard 300 g1 TinHimalt1 BottleMaltina1 BottleNescafe Coﬀ ee 50 g1 TinOgi/Akamu/KokoOvaltine 450 g1 TinYogurt (Indicate Size)BananaKilogramsKilogramsKilogramsImported AppleKilogramsOrangePawpawKilogramsKilogramsPineappleKilogramsKilogramsWater LemonBrown BeansKilograms132 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement1Food and Non-Alcoholic Beverages (continued)Corn FlourKilogramsEluboKilogramsFlourKilogramsFufuKilogramsGroundnutKilogramsGuinea CornKilogramsGuinea Corn FlourKilogramsImported RiceKilogramsLocal RiceKilogramsLocust BeansKilogramsMilletKilogramsOfada RiceKilogramsPigeon BeansKilogramsPlantain FlourKilogramsWheatKilogramsWhite BeansKilogramsWhite GarriKilogramsKilogramsKilogramsKilogramsWhite MaizeYellow GarriYellow MaizeBeefKilogramsEggKilogramsFrozen TurkeyKilogramsGoat MeatKilogramsLive Agric ChickenKilogramsLive Guinea FowlKilogramsLive Local ChickenKilogramsLive Medium TurkeyKilogramsPorkKilogramsTurkeyKilogramsWhole Frozen ChickenKilogramsA.2. LIST OF ITEMS SURVEY MONTHLY 133 List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement1Food and Non-Alcoholic Beverages (continued)AkaraGramsEko (Agidi/Kafa)GramsMoin-MoinGramsMilling Charges1 VisitCatﬁ shKilogramsCrabKilogramsCroakerKilogramsFresh ShrimpsKilogramsMackerelKilogramsRed-Dried ShrimpsKilogramsStock FishKilogramsTilapiaKilogramsTitusKilogramsSwan Bottled Water (Indicate Size)ClEva Bottled Water (Indicate Size)ClRagolis Bottled Water (Indicate Size)ClNestle Bottled Water (Indicate Size)ClAquadana Bottled Water (Indicate Size)ClFive Alive (Indicate Size)ClFunman Juice (Indicate Size)ClCaprisonne (Indicate Size)ClChivita (Indicate Size)ClHappy Hour (Indicate Size)ClLucozade Boast (Indicate Size)ClSachet Water (Indicate Size)1 SachetCoca-Cola 35 cl1 BottleFanta 35 cl1 BottleSprite 35 cl1 Bottle7-Up 1 Bottle134 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement1Food and Non-Alcoholic Beverages (continued)Pepsi1 BottleMirinda1 BottleCassavaKilogramsCocoyamKilogramsIrish PotatoesKilogramsPotatoKilogramsSweet PotatoesKilogramsKilogramsYamAgbono/AkponBitter ColaGramsGramsBitter LeafGramsCabbageCarrotGramsCashew NutCucumberGramsCurry PowderGramsEweduGramsGramsGramsGarlicGramsGingerGramsGroundnut Oil1 Beer BottleKnorr CubesGramsLettuceGramsMelon Seed ShelledGramsMelon Seed UnshelledGramsOnionsGramsGramsPalm NutPalm Oil1 Beer BottleFresh Pepper Sugar CaneGramsGramsTh ymeGramsFresh TomatoGramsA.2. LIST OF ITEMS SURVEY MONTHLY 135 List of Items Survey Monthly (continued)1Food and Non-Alcoholic Beverages (continued)UgwuGramsWater LeafGramsS/NCategory ItemElementary ItemMeasurement2Clothing and Foot WearsAdire YardsAgbada Buba & Sokoto (Men)1 PieceGuinea Brocade (Mallam Style)1 PieceAnkara High Quality Prices6 6 YardsAnkara Low Quality Prices6 YardsBabies Dresses (for female), 2 yrs old1 PieceBrocade (made in Nigeria) 10 YardsChildren WearsOneFemale GownOneOneOneFemale Head TieFemale ShirtFemale Trousers1 PairKampala6 YardsLace (Made in Nigeria) 10 YardsLinen Male Trousers1 PairMen Belt1 PairMen Long Sleeve Shirt1 PieceMen Short Sleeve T-Shirt1 PieceMen Short (Boxers)1 PairNative Cap1 PieceNative Cloth (Aso-Oke)10 lagsNative Dress (Kaftan) Ready Made1Printed Fabric1 YardSinglet (Boys)Skirt (Girls)11Synthetic Materials for Sewing1 YardTies1136 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement2Clothing and Foot Wears (cont.)Two-Piece Suit (Coat and Trouser) Terylene1 PairVelvet (Skirt Material)1 YardWomen’s Brief 100% Poly Amide Double Seat, Elastic Waist Band; Medium Size1PieceChildren Shoes1 PairFemale Sandals1 PairFemale Shoes1 PairMale Sandals1 PairMale Shoes1 PairSlippers1 PairLaundry & Dry Cleaning Services for Two Pieces Suit (Coat and Trouser)1 PieceRepair of Shoes Excluding Cost of Materials1 PairRepair of Cloth (Mending)1 PairTailoring Charges for School Uni-form (for Girls)1 PieceTailoring Charges for School Uni-form (for Boys Shirts and Knick-ers)1 PieceTailoring Charges for Women's Buba & Iro1 PieceTailoring Charges Men's Buba & Sokoto1 PieceTailoring Charges Men's Suit (Coat and Trouser)1 Piece3HealthAmpicillin Capsule of 250 mg Sachet of 10 Capsule1 PacketAspirin Complete Sachet 1 PacketA.2. LIST OF ITEMS SURVEY MONTHLY 137 List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement3Health (cont.Chlroquine, Pack of 10 Tablet1 PacketEpsom Salts, 1 Sachet1 PacketFansidar, Sachet of 3 Tablets1 PacketMultivitamins Complete Sachet1 PacketNivaquine, Pack of 10 Tablet1 PacketNivaquine Syrup 60 ml1 BottleNovalgin, Pack of 20 Tablets1 PacketPanadol, 1 Sachet/ Complete of 10 Tablet1 SachetParacetamol1 SachetTerramycin Capsule: A 250 mg Sachet of 4 Capsules1 PacketBenylin and Codein: 100 ml Bottle1 BottleMultivite Syrup: Small Bottle of 100ml1 BottleMulyivite: Glaxo, 1 Bottle of 60 Tablets1 BottleOreptal: 1 Medium Bottle 300 ml1 BottleInsecticide(Spray)Baton 400 ml1 TinDustin Powder Standard Size 250 gm1 TinMethylated Spirit (Indicate Size)1Shaving Powder1Blood Test in Private Hospital (Malaria/ Typhoid Parasite)1 TestConsultation Fee Chemists 1 VisitConsultation Fee Dental Service 1 VisitConsultation Fee Government Hospitals1 VisitConsultation Fee Private Hospitals 1 VisitConsultation Fee Unorthodox Clinics1 VisitCorrective Eye Glasses1 138 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement3Health (cont.)Hospital Accommodation in Government Hospital, Fee per Day on Admission Excluding Food1 DayHospital Accommodation in Private Hospital, Fee per Day on Admission Excluding Food1 DayLaboratory Service: Urine Test for Presence of Albumen and Glucose in Private Hospital1 TestMidwives1 ServiceNurse1 ServicePhysiotherapist1 ServiceX-Ray Photography, 1 Chest X-Ray in Private Hospital1 TestAndrew Liver Salt1 Sachet of 5 mg1 SachetCombatrin: 1 Pack of 6 Tablets1 PacketsDiabenese: 250 mg, 1 Box of 20 Tablets1 PacketsEye Drop: Visine 15 ml1 BottleRobb in Small Tin of 4 g1 TinTooth Paste: Close Up Small Size 37 g1 TubeCotton Wool 100 g PackCrepe Bandage 2"1 RollDusting Powder Standard Size 250 g1 1 TinGrip Water 100 ml1 BottleIodine: 1 Bottle 15 ml1 BottleMedicated Plaster1 SachetMilton Sterilizing Fluid 500 ml1 BottleOlive Oil Goya 88.7 ml1 BottleOintments Penicillin 20 g1 TubeA.2. LIST OF ITEMS SURVEY MONTHLY 139 List of Items Survey Monthly (continued)S/NCategory ItemElementary ItemMeasurement3Health (cont.)Potash (Potassium Permanganate Crystal) 100 g1 BottleSyringe 5 ml14Furnishing Household Equip-ment and MaintenanceBath: Standard Size, Cast Iron (Coated With Ceramic) Ariston1Crittal Window Frame: 4' × 4' Without Inbuilt Burglary-Proof1Flush Door: Made of Plywood Size 2.5' × 8' 1 Galvanized Iron1Glass Sheet for Crittal Window Plain Std Size 12" × 24"1Glass Sheet for Crittal Window Shadedstd Size 12" × 24"1Louvre Frame with 8 Blades1Louvre Glass, Plain 61 cm1Louvre Glass, Shaded 61 cm1Shower Fittings Iron Type1Wash Hand Basin 40 cm × 55 cm1Water Closet: Complete Set (Local)1Electric Bulb 60 Watts Plain1Electric Iron Philips Dry Iron1Electric Kettle (4 l) Specify Make1Electrical Wire (1 yd 1.5 mm)1Extension Box 6 mmFlorescent Tube (White) 4' 40 Watts1Lamp Holder (Angle)1Socket (Wall Suface) 4 mm1140 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 4Furnishing Household Equip-ment and Maintenance (cont.)Audio Set Cooker1DVD Player1FanFreezerFridgeLaundry IronTV Set1Vhs Player1Bed Frame: Well-Polished Plywood Dimension 4' × 6' 6"11111Bed Linen1Cushion Chair: Wooden Frame With Spring With Arms, Well Polished Single Seater1Furniture (Wardrobe)1Kitchen Cupboard: Ordinary Unpolished with Three Shelves1Mat: Made of Natural Fiber Specify Size1Ordinary Chair: Table Chair with Some Foam Attachment without Arms1Ordinary Chair All Wooden, Standard Size without Arms1Pillow: Foam Filled1Wall Hanger1Wood Bed: Frames and Bed Stead Made of Wood Well Polished 4' × 6' Wood1Writing Table: Well-Polished, 3 Drawers on One Side: Top in Formica11CupboardA.2. LIST OF ITEMS SURVEY MONTHLY 141 4Furnishing Household Equip-ment and Maintenance (cont.)Air Conditional ( Panasonic) 2 horsepower1Batteries Small (For Small Radio) Size AA 1Bed Sheet: Ready Made Printed Fabric Polyester (Up To 25% Cotton) Size 4' × 6' Bed1Blanket Made in Nigeria1Cooking Pot Aluminum Type : 2 Handle with Lid Medium Tower Brand1Dinner Plate, Unbreakable1Disinfectant: Dettol in Plastic Bottle 250 ml1Domestic Employee Steward: On Monthly SalaryOne MonthDomestic Employee: All Duties (Full Time) with Feeding and Accommodation Monthly Per EmployeeOne MonthElectric Cooker: 2 Rings, 1 Flask Th ermocool, Medium Size1Fork Stainless Steel1Gas Cooker: 2 Burners (without Oven) Specify Type1Gas Cooker: 4-Burner Eazee Cooker with Oven1Glasses—Ordinary Drinking Glass Pack of 6Grinder Phillips1Household Utensils Sauce Pan1Insecticide (Spray) Bagon 400 ml1 Tin142 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 4Furnishing Household Equip-ment and Maintenance (cont.)Kitchen Knife with Wooden/Plastic Handle1Lamp Th reads (Wick)1Linoleum (Carpet) Plastic Type Multicolour, Price/Yard1yardPans (Frying Pans ) Medium1Refrigerator 250/300 l Th ermocool Haier1Rug: Single Color, Simplest Type Price Per Sq. MeterSquare meterScoring Powder (Vim) Price of One 500 g1Serving Dishes Medium Size1Standing Fan (Specify Product)1Standing Fan (Specify Product)1Table Knife Stainless Steel1Tablespoon Stainless Steel1Toaster Machine (Phillips)1Tumbler 25 cl Plain With Handle1Washing Machine (Ignis)1Cooker11Microwave Plates1Bowl1Cooler1Foodﬂ ask1Metal Bucket Big Size 341Plastic Basin: 60 cm Diameter1Plastic Bucket With Metal Handle, Big Size 341Plastic Cup about 25 cl1Plastic Plate16" Construction Block1A.2. LIST OF ITEMS SURVEY MONTHLY 143 4Furnishing Household Equip-ment and Maintenance (cont.)9" Construction Block1Asbestos Rooﬁ ng Sheet, 1.2 m × 1.2 m1Asbestos Rooﬁ ng Sheet, 1.2 m × 3 m1Ceiling Slate1Cement: Benue (50 kg Bag)1Cement: Burham (50 kg Bag)1Cement: Dangote (50 kg Bag)1Cement: Elephant (50 kg Bag)1Cement: Larfarge (50 kg Bag)1Corrugated Iron Sheet Comb Brand (20 Sheets)1Corrugated Iron Sheet Hand Brand (20 Sheets)1Emulsion Paint: Nigerlux 4 l1Floor Tiles: Plastic Plain Nigeriate Tiles 300 mm × 300 mm1Gloss Paint: Dulux 4 lGravels Washed 5 cu Meters1Iron Nails 10 cm (4")1Iron Rod 1.3 cm × 9 cm1Iron Rod 2 cm × 9 cm1Labor Rate1Padlock: Yale Medium1Plumbing Pipe 1" (Plastic)1Plumbing Pipe 1/2" (Plastic)1Plumbing Pipe 2" (Plastic)1Plumbing Pipe 4" (Plastic)1Rooﬁ ng Sheet11Sand: ErosionSand: Washed1Stones: Granite1144 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 4Furnishing Household Equip-ment and Maintenance (cont.)Union Key; 2 Leavers Made in England1Wall Tiles:Ceramic Plain 15 cm × 15 cm i.e.. 6" × 6"1Water Paint: Dulux 4 Litres1Wood And Construction Materials For Kitchen Basin1Wood Plank Iroko 2" × 3"1Wood Plank Iroko 3" × 4"1Wood Plank Mahogany 2" × 3"1Wood Plank Mahogany 3" × 4"1Electric Charge (Non-Private Users)1 kwhElectric Charge (Private Users)1 kwhGas in Medium Cylinder (12.5 kg Reﬁ lling Specify)1 CylinderGas in Small Cylinder, i.e., 5 kg Reﬁ lling1 CylinderKerosene: Price of 1 Beer Bottle (60 cl)Beer BottleKerosene: Price of One Gallon1 GallonLiter of Diesel 1 LiterLiter of Kerosene 1 LiterLiter of Petrol 1 LiterBed Room Flat: Rent1 MonthLarge Shop1 MonthMedium Shop1 MonthSmall Shop1 Month2 Bed Room Flat: Rent1 Month3 Bed Room Flat: Rent1 MonthCandle Price of a Packet of 8 Candles, White1 PacketCandle Price of One 1 Duplex1 MonthA.2. LIST OF ITEMS SURVEY MONTHLY 145 4Furnishing Household Equip-ment and Maintenance (cont.)Half Duplex1 MonthMatches Price of One Box1 BoxModern Detached Bungalow 4–5 Rooms Including Sitting Room: Rent1 MonthMortgage Charges 1 ServiceOther Housing Charges (Agreement)1 ServiceRefuse DisposalMonthlyRoom & Parlor, Wall Made of Cement Blocks, in a Bungalow House, Standard Size: Rent1 MonthSelf-Contained with Water Closet: Rent1 MonthSelf-Contained without Water Closet: Rent1 MonthSingle Room, Wall Made of Cement Blocks, in a Bungalow House, Standard Size: Rent1 MonthWater RateMonthly5Miscellaneous Goods and ServicesCar Wash1 VisitCarpenter: Fixing of Door Key Excluding Cost of Key Cost of LaborChildren's Hair Cut By (Established Barber)1 PersonFan Repair: Rewinding of Coil (Cost of Labor Only)Cost of LaborFridge Repair: Replacement of Compressor (Cost of Labor Only)Cost of LaborGrinding of Food Condiments, Soup Ingredients Mixed (e.g., Pepper, Tomatoes, Onions )1 ServiceJewelry (Bangles)1146 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 5Misc. Goods and Services (cont.)Laborer: Cost of Labor Per DayCost of LaborManicure and Pedicure1 ServiceMen's Hair Cut: Adult By (Established Barber)1 PersonNight Watchman: Hired Privately, Duties From 8pm–8am Everyday Charge/Month1 Monthly SalaryPhotocopy 1 Page Document Foolscap Size1 ServicePressing Iron Repair: Replacement Of Element (Cost of Labor)Cost of LaborRadio Repair: Replacement of Transformer Excluding Cost of Material (Labor Only)Cost of LaborShoe Shinning, a Pair of Shoes, (Cleaning, Polishing, and Shining)1 ServiceTelevision Repair: Replacement of Transformer Excluding Cost of Material (Labor Only)1 ServiceWasher Man: Cost of Washing Coat and Trouser1 ServiceWatch Repair General Overhauling1 ServiceWater Carrier1 TinWedding Rings112" × 18" Mirror 5 mm1African Comb; Wooden About 10 teeth1Air Freshener 300 ml1Broom: Ordinary Floor Broom1 BroomCar Brush11Chewing StickA.2. LIST OF ITEMS SURVEY MONTHLY 147 5Misc. Goods and Services (cont.)Cutlass "Machete" Wooden Handle; Large1Eye Glass (Sun Shade)1Hair Drier Super Top Standard Type Jet Cream 125 g1Lady Citizen WatchLips StickLudo, Standard Size, Glazed Complete Set1Magic Shaving Powder1Men's Electronic Citizen Wrist Watch, Simple Type111Mosquito Coil1 1 1 CoilNeedle OrdinaryOﬃ ce Pin PacketPetroleum Jelly Vaseline Small 50 g1Plastic Comb With Handle, Shape Like African Comb11Sewing TreadShoe Polish KIWI Black In A Round Tin of 50 ml1 TinSponge (Local or Woven)1Studs1Suitcase Medium1Tie Clips1Tiger Razor Blade Packet of 1011Tony Montana 100 g Tooth Brush, Jordan1Travelling Bag (Medium)1Walking Stick Wooden Polished Uncovered1Wall Clock (Battery Type)1Women Hair Brush1Women Hand Bag Medium Size1148 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 5Misc. Goods and Services (cont.)Women Hand Bag Small Size16CommunicationBrowsing Fee 1 1 HourDesktop Computer1 UnitInternet Subscription MonthFax Service 1 ServiceMoney Order 1 Stamps Nokia SimpleUnitTelephone at Public Call Lasting 3 Minutes Local within City3 MinutesTelephone Cal Intra State Per Minute Gsm at Business Center1 MinuteLand-Line Subscription and (Sim)1Mobile Subscription and (Sim)17Education Advanced Learner Dictionary1Arts TextbookBall Pen (Bic) Price of One11Cello Tape11 Daily Newspaper, Daily Times Price of One Copy1Envelope 4" × 9" Pkt Of 251Eraser 1Exercise Book 2A, 20 Leaves1Great Wall Sharpener Made in China1Mathematics Set, Oxford1New General Mathematics For Jss1-3 by MF Macrae & Co1New Practical English Jss1-3 by P.A Ogundipe P.S Tregido1Nigerian Integrated Science Project Jss1-3 by Science Teachers Association1Pencil with Eraser: H.B Price of One1A.2. LIST OF ITEMS SURVEY MONTHLY 149 7Education (cont.)Quick Ink Pot Small Pot1Ruler (Wooden): Price of One1Text Book Mathematics: For Primary Four, Macmillian1Weekly Magazine Newswatch1Boarding Fees For Secondary School Charge 1 Term (Public)Per TermNursery School Fees, without Meal Fee per TermPer TermPrimary School Fees; Private, without Meal per TermPer TermPrivate Lesson for Primary Four Pupil Charge per MonthPer TermPrivate Vocational School Fees, for Secretarial Studies Fee per TermPer TermQuranic School Fees; without Meal Fees per TermPer TermUniversity Education Fee; Course of Study Economics One Session; Fee without Meal and AccommodationPer SessionWriting & Drawing (Children Book)18Recreation and CultureAudio Cassettes 1Cable Subscription 1DVD 1DVD Player 1Video Cassettes 1Video CDs 1Audio CDs11Cd Player(Sony)Children Ball; Synthetic Rubber, Diameter 22 cm1150 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 8Recreation and Culture (cont.)Color Fil Kodak 36 Exposures Size 1351Compact Disk (CD) of Popular International Artist1Compact Disk (CD) Original (Popular Indigenous Music Artist)1Guitar(Ordinary)1Pocket Camera: CanonPortable Radio, 3 Band Panasonic 37501Television Color 20" LG1Unrecorded Compact Disc1Video Recorder Sony Model Ed1151Cinema Show: In Town Center Popular Indigenous Film Gate Fee1 PersonFootball Match, for a Division 1 Match Uncovered Seat Gate Fee per Person1 PersonPhotographic Development and Printing 36 Exposures Color: Postcard Size (Charge For Development Plus Printing of 36 Copies)1 VisitRecorded CD of Popular Indigenous Artist19Restaurant and HotelMeal at a Local Restaurant, Total Cost of a Normal Feeding, a Plate of Eba with About Two Pieces of Meat1 PersonMeal at a Local Restaurant for a Plate of Amala and Soup With Two Pieces of Meat1 PersonMeal at a Local Restaurant for a Plate of Cooked Fufu and Soup with Two Pieces of Meat1 PersonA.2. LIST OF ITEMS SURVEY MONTHLY 151 9Restaurant and Hotel (cont.)Meal at a Local Restaurant for a Plate of Cooked Rice and Stew with Two Pieces of Meat1 PersonMeal at a Local Restaurant for a Plate of Fried Rice and Chicken1 PersonMeal at a Local Restaurant for a Plate of Poriage and Chicken1 PersonMeal at a Local Restaurant for a Plate of Pounded Yam and Soup with Two Pieces of Meat1 PersonMeal at a Local Restaurant for a Plate of Tuwo and Soup with Two Pieces of Meat1 PersonMeal at a Standard Hotel, Charge of Full Lunch1 PersonRoom Charge in a Standard Hotel, Single Bed 1 Night10TransportationBreak & Clutch Fluid Heavy Duty Polygard: Super Al Heavy Duty 485 ml1 CanEngine Oil, 1 l 1Tire Gauge ServiceTire RepairCost of LaborBicycle RepairsCost of LaborBrake PadCar Insurance Th ird Party Premium Plus 5 Years Claim1111Diesel Oil LiterDriving License Renewal for Type B PrivateRenewalDriving License Renewal for Type E PrivateRenewal152 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS 10Transportation (cont.)Diesel Oil LiterDriving License Renewal for Type B PrivateRenewalDriving License Renewal for Type E PrivateRenewalFuel (Petrol)1 1 LiterLearner’s Permit1Motorcycle Insurance Th ird Party1Motorcycle License1Motorcycle Repair General Service1Replacement of One Front Shock Absorber of Acar, Cost of Labor Only Cost of LaborVehicle License: Annual Renewal1Bicycle Tube,Diamond for Men1Bicycle Tire, Diamond China for Men1Car Battery: Varta 12 Volts, 45A.H with Acid1Car Battery: Varta 12 Volts, 60 AH with Acid1Car Tire: Dunlop Elite 175 SR 141Exide Battery 12 Volts 45 AH1Fan Belts AutomagaMotor Cycle Tube, 1 Tube Dunlop1Motor Cycle Tire, 1 Indicate Brand E.G Dunlop1Sparking Plug, "Champion" N9y, Price of 4 Plugs1Air Fare Charges for Speciﬁ ed Route, Single Journey Only Locally State Capital to Abuja1 PersonA.2. LIST OF ITEMS SURVEY MONTHLY 153 10Transportation (cont.)Bus Journey Within City per Drop Charge per Person Constant Route1 PersonBus Journey within Inter City, State Routes per Drop Charge per Person Constant Route1 PersonJourney By Motorcycle (Okada/Achaba) per Drop Constant Route1 PersonRail Transport: Economy Charge for About 100 km 1 PersonTaxi Journey; per Drop (About 3 km) per Person Urban1 PersonWater Transport: Waterway Passenger Transportation Constant Route1 Person11Alcoholic Beverages, Tobacco, and KolaStar Lager Beer 600 ml1 BottleHarp Lager Beer (Indicate Size)1 Bottle33 Export Lager Beer (Indicate Size1 BottleSmall Guinness Stout 33 cl1 BottlePalm Wine Beer Bottle Burukutu Beer Bottle Chelsea London Dry Gin (Indicate Size)1 BottleSeaman Aromatic Schnapps (Indicate Size)1 BottleLocal Gin (Ogogoro)Beer BottleBenson & Hedges StickRothmansStickLondon MentholStickConsulateStickSt. Moritz StickKola Nuts Grams154 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS A.3 WEIGHTS OF SOME ITEMS Weights of Some ItemsItemsWeightItemsWeightItemsWeightAbestos0.01Gas 0.36Sand0.01Adire 0.31Gin 0.19Sanitary towels 0.21Advanced Text Books0.35Ginger 0.07Sardine 0.19Ankara 0.50Government hospitals0.17Sausages 0.05Antibiotics 0.05Grease0.01Seasoning0.29Aspirin0.02Groundnut0.14Secondary schools 1.12Audio cassettes 0.03Groundnut oil0.95Shaving powder0.03Audio CDs0.09Guinea corn 0.11Shrimps0.20Audio set0.84Half duplex 0.01Slippers 0.25Bag tea0.06Imported apple0.11Soaps 1.18Banana 0.33Insect killer/disinfectant0.17Socket0.04Beans 0.75Inter-city 0.01Soft drinks 0.44Bed0.90Intermediate textbooks0.11Spaghetti0.18Beer 0.94International ﬂ ight 1.49Spoon and fork0.08Bicycle0.08Internet subscription0.01Stamps 0.01Biscuits 0.16Intra-city 0.01Stapler 0.01Block0.14Iodine0.02Stencils 0.01Bottled water0.39Kampala 0.06Sugar 0.38Bowl0.01Kerosene 0.73Table0.15Bread 1.49Kindergarten 0.01Taxi 1.51Break oil0.01Kitchen basin0.01Th ree bedroom ﬂ at 0.01Brocade 0.62Knives0.02Tissue paper 0.22Browsing fee 0.04Kola0.11Tomato 1.17A.3. WEIGHTS OF SOME ITEMS 155 Weights of Some ItemsItemsWeightItemseightItemsWWeightBucket0.21Labor rate0.01Towel rack0.07Bulb0.05Lace 0.86Turkey 0.14Bungalow 0.01Lamp holder0.03Tuwo0.52Buns 0.02Land-line subscrip-tion and (SIM)0.17TV set 2.80Bus0.11Laundry iron0.26Two bedroom ﬂ at 2.61Cable subscription 0.88Local herbs 0.02Typing sheets 0.04Cake 0.04Luxury bus0.19Tire0.01Canoe 0.01Maize0.52Tire guage0.01Car3.67Malaria drugs 0.22Tire repair0.02Cassava 0.06Male sandals 0.19Universities 0.60Ceiling slate0.09Male shirt0.60Unorthodox clinics 0.01Cement0.14Male shoes 0.87Vegetable 0.97Chairs0.29Male trousers0.41VHS player0.01Chemists 0.13Malt drink0.24Video cassettes 0.05Chicken 1.27Mass transit bus 1.70Video CDs 0.06Children shoes0.09Meat4.75Wall Hanger0.11Children wears0.68Meat/ﬁ sh pies 0.11Wardrobe1.03Cigarettes 0.11Medicated powder0.01Water Closet0.01Cocoa drink 0.47Methylated spirit0.01Water Corporation Charge0.03Cocoyam 0.13Microwave0.18Watermelon 0.07Coﬀ ee 0.07Milk 1.14Wheat0.17Colleges of Education0.74Mini bus1.65Wine 0.13Computer schools 0.51Mini van0.49Wood nail0.03Cooker0.28Miscellaneous 0.40Yam 1.35Cooler0.25Mobile handset1.43Yogurt 0.09Corn Flakes0.12Mobile subscription and (SIM)0.70Cosmetics0.34Money order 0.01Crab 0.03Motor bike0.85Cupboard0.14Motor bike 1.42156 A. QUESTIONNAIRES, ITEMS SURVEY, AND WEIGHTS OF ELEMENTARY ITEMS Weights of Some ItemsItemsWeightItemsWeightItemsWeightCustard0.07Multivitamins 0.03Desktop computer0.62Newspaper/magazine0.34Detergent0.77Noodles0.30Diesel 0.16Notebooks0.18Domestic ﬂ ight 0.01Nursing schools 0.19Doughnuts0.01Ogi0.12Duplex0.01One bedroom ﬂ at 3.29DVD0.01Onions 0.51DVD player0.51Orange 0.48Egg 0.76Others 0.01Electric power 0.90Packaged Juice0.24Electrical wire0.06Palm oil0.72Elementary Textbooks 0.07Pawpaw 0.05Elubo0.33Pencils 0.01Engine oil 0.25Pens 0.02Envelopes 0.01Pepper 0.85Extension box0.10Petrol 3.97Face-to-face 0.76Phone box0.01Fan0.95Pineapple 0.12Fax Service 0.01Pipes 0.01Female sandals 0.13Plank0.06Female shirt0.34Plates0.08Female shoes 0.42Plumbing pipe0.05Female trousers/skirt0.40Polytechnics 0.74Ferry 0.01Pork0.48Fish 3.20Potato 0.38Flour0.01Primary schools 0.94Fluorescent tube0.01Private hospitals 0.38Foodﬂ ask0.04Recharge cards1.22Freezer0.01Rice 2.23Fridge0.84Rod0.03Fufu0.10Rooﬁ ng sheet1.06Gallon0.08Sachet water0.41Garri0.43Salt 0.15Bibliography 157 Desai, N. and D’Mello, L. (2014). An overview on mobile data mining-use the data gener- ated from your mobile phone to obtain useful knowledge. International Journal of Engineering Research and Technology (IJERT), 3(9), pp. 1172–1175. Fixed Income Index Mathematics Methodology, S&P Dow Jones Indices LLC (2017). Gyapong, M., Kamau, E., Najjemba, R., and Ogundahunsi, O. (2014). Disseminating research ﬁndings. World Health Organization Document Production Services, Geneva, Switzerland. Kumar, S. B. and Ramadevi (2016). Survey paper on data mining in mobile devices. International Journal of Advanced Research in Computer and Communication Engineering, 5(6), pp. 331–334. 118 Kaschesky, M., Sobkowicz, P., and Bouchard, G. (2011). Opinion mining in social me- dia: Modeling, simulating, and visualizing political opinion formation in the Web. Proc. of the 12th Annual International Conference on Digital Government Research. DOI: 10.1145/2037556.2037607. Paidi, A. N. (2012). Data mining: Future trends and applications. International Journal of Modern Engineering Research, 2(6), pp. 4657–4663. Rehman, M. H., Liew, C. S., Wah, T. Y., Shuja, J., and Daghighi, B. (2015). Mining personal data using smartphones and wearable devices: A survey. Open Access Sensors, 15(1), pp. 4430– 4469. www.mdpi.com/journal/sensors DOI: 10.3390/s150204430. Tang, L. and Liu, H. (2010). Community Detection and Mining in Social Media. Morgan & Claypool Publishers. DOI: 10.2200/s00298ed1v01y201009dmk003. 105 Tellis, G. J. (2011). Modeling marketing mix. In The Handbook of Marketing Research. SAGE Journals. 110 Zafarani, R., Abbasi, M. A., and Liu, H. (2014). Social Media Mining: An Introduction. Cam- bridge University Press, UK. DOI: 10.1017/cbo9781139088510. 158 BIBLIOGRAPHY Websites Decision Analyst Website (2018). How to build a marketing mix models. https://www.decisionanalyst.com/analytics/marketingmixmodeling/ Cambridge Intelligence Website. https://cambridge-intelligence.com/keylines-faqs-social-network- analysis/ CATALYST Website (2018). How to build a marketing mix model. http://www.catalystinc.com/wp-content/uploads/2015/05/Marketing-Mix- Redesign.pdf International Association for the Measurement and Evaluation of Communication (AMEC), Website. https://www.amecorg.com Author’s Biography 159 MUSTAPHA AKINKUNMI Dr. Mustapha Akinkunmi is a Financial Economist and Technology Strategist. He has over 25 years of experi- ence in estimation, planning, and forecasting using sta- tistical and econometric methods, with particular expertise in risk, expected utility, discounting, binomial-tree valua- tion methods, ﬁnancial econometrics models, Monte Carlo simulations, macroeconomics, and exchange rate modeling. 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He is now an associate professor of ﬁnance and chair of the accounting and ﬁnance department at the American University of Nigeria, Yola, Nigeria.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813428.pdf&bkn=6813427&pdfType=book	S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G Series ISSN: 1939-5221 SERIES EDITOR: Stephen F. Barrett,University of Wyoming LYING BY APPROXIMATION The Truth about Finite Element Analysis Vincent C. Prantil, Milwaukee School of Engineering Christopher Papadopoulos, University of Puerto Rico, Mayag Ÿez Paul D. Gessler, Graduate Student, Marquette University In teaching an introduction to the ﬁnite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the ﬁnite elementmethod to perform parametric studies on potential designs to size parts, weed out less desirabledesign scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many ﬁnite element analysts, in particular, students encountering the method for the ﬁrst time. We present a variety of simple problems in axial, bending, torsion, and shearloading that combine the students’ knowledge of theoretical mechanics, numerical methods, and approximations particular to the ﬁnite element method itself. We also present case studies inwhich analyses are coupled with experiments to emphasize validation, illustrate where interpretations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com w w w . m o r g a n c l a y p o o l . c o m 9 781627 052351 ISBN: 978-1-62705-235-1 90000 P R A N T I L • P A P A D O P O U L O S • G E S S L E R L Y I N G B Y A P P R O X M A T I I O N M O R G A N & C L A Y P O O L LYING BY APPROXIMATION The Truth about Finite Element Analysis Vincent C. Prantil Christopher Papadopoulos Paul D. Gessler S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G Stephen F. Barrett, SERIES EDITOR Lying by Approximation e Truth about Finite Element Analysis Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Lying by Approximation: e Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 e Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 e Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering ermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 iv MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape ermal Optimization Using Bejan’s Constructal eory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and rive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: e DG/K-Based Approach Stephen P. Radzevich 2008 v Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2013 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Lying by Approximation: e Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler www.morganclaypool.com ISBN: 9781627052351 ISBN: 9781627052368 paperback ebook DOI 10.2200/S00503ED1V01Y201305ENG023 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #23 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X ANSYS, Inc. has granted permission for use of the screenshots of ANSYS software results used in this book. ANSYS, ANSYS Mechanical, ANSYS Multiphysics, Workbench, and any and all ANSYS, Inc. product and service names are registered trademarks or trademarks of ANSYS, Inc. or its subsidiaries located in the United States or other countries. All other trademarks or registered trademarks are the property of their respective owners. Lying by Approximation e Truth about Finite Element Analysis Vincent C. Prantil Milwaukee School of Engineering Christopher Papadopoulos University of Puerto Rico Mayagüez Paul D. Gessler Graduate Student, Marquette University SYNTHESIS LECTURES ON ENGINEERING #23 CM&cLaypoolMorganpublishers&ABSTRACT In teaching an introduction to the ﬁnite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the ﬁnite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pit- falls encountered by many ﬁnite element analysts, in particular, students encountering the method for the ﬁrst time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students’ knowledge of theoretical mechanics, numerical methods, and approximations particular to the ﬁnite element method itself. We also present case studies in which analyses are coupled with experiments to emphasize validation, illustrate where interpre- tations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice. KEYWORDS ﬁnite element method, ﬁnite element analysis, numerical methods, computational analysis, engineering mechanics, mathematical modeling, modeling approximation Contents ix 1 2 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi What is Book Is Intended to Be . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Pedagogical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii What is Book Is Not Intended to Be . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Outline of Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Guilty Until Proven Innocent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Guilty Until Proven Innocent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 What a Minimal Requisite Skill Set Looks Like . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 e Ten Most Common Mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Man vs. Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Putting it Together: Toward a New FEA Pedagogy . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Let’s Get Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Qualitative Concepts of Mechanics of Materials . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 e Stress Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Idealized Structural Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 2.3.1 Axial Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Lateral Shear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.3 Bending Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.4 Torsional Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 What Dimension Are You In? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 e Limit of the in (Plane Stress and Pressure Vessels) . . . . . . . . . . . . 24 2.4.2 e Limit of the ick (Plane Strain) . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.3 Analogy of Plane Stress and Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4.4 e Limit of the Round (Axisymmetry) . . . . . . . . . . . . . . . . . . . . . . . . . . 26 St. Venant’s Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Combined Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 A Closing Remark and Look Ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 2.6 2.7 x 3 Where We Begin to Go Wrong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Exceptions to the Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 e Lines in the Sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.1 A Stepped Axial Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.2 A Short, Stubby Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.3 A ick-Walled Pressure Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Utility of the Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3 4 It’s Only a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 e Expectation Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Philosophy of Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.3 e Art of Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 What Are We Approximating? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.5 5.1 5.2 5 Wisdom Is Doing It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.2.1 e Cast of Element Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2.2 Good and Bad Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.2.3 Applying Boundary Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2.4 Applying External Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Further Rules to Live By in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Solution Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Veriﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3 5.4 5.5 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Afterword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Preface xi WHAT THIS BOOK IS INTENDED TO BE In undergraduate engineering curricula, a ﬁrst course in ﬁnite element analysis (FEA) is routinely required, but is often not taken until after the second year of study. Such a class typically includes: 1. an overview of the procedural aspects of the method; 2. a derivation of the mathematical theory for a variety of relatively simple one- and two- dimensional element formulations; 3. practicing the ﬁnite element procedure by hand on select simple problems; and 4. employing the ﬁnite element method using some commercial software package as practiced by engineers in industry. Students are increasingly expected to apply this knowledge in other settings, particularly in the context of their senior capstone design projects. However, students routinely commit a variety of errors in applying FEA. In particular, they lack the maturity to make appropriate modeling decisions and interpretations of their results. is, in turn, inhibits them from using FEA to make sound judgements in their projects. Indeed, the twin abilities to conduct accurate analyses and to make informed judgements lie at the heart of what it means to be a competent professional engineer. Many instructors are aware of this circumstance and recognize the need to coach their students to perform FEA with greater maturity, but they are often mired in teaching strictly according to the treatment of standard textbooks which emphasize underlying derivation and theory. Indeed, there is a need for such deep, rigorous, and detailed study, but not at the expense of learning mature habits. Many professors therefore develop means to teach around the text by providing additional explanations, insights, approaches, and probing questions. Our intent here is to provide just such an alternative resource for professors and instructors of undergraduates who are looking for a fresh and novel approach to teaching FEA that prioritizes the development of practical skills and good habits. Using material compiled from existing course notes and exercises already in use by the authors and their colleagues, we lay a path through the forest of details that an undergraduate or other novice can follow to discover the habits and secrets of a seasoned user. We surmise that in this book already lie many ideas that match what many instructors already intuitively understand and convey as they, on their own, teach around the text. xii PREFACE In laying this path, we deliberately employ an approach to emphasize and exploit the natural ties between classical Mechanics of Materials (MoM) and FEA, and which is motivated, in part, by the philosophy articulated in Papadopoulos et al. [2011]. Of course, equally deep ties exist between elasticity theory and FEA, but as our focus is developing expertise of undergraduates, we appeal primarily to the ties between FEA and MoM. In this approach, we provide examples in which FEA can be used to conﬁrm results of hand calculation, closed form solutions, or standard tables—and vice versa—helping students to build conﬁdence in all. e book then explores more advanced user habits such as formulating expectations, making estimates, and performing benchmark calculations. Broadly speaking, this book responds to the growing call to include simulation as a basic engineering competency, and will help to promote the development of a culture of using simulation in the undergraduate en- gineering curriculum. As such, we envision this book being used as a companion to a traditional textbook in an upper-level undergraduate FEA course and also as an instructional guide for practice in other courses in which FEA is applied, including courses as early as freshman design and introductory mechanics. Even at these early stages, instructors can judiciously draw from the book to plant the seeds of good habits in their students. is book is written in language that is immediately transparent to instructors and accessible to students who have completed a basic course in MoM. Terminologies that might be advanced to the novice user are italicized and explained in the context of their use. PEDAGOGICAL APPROACH e pedagogical strategy of this book is based in the educational theory of constructivism and related research in misconceptions. e essence of constructivist philosophy to which we appeal here is rooted in the work of cognitive psychologist Jerome Bruner, and is succinctly described by Montfort et al. [2009]: “learning [is] a complex process in which learners are constantly read- justing their existing knowledge and, more importantly, the relationships between the things that they know.” Further, this readjustment process requires that the learner not just passively receive information, but actively enter into the “discovery of regularities of previously unrecognized re- lations and similarities between ideas, with a resulting sense of self-conﬁdence in one’s abilities” [Bruner, 1960]. One way to involve students in the processes of readjusting and discovering knowledge is by anticipating their misconceptions and providing exercises and activities that force them to reevaluate their original assumptions and conceptions. For at least three decades, science and engineering educators have realized the importance of identifying and addressing misconceptions, suggesting that educators should directly address misconceptions by some combination of early intervention and an infusion of activities that force students to face the misconceptions head- on [Hake, 1998, McDermott, 1984, Montfort et al., 2009, Papadopoulos, 2008, Streveler et al., 2008]. Broadly speaking, “active learning,” “problem based learning,” “inquiry based learning,” and “student centered learning” approaches aim to accomplish this. Ken Bain, in his book, What the Best College Teachers Do, champions this view: PREFACE xiii Some of the best teachers want to create an expectation failure, a situation in which existing mental models lead to faulty expectations. ey attempt to place students in situations where their mental models will not work. ey listen to student concep- tions before challenging them. ey introduced problems, often case studies of what could go wrong, and engaged the students in grappling with the issues those examples raised [Bain, 2004]. Physics educator Lillian McDermott further adds that “students need to participate in the process of constructing qualitative models and applying these models to predict and explain real-world phenomena” [McDermott, 2001]. It is important to observe that this type of instruction requires a high degree of interaction and feedback on the part of the teacher and a correspondingly high degree of self-inquiry on the part of the learner. In this environment, teachers need to allow students to test ideas, and lend support in tweaking those ideas into a more correct model of how things happen, and students must eagerly participate in this process of discovery. In the spirit of those instructors who have successfully accomplished this, we seek to provide students with the support they need to cognitively rewire. Indeed, many of the examples and exercises are deliberately designed to confront readers with expectation failures and to provide them ample opportunity to develop models that appropriately match reality, but which also require instructors to intervene as supportive mentors. With this approach, novices and students will develop the good habits required of experienced users. In the particular case of FEA, many of the common pitfalls repeatedly encountered by an- alysts are rooted in a mixture of inadequacies in their understanding of MoM theory, modeling, and the useful approximations particular to FEA, as well as their inability to integrate these areas of knowledge. To address these matters, we aim to strike a prudent balance between theory and practical application. We suggest that this is best accomplished by prescribing a minimal requisite skill set, rooted in mastery of MoM, upon which the modeling decisions required in the ﬁnite el- ement method are based. is mastery of the most rudimentary underlying theory helps students make fewer of the errors in judgement when validating their numerical simulations. Ultimately, our emphasis is to provide an instructional approach that is amenable to a prac- ticing engineer rather than a mathematician. We attempt to cultivate the habit of care that is necessary to perform good quality engineering analysis. When answering the question “What is a university for?,” New York Times columnist David Brooks wrote: [to obtain] technical knowledge and practical knowledge. Technical knowledge is for- mulas…that can be captured in lectures. Practical knowledge is not about what you do, but how you do it. It can not be taught or memorized, only imparted and absorbed. It is not reducible to rules; it only exists in practice [Brooks, 2013]. xiv PREFACE In view of this attitude toward practice, we provide guidance for using pre-programmed software. Guidance is oﬀered for both commercial software and academically developed ﬁnite el- ement codes via the online video tutorials found at the wiki site SimCafe (https://confluence. cornell.edu/display/SIMULATION/Home) [Bhaskaran, 2012]. e NSF-sponsored project team at Cornell University [Bhaskaran and Dimiduk, 2010] has graciously supplied ANSYS tu- torials for the collection of illustrative case studies presented here. All tutorials for this book can be found at https://confluence.cornell.edu/display/SIMULATION/Prantil+et+al. In summary, we write this book for student and faculty colleagues who are willing to un- dertake 1. iterative learning in a supportive environment in which students are unafraid to make er- rors, confront misconceptions, and revisit problems, and in which instructors are present to provide support “when things go wrong;” 2. a strong navigational approach that is orderly and progressive, but not necessarily “top down;” and 3. an approach in which MoM theory and FEA are intimately entwined. WHAT THIS BOOK IS NOT INTENDED TO BE Most current textbook treatments of the mathematical theory of ﬁnite elements draw on vari- ational calculus and linear algebra. As suggested previously, we intend this book to serve as a supplement for more advanced undergraduates and as a resource to inform teaching of earlier stage students. Our focus is not on treatment of the mathematical rigor and underpinnings of the ﬁnite element method, but rather a guide to good practice. erefore, this book is not intended to be a reference or text on the formulation, theory, or mathematical underpinnings of the ﬁnite ele- ment method. ere are many excellent treatments outlining the method [Cook et al., 2002, Kim and Sankar, 2009, Logan, 2001, ompson, 2004, Zienkiewicz and Taylor, 2005, Zienkiewicz et al., 2005]. Any one of these would be suﬃcient for an introductory course in an undergraduate mechanical engineering curriculum. is book is also not intended to be a tutorial guide for applying the method or a step-by- step user’s guide to a particular commercial software package, e. g., Kurowski [2013], Lawrence [2012], Lee [2012]. We assume that the instructor using this book is already providing such tutorial instruction or that the reader already has a working knowledge of such. We emphasize, however, that we do provide online video tutorials at the SimCafe wiki site, which include further user guidance and suggested follow-up exercises. We encourage the student or novice reader to open a tutorial or start an FEA session from scratch and directly attempt the exercises and examples that are provided in both the tutorials and the book. PREFACE xv OUTLINE OF BOOK Chapter 1 addresses why humans tend to have an optimism bias in which they think they are correct in more situations than they really are [Conly, 2013]. Digital technology has most likely added to this bias. We review a published list of ten common mistakes made in FEA practice, and we argue that avoidance of these errors begins with the user adopting an attitude of skepti- cism of numerical results until they have been validated. Most analysts agree this is best done by comparison with relevant theory and experimental data. To apply theory, one must be ﬂuent in the very basic mechanics relationships. In Chapter 2 we summarize essential topics from Mechanics of Materials and provide corresponding examples that can be solved using simple, well-known relationships based on one- dimensional modeling assumptions. While these problems do not require use of FEA, they are excellent for oﬀering a ﬁrst exposure to FEA in which the user can quickly build conﬁdence in the method. Moreover, the theory underlying these examples forms the basis for the “minimal requisite skill set” mentioned previously. With this in hand, the user can begin the crucial task of understanding how to interpret FEA results by comparison with a trusted theory. is small set of topics is remarkably useful due to the great number of situations in which they serve as good models for practical situations. However, as problems become more detailed and complex, the applicability of these ele- mentary relations diminishes. Here, a more complex multi-dimensional theory of elasticity may be required but FEA can still be used to obtain reasonable approximate solutions, and basic prin- ciples from Mechanics of Materials can still be applied to interpret results, albeit with caution. erefore, in Chapter 3, we illustrate several examples of problems whose analytical solutions (where tractable) are more involved, and where FEA is eminently useful, although still relatively straightforward. Chapter 4 gets at the core of the list of the common mistakes made when pre-processing the ﬁnite element model. Mistakes that plague many ﬁnite element analysts involve relatively simple errors in input that seem intuitively correct, but which have strong adverse consequences for numerical predictions of displacements and stresses. Finally, in Chapter 5, we present a list of prudent practices as well as pitfalls to avoid in order to achieve meaningful results and to make validation of one’s results a less onerous task. is chapter can serve as an excellent reference as the reader begins to venture in his or her own practice. Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler August 2013 Acknowledgments xvii We gratefully acknowledge Rajesh Bhaskaran, Director of the Swanson Engineering Simu- lation Program at Cornell University, and Robert McBride for providing the ANSYS ﬁnite element tutorials at the wiki site SimCafe (https://confluence.cornell.edu/display/ SIMULATION/Home). We also gratefully acknowledge funding provided to Cornell University un- der Award 0942706 from the National Science Foundation (NSF) for implementation of the SimCafe wiki interface. We greatly appreciate the contributions of Jim Papadopoulos of Northeastern University, who has long been a passionate advocate for introducing FEA practice throughout the under- graduate engineering curriculum. His vision, keen insights, and collaboration on a previous ar- ticle inspired ideas used in this book. We are grateful to him and also to Habib Tabatabai from the University of Wisconsin–Milwaukee for providing a review of an earlier draft of this work which helped us to polish and reﬁne many details. We also acknowledge William E. Howard of East Carolina University. His collaboration on several previous articles linking simulations and experiments formed the basis of several examples in this book. We also express our sincere gratitude to our colleagues Genock Portela Gauthier and Aidsa Santiago Roman of the University of Puerto Rico, Mayagüez. ey are collaborators on a related project sponsored by the National Science Foundation under Award 1044886 that is developing new simulation tools for mechanics courses. Some of the modules developed in this NSF project and related understandings of engineering pedagogy appear in this book. We further acknowledge personal communications and discussion that took place at the 9th U.S. National Congress on Computational Mechanics held in San Francisco in July 2007. Professors Jat du Toit, Mike Gosz, and Göran Sandberg organized the ﬁrst mini-symposium on the teaching of ﬁnite element methods to undergraduates at which some of the ﬁrst ideas for this supplementary text were discussed and took preliminary form. We are grateful to the mini- symposium for both fostering an international debate and proﬀering fruitful discussions leading to this work. Finally, we acknowledge chapter heading character designs illustrated by Tim Decker, Se- nior Lecturer at the Peck School of the Arts at the University of Wisconsin–Milwaukee and Milwaukee Area Technical College. Prior to teaching animation in Milwaukee, Tim was the lay- out artist and animator for the award-winning television series “e Simpsons!,” and animation supervisor for Disney Interactive. He has also appeared as a guest artist in animation and car- tooning for PBS. We are grateful for Tim’s imaginative characterization of numerical analysts practicing the ﬁne art of approximation. xviii ACKNOWLEDGMENTS From Vincent C. Prantil: I wish to dedicate this book to my wife, Laurna, and my children, Carmen and Lorin. eir patience, support, laughter, and love carry me through my journey. ey have also unselﬁshly encouraged and supported the many adventures in my calling as a teacher. I would also like to dedicate this book to my parents, Dolores and Joseph Prantil. ey let me ﬁnd my own way and gave me the wings to follow my dreams. I wish to thank my mentors, Paul Dawson and Anthony Ingraﬀea at Cornell University. eir expertise and dedication to teaching computational methods led me to pursue its pedagogy with enthusiasm. I also thank James T. Jenkins of Cornell University for his unyielding pursuit of excellent theoretical modeling and its use in validating all things numerical. I thank them for, in their own collective words, reminding me to “have fun, keep learning, and to never forget how I thought, how I learned, and how I felt …when I was a student.” I dedicate this book to my students who doubt, prod, question, and keep me young. We travel through the forest together. Finally, I am forever grateful to my Creator who blesses me every day with a mysterious mix of skepticism, faith, failure, humility, humor, energy, and imagination. Ego adhuc cognita. From Christopher Papadopoulos: I dedicate this book to my family, particularly my parents Kimon and Mary Lou. ey provided me with every opportunity to become educated, and all that they have done for me has been motivated by love. I dedicate this book to my sister, Emily, who has inspired me to high academic achievement through her own success, and to Clare, who has been a vital part of my life journey for which I am greatly blessed. I also dedicate this book to my cousin Jim Papadopoulos, who is the lead author of a reference that is frequently cited in this book. I have always admired Jim’s keen mind for mechanics, his dedication to teaching, and his persistence on convincing me of his point of view regarding the need to incorporate FEA practice in my teaching. I thank all of the people who have mentored me in various capacities, particularly my thesis advisor Timothy Healey, undergraduate mentors Sunil Saigal and Omar Ghattas, teachers Dolores Stieper, Susan Spaker, and Richard Piccirilli, and collegial mentors Habib Tabatabai, Yiorgos Papaioannou, and Indira Nair. In their own way, each of them has challenged me, has argued with me, has had patience, and ultimately has supported me in ways that have led to my intellectual and professional growth. To my ﬁrst friends in Puerto Rico, Marcelo Suárez, Jaquelina Alvarez, Basir Shaﬁq, Walter Silva, Ramón Vásquez, and Robert Acar, and many other colleagues, including Marcel Castro, Bill Frey, Héctor Huyke, Sara Gavrell, Luis Jiménez, Aidsa Santiago, and Genock Portela, gracias por darme la bienvenida y que continuemos a trabajar juntos. Finally, I dedicate this book to my many students, from Cornell, Milwaukee, and Mayagüez, who bring me great joy and pride. You are the ones for whom I ultimately write this book. From Paul D. Gessler: I dedicate this book to my grandfather, Donald A. Gessler (1932– 2013). He not only taught me how stuﬀ works, which ignited my interest in engineering, but also never stopped teaching me about how to live life and help others in need, in other words, how the really important stuﬀ works. I would like to thank my parents, Timothy and Shelley, my ﬁancée Elise, the rest of my family, especially brothers Phillip, Peter, and John, and friends and colleagues, especially Marshall Schaeﬀer and Alex Zelhofer. None of my work would be as it is without their inﬂuence, support, and distractions (no matter how unwelcome these distractions sometimes seemed at the time). I would also like to thank my advisor Professor Margaret M. Mathison and the rest of the Marquette University faculty for allowing me to take on this project in addition to my research and graduate coursework. Finally, as always, soli Deo gloria. ACKNOWLEDGMENTS xix Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler August 2013 C H A P T E R 1 1 Guilty Until Proven Innocent I repeatedly tell students that it is risky to accept computer calculations without having done some parallel closed-form modeling to benchmark the computer results. Without such benchmarking and validation, how do we know that the computer isn’t talking nonsense? Clive Dym Principles of Mathematical Modeling If you only make one predictive simulation, it will likely be wrong. Loren Lorig CEO, Itasca International 1.1 GUILTY UNTIL PROVEN INNOCENT One of the many advantages of the ﬁnite element method (FEM) is that it is relatively easy to create a model and use the method to run an analysis. Often, for better or worse, the method has become commonplace enough to be seen as a sophisticated calculator. In addition to enhanced computational speed, this is due to the development and preponderance of graphical user inter- faces (GUI) used as pre- and post-processors to nearly all commercial ﬁnite element software. Yet a great hazard of FEM is also that, with the aid of commercial software, it can be too easy to create a model and run an analysis. e ease of operation can foster “computational complacency” [Paulino, 2000] in validating numerical results. It often appears that the myth that “the computer must be right” is alive and well. While, indeed, algorithms in commercial codes are well debugged and are unlikely to contain programming errors, the user is ultimately responsible for making appropriate modeling assumptions and interpretations of the output. Hand in hand with complacency is the “optimism bias,” in which people tend to believe that they are correct in more situations than they really are [Conly, 2013]. In the context of FEA, even honest users who intend to validate their work might mislead themselves, thinking that results are correct because they appear to correspond to a simple theory that they might be applying inappropriately (for example, out of its bounds of accuracy), or they might be missing 2 1. GUILTY UNTIL PROVEN INNOCENT a key theoretical idea altogether. Like a cancer, computational complacency and the optimism bias can spread. ey can develop into bad habits that thwart the user’s comprehension of some minimal requisite skill set on which use of the numerical method depends. However, before exploring this minimum requisite skill set in detail, the user must ﬁrst realize that he or she should be skeptical toward all results of a numerical simulation until demon- strating a sound reason to accept them. In short, we often tell our students—beginning with the ﬁrst lesson—that, like it or not, algorithmic simulation results are guilty until proven innocent. 1.2 WHAT A MINIMAL REQUISITE SKILL SET LOOKS LIKE Once the analyst understands the need for providing proper input and validating the interpre- tation of output, he or she is ready to learn the fundamental skills that will enable him or her to perform responsible numerical simulations. To motivate this, we ﬁrst provide an analogy with driving an automobile. We can all agree that while a driver need not understand scientiﬁcally the vehicle dynamics or the thermodynamics of the combustion engine, any driver must have a basic sense of how the vehicle and engine operate. For example, braking on ice is less eﬀective than braking on pavement; or maple syrup should not be placed in the fuel tank. Of course it cannot hurt to have some theoretical knowledge, such as to understand that braking distance increases roughly as the square of velocity, or in qualitative terms, “disproportionately.” at is why driving instructors concentrate on teaching elements of automobile acceleration, cornering, smooth braking, and ﬁeld of vision rather than the theory of internal combustion engines. Moreover, the instructor should be seasoned to anticipate and correct errors made by the learner. In the end, the student develops some innate feel for what constitutes “good driving,” and learns to distinguish between “good” and “bad” maneuvers based on experience. Likewise, in the realm of FEA practice, we believe what is called for is the development of a “gut feel” for what constitutes correct behavior and good modeling practice. We contend that the minimal requisite skill set on which good FEA practice is based has two principal components: 1. the ability to apply basic theory of Mechanics of Materials; and 2. the ability to make good modeling decisions, including choice of dimension, element type, mesh discretization, and boundary conditions, based on one’s knowledge of MoM and pre- vious experience. ese requirements are based on the intimate relationship between FEA and the theory of elas- ticity, of which a minimal understanding is constituted by classical Mechanics of Materials. ey also appeal to pedagogical theory that states that confronting misconceptions—particularly when they are deeply held—is an eﬀective means to eventually enable the learner to overcome them and replace them with appropriate conceptions. is anticipates our further remarks in the next sec- tion regarding how to help students confront their misconceptions directly. 1.3. THE TEN MOST COMMON MISTAKES 3 We note that the minimal requisite skill set does not contain an in-depth, rigorous, math- ematical treatment of the theory underlying FEM. Such rigor, while necessary to program al- gorithms or as a prerequisite for graduate studies, is not essential to operate and perform ﬁnite element simulations and correctly interpret their results. For practical applications of FEA, what is imperative is the ability to distinguish between good and bad methods for interfacing with the tool. Note To e Instructor A treatment of the background necessary to use the ﬁnite element method eﬀectively is given by Papadopoulos et al. [2011]. Here we argue that a top-down, theory-ﬁrst emphasis employed in many cur- ricula may not be as necessary as has been thought. We believe that teaching the underlying mechanics can be enhanced by introducing the ﬁnite element method as early as an Introduction to Engineering course in the freshman year. We also feel that hand calculations in Statics and Mechanics of Materials can be reinter- preted and made more appealing by emphasizing them as steps used to validate and benchmark numerical simulations. Finally, in an upper division course in ﬁnite element theory, one may undertake a deeper learn- ing of how to perform an informed computational analysis under the tutelage, guidance, and support of a seasoned, experienced practitioner. 1.3 THE TEN MOST COMMON MISTAKES Computational models are easily misused…unintentionally or intentionally. Boris Jeremić University of California Davis In accordance with our proposed minimal requisite skill set, we now present a useful list of com- monly committed errors in FEA practice. While the advanced user will likely recognize many of these errors (hopefully through direct experience!), the novice who has little or no FEA experi- ence might not fully appreciate their meaning at this point. Nevertheless, they serve as a good preview of issues that will arise, and as a reference to which the novice may return as he or she gains more experience. Recently, Chalice Engineering, LLC [2009] compiled an assessment of mistakes most commonly made in performing ﬁnite element analysis in industrial practice. After 10 years of col- lecting anecdotal evidence in both teaching undergraduates and advising capstone design projects, we found this list to be nearly inclusive of the most common errors encountered by undergrad- uate students in their introductory ﬁnite element method course. e list published by Chalice Engineering is reproduced here verbatim. 4 1. GUILTY UNTIL PROVEN INNOCENT 1. Doing analysis for the sake of it: Not being aware of the end requirements of a ﬁnite ele- ment analysis—not all beneﬁts of analysis are quantiﬁable but an analysis speciﬁcation is important and all practitioners should be aware of it. 2. Lack of veriﬁcation: Not having adequate veriﬁcation information to bridge the gap be- tween benchmarking and one’s own ﬁnite element analysis strategy. Test data some- times exists but has been forgotten. Consider the cost of tests to verify what the analysis team produces, compared with the potential cost of believing the results when they are wrong. 3. Wrong elements: Using an ineﬃcient ﬁnite element type or model, e. g., a 3D model when a 2D model would do, or unreliable linear triangular or tetrahedra elements. 4. Bad post-processing: Not post-processing results correctly (especially stress) or consis- tently. Not checking unaveraged stresses. 5. Assuming conservatism: Because one particular ﬁnite element analysis is known to be conservative, a diﬀerent analysis of a similar structure under diﬀerent conditions may not be so. 6. Attempting to predict contact stresses without modeling contact: is might give sensible-looking results, but is seldom meaningful. 7. Not standardising ﬁnite element analysis procedures: is has been a frequent cause of repeated or lost work. Any ﬁnite element analysis team should have a documented stan- dard modeling procedure for typical analyses encountered within the organisation, and analysts should follow it wherever possible. Non-standard analyses should be derived from the standard procedures where possible. 8. Inadequate archiving: Another frequent cause of lost work. Teams should have a master model store and documented instructions about what and how to archive. Again, this is a quality related issue. For any kind of analysis data, normal backup procedures are not suﬃcient—attention needs to be paid to what information and ﬁle types are to be archived in order to allow projects to be retraced, but without using excessive disk space. 9. Ignoring geometry or boundary condition approximations: Try to understand how in- appropriate restraint conditions in static or dynamic analyses can aﬀect results. 10. Ignoring errors associated with the mesh: Sometimes these can cancel out errors asso- ciated with mistake 9, which can confuse the user into thinking that the model is more accurate than it is. A convergence test will help. 1.4. MAN VS. MACHINE 5 While it may come as no surprise, novice users commit many, if not all, of these errors. But these errors continue to be committed routinely even by advanced users and engineers in industrial practice. As suggested earlier, we attribute this to a lack of a minimal requisite skill set (or an inability to apply such ﬂuently). is lack of understanding is due, at least in part, to computational complacency [Paulino, 2000] and the optimism bias [Conly, 2013] cited earlier. Avoiding such errors is not simply a matter of telling and re-telling the student “how to do it.” Most students learn by repeated attempts in the face of incorrect reasoning and results. It is through repeated corrections in the face of practice that we learn, not simply by being presented with how things ought to work. erefore, before a sense of good modeling practice can truly be learned and internalized, the student must come to appreciate the value of being skeptical about initial numerical simulations, i. e., that they are guilty until proven innocent. Students must realize and care that their intuition might be incorrect. en they must actively work to deconstruct their previously incorrect model, and replace it with a model with deeper understanding. Likewise, the good instructor must provide a supportive environment in which students are encouraged to explore problems in which they are likely to make errors, and then coach them to be self-critical, to realize and understand the errors that they have made. Indeed, as suggested by the attention on student misconceptions in the literature on peda- gogy [Hake, 1998, McDermott, 1984, Montfort et al., 2009, Papadopoulos, 2008, Streveler et al., 2008], when students are forced to work out a problem with judicious questioning and investiga- tion where their initial reasoning was incorrect—again, in Ken Bain’s words, an expectation failure [Bain, 2004]—their learning retention is greater, and their recall and critical thinking skills are enhanced. We take up this point further in the last section of this chapter when we recommend our pedagogical strategy for FEA. 1.4 MAN VS. MACHINE It’s foolish to swap the amazing machine in your skull for the crude machine on your desk. Sometimes, man beats the machine. David Brooks e New York Times It is noteworthy that many introductory texts for the study of ﬁnite element analysis make use of some form or the other of the necessary procedural steps in applying the method in practice. en students are provided exercises in applying these procedural steps by means of hand calculations. e procedural steps that a typical ﬁnite element analysis should include are as follows: Ask what the solution should look like: An analyst must have some idea of what to expect in the solution, e. g., a stress concentration, and other characteristics of the solution, such as symmetry. 6 1. GUILTY UNTIL PROVEN INNOCENT Choose an appropriate element formulation: One needs to understand, from knowledge of the expected solution, what elemental degrees of freedom and polynomial order of approxima- tion are necessary to accurately model the problem. Mesh the global domain: With knowledge of the expected solution and the chosen order of in- terpolation—the estimation of the solution at a general location based on the computed solution at the grid points of the mesh (the order of which could be linear, quadratic, etc.), one can wisely select a number and arrangement of elements necessary to adequately capture the response. Deﬁne the strain-displacement and stress-strain relations: It is important to know what for- mulation your commercial software code has programmed into the analysis module. Clas- sical small strain relations are appropriate for linear, static stress analysis. e user must provide a constitutive law relating stress and strain. Compile the load-displacement relations: e element matrix equations are either derived in closed form a priori or computed via numerical integration within the analysis code. Assemble the element equations into a global matrix equation: is step is performed algo- rithmically with knowledge of the element degrees of freedom and nodal connectivity. is global equation relates externally applied conjugate forces and associated nodal point de- grees of freedom. It represents a generalized form of nodal point equilibrium. Apply loads and boundary conditions: Because there are multiple prescriptions of statically equivalent loads and boundary constraints, their precise prescription must be justiﬁed based on problem symmetry and proximity to internal regions where accurate stress results are most desired. Solve for the primary nodal degrees of freedom: Solve the appropriately reduced global matrix equation. Solve for the derivatives of primary degrees of freedom: is involves calculating generalized reaction forces at nodes and strains and stresses within elements. Interpret, verify, and validate the results: Based on comparisons with initial expectations, ex- perimental data, analytical benchmark results, or other reputable numerical solutions, have the calculated results converged and are they reasonable? Again, the novice might not completely understand or appreciate the meaning of each step at this time. However, he or she can still gain some sense and insight into the procedure. In particular, it is very telling that the steps break down succinctly into those performed by the analyst and those performed by the computer. Even the novice will appreciate the complementary roles of the human and the machine from the very outset. 1.5. PUTTING IT TOGETHER: TOWARD A NEW FEA PEDAGOGY 7 With the advent of high speed computers, it is clear that the machine wins in the battle of raw speed and avoidance of computational error. However, while speed and computational accuracy are necessary, they are not suﬃcient—and not even most important—for producing good FEA results. e machine cannot provide the intellect, strategy, and judgement of the human mind, all of which are crucial to perform good analysis. e myth that the “computer is always right” comes, in part, from the truth that yes, most commercial ﬁnite element software has been suﬃciently debugged, removing most or all internal programming errors. Studies by Jeremić [2009] show that programming errors in commercial codes persist only in a very small percentage of cases. In short, the computer, while working fast, also works nearly ﬂawlessly. It can therefore do the “heavy lifting” required to analyze complex problems that lead to the solution of problems with thousands and even millions of degrees of freedom. But most errors encountered in ﬁnite element analysis are either due to incorrect user input, i. e., garbage in—garbage out, or due to lack of prudent judgement regarding dimensional approx- imations, active degrees of freedom, loading strategy, sensitivity to boundary conditions, or the nature of the correct theoretical solution. at is, they can often be traced to one of two causes: incorrect understanding of ﬁnite element modeling, or poor application of strength of materials, and often both to varying degrees. In most cases, therefore, it is operator error to blame for all of the top ten mistakes [Chalice Engineering, LLC, 2009]. To correct these mistakes, the analyst must look for cause and eﬀect. And as remarked, most often, the code is not the cause, although sometimes the user should inves- tigate if the model programmed in the algorithm is, in fact, the correct model for the application at hand. us, when the task at hand can be described in an eﬃcient and robust algorithmic form, the task should be owned by the machine. In those instances where the task requires judgement and/or compromise, the mind trumps the processor. And this is where the practice of numerical analysis most often goes awry. It perhaps comes as no surprise that the ten most commonly made mistakes are found only in the procedural steps performed by the analyst and none involve the steps performed algorithmically by the computer. is glaring reality is the driving force behind our novel approach to learning the ﬁnite element method wherein we focus on user behaviors rather than on derivations of algorithms. 1.5 PUTTING IT TOGETHER: TOWARD A NEW FEA PEDAGOGY We have reviewed common errors and standard procedure, in which we emphasize the need for the analyst to be skeptical and to take responsibility for making good judgements. Recalling our overall pedagogical philosophy based on constructivism and encounter of misconceptions, we now outline our vision of a new FEA pedagogy that prioritizes user behaviors. We draw from our own notes and examples to provide a set of exercises and case studies in which students can encounter 8 1. GUILTY UNTIL PROVEN INNOCENT common errors and expectation failures in a safe environment, and in which they can iteratively address and correct their misconceptions. We promote three eﬀective approaches to ferreting out these misconceptions: 1. utilizing case studies that present commonly encountered expectation failures in students’ understanding of mechanics; 2. identifying speciﬁc user input, reasoning, or post-processing decisions that result in the speciﬁc misunderstanding of the problem at hand; and 3. validation of results, such as by performing repeated convergence studies to verify numer- ical simulations, comparison with benchmark solutions, or comparison with experimental results. We strongly believe that for the novice user, it is prudent to focus on the procedural steps that require interaction, judgement, and interpretation, particularly through repeated experience confronting errors and making corrections. is is in contrast to traditional approaches in which a signiﬁcant amount of classroom time is spent teaching the underlying mathematical formulation of routines that are ultimately performed without error by the computer, such as rote calculation of element stiﬀness matrices, assembly of global stiﬀness matrices, and solution of the principal degrees of freedom. While we think it is important for students to know that such internal computations are made, deriving such procedures should not be done at the expense of providing repeated expe- riences in which students encounter and correct the errors and misconceptions that we already know they will make. Rather, we believe this time would be better spent on discussions of, say, how stresses vary within and between neighboring elements, and if the modeler’s decision cap- tured this behavior correctly. As misconceptions are overcome, and good procedural habits and intuitions are formed, then the student is all the more pre-disposed to learning and appreciating important aspects of the underlying theory at later stages in their education. In summary, we boil everything down to four concurrent practices. 1. Introduce students to the ﬁnite element method much earlier in their curriculum [Pa- padopoulos et al., 2011], e. g., in elementary Mechanics of Materials. 2. Focus on applications that illustrate and highlight common pitfalls and ways to circumvent them, e. g., choosing proper element formulations, correctly prescribing boundary condi- tions, and validating solution results. 3. Keep mathematical derivations to a minimum and focus these primarily in areas directly related to mechanics principles, e. g., equilibrium and approximation by interpolation. 4. Highlight a succinct list of commonly accepted good and bad practices in applications of ﬁnite element analysis. 1.5. PUTTING IT TOGETHER: TOWARD A NEW FEA PEDAGOGY 9 We note in closing that there is a growing body of work on what modelers feel is appropriate skepticism with which preliminary simulation results should be judged in both academic and industrial environments. ere are a variety of research ﬁndings on the teaching of ﬁnite element analysis to undergraduates [du Toit et al., 2007], computational complacency [Paulino, 2000], and the reliability of simulation results [Hatton, 1999] which the reader may wish to further explore. C H A P T E R 2 Let’s Get Started 11 Seek the model which is simple, but not too simple. Albert Einstein Essentially, all models are wrong, but some models are useful. George E.P. Box Professor Emeritus, University of Wisconsin Note To e Instructor Here we detail the kind of knowledge, rooted in Mechanics of Materials, that is important for using FEA eﬀectively. While some ﬁnite element theory is important, it should not be considered to be a barrier to the early incorporation of FEA in the curriculum; rather, the requisite knowledge is meant to be built throughout the curriculum as the undergraduate student advances. Mechanics educators and practitioners have absorbed some concepts so well that it is easy to forget that these concepts are relatively new to students. Many technical areas must be learned in order to interpret FEA results, catch modeling errors, and guide design. One essential kind of knowledge is comprised of concepts, simplifying physical assumptions, and critical thinking that takes place throughout the undergraduate engineering curriculum. We do not advocate that students learn less mechanics theory. With the advent of powerful analysis tools, we speciﬁcally advocate that students should learn as much if not more—a holistic approach that promotes a qualitative understanding of “what aﬀects something else,” an expanded grasp of deﬁnitions and core concepts. In the Preface and Chapter 1, we proposed that the kind of knowledge that is important for using FEA eﬀectively falls into two categories: 1. the ability to apply basic theory of Mechanics of Materials to formulate initial expectations of results and related estimates, and to interpret or benchmark results and 2. the ability to make good modeling decisions, including choice of dimension, element type, mesh, and boundary conditions, based on knowledge of MoM and previous experience. In this chapter we explore the ﬁrst of these categories, namely the synergy between Me- chanics of Materials and Finite Element Analysis. We begin this chapter with a bird’s eye view of some qualitative aspects of MoM that the reader should begin to appreciate, followed by a review 12 2. LET’S GET STARTED of what we regard are the minimum essential elements of MoM theory required to undertake study of FEA. We close with two examples that can be solved by hand calculation as a means to illustrate the ﬁnite element method. Some colleagues are concerned that use of FEA in early courses might supplant a strong understanding of Mechanics of Materials principles because the eﬀort normally done by hand can now be done by “pressing a few buttons.” We insist that this is neither our point of view nor a circumstance that is likely to occur under a pedagogy that is committed to ensuring that students form good habits of understanding modeling assumptions and validation procedures. We insist that use of FEA requires even more theoretical understanding so that it can be applied with skill. e usual adjuration to “calculate problems ﬁrst by hand” can then be re-interpreted as “take steps to validate and benchmark your FEA solution.” 2.1 QUALITATIVE CONCEPTS OF MECHANICS OF MATERIALS Here we present a list of qualitative concepts that can be read at once by novices and experts, motivated by ideas presented in [Papadopoulos et al., 2011]. While the expert will recognize many of these ideas from experience, the novice can begin to appreciate the qualitative concepts and ideas that a more seasoned practitioner uses with conﬁdence and ﬂuency. We recommend that students periodically return to this list after doing some of the example problems so that they can develop a better feel for how these ideas appear in practice. e presence of this list at the beginning of the chapter should not be interpreted to mean that the student must master this list all at once on ﬁrst reading. Rather, practice itself is what will help the student to internalize these ideas and develop the ﬂuency of an expert. is list of qualitative concepts is as follows. • All structures, no matter how strong, are deformable at least to a small degree. is means that when loads are applied, the material points in the structure move or displace. Many structural elements can be modeled as simple springs as a means to understand the relation- ship of force to displacement in the structure. • Studying the exact geometry of a structure and its actual displacements under loading can be very complicated with many resulting equations being nonlinear. In many structures of practical interest, however, the displacements will remain small compared to the overall size of the structure, and simple small displacement approximations can be made that lead to simpler, linear relations. Such linearity renders the ability to superpose basic solutions, or to scale any solution in load or overall size. • One has the ability to interpret a result in terms of basic ideas or elementary asymptotic solutions. For example, the bending moment transmitted by a cross section; the force and moment equilibrium of loads plus reactions; the maximum bending or twisting strain at an outer ﬁber; and rigid body degrees of freedom of a body or system. 2.2. THE STRESS TENSOR 13 • Stress is a tensor, a directional speciﬁcation of tractions across arbitrarily oriented surfaces. Principal directions exist on surfaces where the shear stress vanishes. ere are no tractions on a free surface, so principal directions are parallel to the surface, and sometimes predictable from symmetry. • For isotropic material failure, we can ignore stress orientation and use a scalar invariant as a failure metric. • e source of stress concentrations is based on speciﬁc geometric features, such as re-entrant corners or cavities. • Structures with a single load path are determinate, and the resultants are known from the load. Structures with multiple load paths are indeterminate, e. g., springs in parallel share the load. Adding material generally increases the load carried by a support, and perhaps even its peak stress. • Indeterminate structures are often called redundant. ey obey the laws of static equilib- rium, but these equations alone are insuﬃcient to determine the force distribution in the system. Additional equations enforcing compatibility are necessary. ese describe how the displacements of material points in the structure must behave in order for the structure to remain intact. • An idealized pinned support neglects modest moments that exist in the actual physical structure. Similar idealizations hold when modeling other classical localized boundary con- ditions such as built-in or compliant constraints. • Analysts must be aware that the world is not rigid, and particularly that prevention of lateral strain is not always realistic. • When calculating stress, users should exploit St. Venant’s principle, i. e., it may be possible to ignore the actual compliance of an end support suﬃciently far away from the point of load application. 2.2 THE STRESS TENSOR In Mechanics of Materials, one is introduced to the basics of stress and strain and their relation in Hooke’s Law. Recall that external loads on a structure produce internal forces and moments that result in internal stresses. e concept of stress describes how reactions of the structure to external loads are distributed across arbitrarily-oriented planes in the structure. Recall that there are fundamentally two basic types of stress: (i) normal stress, (cid:27), and (ii) shear stress, (cid:28), as illustrated in Fig. 2.1. Although it is common to refer to “bending stress,” “torsional stress,” “bearing stress,” “sin- gle shear,” “double shear,” “punching shear,” etc., we emphasize that these names do not represent 14 2. LET’S GET STARTED Figure 2.1: e concept of normal and shear stress and strain components is illustrated on inﬁnitesi- mal volumes. other basic kinds of stress; rather, they are names assigned to internal stresses speciﬁc to commonly studied load cases. All types of stress ultimately can be classiﬁed as either normal or shear. Normal stresses result from: 1. axial loads and deformation of prismatic rods or bars, 2. transverse loads, moments, and the associated curvature in prismatic beams, and 3. approximations of bearing stress. Shear stresses result from: 1. transverse shear forces and the associated lateral deformations in prismatic beams, 2. torsional loading and rotational deformation in prismatic shafts, and 3. approximations in single shear, double shear, and punching shear. 2.3 IDEALIZED STRUCTURAL RESPONSES eories are like maps; the test of a map lies not in arbitrarily checking random points, but in whether people ﬁnd it useful to (use it to) get somewhere. Ronald Giere Perhaps you have noticed that many of the problems studied in an elementary Mechanics of Materials course consist of highly regular structural forms: rods or bars with uniform cross section; circular shafts and pipes; and beams with uniform and prismatic cross sections. Perhaps you never /PSNBM4IFBSOUFSOBM'PSDF(cid:9)4USFTT(cid:10)%FGPSNBUJPO(cid:9)4USBJO(cid:10)thought much about just how simple these forms are, but they possess twin properties almost akin to a lucky accident of nature: 2.3. IDEALIZED STRUCTURAL RESPONSES 15 1. they possess simple closed form stress-strain and load-displacement relationships that are amenable to hand calculations and 2. they are widely useful and applicable in countless examples of engineering design and con- struction. Indeed, the determination of internal stresses in these basic elements follows very simple anal- ysis that is highly accurate. Whether it is obvious or amazing that these common forms should succumb to such simple analysis can be debated by the philosophically inclined. Regardless, this wonderful situation enables engineers to prescribe the use of these objects widely with a high degree of conﬁdence in understanding their behavior. We now review these basic forms in detail. 2.3.1 AXIAL RESPONSE A long slender bar, subjected only to axial end forces, and whose weight is neglected is a ‘two force member’ whose internal forces are parallel to the bar itself. Bars are further assumed to undergo small displacements and exhibit negligible out-of-plane eﬀects, i. e., we assume no change in the cross-sectional dimensions as the material element deforms under normal stress. e internal normal stress can be produced by tensile and compressive axial forces, P , that act purely normal to the cross section as shown in Fig. 2.2. e value of this stress, denoted by (cid:27)axial, is a normal stress given by the well-known relationship (cid:27)axial D In addition, the axial displacement of a long bar of length L under uniform load P is given by : P A (cid:14)axial D PL AE : 2.3.2 LATERAL SHEAR RESPONSE One way that a shear stress can be produced is by distributing a lateral (or transverse) force, V , in the plane of a cross section, as shown in Fig. 2.3. is stress will not, in general, be uniform over the cross section. However, for certain regular shapes its intensity can be estimated using the well-known formula (cid:28)lateral D VQ I t ; where V is the resultant of the lateral force vectors, I is the second area moment of the cross section, and Q and t are, respectively, the ﬁrst area moment of the cross section and thickness 16 2. LET’S GET STARTED Figure 2.2: Average normal stress distributions in a bar due to axial load on faces perpendicular to the load. (or width) of the cross section at the location where the stress is being evaluated. Because the calculation of Q is sometimes involved, an approximation for the maximum shear stress in the section due to this type of loading can be easily obtained by knowing the shape of the cross section, where, for instance (cid:28)lateral, max D ( 4V 3A 3V 2A for circular cross sections, for rectangular cross sections. Figure 2.3: Shear traction is distributed perpendicular to the normal of the cross section. 2.3.3 BENDING RESPONSE Both tensile and compressive normal stresses can also be caused by bending moments, as shown in Fig. 2.4. If the beam has a prismatic section and is symmetric about the transverse plane, the pure bending assumption that ‘plane sections remain plane and normal to the neutral axis’ can be /PSNBM4USFTT4IFBS4USFTT2.3. IDEALIZED STRUCTURAL RESPONSES 17 applied to yield the well-known formula to predict the bending stress at a given distance from the neutral axis: (cid:27)bending D My I ; where M refers to the resultant moment, I represents the cross-sectional property known as the area moment of inertia about an axis passing through the centroid of the cross section, and y represents the distance from the neutral axis toward the outer edge of the cross section where the stress is being evaluated. e displacement of a beam due to a transverse loading can be determined Figure 2.4: Stress distribution due to bending loads varies linearly through the cross section. by integrating the fourth-order diﬀerential equation d4 v d x4 D (cid:0) w EI ; where E is the modulus of elasticity and w is the load per unit length applied transversely to the beam. is basic theory of beam bending is often referred to as Euler-Bernoulli beam theory. 2.3.4 TORSIONAL RESPONSE Shear stresses can also develop when a torque is applied to a shaft. If the shaft is circular or annular in cross section, it can be assumed that cross sections remain parallel and circular. From this assumption, the shear stress due to torsion can be predicted at a point at a given radial distance, (cid:26), away from the center by the well-known formula (cid:28)torsion D T(cid:26) J ; where T is the total torque carried by the section and J is the polar moment of inertia of the cross section. ese stress components are illustrated in Fig. 2.5. Under these conditions, the axial twist (sometimes referred to as angular displacement) along such a shaft of length L can be calculated from the formula where G is the modulus of rigidity. (cid:18) D T L GJ ; /FVUSBM"YJT$PNQSFTTJWF4USFTT5FOTJMF4USFTT18 2. LET’S GET STARTED Figure 2.5: Internal stresses due to torsion loads are distributed as shear tractions. Example 2.1: Simple Truss Analysis A weight is suspended by three bars as shown in Fig. 2.6. All three bars are made of 5000 lbf. 12 in, the diameter of each bar is 0:5 in, and W steel, a D Determine the force carried by each bar. 16 in, b 12 in, c D D D Figure 2.6: A three-bar structure supporting a weight forms an indeterminate truss. A Free Body Diagram (FBD) of point P reveals that there are three unknown forces, as shown in Fig. 2.7. I yxabcQRSW(0;0)PExample 2.1: Simple Truss Analysis (continued) 2.3. IDEALIZED STRUCTURAL RESPONSES 19 Figure 2.7: Free body diagram of point P with bar angle conventions. However, there are only two equations of static equilibrium: X Fx X Fy W W FPQ cos (cid:18)PQ FPQ sin (cid:18)PQ C C FPR cos (cid:18)PR FPR sin (cid:18)PR FPS cos (cid:18)PS FPS sin (cid:18)PS C C 0; W; D D where the angle for each bar is measured in the counterclockwise direction from the pos- itive x-axis. Such a system is called statically indeterminate because the equations of static equilibrium are insuﬃcient to determine the forces in the structural elements. Analysis of a statically indeterminate system requires additional equations that account for the structural deformation, i. e., how the bars deform under their applied load. Inverting the force-displacement relation from Section 2.3.1, F .EA=L/(cid:14), where E is the modulus of elasticity, A is the cross-sectional area of the bar, and L is the (initial) length of the bar, allows us to interpret each bar as a spring with equivalent stiﬀness D EA L : k D Denoting the stiﬀness of each bar by kPQ, kPR, and kPS , and the deformation of each bar by (cid:14)PQ, (cid:14)PR, and (cid:14)PS , we can rewrite the equilibrium equations as follows: X Fx X Fy W W kPQ(cid:14)PQ cos (cid:18)PQ kPQ(cid:14)PQ sin (cid:18)PQ C C kPR(cid:14)PR cos (cid:18)PR kPR(cid:14)PR sin (cid:18)PR kPS (cid:14)PS cos (cid:18)PS kPS (cid:14)PS sin (cid:18)PS C C 0; W: D D I PFPQFPRFPSWxPPQPRPS20 2. LET’S GET STARTED Example 2.1: Simple Truss Analysis (continued) After the load is applied, the point P , which is initially located at .0; 0/, will move to a new location P 0. We use u and v to denote, respectively, the horizontal and vertical components of the displacement from point P to point P 0, as illustrated in Fig. 2.8. Note that by convention, we have illustrated the case such that u > 0 and v > 0, but in general, one or both of these values could be negative. Figure 2.8: e structure deforms and point P displaces as the load is applied. As suggested by Fig. 2.8, both the length and direction of each bar change after the load is applied. However, under many common circumstances, the displacements are small enough such that the change in direction is negligible. erefore we will assume, as an approximation, that each deformed bar is parallel to its original position. is is illustrated in Fig. 2.9 which shows initial and deformed positions of the bar PS near point P , and how the deformation (cid:14)PS is geometrically related to the displacements u and v. I yxabcQRSW(0;0)PP0Example 2.1: Simple Truss Analysis (continued) 2.3. IDEALIZED STRUCTURAL RESPONSES 21 Figure 2.9: e displacement (cid:14)PS is comprised of components along x and y directions. Using basic trigonometry, the deformation of the bar (cid:14)PS is related to the displacement of P 0, .u; v/, by the equation (cid:14)PS (cid:0) D u cos (cid:18)PS C v sin (cid:18)PS : Note the negative sign in front of (cid:14)PS accounts for the convention that positive (cid:14) corresponds to the bar getting longer, but in Fig. 2.8, the bar is contracted. Because the kinematic description of each bar is standardized (Fig. 2.7), the equations for the other two bars are similar without requiring separate derivations: (cid:14)PR (cid:14)PQ (cid:0) (cid:0) D D u cos (cid:18)PR u cos (cid:18)PQ C C v sin (cid:18)PR v sin (cid:18)PQ : ese equations are called compatibility equations because the deformations must be compat- ible so that all bars remain connected at point P 0. In summary, we now have ﬁve equations for the ﬁve unknown variables (cid:14)PQ, (cid:14)PR, (cid:14)PS , u, and v. Notice also that these equations are linear in these variables. is is a consequence of our use of the approximation that the direction of each bar remains unchanged. For this example, we have in mind that the reader will solve the ﬁve equations using a numerical solver such as M or Excel, and then develop a model of this problem using a commercial FE solver. We recommend assembling the structure using beam or bar elements. Depending on the reader’s experience with FEA, it may or may not be clear that both equilibrium and compatibility conditions are simulta- neously enforced as part of a displacement-based ﬁnite element analysis. In our model, using one-dimensional bar (or truss) elements in ANSYS, the ﬁnite element method obtains the theoretical solution exactly (up to machine precision): the bar forces are 1287:5 lb in bar PQ, 3197:5 lb in bar PR, and 1456:6 lb in bar PS; the displacements of the loaded point P 0 I PP0uvPS+ıPS(cid:0)ıPS22 2. LET’S GET STARTED Example 2.1: Simple Truss Analysis (continued) 6:00 are u D (cid:0) post-processing the ﬁnite element results, as shown in Fig. 2.10. 10(cid:0) 10(cid:0) 6:74 4 in and v D (cid:2) (cid:2) 3 in. e deformed shape can be illustrated by Figure 2.10: e structure deforms and point P displaces as the load is applied. e ﬁnite ele- ment result matches the exact result for nodal displacements and bar forces. is example is adapted from Papadopoulos et al. [2013] with permission. 2.4 WHAT DIMENSION ARE YOU IN? e distribution of stress, strain, and displacement in an elastic body subject to prescribed forces requires consideration of a number of fundamental conditions relating material constitutive laws, material properties, geometry, and surface forces. 1. e equations of equilibrium must be satisﬁed throughout the body. 2. A constitutive law relating stress and strain must apply to the material, e. g., linear elastic Hooke’s law. 3. Compatibility must hold, i. e., the components of strain must be compatible with one an- other or the strain must be consistent with the preservation of body continuity. is is a critical matter for FEA that is not always discussed in mechanics of materials. 2.4. WHAT DIMENSION ARE YOU IN? 23 4. e stress, strain, and deformation must be such as to conform to the conditions of loading imposed at the boundaries. Realistically, all problems are three-dimensional, but satisfying all the conditions outlined above can quickly become intractable. Indeed, closed form solutions to three-dimensional bound- ary value problems in linear elasticity can be very involved or even impossible. When possible, it is wise to take advantage of simpliﬁcations in which the displacement , stress, or strain ﬁelds take on a one- or two-dimensional nature. ese opportunities aﬀord themselves when a lower dimensional model captures enough of the essential behavior. For instance, in Example 2.1, we tacitly recommended that the 3-bar structure be modeled with beam or bar elements. is was natural enough, but to elaborate, we assumed that behaviors such as lateral contraction of the bars via the Poisson eﬀect, bending, or other stresses not directed along the axes of the bars were negligible. us, a model that resembles the behavior of a simple axial bar, and its correspondingly simple behavior as described in Section 2.3.1, is suﬃcient. It is unnecessary to develop a ‘true’ three-dimensional model that is more complicated. In general, when modeling, the metaphor to not ‘throw the baby out with the bathwater’ is apt. e ‘baby’ is that which is essential, i. e., the dominant mechanics that we choose to keep in the model, such as the dominant axial behavior of the bars in Example 2.1. e ‘bathwater’ is all of the other mechanics that we choose to neglect, such as the lateral eﬀects in the bars of Example 2.1. ere are several other important situations in which it is appropriate to simplify the dimen- sionality of a problem. is is evidenced when we realize that simple beam deﬂection solutions resolve only the deformed shape of the neutral axis of the beam cross section. Indeed, in the simplest beam bending theory that was reviewed in Section 2.3.2, referred to as Euler-Bernoulli theory, the formulae for axial bending stress and maximum deﬂection are suﬃcient in the limit as the beam length dominates over the remaining two cross-sectional dimensions. In other words, Euler-Bernoulli beam theory holds only in the limit as the beam becomes “long and slender.” e simplest bending relations become progressively more insuﬃcient as the cross-sectional dimen- sions grow and are no longer small compared with the beam’s length. In this limit, one can argue that the beam becomes ‘hopelessly three-dimensional.’ Other opportunities aﬀord themselves when two dimensions, say in a plane, are either com- monly large or small compared with an out-of-plane dimension. In this limit, we have been taught two-dimensional planar solutions for plane stress, plane strain, and axisymmetric conditions. We explore these situations in the following sections. 24 2. LET’S GET STARTED 2.4.1 THE LIMIT OF THE THIN (PLANE STRESS AND PRESSURE VESSELS) ere are many problems of practical importance in which the stress conditions are ones of plane stress. is occurs often in thin members, as shown in Fig. 2.11. In this limit: 1. e stress components (cid:27)x, (cid:27)y, and (cid:27)z do not vary through the thickness, i. e., they are functions of x and y only. 2. Externally applied forces are functions of x and y only. 3. e out-of-plane stress components are identically zero, i. e., (cid:27)z (cid:28)zx (cid:28)zy 0 0 0: D D D (cid:28)xz (cid:28)yz D D For such cases in FEA, a two-dimensional solid or continuum plane stress element is used. Figure 2.11: A state of plane stress will often result in thin sections with loads applied in the plane. 2.4.2 THE LIMIT OF THE THICK (PLANE STRAIN) ere are many problems of practical importance in which the strain conditions are ones of plane strain. For long, prismatic members subject to lateral loading in the x-y plane, as shown in Fig. 2.12, a state of plane strain will result. In this limit: xyyzyx)(xyOTyTx1. e strain components do not vary through the thickness, i. e., they are functions of x and 2.4. WHAT DIMENSION ARE YOU IN? 25 y only. 2. Externally applied forces are functions of x and y only. 3. e out-of-plane strain components are identically zero, i. e., (cid:15)z (cid:13)zx (cid:13)zy 0 0 0: D D D (cid:13)xz (cid:13)yz D D For such cases in FEA, a two-dimensional solid or continuum plane strain element is used. Figure 2.12: A state of plane strain will often result in thick sections with loads applied in the plane. 2.4.3 ANALOGY OF PLANE STRESS AND PLANE STRAIN For similar cross sections, a solution derived for plane stress is strictly analogous to those for plane strain when using the conversions listed in Table 2.1. xyzzxyz26 2. LET’S GET STARTED Table 2.1: Conversions of two-dimensional assumptions Solution To convert to Plane stress Plane strain Plane strain Plane stress E is replaced by (cid:23)2/ E=.1 (cid:0) 2(cid:23)/=.1 E.1 C (cid:23) is replaced by (cid:23)/ (cid:23)=.1 (cid:23)/2 (cid:23)=.1 C (cid:0) C (cid:23)/ 2.4.4 THE LIMIT OF THE ROUND (AXISYMMETRY) Finally, many practical problems exhibit azimuthal symmetry about an axis. When there is no dependence of the deformation on the angle, (cid:18), in Fig. 2.13, the state of stress will not vary in this direction and the stress and deformation ﬁelds reduce to functions of .r; z/ only. Such conditions arise whenever: 1. all cross sections in the r-z-plane experience identical deformations; 2. externally applied forces are functions of r and z only; and 3. there is no (cid:18)-variation of the deformation in the body, i. e., points in the transverse .r; z/ plane always remain in their respective transverse planes following application of the loads. Figure 2.13: An axisymmetric geometry results when there is no variation in the azimuthal ((cid:18)) direc- tion. For such cases in FEA, the body is meshed in the r-z plane and an axisymmetric, two-dimensional continuum element is chosen for the analysis. rz2.5. ST. VENANT’S PRINCIPLE 27 2.5 ST. VENANT’S PRINCIPLE St. Venant’s principle, attributed to Barré de St. Venant, is a statement about the change in stress distribution with respect to distance from a prescribed load or boundary condition. St. Venant’s principle has signiﬁcant implications for ﬁnite element analysis. It may be stated in a number of equivalent ways. 1. e diﬀerence in stresses produced by two sets of statically equivalent forces acting on a sur- face, A, diminishes with distance from A and becomes negligible at distances large relative to the linear dimensions of A. 2. e detailed distribution of applied forces and moments on a boundary aﬀects the internal stress distribution in the vicinity of those applied forces and moments, but at several charac- teristic dimensions away from the reactions, the internal stresses are essentially dependent only on the applied external forces and moments, and not on how these forces and moments are applied. A characteristic dimension is not an absolute dimension, e. g., “2 in,” but rather, is a dimension that is meaningful in proportion to the given system, e. g., “1/3 the width of the bar.” is is illustrated in Fig. 2.14. 3. Only stresses in the vicinity of loads are sensitive to the details of how those loads are applied. 4. If self-equilibrating forces act on a surface area, A, the internal stresses diminish with dis- tance from A. e rate at which the stresses attenuate with distance may be inﬂuenced by the shape of the body and must be estimated independently in each case. 5. Statically equivalent systems of forces and moments produce the same stresses and strains within a body except in the immediate region where the loads are applied. 6. e localized eﬀects caused by any load acting on the body tend to disappear in regions that are suﬃciently far away from the application of the load. Many of the mathematical representations of the simplest loading conditions are them- selves simple. But illustration of the concepts behind these relatively simple formulae are too often lost on students exposed to them for the ﬁrst time. A powerful teaching tool is the use of quality graphical representations and illustrative examples, both of which appear in Steif [2012] and Philpot [2010]. e reader may also ﬁnd interesting two handbooks whose focus is a collec- tion of formulae. ese references are useful for benchmarking solutions and providing bounding cases used in preliminary analysis [Allain, 2011, Pope, 1997]. 28 2. LET’S GET STARTED Figure 2.14: Statically-equivalent sets of applied loads distributed diﬀerently over a boundary or part thereof do not alter the internal stresses and their distribution several characteristic dimensions (here, measured in terms of the width, w) away from the applied loads. Here, a compression specimen is subjected to equivalent loads (P ) over diﬀerent portions of its ends: (a) full end, (b) half end, and (c) point load. Approximately one specimen width into the bar, the state of stress is a uniform constant stress corresponding to P =A. 2.6 COMBINED LOADING Note To e Instructor While students may recognize these idealized loading cases and their respective simple formulae, we often observe that how to linearly superpose these stress components under conditions of even simple combined loading still eludes students even after exposure to the ﬁnite element method. Here we consider a simple illustration for which ﬁnite element analysis is both straightforward and useful in framing students’ hand calculations as benchmarks for simulation results. SimCafe Tutorial 1: Combined Loading in an Idealized Signpost e purpose of this case study is to illustrate how combined loading is handled in a straightforward manner using the ﬁnite element method. It presents a case study wherein students can perform parametric studies varying the degrees to which the combined load- ings are dominated by either axial, bending, torsional, or transverse shear response. It also showcases how internal stresses from combined loads are superposed in a linear analysis. I w(cid:9)B(cid:10)w32w3ww(cid:9)C(cid:10)w32w3ww(cid:9)D(cid:10)w32w3wSimCafe Tutorial 1: Combined Loading in an Idealized Signpost (continued) Follow the directions at https://confluence.cornell.edu/display/ SIMULATION/Signpost to complete the tutorial. 2.6. COMBINED LOADING 29 Example 2.2: Combined Loading in an Idealized Signpost D 28 ft, and h2 700 lbf=ft, Fy e cantilevered signpost shown in Fig. 2.15 has dimensions x1 6 ft, z1 8 ft. e system is subjected to the external loads wz 4 ft, b2 D 900 lbf=ft, 13 ft, h1 w0 net weight of the signpost. e signpost is made of steel, and it is assumed that the signpost will remain in its elastic range. is means that when the external load is removed, the material will return to its original shape without suﬀering permanent deformation. D 8000 lbf, and Fz D D D D D D Figure 2.15: Geometrical description of the signpost illustrating dimensions and loads. e post diameters do and di must be designed so that the total combined normal stresses and combined shear stresses do not exceed allowable values. Assume allowable stresses of 25 ksi and 16 ksi for normal and shear stress, respectively, which already account for an appropriate factor of safety. is example is adapted from Papadopoulos et al. [2013] with permission and with credit due to Genock Portela. 4JHOQPTU$SPTT4FDUJPOdidoxyz'JYFE4VQQPSU4UFFM1PTUFz1h1h2b2z1x1Fy1wzwx=zh1+h2w030 2. LET’S GET STARTED 2.7 A CLOSING REMARK AND LOOK AHEAD In this chapter we reviewed common structural elements and their usual analyses from Mechanics of Materials. We then used these forms to illustrate broader qualitative concepts and to introduce the ﬁnite element method. So far, no major surprises have surfaced, and all of the results are as expected. As we look ahead to the next chapter, we are now ready to examine problems that have greater geometrical complexity and irregularities. While some aspects of the FEA procedure will be the same as those introduced here, they must now be used with more caution, skepticism, and reﬁnement. Moreover, the user will need to learn some new techniques to completely capture essential details in these new situations. C H A P T E R 3 31 Where We Begin to Go Wrong When all you have is a hammer, everything looks like a nail. Anonymous Note To e Instructor We have often told our students that one of the advantages of ﬁnite element analysis is that it is relatively easy to perform. We also add that one of the disadvantages of ﬁnite element analysis is that it can be too easy to perform. As ease of use becomes more prevalent, it can belie the complexity of the actual solution to one’s problem. Clearly, a distinct advantage has always been to give drudgery and repetitive tasks to the machine to free up time for the analyst to spend critically thinking. So the computer is a fast, but not necessarily intelligent, aid in obtaining suﬃciently accurate solutions. e requisite intelligence lives primarily in two places: 1. commercial software’s pre-programmed algorithms that approximately model theories with which students may or may not be familiar and 2. an analyst’s pre-processing of a model formulation and interfacing this model with the commercial software. Where students go wrong can often be traced to one of these two lapses in intelligence. e ﬁrst appears when students attempt problems whose solutions they do not know a priori. In such cases, the theory they know may or may not be relevant or suﬃcient to model the problem. Students often view this as carte blanche for initiating a ﬁnite element analysis. One common pitfall is that it is more diﬃcult to validate a solution you do not know or understand a priori. In such cases, new learners often turn to the theory they know when attempting to validate simulation results. Comparing the results of correct ﬁnite element analysis with expectations using inadequate theory is a common mistake made by students in introductory courses. is is particularly true in courses where commercial software is used as part of the student laboratory experience. We illustrate this ﬁrst “way to go wrong” with three illustrative examples. 32 3. WHERE WE BEGIN TO GO WRONG 3.1 EXCEPTIONS TO THE RULE If you’re running a fever, you will remain home and nurse it…to a point. If your fever reaches 104 (cid:14)F, however, you may consider visiting your doctor or local emergency room. Analogously, the simple formulae discussed in Chapter 2 can suﬀer a similar fate in their predictability as one deviates further from the simplifying physical assumptions on which they are based. Take the model for normal bending stress developed in slender beams: (cid:27)bending D My I : is formula is suﬃciently accurate when beams are “long and slender;” that is, they are beams in which the length along the neutral axis is large compared with the dimensions of the beam cross section. e transverse deﬂections under load must also, typically, be orders of magnitude lower than the beam span. As with all good theory, Euler-Bernoulli beam theory is considered valid in a ﬁeld of geometric dimensions and deformation scales that are bounded by dimensionless ratios. For example, simple beam theory is considered to be applicable when v L (cid:28) 1 I D L (cid:28) 1; where D is a characteristic linear dimension of the cross section. We may even estimate a range of validity by specifying “lines in the sand” beyond which we can apply the results of the simpliﬁed theory: L v (cid:21) 1000 I L D (cid:21) 20: What is important is that these dimensionless “limits of applicability” are somewhat arbi- trary. ey serve only as user-deﬁned risk limits in applying simplifying assumptions. ey serve as warning posts beyond which we may wish to consider whether the true internal bending stresses are suﬃciently modeled by such simple formulae. Of course, the deviations from the simple limit occur gradually as one passes through their range of applicability. Much like the metaphor of a fever, the severity of the dysfunction grows degree by degree. Only ﬁnally at “some limit” (that generally varies from person to person) do we decide the formula is too sick to be used any fur- ther. Like climbers on Mount Everest, if one ignores too many small increments in impending bad weather, one could get caught on the mountain in conditions where equipment suitable for milder weather is no longer appropriate to the task. As the applicability of our simpliﬁcations falter, i. e., for suﬃciently short beams, the predictions of models based on these simpliﬁcations will agree less and less with results observed in practice and in the laboratory. e moral of the story is simple. e formulae examined in Chapter 2 do not suddenly go bad, no more than a fever jumps from mild to extreme. One tends to step out of the range of applicability of these simple formulae slowly, one degree at a time, until we ﬁnally judge predic- tions based on them to be “suﬃciently wrong.” Practitioners of FEA must know the applicability 3.2. THE LINES IN THE SAND 33 of the theories that, in addition to comparison with experimental data, are used to validate any numerical approximation of mechanical behavior. While the applicability of any simple formula is limited, it is still useful because the range of applicability can generally be large. However, no matter how large the region in which these formulae hold, we must be aware of the fences that bound them lest we utilize poor validation tools to benchmark our numerical simulations. e following are some of the speciﬁc places where mechanics idealizations may either break down or become suﬃciently ﬂawed to warrant treading with caution [Papadopoulos, 2008, Papadopoulos et al., 2011]. is list is not inclusive, but we point out several instances where their bearing on validation of FEA is paramount. • While linearity is applicable for small displacements, it is a poor approximation when dis- placements grow “suﬃciently large.” Studying the exact geometry of a structure and its actual displacements under loading can be very complicated with many resulting equations being nonlinear. When this is the case, the advantages accompanying linearity are lost, e. g., the guarantee of unique solutions, ability to superpose basic solutions, and ability to scale any solution in load or overall size. • Stress concentrations based on geometry such as re-entrant corners or cavities are, in gen- eral, not captured by formulae that describe homogeneous states of stress. Stress concen- trations are rooted in the interplay of stresses in orthogonal directions and not describable by one-dimensional simpliﬁcations. • For loading that results in fully three-dimensional, inhomogeneous stress states, any and all formulae that rely on lower-dimensional idealizations are often no longer valid. • When three-dimensional variation occurs, neglect of warpage and lateral strain may not be realistic. • For loading and geometry that are fully three-dimensional, boundary conditions that are idealized in lower dimensions can no longer be speciﬁed in unique terms. ere are a variety of approximations to classic boundary conditions such as a clamped support. 3.2 THE LINES IN THE SAND We do not intend to outline all the boundaries of the simplest theories. is has been undertaken in suﬃcient detail in many good mechanics of material texts such as Philpot [2010], Steif [2012], and Riley et al. [2007]. We wish here to illustrate a few salient examples. ese will serve to highlight what happens in distinct crossings of “lines in the sand,” such as: 1. when stress concentrations defy one-dimensional idealization, 2. when previously-insigniﬁcant deformation modes become non-negligible, and 3. when geometric dimensions dictate three-dimensional stress states. 34 3. WHERE WE BEGIN TO GO WRONG 3.2.1 A STEPPED AXIAL ROD SimCafe Tutorial 2: Stress Concentration in a Stepped Axial Shaft When geometries exhibit discontinuities along a loading path, stress concentrations generally arise. Stress ﬂow is analogous to ﬂuid ﬂow and steep gradients that result in navi- gating sharp discontinuities result in enhanced stress intensity. What may not be evident is that a discontinuity in geometry requires modeling the geometry in multiple dimensions in order to capture how the stress ﬂows through the domain. us, one-dimensional simpliﬁ- cations are not capable of capturing these important eﬀects. e purpose of this tutorial is to showcase perhaps the simplest stress concentration and point out that it can be resolved in two- or three-dimensions. Simple one-dimensional el- ements (i. e., simple axial bar elements) that capture constant stress within an element are in- suﬃcient to capture stress concentrations, even when many elements are used. In other words, the requisite theory is absent, so mesh reﬁnement is of no utility in converging on the solu- tion. When the element formulation does not contain the necessary physics, h-convergence, or using more elements, captures no more of the solution than does a coarser discretization. is tutorial is meant to highlight where it is relatively straightforward to apply FEA and resolve a solution correctly that belies analytical treatment with uniaxial formulae (such as (cid:27)axial D directions SIMULATION/Stepped+Shaft to complete the tutorial. https://confluence.cornell.edu/display/ Follow the P =A). at Example 3.1: A Stepped Axial Rod Consider a stepped shaft under uniform axial load, P , as shown in Fig. 3.1. Figure 3.1: Geometrical description of a shaft with a discontinuous step. Stress concentrations arise due to coupling of the stress response in multiple direc- tions. In the axisymmetric geometry pictured in Fig. 3.1, simpliﬁed two-dimensional theory of elasticity can be employed to derive approximate theoretical expressions for the observed I Drh3.2. THE LINES IN THE SAND 35 Example 3.1: A Stepped Axial Rod (continued) stress risers, by ﬁtting such models to experimental data [Solverson, 1953]. Many stress con- centration factors ﬁt in this manner are collected in Young and Budynas [2002]. For a stepped shaft with circular ﬁllets: h r D h=r 2h=D 3 in 1 in 8 in 3 3=4 D D D D D 0:75; D a simple ﬁt formula for the axial stress concentration is accurate to within 5% and given by: (cid:18) 2h D C3 2h D C 0:831ph=r (cid:0) 0:318ph=r (cid:0) 0:5220ph=r 0:009ph=r C2 D C1 C 1:225 C 1:831 D D (cid:0) D D (cid:0) D 2:236 0:63 1:377; (cid:0) C 2 (cid:19) 3 (cid:19) (cid:18) 2h D C4 C 0:010.h=r/ 2:634 D 0:049.h=r/ 0:176.h=r/ 0:117.h=r/ 2:529 1:8599 0:9654 D (cid:0) D D (cid:0) (cid:0) C (cid:0) K C1 C2 C3 C4 K ) and (cid:27)max D K(cid:27)nom D K P Amin D K 4P (cid:25) .D (cid:0) 2h/2 D 1376 psi: e response of a circular stepped shaft in tension is axisymmetric. An axisymmet- ric analysis undertaken in ANSYS predicts the stress concentration to within the order of accuracy of the simple formula ﬁt, as shown in Figs. 3.2 and 3.3. I 36 3. WHERE WE BEGIN TO GO WRONG Example 3.1: A Stepped Axial Rod (continued) Figure 3.2: e ﬁnite element method predicts the axial stress concentration in a stepped shaft. Figure 3.3: e local axial stress concentration is shown in the vicinity of the step ﬁllet. Because these eﬀects arise from coupling of stress in diﬀerent directions, one-dimensional theories are incapable of modeling stress concentrations in the vicinity of geometric discontinuities such as re-entrant corners or ﬁllets. Users must be careful to remember that in such cases two- or three- 3.2. THE LINES IN THE SAND 37 dimensional simulations are required. Because multi-dimensional analysis is required to capture stress concentrations, it is also required in numerical design considerations of how to alleviate such stress risers. For instance, in the case of the stepped shaft, one might ask the question “Is there any way to alleviate the stress concentration at the ﬁllet without changing the diameter on either side or increasing the radius of the ﬁllet?” A three-dimensional analysis reveals that this is actually possible by undercutting the larger diameter portion of the shaft in the vicinity of the original step, as shown in Fig. 3.4. Figure 3.4: It is possible to alleviate a stress riser without changing either diameter of a stepped shaft. A multi-dimensional ﬁnite element analysis is required to capture these phenomena. is solution is reproduced from [Papadopoulos et al., 2011] with permission, with particular credit due to Jim Papadopoulos. 3.2.2 A SHORT, STUBBY BEAM Euler-Bernoulli beam theory, as introduced in strength of materials courses, accounts for trans- verse deﬂection due to bending only. Bending deﬂections can be said to dominate the deforma- tion response when the span-to-depth ratio of the beam exceeds, say, 15. For progressively shorter beams, the assumption that shear deformation can be neglected when compared with the bend- ing deformation is no longer warranted. In these limits, the shear deformation should be taken into account. Timoshenko beam theory accounts for explicit contributions of deformation due to 38 3. WHERE WE BEGIN TO GO WRONG shear. is is the theory one should apply when the span-to-depth ratio of the beam falls below some prescribed limit. SimCafe Tutorial 3: Stress and Deﬂection in a Timoshenko Beam e purpose of this tutorial is to showcase where simple beam theory begins to break down. In some commercial codes, simple one-dimensional cubic beam elements that capture bending deﬂection do not capture shear deﬂection. Alternatively, Timoshenko beam theory may be used by default in the element formulation (as with the BEAM188 element in ANSYS v14). When shear deﬂection is accounted for in the one-dimensional element formulation, results for the beam’s tip deﬂection will not agree with tip deﬂections predicted by simple Euler-Bernoulli beam theory when the beam is relatively short. Again, attempts to capture this eﬀect with h-convergence will ultimately fail when the necessary physics is not contained in the element formulation. When it is and the results are compared to simpler theory, the disagreement may be substantial. Once again, h-convergence captures no more of the solu- tion than does a coarser discretization. is tutorial is meant to highlight when it is relatively straightforward to apply three-dimensional FEA and resolve a solution correctly that belies PL3=3EI ). analytical treatment with simple formulae (such as bending tip deﬂection v https://confluence.cornell.edu/display/ at Follow the directions D SIMULATION/Stubby+Beam to complete the tutorial. Example 3.2: Large Depth-to-Span Ratio Beams Consider a relatively short tip-loaded cantilevered I-beam, as shown in Fig. 3.5. Figure 3.5: A simple cantilever beam is loaded under transverse point tip load P . e behavior of relatively short beams can be numerically approximated by either one- dimensional beam elements that account for shear deﬂection or a fully three-dimensional analysis. One should note, however, that while one-dimensional Timoshenko beam ele- ments have interpolation functions for shear deformation, they do not capture the complete three-dimensional state of stress within the beam. For instance, in short cantilever beams the I xyPL2cExample 3.2: Large Depth-to-Span Ratio Beams (continued) normal stress component at the clamped edge can no longer be predicted with the simple bending formula in Chapter 2. 3.2. THE LINES IN THE SAND 39 Figure 3.6: Cross section of a short I-beam and a corresponding three-dimensional solid model that can be imported into many commercial ﬁnite element software packages. e solid model is meshed for an I-beam whose span is 24 in. With a span-to-depth ratio of only 3, the actual deformation and stress response will not be modeled well by Euler- Bernoulli beam theory. ree-dimensional ﬁnite element simulations indicate that the shear deﬂections are on the order of those from simple bending theory and the wall normal stresses deviate substantially from those predicted by simple bending theory. Typical contours of displacement and stress for the three-dimensional model are shown in Figs. 3.7 and 3.8 for a tip load of 1000 lb. I (cid:25)JO(cid:17)(cid:15)(cid:20)(cid:18)(cid:19)(cid:22)JO(cid:25)JO(cid:17)(cid:15)(cid:21)(cid:20)(cid:24)(cid:22)JO(cid:17)(cid:15)(cid:22)JO40 3. WHERE WE BEGIN TO GO WRONG Example 3.2: Large Depth-to-Span Ratio Beams (continued) Figure 3.7: Both shear and bending contribute to the total transverse deformation of short beams. Figure 3.8: e axial stress at the ﬁxed wall deviates substantially from that predicted by one- dimensional beam theory. Additional three-dimensional models can be run to examine the eﬀects of the length of the beam. Such analyses verify the dependence of both the tip deﬂection and normal wall stress on the beam’s span-to-depth ratio, as evidenced by results in Figs. 3.9 and 3.10. 3.2. THE LINES IN THE SAND 41 Figure 3.9: e tip deﬂections in short beams predicted by Euler-Bernoulli beam theory become progressively inaccurate for relatively short beams. Figure 3.10: e normal stress at the ﬁxed end predicted using Euler-Bernoulli beam theory in short cantilever beams can underestimate the actual normal stress substantially. 3.2.3 A THICK-WALLED PRESSURE VESSEL e simple formulae outlined in Chapter 2 represent nearly all states of uniform or linearly vary- ing stress. Radial and hoop stresses in pressure vessels become uniform through the thickness as the radius-to-thickness ratio becomes large. Because these formulae are simple and because the variation of both radial and hoop stress becomes nonlinear for thick vessels, analysts may be tempted to push the limits of the simple formulae. Here we point out that, as with the other simple formulae, the deviation from the uniform stress state occurs gradually. When the radius- 24681012(cid:0)80(cid:0)60(cid:0)40(cid:0)2004QBO(cid:14)UP(cid:14)EFQUISBUJP(cid:9)(cid:14)(cid:10)1FSDFOU&SSPS(cid:9)(cid:6)(cid:10)0510152025(cid:0)80(cid:0)60(cid:0)40(cid:0)2004QBO(cid:14)UP(cid:14)EFQUISBUJP(cid:9)(cid:14)(cid:10)1FSDFOU&SSPS(cid:9)(cid:6)(cid:10)42 3. WHERE WE BEGIN TO GO WRONG to-thickness ratio falls below 10, errors arising from predicting stresses with thin-walled formulae become appreciable and thick-walled formulae become increasingly necessary. SimCafe Tutorial 4: Hoop Stress in a ick-Walled Pressure Vessel e purpose of this tutorial is to illustrate how thin-wall pressure vessel theory grad- ually loses applicability as the radius-to-thickness ratio decreases. As before, this happens gradually as the vessel walls become thicker. is tutorial is meant to highlight where it is relatively straightforward to apply three-dimensional or axisymmetric FEA and resolve a solution correctly for thick-walled vessels. Follow the directions SIMULATION/Pressure+Vessel to complete the tutorial. at https://confluence.cornell.edu/display/ Example 3.3: A Hydraulic Test Stand Consider a hydraulic pressure vessel used to apply loads to experimental ﬁxtures in an undergraduate statics and strength of materials laboratory, as shown in Fig. 3.11. Figure 3.11: Hydraulic test stands are typically moderately thick-walled pressure vessels. Consider that the pressure vessel is verging on the limits of the thin-wall theory. e outer diameter is 4 in with an inner diameter of 3 in and a 0.5 in wall thickness, giving an I BYJBMBYJBMbap3.2. THE LINES IN THE SAND 43 Example 3.3: A Hydraulic Test Stand (continued) average radius-to-thickness ratio of 3.5. Exploiting symmetry, an axisymmetric analysis of half the vessel is created. e vessel is internally loaded with a constant pressure of 1000 psi. e axisymmetric deformed mesh and internal stresses indicate a stress riser in the bottom of the tank where membrane and bending stresses coincide, as shown in Fig. 3.12. Figure 3.12: Pressure vessel hoop stress maximum occurs in the bottom of a thick-walled vessel. Far from the discontinuity of the vessel corner, the hoop and radial stress variations in the axial direction in the cylinder wall vanish, as shown in Fig. 3.13. Figure 3.13: Pressure vessel hoop stresses are no longer uniform through the wall of a thick- walled vessel. I 44 3. WHERE WE BEGIN TO GO WRONG Example 3.3: A Hydraulic Test Stand (continued) Paths through the domain may be deﬁned in many commercial ﬁnite element software packages. Here, the variation of hoop stress through the wall thickness is not negligible. e results shown in Fig. 3.14 show the maximum value on the inner diameter predicted correctly by thick-wall theory. Figure 3.14: Radial variation of hoop stress in the uniform section of the cylinder wall shows a peak value at the inner wall that is underestimated by thin-wall theory. When we vary the vessel thickness, the gradual degradation of the predictions using thin- walled formulae become evident, as shown in Fig. 3.15. Figure 3.15: Hoop stresses in thick-walled pressure vessels are underestimated by relations based on thin-walled pressure vessel theory. 010203040(cid:0)40(cid:0)200"WFSBHFSBEJVT(cid:14)UP(cid:14)UIJDLOFTTSBUJP(cid:9)(cid:14)(cid:10)1FSDFOU&SSPS(cid:9)(cid:6)(cid:10)3.3. UTILITY OF THE FINITE ELEMENT METHOD 45 3.3 UTILITY OF THE FINITE ELEMENT METHOD e deviations from the simplest stress states that occur in the examples of Sections 3.1 and 3.2 are easily handled by the ﬁnite element method. Deviations such as stress concentrations may be predicted using approximate formulae, but these are almost always dependent on details of the specimen geometry; FEA, in contrast, is simple enough to apply in all of these cases and does a good job predicting the correct behavior for elastic deformation and stress. As the ﬁnite element method becomes more pervasively used in industry, we feel there is utility in introducing the method earlier in engineering curricula [Papadopoulos et al., 2011]. Distinct advantages to introducing the method throughout one’s undergraduate studies include reducing the drudgery and potential errors of computation, focusing on the theory of mechanics, while enabling students to approach more complicated problems that escape the realm of closed-form solutions. Now recall our earlier point that when using pre-programmed software, the majority of the errors and their severity are attributable to the user. ese include faulty input, poor modeling, poor pre-processing, and ignorance of the software protocol. Analogous errors of using a wrong formula or remaining ignorant of a key formula can occur when using hand calculations [Jeremić, 2009, Papadopoulos et al., 2011, Prantil and Howard, 2007, 2008]. e potential for such error in problems like the ones in this chapter is high because the theoretical solutions are likely beyond what most undergraduate mechanical engineering students have learned. Here FEA can be very beneﬁcial to allow students to explore behavior beyond their basic theoretical knowledge, and it can serve as a bridge for them to discover more advanced theoretical treatments that appear, such as Gieck and Gieck [2006] and Young and Budynas [2002]. Such books are good references for ﬁnite element analysts to have at hand for validating numerical solutions for problems whose analytical or empirical solutions have been determined. Using these solutions as benchmarks for FEA analyses helps reinforce the practice of ﬁnding published and veriﬁed solutions for comparison with numerical simulations. is further underscores our earlier point that we advocate early introduction of FEA in the curriculum, even when it appears to precede the students’ current level of engineering knowledge [Papadopoulos et al., 2011]. While applying the ﬁnite element method in these cases is relatively straightforward, for more complex geometries and boundary conditions, the prescription of model details leads to sit- uations in which it can become progressively easier for analysts to go wrong applying the method. We discuss illustrative case studies for two such boundary value problems in Chapter 4. C H A P T E R 4 It’s Only a Model 47 A model is a lie devised to help explain the truth. Anonymous e truth is always too complex. Bruce Irons and Nigel Shrive e Finite Element Primer Note To e Instructor e second lapse in intelligence in applying the ﬁnite element method occurs when users understand the problem they want to solve, and understand the theory that they believe holds for the problem at hand. e issue is whether the analyst properly poses the ﬁnite element formulation of the problem. ese types of errors can occur when analysts pre-process a model and 1. apply loads or boundary conditions incorrectly, 2. use an inadequate element formulation for the solution desired, or 3. analyze the problem in an inappropriate dimension, i. e., pose the problem as two-dimensional when three-dimensional analysis is required. In this scenario, the user falls prey to an old adage wherein the computer is doing what they tell it to do rather than what they want it to do. Here we pose two deceivingly simple problems that cause new learners to often make these common mistakes in problem formulation. 48 4. IT’S ONLY A MODEL 4.1 THE EXPECTATION FAILURE We expect regularities everywhere and attempt to ﬁnd them even where there are none. Events which do not yield to these attempts we are inclined to treat as “background noise,” and we stick to our expectations even when they are inadequate. Karl Popper Conjectures and Refutations: e Growth of Scientiﬁc Knowledge As we mentioned in the Preface and elsewhere, we strongly believe in using expectation failures as part of our teaching strategy. Because they are crucial to the examples in this chapter, we repeat the words of Ken Bain to remind the reader of their meaning and importance: Some of the best teachers want to create an expectation failure, a situation in which existing mental models lead to faulty expectations. ey attempt to place students in situations where their mental models will not work. ey listen to student concep- tions before challenging them. ey introduced problems, often case studies of what could go wrong, and engaged the students in grappling with the issues those examples raised [Bain, 2004]. Among the list of common errors made in FEA practice, in this chapter we address misconcep- tions regarding either 1. the real physics governing the problem or 2. the construction of the ﬁnite element model approximating these physical mechanisms. So an analyst harbors some misconception regarding underlying physical phenomena or details of an appropriate numerical approximation. But, and this is critical, they begin to assure themselves that they do understand. Perhaps they do not remember that “the truth is always too complex” and either our broad simpliﬁcations of reality (the simple formulae) or the ﬁnite ele- ment model approximations (say, lower-order interpolation ﬁnite elements) are insuﬃcient for the problem at hand. As we discussed in Chapter 3, analysts will proceed as if these simpliﬁcations adequately represent the real behavior. In these cases, analysts may trust the incorrect numerical analysis. Even when presented experimental evidence that does not validate the computational results, analysts can still “cling with fervor” to these incorrect results. Such computational compla- cency may be born of rationalizing that because the software has more theory programmed into it than the user has learned, the computer is more likely right. In ﬁnite element analysis, expectation failures can arise in the following ways. 1. One prescribes boundary conditions that either over- or under-constrain the boundaries by 4.2. PHILOSOPHY OF MATHEMATICAL MODELING 49 (a) not removing all rigid body translation and rotation or (b) overly constraining degrees of freedom along a particular direction that preclude de- formation and Poisson eﬀects in orthogonal directions. 2. One chooses inappropriate ﬁnite element formulations, such as (a) planar or one-dimensional elements that are not appropriate for the observed behavior, (b) ﬁnite elements with inadequate degrees of freedom, or (c) ﬁnite elements with inadequate order of interpolation. 3. Lower-order interpolations appear to predict behavior more accurately than higher-order interpolations. 4. Meshes with fewer active degrees of freedom appear to predict more accurately than meshes with more active degrees of freedom. We wish to illustrate these points with two examples where ﬁnite element modeling can go wrong. Remember, whether or not simpliﬁed theory is appropriate, incorrect ﬁnite element results are typically cases of analyst error. 4.2 PHILOSOPHY OF MATHEMATICAL MODELING e great masters do not take any model quite so seriously as the rest of us. ey know that it is, after all, only a model, possibly replaceable. C.S. Lewis e game I play is imagination in a tight straightjacket. at straightjacket is called the laws of physics. Richard Feynman S.L. Hayakawa is noted for pointing out that “the symbol is not the thing symbolized; the word is not the thing; the map is not the territory it stands for” [Dym, 2004], echoing Richard Feynman who recalled that his father “knew the diﬀerence between knowing the name of something and knowing something” [Public Broadcasting System–NOVA, 1993]. When engineers attempt to formulate models for systems and processes, it is incumbent upon us to remember that the process, the system is “the thing,” “the territory.” e model is a symbol, word, or map that in some way names the thing. ey are not the same. To model some process well requires recasting its real nature into a simpliﬁed shell that allows its basic nature to be captured in mathematical form, a set of equations whose solutions tell us something about how the model system behaves under a given set of controlled conditions. An abstraction of the process is shown in Fig. 4.1. 50 4. IT’S ONLY A MODEL Figure 4.1: A mathematical model is devised by suﬃciently simplifying a problem statement such that its formulation can be cast in equation form. Similar conceptualizations have been illustrated elsewhere and these overviews of model- ing are well worth reading: Carson and Cobelli [2000], Dym [2004], Greenbaum and Chartier [2012]. In order to numerically model a system, we must observe the system in nature. We must: 1. collect all information relevant to how the system behaves, 2. detail what we need to ﬁnd out or predict, 3. specify how well we need to know or predict this behavior, and 4. seriously ask a singularly important question: “What do we expect to happen?” 3FBM8PSME4JNQMJGZJOH1IZTJDBM"TTVNQUJPOT.BUIFNBUJDBM.PEFM%JTDSFUJ[FE.PEFM/VNFSJDBM4PMVUJPOOUFSQSFUBUJPOPG3FTVMUT3FWJTJU4JNQMJGZJOH"TTVNQUJPOT4.2. PHILOSOPHY OF MATHEMATICAL MODELING 51 We should have a knowledgeable, informed expectation of how the system will respond to dis- turbances, excitation, or loading based on practical experience, prudent observation, and one’s understanding of the relevant physics. In any given process, only a few physical mechanisms tend to dominate the behavior. Mak- ing physically simplifying assumptions means deciding what physical mechanisms to retain (recall the baby) and which to neglect (recall the bathwater). e modeler needs to retain the dominant physics and neglect all higher-order eﬀects, making the model as simple as possible, but no sim- pler. Making appropriate simplifying assumptions is an art whose mastery comes only gradually with continued experience. After appropriate simplifying assumptions are made, application of a conservation or bal- ance principle results in a diﬀerential equation for the boundary value problem. Finite element methods provide a piecewise approximation to the solution of this diﬀerential equation. In con- structing ﬁnite element models, the major inputs from the user are 1. the choice of ﬁnite element, which dictates the incremental solution interpolation between nodes and 2. the speciﬁc prescription of boundary conditions for the global domain. We’ve already learned that beam behavior can be approximated using one-dimensional and three- dimensional models. Here we will use both and compare the results to experimentally measured values. Recall that boundary value problems are described fully by a governing diﬀerential equa- tion coupled with an admissible set of appropriate boundary conditions. For static analyses, the boundary conditions must remove all rigid body translations and rotations. Upon applying admissible boundary conditions, we solve for displacements throughout the global region. Most commercial ﬁnite element software then post-processes the displacement solution to compute 1. reaction forces corresponding to applied displacement constraints and 2. internal stresses which may be displayed or contoured. One goal in model development is to start with the simplest approximation that captures the physics and provides perhaps crude, but reliable qualitative predictions of system behavior. We will seek to iterate on the model to provide more quantitative results, and then to validate the numerical predictions with experimental observations and test results. All models are approxima- tions whose errors most commonly arise from 1. expectation failures, 2. faulty simplifying assumptions, 3. poor discretization of the domain, 52 4. IT’S ONLY A MODEL 4. poor choice of element interpolation function, 5. incorrect post-processing, or 6. misinterpretation of results. To validate a numerical solution, it is prudent to perform initial benchmark solutions on repre- sentative problems with simpliﬁed geometries and boundary conditions. Preferably, these prob- lems are ones whose solutions are known either in closed form or bounded by analytical solutions from above and below. Beyond this, all system modeling employing numerical simulation requires model iterations. Based on previous results, subsequent analyses must be entertained that: 1. relax simplifying assumptions, 2. reﬁne the discretization, or 3. employ higher-order interpolation between solution grid points. Such model iterations must be performed until the solution converges and independent validation is achieved. Finite element analysis is a numerical approximation in which the global solution to a large- scale boundary value problem is approximated by a series of ﬁnite range functions that are them- selves lower-order Taylor series approximations that approximate the local behavior of the solu- tion with suﬃcient accuracy. ese local representations of the solution are based on the Lagrange polynomial interpolation functions that characterize each ﬁnite element. 4.3 THE ART OF APPROXIMATION Modeling and the approximations made therein are an art. When devising numerical approxi- mations on top of the requisite simplifying assumptions, any model is never, strictly speaking, correct, but (hopefully) correct enough. Nearly all numerical approximations in ﬁnite element modeling are approximations to theoretical solutions characterized by high levels of continuity and diﬀerentiability. But these approximations consist of piecewise, lower-order Lagrange poly- nomial ﬁts between grid points at which nodal equilibrium is explicitly satisﬁed. e levels of continuity in displacement sacriﬁced in the weighted residual are the inherent penalty for the approximation that allows average solutions to continuous diﬀerential equations to be obtained from simpler algebraic matrix equations. In some crude sense, numerical analysis is the ﬁne art of lying by approximation. e concept of piecewise polynomial interpolation of a solution over a ﬁnite domain is rooted in appropriately truncated Taylor series expansions. In some deﬁned neighborhood of the nodes, a continuous function has an inﬁnite number of truncated Taylor series approximations. e applicable neighborhood over which each series is considered valid then depends on the order of the truncation. 4.4. WHAT ARE WE APPROXIMATING? 53 Figure 4.2: A generic function is shown over some global domain. D D e(cid:0) Consider the function f .x/ x sin.3x/, plotted in Fig. 4.2. In the vicinity of the point 2, the second-order Taylor series approximation represents the function with some level of x 2, as shown in Fig. 4.3. e linear, ﬁrst-order accuracy in some prescribed neighborhood of x D Taylor series approximation is a reasonable representation over yet a smaller window. e zeroth- order Taylor series allows for no interpolation. en it follows that the neighborhood over which an element’s interpolation function approximates a known solution with acceptable accuracy will determine the appropriate element size you want in your discretized domain. erefore, it follows that you cannot know how to best discretize your domain without knowing what element inter- polation, i. e., element type, you have chosen. As we will see, how well higher-order derivatives of these interpolating functions represent the derivatives of the actual solution must be considered in order to determine the accuracy of the stresses predicted by the numerical model. 4.4 WHAT ARE WE APPROXIMATING? e primary solution variables in FEA are displacements at discrete grid points we call nodes. A discrete solution using the ﬁnite element method always delivers an approximate overall solution in the entire domain characterized by 1. maintenance of force equilibrium at all nodes and 2. sacriﬁce of inter-element force equilibrium in neighboring ﬁnite elements that share par- ticular nodal points. 01234(cid:0)0:200:20:40:6xf(x)54 4. IT’S ONLY A MODEL Figure 4.3: Progressively higher-order truncated Taylor series approximations to an arbitrary function model the function’s behavior well over progressively larger local neighborhoods. e displaced conﬁguration of an elastic body is precisely the set of nodal point displace- ments superposed on the original undeformed conﬁguration. e deformed body acts as an elab- orate three-dimensional spring that, upon unloading, would return instantaneously to its original size and shape. e set of nodal point displacements comprise a set of coeﬃcients that each mul- tiply basis functions whose collected weighted sum represents an approximation of the continu- ous displacement ﬁeld in three dimensions. Finite element analysis is, in one sense, a piecewise Lagrange polynomial interpolation of this continuous ﬁeld into many lower-order polynomials whose continuity requirements at nodal points are dictated by the order of truncation of the local Taylor series. It is, therefore, the order of the interpolation or shape function that dictates the variation of displacement along the interior of the ﬁnite element. Now let’s consider an idealized ﬁnite element analysis as an example of: 1. developing and solving a mathematical model, 2. showcasing where particular errors made in ﬁnite element practice might occur, and 3. illustrating where theory embedded in ﬁnite element formulations is no guarantee that using ﬁnite element analysis will result in an accurate simulation. 01234(cid:0)2(cid:0)1:5(cid:0)1(cid:0)0:500:51xf(x)f(x)(cid:17)UI(cid:14)PSEFS5BZMPSTFSJFT(cid:18)TU(cid:14)PSEFS5BZMPSTFSJFT(cid:19)OE(cid:14)PSEFS5BZMPSTFSJFT4.4. WHAT ARE WE APPROXIMATING? 55 SimCafe Tutorial 5: Four-Point Bend Test on a T-Beam e purpose of this case study is to showcase how the manner in which boundary conditions are applied can change with the number of dimensions in the analysis. Prescription of a single unique “appropriate” set of boundary conditions may no longer exist in a three- dimensional model vs. its one-dimensional analog. In the case study described here, multiple prescriptions of a “simple support” lead to signiﬁcantly diﬀerent predicted bending stresses even in the fairly benign circumstances encountered in a four-point bend test. Follow the directions at https://confluence.cornell.edu/display/ SIMULATION/T-Beam to complete the tutorial. Example 4.1: Four-Point Bend Test on a T-Beam Consider that we are examining a long, slender T-beam loaded at two symmetric loca- tions on its top surface while being simply supported at its ends along triangular knife-edge supports as shown in Figs. 4.4 and 4.5. e load was applied with a hydraulic cylinder ap- paratus. Strain gages mounted at several locations between the loading points (where the moment was constant and the transverse shear force was zero) were monitored during the test. We know that the beam is made of isotropic steel with a span of 30 in and constant cross-sectional properties. We wish to accurately predict its peak bending stress. Figure 4.4: A T-section beam cross section is pictured, along with a schematic of the loads ap- plied in a four-point bend test. I 3JO0:3125JO30JOPP7JO4ZNNFUSJDMPBETPBQQMJFEPWFS(cid:17)(cid:15)(cid:22)JOMFOHUI5:75JO0:5625JO0:375JO56 4. IT’S ONLY A MODEL Example 4.1: Four-Point Bend Test on a T-Beam (continued) Figure 4.5: e T-section beam is simply supported along triangular knife edges at each end. We assume the load is quasi-static. e material remains in the elastic range, the beam is long and slender enough for Euler-Bernoulli beam theory to be a suﬃcient representation of the deformation and internal stress response. We neglect contributions to the deformation from shear deﬂection. We assume the vertical transverse loads from the hydraulic press can be modeled as pressures over small contact patches. We also assume the simple support at the ends of the beam constrain the transverse displacements at the beam’s bottom ﬂange in contact with the knife-edge support. Having chosen a one-dimensional beam element, we are assuming a cubic interpola- tion of transverse deﬂection between node points to represent a global solution that is cubic. One would then expect to generate exact results [Irons and Shrive, 1983] as there are no trun- cation errors in the approximation. A linear distribution of normal, bending stress through the depth of the section would then be the expected result. e simplest discretization is shown in Fig. 4.6. Figure 4.6: A one-dimensional ﬁnite element mesh using beam elements is loaded with idealized point loads. Comparisons of the normal bending stress results of the one-dimensional analyses with those determined from strain gage test data from the lab allowed for some interesting comparisons, as shown in Table 4.1. Here we report the stresses in dimensionless form where I Example 4.1: Four-Point Bend Test on a T-Beam (continued) the actual stress is normalized with respect to the characteristic bending stress 4.4. WHAT ARE WE APPROXIMATING? 57 PLh 2I : (cid:27) O D is illustrates a further point about the ﬁnite element method. It is entirely devoid of any reference to the chosen system of units. ese are entirely at the discretion of the user. One need only prescribe a consistent set of units in order to interpret results meaning- fully. Because the units are discretionary, results from linear static analyses scale linearly with load and dimensionless results are rendered independent of the actual speciﬁc load, section properties, or material constants chosen. Table 4.1: Results of one-dimensional beam analyses Experiment Euler-Bernoulli beam theory FEA: beam elements (cid:27)bottom= (cid:27) O 0.1108 0.1134 0.1134 (cid:27)top= (cid:27) O -0.2464 -0.2724 -0.2724 Based on these results, in which physical experiment, simple beam theory, and ﬁnite element simulation are in good agreement, we could conclude that we have obtained an accurate answer for the peak bending stresses in the beam, and in particular, that the use of beam elements is an appropriate choice for the ﬁnite element model. We further comment 15 in). that the alert reader should surmise that the peak stresses occur at the midpoint (x Recall that models are approximations of reality, and it is quite possible that more than one model is capable of producing an accurate result. It is well worth asking if a fully three- dimensional analysis would also verify these results. is may, in fact, be what one expects at ﬁrst glance. D To investigate this question, a three-dimensional model is created in which the hy- draulic loads are approximated as pressure loads over the small contact areas. We also assume that the knife-edge supports at the left and right ends can be modeled by constraining the transverse (z-direction) and out-of-plane (y-direction) displacements at all points along left and right edges of the beam’s bottom ﬂange (that is, along the edge lines parallel to the y-direction), as shown in Fig. 4.7. I 58 4. IT’S ONLY A MODEL Example 4.1: Four-Point Bend Test on a T-Beam (continued) Figure 4.7: Simple support boundary conditions used in the ﬁnite element model are applied throughout the cross section. Preliminary results indicate that the stress variation is fairly linear through the cross section, as depicted in Fig. 4.8. Figure 4.8: Axial stress distribution in the three-dimensional beam model varies linearly through the section. But the normal bending stress at the extreme ﬁbers predicted by the three-dimensional ﬁnite element model does not agree with experiment as outlined in Table 4.2. e stresses are under-predicted on top by 11% and on bottom by 52%. I All translational DOF fixedfor all nodes at the supports4.4. WHAT ARE WE APPROXIMATING? 59 Example 4.1: Four-Point Bend Test on a T-Beam (continued) Table 4.2: Results of one- and three-dimensional beam analyses Experiment Euler-Bernoulli beam theory FEA: beam elements FEA: solid elements (cid:27)bottom= (cid:27) O 0.1108 0.1134 0.1134 0.0536 (cid:27)top= (cid:27) O -0.2464 -0.2724 -0.2724 -0.2184 At this point we have arrived at an expectation failure, for the results from our “obvi- ously correct” three-dimensional model do not match the accepted values from the previous analysis. In the spirit of our pedagogical approach, it is now incumbent upon the student to speculate as to why this has occurred, and likewise, it is imperative that instructors support- ively coach their students toward a more correct understanding of the solution. For instance, some possible reasons for our discrepancy include the following. • e simple beam calculations were made with a cross section that neglected the ﬁllets between the web and ﬂange. e solid-element model includes the ﬁllets, resulting in a stiﬀer structure. e error introduced by neglecting the ﬁllets is less than 0.5% for this geometry. • Experimental errors, including reading of the applied pressure, locations of the sup- ports and load application points, inaccurate modulus of elasticity, and strain gage er- rors, caused the measured strains to be inaccurate. If only the three-dimensional model were being compared to the experimental results, this might have been a reasonable conclusion. However, the agreement of the simple beam calculations and beam ﬁnite element model results with the experimental results may cast doubt on the accuracy some particular aspect of the solid-element model. • ere are not enough elements through the thickness in the solid-element model to al- low for the bending stresses to be accurately calculated. While this is a possibility, closer examination of the maximum and minimum stresses predicted by the solid-element model shows that the neutral axis location (assuming a linear distribution of stress) is more than 0.5 in away from the centroid of the cross section. is result suggests that some other type of loading is being introduced into the beam. Having considered and eliminated these possible explanations as likely, we are led to suspect the boundary conditions. e three-dimensional model made use of boundary conditions whose equivalent eﬀect is to allow only rotation about the y-axis (along the knife-edge sup- port). Indeed, the boundary condition illustrated in Fig. 4.7 seems to be a good representation of the physical constraint, as the real beam rests on a support that extends across the entire I 60 4. IT’S ONLY A MODEL Example 4.1: Four-Point Bend Test on a T-Beam (continued) ﬂange, and one is predisposed to visualizing this simple rotation condition. Note that the portion of the beam that extends beyond the support is not included in the ﬁnite element model. However, the boundary conditions restrict displacements that are possible with the three-dimensional model and which exceed the conditions imposed by the actual knife-edge constraint. In particular, the ﬂange of the beam does not remain perfectly ﬂat. Rather, it rests freely on the support and is free to deform in the direction transverse to the beam’s neutral axis and throughout the entire depth of the beam. Since the axial strain varies with distance away from the neutral axis, the transverse strain due to Poisson’s ratio also varies. is variation of transverse strain, not accounted for in one-dimensional analyses, results in curvature of the ﬂange. You can easily visualize this eﬀect by bending a rubber eraser between thumb and foreﬁnger and noticing the curvature transverse to the applied bending. It nevertheless still seems reasonable that some three-dimensional model should work. We can modify the boundary conditions to allow the model to curve in the transverse direc- tion. ese alternative boundary conditions are relaxed to apply to the two corner nodes on each end of the beam only. e deﬂected shape of a slice of the beam section with these new boundary conditions applied is illustrated in Fig. 4.9. Although the deﬂections are greatly exaggerated, the tendency of the beam ﬂange to curve rather than sit ﬂat on the support is clearly evident. is relaxation of the constraint on the ﬂange appears to have rather strong eﬀects on the predicted bending stresses. Figure 4.9: Modiﬁed boundary conditions applied to the ﬁnite element model result in an altered deformed shape of the beam at these supports. I x- and z-displacements fixedAll translationalDOF fixed4.4. WHAT ARE WE APPROXIMATING? 61 Example 4.1: Four-Point Bend Test on a T-Beam (continued) As reported in Table 4.3, the new results for peak bending stresses using the relaxed constraints are much closer to the experimental results than those using the stricter con- straints. Table 4.3: Results of alternate beam analyses Experiment Euler-Bernoulli beam theory FEA: beam elements FEA: solid elements, loosely-pinned supports FEA: solid elements, fully-pinned supports (cid:27)bottom= (cid:27) O 0.1108 0.1134 0.1134 (cid:27)top= (cid:27) O -0.2464 -0.2724 -0.2724 0.0946 -0.2230 0.0536 -0.2184 ere are several important lessons to take away from this exercise. 1. With the loosely pinned supports, the error in maximum bending stress on the bottom of the beam is reduced from 52% to 16%, while the maximum bending stress on the top of the web is now even more accurate than the one-dimensional results. 2. For beams whose depth-to-span ratio is not small, Poisson eﬀects on stresses may be signiﬁcant. Furthermore, these eﬀects are accentuated because the end constraints are placed along the beam ﬂange surface which is not on the neutral axis. Beam theory inherently assumes that all constraints are placed at the neutral axis. 3. e one-dimensional results may agree well with experiment because of the proximity of the ﬂange, where actual boundary conditions are placed in the experiment, to the actual neutral axis. 4. While a three-dimensional model can account for out-of-plane eﬀects, the precise form of the boundary conditions can have strong eﬀects on stresses. 5. Solid elements are not always the best choice for an analysis when this choice is made irrespective of the boundary conditions. Often, realistic deformations result that may be outside of the realm of one’s limited experience. With easy access to a part or assembly modeled with a solid modeling program, it may seem logical to import and analyze the structure with three-dimensional elements for no more important reason than ease for the analyst. I 62 4. IT’S ONLY A MODEL Example 4.1: Four-Point Bend Test on a T-Beam (continued) 6. Very often the part or assembly modeled with a solid modeling program has been cre- ated without previous knowledge of where and how loads and boundary conditions will need to be applied in a subsequent ﬁnite element analysis. Often, analysts will struggle with wanting to import these solid model part or assembly ﬁles nonetheless. is may lead or even force them to place less than optimal loadings and boundary conditions where they otherwise might not. 7. Constraints that produce only negligibly small diﬀerences in strains can result in sig- niﬁcant diﬀerences in internal stresses. 8. In this example problem, an analysis with over 14,000 three-dimensional solid elements produced inferior results compared to an analysis with four simple one-dimensional beam elements. Use of three-dimensional analysis does not guarantee more accurate results. Because there are still discrepancies between the three-dimensional stress predictions and experimen- tal results, we suggest that, as an exercise, students should further relax the boundary con- straints along the ﬂange to allow displacement along the beam’s longitudinal axis. Since the ﬂange is below the neutral axis, and there is bending, a compressive force will develop along the bottom of the ﬂange if both ends of the beam are ﬁxed in the axial direction. In this way, the extent to which this additional axial force does or does not aﬀect the maximum bending stress can be explicitly determined. SimCafe Tutorial 6: Large Depth-to-Span Ratio Beams e purpose of this case study is to illustrate how assumptions of planar behavior aﬀect numerical simulation of simple beam bending. e plane stress and plane strain assumptions lead to bounds on the actual three-dimensional behavior. While this analysis is simple to perform, the results are not so readily validated by those who are not ready to question when the planar approximations are reasonable to apply. Such reasoning can lead analysts to con- clude that numerical results have “converged” on a result which is inaccurate by over 100%. e point of this exercise is to have analysts convince themselves that simpliﬁed theories are often bounds and that geometries that do not cleanly and unambiguously lend themselves obviously to either (thin or thick) limit, may still be ones for which one limit is reasonable and applicable. Also, an intuitive feel for making and applying these simpliﬁcations often still eludes users of the ﬁnite element method. is case study is an exercise in boundary condi- I 4.4. WHAT ARE WE APPROXIMATING? 63 SimCafe Tutorial 6: Large Depth-to-Span Ratio Beams (continued) tion prescription, choosing appropriate ﬁnite element formulations, simulation convergence, and applying caution in interpreting one’s results. Follow the directions at https://confluence.cornell.edu/display/ SIMULATION/2D+Beam to complete the tutorial. Example 4.2: Large Depth-to-Span Ratio Beams A simply supported beam of rectangular cross section is point loaded at some arbitrary 25 in, point along its length as shown in Fig. 4.10. Consider a beam where L h 3 in, and load P 100 in, a 1000 lbf. 8 in, b D D D D D Figure 4.10: A beam with rectangular cross section is simply-supported while an oﬀ-center point load is applied. While, in general, a ﬁnite element analysis will more accurately predict deﬂections than, say, internal stresses (we will discuss this in more detail in Chapter 5), this example illustrates a case in which even the deﬂections can be poorly modeled. We wish to examine the implications of analyzing the problem with one-, two-, and three-dimensional element formulations. Analysts must choose and defend their method of analysis including all im- plications that dimensional space imposes on the results. Examples of the simplest meshes for either plane stress or plane strain analyses using continuum elements are illustrated in Fig. 4.11. Analysts may suppose that Euler-Bernoulli beam theory applies for these long, slender beams, presumably because it is the theory with which they are most familiar, and/or because it seems to work in other apparently similar examples, such as our previous example with the T-beam. However, while this assumption is intuitively appealing, we will see that it leads to a variety of pitfalls. Perhaps other expectation failures are in the oﬃng. Let us proceed with a narrative of this example assuming that the Euler-Bernoulli theory holds, although this has not yet been veriﬁed. Under this assumption, the curious analyst, in light of the previous example, might simulate the beam with several models. Due I yxPaL(cid:0)abh64 4. IT’S ONLY A MODEL Example 4.2: Large Depth-to-Span Ratio Beams (continued) to the rectangular section of the beam, one-, two-, and three-dimensional models might be appropriate. Figure 4.11: Typical mesh discretizations using (a) linear 3-node triangular elements and (b) bi-linear 4-node quadrilateral elements. e analyst proceeds to simulate the beam using a variety of elements: one-dimensional beam elements, plane strain triangles, plane strain quadrilaterals, plane stress triangles, plane stress quadrilaterals, and three-dimensional brick elements (using what the analyst believes to be suﬃciently relaxed end constraints, as per the previous example). e results for max- imum deﬂection are reported in Fig. 4.12. All results are reported in dimensionless form, normalized by the characteristic deﬂection PL3 EI : v O D According to these results, and still believing that Euler-Bernoulli beam theory is cor- rect, the analyst would see that the maximum converged transverse deﬂection predicted by plane stress conditions underestimates the deﬂection predicted by Euler-Bernoulli beam the- ory by nearly 50%; by comparison, the maximum converged transverse deﬂection predicted by plane strain conditions overestimate the prediction of Euler-Bernoulli theory by 40%. e analyst also realizes that the converged results from the three-dimensional brick elements appear to be in agreement with the converged plane stress results, but that a coarse mesh in- stance of the plane strain model seems to agree well with the expected Euler-Bernoulli beam theory. How does the analyst sort out these mixed messages? I (cid:9)C(cid:10)(cid:9)B(cid:10)Example 4.2: Large Depth-to-Span Ratio Beams (continued) 4.4. WHAT ARE WE APPROXIMATING? 65 Figure 4.12: Maximum deﬂection predicted by ﬁnite element models assuming two-dimensional plane strain, two-dimensional plane stress, three-dimensional, and idealized one-dimensional behavior are compared with predictions from Euler-Bernoulli beam theory. ere is now a subtle point to make about this problem in comparison to the previous problem with the T-beam. Whereas in the previous problem the neutral axis was near the bottom of the beam, in this case it is not. Rather, it lies at mid-depth, and is hence far away from the location of the support pins that are at the bottom of the beam. is gives our ﬁrst clue that regular Euler-Bernoulli beam theory is not applicable here. Secondly, given that a fully three-dimensional analysis using solid elements can prop- erly be speciﬁed to match the given boundary conditions, and given further that the three- dimensional formulation can account for the Poisson eﬀects and out-of-plane curvature (which turn out to be signiﬁcant), the three-dimensional analysis appears to give an accurate result. Because the converged plane stress solution agrees with the three-dimensional theory, and because the plane stress elements do not preclude out-of-plane Poisson eﬀects, we have even further indication that the three-dimensional (and hence two-dimensional plane stress) solutions are valid. I 0246810121416182000:511:522:533:5410(cid:0)2/VNCFSPGFMFNFOUTUISPVHIUIJDLOFTT(cid:13)n%JNFOTJPOMFTTNBYJNVNEFnFDUJPO(cid:13)vNBY/(PL3/EI)&VMFS(cid:14)#FSOPVMMJCFBNUIFPSZ1MBOFTUSBJOUSJBOHMFT1MBOFTUSBJORVBESJMBUFSBMT1MBOFTUSFTTUSJBOHMFT1MBOFTUSFTTRVBESJMBUFSBMTiSFF(cid:14)EJNFOTJPOBMIFYBIFESB66 4. IT’S ONLY A MODEL Example 4.2: Large Depth-to-Span Ratio Beams (continued) We can use this example to raise the general point that simple beam theory is not suf- ﬁciently accurate for beams with high depth to span ratios where the pinned boundaries are placed at the bottom surface of the beam cross section. Nevertheless, too often even experi- enced analysts too often take for granted that it applies universally as an accepted solution for slender beam problems. We point out that this type of qualitative reasoning is not trivial. e analyst’s ability to undertake this reasoning correctly depends on two key issues that have been articulated repeatedly throughout this text: • the analyst is willing to anticipate, confront, and let go of misconceptions, even when they appear to be intuitive and based on prior understandings; and • the analyst has suﬃcient understanding of Mechanics of Materials and understands how to think through the diﬀerences in the models considered. e consequences of getting this analysis wrong, in this case, can be far reaching. e analyst who insists on sticking with the Euler-Bernoulli beam theory not only will persist with that error, but as a consequence might make other poor judgements, such as believing, as is apparent in this case, that a relatively coarse mesh under plane strain conditions is also generally correct! is could, in turn, lead to the analyst to not performing suﬃcient mesh reﬁnement studies in other problems, and to accept other erroneous plane strain solutions. In closing this example, we note that elementary beam theory would, in fact, be rea- sonable if one were to take in account the nature of the support boundary conditions. Some users will notice that the plane stress solutions converge to a maximum deﬂection nearly half that obtained by simple beam theory. In this case, they may investigate the possibility of pin- ning the end supports of the two-dimensional mesh at the mid-plane location of the neutral axis. is, of course, lowers the area moment of inertia by close to a factor of two, bringing the theory and two-dimensional analysis into very good agreement. Alternatively, they can apply beam theory employing oﬀset neutral axes, i. e., one-dimensional beam element line models with a moment of inertia about some point well below the neutral axis as will be the case for pin supports on the bottom edge of the beam. is exercise illustrates the rather strong dependence of the solution of the boundary value problem on the precise prescrip- tion of the support boundary conditions, as well as the bounding nature of two-dimensional continuum approximations for truly three-dimensional problems. When one accepts that the three-dimensional analysis is accurate, users can become under- standably frustrated that a two-dimensional analysis is always an approximation whose accuracy they have to be prepared to verify. While a three-dimensional analysis may be accurate for this particular problem, it requires substantially more computational eﬀort and cost than the corre- sponding two-dimensional plane stress approximation. 4.5. LESSONS LEARNED 67 4.5 LESSONS LEARNED ese two case studies point out several realities in application of the ﬁnite element method. 1. When one proceeds to higher dimensions, while Poisson eﬀects, i. e., lateral dimensional changes and out-of-plane warping, are captured, the precise manner in which classical boundary conditions such as simple supports or clamped supports are applied can have signiﬁcant inﬂuence on the numerical results. 2. Improper boundary conditions can lead one to purposefully choose poorer element formu- lations and coarser meshes in attempts to validate a solution. 3. While one- and two-dimensional idealizations help reduce computational eﬀort, they must be understood and substantiated. ese lessons illustrate several of the common errors encountered in using the ﬁnite element method [Chalice Engineering, LLC, 2009]. ese include: 1. using wrong elements for an analysis, 2. incorrectly prescribing boundary conditions, 3. incorrectly applying theory for solution validation, 4. assuming ﬁnite element analysis is conservative, and 5. using ﬁnite element analysis for the sake of it. ere are arguably only two types of errors made in numerical simulation: either in faulty assumptions regarding the relevant physics governing the engineering system or discretization error in the numerical solution algorithm employed. Good analysts must understand and take responsibility for both. Modeling is, therefore, necessarily an iterative enterprise involving re- assessing the validity of one’s physical assumptions as one hones in on an acceptable solution. Because our numerical simulations are only approximations, this book has emphasized that users should be skeptical of their solutions prior to validating them. Further interesting reading re- garding modeling approximation and anomalies can be found in Deaton [2010, 2013], Dvorak [2003], Fleenor [2009], Grieve [2006], and Kurowski [2001, 2002a,b,c]. C H A P T E R 5 69 Wisdom Is Doing It In theory, theory and practice are the same. In practice, they are not. Albert Einstein Do you know the diﬀerence between knowledge and wisdom? Wisdom is doing it! Dan Millman A Peaceful Warrior Sometimes it is said that the application of science or a theory is “as much an art as a science.” e practice of the ﬁnite element method ﬁts the bill. Several authors have collected their own practical tips for application of the method. But, in general, books primarily about ﬁnite element theory do not present details regarding use of the method in practice. Books that attempt to address practical advice about applying the method in practice [Budynas, 2011, Kim and Sankar, 2009] almost always address issues that can be traced to the original list of ten most common mistakes presented in Chapter 1. Consider that the method is comprised of the following. 1. Preliminary analysis, which may entail: (a) simplifying the problem to obtain an analytical solution or estimation based on theory, (b) obtaining theoretical solutions representing upper or lower bounds for the solution, or (c) calculating the order of expected values for deﬂections and stresses and locations for their respective maxima/minima. 2. Pre-processing, which usually includes: (a) choosing an appropriate ﬁnite element formulation, (b) discretizing the domain globally, (c) reﬁning it locally in areas of interest, and (d) applying loads and displacement constraints. 70 5. WISDOM IS DOING IT 3. Solving the equations. 4. Post-processing the solution variables to compute (a) reaction forces and (b) internal stresses. 5. Interpreting and validating numerical solution results. Referring to the list of most commonly made mistakes reported in Chapter 1, we attempt to correlate this list with the steps performed in the ﬁnite element method in Table 5.1. Five of the ten common errors might be avoided by paying particular attention to a well-performed pre- liminary analysis. Errors in pre-processing result in four of the typical errors. ere is substantial overlap as preliminary analysis directly aﬀects the most substantial step in pre-processing, which is discretizing the domain. Finally, three commonly made mistakes can be avoided with prudent post-processing. e solution of the equations for nodal point equilibrium usually results in no errors. Note To e Instructor While it is always important for students to know what a piece of computational software is doing on their behalf, having students mathematically carry out the steps of computing element equations, assembling them into a global matrix equation, reducing its rank once the boundary conditions have been decided, and solving the reduced set of equations will all be done for them in practice by commercial software. Because of the relative importance of the other mistakes they will likely make, we question the utility of assigning students problems requiring this mathematics. Many times, these are precisely the types of assignments that are given in an introductory course in the ﬁnite element method. It may behoove all of us who teach the method to realize that if we only have a single chance to speak to students on behalf of the method, we should at least discuss the list of places they will likely make mistakes. We also might be of better service to their education by assigning open-ended problems that require them to focus more on the steps where they are most likely to err while we are available to intervene and correct any ongoing misconceptions and poor practices before they become matters of routine. Table 5.1: Mistakes listed by Chalice Engineering, LLC [2009] fall solely within portions of the analysis process performed by the analyst Analysis Step Preliminary Analysis Pre-processing Solution Post-processing Mistakes Made 1,2,3,7,9 3,6,9,10 0 2,4,5 5.1 PRELIMINARY ANALYSIS 5.1. PRELIMINARY ANALYSIS 71 Often, engineers go wrong early by ignoring what may arguably be the most important step. is is the preliminary analysis. is preliminary analysis takes place before one ever turns on the com- puter. Preliminary analysis consists of asking the question “What does one expect to happen?” To answer this question, one must apply mechanics theory. While most practical problems preclude analytical solutions, one can often simplify the problem to the extent where the order of deﬂec- tion and stresses can be estimated and one can identify where their respective maxima are likely to occur. Sometimes simpliﬁcations of the real problem will lead to simpler solutions that may repre- sent upper and lower bounds on deﬂections and stresses. Example 4.2 is a case in point. e ﬁnite element model is then created and analyzed to obtain a more precise, albeit approximate, solution whose quantitative results can be used for design purposes. When engineers neglect this step, they place themselves at a distinct disadvantage when attempting to later validate their numerical solution. It also places an analyst at a distinct disadvantage for pre-processing intelligently. It is often claimed by students that if they could compute the analytical solution, they wouldn’t need the ﬁnite element method. But, in the end, this is a convenient rationalization to avoid the work involved in preliminary analysis. It is a crucial step if for no other reason than that it feeds so heavily into the most important decision made in pre-processing: discretizing the domain. 5.2 PRE-PROCESSING Apart from preliminary analysis, the most common errors are made in pre-processing or estab- lishing the numerical model of a real physical process. But preliminary analysis plays a critical role in reasons analysts go wrong in creating their models. Recall our discussion in Chapter 4 regarding what we are approximating, speciﬁcally the discussion centered on Figs. 4.2 and 4.3 for piecewise interpolation. Because there is no single, unique way to discretize the domain, creating a good quality mesh is a skill often best acquired through experience. Creating a good domain discretization requires ﬁrst knowing something about the solution you are trying to approximate over that domain. is is because the ﬁnite element method approximates this solution with piece- wise lower-order polynomial interpolations (the ﬁnite elements themselves). For instance, if one is trying to approximate a periodic solution using elements with linear interpolation, one should be asking the question “How many linear segments are required to suﬃciently model a sinusoidal function over the domain prescribed?” So the decision of the element type, i. e., the solution in- terpolation polynomial order, and the decision on mesh density are intimately tied together given one knows something about the expected solution. An equally important consideration is that the internal stresses in a deformed model are related to strains, which are higher-order derivatives of the displacement ﬁeld. is has conse- quences that may best be illustrated by example. Consider a long, slender beam that is simply supported at both ends and loaded uniformly along its length as shown in Fig. 5.1. Over the 72 5. WISDOM IS DOING IT entire domain, the exact bending moment varies quadratically and the exact shear force varies linearly. Figure 5.1: A uniformly loaded, simply supported, long, slender beam exhibits transverse deﬂection that varies as a fourth-order polynomial along its span. e exact solutions are vexact D Mexact D Vexact D 2s3 s4(cid:1) (cid:0) wL4 24EI wL2 2 wL 2 (cid:0) s (cid:0) (cid:0)s (cid:0) C s2(cid:1) .1 2s/ ; (cid:0) (cid:1) D D D 1 lbf 24 lbf=ft, and EI where s x=L. If we decide to model this beam with a mesh containing three cubic, one- dimensional beam elements, we will eﬀectively be choosing to model the quartic function with three piecewise cubic functions. Consider a beam with length L 1 ft uniformly loaded with ft2. e normalized deﬂections predicted by this ﬁnite element w model are shown in Fig. 5.2, which clearly have excellent agreement with the analytical solution. Because bending moment varies linearly in a cubic beam element, the ﬁnite element pre- diction for the bending moment (and therefore the bending stress) over the beam then models a quadratic function with three linear segments. Finally, the linear variation of shear force is ap- proximated by three piecewise constant segments. ese FEA solutions are shown in Figs. 5.3 and 5.4, respectively. It is important to realize that while deﬂections are approximated well in this case, bending stress and shear force will only be captured reasonably well by successively localized reﬁnements in mesh discretization. D Considering the correlation of the FEA prediction with the corresponding exact solution, the higher the order of the derivative of the displacement one wishes to approximate, the poorer the method does with any given mesh. e implication is that one generally needs a ﬁner dis- cretization to capture stresses accurately than to capture the deformed shape. In other words: wL5.2. PRE-PROCESSING 73 Figure 5.2: Displacement predicted by three piecewise continuous cubic interpolations very closely approximates the single quartic analytical variation in deﬂection. Figure 5.3: Bending moment predicted by the three element model is piecewise linear. is prediction captures the quadratic moment variation less closely than the cubic displacement interpolation captures the deformed shape. 00:20:40:60:81(cid:0)0:3(cid:0)0:2(cid:0)0:10/PSNBMJ[FEQPTJUJPO(cid:13)s=x/L/PSNBMJ[FEEFnFDUJPO(cid:13)v"OBMZUJDBM'&"00:20:40:60:810123/PSNBMJ[FEQPTJUJPO(cid:13)s=x/L/PSNBMJ[FECFOEJOHNPNFOU(cid:13)M"OBMZUJDBM'&"74 5. WISDOM IS DOING IT Figure 5.4: Transverse shear force predicted by the three element model is piecewise constant. is prediction captures the linear shear force variation less closely than the linear moment interpolation captures the quadratic bending moment. 1. the global displacement solution is generally more accurate than the global stress solution; 2. the discretization necessary to capture stresses accurately is ﬁner than that needed to capture deformations accurately; and 3. what constitutes an acceptable mesh will be determined by whether one wishes a more accurate answer for deformation or stress. It is, therefore, absolutely essential to know what element type one is using to properly mesh the problem domain and interpret one’s results. 5.2.1 THE CAST OF ELEMENT CHARACTERS An excellent presentation and discussion of practical element formulations is given in Budynas [2011]. Basically, one can place the majority of ﬁnite element formulations in one of ﬁve cate- gories. 1. One-dimensional formulations for purely axial response (bar elements). Most elements are two-noded and utilize linear interpolation functions. 2. One-dimensional formulations that account for axial and out-of-plane bending response (beam elements). Most elements are two-noded and utilize cubic polynomial interpolation functions for transverse deﬂections. 00:20:40:60:81(cid:0)10(cid:0)50510/PSNBMJ[FEQPTJUJPO(cid:13)s=x/L/PSNBMJ[FETIFBSGPSDF(cid:13)V"OBMZUJDBM'&"5.2. PRE-PROCESSING 75 3. Two-dimensional solid elements that account for two-dimensional in-plane stress states (plane stress/plane strain/axisymmetric solid or continuum elements). ese elements may be triangular or quadrilateral. Typically, linear and parabolic interpolation functions are available. ese eﬀectively behave like two-dimensional analogs to one-dimensional bar elements. 4. Two-dimensional elements that respond to out-of-plane loads and moments (plate or shell elements). Plate elements eﬀectively behave like two-dimensional analogs to one- dimensional beam elements. 5. Full three-dimensional solid elements. Typical elements are tetrahedral and hexahedral (brick) elements. Both linear and parabolic interpolation functions are oﬀered in most ele- ment libraries. ese element formulations are illustrated in Table 5.2. With regard to speciﬁc element formulations: 1. One-dimensional element formulations cannot capture stress concentrations and should be avoided where such stress risers are expected. 2. Two-dimensional element formulations can reduce the computational mesh size by orders of magnitude when conditions of plane stress, plane strain, or axisymmetry apply. Two- dimensional analysis should be considered in these limits. 3. For such two-dimensional element formulations, generally quadrilateral elements (of the same order interpolation) outperform triangular elements. 4. Two-dimensional element formulations used to capture in-plane bending should contain a minimum of three to ﬁve elements across the cross section perpendicular to the bending axis. Generally, where in-plane bending occurs in two-dimensional analysis, one should consider use of a higher-order, usually parabolic element interpolation. 5. One should avoid using three-noded triangular plate elements for out-of-plane bending as they are particularly stiﬀ. In such analyses, the number of degrees of freedom necessary for a convergent solution will often dictate use of a higher-order element interpolation. 6. For three-dimensional solid analysis, hexahedral (brick) elements generally outperform tetrahedral elements, but tetrahedral elements will often be used by automated mesh gen- erators because they can most easily ﬁll generally complex three-dimensional regions. 7. When using tetrahedral element formulations in three-dimensional analysis, it is preferred to use a higher order, i. e., parabolic interpolation of displacements. 8. ree-dimensional solid elements often do not include rotational nodal degrees of freedom. erefore, modeling global rotation at a boundary becomes yet a further approximation. 76 5. WISDOM IS DOING IT Table 5.2: Basic ﬁnite element types Element 1D Linear Schematic 2D Triangular 2D Rectangular 3D Tetrahedral 3D Hexahedral 5.2.2 GOOD AND BAD ELEMENTS Good quality meshes typically employ: • aspect ratios as close to unity as is feasible, i. e., equal side lengths in any single element; • element shapes that avoid irregularities such as excessively small or large corner (skew) an- gles, e. g., 90(cid:14) angles in quadrilaterals and 60(cid:14) angles in triangles; • gradual transition in element size. Rapid transitions in element size should be avoided whenever possible; and 5.2. PRE-PROCESSING 77 • mesh reﬁnement where the stress gradients are large. Poor quality elements will inevitably appear in complex geometries, particularly when an analyst employs automatic mesh generators. Typically, commercial software will ﬂag such elements with warnings and alert the user. An analyst is then responsible for adjusting the mesh locally, perhaps manually if necessary, to assure good quality results. In general, it is diﬃcult to avoid having an arbitrarily oriented element in a region of con- stant stress in a mesh. For this reason, element formulations are tested to ensure they can predict reasonably constant stress values in such cases. is is called the patch test. All good elements should be able to pass the patch test [Irons and Shrive, 1983]. A nice discussion of good and bad element behaviors is presented in Irons and Shrive [1983] and Kim and Sankar [2009]. Many good meshing strategies are outlined by Budynas [2011]. 5.2.3 APPLYING BOUNDARY CONSTRAINTS Several rules of thumb are necessary to consider when applying boundary constraints. 1. Be sure the boundary conditions applied to the model always remove all rigid body trans- lation and rotation, i. e., “always tie down the horse.” Some commercial software packages will attempt to solve such ill-posed problems and deliver no results. 2. Errors in boundary conditions can be subtle and hard to recognize. For example, consider the two-dimensional constraints applied for the simple supports in Example 4.2. Because they are not applied along the neutral axis of the beam, the apparent ﬂexural stiﬀness of the beam is nearly twice that one would calculate using elementary beam theory. 3. Applying idealized boundary conditions becomes more diﬃcult in higher dimensions. For instance, applying a simple support is straightforward in one-dimensional elements, but in two and three dimensions, there are multiple ways to apply the constraint at the domain edges. is same quandary occurs when applying any idealized boundary constraint such as a clamped edge in two or three dimensions where rotational degrees of freedom are not available and constraints on the local slope of the deformed structure cannot be explicitly constrained. 4. Local results, particularly maximum deﬂections or stresses, can be very sensitive to small variations in the application of boundary condition constraints. 5.2.4 APPLYING EXTERNAL LOADS Several rules of thumb should be considered when applying loads to the structure. 78 5. WISDOM IS DOING IT 1. Point loads are idealized load applications and will generally result in unreasonably large internal stresses in the vicinity of the application point. One should consider applying lo- calized pressures when possible. 2. Usually, when concentrated loads are applied the stresses resulting from statically equivalent loads will be independent of the method of application a distance away from the load that is of the order of the transverse dimensions of the structure locally. is is the principle of St. Venant. It should be employed liberally in application of the ﬁnite element method and in interpreting its results. 3. In an analogous manner as with prescribing boundary constraints, when one models do- mains in two or three dimensions, element formulations may not have rotational degrees of freedom. For such cases, application of a concentrated moment or couple is no longer unique and not as straightforward as it is when using one-dimensional elements. In such cases, one should consider experimenting with diﬀerent possible prescriptions of the cou- ple using local point loads and compare stresses a St. Venant’s decay distance away from the concentrated moment. 4. Generally, the order of complexity of the solution to boundary value problems will increase with the order of the loading. Given a speciﬁc ﬁnite element formulation, the more complex the loading, the more approximate the solution. is was illustrated in the beam example of Fig. 5.1. Such one-dimensional beam elements capture bending stress and shear forces exactly when only point loads and couples are applied. ese same bending stresses and shear forces are only approximately predicted when distributed or more complex loading is applied. 5.3 POST-PROCESSING Computer graphics has achieved such a level of polish and versatility as to inspire great trust in the underlying analysis, a trust that may be unwarranted. (One can now make mistakes with more conﬁdence than ever before.) R.D. Cook, D.S. Malkus, and M.E. Plesha Concepts and Applications of Finite Element Analysis, 3rd Edition ere are several rules of thumb to consider when post-processing results. 1. Plotting deformed shapes of structures is a good way to spot particular errors in application of boundary constraints. 2. Element stresses are most accurate at internal integration points where they are calculated. ese stresses are averaged at nodes shared by elements. e nodal-averaged stresses are interpolated between nodes, contoured, and then, generally, artiﬁcially smoothed to create contoured results. 5.4. FURTHER RULES TO LIVE BY IN PRACTICE 79 3. When displaying stress contours, it is often good practice to contour element values directly as well as the nodally averaged values. is is a good practice because: (a) If the element stresses are observably discontinuous to the eye, then the stress gradients are larger than the mesh is capable of predicting and one should reﬁne the mesh. (b) If the element stresses are not overly discontinuous, then the smoothed contours are suﬃcient to represent the overall character of the solution. 5.4 FURTHER RULES TO LIVE BY IN PRACTICE One can establish a set of ground rules that can serve as a starting point for good practical ﬁnite element analysis. Again, this list, while not exhaustive, attempts to address several of the most common errors made in applying the ﬁnite element method. 1. Use the ﬁnite element method only when it is necessary, i. e., when the simplest formulae outlined in Chapter 2 or other analytical methods are not generally applicable. 2. ere are no units involved in formulation of the ﬁnite element method. An analyst must always use dimensionally consistent units and interpret results accordingly. 3. e ﬁnite element discretization results in a model that is too stiﬀ, implying: (a) models upon which only displacement boundary conditions are applied will, in general, result in stresses that are higher than the actual stresses; (b) models upon which only force boundary conditions are applied will, in general, result in displacements that are smaller than the actual displacements; and (c) no general conclusions can be made once the boundary constraints are mixed, which is most often the case. 4. One should not generally assume that ﬁnite element analysis is conservative. 5. It is not necessarily true that three-dimensional analysis outperforms two-dimensional anal- ysis or that two-dimensional analysis outperforms one-dimensional analysis. 6. One should consider mesh reﬁnements in regions where there are large gradients in material stiﬀness such as dissimilar material interfaces or large discontinuities in load-bearing areas. 7. Consider applying the principle of St. Venant in order to avoid modeling geometric fea- tures wherein the stress results are not of primary importance, e. g., details at or near load application points. 80 5. WISDOM IS DOING IT 8. Exploit global symmetry wherever and as much as possible. 9. When importing geometries from solid modeling software, it is important, when possible, to create the solid model with design intent. By this, we mean that solid geometry entities such as grid points and surfaces should be strategically created such that boundary condi- tions can be placed on nodes and element edges that lie, respectively, on these solid entities. is practice allows one to usually perform mesh reﬁnements and iterations without the inconvenience of re-applying the boundary conditions. 5.5 SOLUTION VALIDATION Believe nothing, no matter where you read it or who said it, unless it agrees with your own reason and your own common sense. Buddha Nobody believes a model except the one who devised it; everyone believes an experiment except the one who performed it. Albert Einstein Perhaps not all experimentalists are so cautious nor all modelers as careless, but, as evidenced by the common errors made by analysts, it can seem as if those who computationally model systems can be led to a false sense of security in their numerical solutions. We like to recommend that all numerical model results must, initially at least, be viewed through skeptical spectacles. If one treats at least one’s initial ﬁndings as guilty until proven innocent, one will be less likely to accept results that are incorrect. In general, an engineering analysis can be accomplished either 1. theoretically, from ﬁrst principles, 2. approximately, using numerical analysis, or 3. empirically, using discrete experiments. Having all three one might consider the mother lode. But, in any analysis, we should shoot for results of one approach to be benchmarked or validated by one or both of the others. Here we deﬁne validation as the process of determining the degree to which a model is an accurate rep- resentation of the real world from the perspective of the intended uses of the model. In essence, validation provides evidence that the correct model is solved to a given level of accuracy. As we are attempting to prove the results of our numerical analyses innocent, we should validate all results with either theoretical results or experimental data. While theoretical results are often precluded in real applications, they may have limited applicability when they represent 5.6. VERIFICATION 81 1. upper and lower bounds of the real solution or 2. the correct solution in only part of the global domain. When using experimental results for validation, one should consider the following. 1. ey are often considered the harbinger of truth. 2. Boundary constraints more easily realized in the laboratory can sometimes be diﬃcult to realize in a computational model, for example, machine compliance for a tensile test speci- men. 3. Boundary constraints more easily realized in discrete analysis can sometimes be more diﬃ- cult to achieve in the laboratory. 4. Experiments can be costly and time-consuming. Numerical analyses should not be trusted without either theoretically or experimentally validat- ing the solution. Neither should the results of numerical analyses be accepted without proper examination of insensitivity to the mesh discretization. As in Example 4.2, a proper convergence study should always be attempted. Correct results can only be obtained in the limit as the results are no longer sensitive to the use of any ﬁner discretization of the global domain. We term such convergence mesh insensitivity. When the results fall within a speciﬁed insensitivity to the mesh or element size, one can conclude the numerical analysis has converged. It is important to note that this is a necessary but not suﬃcient condition for the computational results to be acceptable or a correct solution to the problem posed. Recall that the solutions in Example 4.2 eventually converged, but those assuming plane strain conditions were incorrect, i. e., they solved the wrong problem. 5.6 VERIFICATION Extensive tests showed that many software codes widely used in science and engineering are not as accurate as we would like to think. Les Hatton Oakwood Computing By veriﬁcation, we refer to the process of determining that a model implementation accurately represents the developer’s conceptual description. Veriﬁcation provides evidence that the numeri- cal model is solved correctly. It is tacitly assumed that commercial software is completely debugged before a version is released. Les Hatton at Oakwood Computing has presented interesting ﬁnd- ings that indicate errors in software and programming, while small in number, do occur. is sometimes happens in commercial FEA software. Most instances of which we are aware have 82 5. WISDOM IS DOING IT been in the post-processing software. While the primary variable solution is most often entirely correct, sometimes listings and contour plot variables are not stored correctly and are subsequently improperly displayed. Luckily, these instances are rare and not a primary cause of errors on the part of the analyst. In any case, they can be caught by prudent use of preliminary analysis. We believe that the majority of textbooks addressing introductory ﬁnite elements primarily and predominantly emphasize the mathematical foundation and procedural application of the method. We have emphasized, rather, a practical approach based on recognition that most errors made in application of the method are in pre- and post-processing and are made mostly in model development. Further interesting reading regarding issues of practical application of the ﬁnite element method can be found in Dunder and Ridlon [1978], Dvorak [2003], Gokhale et al. [2008], Morris [2008], and Sastry [2010]. Summary 83 e most common mistakes made by novice users of the ﬁnite element method involve procedural steps performed explicitly by the user. Exercises in many textbooks emphasize mathe- matical elements of the procedure performed strictly by the computer. We have introduced an al- ternative examination of the method used in practice that focuses on a published list of commonly made mistakes. Examination of the root causes of such mistakes reveals that they are intimately tied more to a user’s command of underlying theory of strength of materials and less to a user’s ability to reproduce mathematical computations undertaken by the processor. We outlined a basic requisite skill set necessary to undertake use of the ﬁnite element method. en we explored excursions where ﬁrst the underlying theory no longer holds, and then ultimately where users are most likely to interface with the software in a faulty manner. Fi- nally, we posited a short listing of rules for applying the ﬁnite element method in practice. While this list is generally acknowledged by many practitioners, we ﬁnd that it is typically relegated to more of an aside and less of a central theme. We provided relatively simple examples to showcase where mistakes are made when one does not follow practical rules of thumb from the start. If the method is taught with more of this emphasis on expectation failures of newly learned mechanics of materials, and more prudent attention to questioning computational complacency, it is our hope that the occurrence of these common mistakes may be reduced. Also, an earlier intro- duction to the method as a practical tool may prove to be a useful precursor to better and deeper learning of the mathematics underlying ﬁnite element interpolation. We argue that, instead of emphasizing steps performed well by the computer, becoming competent in ﬁnite element anal- ysis should focus on the steps of the process where analyst’s choices have the greatest impact on the results. Afterword 85 is book was written to supplement texts on FEA theory with prudent rules for practice by focusing speciﬁcally on errors commonly made in industry. Based on our experience teaching the method to undergraduates, we included examples where students have faltered in the past and couched these in terms of expectation failures. After reading this book, if you have comments on the presentation of the exercises or wish to suggest additional examples that emphasize expecta- tion failures, feel free to contact the authors at [email protected]. ank you, in advance, for any input you have. Bibliography 87 Allain, R. (2011). Just Enough Physics. Amazon Digital Services. 27 Bain, K. (2004). What the Best College Teachers Do. 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SDC Publications. xiv Lawrence, K. L. (2012). ANSYS Workbench Tutorial Release 14. SDC Publications. xiv Lee, H.-H. (2012). Finite Element Simulations with ANSYS Workbench 14. SDC Publications. xiv Logan, D. L. (2001). Applications in the Finite Element Method. Brooks Cole Publishing Com- pany. xiv McDermott, L. C. (1984). Research on Conceptual Understanding in Mechanics. Physics Today, 37:24–34. DOI: 10.1063/1.2916318. xii, 5 McDermott, L. C. (2001). Oersted Medal Lecture 2001: Physics Education Research: e Key to Student Learning. American Journal of Physics, 69:1127–1137. DOI: 10.1119/1.1389280. xiii Montfort, D., Brown, S., and Pollack, D. (2009). An Investigation of Students’ Conceptual Un- derstanding in Related Sophomore to Graduate-Level Engineering and Mechanics Courses. Journal of Engineering Education, 98:111–129. DOI: 10.1002/j.2168-9830.2009.tb01011.x. xii, 5 Morris, A. (2008). A Practical Guide to Reliable Finite Element Modeling. J. Wiley and Sons. 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E., editor (1997). Rules of umb for Mechanical Engineers: A Manual for Quick, Accurate Solutions to Everyday Mechanical Engineering Problems. ROTpub. 27 90 BIBLIOGRAPHY Prantil, V. C. and Howard, W. E. (2007). Teaching Finite Element Simulation in Conjunction with Experiment and eory in an Integrated Systems Design. In 9th U.S. National Congress on Computational Mechanics. 45 Prantil, V. C. and Howard, W. E. (2008). Incorporating Expectation Failures in an Undergrad- uate Finite Element Course. In American Society for Engineering Education Annual Conference and Exposition, volume 1. ASEE, Curran Associates, Inc. 45 Public Broadcasting System–NOVA (1993). e Best Mind Since Einstein - Richard Feynman Biography. Television Production. 49 Riley, W. F., Sturges, L. D., and Morris, D. H. (2007). Mechanics of Materials, 6th Edition. J Wiley and Sons. 33 Sastry, S. S. (2010). Accepted Practices in Practical Finite Element Analysis of Struc- tures. In http://www.nafems.org/downloads/india/webinar/mar_10/accepted_fe_ practices_nafems_india.pdf. 82 Solverson, R. (1953). Stress Concentrations in Fillets. Master’s thesis, California Institute of Technology. 35 Steif, P. S. (2012). Mechanics of Materials: An Integrated Learning System. J Wiley and Sons. 27, 33 Streveler, R., Litzinger, T., Miller, R., and Steif, P. (2008). Learning Conceptual Knowledge in the Engineering Sciences: Overview and Future Research Directions. Journal of Engineering Education, 97:279–294. DOI: 10.1002/j.2168-9830.2008.tb00979.x. xii, 5 ompson, E. G. (2004). Introduction to the Finite Element Method: eory, Programming and Applications. John Wiley and Sons. xiv Young, W. C. and Budynas, R. G. (2002). Roark’s Formulas for Stress and Strain, 7th Edition. McGraw Hill. 35, 45 Zienkiewicz, O. and Taylor, R. (2005). e Finite Element Method for Solid & Structural Mechan- ics, 6th Edition. Elsevier, Butterworth-Heinemann Publishing. xiv Zienkiewicz, O., Taylor, R., and Zhu, J. (2005). e Finite Element Method: Its Basis & Funda- mentals, 6th Edition. Elsevier, Butterworth-Heinemann Publishing. xiv Authors’ Biographies 91 VINCENT C. PRANTIL Vincent C. Prantil earned his B.S., M.S., and Ph.D. in Mechanical Engineering from Cornell University where he was awarded e Sibley Prize in Mechanical Engineering and held an An- drew Dickson White Presidential Fellowship. He was a Senior Member of Technical Staﬀ at Sandia National Laboratories California in the Applied Mechanics and Materials Modeling Di- rectorates for 11 years. His research interests lie in microstructural material modeling, dry gran- ular materials, metals plasticity, ﬁnite element, and numerical analysis. He was jointly awarded an R&D100 award for co-developing the Sandia Microstructure-Property Model Software in 2000 and held the Otto Maha Research Fellowship in Fluid Power at the Milwaukee School of Engineering (MSOE) from 2006–2008. He joined the faculty in the Department of Mechanical Engineering at MSOE in September 2000 where he presently specializes in ﬁnite element model development, numerical methods, and dynamic systems modeling. CHRISTOPHER PAPADOPOULOS Christopher Papadopoulos earned B.S. degrees in Civil Engineering and Mathematics in 1993 at Carnegie Mellon University, and his Ph.D. in eoretical and Applied Mechanics in 1999 at Cornell University, where he was a National Science Foundation Graduate Research Fellow. He is currently a member of the faculty of the Department of Engineering Science and Materials at the University of Puerto Rico, Mayagüez (UPRM), where he has worked since 2009. He was previously a member of the faculty in the Department of Civil Engineering and Mechanics at the University of Wisconsin–Milwaukee from 2001–2008. Chris is currently the principal investiga- tor of two NSF projects, one in appropriate technology and engineering ethics, and the other in mechanics education. He has additional research interests in nonlinear structural mechanics and biomechanics. Chris currently serves as Secretary and Executive Board Member of the ASEE Mechanics Division and he is the chair of the Mechanics Committee in his department. He is also a member of a campus committee that arranged for an art exhibit honoring the life of Roberto Clemente to be donated to the UPRM campus from the Smithsonian Museum. Chris is a pas- sionate educator and advocate for humanitarian uses of technology. In his free time he enjoys swimming, cycling, running, cooking, and learning the languages of the Caribbean. 92 AUTHORS’ BIOGRAPHIES PAUL D. GESSLER Paul D. Gessler is currently a graduate student pursuing his M.S. in the Mechanical Engineering Department at Marquette University in Milwaukee, Wisconsin. He earned his B.S. in Mechan- ical Engineering from the Milwaukee School of Engineering in 2012. Paul’s main interests are using modeling and simulation at an appropriate abstraction level to improve the product design and systems engineering process. He has experience with a wide variety of commercial FEA/CFD codes and has written several bespoke codes for ﬂuid, structural, and thermal system analysis. Paul hopes to be a proponent of model-based design practices in industry throughout his career.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=9110817.pdf&bkn=9110816&pdfType=book	Introduction to Engineering Research Wendy C. Crone, University of Wisconsin-Madison Undergraduate and first-year graduate students engaging in engineering research need more than technical skills and tools to be successful. From finding a research position and funding, to getting the mentoring needed to be successful while conducting research responsibly, to learning how to do the other aspects of research associated with project management and communication, this book provides novice researchers with the guidance they need to begin developing mastery. Awareness and deeper understanding of the broader context of research reduces barriers to success, increases capacity to contribute to a research team, and enhances ability to work both independently and collaboratively. Being prepared for what’s to come and knowing the questions to ask along the way allows those entering researcher to become more comfortable engaging with not only the research itself but also their colleagues and mentors. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com store.morganclaypool.com C R O N E I N T R O D U C T I O N T O E N G I N E E R I N G R E S E A R C H M O R G A N & C L A Y P O O L Introduction to Engineering Research Synthesis Lectures on Engineering, Science, and Technology Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Introduction to Engineering Research Wendy C. Crone 2020 Theory of Electromagnetic Beams John Lekner 2020 The Search for the Absolute: How Magic Became Science Jeﬀrey H. Williams 2020 The Big Picture: The Universe in Five S.T.E.P.S. John Beaver 2020 Relativistic Classical Mechanics and Electrodynamics Martin Land and Lawrence P. Horwitz 2019 Generating Functions in Engineering and the Applied Sciences Rajan Chattamvelli and Ramalingam Shanmugam 2019 iv Transformative Teaching: A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam, Brooke Coley, and Audrey Boklage 2019 Ancient Hindu Science: Its Transmission and Impact on World Cultures Alok Kumar 2019 Value Rational Engineering Shuichi Fukuda 2018 Strategic Cost Fundamentals: for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese 2018 Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw 2018 Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi 2018 Empowering Professional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimization (with illustrative case study problems and solutions), Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 v The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 vi Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 vii Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2020 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Introduction to Engineering Research Wendy C. Crone www.morganclaypool.com ISBN: 9781681737997 ISBN: 9781681738000 ISBN: 9781681738017 paperback ebook hardcover DOI 10.2200/S00995ED1V01Y202002EST006 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY Lecture #38 Series ISSN Print 2690-0300 Electronic 2690-0327 Introduction to Engineering Research Wendy C. Crone University of Wisconsin–Madison SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY #38 CM&cLaypoolMorganpublishers&ABSTRACT Undergraduate and ﬁrst-year graduate students engaging in engineering research need more than technical skills and tools to be successful. From ﬁnding a research position and funding, to getting the mentoring needed to be successful while conducting research responsibly, to learning how to do the other aspects of research associated with project management and communica- tion, this book provides novice researchers with the guidance they need to begin developing mastery. Awareness and deeper understanding of the broader context of research reduces barri- ers to success, increases capacity to contribute to a research team, and enhances ability to work both independently and collaboratively. Being prepared for what’s to come and knowing the questions to ask along the way allows those entering researcher to become more comfortable engaging with not only the research itself but also their colleagues and mentors. KEYWORDS engineering research, technical communications, research ethics, project manage- ment, mentoring xi To my family. Contents xiii 1 2 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii Introduction to Engineering Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Who is This Book for? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 How Research is Diﬀerent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2.1 Engineering Research Deﬁned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Engineering Research Careers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Finding the Right Research Position for You . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 2.2 Societal Implications of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Identifying a Research Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Undergraduate Research Experiences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 The Graduate School Application Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Is Graduate School Right for You? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 The Graduate School Application Packet . . . . . . . . . . . . . . . . . . . . . . 20 2.4.3 The Application Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.4 Visiting a Graduate Program You Would Like to Attend . . . . . . . . . . 24 2.4.5 Getting Accepted into a Graduate Program . . . . . . . . . . . . . . . . . . . . 27 2.5 Funding of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5.1 U.S. Model of Research Universities . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Funding Your Graduate Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.2 Fellowship Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.3 2.6 Understanding the Organization of Your Research Group . . . . . . . . . . . . . . . . 32 xiv 3 4 5 Becoming a Researcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 Developing a Relationship with Your Research Mentor . . . . . . . . . . . . . . . . . . 35 3.2 Aligning Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Developing Expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4 Developing Your Own Identity as a Researcher . . . . . . . . . . . . . . . . . . . . . . . . 43 Tracking Your Development as a Researcher . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.5 3.6 Being an Eﬀective Team Member and Collaborator . . . . . . . . . . . . . . . . . . . . 48 3.7 Working with a Diverse Research Team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.8 Developing Global Competency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.8.1 Other Resources on Global Competency . . . . . . . . . . . . . . . . . . . . . . . 64 3.9 Networking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Building on the Research of Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.1 The Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Valuing What Came Before You . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.2 Reading Journal Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Reading Critically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.4 Literature Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Proper Citation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.6 4.7 Citation Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.8 Preparing a Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.9 Crediting the Work of Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Conducting Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.1 Scientiﬁc Habits of the Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.1.1 Other Resources on Scientiﬁc Method . . . . . . . . . . . . . . . . . . . . . . . 106 5.2 Developing a Research Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3 Getting Started and Staying Motivated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Project Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4 5.4.1 Project Management Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.5 Scheduling Committee Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.6 Navigating Roadblocks and Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Research Ethics (Error, Negligence, Misconduct) . . . . . . . . . . . . . . . . . . . . . 126 5.7 5.7.1 Misconduct Case Studies and the D.I.S.O.R.D.E.R. Framework . . 129 5.7.2 Other Resources on Research Ethics . . . . . . . . . . . . . . . . . . . . . . . . . 132 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.8 6 7 8 9 xv Documenting Your Research Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.1 Keeping a Research Notebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.1.1 Documenting Your Research in a Paper Laboratory Notebook . . . . 137 6.1.2 Documenting Your Research in an Electronic Research Notebook . 139 6.1.3 Regular Evaluation of Your Research Notebook . . . . . . . . . . . . . . . . 139 6.2 Data Storage and Backup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Avoiding Data Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.3 Sharing Your Research via Oral Communication . . . . . . . . . . . . . . . . . . . . . . . 147 Informal Conversations with Other Researchers . . . . . . . . . . . . . . . . . . . . . . 147 7.1 Informal Conversations with Nonspecialist Audiences . . . . . . . . . . . . . . . . . . 148 7.2 Engineering Outreach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.3 7.4 Poster Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7.5 The Research Talk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Resources on Oral Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.6 Sharing your Research via Written Communication . . . . . . . . . . . . . . . . . . . . 165 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Translating Technical Topics in Written Formats . . . . . . . . . . . . . . . . . . . . . . 165 Basic Principles of Technical Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.2.1 Dealing with Writer’s Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Standard Formats in Technical Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.3.1 Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.3.2 Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.3.3 Technical Writing for a Proposal, Thesis, or Journal Article . . . . . . . 172 Reﬁning your Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 8.4.1 Writing Workshops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Issues Surrounding Authorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Publishing your Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Resources on Written Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Safeguarding Your Personal Health and Happiness . . . . . . . . . . . . . . . . . . . . . 185 9.1 The Challenges You May Face in Graduate School . . . . . . . . . . . . . . . . . . . . 185 9.1.1 Graduate Student Mental Health . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 9.2 Steps You Can Take to Be Healthier and Happier . . . . . . . . . . . . . . . . . . . . . 187 9.3 Getting Sleep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 9.4 Getting Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 xvi 9.5 Eating Healthy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 9.6 Creative Outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Employing Mindfulness Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 9.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 9.8 Making Time for it All Afterword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Foreword xvii You may be dipping your toe into engineering research as an undergraduate or you may have decided that a graduate degree in engineering is the right path to pursue. In either case, there are a number of things that you can learn up front that will make your research experience a positive one and will give you more time and capacity to be the most creative and innovative person that you can be. Engineering research is a very diﬀerent endeavor than the traditional coursework that you have taken up to this point in your academic career. Students often learn about the broader context of engineering research and the ancillary skills needed to be a successful researcher as they stumble across the need for them. However, that unstructured process is wasteful and takes away from opportunities for discovery and innovation. This book provides guidance and resources on topics ranging from reading journal articles and responsible conduct of research to project management and technical communication. It will serve as a supplement to your interactions with research mentors, advisors, and peers as you engage in engineering research. Student Perspective Students who have recently begun engaging in research have fresh and insightful viewpoints on both the context and process of research that is best expressed through their own voices. Throughout this book you will ﬁnd per- spectives from students who are reﬂecting on their experiences conducting research projects. These insights and comments are intended to give you a review on research from a diﬀerent lens. Preface xix Both research as an undergraduate and the transition into research as a ﬁrst-year graduate stu- dent is unlike most of the coursework and school experiences that one has had prior to entering into such an undertaking. Although we carry our technical expertise with us, there are often gaps in knowledge. Additionally, the research enterprise itself is foreign. Without the proper guid- ance and support, many students ﬂounder and struggle to set themselves on a successful course. This seems wasteful of people’s time, disheartening to the individuals involved, and ultimately adds to the attrition seen in graduate programs. Several years ago, I co-authored an article on topics important to the broader context of engineering research based on an undergraduate course in engineering research developed at the University of Wisconsin–Madison.1 Additionally, summer undergraduate research experiences at campuses and national laboratories have developed accompanying workshops,2;3;4 courses,5;6 and even “boot-camp” experiences7 that help students to ﬁnd and understand the scientiﬁc lit- erature, appreciate the societal impact of engineering research responsible conduct of research, communicating research ﬁndings, research careers, and the graduate school application process. This broader training outside the of the speciﬁc research experience has been long advocated by the Council on Undergraduate Research as critical to “socializ[ing] students in the research laboratory culture.8” The semester-long Introduction to Engineering Research course developed for the Engineer- ing Physics undergraduate degree program and taught at University of Wisconsin–Madison ad- 1Cadwell, K., Crone, W., 2008. Training undergraduates in the broader context of the research enterprise, ASEE Annual Conference and Exposition, Conference Proceedings, 1364, 1–9. 2The Undergraduate Research Center for Sciences, Engineering and Mathematics and the Center for Academic and Research Excellence, University of California at Los Angeles, http://college.ucla.edu/urc-care/. Accessed January 2008. 3Wilson, R., Cramer, A., and Smith, J. L., 2004. Research is another word for education, from Reinvigorating the Un- dergraduate Experience: Successful Models Supported by NSF’s AIRE/RAIRE Program, L. R. Kauﬀman and J. E. Stocks, Eds., Council on Undergraduate Research, Washington, DC. 4The University of Washington Undergraduate Research Program. http://www.washington.edu/research/urp/, accessed January 2008. 5The University of Virginia Department of Science, Technology, and Society Undergraduate Thesis Project, http:// www.sts.virginia.edu/stshome/tiki-index.php?page=Undergraduate+ Thesis accessed January 2008. 6Katkin, W., 2004. The integration of research and education: A case study of reinventing undergraduate education at a research university, from Reinvigorating the Undergraduate Experience: Successful Models Supported by NSF’s AIRE/RAIRE Program, L. R. Kauﬀman and J. E. Stocks, Eds., Council on Undergraduate Research, Washington, DC: 2004. 7Bahr, D. F. and Findley, K. O., 2007. An intensive ‘camp’ format to provide undergraduate research experiences to ﬁrst year students. Materials Research Society 2007 Fall Meeting: Session W4: Implementing New Course Materials and Strategies, November 28. 8Merkel, C. A. and Baker, S. M., How to Mentor Undergraduate Researchers, Council on Undergraduate Research, Wash- ington, DC, 2002. xx PREFACE dressed the topic above as well as the importance of diversity in research, research collaboration, safety, and intellectual property. This course was later adapted and implemented at Washington State University and University of Central Florida in a National Science Foundation funded ef- fort. The evaluation of the implementations on their campuses showed that “there was a measur- able increase in the understanding of undergraduate research in the students at all institutions.9” The subsequent work performed showed that the mode of delivery did not inﬂuence the student outcomes. “Similar gains in conceptual awareness between each course format and at each insti- tution” were shown with a one-week faculty-led boot camp, a three-day peer mentor-led course, and a semester-long faculty-led course.10 Thus, I believe that the usage of the content provided in this book can be successfully adapted to a number of diﬀerent delivery modes. I wholeheartedly agree with the assessment of Schneider et al. that “By introducing stu- dents to the nuances of the research environment, we believe that preresearch courses reduce bar- riers to involvement and provide conﬁdence and knowledge for all students who participate.11” In our evaluations of the Engineering Physics degree program at the UW–Madison, upon which this book is based, the students who completed the program rated their research conﬁdence and skill levels highly. The majority of students felt that they were able to make contributions to a research team, explain their research topic to other engineers as well as non-engineers, docu- ment their research, provide their peers with constructive feedback on their research projects, and identify research misconduct issues. They also reported that they gained skills in conducting a literature search, understanding journal papers, conducting a research project, working both independently and collaboratively, utilizing scientiﬁc method, dealing with setbacks, giving and receiving feedback, presenting information, and articulating questions. These topics are also highly relevant to the ﬁrst-year graduate student. Even if a student has had a prior undergraduate research experience, revisiting topics can lead to deeper understanding and further skill development. My goal is that students using this book, either independently or while engaged in a research professional development program/course, will be able to gain the skills they need to be successful and achieve a high level of conﬁdence in their research capabilities. Wendy C. Crone February 2020 9Burkett, S. L., Lusth, J. C., Bahr, D., Pressley, S., and Schneider, K., 2013. Three training programs for preparing undergraduates to conduct research. Proc. American Society for Engineering Education Annual Conference, Atlanta, GA. 10Schneider, K. R., Bahr, D., Burkett, S., Lusth, J. C., Pressley, S., and VanBennekom, N., 2016. Jump starting research: Preresearch STEM programs. Journal of College Science Teaching, 45(5), p. 13. 11Schneider, K. R., Bahr, D., Burkett, S., Lusth, J. C., Pressley, S., and VanBennekom, N., 2016. Jump starting research: Preresearch STEM programs. Journal of College Science Teaching, 45(5), p. 13. Acknowledgments xxi This book is based on my experiences as a research mentor, graduate advisor, instructor in the College of Engineering, and an administrator in the Graduate School of the University of Wisconsin–Madison. I am grateful to all of the undergraduate and graduate research assis- tants who worked with me over the years, not only for their research contributions, but also for how they helped me to develop and learn as a mentor. Although I have taught the course “Introduction to Engineering Research” for more semesters than I can count, it would not have been as successful without the help of a number of key individuals over the years. I would like to thank Professors Greg Moses, Jake Blanchard, and Carl Sovinec as well as other colleagues at the University of Wisconsin–Madison for their collaboration and shared vision in developing the Engineering Physics degree program and the research sequence upon which this book is based. I also appreciate the opportunities I had to interact with students in the Engineering Physics undergraduate program and especially for their phenomenal engagement, performance, and feedback. I am especially grateful to former undergraduate and graduate students whose perspectives, insights, and comments are included in the Student Perspectives. These are in- cluded in the book with permission from Grant Bodner, Christopher Coaty, Aidan Combs, Brian Cornille, David Czajkowski, Chelsea D’Angelo, Tom Dobbins, Chris Everson, Thomas E. Gage, Brad Gundlach, Cale Kasten, Matt Klebenow, Brian Kupczyk, Geoﬀ McConohy, Hugh Ni, Blair Seidlitz, Dan Segal, and Vladimir Zhdankin. I would also like to thank my father, Richard Crone, and husband, Alan Carroll, for proofreading drafts, and my editor, Paul Petralia, for both his patience and nudging to help me get this book completed. Dr. Katie Cadwell, who was a postdoctoral research associate with the University of Wisconsin–Madison Materials Research Science and Engineering Center (MRSEC) and is now a Professor at Syracuse University, helped to collect valuable learning resources in an earlier expansion of the course. She also helped to make aspects of it accessible to students outside Uni- versity of Wisconsin–Madison, and worked with Prof. Naomi Chesler and myself on a related project connected to the undergraduate engineering design experience. I appreciate the funding support received from the National Science Foundation through the MRSEC (#DMR-0079983 and #DMR-0520527) and the University of Wisconsin–Madison College of Engineering 2010 grant for Transforming Undergraduate Education in the College of Engineering. Any opinions, ﬁndings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reﬂect the views of the National Science Foundation nor the University of Wisconsin–Madison. xxii ACKNOWLEDGMENTS I had the pleasure of serving in several diﬀerent administrative roles in the Graduate School at the University of Wisconsin–Madison for ﬁve years. These roles included Associate Dean for Graduate Education and Interim Dean, where I provided leadership for all aspects of the graduate student experience, including admissions, academic services, academic analysis, funding, professional development, and diversity. At the time, the University of Wisconsin– 9,000 in over 140 Master’s Madison Graduate School had a diverse graduate student cohort of and 100 doctoral ﬁelds across the University. I learned an immense amount from my colleagues in the Graduate School and my faculty and staﬀ colleagues across the University who devote time and energy to graduate education. These experiences and interactions also allowed me to see graduate education from a broader perspective beyond that of the graduate programs in the College of Engineering where I have served as a graduate advisor and research mentor for over 20 years. This book draws from this range of experiences to provide the best guidance and advice I can give to those entering engineering research at the undergraduate or graduate level. (cid:24) Wendy C. Crone February 2020 xxiii Credits Table 3.1 Sec. 3.7 Figures 4.1–4.4 Questions on page 85 Page 97 Sec. 5.7.1 Page 129 Adapted with permission from C. Eugene Allen, Emeritus Dean and Distinguished Teaching Professor, and Former Associate Vice Pres- ident for International Programs, Vice President and Provost, Uni- versity of Minnesota, Minneapolis, MN. Strategies for recognizing and overcoming bias adapted with per- mission from Molly Carnes, Eve Fine, Manuela Romero, and Jen- nifer Sheridan. “Breaking the Bias Habit.” Women in Science and En- gineering Leadership Institute (WISELI), University of Wisconsin– Madison, https://wiseli.wisc.edu. Reproduced from Gall, K., Dunn, M. L., Liu, Y., Labossiere, P., Sehitoglu, H., and Chumlyakov, Y. I. (2002). Micro and macro de- formation of single crystal NiTi. Journal of Engineering Materials and Technology, 124(2):238–245, with the permission of ASME. Reproduced from Maboudian, R. and Howe, R. T. (1997). Criti- cal review: Adhesion in surface micromechanical structures. Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Struc- tures Processing, Measurement, and Phenomena, 15(1):1–20, with the permission of the American Vacuum Society. From The Thinker’s Guide to Engineering Reasoning: Based on Critical Thinking Concepts and Tools, 2nd ed., (“the work”) Richard Paul © 2013. Used by permission of Rowman & Littleﬁeld Publishing Group. All rights reserved. Courtesy of Springer Nature. D.I.S.O.R.D.E.R. Framework used with permission of Lisa Newton, Professor Emerita of Philosophy, Fairﬁeld University. Reprinted by Permission of the National Society of Professional En- gineers (NSPE). www.nspe.org xxiv CREDITS Page 153 Tips for interacting with the public from Bringing Nano to the Pub- lic: A Collaboration Opportunity for Researchers and Museums by Wendy C. Crone, 2006. Reprinted with permission of the Nanoscale Infor- mal Science Education Network, Science Museum of Minnesota, St. Paul, MN. www.nspe.org Figure 7.1 From Escape from the Ivory Tower by Nancy Baron. © 2010, by the author. Reproduced by permission of Island Press, Washington, DC. Assignment 8-1 Laboratory-to-Popular assignment adapted with permission from Caitilyn Allen, Professor, Department of Plant Pathology, Univer- sity of Wisconsin–Madison. Sec. 8.4.1 Writing Workshop and “Some Suggestions for Responding to a Col- league’s Draft” developed in collaboration with Bradley Hughes, Di- rector of the University of Wisconsin–Madison Writing Center. Contribution list in Sec. 8.5 From Responsible Conduct of Research by A. E. Shamoo and D. B. Resnik. © 2009 Oxford University Press. Used by permssion. Page 203 Photo by Edna M. Kunkel C H A P T E R 1 1 Introduction to Engineering Research 1.1 WHO IS THIS BOOK FOR? The information provided within these chapters is designed for both ﬁrst-year graduate stu- dents and undergraduate students engaging in on-campus or summer research opportunities. For those already in a graduate program, some portions of Chapter 2 will not be relevant. For those just beginning to consider graduate study as a future path, the later chapters will provide you important information for undergraduate research you are currently undertaking as well as some insights on what is ahead of you as you transition into graduate school. Rather than being an exhaustive resource, this book is meant to supplement your interac- tions with research mentors, advisors, and peers. There are also other numerous references cited and bibliographies provided that will help you to delve into more detail on particular subjects. You should strive to seek out multiple perspectives on critical topics of importance to you as you move through your engineering research experience. 1.2 HOW RESEARCH IS DIFFERENT Engineering research is a very diﬀerent endeavor than the traditional coursework that you have taken up to this point in your academic career. Research is a process of discovery, which means that it has a very open-ended quality as a result. This open-endedness may not be something you are as initially comfortable with depending on your background, but the prior knowledge and the skills that you have developed thus far are still valuable and will help you make a contribution with your research. Discovery is not done in a vacuum. There is nearly always some prior work in an area or related ﬁeld that can help us build a foundation from which we can launch our work. The research of today builds upon the ﬁndings of yesterday. You may ﬁnd that you are building on work ranging from 5 months to 50 years ago, so understanding what has come before is an essential part of the process. If your purpose is discovery, then there is no point in rediscovering something that is already known and published. Sometimes, however, as part of the process, you may want or need to replicate the work of others, either as a way to learn a technique or to conﬁrm those results. 2 1. INTRODUCTION TO ENGINEERING RESEARCH Research should also be a mentored experience. You will have many people—your peers, those a bit ahead of you in their studies, staﬀ, and faculty—who you will interact with and rely on for direction, advice, and support. In contrast to the image that many have of research, it is not a solitary activity. In fact, much of the engineering research that is done today occurs in a team environment. These teams are frequently interdisciplinary and may include people from a range of engineering and non-engineering disciplines. Working with people from other disciplines helps us to tackle challenges and open research questions that we might not otherwise be able to make progress on alone. The research group that you work within may be a handful of people or an international collaboration that numbers in the hundreds. Either way, cultivating the relationships within this group and connecting with people related to your research, both on and oﬀ campus, will be a critical factor in your success. The undertaking of research is also something we do with our colleague’s and society’s trust that we will behave ethically. As individuals within a broader community of researchers, we have the obligation to be responsible and honest. This is required in all aspects of the work, from the design of an experiment to the publication of the results. Our analysis must be conducted with an impartial eye; the results must be presented without manipulation; and, discussion of our research with the broader community of scholars and the public must be done with integrity. With these principles in mind, you will have the best opportunity to create new knowledge, advance understanding in your ﬁeld, and become a respected member of your discipline. Ultimately, your goal will be to make what is often referred to as a “unique contribution” to your ﬁeld. This may seem a daunting task as you enter into research, but as you gain more knowledge about your research area you will soon ﬁnd that there are a number of things that are not known. You, with the help of your research mentor, will be able to identify an area where you can pursue the creation of new knowledge. It will likely leverage the work of those who have come before you, both in the research group you have joined and in the ﬁeld as a whole, but you will ﬁnd a way to make a contribution that is your own. Eventually, you will ﬁnd that you begin to surpass your research mentor in speciﬁc knowledge areas and can begin to think independently about new research endeavors to undertake. 1.2.1 ENGINEERING RESEARCH DEFINED When we hear the word research we often think of it as being synonymous with acquiring new knowledge or even developing some “objective truth.” Engineering conjures up images in our mind of applications ranging from computers to bridges. For many, engineering implies im- proving our way of life or driving technological advancement. When the term “engineering research” comes up, it may be hard to reconcile for some. Is it the creation of new knowledge exclusively? Is it the application of new science to existing applications? Is it the development of new applications? The answer is all of the above and more. The basic commonality we ﬁnd in all engineering research is that people are trying to answer questions that have not been asked or answered before, to solve problems that humanity 1.3. ENGINEERING RESEARCH CAREERS 3 will ﬁnd useful in some way. We do this through a process of inquiry that relies on careful exploration using scientiﬁc method. The answers we ﬁnd may be immediately applicable or they may add to a base of knowledge that will only see application at a much later date. There is a spectrum of research from basic to applied. In many cases the same type of basic research might be found in both science and engineering departments and collaborations across these disciplines are common in such circumstances. In a report from the National Academy of Engineering, “Basic research in engineering is by deﬁnition concerned with the discovery and systematic conceptual structuring of knowledge.1” In contrast to basic research, applied research is much more closely tied to an immediate need and may even be conducted jointly or under a research contract with a company. Across this broad spectrum, an engineering research project might be motivated by some esoteric curiosity tied to the long-term needs of humanity or by an immediate need in a particular community. Regardless of the origins of the research question, the tools we use to answer them, and the time frame in which the results will be applied, these are all a part of the spectrum of engineering research that you will ﬁnd happening on a day to day basis in universities, national laboratories, and industry. ASSIGNMENT 1-1: INDIVIDUAL ASSIGNMENT – ENGINEERING RESEARCH DEFINED Talk to at least three individuals spanning the spectrum of experience with research related to your general ﬁeld of interest (e.g., undergraduate student researcher, graduate student researcher, postdoctoral researcher, academic staﬀ researcher/scientist faculty member). Ask these individ- uals to discuss the topic of “engineering research” with you. What makes a good research ques- tion? How do they approach conducting their research? What do they ﬁnd interesting/exciting about research? Write a 500-word summary of what you have heard that includes both the sim- ilarities and diﬀerences between the answers obtained from your discussions. 1.3 ENGINEERING RESEARCH CAREERS There are a wide range of research careers available to people with an advanced degree in en- gineering. These careers occur most prevalently in industry, government, and academic sectors. Even within one of these sectors the types of jobs that involve research can vary dramatically. One way to explore the range of options for engineering research careers is to take a look at current job postings in your area of study. Looking at the position descriptions can give you an idea of the work activities and job responsibilities. It will also give you an idea of qualiﬁcations and prior experience expected. Some positions may require a minimum education level of a 1National Academy of Engineering. Committee on Forces Shaping the U.S. Academic Engineering Research Enterprise, 1995. Forces Shaping the U.S. Academic Engineering Research Enterprise. National Academy Press. 4 1. INTRODUCTION TO ENGINEERING RESEARCH Master’s degree (M.S.), a doctor of philosophy (Ph.D.), and/or a number of years of professional experience. Finding the kinds of positions that might interest you in the future will provide you with the components of a roadmap for the preparation you will want to pursue. Although you will likely be most familiar with a traditional faculty position in academia from your experience as a student, the range of research-related careers within the conﬁnes of academia is quite broad. Within the faculty ranks alone, the emphasis on research varies be- tween positions depending on the type of institution. A four-year college, for instance, might stress engagement with undergraduate research but have lower levels of expectation on research productivity and a larger amount of time committed to teaching. The research and teaching expectations at research-intensive institutions will vary, but they usually stress research with graduate students, and have a higher level of expectation for obtaining grant funding and pro- ducing publications. At larger research-intensive academic institutions there are also a number of non-tenured research positions to be aware of. These often carry titles like instrumentation specialist, scientist, and research professor. Graduate education both at the M.S. and Ph.D. levels is valuable for people interested in a variety of career paths. Ph.D. recipients don’t just end up in academia, but are also sought after by industry and government for their expertise and ability to be innovators and thought leaders.2 Research laboratories span a range of institutions from government laboratories, some with defense-related missions (e.g., Sandia National Laboratories, National Renewable Energy Laboratory, and Argonne National Laboratory, U.S. Naval Research Laboratory), to other non- governmental research labs, some of them with connections to or histories with universities (e.g., Southwest Research Institute, Draper Laboratory, MIT Lincoln Laboratory). Many medium to large companies also have a research (or research and development) department, unit, or seg- ment of the organization—a few of these being quite large and well-known research enterprises (e.g., IBM Research, GE Global Research, ExxonMobil’s Research and Engineering Technol- ogy Center, DuPont Experimental Station). The types of expertise needed and range of jobs available are quite broad as you may imagine. In some engineering disciplines, there is a growing expectation that a person complete a postdoctoral experience after completing their Ph.D. and before obtaining that ﬁrst “permanent” position. Postdoctoral research positions they are most prevalent in academic settings, particu- larly large, research universities, although they are also available in some industry and govern- ment sectors. These positions are usually full-time paid jobs. Some fellowship opportunities are also available for postdoctoral research positions, both in academia and national laboratories. 2Council of Graduate Schools, 2013, Open Doors with a Doctorate. 1.3. ENGINEERING RESEARCH CAREERS 5 ASSIGNMENT 1-2: INDIVIDUAL ASSIGNMENT – INVESTIGATING ENGINEERING RESEARCH CAREERS Identify an engineering research job sector that you would like to learn more about: industry, government, or academia. Find three diﬀerent job advertisements in that job sector using on- line resources such as monster.com, usa.gov, and chronicle.com. Ideally, these job postings should advertise a research position related to your area of study. Compare and contrast the positions. Consider things such as the education and prior experience required, duties and re- sponsibilities that the position would entail, and location of the job. Choose the position that you ﬁnd most interesting and identify the kinds of things you would need to do in the next 5–10 years to make yourself an ideal candidate for this position. C H A P T E R 2 7 Finding the Right Research Position for You 2.1 SOCIETAL IMPLICATIONS OF TECHNOLOGY Engineers help to shape the world and our personal experiences in it. Engineering design and research impacts nearly every aspect of our lives: the indoor plumbing and sanitary systems we take for granted, the transportation vehicles and networks we utilize to move about our commu- nities and the world, the structures we live and work in, our communication and entertainment systems, the power production and distribution networks we rely on, and the medications and devices that keep us healthy, just to name a few. Engineers also have the ability to address the grand challenges that face society and improve the human condition by doing so. These chal- lenges exist throughout the array of human experience, from ensuring a stable food supply and clean drinking water for the world’s population, to the further development of artiﬁcial intelli- gence and treatment of neurological disease by reverse engineering the brain. It is an exciting and important moment in human history for engineers. The world depends on us, both to maintain our current standard of living and to innovate in new and unprecedented ways to bring us into a better future. We have the capability and the responsibility. ASSIGNMENT 2-1: INDIVIDUAL ASSIGNMENT – YOUR ENGINEERING GRAND CHALLENGE Read the National Academy of Engineering’s “Grand Challenges for Engineering” list1 and identify the challenge most closely related to your research interests. Summarize the challenge and describe the ways in which research in your ﬁeld of study have already impacted this topic and how you imagine future research can make an impact on this challenge topic. 1National Academy of Engineering, “NAE Grand Challenges for Engineering,” http://www.engineeringchallenges.org. 8 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU 2.2 IDENTIFYING A RESEARCH PROJECT Sometime students think that in order to engage in research you have to come up with the idea yourself at the very start. This is quite a challenge if you are new to a ﬁeld and have little prior experience with research. Identifying a research project that you can undertake usually involves a very diﬀerent process. Experienced researchers are often looking for students to help them with new and ongoing research projects. So, what you are actually seeking is a match between your interests and existing research projects that are available. Student Perspective “[R]esearch never really ‘ends.’ What I mean by this is that even when a group gets a paper published on an experiment it doesn’t end there. Fre- quently, the group continues to do research on the same topic using the ideas and results from their last paper. I guess this does make sense to me, but again it was something I never really thought about. In some way, I suppose I as- sumed that after one project was ﬁnished, they would look for something new and exciting. But, once an experiment is completed, there is almost always further research to be done to learn even more about the topic.” Whether you are an undergraduate student or a graduate student, you should enter into a research project that meshes well with your interests. Don’t just take on a project for the money or because it is the ﬁrst one oﬀered to you. Cast your net wide and look for a variety of projects that might ﬁt your interests as well as a research mentor who would be a good match for your personality and needs. After you ﬁnd the right research project to pursue, your intrinsic interest will motivate you through the diﬃcult parts and ultimately help you to be more successful. In order to identify research projects and mentors that are a good ﬁt, ﬁrst identify the areas of engineering that interest you. Explore your options by reading about current research in those areas and talking to people who have experience with ongoing research. Utilize a variety of sources including websites and recently published journal papers. As you begin to identify individual faculty members you might be able to work with, try to engage in face-to-face or email conversations with these potential research mentors. It is easy to be energized by someone’s enthusiasm for their work, but don’t ﬁxate on the ﬁrst thing you learn about. Look broadly and determine what options might be available to you. Even if you are entering a summer research opportunity, rather than a new degree program, often there are choices of projects available to you and faculty mentors within the program that you can identify as your top choices. Some people stumble across the perfect research position immediately, but often students need to make some eﬀort to both identify potential research mentors and ﬁnd ones who are willing to add you to their research group. Often available research funding can be a barrier. If you are an undergraduate student looking for research experience, you might choose to do 2.2. IDENTIFYING A RESEARCH PROJECT 9 this work for credit rather than pay. That option may open additional opportunities that would otherwise not be possible. Graduate students frequently have the challenge of ﬁnding a good match between their interests and the funding available for a research assistantship. If you have obtained a fellowship, this becomes less of an issue, but most students will need to ﬁnd support either as a research assistant or a teaching assistant. Consider these strategies if you are having diﬃculty obtaining a research position. • Cast a wide net so that you don’t limit your options too severely up front. • Be as ﬂexible with your research interests as is reasonable. • Consult with faculty you have taken classes from; ask about openings they may know of or colleagues they would recommend. • Seek out new faculty (e.g., assistant professors) who may be looking to grow their research group. • Identify research centers or facilitates that may have positions available. After you have explored what is available to you, some introspection will be called for. If you ﬁnd that you have developed a keen interest that is not represented at your institution, you may have to consider making a change. As an undergraduate, you can consider looking for summer research opportunities elsewhere, transferring to another institution, and/or pursuing your later graduate studies at an institution with a better ﬁt with your interests. As a graduate student, hopefully you will have taken on this exploration while looking for the right graduate school for you, but, if you ﬁnd yourself at an institution where your interests are not represented, you have to make some decisions. Stay or go elsewhere? Some programs allow for a “coursework only” Master’s degree that you can ﬁnish up more quickly so that you can move on to another institution sooner. If you can ﬁnd a research project peripherally related to your interests, you might want to consider pursuing this for your Master’s degree research and then make a change when you begin your Ph.D. or ﬁrst industry position. This is not as unusual as you might think. I have known many students who have made a signiﬁcant change after their Bachelor’s or Master’s degree. Their prior experience is not a waste, they will be able carry their skills and knowledge forward and may be able to use them in unanticipated ways. Some students ﬁnd themselves paralyzed at having to choose which research project they will take on. If you ﬁnd research areas at your institution that excite you—which is often the case—you may ﬁnd that you have more options that you expected. The important thing to re- member is that it does not have to be a decision you are married to forever. Although it is likely that your research career will be related to the general area of study you are currently pursuing, it is also likely that your research career will be long and varied. The research I did as an un- dergraduate was in the same basic ﬁeld as my graduate work, but not thoroughly connected to it. Also, the speciﬁc research I did for my master’s degree was diﬀerent from my Ph.D. (and 10 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU diﬀerent from what I do now as a faculty member). You can choose to stay in the same area or you can use the skills you have learned in related areas. You will ﬁnd that much of what you gain in both your coursework and research experience is transferable and can be used in other areas of engineering application. There are often opportunities to move around and try new things as you progress in your studies and career. Technology also moves quickly, so even if you begin your career in a particular specialty area, it is likely that you will have to learn and expand your expertise over time. Outside of academia, change is even more common—switching between companies or organizations, working in diﬀerent positions—and often require diﬀerent competencies and your own personal career management.2 Most researchers, even faculty researchers, change their research focus over the course of their careers even if they stay at the same institution. Who your research mentor will be is as important as the topic of your research project. Research mentor ﬁt is often overlooked, but as Megan Poorman, GradHacker blogger, points out: “Choose your mentor wisely: this is the biggest factor in your job satisfaction and degree progress. Your advisor sets the tone for the lab and can either help or hinder your professional development and your research progress. Find someone with whom you can communicate and who will be on your side, looking out for your best interests. I would choose the mentor over the research project. Obviously, you should be excited about the research, but projects change and morph over time, your mentor likely will not. Choose wisely.3” A Research Mentor Who Wants You to Succeed Some of the proudest moments in my professional life have been be- cause of the success of my students, either currenter or former. When they give a fantastic research presentation, earn a prestigious award, win a fellow- ship, get their dream job, or achieve the promotion that they were seeking, I feel great pride. I hope that in some way I have helped them to make these successes for themselves. Although I have been described variously as sympa- thetic, supportive, and demanding as a research mentor, these are consistent descriptions, given that my goal is to ﬁgure out the needs of each of my stu- dents and help them to be their best and achieve their goals. But when it comes right down to it, each individual is their own person ﬁguring out who they are and who they want to be. You need to ﬁnd the right research mentor for you who will help you be your best and work towards your goals. Consider some of the following questions when you are interacting with potential research mentors. 2Seibert, S. E., Kraimer, M. L., and Crant, J. M., 2001. What do proactive people do? A longitudinal model linking proactive personality and career success. Personnel Psychology, 54(4), 845–874. 3Poorman, M., 2019. GradHacker, “Hacking Grad School,” Inside Higher Ed. https://www.insidehighered.com/blogs/gradhacker/hacking-grad-school. • How much time and attention do you need and does it match with the potential re- search mentor’s availability? 2.2. IDENTIFYING A RESEARCH PROJECT 11 • Does this individual provide the following to their research students: – constructive feedback? – assistance in setting realistic goals? – feedback about expectations? – information about funding opportunities? – professional development opportunities and connections? – aid with the job search? • Do you need someone who will be encouraging and nurturing or are you more com- fortable with a higher level of autonomy and independence? • Do more experienced students and the graduates from the research mentor’s group develop professional independence and transition to the status of junior colleague? • If you are interested in a particular career outcome after your degree, will this mentor be able to support this interest and help to launch you on this trajectory? Even when you ﬁnd the “perfect ﬁt,” it is important to realize that you will need to develop other mentors beyond your primary research mentor throughout your research experience. The pool of possible mentors is large and includes other faculty members, research staﬀ members, postdoctoral researchers, as well as other students at both the graduate and undergraduate levels. Student Perspective “Other goals that might help me to become an independent researcher include making sure to seek the advice of the experienced researchers and research mentors I may work with in the future, and staying honest with myself about who I am and what I want. Taking guidance from mentors and forming close relationships with them seems to me to be one of the main ways people ﬁnd their place in the research world. Mentors know how the research world works and can give good advice to young researchers on what steps to take to get where they ultimately want to be. This is where the second goal is important. I want to remain conscientious about where my path leads me and to make sure at all times that I am not being funneled into an area or profession that will be unfulﬁlling. I don’t want to look back in my middle ages and wonder what happened.” 12 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU ASSIGNMENT 2-2: GROUP ACTIVITY – RESEARCH INTERVIEWS WITH OTHER STUDENTS Overview: This activity will give you the opportunity to ﬁnd out about the research that others are interested in and express your own interests about research. The objectives for this activity depend on your prior experience. 1. For students with research experience: you will have the opportunity to practice your com- munication skills in the context of the research you are conducting and reﬂect on the progress you have made as a researcher. 2. For students inexperienced with research: the interviews will give you the opportunity to learn more about the kinds of research being undertaken on your campus. The in-class interview activity should also help to increase your comfort level when talking to potential faculty research mentors outside of class. Preparation: be sure take time to think about the following in preparation for the interviews. For students inexperienced with research: • Brainstorm questions that you might ask. (Note: you will be doing more than one interview and you will be conducting interviews with students having diﬀerent levels of research experience.) • Some suggested started questions might include the following: – What is your area of research? – How did you get involved with the research are you are currently working in? – Has your research experience been what you expected? – Have you run into any stumbling blocks in your research? How did you overcome them? – What approaches would you suggest for ﬁnding a research project? • You will need to listen actively and do your best to ask probing follow-up questions based upon hearing the initial response. For students experienced with research: • Consider the starter questions posed above and what you feel would be the most valu- able information to discuss with a student inexperienced with research. • Use the strategies discussed in Chapter 7 to organize your thoughts. 2.2. IDENTIFYING A RESEARCH PROJECT 13 ASSIGNMENT 2-3: INDIVIDUAL ASSIGNMENT – PROFESSIONALISM IN EMAIL INTERACTIONS There will be many occasions throughout your research career where you will need to initiate contact with someone via email. This is an important opportunity for you to make a good ﬁrst impression by displaying professionalism in your email communications. It can be a big mistake to approach this initial interaction casually or sloppily. Write precisely and clearly so that your meaning is understood. It is not appropriate to include emoticons or emoji, but you want to be sure that your message comes across with the right tone. Don’t use humor or sarcasm. Check your spelling and grammar. Err on the side of formality. The person reading the email will make a lot of assumptions about you based on the limited information that the email contains. You want to ensure these assumptions are as positive as possible. The message should begin with a salutation. “Dear Prof. Smith” is appropriate, “Hey” is not. State your request up front. Tell the person who you are and why you are making this request. Indicate how you would like to follow up (e.g., “I would appreciate it if we could set up a meeting. I am available….”, or “Thank you in advance for your reply.”) Your message should include enough information to be clear, but not be so long that it will not be read. At the bottom of your message you should have a signature block with your contact in- formation. Something simple like the following will suﬃce: Ima N. Gineer Undergraduate Student, Engineering Mechanics Program University of Wisconsin-Madison Cell: 999-999-9999 Your assignment is to compose an email to a faculty member using the above guidance. This message should do one of the following. • Request an opportunity to meet and discuss the research being undertaken in their research group. • Identify a research question related to a published journal article that you have read and request guidance on what additional follow up reading might help you to answer your question. • Inquire about the availability of a research position. 14 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU • Pose a question about an area of content of a course you are currently taking and request their guidance. • Inquire about an interesting course that you anticipate they will teach in the future. ASSIGNMENT 2-4: INDIVIDUAL ASSIGNMENT – CONVERSATIONS WITH POTENTIAL FACULTY RESEARCH MENTORS STEP 1: Identify ﬁve faculty members you will contact about research projects. In addition to identifying their name and research interests, ﬁnd their contact information, including email address, phone number, and oﬃce hours. STEP 2: Summarize the area of research that each faculty member specializes in. Look for a recent news article, webpage summary, or journal publication to give yourself a bit more back- ground about their work. Note that often faculty research interests change over time although web pages may not be revised frequently, but this information will at least provide you with some relevant background about their research interests. STEP 3: Draft an email of introduction. Use professional language, including the appropri- ate salutation (e.g., Dear Prof. Smith). Consider attaching a resume showing your prior work experience—even if your work experience is not research-related, it shows that you can hold a job and perform it reliably. Indicate in your message how you will follow up with contacting them (e.g., I plan to visit your oﬃce hours next week so that I can learn more about your current research interests). After using spell check, send your emails. STEP 4: Follow through with your follow up! Ideally you should talk to the faculty members you have contacted either in person or by phone. Come to the conversation prepared to do the following: • Describe what you ﬁnd interesting about the research they have done. • Discuss your experience and interests. • Ask about their current research and future research interests. • Specify what you are hoping for as a result of the conversation. UNDERGRADUATE RESEARCH EXPERIENCES 2.3 If you want to learn about research, it is a great idea to start early while you are an undergraduate student. There are many advantages to doing research as an undergraduate—you can learn about 2.3. UNDERGRADUATE RESEARCH EXPERIENCES 15 the process of research to determine if this is something you are interested in doing more of, you can try out a particular research area to see if it is something you would like to pursue further, and you can gain some basic research experiences that will be to your advantage when you apply to graduate programs. Student Perspective “This experience [as an undergraduate researcher] was a valuable one. It taught me a lot about myself and what I really wanted to do and was in- terested in. It also gave me a great look at one style of lab organization in terms of people and project roles within the group. I was able to work on and realize the importance of networking and general looking out for myself in research.” The types of research positions available for undergraduates on university campuses vary. They range from “bottle washer” positions to those that involve doing an independent research project. Often it is the case that a research position is a combination of diﬀerent tasks at a variety of levels, from glamorous to tedious. (Someone must wash the glassware, right?) Undergraduates are often hired into research labs to help out with some of the work that might be a little bit more routine, but these are still great research opportunities because it allows you to learn about the work taking place in that research group and gives you the potential to work your way up, and take on more responsibility, as you prove yourself to be capable and dependable. Additionally, undergraduate research is usually a bit lower stress and forgiving of failure. Student Perspective “I think one of the main expectations that the group has for me is that I’m not afraid of failure. By this, I mean that the project I’m working on has never been done the way they are asking me to do it. Because I am not a Ph.D. or Master’s student, I am the perfect person to conduct the experiment because I don’t have any pressure to produce publishable results and I’ll be able to focus more on the research at hand. Although they do have high hopes for the project I’m working on, I won’t have the pressure that the typical Ph.D. or Master’s student would have. So, I guess my biggest goal for my project is to produce results that the group can do something with. But, also to be optimistic if they don’t always turn out as I had hoped.” Many undergraduates ﬁnd meaningful research experiences on their home campus. There are a variety of diﬀerent ways to connect in with research, and a variety of ways that you can go about getting compensated beyond the experience you will gain. You can look for jobs that are paid positions. These range from entry-level positions that pay minimum wage to more high- paying positions that use your technical skills. This may begin as a part-time job, where you 16 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU are assisting with day-to-day needs in a laboratory and grow into a research experience as you develop your skills and show initiative. Or, you may have the opportunity to conduct research for credit. For instance, as an independent study project under the supervision of a faculty member. Some campuses also oﬀer scholarship or fellowship opportunities connected to research. Often these kinds of opportunities will allow you to propose a speciﬁc research project with a research mentor and apply for some funding to complete that research activity. If you have a research area(s) in mind that you would like to get experience with, you might be able to ﬁnd a research group working in that area that would be willing to let you attend group meetings and/or spend time shadowing a graduate student. Your academic advisor will be able to give you information about the options available to you on your campus and how to go about pursuing them. In all of these cases, you need to be able to devote enough time to do the research to make it worthwhile for both you and your research mentor. I suggest that you need to devote at least 10 hours per week so that you can spend enough time to become competent and productive. That also means putting in time every week in order to make research progress. In a paid position you will be paid by the hour. If you are getting course credit the expectation is usually a minimum of 45 hours per semester credit. If you assume a standard length semester and three credits of research, this would be roughly equivalent to 10 hours per week. At the end of the semester you will likely need to produce some kind of document, like a report or poster, which summarizes your research project and the progress that you have made. Now the question is how to ﬁnd a research position. The ﬁrst thing you want to do, before you start sending emails and knocking on doors, is to ﬁgure out what kind of research is of most interest to you. Take a look at what kind of research is being conducted on your campus. The websites of faculty members, research groups, and research centers can provide useful informa- tion, but keep in mind that the research projects that are actively being conducted may not be represented on the website yet. Although the projects being discussed on the website may not be ongoing, it should still give you a ﬂavor for the type of research being done in that research group. The next task is to prepare yourself: put together a professional-looking resume. If you don’t know where to start, the career services oﬃce will likely have helpful information, and possibly even workshops to assist you in creating a resume to highlight your experiences and skills. You also need to be prepared to talk to a faculty member about your research interests, as well as your background and capabilities. You should not just show up and say “Hi, I want a job.” You need to be able to articulate your interest in the research area that faculty member is engaged in, and talk about the qualities and capabilities that you could bring to the research group. You may not think you have much to talk about without prior research experience, but you may have qualities like dependability, skills that you have developed through hobbies, and background that you have obtained in courses, that you can speak about. It is likely, however, that having access to these kinds of opportunities will require some persistence on your part. Research positions for undergraduates on most campuses are relatively 2.3. UNDERGRADUATE RESEARCH EXPERIENCES 17 rare. If you throw up your hands and give up at the ﬁrst obstacle, you will be unlikely to ﬁnd the sort of experience that you are interested in. This is also good preparation for doing research, because doing research will require persistence and the ability to work your way around the roadblocks that appear. There are a variety of strategies that you could employ and you should begin with the one you feel most comfortable with. • One way to initiate contact is to send an email of introduction with your resume as an attachment. Even if you don’t hear back from the faculty member right away, you can then follow up during the faculty member’s oﬃce hours. • You can talk to your academic advisor to ﬁnd out if they have a suggestion for who may have research openings that you can apply for. • You may have friends and classmates who are already involved in research. You can talk to them about whether there are openings in their research group, and if they would make an introduction to their research mentor on your behalf. • You can talk to professors you have taken classes from and have done well in. They might have a research opening, or they might be able to suggest who would. • Use your network. Talk to people about your interests and what you would like to do. You never know, the person you see on the bus every day, or the person you know from your soccer club, might be just the contact you were looking for! Expect that it will take more than one contact attempt with a prospective research mentor, as well as more than one potential research mentor on your contact list. Student Perspective “I tried once again to reach this professor through email, but realized that I’d have to try for an in-person meeting if I was going to get anywhere. I quickly learned that this professor was extremely busy. I spent a lot of time that semester waiting in the hallway to meet with him. After more than a month of rescheduled or missed meetings, I got an interview and soon began work ... I think the clearest lesson I learned during the process of getting [a research position] was that sometimes you have to be a little impertinent to get noticed.” An alternative or additional way to gain research experience as an undergraduate is to apply for a summer undergraduate research program. These are often called research experiences for undergraduates, but they have various titles and are oﬀered by a number of diﬀerent organizations. For instance, the National Science Foundation (NSF) sponsors numerous research experiences 18 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU for undergraduate (REU) programs around the country, mainly based at university campuses. Several national laboratories oﬀer summer research opportunities, such as the Sandia National Lab Summer Internships and the NIST Summer Undergraduate Research Fellowship (SURF). There are also a few international opportunities to do research such as the DAAD Research Internships in Science and Engineering (RISE) that sponsors U.S. student to go to Germany for research opportunities. In your conversations with your academic advisor and professors, you can ask about summer opportunities that they might know of at other campuses and institutions. These summer programs are almost always paid opportunities and there is usually some coverage for living expenses. The quality of the research experience can vary, so you will want to be sure that the ones you are applying to provide authentic experiences in research. Look into the range of diﬀerent things that might be available to you. If you are persistent about seeking them out, you are likely to ﬁnd a really great research position. Regardless of the speciﬁcs of the position, and how it is compensated, you should approach it in a professional manner. Once you obtain a research position you need to be responsible with how you conduct yourself and how you take on the work. Ideally, you will also show initiative by thinking creatively and innovatively about the details of the project. As you exhibit these traits within a research setting, you be given more responsibility as time goes on. If your contributions are not noticed, then you need to point them out and ask for more responsibility so that you can show what you are capable of contributing. Research shows that that being proactive is directly linked to career success and satisfaction.4 Sometimes You Don’t Have to Make a Choice One of my undergraduate advisees, who is already engaged in an ex- tensive on-campus research experience, is now thinking about the tradeoﬀs between gaining more research experience in a diﬀerent area through a sum- mer research program vs. studying abroad. It’s a tough choice, but my main piece of advice is that she may not need to choose. It may be possible for all of it to happen, just over a larger time span than she originally imagined. It is easier, and more common, to study abroad as an undergraduate than as a graduate student. However, it is possible to put oﬀ study abroad without giving up the opportunity all together. I spent a semester in Australia as a graduate student, but I had to independently organize it rather than join an orchestrated program with multiple students. There are pluses and minuses to the diﬀerences in those experiences, but both will give you an opportunity to immerse yourself in another culture. Summer research experiences can be a great way to get experience with another area of research and another institution. If there is a speciﬁc area of 4Seibert, S. E., Kraimer, M. L., and Crant, J. M., 2001. What do proactive people do? A longitudinal model linking proactive personality and career success. Personnel Psychology, 54(4), 845–874. 2.4. THE GRADUATE SCHOOL APPLICATION PROCESS 19 research you are interested in exploring a bit more prior to graduate school, you can look for a program at a diﬀerent institution that would provide you with an experience related to your interests. The other consideration may be money. Summer research programs usually pay several thousand dollars and sometimes provide you with a place to live. Study abroad programs are generally something you must fund your- self as an undergraduate student. (There are some exceptions, with a few scholarships that are available, and funding opportunities for graduate stu- dents to do research abroad.) 2.4 THE GRADUATE SCHOOL APPLICATION PROCESS 2.4.1 IS GRADUATE SCHOOL RIGHT FOR YOU? Graduate school is an excellent way to continue your education, deepen your engineering skills, and open yourself to other career opportunities. However, graduate school should not be viewed as simply an extension of your undergraduate studies. In most cases, earning a Master’s degree or Ph.D. will take more than a few extra classes. Particularly for the Ph.D., it takes an interest in and serious commitment to research. When considering applying to graduate school, examine your motivations. Because you are not sure what to do next, don’t want to venture into the “real world” yet, or think the job market is tough are NOT good reasons to go to graduate school. In fact, these unsuitable motivations will likely show in your graduate school application materials and make it very diﬃcult for you to get accepted. That being said, I encourage all of my advisees with good GPAs to seriously consider graduate studies. Maybe it is not something they are interested in embarking on right away, but it should be kept in mind in the coming years. Of engineers holding a B.S. degree, 40% go on to get a Master’s degree and 9% go on for a Ph.D.5 Many companies will consider whether or not someone has an advanced degree at hiring and/or promotion. Some companies will even provide funding for courses and/or a graduate degree. Once you have decided to consider graduate studies, then you need to decide if you want to apply to get a Master’s degree (often called terminal Master’s) or to a Ph.D. program where you will likely complete a master’s degree on your way to your Ph.D. It is alright to not be 100% certain of your goals at the point of application, but you should represent yourself honestly and indicate how strong your desire is to continue on for a Ph.D. In many programs this can be a deciding factor for entry and for funding, so you should try to choose programs to apply to that will be a good ﬁt for your goals. 5National Academies Press, Understanding the Educational and Career Pathways of Engineers, 2018. https://www. nap.edu/catalog/25284/understanding-the-educational-and-career-pathways-of-engineers. 20 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU Going Corporate After I completed my Master’s degree, I began working in industry (which I really enjoyed). As I learned more about the company and the engi- neering positions available, I realized that I was keenly interested in research and development. My main motivation for returning to graduate school was that the jobs that I was most interested in obtaining in the future required a Ph.D. This was a strong motivation to go back to graduate school. It turned out later on that I found teaching and research to be my passions, so I never did go back for that industry dream job that I had my eye on. Sometimes my path has not been a linear one, but all the experiences I gained along the way have been valuable. ASSIGNMENT 2-5: GROUP ACTIVITY – GRADUATE SCHOOL FIT In small groups, brainstorm about what qualities are important for being successful at graduate- level research. Share these with the class. In small groups, discuss why you might pursue graduate studies immediately after com- pleting the B.S. degree or wait 2–5 years; advantages and disadvantages of both. Share these with the class. ASSIGNMENT 2-6: INDIVIDUAL ASSIGNMENT – GRADUATE SCHOOL APPLICATION EXPERIENCE Identify a current graduate student in the ﬁeld of study you are interested in pursuing. Talk to that person about their experience in applying to graduate schools. 2.4.2 THE GRADUATE SCHOOL APPLICATION PACKET Understanding the main components of the graduate school application packet, well in advance of when you plan to apply, will help you to build the strongest application possible. The main pieces of most application packets will be information from your undergraduate institution, such as your grade point average (GPA) and transcript, your Graduate Record Examination (GRE) scores (if required), and letters of recommendation. You will also need to write one or two essays for the application where you will commonly be asked to describe experiences that make you 2.4. THE GRADUATE SCHOOL APPLICATION PROCESS 21 well suited for this graduate program and your long-term goals related to the pursuit of this advanced degree. Nearly all graduate school application will require letters of recommendation (usually three, sometimes four). These are important because they are often the best predictor of whether or not an applicant will be successful in a particular graduate program. Some of these letters will be written by faculty members—ideally ones who have interacted with you on a research project, a student organization/team, or as an instructor (ideally in more than one class). It is also rel- evant to ask a supervisor or manager from a current or prior work experience even if it is not speciﬁcally engineering related (they can speak to issues such as reliability and initiative). You may also have some more extensive involvement in a volunteer activity. A letter from someone in authority in that organization might also prove useful. Help your recommenders write you the best letter possible. Give them plenty of advance notice and a reminder when the deadline is a few weeks away. Provide them with materials to refer to such as your resume and/or your application essay(s). Remind them explicitly how you have interacted previously (e.g., “As you may recall, I took Advanced Mechanics of Materials from you last Fall semester and my team completed a design project on…”). Provide them with a list of items you would like them to address in your letter (e.g., “I am hoping you can speak to the work I did in the lab over the last several years, especially the project where I refurbished the testing equipment and developed new protocols for operation. In addition to working in the lab 15 hours a week, I was also a member of the Marching Band and maintained a 3.5 GPA.”). ASSIGNMENT 2-7: INDIVIDUAL ASSIGNMENT – GRADUATE SCHOOL APPLICATION REQUIREMENTS Identify a graduate program that you would like to apply to and determine the deadline for application and the application materials you will be required to submit. Look for requirements such as minimum GPA and GRE test scores (usually just general, but some programs require a specialty exam). Determine what documents (e.g., transcripts), essay(s), and letters of recommendation will be needed. Read the instructions to determine if there are any speciﬁc expectations for what should be addressed in the essay(s), and if your resume should also be included in your application materials. 22 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU 2.4.3 THE APPLICATION TIMELINE A common timeline for the graduate school application process. Summer/Early Fall • • Identify some graduate programs that you are interested in applying to and identify the application requirements and deadlines. Determine whether or not the GRE General Test and GRE Subject Test are required (although the General Test is usually expected, the Subject Test is not common for most engineering graduate programs). In preparing for the GRE General Test, I do not generally recommend spending money on a preparation course. Your score will be close to its maximum if you take a few practice exams to familiarize yourself with the test format and the way in which questions are posed. Educational Testing Service (ETS) oﬀers free practice tests and software which you can use to emulate the actual test environment (see http://www.ets.org/gre). • By the end of October you should have taken the GRE (although it is available year- round). Mid Fall • Identify and contact people who will provide you with letters of recommendation (see above for ideas about who you should consider asking for a letter). • Finalize the list of programs you will apply to. Identify faculty members in each of these programs whose research you ﬁnd interesting and initiate contact with them by email or phone. • Begin preparing your applications. Look for graduate school application workshops and/or a faculty member who will read over your application materials for you and provide you with feedback. Late Fall/Early Winter • Complete your applications and submit them BEFORE the published deadline. Often, the review of applications begins prior to the cutoﬀ deadline and you would like your application to receive the fullest consideration. • Thank your recommenders for taking the time to write letters of recommendation for your applications. Send a brief note of appreciation—ideally in an “old fashioned” thank-you card, or at the very least via email. Winter 2.4. THE GRADUATE SCHOOL APPLICATION PROCESS 23 • Follow up with faculty members in the programs that you have applied to. Contact only those who you are keenly interested in working with, but be persistent in attempting to get through to them. If your email message does not get a response, then make a phone call. Also, consider asking your letter writers if they know any of the individuals you have identiﬁed and ask if they would be wiling to write an email of introduction for you. • Many departments oﬀer a visit weekend for prospective graduate students. Ask the department student services coordinator or faculty you have been in contact with if there would be an opportunity for you to visit the campus and meet with faculty and students. Often, some or all of the travel costs are paid for, but, even if they are not, you should make your best eﬀort to attend. Late Winter • Attend prospective graduate student visit weekends that you have been invited to. Meet with faculty and graduate students and gather as much information as possible. It is a two-way interview: you are trying to present yourself in the best possible light and you are trying to determine if this graduate program is a good ﬁt for you. See the list of “Questions to Ask Yourself and Others” below. Spring • Consider the oﬀers that you have received. Note that some programs make separate oﬀers for admission and funding, so be certain that you understand the implications of each oﬀer. • YOU CAN ONLY SAY YES to one. Nearly all universities in the U.S. are members of the Council of Graduate Schools and honor the April 15th resolution.6 This means that students should not be obligated to respond to an oﬀer prior to April 15th. This gives each student an opportunity to see all oﬀers available to them prior to making a commitment. Additionally, this means that you can only accept one oﬀer. A student who accepts an oﬀer has made a commitment and should not accept any other oﬀer without getting a written release. • Inform your advisor and recommenders of your decision so that they know where you are going next. Provide them with an email address contact that will be yours for the long term if your current student account will close after your graduation. Keep in touch periodically over the coming years—ideally more frequently than when you need another letter of recommendation for a fellowship or job application. 6Council of Graduate Schools, “April 15 Resolution: Resolution Regarding Graduate Scholars, Fellows, Trainees, and Assistants,” http://cgsnet.org/april-15-resolution. 24 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU Many programs also accept students mid-year. Look at the deadlines and talk to faculty in those programs to determine when you should have your application submitted. From there you can adjust the timing discussed above. In parallel to the graduate school application process you should also consider applying for graduate school fellowships. Also, unless you are independently wealthy or have a particular aversion to teaching, you should check all of the above if the application asks if you are inter- ested in being considered for a teaching assistantship (TA), research assistantship (RA), and fellowship. 2.4.4 VISITING A GRADUATE PROGRAM YOU WOULD LIKE TO ATTEND To make a well-informed decision, you should ideally visit the university and interact with the faculty and graduate students there. Many graduate programs organize visit weekends in the late winter/early spring. These are a great opportunity that you should try to take advantage of, if at all possible. You will have access to faculty and students on the visit and you will be able to see the facilities, campus, and community. Some programs invite only students that they have accepted into the program. Others will invite admissible students they would like to consider for funding oﬀers. If the programs you are interested in do not plan a visit weekend, you can arrange to visit on your own. The best point of initial contact would be the staﬀ member in charge of the graduate program (e.g., program coordinator) or the faculty director of graduate studies (e.g., chair of the graduate studies committee). If you can’t visit then you should make arrangements to set up virtual or phone conversations with the director of graduate studies and other faculty members you may be interested in working with. You should think of a visit weekend like an interview. You are being interviewed, but you are also interviewing them. Everyone involved should be trying to determine if there is a good ﬁt. Although you would not be expected to wear a suit, do present yourself professionally (business casual attire is usually appropriate). Be ready to present your experience and background clearly and succinctly. If you have engaged in undergraduate research, you may want to print out a few slides or have a copy of a research paper you wrote in order to share your prior experience more eﬀectively. Do your homework before you go on the visit. Learn as much about the university and faculty in the program as you can. If you are interested in working with a particular research mentor, become familiar with their recent research publications. Prepare questions that will help you determine if this is the right ﬁt for you (see the list below). “Questions to Ask Yourself and Others While Considering a Graduate Program” 2.4. THE GRADUATE SCHOOL APPLICATION PROCESS 25 This is a broad list of questions. Some of these questions are intended for you to answer yourself. Others you can ﬁnd the answer to by exploring the university website. Some are questions you should ask of the faculty you speak with. Others you should ask of graduate students who are already in the program. Overarching Questions to Ask Yourself Am I most interested in experimental, computational, or theoretical research? Would I rather be in an established group or do research with a more junior faculty member? How much time and attention do I expect to get from my thesis advisor/research men- tor? Am I interested in interdisciplinary research and does this position ﬁt with those in- terests? Are the other students in the research group people that I can get along with? School/City/Lifestyle Is the campus a safe place? What safety programs are available (i.e., emergency phones, campus escorts)? Is housing easy/diﬃcult to ﬁnd? What are living expenses like? Is there a reliable mass transit system? Are there bike paths for commuting to campus? What kinds of entertainment are available? Will I be able to pursue the recreational activities I am interested in? Do I feel comfortable in this community/area of the country? Can I see myself living here for the next 5 years? (cid:24) Program/General Atmosphere What is the reputation of the program? How is the quality of the teaching? 26 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU Are the required and elective courses ones that I am interested in taking? How fre- quently are they oﬀered? Are graduate students happy here? How is the rapport among students, staﬀ, and faculty? How is the atmosphere for women and underrepresented minority students? What is the oﬃce space policy for new graduate students? Are the labs and facilities broadly accessible? How do I get trained to use these facilities? Do faculty members collaborate on research or work separately? Is collaborative re- search encouraged and supported? Funding/Financial Aid Do I need to ﬁnd/choose a thesis advisor before accepting an oﬀer to join the program or do I have the opportunity to spend a semester or two on campus before I decide? How do I apply for a teaching and/or research assistantship? What fellowship opportunities are available from the program/university? Am I auto- matically considered for these opportunities or do I need to apply? Is a tuition waiver included in my funding oﬀer? Is health insurance included in my funding oﬀer? What are the vacation/sick leave/family leave policies? What is the stipend level? Do students live easily on this amount? Does the funding continue through the summer months? If I am oﬀered an assistantship appointment, what are the work expectations? What are the responsibilities associated with a teaching assistantship (TA)? Is there training for new TAs? How is my performance evaluated? Who is my supervisor? Who do I talk to if I need help with a problem in the classroom? Research Mentor/Thesis Advisor How stable is his/her research funding? 2.4. THE GRADUATE SCHOOL APPLICATION PROCESS 27 Does the advisor have tenure? If not, what is the tenure rate at this institution? What is the advisor’s reputation in the department? How do the advisor’s current students feel about working with this person? Does the advisor treat students respectfully? Does the advisor stand up for his/her students when a political situation arises? Does the advisor give a lot of supervision or are students expected to work more inde- pendently? How is one’s thesis topic determined? How is authorship handled on journal publications? Will the research require traveling or working remotely? How long does it usually take for the advisor’s students to graduate? Are there opportunities available to attend a conference or two each year? Where have previous students gotten jobs? 2.4.5 GETTING ACCEPTED INTO A GRADUATE PROGRAM Diﬀerent programs will handle graduate applications diﬀerently. However, there is likely a com- mittee that determines an applicant’s overall ﬁt for the program and selects the best applicants for broader circulation among the faculty members in the graduate program. For large programs and Master’s programs that do not have funding associated with them, it is more likely to be a decision made at the committee level. For a Ph.D. program there is more match-making re- quired because you will need to have an interest in the research taking place in a faculty members lab and they will need to have funding to support you as a research assistantship. In many graduate programs there needs to be at least one faculty member who is interested in taking you on as an advisee in order for your application to progress. There are always excep- tions though. Some programs have fellowship and teaching assistantship support that allows them to bring in more students without the promise of a research assistantship. And, students who have received a large external fellowship have more ﬂexibility because they can often work with the faculty member of their choice without as much concern over the availability of funding for the research. I’ll note, however, that the fellowships do not generally cover research expenses, so even a fully supported fellow is not “free” for the faculty research mentor. They will need to 28 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU have the necessary funds to cover the expenses of the research and the time to provide research mentoring. Getting Paid to Learn Unlike some other disciplines, engineers are frequently given the op- portunity to earn a stipend while doing research that will directly beneﬁt their own degree progress. When I occasionally hear it taken for granted and ex- pected that their education should be completely paid for, I shake my head in wonder at the entitled attitude of this individual. Having served in graduate school administration, I am able to state deﬁnitively that in many other ﬁelds of study graduate students must fund their education by working positions that have no bearing on their research progress and their work may not even be connected to their disciplinary expertise. In fact, having to pay for one’s education in such away usually extends time to graduation dramatically. As noted above, at some institutions your acceptance into the graduate program may be separate from an oﬀer of assistantship funding. Be certain to understand the details of your particular situation before accepting an oﬀer. 2.5 2.5.1 FUNDING OF RESEARCH U.S. MODEL OF RESEARCH UNIVERSITIES Students often come with misconceptions about where and how research funding is obtained. What students rarely appreciate is that research funding is very diﬃcult to obtain. In most cases the funding for research (including a research assistantship) was obtained through a hard- fought and competitive proposal process. It is likely that their research mentor has spent an enormous amount of time and intellectual energy writing multiple proposals, of which only a subset is actually funded. The vast majority of research proposals that are written and submitted for consideration are rejected without being funded. Therefore, being supported on a research assistantship funded by a research grant is a privilege not an entitlement. Student Perspective “The thing I found most surprising about how research is conducted is the method by which most funding is procured and the overall attitude of researchers toward that source. When I ﬁrst started learning about aca- demic research, I expected budgets from research institutions to pay a large percentage of research costs. I believed that these budgets were heavily sub- sidized by student tuition and the earnings from previous research achieve- ments at those institutions. This is not typically the case. Grants from the 2.5. FUNDING OF RESEARCH 29 federal government are the single largest source of funding for the majority of universities and ﬁelds. Whether the funding is from a government agency such as NASA or the DOE, or from the Department of Defense, the money still comes from the American tax payer.” Grant funding may come from a federal source (such as the National Science Foundation or National Institutes of Health) or a private foundation (such as the American Heart Associ- ation or the Petroleum Research Fund). Research contracts are also a common funding source as well, and commonly come from federal sources (such as the Air Force Oﬃce of Scientiﬁc Research) or a private company (both small and large). Depending both on the source of the funding and the speciﬁc type of funding there may be very well-deﬁned timelines and deliv- erables associated with the research. Some funding may require monthly, quarterly, annually, and/or ﬁnal reporting associated with the project progress and outcomes. In other words, re- search funding comes with strings attached. Given the overall framework of funding, I suggest to graduate students that they should treat their assistantship as professional employment. If you have an assistantship, you are being paid for your engineering skills through both the stipend (i.e., paycheck) and tuition (i.e., waiver of tuition). If you were working in industry, you would be expected to treat the job professionally, put in your best eﬀort, and achieve regular progress. The same is expected in your graduate research. 2.5.2 FUNDING YOUR GRADUATE STUDIES For graduate students in engineering, and particularly students pursuing a Ph.D. program, grad- uate school is usually paid for by a fellowship, a research assistantship, or a teaching assistantship. Student Perspective “I believed that you still had to spend lots of money to attend grad school. I am extremely pleased to know that through applying for fellowships and with how most engineering departments work, pretty much everything from living expenses to tuition and lab funding is potentially covered.” Fellowships come in many shapes and sizes. Some universities have fellowships to provide and others are available through external programs. A fellowship may provide a “full ride” that pays for all of your tuition and stipend expenses (for one or more years), or it may simply be a supplement to other types of assistantship funding. A full fellowship gives you a huge advantage because a potential research mentor does not need to ﬁnd as much funding to support you. No graduate student is truly “free” because the research mentor must have the time to interact with you and be able to support other research expenses especially for experimental work, but it is 30 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU much easier for a research mentor to take on a fellowship student than to ﬁnd funding for an assistantship. Fellowships provided by a university are usually ones that you are automatically considered for when you apply to the graduate program. The best way to ensure that you have a good chance at being considered for one of these is to have the best graduate school application possible and to submit it early. Do not wait until the deadline!! Many fellowship and assistantship opportunities will already be gone if your application is in the last batch of applicants to be considered. There are also a variety of fellowships that you can apply for yourself as a senior under- graduate or a ﬁrst-year graduate student. Your academic advisor or research mentor will be able to point you toward ones that might be a good ﬁt for you, but you should consider looking into some of the following: Department of Energy Computational Science Graduate Fellowship Hertz Foundation’s Graduate Fellowship National Science Foundation Graduate Research Fellowship (NSF GRF) National Defense Science and Engineering Graduate Fellowship Program (NDSEG) National Defense Science, Mathematics and Research for Transformation (SMART) Scholarship NIH Kirschstein-NRSA Individual Predoctoral Fellowship Tau Beta Pi Association Graduate Fellowship in Engineering As you progress through your graduate studies there are also additional fellowships avail- able at later stages, particularly dissertation fellowships that are designed to help students ﬁnish up their Ph.D. program. There are two basic types of support provided through universities that will fund your graduate studies. There were some variations on the speciﬁc titles depending on the institution, but many intuitions use the names research assistantship (RA) and teaching assistantship (TA). These assistantships usually provide for both tuition and a stipend for your living expenses. In return, you will be working on a research project or by teaching undergraduate students. In many cases, research assistantships have a great deal of overlap with the research you will ultimately use for your thesis or dissertation. So, you are getting paid to do the research you would have needed to do anyway. Although the RA position may have a percentage appointment or certain number of hours associated with it, you will likely need to spend more time than what you are paid for in order to complete your degree in a timely manner. A good way to think about it is that you need to do a certain amount of research in order to earn your degree, and you are lucky enough to get paid for a portion of it! 2.5. FUNDING OF RESEARCH 31 As discussed above, there is more match-making needed in this case because you will need to be highly qualiﬁed, ﬁnd a good ﬁt between your research interests and a faculty mem- ber’s research program, and have this match up with available funding support. Once you have identiﬁed schools that you are interested in attending, you also need to look at the research in- terests of the faculty members and contact them about the availability of funding. If they have an RA position available and you are a good match, then they may make you an oﬀer! In some cases graduate students may be brought into a degree program and initially funded by a teaching assistantship. In other cases, the TA opportunities may come later in the graduate experience and something that you do after you have progressed in your degree program. The type of work that a TA would do depends on the speciﬁc position and may include grading, holding oﬃce hours to answer student questions, running a discussion section, or teaching the lecture component of a course. Regardless of the position, there will be an instructor or faculty member in charge of the course, and you may also be working with other TAs on the same course. Teaching assistantships, although excellent skill building opportunities, will not be as di- rectly related to your degree progress. If you are interested in an academic career path, the op- portunity to be a TA can help you gain invaluable experience. Even if you are not interested in being a faculty member some day, teaching a subject provides an opportunity for you to deepen your own understanding of it. If you are in front of a classroom for a portion of your TA work you will also be able to hone your presentation and explanation skills. Employers of every type appreciate these skills. For students planning to pursue a Master’s degree only, the funding opportunities are fewer. Sometimes RA and TA positions are available, but if you do not intend to continue on for a Ph.D. it is more likely that you will be paying tuition for the degree. Regardless, the investment in a Master’s degree should pay oﬀ. On average, your salary will be higher,7 your lifetime earnings with a M.S. vs. a B.S. are higher, and the unemployment rate is lower.8 Employers are also increasingly requiring a Master’s degree.9 Finally, there are student loans. Generally speaking, if you have student loans coming into graduate school, you will be able to defer your payment of them while you continue your studies. It’s also often possible to get student loans for graduate studies to support the cost or supplement funding you have from the university.10 7Doubleday, J., 2013. Earnings Gap Narrows, but College Education Still Pays, Report Says, Chronicle of Higher Educa- tion, October 7. 8Council of Graduate Schools, 2013. “Open Doors with a Doctorate.” 9Council of Graduate Schools, 2013. “Why Should I Get a Master’s Degree.” 10Council of Graduate Schools, 2013. “Financing Graduate Education.” 32 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU 2.5.3 FELLOWSHIP APPLICATIONS As mentioned in the previous section, fellowships come in all sorts of shapes and sizes, from a “full ride” to a small supplement. However, there are a number of commonalities in the appli- cation process for those you would need to apply to yourself. This happens independent of the university you are applying to or attending, so you will need to manage those deadlines in ad- dition to graduate school application deadlines. Look into these opportunities early. Although the deadlines vary quite a bit, many of them are due BEFORE the standard graduate school application deadlines. As you look into each fellowship opportunity, carefully read the eligibility criteria. You will not want to waste time on an application where you do not meet the basic criteria or where you are not a good ﬁt. Keep in mind that in some cases you will be applying as a senior undergraduate and in others as ﬁrst year graduate student. Some fellowship competitions allow you to apply in more than one year as well. Don’t try to do this all on your own, without feedback. You will have a much higher likelihood of being successful if you plan ahead and seek out guidance. Determine if there is help available on your campus that will guide you in the fellowship application process. If there are workshops oﬀered, seek these out and attend. There may be one-on-one help available if your campus has a writing center. You may also be able to seek feedback on portions of your application from an academic advisor or faculty member willing to read the essay portions. You should also use your network to ﬁnd out if you know someone who has been successful in getting one of these fellowships. Being able to look at a successful fellowships packet will give you a model to emulate. In addition to the fellowships available for your studies, there are also often small pockets of money that can help to defray other costs. Keep an eye out for other opportunities along the way, such as travel grants and other supplemental funding. Then later in your graduate studies, when you become a dissertator, look at fellowship opportunities again. Although there are not as many options as there are at the beginning of your graduate studies, in many ﬁelds there are dissertator fellowships that you can apply to which will help speed up your degree completion. 2.6 UNDERSTANDING THE ORGANIZATION OF YOUR RESEARCH GROUP After you have joined a research group (or even while you are in the process of determining if a research group is a good ﬁt for you), it is important to understand how the group is organized. There will be research projects underway—some ramping up, some ongoing, and others winding down. You will be involved in at least one in detail, but you should also understand the basic themes of the other topics that your colleagues within the research group are engaging with. Having the basic framework of the research topics will allow you to sort and process additional 2.6. UNDERSTANDING THE ORGANIZATION OF YOUR RESEARCH GROUP 33 information that you pick up in research group meetings, conversations with other research group members, and interactions with your research mentor. Student Perspective “My research group … usually meets on a weekly basis to give updates on progress and get advice on how to proceed if we have a problem. I ﬁnd this to be very beneﬁcial because it helps me get a feel for what everyone else in my group is working on. Although it is hard to follow a lot of the time, it’s good to learn what their projects are…” Initially these interactions, particularly in research group meetings, may seem like a waste of time because nearly everything that is discussed is going over your head. But it is important to persist and try to follow as much of the information being exchanged as possible. You can also connect with one of the other more experienced students afterward to ask then to help you ﬁll in some of the gaps. With time, you will be able, not only to understand more of what is being discussed, but also help provide useful feedback and ideas to the group yourself. Just keep in mind that it takes time to come up to speed, but you will make progress if you set goals for yourself that sometimes feel like a stretch. Student Perspective “Where I used to attend group meetings with glazed over eyes, I am now able [to] see what the other people are actually doing. However, I am usually not able to contribute too much because I still lack a signiﬁcant amount of knowledge. Therefore, my main goal in the coming year is to be able to talk more in group meetings and provide the other group members with some helpful comments.” Student Perspective “I think the most crucial element in my development during these meetings was that with every passing week, I felt more and more comfort- able with the research, eventually to the point where I could try to suggest explanations and various solutions to problems in conjunction with the same inputs from the other members of the meeting. Having my ideas consid- ered in a setting with three other people with considerably more experience in the ﬁeld was very rewarding. The collaborative eﬀort of people from dif- ferent backgrounds to develop solutions to a problem or explanations for a phenomenon has become one of my favorite elements of research.” 34 2. FINDING THE RIGHT RESEARCH POSITION FOR YOU You may be paid to do research (for instance as a research assistant or as hourly pay) or you may be doing research for credit. Either way, it is likely that there is some type of funding supporting your salary and/or the purchases of resources that you need to conduct the research. You should understand what the funding source is for the research you are pursuing. It may be a federal grant, an industry contract, institutional funds that your research mentor has at their disposal, or some other mechanism. There may be multiple funding mechanisms supporting the various projects and people involved in the research group. As a member of a research group, you also need to get to know the others engaged in the research group aside from your research mentor. Research groups come in many diﬀerent sizes, from the small tight-knit groups to large international collaborations. There may be undergrad- uate researchers, graduate students, postdoctoral researchers, scientists, and faculty members. Your research group may also be collaborating with other research groups. These people may be working directly with you, using similar or complementary techniques, sharing research space with you, or they may be working at a diﬀerent location or on a project that does not overlap with yours. Regardless, it is important to know who the research group members are and how they are connected to the work you are undertaking. ASSIGNMENT 2-8: INDIVIDUAL ASSIGNMENT – MAP THE ORGANIZATION OF YOUR RESEARCH GROUP Create a visual depiction, or map, of the research you are currently working in (or planning to join). Talk with your research mentor and other lab members to understand what projects are underway, who are the people involved, and how the research is funded. You might depict one or more of the following. • A diagram of the funded projects showing how they are interrelated, who is working on each, and what funding supports each person/project. • For a highly collaborative group: this would include how the group collaborates with other individual researchers, research groups, and institutions across the ongo- ing projects. • For an experimental group: the layout of physical lab space, how the experiments are organized, who utilizes on each piece of equipment, and how they projects/people are funded. • For a computational group: the research projects that the group has going on and con- nections between the projects, people, and software being used/developed. C H A P T E R 3 35 Becoming a Researcher 3.1 DEVELOPING A RELATIONSHIP WITH YOUR RESEARCH MENTOR Research groups can be set up in a variety of diﬀerent ways and range in size from 1 to 100 . C You may be working one-on-one with your research mentor or you may be working in more of a group setting where you meet with your research mentor along with others working on the same or related projects. In larger research groups you may ﬁnd that there are researchers at a variety of diﬀerent levels. This might include undergraduate students, graduate students, postdoctoral researchers, engineers, scientists, and faculty members. In some cases, your most immediate research mentor may be someone at a level just above your own. For instance, you may be an undergraduate researcher working most directly with a graduate student mentor. Ultimately the responsibility for the research group, its direction, and the projects being pursued are determined by the lead faculty member or lead scientist/engineer, sometimes called the principal investigator or PI. This individual is also your research mentor (maybe you will think of this person as your Mentor with a capital M), but your interactions with this individual may be less frequent and may be in a group setting rather than one-on-one. You should not discount the others in the research group as they may provide you with invaluable information, advice, and mentoring that could prove to be important to your success. Student Perspective “I had some previous research experience at [a] National Lab. … I had a mentor and a co-mentor that were constantly guiding me. I would meet with them several times per week to discuss how progress was going and ask [any] questions that I had. [My] two mentors also had oﬃces right down the hall from mine and had an open-door policy so I could stop in and ask anything if I got stuck. This was so helpful to the ease and speed of my workﬂow. I could work on my project and when I ran into a problem, I would try to solve it on my own ﬁrst, but if I couldn’t ﬁgure it out, I could easily consult one of my mentors for help. Sometimes if they couldn’t ﬁgure out the problem, they would point me in the direction of other researchers around the lab. This was a neat experience to draw on the expertise of researchers from diﬀerent groups. I got to meet new people and learn about what they were working on while 36 3. BECOMING A RESEARCHER also getting a new perspective on the problem I was originally trying to solve. Prior to coming to grad school, I had guessed that my advisor would be play a similar role as my mentors at [the National Lab]. This semester has taught me otherwise. I didn’t take into consideration the seemingly countless other obligations that grad school advisors have such as teaching, doing their own research, being active members of academic organizations which causes their time to be limited. Therefore, I do not have the same two-to-one relationship as I had at [the National Lab] which makes my work more independent. I think this is a good, and necessary step for me to take in my research career. This has made my problem solving skills much better and also has made me get to know the areas of expertise of the other students and staﬀ members in my group. I’m learning who can possibly help me depending on the issue that I have run in to.” The Guides at Your Side I would be hard pressed to count the number of mentoring relation- ships I have had over my career. Certainly somewhere in the multiples of hundreds, if I consider both those where I have been the mentor and those where I have been the mentee. These relationships have ranged from a few weeks to decades and have varying levels of involvement, but the common theme is a goal to help the other learn, evolve and be successful at what they are trying to accomplish. The more everyone understands the goals and mo- tivations at the heart of a mentoring relationship, the more successful the results will be. This relies on communication and working to develop a rap- port that will ultimately lead to a productive outcome. Regardless of the size of the group and who speciﬁcally is your research mentor(s), you will need to take an active role in getting the mentoring you need to be successful with your research. Initially, you will be learning the basics of the project and the techniques you will be using, but even at this early stage you need to take ownership of your progress. Let your mentor know what you do know, and what you need help in learning, so that s/he can help you identify the resources that can assist you. As you gain more experience you are likely to be given more independence, both in terms of working more independently on speciﬁc tasks but also in carrying forward with the next steps before your next check-in with your mentor. In the business world the term is called “managing up”—making the management of you as an employee easy for your boss—you can use these same ideas in a mentoring relationship by “mentoring up.” In an article titled “Making the most of mentors: A guide for mentees,” 3.1. DEVELOPING A RELATIONSHIP WITH YOUR RESEARCH MENTOR 37 the authors1 suggest that you take responsibility for the mentoring relationship by “guiding and facilitating the mentor’s eﬀorts.” When working with a mentor, you have to ﬁgure out what you need from that person in terms of time, energy, and inﬂuence, and help that person to help you. Your goal is to ask for the help you need in a way that is easy for that person to give it to you. You may need other things from them—like letters of recommendation for a scholarship/fellowship for instance—and you need to make them aware of these needs as well as make it easy for them to meet your needs. Tell them about your goals, and where you want to go with you career. Tell them what would help you if you know and, if you don’t, ask them what might help you to achieve your goals. With your research mentor, determine how regularly will you meet—this may be more frequent at ﬁrst and at critical points in the research or your degree process, so you may need to revisit and renegotiate the frequency of your interactions. If your mentor does not have regular meetings with you, take responsibility for requesting and scheduling these. Go beyond simply following through with the tasks that have been assigned to you and think ahead to what should come next, set goals that you can discuss, generate ideas for overcoming the research obstacles you have run into, and be responsive to the feedback you receive from your mentor. Most impor- tantly, when you have an opportunity to interact with your research mentor, you should strive to be prepared. • Have a clear plan, at least for the next step of your research. • Be prepared to discuss what you have accomplished recently and what you plan to do next. • Have questions to ask based on your research progress and/or your reading of the lit- erature related to your project. • Listen to your research mentor’s responses, and write them down (either immediately or just after the interaction). • Act on your plan and the suggestions made to you by your research mentor between now and your next interaction. Student Perspective “It was good to realize that the student is in some way expected and encouraged to dictate the schedule and ﬂow of meetings. This made me more conﬁdent to meet with my professor and decide what an appropriate pace for my research is. 1Zerzan, J. T., Hess, R., Schur, E., Phillips, R. S., and Rigotti, N., 2009. Making the most of mentors: a guide for mentees. Academic Medicine, 84(1):140–144. 38 3. BECOMING A RESEARCHER In my experience, the most eﬀective and successful research students come to each meeting (whether it be in an individual or group format) with results in hand (either on a piece of paper or in a set of slides on their computer). They have thought about the results and what they mean, are ready to discuss them or ask questions about them, and have prepared a list of next steps that they will take. They take notes on what we discuss and what we decide to do (either in a lab notebook or a computer ﬁle). They identify resources they need, or questions that they have, so that I can help them move the research forward by pointing them in the right direction, connecting them to a person with the expertise they need, or purchasing something that is required for the research. These successful research students are also constantly keeping up with the literature, identifying recent publications that are relevant to their project. They bring those papers to my attention and they share relevant papers with other members of the research group. They also keep track of their own degree progress—deadlines for examinations, course requirements for the degree program, etc. In addition to sharing information with me, they share information with their peers, and mentor those who come in after them, either formally or informally. The reason these individuals are so successful is that they have taken ownership of their progress and help me to help them advance and succeed. Student Perspective “The change has been very gradual, but I’m starting to feel conﬁdent in my ability to understand the day-to-day research goals of the research group, and maybe more importantly, to know what questions to ask and when to ask them. This is a transition that I think many new researchers go through. How it often worked for me at ﬁrst was that, when an unfamiliar topic came up, I doubted that I even had the technical background to have the means to learn about it. Not wanting to waste the time of the people who seemed to be familiar with the subject, I generally kept my questions to myself.” You can’t expect to know everything when you setup into a new research project, but your goals should be to come up to speed quickly and ask relevant questions that will help you to obtain the background information you need. The worst thing to do is pretend you know something when you don’t. Your research mentor, and the colleagues you work with, can’t help you get to where you need to be if they don’t know that you are lost. Phil Dee, who wrote the book Building a Successful Career in Scientiﬁc Research, highlights this as a foundational element providing “the ground rule” for your relationship with your research mentor: “communicate with your boss.2” If you step back and think about it, you will see that academic research is a symbiotic relationship between the research mentor and the student. You and your research mentor must 2Dee, P., 2006. Building a Successful Career in Scientiﬁc Research: A Guide for PhD Students and Postdocs. Cambridge Uni- versity Press. 3.1. DEVELOPING A RELATIONSHIP WITH YOUR RESEARCH MENTOR 39 depend on each other. In other words, it is mutually beneﬁcial for you to be successful. My colleague, Prof. Irving Herman at Columbia University, wrote a somewhat tongue-in-cheek guide for graduate students in which he espoused the “The Laws of Herman.3” Several of the laws are about the symbiotic relationship mentioned between you and your research mentor, the last two being “Whatever is best for you is best for your advisor.” and “Whatever is best for your advisor is best for you.” Meaning that your success is to everyone’s advantage. Both Dee and Herman also bring up the topic of writing, which is a critical skill for every researcher at every level. If it is not something that you feel you are good at yet, don’t worry, you will have many opportunities to practice and you will become better the more you write! If you take my advice above about preparing for meetings with your research mentor, you will automatically be writing something about your research. It may be in a bulletpoint list initially, but if you save these regular meeting notes you will ﬁnd that later on, when you are at the stage of writing about your research, you can go back to these notes for reference and turn portions of your notes into sentences and even paragraphs. The other advantage of this chronological archive of information you have created along the way is that it can help you to refresh your memory about what you did to get to where you are, and the questions you were posing and answering. Although a thesis or journal article that you will write is not a historical recounting of every step and misstep that you took, a review of this information can help you to see the larger picture of your work. ASSIGNMENT 3-1: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON GIVING AND RECEIVING FEEDBACK Write a one-page reﬂection on giving and receiving feedback. First, describe a time that you received feedback that you (ultimately) found valuable. Discuss how you reacted to it at the time and how you looked back on this feedback as time passed. Then, describe a time that you provided feedback to someone else. Discuss the reaction/response you observed in the other person at the time and as time passed. Also discuss how you would have reacted if someone had provided you that same feedback in the same way. 3Herman, I. P., 2007. Following the Law. Nature, 445, 11. 40 3. BECOMING A RESEARCHER ASSIGNMENT 3-2: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON DEE’S RULES Consider the following “rules” from Phil Dee’s chapter on “Choosing and Handling your Ph.D. Adviser”4: Rule 1: The ground rule: communicate with your boss. Rule 2: Keep your boss informed. Rule 3: Discover what makes your boss tick. Rule 4: Earn your boss’s respect. Rule 5: Assert yourself. Rule 6: The golden rule: write for your boss. Note that Phil Dee uses the term boss, where others use advisor, and this book most commonly uses research mentor. Although these terms can have diﬀerent connotations, we are each talking about the same person (boss = advisor = research mentor). Choose one of the rules above and discuss how you have seen this apply to your own research experience (or how you would expect it to emerge in a future research experience). 3.2 ALIGNING EXPECTATIONS Some research opportunities and relationships come with clearly outlines expectations, but this is not always the case. When it is not discussed up front, it is up to you to seek clariﬁcation. Formalizing the relationships and the expectations can often be helpful. Many faculty are begin- ning to use written agreements with their students called variously a mentoring contract, mentor agreement, research agreement, or advising statement.5;6 These can cover a wide range of topics, but the basic intent is for both he mentor and the mentee to understand the expectations of the relationship for the duration of the degree program. 4Dee, P., 2006. Building a Successful Career in Scientiﬁc Research: A Guide for Phd Students and Postdocs, Cambridge Uni- versity Press. 5Branchaw, J., Pfund, C., and Rediske, R., 2010. Entering Research: A Facilitator’s Manual: Workshops for Students Beginning Research in Science. WH Freeman. 6Masters, K. S. and Kreeger, P. K., 2017. Ten simple rules for developing a mentor—mentee expectations document. PLoS Computational Biology, 13(9). e1005709. https://doi.org/10.1371/journal.pcbi.1005709 and https://doi. org/10.1371/journal.pcbi.1005709.s001. 3.3. DEVELOPING EXPERTISE 41 These expectations usually revolve around the topics of: • • shared goals including your career goals and what will be needed for you to achieve them; research skills you will need to develop to complete your project; • work hours (number, time of day, days of week), work/life balance, and vacation time; • graduate assistantship stipends, type of funding over time (e.g., RA vs. TA), and sum- mer support; • degree progress milestones and deadlines/goals for when they will be achieved; • • • fellowship applications and grant writing assistance; expectations for documentation of research, publication, and authorship; and conﬂict resolution. Traditionally the alignment of expectations has been either done more informally (or not at all). When it does occur informally, it likely happens over the course of time. Regardless of whether it is informal or formal, if your mentor does not embark on a conversation about these topics with you, it is something you will need to bring up. It can be anxiety provoking to be in the dark about what is expected of you. Having you understand your mentor’s expectations will help you to meet them, but equally important, having your mentor understand your goals will help you to achieve them. Student Perspective “Over the meetings I’ve had with my research mentors, I’ve learned that the expectations they have for me and skills they suggest I work on de- veloping seem to be centered around the idea of taking the time necessary to carry out my research carefully.” 3.3 DEVELOPING EXPERTISE In your pursuit of a research career, you will be transitioning from a novice learner to an expert in your chosen area of focus. But we should consider what is meant by the term expert. An expert is not someone who knows all the answers. An expert has signiﬁcant knowledge on a topic, appreciate which knowledge is applicable in the given situation, and can seemly exert little eﬀort in solving a problem. An adaptive expert is someone who approaches a new situation ﬂexibly, applies their existing knowledge and skills, but is always seeking to learn more. It is 42 3. BECOMING A RESEARCHER important to recognize that experts must be lifelong learners to maintain and strengthen their expertise. The U.S. National Research Council undertook an eﬀort to link the research and practice on the topic of learning which culminated in a seminal book titled How People Learn7 (cited well over 22,000 times in the literature). Key principles they summarize on the topic of how experts diﬀer from novices include the following. • • • • “Experts notice features and meaningful patterns of information that are not noticed by novices.” “Experts have acquired a great deal of content knowledge that is organized in ways that reﬂect a deep understanding of their subject matter.” “Experts’ knowledge cannot be reduced to sets of isolated facts of propositions but, instead, reﬂects contexts of applicability: that is, the knowledge is “conditionalized” on a set of circumstances.” “Experts are able to ﬂexibly retrieve important aspects of their knowledge with little attentional eﬀort.” Everyone is a Novice We are all novices and experts, it just depends on the topic area. I am still in the novice learner stage when it comes to baseball. I know the basics of the game, but when a fast and complex play occurs, I don’t always follow exactly what happened and can’t begin to predict the outcome. Happily, when I’m at one of my son’s games, other parents watching the game with me are more expert. They are happy to explain what happened so that I can further develop my knowledge of the game. I won’t ever have the expertise of a long- time player, but I’m working on becoming a more expert fan! For instance, expert mathematicians notice patterns and identify classes of problems in order to develop an approach to a solution. They have not only solved many problems before, but they have also stepped back to consider the underlying principles of each problem and how solutions can be classiﬁed. This is the opposite of what I often see in novice engineers—they are often too quick to throw down an equation and immediately start plugging in numbers. As a student begins to reﬁne and improve their approach, they ﬁnd that they are most successful when they ﬁrst look at a problem and think about what category of approach might work best, then work with the appropriate equations and manipulate them, and ﬁnally, at the end, plug in values and ﬁnd a numerical solution. When using this more advanced approach, students 7National Research Council, 2000. How People Learn: Brain, Mind, Experience, and School–Expanded Edition, National Academies Press. 3.4. DEVELOPING YOUR OWN IDENTITY AS A RESEARCHER 43 ﬁnd that the parallels which can be drawn between problems become more obvious because the patterns become more recognizable. I advocate that students start developing their intuition about problem solving in a new area of learning by developing an initial “guess” associated with speciﬁc problems—Do you ex- pect it to be positive or negative? What magnitude would it be? What units? Then at the end of the problem, you check your solution back against the guess. If they agree, and the answer is conﬁrmed, then you can build conﬁdence in your intuition. If they don’t agree, then either your guess was oﬀ or you made an error in your solution. If your guess was wrong, the solution process may shed light on where your intuition was oﬀ. If you feel conﬁdent in your guess, then it may help you to identify where you made an error in your solution. The process of thinking about the problem up front, and the retrospective analysis of the solution, will help you to advance toward more expert thinking. This does not just apply to coursework, it applies to research as well. You should have a hypothesis (a guess) before you begin, and you should design your research to explore that hypothesis to prove or disprove it. Whether it is coursework or research, it takes an investment of time to develop your skills and begin to work toward expertise. Time on task has a big impact. But you must seek more than superﬁcial knowledge. You need to develop expert knowledge that is both conditionalized on the context and centered around big ideas.8 As you build expertise in an area you will notice that your performance will become automatic and ﬂuid. ASSIGNMENT 3-3: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON EXPERTISE Consider areas of expertise that you have observed in others (such as your research mentor, others in your research group, classmates, etc.). Reﬂect on areas of expertise that you are developing with respect to your research. What can you do to either deepen your expertise in one of these areas, or develop expertise in an area you recognize as important to your research? 3.4 DEVELOPING YOUR OWN IDENTITY AS A RESEARCHER As you engage in your academic career and through your experience as a researcher, one of your goals should be to become an independent, critical thinker. In your academic pursuits (and in life) you are on a continuous journey of learning. This journey is facilitated by self-awareness, reﬂection, and authentic experiences that will prepare you for where you will go next. 8National Research Council, 2000. How People Learn: Brain, Mind, Experience, and School–Expanded Edition, National Academies Press. 44 3. BECOMING A RESEARCHER Self-awareness means knowing your own strengths and weakness, knowing what ex- cites you and makes you curious, and knowing how you handle yourself when faced with both success and failure. Reﬂection involves you taking the time to think about things that happen to you in life. How did you handle a challenge? How did you react to praise or criticism when it was given? How might you do things diﬀerently the next time? Reﬂection can be done all inside your own head, by journaling your experiences, or by talking to others in thoughtful conversation. Authentic experiences are real-world activities that give you an actual taste of what it is like to do something. Sometimes this can be accomplished through a class assign- ment, but most often this means getting out into the professional world and trying your hand at something. In addition to research experiences, other valuable authentic experiences include internships for a company or national laboratory, and volunteer opportunities like Engineers Without Borders. What you will gain from these ex- periences will not only be technical experience, but also knowledge about yourself; who you are and who you want to be. Becoming who you want to be can be thought of as self authorship. Marcia Baxter Magolda deﬁnes the term self authorship, or internal identity, as “simultaneously a cognitive (how one makes meaning of knowledge), interpersonal (how one views oneself in relationship to oth- ers), and intrapersonal (how one perceives one’s sense of identity) matter.9” As you develop as a person and as a researcher, you will rely more on yourself for interpreting data rather than the interpretation of others; you will also begin to interact as a junior colleague, rather than a student with your peers and research mentor(s), and you will begin to develop your own iden- tity as a researcher. Inherent in becoming a self-authored individual, and critical to your success as a researcher, will be your ability to realize that “the complexity of the world simultaneously requires systematic thinking, the ability to judge knowledge claims oﬀered by authorities, con- structing convictions, and openness to new possibilities.10” All of this may seem a tall order at the moment, but moving from authority dependence to self authorship, whether it be professors or parents, is important in both your professional and private lives. Student Perspective “I think this is what’s most important for engineers in their capacity for self authorship. Through their education, they are able to form their own opinions, think critically, and problem solve. However, this means nothing 9Baxter Magolda, M., 1999. Creating Contexts for Learning and Self-Authorship: Constructive–Developmental Pedagogy, Vanderbilt University Press, p. 10. 10Baxter Magolda, M. and King, P. M., 2004. Learning Partnerships: Theory and Models of Practice to Educate for Self Au- thorship, Stylus, Sterling, VA, p. 3. 3.5. TRACKING YOUR DEVELOPMENT AS A RESEARCHER 45 if they are unable to share these opinions, listen to others, or form lasting personal and professional relationships.” The ultimate goal of higher education is to produce learners that have the following ca- pacities.11 • “Cognitive maturity, characterized by intellectual power, reﬂective judgment, mature decision making, and problem solving in the context of multiplicity. • An integrated identity, characterized by understanding one’s own particular history, conﬁdence, and capacity for autonomy and connection, and integrity. • Mature relationships, characterized by respect for both one’s own and others’ particular identities and cultures and by productive collaboration to integrate multiple perspec- tives.” ASSIGNMENT 3-4: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON YOUR DEVELOPMENT AS A RESEARCHER An important part of becoming a mature, independent researcher is discovering yourself. What interests and excites you? What motivates you? Write a two-page self-evaluation on your development as a researcher. Reﬂect on where you have been, where you are now, and what you will work on next in your development as a researcher. Revisit this assignment periodically. First complete the writing assignment described above, and then look back on previous assignments to remind yourself of where you have been and how you are developing. 3.5 TRACKING YOUR DEVELOPMENT AS A RESEARCHER Initially, it may not seem relevant to track your progress in research, but in the long run it can prove exceptionally helpful. In particular, if you have some long term goals in mind (like submitting a research paper for publication, earning your Ph.D., or getting a faculty position) you can break down the larger goals into smaller steps that you will need to take, and track your progress along the way. 11Baxter Magolda, M. and King, P. M., 2004. Learning Partnerships: Theory and Models of Practice to Educate for Self Au- thorship, Stylus, Sterling, VA, p. 6. 46 3. BECOMING A RESEARCHER Student Perspective “With this being my ﬁrst semester in a lab, it has been a large learn- ing curve and looking at it now, it really puts into relief all the skills I need to further develop. I started out having to learn the safety procedures, loca- tion of everything in the lab, and other basics. Whether it was following the pipette rules and maintaining a clean working environment, it was all part of the learning curve. Evaluating now, it is evident the skills I need to develop. My basic laboratory skills are quite suﬃcient, but there is a large amount of equipment I will need to know how to use.” As a researcher, there are a variety of things that you will need to focus on, and master, in the years to come: • • • • • • a knowledge of the discipline in general and your speciﬁc subdiscipline specialty; a basic understanding of, and experience in, the steps and techniques of engineering research; ability to employ the scientiﬁc habits of mind that engineering research requires; awareness of ethical, social, political, and economic inﬂuences on, and impacts of, en- gineering research; skills in written and oral technical communication; and skills in collaboration and teamwork. An Individual Development Plan (IDP) can help you to make progress on several fronts. For example, the American Association for the Advancement of Science (AAAS) has developed on online tool called My IDP available at http://myidp.sciencecareers.org/. For early- stage researchers the tool is helpful for identifying your skills, interests, and values and providing you with career paths that may be a good ﬁt for you. Additionally, this tool helps researchers at various career stages in goal setting in areas like skill development, project completion, and career advancement. The SMART goal strategy emphasizes creating goals that are “speciﬁc, measurable, action-oriented, realistic, and time-bound,” hence the acronym. Using the “SMART” Principle12 S—Speciﬁc—Is it focused and unambiguous? M—Measurable—Could someone determine whether or not you achieved it? 12Goal-setting strategies for scientiﬁc and career success, Fuhrmann, C. N., Hobin, J. A., Cliﬀord, P. S., and Lindstaedt, B., 2013. Science, AAAS, Dec. 3. http://www.sciencemag.org/careerscareersresearch/2013/12/goal-setting- strategies-scientific-and-career-success. Accessed January 2018. 3.5. TRACKING YOUR DEVELOPMENT AS A RESEARCHER 47 A—Action-oriented—Did you specify the action you will take? R—Realistic—Considering diﬃculty and timeframe, is it attainable? T—Time-bound—Did you specify a deadline? Achieving your goals will take investment of time, but you will eventually be able to see gains. You will begin to understand more of the seminar talks you attend and the journal articles you read. You will gain the ability to operate independently and more eﬃciently. You will begin to contribute new ideas to the research conversations you engage in. You may end up develop- ing specialty expertise that others in your research group rely on. As you invest more time and intellectual energy in your research, you will be begin to see payoﬀs in terms of progress and recognition for your research accomplishments. ASSIGNMENT 3-5: INDIVIDUAL ASSIGNMENT – QUALITIES OF A SUCCESSFUL RESEARCHER List ten qualities that you will need to be a successful researcher. How far along in your devel- opment are you in achieving these qualities? How can you go about developing these qualities further? ASSIGNMENT 3-6: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON MENTOR FEEDBACK Individuals grow accustomed to receiving and accepting feedback in diﬀerent ways and may react diﬀerently to the feedback depending on who it comes from, the context in which it is provided, and our mood at the time of receiving it. Some of us are more eﬀective at either or both giving and receiving advice than others, but we can all become better. Before asking for feedback on your work or your development as a researcher, prepare yourself to receive it openly. Receiving feedback can be easier to handle when you ask for speciﬁc feedback on an area you already know you want to improve on and put the feedback to good use right away. If you have a research mentor, request a meeting to receive feedback regarding the self- assessment above. Chose at least one area where you believe you have demonstrated strength, and at least one area where you believe you need additional development that you are ready to undertake. 48 3. BECOMING A RESEARCHER Prior to the meeting, consider how you can be open to receiving the feedback you are going to receive. After the meeting, write a one-page reﬂection about what you heard and your reaction to it. Be sure to express gratitude for the time your mentor takes with you to discuss this topic. ASSIGNMENT 3-7: INDIVIDUAL ASSIGNMENT – SELF ASSESSMENT Use the “Evaluation of Research Progress and Researcher Development” rubric in Table 3.1 to conduct a self-assessment. It covers a range for skills, from Research Documentation to Stress Management. Your speciﬁc research project will also require speciﬁc skills, so space is provided at the end of the self-assessment for you to deﬁne these and track your progress on their mastery. Note that the skills are cumulative (from the left column, to the middle, and ﬁnally the right column). If you have Mastery in an area, you will have demonstrated the items listed under Beginning and Developing, as well as Mastery. As you enter into research, it is likely that you are at the Beginning stage in most all areas. Take a look ahead to the next level and see what items you should be working on in your development. If you don’t know how to make progress on this next level, it is likely that your research mentor will be able to give you some strategies for making progress. Periodically assess yourself for your research progress and development as a researcher (pages 49–55). Consider sharing the assessment with your research mentor to prompt discussion about where you are in your development as a researcher and how you can make progress in areas you would like to improve in. Although you may be able to achieve mastery in some areas during your degree progress, other topics may be something you work on throughout your career. 3.6 BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR Being an eﬀective team member requires a wide range of social and organizational skills. You may already come equipped with many of these skills given your prior experience, but there are likely areas in which you may need to gain experience or improve on your current capabilities. One of the earliest aspects of being a good team member that you may encounter is the etiquette and expectations of participating in a team meeting. In the context of research, this comes up in research group meetings or lab meetings. There are several strategies that you can employ to determine the appropriate type and level of engagement expected of you. Another basic strategy is simply to ask the question of those who are already in the know. This can be posed to your research mentor, and you can also ask other research group members to give their impressions of the expectations. This may mean coming prepared with certain materials in 3.6. BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR 49 Table 3.1: “Evaluation of Research Progress and Researcher Development” rubric (Continues.) Evaluation of Research Progress and Researcher DevelopmentMilestones and TimelineTh e ability to set realistic goals and use time and resources eﬀ ectively; to obtain the maximum beneﬁ t from a minimum investment of time and resources.r BeginningDemonstrated by:• focusing on tasks at hand without dwelling on past mistakes• completing assignments on time• making use of reference books and literature • coordinating and working with others on group project assignments• preparing for scheduled appointment times • using unscheduled time eﬃ cientlyr DevelopingDemonstrated by:• planning ahead• setting up an eﬀ ective schedule• coordinating schedule with others• demonstrating ﬂ exibility • moving forward when mistakes are made• accepting responsibility in group activities• identifying alternative resources• using library and internet resources eﬀ ectively• updating solutions based on review of available literaturer MasteryDemonstrated by:• setting priorities and reorganizing as necessary• performing multiple tasks simultaneously• delegating when appropriate• following up on projects in a timely manner• managing meeting time eﬀ ectively• considering professional goals in the context of project• demonstrating the ability to say “no” if requests made in conﬂ ict with set goals• actively seeking resources to solve problems or answer questions• using limited resources creativelyResponsibilityTh e ability to fulﬁ ll commitments and to be accountable for actions and outcomes.r BeginningDemonstrated by:• being punctual• completing tasks on time • following through on commitments• accepting responsibility for own actions and outcomes• recognizing own limitsr DevelopingDemonstrated by:• providing constructive feedback to the appropriate person(s)• oﬀering and accepting help• completing projects without prompting• contributing to the provision of a safe and secure environmentr MasteryDemonstrated by:• promoting education• accepting leadership roles• delegating as necessary50 3. BECOMING A RESEARCHER Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric (Continues.) ProfessionalismTh e ability to exhibit appropriate professional conduct and to represent the profession eﬀ ectively.r BeginningDemonstrated by:• following University, Department, and research group policies• demonstrating honesty, integrity, and respect to others• seeking opportunities for leadership• demonstrating an awareness of the professional role of the engineer in society r DevelopingDemonstrated by:• participating in professional activities/organizations• identifying positive professional role models• discussing societal expectations of the engineering profession• awareness of the impact of ethical issues and legal issues on the engineering profession• acting on moral commitmentr MasteryDemonstrated by:• acting in a leadership role• actively participating in professional organizations• actively promoting the engineering profession• advancing the engineering profession outside of the academic programCommitment to LearningTh e ability to self-assess, self-correct, and self-direct; to identify needs and sources of learning; and to continually seek new knowledge and understanding.r BeginningDemonstrated by:• identifying problems• identifying needs for further information• formulating appropriate questions• identifying and locating appropriate resources• attending class consistently• showing evidence of preparation prior to class• showing attentiveness• demonstrating a positive attitude toward learning• participating in small groups• oﬀ ering own thoughts and ideasr DevelopingDemonstrated by:• identifying own learning needs based on previous experiences• setting personal and professional goals• seeking new learning opportunities• seeking out professional literature• prioritizing information needs• reconciling diﬀ erences in opinions or information• analyzing and subdividing large questions into components• demonstrating conﬁ dence in presenting materialr MasteryDemonstrated by:• researching and studying areas where knowledge base is lacking• reading articles critically and understanding limitations• accepting that there may be more than one answer to a problem• recognizing the need to verify and then verifying solutions to problems• formulating and re-evaluating position based on available evidence• demonstrating conﬁ dence in sharing new knowledge3.6. BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR 51 Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric (Continues.) Communication SkillsTh e ability to communicate eﬀ ectively (i.e., speaking, body language, reading, writing, listening) for varied audiences and purposes.r BeginningDemonstrated by:• understanding and applying English (verbal, written, grammar, spelling, expression)• communicating appropriately per situation • providing appropriate feedback to team members and faculty• recognizing diﬀ erences in communication styles• recognizing impact of non-verbal communication: maintaining eye contact, listening activelyr DevelopingDemonstrated by:• modifying communication when necessary• reﬂecting, clarifying, and restating messages• utilizing non-verbal communication to augment verbal messages• exhibiting appropriate communication per situation• maintaining quality in written work• maintaining quality in oral work• utilizing technology r MasteryDemonstrated by:• modifying written and verbal communication to meet needs of various audiences• presenting verbal or written messages with logical organization and sequencing• maintaining open and constructive communication• communicating professional needs and concerns• utilizing communication technology eﬀectivelyInterpersonal SkillsTh e ability to interact eﬀ ectively with faculty research mentor, scientiﬁ c staﬀ , graduate students, team members, and other department personnel, and to deal eﬀ ectively with cultural and ethnic diversity issues.r BeginningDemonstrated by:• maintaining attentive behavior • demonstrating acceptance of limited knowledge and experience• communicating with others in a respectful, conﬁ dent manner• appropriate behavior in discussion• maintaining professional demeanor in interactions• respecting diﬀ erences in others• recognizing impact of non-verbal communication r DevelopingDemonstrated by:• seeking to gain knowledge and input from others• assuming responsibility for own actions• establishing trust and motivating others• recognizing impact of non-verbal communication and modifying accordingly• discussing problems with the appropriate person(s)r MasteryDemonstrated by:• approaching others to discuss diﬀ erences in opinions• talking about diﬃ cult issues with sensitivity and objectivity• responding eﬀ ectively to unexpected situations• delegating to others as necessary52 3. BECOMING A RESEARCHER Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric (Continues.) Use of Constructive FeedbackTh e ability to identify sources of feedback, to seek out feedback, and to eﬀ ectively use and provide feedback for improving personal interaction.r BeginningDemonstrated by:• using active listening skills• showing a positive attitude• critiquing own performance• maintaining two-way communication• actively seeking constructive feedback and assistancer DevelopingDemonstrated by:• assessing own performance accurately• seeking, accepting, and integrating feedback from others• developing a plan of action in response to feedback r MasteryDemonstrated by:• considering multiple approaches when responding to feedback• modifying feedback given to others according to their learning styles• engaging in non-judgmental, constructive, problem-solving discussions• reconciling diﬀerences with sensitivityCritical Th inkingTh e ability to question logically; to identify, generate, and evaluate elements of logical argument; to recognize and diﬀ erentiate facts, illusions, assumptions, and hidden assumptions; and to distinguish the relevant from the irrelevant.r BeginningDemonstrated by:• considering all available information• recognizing gaps in knowledge base• articulating ideas/problems• raising relevant questionsr DevelopingDemonstrated by:• understanding scientiﬁc method• critiquing hypotheses and ideas• formulating alternative hypotheses and ideas• examining new ideas• being able to distinguish relevant from irrelevant information • recognizing fact vs. opinionr MasteryDemonstrated by:• exhibiting an openness to contradictory ideas• assessing issues raised by contradictory ideas• justifying selected solutions• determining eﬀectiveness of applied solutions• identifying complex patterns of associations• demonstrating intuitive thinking• distinguishing when to think intuitively vs. analytically• recognizing own biases and suspending judgmental thinking• challenging others to think critically3.6. BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR 53 Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric (Continues.) Scientiﬁ c LiteracyTh e ability to use processes and skills of science to conduct investigations; to recognize and deﬁ ne prob-lems, analyze data, develop and implement solutions, and evaluate outcomes.r BeginningDemonstrated by:• recognizing problems• identifying questions • knowing the basic steps of the problem-solving process (stating the problem, describing known solutions, identifying resources needed to develop solutions, beginning to examine multiple solutions to the problem)• seeking to ﬁ ll gaps in knowledge • understanding diﬀ erences between primary, secondary and other sourcesr DevelopingDemonstrated by:• distinguishing between fact and hypotheses • applying the problem-solving process• prioritizing problems• consulting with others to clarify the problem• identifying contributors to the problem• accepting responsibility for implementing solutions• considering consequences of possible solutions• generating alternative plans when diﬃ culties or obstacles present themselvesr MasteryDemonstrated by:• forming possible solutions • designing a data collection scheme and collecting data• drawing conclusions about the validity of the possible solution• seeking alternative hypotheses and contradictory ideas • evaluating outcomes• reassessing solutionsResearch DocumentationTh e ability to eﬀ ectively document research approach, progress, hypotheses, and outcomes.r BeginningDemonstrated by:• recording research ﬁ ndings • identifying methods usedr DevelopingDemonstrated by:• keeping record of research progress• writing out steps to possible solution• providing documentation that others can followr MasteryDemonstrated by:• describing thought processes, hypotheses and outcomes • supporting methods chosen with literature references • using project managements tools to stay on task 54 3. BECOMING A RESEARCHER Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric (Continues.) Stress ManagementTh e ability to identify sources of stress and to develop eﬀ ective coping behaviors.r BeginningDemonstrated by:• recognizing own stressors or problems• recognizing stress or problems in others• seeking assistance as necessary• demonstrating appropriate responses • maintaining professional demeanor r DevelopingDemonstrated by:• accepting constructive criticism appropriately• handling unexpected changes appropriately• maintaining balance between professional and personal life• establishing outlets to cope with stressorsr MasteryDemonstrated by:• recognizing when problems are unsolvable• demonstrating a preventive approach to stress management• oﬀ ering solutions for stress reduction • assisting others with stress• establishing a support network• prioritizing multiple commitments• tolerating inconsistencies• responding calmly to urgent situationsProject-Speciﬁ c Research Skill 1r BeginningDemonstrated by:r DevelopingDemonstrated by:r MasteryDemonstrated by:3.6. BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR 55 Table 3.1: (Continued.) “Evaluation of Research Progress and Researcher Development” rubric Project-Speciﬁ c Research Skill 2r BeginningDemonstrated by:r DevelopingDemonstrated by:r MasteryDemonstrated by:Project-Speciﬁ c Research Skill 3r BeginningDemonstrated by:r DevelopingDemonstrated by:r MasteryDemonstrated by:56 3. BECOMING A RESEARCHER advance, listening attentively and asking for clariﬁcation at key points, asking critical questions about the topic at hand, or contributing to the discussion by giving thoughts and ideas. It is better to ask in advance of the meeting what the expectations are so you are not unprepared, however you can simply choose to attend a meeting or two and use your observation skills to take careful note of how the interactions work and who is expected to speak and about what topics. It is highly likely that the expectations for your participation initially will be much lower and will increase with your experience and time within the group. As you get more comfortable in the group you may ﬁnd that you are talking more. However, always be certain that your contributions are succinct, meaningful, and on topic so that the meeting is maintaining forward momentum and you are not being wasteful of other people’s time. Although you may feel “out ranked” because of your limited experience, don’t discount the insights that can come from a new person’s prior experience or simply a fresh set of eyes on the topic. In general, you want to be respectful of your research mentor’s and other team members’ time. This means that you should arrive on time when a meeting or event has been scheduled, and you should come prepared. In the case of a one-on-one meeting with your research mentor, this means having thought through what outcomes you would like to get from the meeting, as well as what your research mentor will expect to learn from you about your progress. If you will be presenting a literature review or some results from your own research, you will want to have this material organized and ready to discuss. If you will be needing to use audio visual equipment, you will want to arrive at the room in advance and have everything set up and ready to go so that meeting time is not wasted while you’re trying to get the equipment to work. Outside of meetings you are likely to have a variety of diﬀerent kinds of interactions with other team members. If you need help from someone, it is perfectly reasonable to ask for it, but you should strive to make it as convenient as possible for them to provide it to you. If you will be trained on a piece of equipment or a technique, ask if there is information that would be helpful for you to read in advance so that you can come better prepared. When you are being trained, give it your undivided attention and take notes. Ask clarifying questions and for repetition if necessary, so that you can minimize the likelihood that you will need to return again for repeated training. Student Perspective “There was a very frustrating period of time where I wasted a lot of time trying to make the experiment work with my limited knowledge … when all I had to do was ask a grad student for advice. Back then, I often forgot that scientiﬁc research is a collaborative eﬀort and that asking others for help can often save you a lot of time.” Often collaborative research requires interdependencies between your research outputs and the input needs of others in your research group. It can be complicated to move the re- 3.6. BEING AN EFFECTIVE TEAM MEMBER AND COLLABORATOR 57 search forward in an eﬃcient manner. A high level of communication is required so that each researcher understands exactly what is needed and what is being promised. It is also important to have a clear understanding of the time frames in which activities will be taking place. What you might consider to be a small delay could negatively impact someone else’s later progress more signiﬁcantly. A shared calendar, project management timeline, and/or scheduling software can assist in making certain that everybody is aware of the timing of a particular project milestones and deliverables so that the research can be kept on track and moving forward. Although your research mentor may provide this for you, if it is not already available you should consider con- sulting with your research mentor, and other group members, about putting something in place that would be helpful to everyone. As your engagement in research progresses, you may need to lead a meeting. That may be an informal meeting between members of your own group to resolve an issue, or a meeting with members of another research group to coordinate eﬀorts in a joint project. Whether formal or informal you should come to the meeting with clear goals in mind and the order in which you would like to address topics. A written agenda is often helpful. Taking time to prepare an agenda in advance can make the meeting run smoothly and ensure that you will accomplish your goals. It also allows everyone to see the plans for the meeting and make any needed adjustments to the order and topics up front. Facilitating a productive and respectful discussion can sometimes be challenging. Al- though it may seem too formal to start the meeting by agreeing to a set of ground rules, you can insert them into the meeting when needed. For instance, if the conversation is going too far oﬀ topic, you can bring people back by saying something like “that’s interesting, but we have limited time today so we’ll need to stick with our agenda to get done.” When you are leading a meeting one of your responsibilities is to ensure that everyone has an opportunity to provide input and express their opinions. If one of the group members is getting talked over, or ignored, you can say “we need to be sure we hear from everybody on this topic, let’s go around the room and get each person’s input.” There are numerous ways to be eﬀective, one strategy is to watch others who are eﬀective where you want to build skill and emulate them. Being an eﬀective team member also means getting to know the others on the team. A basic understanding of the other individuals you interact with can help to reduce friction and avoid conﬂict. For instance, something simple like asking about people’s music preferences before playing your favorites at high volume in the lab can help to avoid irritation of other group members. Or if you are always requesting to meet in the early evening when a team member needs to pick up a child at day care, you could come across as insensitive when you had no intention of doing so. Even if you do take preventive measures, conﬂict can still come up. Rather than avoiding or ignoring the situation, you can often achieve a better result by addressing the issue sooner rather than later. Approach the individual or group with openness and seek to understand the issue. It 58 3. BECOMING A RESEARCHER is likely that your eﬀort will be appreciated, and you can work together to ﬁnd an appropriate resolution. 3.7 WORKING WITH A DIVERSE RESEARCH TEAM Depending on your prior experience and how well aligned it is with the atmosphere of the research group that you are joining, you may ﬁnd that you have some adjustments to make as you begin to engage in a new research project. You may come to research with the idea that you will be the “lone genius” who operates entirely independently. This is exceptionally rare, and not particularly realistic when one is just beginning to engage in research. Most engineering research is conducted in a team environment. It may be a team of two—you and your research mentor—but more often it is a team of several or many. The team usually includes a faculty member (or members) and graduate students. Many also incorporate undergraduate researchers, postdoctoral researchers, and scientists. These people may all be in the same building at the same institution, they may be spread across a campus, or they may be distributed at diﬀerent institutions across the country or even throughout the world. There are good reasons for this. Teams of people are able to tackle more complex and broader reaching research problems. As a result of how research is organized, this inevitably means that you will need to work with others eﬀectively. Not everyone in your research team will come to the group with the same background and experiences. If you think about even the most apparently homogeneous group of people you have interacted with, you can identify ways in which the group is diverse— for example the people in the group may look like each other but they may practice diﬀerent religions, identify with diﬀerent political groups, or spent their childhoods being raised in dif- ferent environments. Each one of these diﬀerences gives the group broader experiences to draw from, and if it is a group of engineers this diversity may inﬂuence the way in which design de- cisions are made or research problems are posed. Ideally, we would strengthen the diversity of our engineering work groups to include people from a wide range of diﬀerent backgrounds, and have diversity along many other spectrums, such as gender, race, etc. Companies recognize and hire with diversity in mind because research has shown that diverse groups are more produc- tive, creative and innovative.13 This is true for engineering research environments as well and engineering design. We all beneﬁt from the higher-quality ideas—in terms of feasibility and eﬀectiveness—that are produced by diverse groups and the critical analysis of alternatives when a wider variety of viewpoints is discussed. 13Women in Science and Engineering Leadership Institute, “Beneﬁts and Challenges of Diversity,” University of Wisconsin–Madison, http://wiseli.engr.wisc.edu/docs/Benefits_Challenges.pdf. 3.7. WORKING WITH A DIVERSE RESEARCH TEAM 59 Student Perspective “Education has also taught me a great deal about relationships with other people. Speciﬁcally how to work with others that may not share the same viewpoint as your own. Particularly in the ﬁeld of research, tolerance of everyone’s ideas is critical for success.” In order to build and maintain an eﬀective diverse team we need to recognize some things about human nature. Whether we like it or not, we all carry unintentional biases (also called implicit biases) that are “habits of mind” and are inﬂuenced by where we have grown up and spent our lives. Harvard University psychology researcher Prof. Mahzarin Banaji was quoted as saying “Implicit biases come from the culture. I think of them as the thumbprint of the culture on our minds.”14 As an example, if someone is asked to list the stereotypical characteristics of a man, they’ll come up with many of the following: tall, physically strong, respected, intelligent, has high status, leaders, sexist, like sports, providers, aggressive.15 However, even though we can list these stereotypes (women and men carry the same stereotypes in their mind about women and men) it does not mean we believe all men have these characteristics. We know that any individual man does not embody all, or even most, of these and I am certain that we could ﬁnd some men who don’t display any of the characteristics on the list. Similarly, the stereotypical characteristics of women can be listed: emotional, caring, soft, care about appearance, talkative, small built/petite, submissive, dependent, motherly, feminine.16 But again, we don’t expect that every woman we meet will conform to these characteristics. And it is not just gender at play. We hold numerous biases about all sorts of things like race, ethnicity, age, country of origin, etc. The problem comes when we make quick decisions or have limited information. When we do this we fall back on our stereotypes. Say there is an election for county sheriﬀ and all you know about the slate of candidates is that one has a male name and the other has a female name. The responsible thing to do would be to not vote without knowing more information, but many people will vote and with such limited information the stereotypes may have inﬂuence: we tend to think of police oﬃcers needing to be physically strong and in the role of sheriﬀ they would have to serve as a leader. These are two characteristics we more readily associate with men than with women. These associations could push the voter toward the male candidate, even though we know nothing about the actual qualiﬁcations of the two individuals running in the election. 14Hill, C., Corbett, C., and St. Rose, A., 2010. Why so few? Women in science, technology, engineering, and mathematics, American Association of University Women. Washington, DC. 15Ghavami, N. and Peplau, L. A., 2013. An intersectional analysis of gender and ethnic stereotypes: Testing three hy- potheses. Psychology of Women Quarterly, 37.1, 113–127. 16Ghavami, N. and Peplau, L. A., 2013. An intersectional analysis of gender and ethnic stereotypes: Testing three hy- potheses. Psychology of Women Quarterly, 37.1, 113–127. 60 3. BECOMING A RESEARCHER Unfortunately, these issues of unconscious bias play out in subtle ways that can have big impacts: who gets hired for a job,17 who gets the award,18 who gets the grant funding.19 Because most of us would want the most qualiﬁed person to get the job, the student with most potential to get the fellowship, and the best idea to get the grant funding, we need to be aware of our biases and work against applying them unintentionally. Student Perspective “[Thinking] about our inner biases and how they inﬂuence our lives and decisions was awakening. How easily we can form biases based on mis- information and then base judgments on those facts and then follow it by the act of actually defending our biases was a good realization.” The ﬁrst thing to recognize is that you are not a bad person because you have biases. Everyone has them. What we all need to do is to recognize our own biases and work to overcome them. Some useful strategies are as follows.20 Recognize and Replace: Become more aware of the biases that you carry and work to replace them by thinking of counter examples. The research shows that it is fruitless in the long run to simply try to repress stereotypes—this backﬁres.21 Challenge your automatic thoughts with concrete examples. Visualize an engineer. Now visualize someone you know, who is an excellent engineer and also belongs to a group that is underrepresented in engineering. Intergroup Contact: Much of our work as engineers is done collaboratively and in teams. Get to know the other research group members as individuals.22 Challenge your assumptions of who they might be given the stereotypical information available on the surface. Pay attention and don’t dismiss information that does not ﬁt with the 17For example, see Segrest Purkiss, S. L., Perrewe, P. L., Gillespie, T. L., Mayes, B. T., and Ferris, G. R., 2006. Implicit sources of bias in employment interview judgments and decisions. Organizational Behavior and Human Decision Processes, 101.2, 152–167. 18For example, see Lincoln, A. E., Pincus, S., and Schick, V., 2009. Evaluating science or evaluating gender. American Physical Society News, 18.8. 19For example, see Ley, T. J. and Hamilton, B. H., 2008. The gender gap in NIH grant applications. Science, 322.5907, 1472–1474. 20Adapted from Carnes, M., Fine, E., Romero, M., and Sheridan, J. Breaking the bias habit, Women in Science and Engineering Leadership Institute (WISELI), University of Wisconsin–Madison, https://wiseli.wiscweb.wisc.edu/ workshops/bbh-inclusive-campus/; see also Carnes, M., Devine, P. G., Manwell, L. B., Byars-Winston, A., Fine, E., Ford, C. E., Forscher, P., Isaac, C., Kaatz, A., Magua, W., Palta, M., and Sheridan, J., 2015. The eﬀect of an intervention to break the gender bias habit for faculty at one institution: A cluster randomized, controlled trial. Academic Medicine, 90(2):221– 30. 21Macrae, C. N., Bodenhausen, G. V., Milne, A. B., and Jetten, J., 1994. Out of mind but back in sight: Stereotypes on the rebound. Journal of Personality and Social Psychology, 67(5), 808. 22Pettigrew, T. F. and Tropp, L. R., 2006. A meta-analytic test of intergroup contact theory. Journal of Personality and Social Psychology, 90(5):751–83. And Lemmer, G. and Wagner, U., 2015. Can we really reduce ethnic prejudice outside the lab? A meta-analysis of direct and indirect contact interventions. European Journal of Social Psychology, 45(2):152–68. 3.7. WORKING WITH A DIVERSE RESEARCH TEAM 61 stereotype. Appreciate the strengths that they bring to the shared goals your research group is working toward. Model Inclusion: Use inclusive language. When a joke is inappropriate, don’t laugh. Approach students who may be diﬀerent from you and get to know them. Don’t always interact with the same people; mix with others and get to know them better. Perspective Taking: Develop your ability to take someone else’s perspective and see the world through their eyes.23 Use your empathy skills to see their perspective. ASSIGNMENT 3-8: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON PERSPECTIVE-TAKING Practice perspective-taking. Think about your early experiences with engineering research: What did you feel like walking into the ﬁrst research group meeting or research seminar? What were your ﬁrst impressions about the people? What do you think people assumed about you? Now consider someone who would be in this same situation who is from a background or group other than your own (e.g., diﬀerent gender, race, ethnicity). How do you think it would it feel for that person to walk into their ﬁrst research group meeting or research seminar? Write a 300–500 word reﬂection on this topic. ASSIGNMENT 3-9: INDIVIDUAL ASSIGNMENT – CASE STUDY Instructions: Read the brief case description provided. Reread while noting the important information and questions that are raised in your mind about the information provided, the individuals in- volved, and their situation. Determine both the basic issues and any deeper underlying issues at play. Consider the questions posed at the end of the case and how you would respond to these questions, as well as other questions that could be asked of this case. Write a one-page response that includes a brief summary of the case and its issues, your answer to the questions posed, and recommendations based on your understanding of the situation posed in the case. 23Todd, A. R., Bodenhausen, G. V., Richeson, J. A., and Galinsky, A. D., 2011. Perspective taking combats automatic expressions of racial bias. Journal of Personality and Social Psychology, 100(6), 1027. 62 3. BECOMING A RESEARCHER Case description: Jeﬀ is excited to begin his research career and join Prof. Jones’ research group. Now that he has moved to town and gotten settled he’s eager to start getting acquainted with the other research group members. He has just been assigned a desk and has begun to meet the other students in the group with the help of Sam who Prof. Jones has asked to show him around. While he and Sam are talking with other students in the group, Jeﬀ notices another student come into the room and go to a desk in the corner without greeting anyone. Later as Sam is showing him around the building Jeﬀ realizes that he did not get introduced to the student at the corner desk and asks Sam who she is. Sam replies “Oh, that’s Ellen,” and continues talking about other points of interest in the building. After working in the groups for a couple of weeks and seeing Ellen come in every day and go to her desk in the corner without any interaction among the group, Jeﬀ decides that there must be some issue with Ellen and proceeds to ignore her like the rest of the group members. Questions to consider: Should Jeﬀ introduce himself to Ellen even though neither Sam nor Ellen have initiated an introduction? Is it appropriate for Jeﬀ to inquire with other research group members about Ellen to ﬁnd out more about the situation? How can Jeﬀ go about engaging with Ellen given that they are both members of the same research group? Would your answers above change if the person’s name was Shaheed instead of Ellen? How do stereotypes play into your answers for Ellen, and for Shaheed? 3.8 DEVELOPING GLOBAL COMPETENCY One important way to broaden your horizons and become a more culturally competent engineer is to spend time in another country. Ideally, you will do this in an immersed way and with a structured program. Study abroad is an option, both as an undergraduate and as a graduate student. There are also opportunities to work abroad and conduct research abroad. And of course, you can attend conferences in other countries. The more time you are able spend, and the quality of your immersion in the culture of that county, the more it will increase the impact of the experience. Student Perspective “There is a fairly evident way in which my interpersonal foundation is lacking as a result of my education and more speciﬁcally its location. I grew up in a community that was predominantly white with some amount of people of Asian descent. This has to some extent limited the variety of cultures to which 3.8. DEVELOPING GLOBAL COMPETENCY 63 I have been exposed. This means that there are many cultures in which I still have something of a gap to cross to develop mature relationships. The global nature of research will allow me to have contact with many more cultures and start to understand them so that I can continue to work on my interpersonal foundation of self-authorship.” Increasing your cultural competence will beneﬁt you in the long run regardless of your career goals. The world is more interconnected than it has ever been and the ﬁeld of engineering is inherently a global one. Research teams are becoming more global and international collabo- rations commonplace. As a result, employers are interested in hiring individuals with the skills to operate in a range of settings and with people form a variety of backgrounds. What does an immerse experience give you—both positive and negative? There are chal- lenges in navigating a new culture and place. You will have experiences that stretch you a bit and force you to be more ﬂexible and adaptable. You will also need to be self-reliant, and it will enhance your independence. You will learn about yourself through your experiences with the culture you are immersed in. Marcia Baxter Magolda connects it to the self authorship (identity development) ideas discussed previously: “Intercultural maturity includes the ability to use mul- tiple cultural frames to construct knowledge, engaging in meaningful relationships with diverse others that are grounded in appreciation of diﬀerence, and the capacity to openly engage chal- lenges to one’s beliefs.24” Particularly as you work with people from other cultures, it is critical that you are able to see ideas and events from more than just your own perspective. “Mature relationships are characterized by respect for both one’s own and others’ particular identities and cultures as well as by productive collaboration to negotiate and integrate multiple personal needs.25” Student Perspective “Interactions and team-work with classmates and teachers coming from various linguistic, cultural and religious backgrounds has made me un- derstand the intricacies of society, a way to relate to people and build rela- tionships both personal and professional.” Some humorous illustrations of how cultural diﬀerences can impact both understanding and ability to work together came out as a series of commercials (adverts) from HSBC, a large international banking and ﬁnance origination. They illustrate a few cultural diﬀerences around the world with a bit of humor thrown in. In one of their ads they show a British gentleman in a restaurant in China with business colleagues who are hosting them (search www.youtube.com 24Baxter Magolda, M. and King, P. M., 2004. Learning Partnerships: Theory and Models of Practice to Educate for Self Au- thorship, Stylus, Sterling, VA, p. 5. 25Baxter Magolda, M. and King, P. M., 2004. Learning Partnerships: Theory and Models of Practice to Educate for Self Au- thorship, Stylus, Sterling, VA, p. 9–10. 64 3. BECOMING A RESEARCHER for “HSBC ‘Eels’ Ad”). The British gentleman ﬁnishes his main course of eel and the Chinese colleagues become agitated and order him another bigger eel. The narrator explains “The English believe it is a slur on your host’s food if you don’t clear your plate. Whereas the Chinese feel that you are questioning your generosity if you do.” After clearing his plate a second time even though he has obviously had too much to eat given his peaked appearance, the host orders more again and we see a gigantic eel being wrestled in the kitchen, presumably for yet another massive main course. ASSIGNMENT 3-10: INDIVIDUAL ASSIGNMENT – INTERNATIONAL EXPERIENCE INDICATORS SELF-EVALUATION Complete the International Experience Indicators self-evaluation tool on the following pages and see how you score. Use the second and third columns to reassess yourself in a year or two to judge whether you are making progress. Numbers in brackets are the points to be assigned for any experience. A range in points is indicated to diﬀerentiate the extent and/or quality of the experience with regard to how much you believe your international perspectives and understanding were enhanced. ASSIGNMENT 3-11: INDIVIDUAL ASSIGNMENT – REFLECTIVE WRITING ON INTERNATIONAL EXPERIENCE Choose two strategies for increasing your score on the International Experience Indicators. Ex- plore how you could implement these strategies and discuss what you would need to do to carry them out. For example, simpler strategies include reading an international newspaper weekly, learn- ing about the home country of the people in your research group, or inviting a new international student in your program to your home for dinner. High investment strategies include enrolling in a study abroad program, volunteering for Engineers Without Boarders, seeking an interna- tional work placement, or taking a language or culture course (Table 3.2). 3.8.1 OTHER RESOURCES ON GLOBAL COMPETENCY References courtesy of Dr. Laurie Cox, Assistant Dean and Director International Student Ser- vices, University of Wisconsin–Madison: Table 3.2: “International Experience Indicator” rubric (Continues.) 3.8. DEVELOPING GLOBAL COMPETENCY 65 International Experience IndicatorsSelf-Assessment Points (you make the judgment)Today's Date:Have a passport and have traveled outside the U.S.to:• English-speaking country (1-2pts/time with maximum of 6pts)• Non-English-speaking country (1-5pts/time with maximum of 10pts)Have lived in another country continuously for more than two months:• In a city/town of a non-English-speaking country (5-12pts)• In a village or rural area of a non-English-speaking country (7-15pts)• English-speaking city/town or rural village (3-7pts)Expansion of understanding other cultures or global issues from living with or married to someone from another country (1-10pts)Work with international colleagues on a regular basis in my work, program, major, or department through my university or outside organizations (1-10pts)Interact with and share perspectives about global issues on a regular basis with friends or international colleagues outside the U.S. (1-10pts)Currently live or have lived and been active in a neighborhood/community with multi-cultural diversity due to presence of recent immigrants or international peo-ple. (1-10pts)Hosted international student(s), faculty, scholars, or colleagues in my home• For a week or less (2pts)• For 1-10 weeks (3-6pts)• For more than 10 weeks (7-10pts)Had to successfully address a personally embarrassing situation in another culture because of my own cultural ignorance (1-10pts)Regularly exposed to international perspectives through reading an international newspaper, news publication or non-disciplinary journal published outside the U.S. and/or regularly listen to international radio or TV broadcasts of news and issues (1-10pts)Interact regularly with international people in a club/organization (1-3pts)Gave a presentation(s) or lecture in a language that is not my native language (3-7pts) 66 3. BECOMING A RESEARCHER Table 3.2: (Continued.) “International Experience Indicator” rubric Knowledge of language(s) other than your native language: ReadingSpokenWritten• Language A (1-10pts)• Language B (1-10pts)• Language C (1-10pts)• Language D (1-10pts)Participated in an education, research, work, or volunteer program abroadIn non-English- Speaking CountryIn English- Speaking Country• Four weeks or less in duration (4-7pts)(3-5pts)• Four to eight weeks in duration (7-10pts)(5-8pts)• Semester program (10-15pts)(8-11pts)• Two or more semesters (15-20pts) (11-15pts)Completed course(s) that greatly expanded my international competence• Course A (1-4pts)• Course B (1-4pts)• Course C (1-4pts)Completed course(s) that somewhat advanced my international competence• Course A (1-2pts)• Course B (1-2pts)• Course C (1-2pts)Wrote a research paper on a topic that greatly expanded my international competence• Paper A (1-4pts)• Paper B (1-4pts)Self-evaluation of your openness and understanding of diﬀ erent cultures and your ability to interact with people from diﬀ erent countries (1-10pts)Total: Althen, G., American Ways: A Guide for Foreigners in the United States 3.9. NETWORKING 67 Althen, G., Learning Across Cultures Axtell, R., Gestures: The Do’s and Taboos of Body Language Axtell, R., Do’s and Taboos around the World Chai, M-L. and Chai W., China A to Z: Everything You Need to Know to Understand Chinese Customs and Culture Morrison, T., Kiss, Bow or Shake Hands Nahm, A., An Introduction to Korean Culture 3.9 NETWORKING Your professional network may have more inﬂuence on your success that you might imagine. The people in your network can provide valuable feedback on your ideas, technical expertise in areas you are less experienced in, opportunities for collaborations that allow you to approach new research questions, contact with others in your discipline who you would like to work with in the future, and much more. Student Perspective “The most surprising things I learned so far about research would be the importance of professional networking and communication. My previ- ous image of research community is that researchers largely focus on the lab work and have few contacts with anyone besides their colleagues. Therefore, I used to believe academic ability should outweigh any other abilities, and my main focus in the school had always been school work and grades. It was not until I [began a research position] that I realized what I believed was wrong. As I learned more about how research [is] conducted, I found professional networking and communication much more important than I thought.” How do you create a professional network for yourself? You must make connections with people. They can range from casual acquaintances to friendships, but the key is to know other people in your discipline, in other disciplines, and in the community at large. Get to know them and let them get to know you. Oﬀer your knowledge and expertise, when they need it, and they will be likely to return the favor at some other time. These connections can develop within the research group through day-to-day contact, within the program or department through hallway conversation and interactions at seminars and social functions. Connections can be made at the bus, at the gym, or in a coﬀee shop. The key is to talk to people. If you sit down in class or at 68 3. BECOMING A RESEARCHER a seminar ﬁve minutes before it starts, take the opportunity to introduce yourself to the person next to you. Ask them about themselves and engage in a conversation. For some of us this is easier said than done, but with a little practice it becomes more comfortable. As you become further engaged in your discipline you will begin to attend seminars, work- shops, and conferences associated with the topic area of your research. This is an important part of your professional development in several respects: you will have an opportunity to learn about the most recent developments in your ﬁeld; you will have opportunities to present your own research in either a poster session or a presentation; and you will have an opportunity to broaden your professional network. This last piece is often overlooked, but very important. In order to develop your network, you will need to engage with people informally. This can be done with the people you sit next to before or after a session, joining a hallway conversation or a coﬀee break, asking someone to have lunch or dinner with you, taking part in a student mixer, and attending luncheons, receptions, or other organized social events. I suggest that students attend these events with a goal in mind. Maybe it is as simple as deciding that you will try to talk with ﬁve people you have not met before, or that you will seek out advice about a particular aspect of your research with people that you meet, or that you will inquire about graduate school or postdoctoral research opportunities at their institution. Giving yourself such a goal can help you to overcome any reluctance that you might have to engage in these settings and provide you with a meaningful task that will help you both in terms of building your network and acquiring information that you need. With a Little Help from Your Friends Although I have my own professional network, I have found over the years that the networks that my students develop can be just as valuable to our work. I recall a research project where we were stuck on the interpreta- tion of some data we had obtained. The data was produced by a technique that my group had less expertise with than most, but it was critical to the particular experiment we were conducting. One option was to simply repeat the experiment, but it was still a question as to what that would tell us. In- stead, we looked for an expert to talk to ﬁrst. The graduate student working on the project knew of someone in another lab who had used the technique extensively, so he dropped by to chat with him. This developed into a half- hour conversation with several other lab members in this group over coﬀee. The graduate student walked away with new ideas as to how to approach the problem with a diﬀerent technique that would help us to interpret our data. This half-hour conversation turned out to be invaluable to the research and saved us signiﬁcant time. 3.9. NETWORKING 69 Student Perspective “I had the impression that scientists did most of their work in solitude, with essentially all contact being with a few nearby colleagues such as collab- orators, advisors, or lab partners. I understood that the goal of science was to share knowledge, but I felt that this was done purely through publications and lectures. I did not notice the existence of any network beyond this. It is true that a scientist does work alone for much of the data-collecting phase of a research project. However, I learned that a researcher must be involved with a larger community to be successful in the profession. Hence, there was a vast network of connections between researchers that I had not noticed … Networking with people that have similar interests in the department is a clear objective, but I learned that it was also beneﬁcial to connect with people at other campuses all around the world.” The other critical aspect of developing your professional network involves broadening your mentoring relationships beyond that of your research mentor, so that you can get diﬀerent per- spectives and a range of constructive criticism, advice, and/or support. Often people think of the mentor-mentee relationship as an exclusive dyad, but in contemporary terms you are seldom the sole mentee in your mentor’s life and, even if you were, you can’t expect to get everything you need from one individual. Thus, mentoring should occur on multiple levels with multiple indi- viduals, including your research mentor, your peers in and outside your research group, other faculty and staﬀ, and key individuals in your network. You can think of this as a “constellation” of supporting individuals in a variety of mentor-related roles. Longitudinal research studying career success has shown, that while the quality of your primary mentor signiﬁcantly impacts your short-term career outcomes, it is the “composition and quality of an individual’s entire constellation of developmental relationships that account for long-run protégé career outcomes.26” Having many and varied mentors will give you a broader range of perspectives, a wider reaching network, and more opportunities over the course of your career. This constellation of mentors is not something that you create overnight and it frequently grows out of the network connections that you build. You should consider who is already in your constellation of mentors, and watch for other individuals who you can get good mentoring from. 26Higgins, M. C. and Thomas, D. A., 2001. Constellations and careers: Toward understanding the eﬀects of multiple developmental relationships, Journal of Organizational Behavior, 22, 223–247. 70 3. BECOMING A RESEARCHER ASSIGNMENT 3-12: GROUP ACTIVITY – WHO IS IN YOUR NETWORK? Individually: Spend 5 minutes listing the people or groups in your network on a piece of paper. As a Group: Discuss the types of people in each individual’s network. Is your network actually broader than you initially thought? Brainstorm about what actions you can take immediately to broaden your network further. What strategies can you use to maintain your network? ASSIGNMENT 3-13: INDIVIDUAL ASSIGNMENT – DEVELOPING YOUR PROFESSIONAL NETWORK Identify your goals related to developing your professional network. Do you want to improve your network to facilitate your research? Do you want to develop a network that will help you get into graduate school? Or ﬁnd a job? Build a list of contacts: • • • Identify relevant people. If you don’t know individual names, identify the types of people you need in your net- work and then seek out individuals who are that type. Identify professional organizations where you might meet people important for your network. Develop a strategy to court these people individually. • Using online social networks like Facebook, LinkedIn, and other online tools can help you reach your networking goals. 3.9. NETWORKING 71 • BUT meeting someone who is in your network helps to solidify the relationship. How can you arrange to meet each person face-to-face? • Don’t ask for something at your ﬁrst contact with someone you have just met. And as the relationship develops, take care not to always ask for something every time you interact with a person. • Reciprocity is important. Try to ﬁgure out a way for you to give something. This is why it is important to build your network before you need it. What can you do to follow up occasionally with these people? • Schedule time each week to tend your network. • Be reasonable with the frequency of contact. For some people who you have gotten to know in more depth, your contact may be quite regular but for others it may be as little as once a year. What courtesies should you follow? • Respect the time of others. • Send a thank-you note when someone has provided you with something you truly appreciate. • Be prepared and willing to reciprocate. • Ask permission before you use someone as a reference. ASSIGNMENT 3-14: INDIVIDUAL ASSIGNMENT – DEVELOPING YOUR PROFESSIONAL NETWORK Departments on campus and professional conferences often hold social events such as a mixer or reception. These are great opportunities to broaden your professional network. But, it’s often helpful to think about how you will start a conversation before you are actually in the position to do so. After saying “Hi, my name is…,” what comes next? You need a strategy to engage with someone you have just met to learn more about them and let them get to know you. So, try asking questions. Depending on the context you can start with something simple like: what’s your major? Or. What brings you to this event/place? You might even ask if they have heard about a recent article you have read or ask about what courses they are taking/teaching this/next 72 3. BECOMING A RESEARCHER semester. If you are at a conference you can ask them what sessions they have been attending or comment on a keynote talk that happened earlier in the day. Brainstorm three questions you could ask or conversation starters you could use to engage in a conversation with someone you have just met. Consider three diﬀerent situations: talking to a person at a nearby table in a coﬀee shop or cafeteria; sitting next to someone ﬁve minutes before a class or seminar begins; mingling at a social event associated with a professional function. Now put it into action. Set some goals for yourself, such as: meet three new people over the next week; get to know two other people in my major; talk to someone more senior than myself who is in my professional area. ASSIGNMENT 3-15: INDIVIDUAL PROJECT – STARTING YOUR OWN PEER MENTORING GROUP27 Step 1: Identify a common topic of interest for the group, e.g., fellowship proposal writing, journal club in your research area, qualifying exam preparation, dissertator support group, etc. Step 2: Identify a few peers who you would like to invite to join you in the group. Have a con- versation with each of them about their interest in meeting regularly on this topic. Identify the best venue for the meetings and timing for the meetings. Take into account that some members may have other obligations that prevent them from meeting at certain times or on certain days of the week. Step 3: Set up a text group or listserve with the initial members and send out a formal announce- ment, e.g., an email might include the following: “Thank you for agreeing to join me in our TOPIC group. I have reserved ROOM/BUILDING for our ﬁrst meeting on DATE/TIME. At this initial meeting I propose that we develop an agenda for our group and plans for our future meetings over the semester.” Step 4: Develop consensus within the group about the formality of meetings, frequency of meet- ings, optimal size of the group, and responsibilities of the group members. Step 5: Grow the group to a sustainable size. This can be accomplished through the networks of the initial group members or talking with a staﬀ member aﬃliated with your degree program about other individuals they may know of who would be interested in the group. Step 6: As the “convener” of the group, you will be responsible for sending out reminders for meetings and keeping the momentum of the group going. It is good practice to rotate the “con- vener” responsibility to a new individual for a group that meets for more than a few months. 27Adapted from Crone, W. C., 2010. Survive and Thrive: A Guide for Untenured Faculty, Morgan & Claypool Publishers. C H A P T E R 4 73 Building on the Research of Others 4.1 THE LITERATURE Together the collection of journal publications, conference proceedings, handbooks, mono- graphs, books, and student dissertations/theses is referred to as “the literature” and provides a foundation of knowledge for you and others to build upon. Your primary exposure to engineering concepts may have been through textbooks up until a certain point in your education. As you pursue more advanced study, and particularly research, you will more regularly gain information from journal articles, along with other sources, such as conference proceedings, technical handbooks, and edited collections (books where each chapter is contributed by diﬀerent authors). The purpose of journal articles is to provide an open report of ﬁndings and new discoveries in a timely manner. These papers will contain details that you will not be able to ﬁnd anywhere else. Certainly the most recent ﬁndings in a particular research area will only be available in journal articles and conference proceedings, but you will also ﬁnd that journal articles published decades ago may also be critical to you in your research. These are sometimes referred to as seminal papers if they contain the origins of a research idea, completely changed the way a topic was understood, or provide results that are continuing to be foundational to the ﬁeld. Ideally, you will want to read and rely only on articles that are published in peer-reviewed, archival journals and conference proceedings. These may be available in both paper and electronic formats, but the key issue is the reliability of the information being presented. The archival nature of journal publications also ensures their longevity and provides a searchable record of ﬁndings. Just because someone has published something, does not mean that it is correct. However, you will ﬁnd that more reliable information can be found in reputable journals that have a rigorous peer review process. The “Impact Factor” of a journal will also give you a guide as to the stature of the journal in its ﬁeld.1 Regardless of where something is published and by whom, you must look at all information that you read with a critical eye. 1The Impact Factor of a speciﬁc journal is based on a calculation involving the number of times that the papers in that journal are cited by others. These values vary by ﬁeld so it may be helpful to look at how the Impact Factors of journals within a ﬁeld compare to each other. You can ﬁnd Impact Factor information from a variety of sources, but they trace back to the Journal Citation Reports ( JCR) and the information is integrated into Web of Science, as well as other indexing systems. 74 4. BUILDING ON THE RESEARCH OF OTHERS There are a range of diﬀerent types of journal articles that you will ﬁnd in the literature which will vary in length and content. Some journals, and the articles published within, will specialize in various ways—for instance you may ﬁnd a journal in your ﬁeld that specializes in instrumentation or experimental methods, another that focus on modeling and computation, etc. Additionally, there are short communications, some of which are speciﬁcally designed for rapid publication of new ﬁndings, full length articles that present original research in full de- tail, and review articles that synthesize the state of the art concerning a particular topic. You may ﬁnd review articles to be very helpful, especially as you are entering into a new area of in- quiry. A review article, if done well, will not only summarize the research that has come before, but will also synthesize these results, present challenges and future directions for research, and provide some commentary on future directions in the ﬁeld. Conference papers/proceedings are also prevalent in some disciplines and in some cases may be the higher proﬁle publication of a disciplinary area. The literature in a research subject area can be very challenging to navigate initially and it is often a good ﬁrst step to ask your research mentor to suggest key articles that you should read and indicate which journals are the most relevant to your research. This will give you a good foundation to start building your familiarity with the literature in your research area. Your initial exposure will be challenging. But be assured, as you read more, you will understand more of what you read. 4.2 VALUING WHAT CAME BEFORE YOU The literature contains a vast amount of information which grows at an ever-increasing pace each year. You may feel that there is so much to read and learn about that it is pointless to even begin. But begin you must. With each paper your knowledge and understanding will grow, along with your ability to discern when you have found an important research contribution that will inﬂuence your own work. You will also develop the ability to occasionally disagree with and challenge some of the methods, results, and conclusions that have been previously published. Scientists and engineers read the literature for a number of important reasons: to learn what others have done so we don’t reinvent the wheel; to build upon the prior published work in order to advance our own research; to keep abreast of the recent ﬁndings from other research groups; to be able to describe how our own research ﬁts into a broader context of the ﬁeld; and to distinguish our contributions from the contributions of others. Early in your research career, your purposes in reading the literature may be a bit diﬀerent. If you are applying to a graduate program and interested in working with a particular faculty member, it will be important for you to become familiar with their prior research. Certainly you will look at their webpage, but it is also important to look at what journal articles they have published in the last few years to get a better idea of the trajectory of their recent research. If you will be meeting with a faculty member on a campus visit, you may want to choose a journal article that this faculty member authored recently so that you can read it prior to your visit. 4.2. VALUING WHAT CAME BEFORE YOU 75 Although you don’t need to understand everything in the paper, you want to read it carefully enough to have intelligent questions to ask regarding the paper. Keep in mind that this is likely to be a publication about a research project that is complete and no longer active. Although it is a good starting point for a discussion, it may or may not be representative of the research that this faculty member is currently doing. In your conversation you will want to ﬁnd out the direction of their current and future research projects. This information will be important for you in order to determine if there is a good match between your interests and the direction of this faculty member’s research group. Know What You Don’t Know I am always encouraged when a student I have invited to join my re- search group asks for a few relevant journal articles to read before their po- sition begins. This usually happens with the best of the undergraduate re- searchers who will be joining the group for a summer research opportunity and the graduate students who will be joining our research group in the next semester. Asking the question is a positive indicator, but then having the fol- low though to read the article before they arrive is a good sign that they will be a successful researcher. I never expect that the student will understand ev- erything they are reading at this stage. The outcome I like to see is that they show up on the ﬁrst day with questions about what they have read and how these articles relate to what they will be doing. When you have joined a research group—ideally even before you arrive in that group— read the papers that the research group has published recently. Not only will this give you some relevant background on the types of research that the group has undertaken and the techniques they have used, the author list of each paper it will also give you an idea of who has been work- ing together—which students, postdocs, and scientists have contributed to which projects, and which other faculty the research group collaborates with most frequently. An important area of value to you as you embark in a new research area will be the literature most relevant to the project you will be working on. Some of this may have been published by the research group you are joining, but much of it will likely have been published by other research groups around the world. Your research mentor will be able to help you identify some of the most relevant journal articles that you should become familiar with initially. Read these articles carefully and save them—they may be articles that you will want to go back to and reread after you have begun working on your research project. Pay attention to the author lists and watch for new papers to come out from these same authors—those new articles may also be relevant to your work. A later chapter will go into more detail on author order, but it is usually most relevant to note the ﬁrst author, last author, and corresponding author(s). Keeping abreast of the relevant literature in your area is an important aspect of your development as a researcher. 76 4. BUILDING ON THE RESEARCH OF OTHERS Eventually, you will be the one pointing out new articles that have appeared in the literature to your research mentor! Learning How to Read Over time, everyone develops their own approach to reading journal articles for both eﬃciency and getting the most information out of your lit- erature search. My own style is to ﬁrst focus on the abstract and conclusion to decide whether or not I need to spend more time with the article. Then I usually go to the ﬁgures next. If a paper is well done, the ﬁgures and their captions give you an outline in a visual format. Then I will begin at the be- ginning and give the article a quick read. If I ﬁnd that I am still interested and need more detailed information, then I take a second read in a much more thorough fashion. I will work through equations, delve into the meth- ods, carefully compare the ﬁgures to the text, question the assumptions made, ponder the conclusions drawn, and decide what it is that I can take away from this paper that will be useful to me. I also look at the references cited as well as who has cited the paper, so that I can ﬁnd other relevant journal papers to read. For seminal papers on a topic, I may reread them a third, fourth, or tenth time over the course of years. Each journal article you read will build your knowledge and make you more skillful at extracting the key concepts and pieces of information that you need. Settling on you own approach will come with experience. You will also need to keep track of the papers you read and the ideas that have come from them (tools for doing this will be discussed in more detail in the section on Citation Manage- ment below). When you eventually put together your own research ﬁndings for presentation and publication it will be critical for you to cite the work of others. You will need to show that you are knowledgeable about the literature in your area of research and you will need to give credit for the ideas of others that have contributed to your own work. The best researchers are those who show how their own work builds on and extends the ﬁeld by acknowledging the work of others. Student Perspective “Information is continuously ﬂowing throughout the globe and with the elaborate access we have to it, via Internet and also extensive communi- cation modes; an individual has at his disposal a plethora of work, ideas and information about almost everything. This can be at times dangerous, as we as people forget that though we have access to all this information, we don’t have ownership over it. These works or ideas aren’t ours; they’re someone else’s intellectual property.” 4.3. READING JOURNAL ARTICLES 77 4.3 READING JOURNAL ARTICLES Journal articles tend to have a similar structure, although some variations may be found depend- ing on the style requirements of the particular journal. An important aspect of reading journal articles is knowing about all the information that is there for you to ﬁnd. Common components include: author information; an abstract; an introduction and/or background section; a methods or techniques section; results; discussion; conclusion; acknowledgments; and references/citation information. The examples shown on the following pages (Figures 4.1–4.4) come from two sam- ples articles published in peer reviewed journals. The paper by Gall et al.2 is a research article containing new experimental results, whereas the paper by Maboudian and Howe3 is a review article providing the current state of understanding on a topic. Every journal article begins with a title. There are many styles to creating a title, but they should be descriptive of the content. The title can often give you a hint as to whether or not you want to read the article, but the most succinct and descriptive piece of the article is the abstract. It should give you a good idea of whether or not you want to read further. The ﬁrst page of the journal article will also contain author names and aﬃliations. The aﬃliations will often give you a hint about the disciplinary background of the authors, given the department or unit that they are aﬃliated with, as well as the institution where the research was conducted. In collaborative projects you will sometimes see authors listed from multiple institutions. For instance, it may be that experiments were conducted at one institution and the modeling work was conducted in a diﬀerent research group at another institution. Sometimes the journal will also provide information about the publication timeline. For instance, when the article was ﬁrst received and when it was accepted for publication. This infor- mation together with the actual publication date gives you a sense of how quick of a turnaround this journal does in their review process, which may be important to you when you consider journals to submit your own work to (Figures 4.1 and 4.3). You will also ﬁnd the title of the journal, volume and number of the journal, and page number(s) on the ﬁrst page. Together with the title and author list, you can compile a complete citation for the article. For example: Salick, M. R., Napiwocki, B. N., Sha, J., Knight, G. T., Chindhy, S. A., Kamp, T. J., Ashton, R. S., and Crone, W. C., 2014. Micropattern width dependent sarcomere 2Gall, K., Dunn, M. L., Liu, Y., Labossiere, P., Sehitoglu, H., and Chumlyakov, Y. I., 2002. Micro and macro defor- mation of single crystal NiTi. Journal of Engineering Materials and Technology, 124(2), 238–245. 3Maboudian, R. and Howe, R. T., 1997. Critical review: Adhesion in surface micromechanical structures. Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, 15(1), 1–20. 78 4. BUILDING ON THE RESEARCH OF OTHERS Figure 4.1: Title, author information, and abstract for a research article (top) and a review article (bottom). development in human ESC-derived cardiomyocytes. Biomaterials, 35(15), 4454– 4464. It should be noted that there are multiple citation styles and most citation management systems will output information in whatever the style you need. The citation shown above uses the Chicago style based on The Chicago Manual of Style. Each journal will have a required citation format, some of which adhere to one of the common styles and some that are unique to the journal. Often on the ﬁrst page, but sometimes at the end of the article, you will ﬁnd contact information for the corresponding author (Figure 4.2). This is an individual that you can contact with questions about the paper if you are delving deeply into its content. This contact information should not be used frivolously, but if you have a serious question that you have not been able Author Namesand AﬃliationsTitleAbstractTitleAbstractAuthor Namesand AﬃliationsPublicationTimeline4.3. READING JOURNAL ARTICLES 79 Figure 4.2: First page of a sample review journal article. to ﬁnd the answer to in any other way, it is reasonable to make contact with the corresponding author. Although some short papers will not separate out the article into sections, most will have some variation of the following section titles: Abstract, Introduction, Background, Methods, Results, Discussion, Conclusion, Acknowledgments, References. You will notice throughout, and particularly in the Introduction/Background sections, that prior published work related to the subject has been cited (Figure 4.3). Even if the current article does not contain exactly the information you are looking for, these citations will refer you to other references that may be useful. Following this trail of breadcrumbs can sometimes be more fruitful than a search engine because the work being cited has been read by these authors and deemed useful and relevant enough to include in their article. In a way, this is an additional level of review and thus a reason why these papers are worth taking a look at beyond the many others that may pop up in a literature search on the topic. Depending on what you are trying to glean from a particular article may mean that you will spend more or less time with it or delve into more detailed reading of particular sections. In many cases, you are simply interested in the ﬁndings and what the authors have contributed to the ﬁeld. The Discussion and Conclusion are likely the sections of the article that you will read more than once. Or, if you are an experimentalist, and you are speciﬁcally looking for a Author Namesand AﬃliationsTitleCorresponding AuthorContact InformationJournal Name, Volume, Date80 4. BUILDING ON THE RESEARCH OF OTHERS Figure 4.3: First page of a sample research journal article. method relevant to a process or technique you need to accomplish in the lab, then you may be most interested in the Methods section. In a diﬀerent situation you could be trying to ﬁgure out the best way to show the data that you have collected or produced, so the ﬁgures in the Results section would be your focus. Keep track of the papers you have read—ideally using a citation management system like what is discussed later in this chapter—it is likely you may want to cite the paper in something that you will write later (e.g., a report, thesis, or journal article of your own) and you may want to reread that paper again at a later date. It is often the case that you get more from a article on a second (or tenth) reading, especially when you have had a chance to learn more about the topic through your own research and other things you have read in the literature. Usually at the end of the paper you will ﬁnd an Acknowledgments section. This might include individuals or facilities that aided the research, but whose contributions did not rise to the level of authorship. It will also include the funding source(s) that made this research possible (Figure 4.4). In some cases this might indicate a possible conﬂict of interest, or bias, in the interpretations of the ﬁndings because of this support (for instance, there have been accusations of researchers supported by Google who wrote about Google in articles but did not acknowledge that they had received funding from them). The funding sources listed will also give you an idea of what federal agencies or foundations are interested in supporting this type of work. It is AbstractPublication TimelineTitlePublication DateIntroductionCitation ofReferences4.3. READING JOURNAL ARTICLES 81 Figure 4.4: Conclusions, Acknowledgment, and References sections of two sample journal ar- ticles. possible that you may want to look to apply for funding from one of these sources in the future, through fellowship or grant opportunities. The References section gives you the complete information for all of the citations in the paper (Figure 4.4). This is a valuable resource for you because the paper has identiﬁed other relevant literature which you may be interested in reading. Finally, the last item to be aware of is Supplemental Material. A growing expectation in publication is for the authors/journal to provide additional on-line supplemental content that is relevant to the article. Usually a link will be given somewhere in the article that sends you to a page with additional content on the publisher’s website. You might ﬁnd in the supplement that more results are available, details of the methods are given, or code used in the research is being provided for others to download and implement. Sometimes critical information for your research will be found in the Supplemental Material, so do not forget to watch for a link to it! ConclusionsAcknowledgmentsand Funding SourcesReferences82 4. BUILDING ON THE RESEARCH OF OTHERS Remember that for an important article with high relevance to your research, you should expect that you will need to read it more than once. To really understand what you need to, you may also need to do some additional learning outside of the article and talk to others about the meaning of certain aspects. Student Perspective “Learning how to eﬀectively locate relevant papers and navigate through scientiﬁc literature is a critical skill to develop. Simply ﬁnding the right journal articles is only part of the process of conducting a thorough literature search. In order to actually gain understanding and beneﬁt from scientiﬁc publications, I need to develop skills in critically analyzing the re- search methods and conclusions which are presented. This skill is developed with practice in reading journal articles, which will help with gaining fa- miliarity with projects related to mine and their associated terminology. As my research advisor has pointed out, fully comprehending the meaning of a certain publication often requires more than one reading, even for someone well versed in the subject matter. It is therefore best to be honest with myself about what I do and do not understand, and to give myself time to become knowledgeable.” ASSIGNMENT 4-1: INDIVIDUAL ASSIGNMENT – SUMMARIZING WHAT YOU HAVE READ Choose a journal article of interest to you. Read the article and become familiar with the main points being put forward by the author(s). Summarize the article in a short paragraph, high- lighting the main points that you have identiﬁed. Refrain from just rewording the abstract that was written by the author(s). Write from your own understanding of the article, even if you feel that understanding is incomplete. Use your own words, even if they are not as technical as the one used in the article. ASSIGNMENT 4-2: GROUP ACTIVITY – JOURNAL CLUB A strategy for becoming familiar with and keeping up with the literature is what is commonly referred to as a Journal Club. These are used more often in some ﬁelds than in others. Some 4.3. READING JOURNAL ARTICLES 83 research groups hold their own journal clubs with faculty participating. Some groups of graduate students take it upon themselves to create a Journal Club group in order to help each other read, understand, and interpret the literature. Journal Clubs run in a variety of ways, but they have commons features: the group has a research theme, everyone participates by choosing and reviewing journal articles as well as commenting on the ones chosen by others, and the end goal is for everyone to increase their knowledge of the topic area. In many cases the expectation is that everyone has looked at the article prior to the Journal Club meeting. K. Barker suggests the following guidance for discussing a paper in Journal Club fashion in her book At the Helm4: • • • • • • • “Summarize the main point of the paper.” “Describe the paper in detail.” “Analyze the data.” “Itemize the strengths and ﬂaws in the paper.” “Compare the paper to other papers.” “Is the paper well written and the data clearly presented?” “Predict the next step in the research.” As a Journal Club presenter you should come well prepared. This is important so that everyone is making the best use of their time, and it is part of showing that you are a professional who takes research seriously. Your ability to present a paper successfully will improve over time, as will the depth of analysis you can bring to each paper you review. As you begin in this process, choose a paper that is central to the research you are conducting. When my students present in lab meeting about a paper they have read, I suggest that they attempt to answer the following questions in their presentation of the work. • Describe the paper. – Who authored this journal paper? What institution are they from? – How is that researcher or group related to your research group? – What is the problem being studied? How is this problem related to your research? • Summarize the main point of the paper. – What are the key methods used? – What are the main results? 4Barker, K., 2002. At The Helm: A Laboratory Navigator. 84 4. BUILDING ON THE RESEARCH OF OTHERS • Detail both the strengths and ﬂaws of the paper. – Is the paper well written and the data clearly presented? – What are the assumptions in the paper? How realistic are they? • Take a deep look into the data presented. – What story does each ﬁgure tell? – Is there supplemental data provided that should also be considered? – How sensitive are the results to the assumptions? – What did you learn from this paper? How is this relevant to your research? • Compare the paper to prior published work and relate it to your own research. – What are the similarities and diﬀerences of this research compared to other related research? – How does it connect with your research? Similar/diﬀerent approach/methods/ﬁndings? • Discuss potential opportunities for future work based on this paper’s ﬁndings. – What do you think the authors are working on now? – What would be a natural extension of this work? Note that you may not be able to address all of these topics given the time constraints, so you may have to prioritize. 4.4 READING CRITICALLY It’s important to note, especially for those new to research, that not everything that is published is perfect, or even correct. There are a variety of reasons for this. Some of them quite innocent: maybe the understanding the ﬁeld has changed/deepened since the article was written so it is no longer the appropriate methods or interpretation. Maybe there was an error in the publication process that made an equation incorrect (check to see if there is an Errata for the paper because the error may already have been discovered). Maybe the results are reported accurately, but the interpretation might be made diﬀerently by others. Or, maybe the paper is just poorly written and diﬃcult to read. Student Perspective “Before this semester, I generally interpreted published research as always having the most accurate information about a subject. However, I 4.4. READING CRITICALLY 85 learned in class and from my research mentor that sometimes journal articles contain inaccuracies. My most vivid example of this was when my research mentor asked me to read an article relating to the project I was interested in. After reading the article, a theory mentioned still was unclear and I could not ﬁnd any background information online. When I asked my mentor about the theory, he said that the group that published the research was more in- terested in producing a product than explaining a phenomena and the theory they proposed was not very sound. Indeed, it seems that some published ar- ticles oﬀer the chance for the scientiﬁc community to debate and arrive at a conclusion rather than accept an article as fact.” Unfortunately, there is also the darker side of error, negligence, and misconduct where what has been published was intentionally misleading or incorrect. This may be the fault of one, some, or all of the authors. This topic will be discussed in more detail in Chapter 5. Our role as a researchers is to always question, rather than take things at face value. This applies to your own results and conclusion in addition to the results and conclusions of others. As you read about the work published by others, you are determining if the research is trustworthy and done in a reliable way by examining the methods used and determining if the conclusions are supported by evidence. One way to do this is to draw your own conclusions about the work before reading the conclusions section and then compare yours to those of the authors. This will be very challenging to do initially, but as you gain more experience it will become easier. Among the recommendations for analyzing an engineering document in the advice of Paul, Niewoehner, and Elder5 are the following items that focus on reading critically: Data “Is the data accurate? How was accuracy established?” “Is there data missing? Is there adequate data?” “Is the data of suﬃcient quality?” “What controls were applied to isolate causal factors?” “Is the entire dataset presented? What criteria were used to select the presented data sample from the complete set?” Concepts “Are the appropriate theories applied?” 5Paul, R., Niewoehner, R., and Elder, L., 2007. The Thinker’s Guide to Engineering Reasoning, The Foundation for Critical Thinking. www.criticalthinking.org. 86 4. BUILDING ON THE RESEARCH OF OTHERS “Have alternatives concepts been considered?” “Are concepts used justiﬁable?” Point of View “Are there competing theories that could explain the data?” “Have alternative ways of looking at the situation been avoided in order to maintain a particular view?” Assumptions “Are the assumptions articulated/acknowledged?” “Are the assumptions legitimate or necessary?” “Do the assumptions take into account the problem’s complexity?” Conclusions “Are there alternative conclusions?” “Is speculation misrepresented as fact?” “Do the conclusions follow from the assumptions?” “Is further testing required?” Last, you should determine if the authors or others have found problems with the pa- pers you are citing. Journal articles can be retracted after they are published. John M. Budd, a professor in the School of Information Science and Learning Technologies at the University of Missouri at Columbia, reported that between 1999 and 2009, 1,164 articles were retracted from biomedical journals and “55% of the articles included in this analysis were retracted for some type of scientiﬁc misconduct.6” Jennifer Howard, a Chronicle of Higher Education Reporter, advises: “Authors, you really ought to take a look at the journal articles you cite. Not only is it the responsible thing to do, it will save you the embarrassment of discovering after the fact that you have given a nod to a retracted or discredited paper.7” If you are not downloading and looking at the article yourself because you are simply copying someone else’s citation you will not see the retraction notices. You need to get a copy of the original source, read it, and draw your own conclusions in order to cite the work reliably. 6Budd, J. M., Zach C. C., and Anderson, K. M., 2011. Retracted publications in biomedicine: Cause for concern. In Association of College and Research Libraries Conference, pp. 390–395. 7Howard, J., 2011. Despite warnings, biomedical scholars cite hundreds of retracted papers. The Chronicle of Higher Education. 4.5. LITERATURE SEARCH 87 4.5 LITERATURE SEARCH A literature search begins with a topic and the key terms that are relevant to that topic. An impor- tant ﬁrst step is to get familiar with the terminology and jargon that is relevant to your research. Attend seminars, engage in research group meetings, and talk with others in your research area to begin becoming ﬂuent with the terminology and jargon commonly used. Wikipedia can be a useful resource to get a basic understanding of the topic and terms. Your research mentor may also suggest some textbooks or journal articles that are helpful. At some point you may be speciﬁcally asked to conduct a literature search. Your research mentor may give speciﬁc key words to use, a question to answer, or a general topic area for you to explore. Regardless of whether you are speciﬁcally requested to do so or not, conducting literature searches is an important part of the research process that you will need to undertake. In the early stages of your research project you may simply be looking for background information, and a general idea of what has already been published on your topic area. Later you may need to go to the literature to answer a speciﬁc question, such as the details of an experimental technique of an algorithm. Literature in your speciﬁc research ﬁeld is important, but also keep in mind that literature in related ﬁelds may also provide you with valuable transferable information. As you continue on your research project, you will also need to keep up on the most recent publications periodically so that you can be certain that your work has not been “scooped” by someone else. If someone publishes speciﬁcally on your research topic, you will want to know about it right away so that you can work with your research mentor to determine if you still have complementary research to publish in the area or if you will need to adjust the focus of your research so that you can produce results that distinguish you form the previously published work in the ﬁeld. Check with other individuals in your research group and the librarians at your institution to determine what resources are available to you, both in terms of abstract and indexing databases where you can search for relevant content and access to electronic copies of the articles you are interested in. For instance, Web of Science is one of my favorites, but you may ﬁnd that there is a diﬀerent database that is more relevant to the literature search that you need to do in your research area. Other abstract and indexing databases are freely available like Google Scholar and PubMed. Some journal articles are available free of charge as open access. However, many others that you would otherwise have to pay for will be available through your institutions library, either directly or through an interlibrary loan function. You will need to talk with others in your research group and the librarians at your institution to determine what is available to you. Finding that Golden Nugget Panning for gold is a good analogy for the literature search; you are looking for the gold nuggets hidden among a lot of sand and gravel that that you will need to sift through. One of the challenges is distinguishing be- tween useful and irrelevant papers so that you can identify information that 88 4. BUILDING ON THE RESEARCH OF OTHERS addresses your needs. This can be harder at ﬁrst, but once you have built up some experience you will develop skills that make it quicker. I have always personally enjoyed the process of the literature search; I love the accomplish- ment of ﬁnding that gold nugget, and using it to help me bring about the research idea that I have in mind. Student Perspective “And even though looking back it took me a laughably long time to complete this initial literature review, it deﬁnitely taught [me] an important lesson. Of course I learned how to more successfully carry out a literature re- view; which search engines to use, how to intelligently read papers and look into other references etc. More than that though, I learned how to break a task up into manageable chunks; this makes the task seem much less daunt- ing, which personally gives me much more conﬁdence and optimism.” There are numerous strategies for approaching the literature search. They ﬁt into two basic categories: start broad and sift down vs. start narrow and expand up. Each can be employed successfully and often you will want to use a combination of strategies, but let’s consider one example of how you might begin. When I am just entering into a new area, I like to start broad, so that I get a sense of the scope of the literature that is available. Once you include all of the relevant terms to your search you will likely have a mountain of literature to look at. When employing this strategy, I will need to quickly eliminate items that have come up in my search by deciding the things that I am NOT interested in. Take functionally graded materials for instance. In Google Scholar I might start by simply typing those three words: functionally graded materials. In Web of Science I might search on the topic using: functional* grad* material* (the * is a wildcard symbol that tells the database to include things that have alternate endings like functional and functionally, graded and gradient, material and materials). In Web of Science this search gives me nearly 20,000 results. Yikes! It’s a HUGE research area, but it is unlikely that all of these results are relevant to my interest. Maybe I am most interested in polymeric materials, so I reﬁne my search by using polymer* as another key word with the AND operator requiring both terms to appear in the database record. This has already narrowed it down to a little over 1,000. The research application I am interested in also requires that the material is biocompatibility. I’m not interested in the biocompatibility research itself right now, but I want to make sure the materials can be used in the way I want, so in that case I might want to include a term like cell culture in order to include only those materials that are useful in that circumstance. This narrows it down to a more reasonable 45 results. Now I’ll start sorting through titles and abstracts to decide which ones of these may be 4.5. LITERATURE SEARCH 89 relevant to my research. I still have a lot of papers to consider but I’d at least narrowed down my search by including a few additional parameters. When I am looking at the results that a search engine produces for me, I want to consider the titles ﬁrst. For the ones that look relevant I will look through the abstract and excluded many of the ones I read, because this added information tells me right away that they’re not likely to be very useful to me. When I do ﬁnd an abstract that looks relevant, I can then open the PDF of the article and skim through the paper. I personally tend to focus on the ﬁgures ﬁrst, and if some of them look relevant read the conclusions next to see if there is likely to be useful information in the article. At this stage I don’t necessarily want to read the whole paper because I’m still in the middle of literature search, so if the abstract and the conclusions look promising I will save that PDF and come back to it later for more detailed reading. Even of the ones I have saved, only a fraction will ultimately be useful to me when I read them more thoroughly. As you are doing the search it is always important to also think about diﬀerent ways in which the terminology may be used. After you have read through a number of titles and abstracts, you may realize that there is an additional term or reﬁnement of a term that may give you more relevant results. You are seldom done after just one try and you will probably want to re-run your search with slightly diﬀerent key words after you have become more familiar with the topic. It’s also important to realize that not all databases have access to the same collections of resources. You may need to use more than one. Often your research mentor, or a reference librarian, can point you toward the most relevant databases for your discipline. A librarian can also tell you how to access search engines and databases remotely, so that you can access the literature even when you are oﬀ campus. Once you ﬁnd some papers that are particularly relevant to your research question, you can use those with the search engines to look both forward and backward in time. Start with an article that you had already found to be relevant, then go backward and forward in time by looking at the papers that this article cites and who have cited this article since it was published. Abstract and indexing databases like Web of Science and Google Scholar have this functionality. You might ﬁnd some nice new nuggets this way. You can also set up a various diﬀerent alters with most of these systems to notify you of future publications when they appear. If you have developed a set of useful search parameters, you can set an alert to notify you whenever an newly published article meets those same parameters. A citation alert on particularly relevant article that you have already identiﬁed will notify when another new article comes out that cities this previous one. You can also set up a citation alert on key authors in the ﬁeld so that you are notiﬁed when they have a new publication appear. However, even with these alerts in place, you will need to regularly revisit your literature search to identify if new publications have appeared. Review articles can also be an excellent place to resource if one has been written in your research area. Happily, the authors of the review article will have already done the hard work of pulling together and summarizing the relevant research papers on the topic. However, your search does not end with the review article. You will want to get a copy of the most relevant 90 4. BUILDING ON THE RESEARCH OF OTHERS papers that the review article cites and read them yourself. You will also want to see what other papers have cited the review since it has been published because there may be more recent papers that are also important for your research. To ﬁnd review articles, you will want to use the key words relevant to your topic and include the word “review” if you are searching in an index like Google Scholar, or in a database like Web of Science, there is a Review button you can click. This will narrow your search results to only the ones that have been identiﬁed as review articles, so that you can take a look at those in more detail. You also need to recognize that journal articles may not be the only source of relevant information on your topic. You will want to look at patents, government reports, handbooks, and books that are available through the internet, or your institution’s library. Some of these resources can be a little bit more diﬃcult to identify. I have found over my career that the refer- ence librarians can be an incredibly valuable resource for helping you to identify how to access the information that you need. If you have such a person available at your institution, you should take the opportunity to get to know them. ASSIGNMENT 4-3: INDIVIDUAL ASSIGNMENT – LITERATURE SEARCH WITH KEY WORDS Work with your research mentor to identity key words for a useful literature search that you can undertake and get their suggestion on which databases to use in your search. Conduct the literature search using these key words and identify the 5–10 most relevant journal articles on this topic. ASSIGNMENT 4-4: INDIVIDUAL ASSIGNMENT – PATENT SEARCH Use the United States Patent and Trademark Oﬃce website at www.uspto.gov to conduct a patent search using key words that are relevant to your area of research. (Note that this website provides a number of resources for how to conduct a search eﬀectively.) Identify 1–2 patents most closely associated with some aspect of your research and summarize your ﬁndings. 4.5. LITERATURE SEARCH 91 ASSIGNMENT 4-5: INDIVIDUAL ASSIGNMENT – GOVERNMENT REPORT SEARCH Conduct a search for technical government reports that are relevant to your area of research. You may need to work with your reference librarian to identify a relevant database, or you may be able to start with one of the following: U.S. Department of Defense, Defense Technical Information Center, www.dtic.mil NASA Technical Reports Server, ntrs.nasa.gov U.S. Department of Energy Oﬃce of Scientiﬁc and Technical Information, www.osti. gov ASSIGNMENT 4-6: INDIVIDUAL ASSIGNMENT – DISSERTATION SEARCH Students completing a master’s degree often do so with a research thesis, and all Ph.D. students produce a dissertation on their research as the main degree requirement. These are often archived documents and many of repository such as Proquest. Identify ﬁve relevant thesis or dissertation titles by conducting a search through your university’s library catalog/database or by using Pro- quest Dissertation Express at https://dissexpress.proquest.com/search.html. (If you ﬁnd that you are interested in learning more about one of these titles, contact your library about access before ordering a copy. Often you can obtain access to a copy through your institution’s library.) ASSIGNMENT 4-7: INDIVIDUAL ASSIGNMENT – ALTERNATIVE SOURCES SEARCH Use your institution’s library to identity e-books and online handbooks that are relevant to your area of research. Identify 3–5 relevant resources. Choose one of these and write a one paragraph summary of the resource and how it is related to your research interests. 92 4. BUILDING ON THE RESEARCH OF OTHERS 4.6 PROPER CITATION When you discuss someone’s work, either in a presentation or in writing, you need to identify where those ideas came from originally. By including the citation, you have identiﬁed to the listener or reader that what you are discussing has its origins in the work of others. The format of the citation may vary depending on the requirements of who you are preparing the work for (e.g., your instructor or a journal). The easiest way to include a citation in written work is to use a footnote (the reference is included at the bottom of the page) or an endnote (the reference is included at the end of the paper). In the case of a presentation where you have included an image or ﬁgure from a source such as a journal article or a website, it is most common to provide the reference information directly on the slide. In this case a short citation is ﬁne, but you will need to provide enough information so that someone else can ﬁnd the original source. For instance, you might use one of the following formats: Mature primary cardiomyocyte image from www.e-heart.org Image Credit: Srivinasan, Protocol Exchange, 2011. [Salick, M. R., et al., Biomaterials, 2014] Even if the material is unpublished, you need to provide credit to the source. For instance, you might credit a colleague with: J. Rogers, with permission. Or for your own work not yet published: B. N. Napiwocki, et al., in preparation. For written work, there are a number of ways in which the citation may appear. As you are reading journal papers you will have noticed superscript numbers, numbers in brackets, or parenthetical notations that include author names: superscript1, some type of parentheses (1), the name of the author (Crone, 2010) or authors (De, et al. 2002). These citations identify con- cepts and results that are culled from other sources and the notations refer you to the particular source in the References section at the end of the article. For instance, the following sentence appears in the Johnson, et al., 2004 article whose citation is given above: “In an aqueous environment, stimuli-responsive hydrogels undergo a reversible phase transformation that results in dramatic volumetric swelling and shrinking upon ex- posure and removal of a stimulus. Thus, these materials can be used as muscle like actuators [1], ﬂuid pumps [2], and valves [3].” The numbers in brackets, e.g., [3], refer to the reference section of the paper. In this case, an article detailing the use of a stimuli-responsive hydrogel for each component application is given. If you were particularly interested in valves, then you would want to look at reference 3. In other journals, instead of the number appearing in brackets [ ] or parenthesize ( ), it will appear as a superscript as in this example8: 4.7. CITATION MANAGEMENT 93 “One of the drawbacks of coil embolization is coil compaction over time, leading to recanalization of the aneurysm. Some degree of aneurysm recanalization occurs in as many as 20% of cases.1 3 In larger aneurysms, placement of multiple coils can be time consuming, and longer procedural times may lead to increased morbidity and mortality.3 An alternative to coil embolization is the use of liquid embolic agents. It is thought that ﬁlling aneurysms with such polymers will reduce many of the shortcomings associated with coiling, such as coil compaction.4;5” (cid:0) The other common style you will see includes the author and year of the publication in the body of the text. Although this makes the sentence longer, the reader does not have to repeatedly look back to the references section to see whose work is being referred to. For example9: “Previous studies have reported lineage reprogramming into a diverse range of diﬀer- entiated cells types, including neurons (Vierbuchen et al., 2010), hepatocytes (Sekiya and Suzuki, 2011), and cardiomyocytes (CMs) (Ieda et al., 2010; Song et al., 2012).” The abbreviation “et al.” will often appear in citations. This refers to the Latin phrase et alia meaning “and others.” When the author list is long, usually more than two, the ﬁrst author’s name is given and followed by et al. to indicate that the paper had multiple authors although all of their names are not listed. Generally, in the references section, the entire author list is included. Every citation style is a bit diﬀerent and some journals will even deviate from the more common citation styles (e.g., Chicago, IEEE, APA), so you will have to adapt your own writing depending on the requirements. 4.7 CITATION MANAGEMENT If you are not already familiar with one, now is the perfect opportunity to learn about citation management systems. Keeping track of all the journal articles and other references that you will begin to accumulate on your research project will quickly turn into a big organizational challenge. Happily software systems have been developed that can be a huge timesaver for you, allowing you to easily collect relevant references, organize them, and cite them in your writing. Examples if such programs include EndNote, Zotero, and RefWorks, but there are many to choose from. Your institution may provide you access to one of these programs, or you may decide to purchase one of these pieces of software for yourself. If you are new to a research group, 8Moftakhar, R., Xu, F., Aagaard-Kienitz, B., Consigny, D. W., Grinde, J. R., Hart, K., Flanagan, C. E., Crone, W. C., and Masters, K. S., 2015. Preliminary in vivo evaluation of a novel intrasaccular cerebral aneurysm occlusion device. Journal of Neurointerventional Surgery, 7(8), 584–590. 9Lalit, P. A., Salick, M. R., Nelson, D. O., Squirrell, J. M., Shafer, C. M., Patel, N. G., Saeed, I., et al., 2016. Lineage reprogramming of ﬁbroblasts into proliferative induced cardiac progenitor cells by deﬁned factors. Cell Stem cell, 18(3), 354– 367. 94 4. BUILDING ON THE RESEARCH OF OTHERS you should ask your research mentor, or the group members, if the group has a designated citation management system. In some research groups, citation management system content is shared among group members. Although the diﬀerent citation management systems all contain the same basic functionality, each is a bit diﬀerent and it may be helpful to look into the details of the options available or talk to a reference librarian before you choose one for yourself. Spend Time to Save Time I was slower than I should have been to adopt a citation management system. When I ﬁnally did so, I realized that I had wasted enormous amounts of time by not doing it sooner. My suggestion to you is to start early and save yourself the time upfront! Even so, moving into a citation management system after you already have a collection of journal articles is not as over- whelming as it might seem and fully worth the time investment. The basic functionality of these systems comes into play beginning with your literature search as you identify articles that are particularly important to your research. Many of the databases that you will use (like Google Scholar and Web if Science) have the functionality to automatically insert the citation into your management system with the click of a button. In most cases, the citation management systems can be connected with your institution’s library so that the system can pull the PDF of the article from the library into the management system. Additionally, you can use the management system to organize these references and make addi- tional notations and comments about them as you read and utilize them further. Finally, when it comes time to cite the article as a reference in a paper or report that you are writing, many of the word processing programs available have add-ons that work with the citation management system so that you can easily integrate your citations without a lot of extra work. If you have ever built and formatted a bibliography by hand, you know what a time consuming and irritating task that can be. With one of these systems fully in place, the insertion of a citation into your paper is just a few clicks of a button; the citation is attached to the appropriate place in the paper, and the bibliographic information is included at the end of the paper in your references section. These systems also allow you to make separate project folders so that you can keep related references bundled together and easier to ﬁnd. This may not seem very important when you are just starting out, but it will be very handy to have your citations grouped as the number of them grows over time. Using folders or groups also means that you can easily use your citation management system, not only for your research, but also for your coursework and other projects that you undertake. 4.8. PREPARING A REVIEW 95 ASSIGNMENT 4-8: INDIVIDUAL ASSIGNMENT – INVESTIGATING HOW CITATION MANAGEMENT SYSTEMS WORK Find a peer or research group member who uses a citation management system. Talk with them about how they use the system and its functionality. Identify at least two new functions or tips about usage that you did not previously know about. ASSIGNMENT 4-9: INDIVIDUAL ASSIGNMENT – COMPARING CITATION MANAGEMENT SYSTEMS Choose two citation management systems and compare their functionality. Describe the pros and cons of the systems in a two-paragraph summary. Consider at least six of the following topics in your comparison: • Cost (short term while you are a student and long term after you have left the university) • Operating systems requirements • Plugins available for word processing programs such as Word and LaTex • Attachment limits for article PDFs • Ability to annotate with your own notes and PDF markups • Ability to create new or edit existing citation styles • Folder organization and sorting capabilities • Duplicate citation detection • Capability to collaborate and share with others in your research group • Export options between other citation managers 4.8 PREPARING A REVIEW There are a variety of instances in which you may be asked to review the written work of others. As a student, this most frequently occurs in course settings where you may be asked to do a peer review on a paper written by another student in the course. Alternatively, an instructor 96 4. BUILDING ON THE RESEARCH OF OTHERS may assign a journal paper review as an assignment in an advanced engineering course. More advanced engineering graduate students may even be asked to provide input on a review of a manuscript submitted to a journal. This might be done in collaboration with your advisor or through your advisor’s recommendation. Regardless of the particulars of the situation, there are numerous commonalities to the review process. A later chapter will focus on providing feedback to a colleague in a classroom setting, such as a writing workshop. Here we will focus on providing a critical review of a journal article. Get Critical The ﬁrst time I was asked to review a journal article, it was for an assignment in a ﬁrst-year graduate course. We were told to choose an article of interest and turn in a critical review. That was the extent of the instruction and I had no idea of where to start! In many ways, this section is written for those of you faced with such an assignment. However, even if you don’t have to do a critical review for a course, it is a good habit to always read critically and this information should help you get started on the path to doing so. It is important to ﬁrst understand the expectations of those asking for the review. In the case of a journal, they are very likely to provide you with a set of criteria, or some brief instruc- tions, on the feedback that they would like to receive. In addition to looking for a good article, they want to make sure that the article is a good ﬁt for their journal. You will also have access to the journal’s scope through its website. You can use the scope information to tell you whether the manuscript ﬁts with the journal to which it has been submitted. You will need to begin by reading the manuscript thoroughly. It will likely require multiple passes through the manuscript in order for you to complete your review, but in the ﬁrst reading you will get a general sense of the article. You may also take away an impression of its overall strengths and weaknesses in this ﬁrst reading. During this ﬁrst reading keep in mind a few questions. What is the key takeaway message? Does the abstract give a compelling and yet reasonable summary? What points did you ﬁnd initially confusing? Are the ﬁgures clearly presented? Are the terms deﬁned and the equations understandable? Do the conclusions follow from the results? What is the signiﬁcance of the ﬁndings presented? Is prior published work appropriately cited? Is the paper written with good organization and grammar? 4.8. PREPARING A REVIEW 97 In your review you will be seeking to help the authors improve their manuscript so that the future readers can easily understand it. You will need to be on the lookout for both scientiﬁc problems in the methods and analysis, as well as writing issues such as clarity and presentation. Your review should be detailed enough to help the authors improve their manuscript regardless of whether or not you recommend to the editor that it be accepted for publication in this particular journal. The decision of whether or not to publish will ultimately be the editors to make, but you will need to give an option if it should be accepted (with minor or major revisions) or rejected based on the quality and impact on the ﬁeld. As you get more involved in your research area you will begin to learn which journals are the most important in your ﬁeld and you should become familiar with their scope and criteria for publication as you begin to work toward publishing your own research. Every journal has deﬁned its scope to identify what research it will publish. For example, the journal Experimental Mechanics is published by Springer with the Society for Experimental Mechanics, a professional organization that I have been a member of for 30 years. If you go to the journal website you will ﬁnd the following information describing the scope of that journal10: • Explores experimental mechanics, including its theoretical and computational analysis. • Addresses research in design and implementation of novel or enhanced experiments to characterize materials, structures, and systems. • Spans research in solid and ﬂuid mechanics to ﬁelds at the intersection of disciplines such as physics, chemistry, and biology. • Extends the frontiers of experimental mechanics at both large and small scales. Below are some example criteria provided to the reviewers to give you an idea of what is commonly requested. Each journal will give instructions to its reviewers and may have special- ized criteria to consider, but the recommendations for reviewing provided by Springer Interna- tional Publishing are representative of the type of requests you would see. Evaluating Manuscripts11 When you ﬁrst receive the manuscript it is recommended that you read it through once and focus on the wider context of the research. Springer Publishing recommends that you ask questions such as the following. 10Experimental Mechanics, mechanics/journal/11340. Springer International Publishing, https://www.springer.com/engineering/ 11Evaluation Manuscripts, Springer International Publishing, https://www.springer.com/us/authors-editors/ authorandreviewertutorials/howtopeerreview/evaluating-manuscripts/10286398. 98 4. BUILDING ON THE RESEARCH OF OTHERS • What research question(s) do the authors address? Do they make a good argument for why a question is important? • What methods do the authors use to answer the question? Are the methods the most current available or is there a newer more powerful method available? Does their overall strategy seem like a good one, or are there major problems with their methods? Are there other experiments that would greatly improve the quality of the manuscript? If so, are they necessary to make the work publishable? Would any diﬀerent data help conﬁrm the presented results and strengthen the paper? • Were the results analyzed and interpreted correctly? Does the evidence support the authors’ conclusions? • Will the results advance your ﬁeld in some way? If so, how much? Does the importance of the advance match the standards of the journal? • Will other researchers be interested in reading the study? If so, what types of re- searchers? Do they match the journal’s audience? Is there an alternative readership that the paper would be more suitable for? For example, a study about renal disease in children might be suitable for either a pediatrics-centric journal or one that is targeted at nephrologists. • Does the manuscript ﬁt together well? Does it clearly describe what was done, why it was done, and what the results mean? • Is the manuscript written well and easy to read? If the manuscript has many mistakes, you can suggest that the authors have it checked by a native English speaker. If the lan- guage quality is so poor that it is diﬃcult to understand, you can ask that the manuscript be corrected before you review it. After your ﬁrst reading, write one or two paragraphs summarizing what the manuscript is about and how it adds to current knowledge in your ﬁeld. Mention the strengths of the manuscript, but also any problems that make you believe it should not be published, or that would need to be corrected to make it publishable. These summary paragraphs are the start of your review, and they will demonstrate to the editor and authors that you have read the manuscript carefully. They will also help the editor, who may not be a specialist in this particu- lar topic, understand the wider context of the research. Finally, these paragraphs will highlight the manuscript’s main messages that will be taken away by readers. You can then proceed in evaluating the individual sections of the paper. (Note that Springer’s website gives additional detailed questions to consider in each section of the manuscript.) Most engineering journals use a “closed” peer review process where you will know the identities of the authors, but they will not be informed of your identity. Even though your review 4.9. CREDITING THE WORK OF OTHERS 99 will be anonymous in this sense, you should always behave respectfully and professionally in your review. It is also likely that your criticism will be better received if you note what the authors did well, in addition to what they need to improve. Additionally, keep in mind that as a reviewer you are seeing research before it is published and publicly available, but you must keep this information conﬁdential until the publication is released. As a future author of a journal paper the review criteria described above and the practice of being a reviewer will be helpful in allowing you to evaluate your own manuscript with a critical eye prior to its submission. ASSIGNMENT 4-10: INDIVIDUAL ASSIGNMENT – WRITING A JOURNAL ARTICLE REVIEW Choose a journal article relevant to your area of research. Conduct a 2-page written review. Begin with a 1–2 paragraph summary of the paper. Conduct the remainder of the review us- ing the “Evaluating Manuscripts” guidance from Springer above or the review criteria from the journal in your area of research (ﬁnd the journal’s website and look for the guidelines for referees/reviewers). ASSIGNMENT 4-11: INDIVIDUAL ASSIGNMENT – ANNOTATED BIBLIOGRAPHY Compile an annotated bibliography of a research topic of your choice. This topic may be related to a seminar that you have attended this or a research topic in your own subdiscipline area of interest. Your annotated bibliography must contain a minimum of eight journal articles. For each article you must give the full citation (using a standard style such as APA or Chicago) and a brief description (roughly 150 words) of the main purpose and ﬁndings of the paper. Include a topic title at the top of the top of the bibliography. 4.9 CREDITING THE WORK OF OTHERS Very seldom is research done in a vacuum. In the vast majority of cases research is built on prior work that has been documented by others, often in journal publications. Even truly interdisci- plinary research done at boundary areas not previously explored, often borrow the techniques and approaches from one discipline or the other and apply them in a new ﬁeld or to ask new questions. As a member of the research community it is essential that you not only know what 100 4. BUILDING ON THE RESEARCH OF OTHERS research has been done previously but also cite that prior work as the foundation of your own when it is appropriate. Student Perspective “The whole of the scientiﬁc pursuit is based on openness and peer- review, and it constantly builds on previous discoveries. As the step-by-step process continues, what was learned before must be acknowledged and re- spected.” On the positive side, citing the work of others also helps to build your own credibility. When you have informal conversations with people in your ﬁeld, write reports and publications about your research, present at a conference, or give a formal research talk on y our campus, it is critical that you discuss the background of your research area. In doing so you will need to identify who made the early ﬁndings, who established critical techniques, and who has presented research results that you have built upon or contradict your own. Depending on the speciﬁc circumstances, there are a variety of ways in which other people’s ideas are credited. What is critical is that you ﬁnd a way to acknowledge the work of others and distinguish it from your own. If you do not do so you are at risk of committing plagiarism. Student Perspective “‘Word-for-word plagiarism’ happens when the method of expression and sentence structure are largely maintained. ‘Patchwork paraphrase’ is the paraphrase that contains the language from the author without rephrase and some writer’s own words. Both situations are considered plagiarism since the writer has only changed around a few words and phrases or changed the order of the original’s sentences. For an acceptable paraphrasing, the information in the original sources is accurately relayed and expressed in the writer’s own words.” Sometimes plagiarism is done intentionally. This is a risky proposition, especially given the techniques that are now available at universities and with publishers for identifying plagiarism. Even if you think you have found a way to cut corners by taking credit for someone else’s work and get away with it, don’t do it. It not only carries high risk of repercussions; it also carries a risk of luring yourself into other dishonest actions that not only jeopardize your career, but also the careers’ of those around you and the integrity of the research in your ﬁeld.12 12Ariely, D., 2012. The (Honest) Truth About Dishonesty, Harper Collins Publishers, New York. 4.9. CREDITING THE WORK OF OTHERS 101 Student Perspective “This has become a bigger problem because it is so easy to access tons of information from diﬀerent sources on the internet and it can be tempting to copy and paste and then rearrange and change a few words here and there in sentences. It can also be diﬃcult to ﬁnd the author information and dates of publication on some websites so some people may think they either do not need to cite the source or just simply don’t do it. Another issue is the availability of online essay writing services. These services will prepare essays for students for a fee. It is plagiarism to hand in one of these essays because it is passing work oﬀ as your own that you did not do.” Sometimes plagiarism is committed because the rules are not well understood. However, ignorance of this in an academic setting will not be excused and often has severe consequences. If you are unsure how your institution deﬁnes plagiarism, look it up. Identify campus resources (e.g., a Writing Center) and look for guidelines and workshops on how to avoid plagiarism. ASSIGNMENT 4-12: INDIVIDUAL ASSIGNMENT – WATCHING THE CREDITS While reading a journal article or listening to a seminar presentation, pay close attention to how prior research is credited. How is sentence structure used in combination with the citations? Is the work of others mentioned with the researcher name(s), if so is the ﬁrst author indicated or the principal investigator of the research group? Does the author or speaker also cite their own work? If so, how is this done similarly or diﬀerently to citing the work of others? Write a brief summary about your observations, including a few representative examples. There may be some variation within your discipline, so continue to pay attention to how the work of others is credited when you are reading about and listening to research. C H A P T E R 5 103 Conducting Research SCIENTIFIC HABITS OF THE MIND 5.1 Much has been written on the scientiﬁc method throughout history. Historian of science Daniel Siegel of the University of Wisconsin–Madison tells us that scientiﬁc method is a complex topic but often philosophers categorize scientiﬁc method into three idealized types: empiricist, rationalist, hypothetical.1 • The empiricist methodology, championed by Sir Frances Bacon during the Scientiﬁc Revolution, is based on experience, observation, and experiment. The basic idea is that generalizations can be developed from careful observations and categorizations. The basis of this method is to avoid prejudices and be guided by one’s experience. An ex- ample of this methodology is taxonomy. However, this method cannot address all areas of science eﬀectively and answer all questions we may want to pose. • The rationalist methodology, promoted by Renee Descartes in the 17th century, is based on reasoning. The method begins with careful contemplation and consideration of how things must be. Geometry is an excellent example of this method. You begin with basic, self-evident axioms and then from there you can reason to a conclusion. If the appropriate basic principles can be found, then the rest can be developed through reason. Although its utility in isolation is limited, this is a powerful method in com- bination with the other methods. Prof. Siegel gives the example of the principle of conservation of energy, which is a constitutive principle of science which can be ap- plied to a wide range of topics and can guide thinking and new experimentation. • Hypothetical methodology is based on suppositions and conjectures. This was a method frequently used in science historically, but often denied. You imagine possibil- ities, try out ideas, and ask the question: If my supposition was true, what consequences would there be to things that I can observe directly? This method allows scientists to get beyond the limitations of what can be observed directly. For example, the idea of the atom came well before direct observations were possible, but the hypothesis of the existence of atoms has logical consequences that can be observed through experiments. The hypothesis must be a testable, or veriﬁable, in order for it to be a scientiﬁc method. Although this is an indirect method, it is very powerful. 1Siegel, D., video on “The Scientiﬁc Method,” in “Professional Development,” Materials Research Science and Engineer- ing Center, University of Wisconsin-Madison, https://education.mrsec.wisc.edu/professional-development/. 104 5. CONDUCTING RESEARCH If we look at the practice of science and engineering research today, we ﬁnd that most often a combination of these methods is used. We can do research using a mixture of methods according to the needs of the research problem we are approaching. ASSIGNMENT 5-1: GROUP ACTIVITY – DIET COKE AND MENTOS This activity explores scientiﬁc method through two sets of results. The ﬁrst is from the popular Discovery Channel T.V. show, MythBusters. In Episode 57: Mentos and Soda (ﬁrst aired August 9, 2006), the show investigates the cause of the explosive reaction between these two ingredients. The results of the reaction can be found in numerous videos through an Internet search using the key words: diet coke and mentos. See https://go. discovery.com/tv-shows/mythbusters/ for episodes. The second set of results comes from the experiments in an article “Diet Coke and Mentos: What is really behind this physical reaction?” by Tonya Shea Coﬀey (American Journal of Physics, 76(6), (2008) pp. 551–557). After viewing the MythBusters episode and reading the journal article, discuss the scientiﬁc method approaches taken in each. Consider the following questions. MythBusters Episode • What aspects of the scientiﬁc method are incorporated into the experiments presented, and what aspects are lacking? • What hypotheses have the hosts made? Do they add new or modify their hypotheses as they continue with experimentation? • Do you agree with the conclusions of the hosts? • Is the question closed, or must further research be done? Coﬀey Paper • What aspects of the scientiﬁc method are incorporated into the experiments presented, and what aspects are lacking? • What if any issues did you have with the experiments, methods, and analysis that they chose? • Do you agree with the conclusions of the author? • Is the question closed, or must further research be done? Comparison of the Two Studies 5.1. SCIENTIFIC HABITS OF THE MIND 105 • Compare and contrast the methods, experiments, and conclusions of the Coﬀey paper with the MythBusters study. • Which of the studies better adheres to the scientiﬁc method? • How does presentation style matter to the general public vs. the scientiﬁc community (would you choose to highlight one of these studies over the other when discussing the results with a friend or colleague)? ASSIGNMENT 5-2: GROUP ACTIVITY – MONTY HALL EXPERIMENT Ken Overway at Bridgewater College Developed an activity based on an old television show called “Let’s Make a Deal,” hosted by Monty Hall.2 In the show, contestants have the chance to win a big prize if they choose the correct door out of three options. After they have made their initial choice, the host eliminates one of the remaining doors that does not have a prize. At that point, the contestant is oﬀered the choice of staying with their original choice or switching to the one remaining door. What choice should the contestant make in order to have the best chance of winning the prize? Develop a hypothesis statement about the anticipated outcome of the relative odds of winning the prize at the end by choosing to switch vs. stay. Consider why you have decided on this hypothesis. Then collect empirical evidence, ideally by working with a partner so that you have a host and a contestant. Complete 20 trials of the game. Analyze the results and determine if you ﬁnd the evidence to support or refute your hypothesis. Finally, restate or reaﬃrm your hypothesis based on this evidence. (Note: A thorough discussion of the background and activity are given by Overway.) ASSIGNMENT 5-3: INDIVIDUAL ASSIGNMENT – COMPARING THE EVIDENCE Choose a science question that has received coverage by the media and is perhaps a subject of controversy. A number of health questions fall under this category, e.g., How does living near 2Overway, K., 2007. Empirical evidence or intuition? An activity involving the scientiﬁc method. Journal of Chemical Education, 84, 606. http://jchemed.chem.wisc.edu/Journal/Issues/2007/Apr/abs606.html. 106 5. CONDUCTING RESEARCH high voltage power lines aﬀect people? Does cell phone use cause brain tumors? Will ingesting large amounts of vitamin C help to prevent a cold? Investigate your topic using a variety of sources, including web searches, online encyclo- pedias, and scientiﬁc journals. Can you ﬁnd scientiﬁc journal articles that disagree with one another? After completing your investigation, consider the following questions. • What types of evidence are available on this question? • Does the media coverage accurately describe the research reported in journal articles? • How might inaccuracies in the media portrayal of research ﬁndings occur? • What responsibilities do scientists and engineers have to convey their ﬁndings to the public? • If scientiﬁc journal articles come to opposing conclusions, can you identify ﬂaws in the methods or conclusions of these articles? • What conclusion do you draw from your investigation, and why? 5.1.1 OTHER RESOURCES ON SCIENTIFIC METHOD This section only touches on a very large topic that has been the subject of inquiry for centuries. For additional content, the following references are suggested. American Association for the Advancement of Science, 1990. Science for All Americans, Project 2061, 183–187. See Chapter 12: Habits of Mind. Niewoehner, R., Paul, R., and Elder, L., 2007. The Thinker’s Guide to Engineering Rea- soning, The Foundation for Critical Thinking, p. 57. Paul, R. and Elder, L., 2006. A Miniature Guide for Students and Faculty to Scientiﬁc Thinking, The Foundation for Critical Thinking, p. 49. Wolfs, F. “Introduction to the Scientiﬁc Method,” University of Rochester, http:// teacher.pas.rochester.edu/phy_labs/AppendixE/AppendixE.html 5.2 DEVELOPING A RESEARCH PROPOSAL Diﬀerent types of research take diﬀerent time frames to accomplish. You need to be aware of this, and you should also engage your research mentor to help you develop a research project that is appropriate. Depending on whether you are embarking on a summer research experience, a master’s thesis, or a Ph.D. dissertation, the scope of your research project will necessarily be quite diﬀerent. Your project might be quite independent of the work of others, or other researchers 5.2. DEVELOPING A RESEARCH PROPOSAL 107 may be depending on the results you produce in order to carry on their work. It may also be the case that your research is a contribution in a much larger, longer-term eﬀort, but you should have an idea of what milestone(s) you are trying to achieve. Understanding these aspects up front are important to appreciating how your research ﬁts into the research group you are joining and the broader ﬁeld that your work connects to. Student Perspective “I think the most surprising thing I learned about the nature of research this semester was the time frame on which research is carried out. Although I wasn’t under the assumption that research is instantaneous or that a project could be ﬁnished in a week, I never really thought about the actual time frame of it all. But, now I realize that some research projects can take years, even decades to get publishable results.” After you have the basic of the research you will be undertaking you need to be able to express it clearly and succinctly in your own words. This can be harder than it sounds because you need to have done some reading and had some conversations with your research mentor so that you can develop a good background understanding of the area of research that you are undertak- ing. Then you need to write out the research question in a way that everyone will understand— you, your mentor, others in the ﬁeld, and people outside the ﬁeld. Use the least amount of jargon possible and rework this short statement until you can hand it to someone who does not know your research area; success is when they understand what you are planning to do and can explain it back to you based on what you have written. If they can’t, listen carefully to their questions because this will likely help you to identify where you may have leaps in logics or fuzziness in your explanation. Student Perspective “One of the former … students advised that we should be able to write down the basic idea of our thesis on a napkin. This doesn’t mean I should ex- pect to know what results I will achieve or what questions I will answer along the way, but having a clear question in mind at the start of the project is im- portant. Before beginning and while performing the research, it is important also to set realistic goals.” Often as part of research you will need to take a role in preparing a proposal. This may be a requirement of your degree program, part of a fellowship application, or something you work on with your research mentor to submit to a funding agency. There are a variety of styles and expectations depending on the speciﬁc proposal being written. The ﬁrst step you should take is to learn about the expectations—check your program requirements, fellowship application 108 5. CONDUCTING RESEARCH instructions, or funding agency guidelines. The next step is to see if you can ﬁnd a good example to help you understand what a succesful proposal looks like—use your network to see if you can ﬁnd someone willing to share a copy of theirs. These steps will help you prepare to write a successful proposal of your own. In some cases, you will need to frame your research with a hypothesis. If you have not been given a hypothesis to explore by you research mentor, you will have to come up with your own hypothesis after you have read the literature and immersed yourself in your research group to learn, explore, and develop your ability to come up with a new idea. Regardless of whether the idea originates from you or your research mentor, you need to make sure that someone else has not already answered this question. This means taking a deep dive into the literature (not just the last 10 years) and looking into both the literature of the speciﬁc subdiscipline in which you are engaged and other related research areas. Use more than one search engine, as each has slightly diﬀerent coverage and indexing nuances. Then you can go about fashioning a testable hypothesis around your idea. To propose this work, you will not only need a research question or hypothesis, but you will also need to have a plan for how to go about carrying out the research. Determine what you will need to do to test this hypothesis. Will you approach it with theory, modeling, experiment, or some combination? Determine the facilities, tools, materials, and background knowledge you will need. Do you have access to these or can you ﬁnd a way to gain access? Develop a plan for the steps you will take to complete the research. Identify alternative strategies you will use if your initial approach does not work out as expected. All along the way, get input from your research mentor, other experts, and others in your research group. There is a balance however, and at some point, you need to start on the research itself. This might mean conducting a preliminary experiment or making a simpliﬁed model to test out some of your ideas. If you are able to capture some data or show some initial results this can be very useful to include in the proposal. It shows that you have already been able to make some progress on your idea and that you have the fundamental skills needed to carry out the research you are proposing. Student Perspective “One of the tendencies I had (and still pops up at times) is that I wanted to understand all the theory, papers, and work out there ﬁrst so I knew what I was doing in my experiments and not wasting time. I almost feared just running a trial or two to better understand, and often without doing so I had no chance. I received advice to spend more time in the lab. That looking for research papers was good for understanding where things have been, save time when implementing earlier found discoveries or techniques, and even inspires new ideas. However, the quickest way to see what works and doesn’t will be through trial and error, learning form each experiment.” 5.3. GETTING STARTED AND STAYING MOTIVATED 109 Figure 5.1: Proposal submission process. If you are writing a fellowship proposal or working with your research mentor on a pro- posal to be submitted to a funding agency, it is helpful to understand how the decision process works once you have submitted the proposal. Most funding agencies and foundations follow the same general submission process and have the same basic steps. The schematic3 in Figure 5.1 provides a general sequence for how this often occurs. Your research mentor can help you to determine if this is a good representation for the proposal process that you are currently under- taking. 5.3 GETTING STARTED AND STAYING MOTIVATED Research is inherently challenging, but it can also be fun and exciting if you make the commit- ment and put in the eﬀort. The front-end investment of time is often high and it usually requires you to do a signiﬁcant amount of learning and skill building before you can make progress. Student Perspective “In the lab, I’ve been given much more independence and responsibil- ity. This has forced me to take more initiative than I had to previously, but 3Adapted from: Barker, K., 2006. At the Bench: A Laboratory Navigator, Updated Edition, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY. SubmissionGranting AgencyChoose an agency andprogram where your workwill have a good ﬁt.Identify the Program Managermost relevant to your topic.Use the constructive criticismprovided by the reviewers toimprove your work.Does the agency allow you toprovide a list of reviewersdisallowed from reviewingyour work?Program ManagerReviewersGrant Review PanelWrite aDiﬀerent ProposalRewrite with New Ideasor Preliminary DataConduct ResearchFunding GrantedFunding Denied+ Score orReview- Score orReviewVery -Slightly -110 5. CONDUCTING RESEARCH also allowed me to ﬁgure things out for myself. This isn’t to say that I wasn’t working hard before this, but I had a little bit more of a “safety net” when doing my work. Although this extra responsibility may entail a little bit work on my part, it is also much more rewarding.” Students are used to taking classes and having an externally determined schedule of home- work deadlines, project due dates, and exams. Sometimes it can be diﬃcult to transition to re- search when the work schedule and deadlines are most often self-imposed. Your research mentor does not want to spend the time it would take to micromanage your research project and lay out every step for you. Initially, you will require more guidance, but quickly you need to take on this responsibility for yourself. Often students ﬁnd it easiest to make progress if that have a regular work schedule for research (i.e., speciﬁc hours set aside each day when research will take place). You need to have a basic plan in mind and list of tasks that need to be accomplished, but you will also need to be ﬂexible and adjust as the need arises and obstacles pop up. Student Perspective “I realized that when taking on a research project, there is no room to make excuses and if you want to successfully complete a project you must always take the initiative and go the extra mile.” Learning to work carefully and with intention is also a critical research skill. Mistakes will happen, things will break, and that will be forgiven if you own up to the issue quickly and take action to prevent it from happening again. Time and money can be wasted. The worst thing you can do is risk the safety of yourself or others, so you must be certain you understand the potential safety hazards before you take action. Student Perspective “The most important lesson that I’ve learned is that it is always im- portant to be careful. I have experienced several occasions when I didn’t have time to do things right, so I had to ﬁnd time to do them twice. Not only does this cause lost time, but it also incurs ﬁnancial costs. I must always be sure to slow down, check, double check, and then proceed. This is the most crucial skill for an experimentalist.” Even if you are handed a project concept by your research mentor at the beginning, it will not only be your responsibility to carry it out but you will also need to take it to the next level. Because the very nature of research means that it has never been done before, it often does not go quite as it is planned. Changes in the scope and direction of the research often occur as the research progresses. Sometimes things don’t work out and you have to develop a new path 5.3. GETTING STARTED AND STAYING MOTIVATED 111 forward. If you have been thinking about the research deeply along the way, you may have noted opportunities for other exploratory work or alternative hypotheses. Regardless of how much time you invest and your level of perseverance, there will still be low points. Everyone struggles at some point with either getting started or staying motivated while conducting experiments, coding, writing, etc. This can happen for a variety of reasons. The beginning of a project can feel daunting because you don’t know where to begin or you are afraid you will make a mistake. The middle of a project can feel like chaos sometimes, especially when the direction you had started in does not work out and you have to rethink things. And there can be struggles at the end with just getting that last bit done or writing about what you have already accomplished. These are normal experiences and they are not insurmountable. Often you can get back on track by asking for advice. Turning the Tide In a book I wrote for junior faculty called Survive and Thrive: A Guide for Untenured Faculty [Morgan & Claypool Publishers, 2010] I talk about the challenges of doing creative work like research: “I have come to believe that these ups and downs are a natural part of the cycle of any career that demands creativity. Smart creative people can’t be smart and creative 100 believe that the denial we actively engage in often exacerbates the problem. So, I’ll admit it to you, I have had slumps. For the most part, I too have hidden them from my colleagues. For me, I think it is primarily the fear of being accused of being a fraud—the old “imposter syndrome.” But what I have discovered over the years is that, if I can ﬁnd one trusted colleague that I can feel comfortable talking with honestly and assured in their ability to keep my confessions conﬁdential, the conversation relieves much of the burden and is often enough to turn the tide and give me the means to get myself out of the slump. When I have initiated these conversations, I have also found my colleague telling me “I’ve been feeling the exact same way recently” or “I remember feeling the same way you are now back when.” Knowing you are not alone also relieves some of the self-doubt.” Student Perspective “In a naïve way, I previously believed that if you worked hard enough, progress will always be made. This may be true, but I have learned to gain motivation in the small accomplishments and even the disappointments that end up setting you back on track.” Often people who have not run into serious motivational slumps before are the most challenged because they have not developed strategies to turn things around. It’s also the case 112 5. CONDUCTING RESEARCH that strategies which have previously worked for you in other situations or at other times may fail you at some point. Thus, it is helpful to have a collection of strategies that you can choose from to help you build or regain your momentum. Here are a few to consider. • Use your calendar to block out time for speciﬁc activities. If you don’t actually have time in your calendar for research and you expect to “ﬁt it in” then you need to treat your research time more like an appointment that you must keep. The simple act of spending time on tasks will help you to make progress and get back to a productive trajectory. During these blocks of research time you should be free from distraction (devices oﬀ if possible, no additional screens or popups to distract you). • Break larger tasks down into smaller ones, pick the task that seems easiest and do that one ﬁrst, then take each one in turn. • Create “To Do” lists where you to prioritize critical items and focus on those initially. Using the Project Management strategies are essential (discussed further in the next section), but you may have to break things down into smaller steps and provide yourself with a very speciﬁc, task oriented “To Do” list every day. Be realistic about that you put on the list given the time you have available and pause to take some pleasure in crossing oﬀ an item once it is done. • Team up with a peer working on a similar kind of project and help each other to set goals and keep them. • Sometimes it is as simple as just getting started. Set a timer for 25 minutes. Press start and work until the timer goes oﬀ. After the timer goes oﬀ, take a short break—ideally you will get up and stretch if you have been sitting or sit down and rest if you have been standing, you might also choose to listen to a piece of music or grab a refreshment— but this is also a timed event. Your break should be a short one (3–5 minutes) and then reset the timer for another 25 minutes of work. This is a time management strategy called the Pomodoro Technique and there are apps available, although a simple timer is all that is really needed. The most important thing to remember is that what gets you started and what keeps you motivated is a personal thing. There are a number of diﬀerent factors that may inﬂuence your motivation, including the variety in the tasks you undertake, the ﬂexibility you have in the work, and the level of responsibility you are given. Consider what factors inﬂuence your motivation and you may be able to talk to your research mentor about making modiﬁcation so that you can maximize these aspects. Ultimately, you are responsible for understanding what works best for you to keep moti- vated and then use that strategy. If it stops working, try out a diﬀerent strategy. The ones given above are just a small sample, if this is a topic you want to learn more about, there are plenty of resources available. Consider looking into campus workshops that might be available and books that might be useful to you. I found that The Power of Habit by Charles Duhigg and Drive: The Surprising Truth About What Motivates Us by Daniel Pink to have some interesting and useful strategies. 5.4. PROJECT MANAGEMENT 113 5.4 PROJECT MANAGEMENT Project management generally involves ideas, people, resources, and time. Often in engineering research you are handed an idea as you walk into a project, however, this idea is likely to be incomplete or even contain fundamental ﬂaws that you will only be able to discover as you engage with the research over time. As a result, you will need to manage the ideas as you go— altering assumptions, reframing hypotheses, developing ideas to get yourself around roadblocks. These modiﬁed and new ideas may be ones you generate yourself, or they may be ones that you generate with your research mentor, your collaborators, and/or your research group. For your research project you will need to track and manage these ideas through the evolution of the project and check in with your research mentor about how the ideas are modifying your project over time. Ideas—You will have to manage ideas as they shift and change over time when new information and data become available. Write these ideas down. Forcing yourself to articulate them will help to reﬁne your thinking. Revisit this over time and think about how things have changed with new information you now have. You may in fact have to shift your project or redeﬁne your hypothesis. The ideas themselves have to be actualized by someone—usually you—but often in en- gineering research there is collaboration and teamwork involved. The people involved may be simply you and your research mentor or it may include you, your research mentor, and many other people involved with a large collaborative project. Usually it is somewhere in between— involving you, your research mentor, other students in your research group, and maybe a key collaborator. In some cases it may be as simple as working with another graduate student or technician in the group to learn how to perform a task or us a piece of equipment that you will need. If everyone works with the same research mentor it is often fairly straightforward; in other cases you may need to discuss with your research mentor about how to navigate getting the help you need. A more involved people management aspect of research is working in a more supervisory role, for instance with an undergraduate research assistant. People—The people management aspects of a project involve both managing yourself and the interactions with others you are working with, including your interactions with your research mentor. Take responsibility and determine how best to interact in order to move your research forward. Strive to develop productive working rela- tionships. 114 5. CONDUCTING RESEARCH You may think it is your research mentor’s responsibility to manage you, but it is also your responsibility to manage your relationship with your research mentor. As discussed previously in concepts surrounding “mentoring up,” you need to take ownership in managing this relationship so it is the most productive possible. Also, you need to understand that your research mentor has a broad range of responsibilities and you need to take into account the time they will have available to devote to you. Recognize that the amount of time available and when it is available may not be exactly when it is most ideal for you, so you will need to plan ahead and make adjustments. This means considering their availability for meetings, how quickly they can respond to questions that arise, and how long it will take them to review drafts of your writing. As you progress in your graduate degree program you will have a committee that is made up of several faculty who you will interact with. These individuals may be variously involved with details of your research, evaluation of your progress, your preliminary examination (the written and/or oral exam that determines your readiness to become a dissertator in the Ph.D. program), and the ﬁnal defense of your thesis/dissertation (i.e., the oral presentation you make about your research at the end of your degree program). You should be able to determine the speciﬁc requirements of your degree program and who is involved at each stage from handbook information provided to you by the program and conversations with your research mentor. When working with your committee and scheduling time for key events such as the ﬁnal defense of your thesis/dissertation, you must also take into account their schedules and availability. You will need to know when they will be in town or otherwise available (via phone call, video conferencing, or some other electronic means) and how that relates to the timeframe in which you would like to ﬁnish as well as the deadlines set by your university. It will also be important for you to ensure that you planning timeline provides enough time for them to give you feedback and read whatever written materials you are expected to provide them. This requires advance planning for the semester you expect to complete a major milestone and the semester you plan to ﬁnish your degree. In order to get your project done you will likely need some resources. Even a theoretician, who only uses pencil and paper to do their research, needs resources (e.g., a paycheck). As a principal investigator some day you would have to worry about where the money comes from (i.e., getting grants and contracts) and how to manage the expenditures of money responsibly to get the research project done. As a student you will need to worry about money in a couple of ways too. You need money to live oﬀ of, possibly this comes through the research grant or a fellowship so it is less to worry over, but you may have to do other non-research work like a teaching assistantship that will help to pay your bills and cover your tuition. Needing to earn income through a non-research related position will inevitably cut into the time you spend on research. At some stage you may decide to seek other alternatives like a student loan so there are fewer time constraints. Resources—From personal ﬁnance to the resources required of your research project, you will need to understand the resources available to you. Determine where the 5.4. PROJECT MANAGEMENT 115 funding for your project comes from and what constraints exist regarding that fund- ing (how much is available, what it can be spent on, when it expires, and what pro- posals are being planned for future research funding related to your project). There are variety of diﬀerent kinds of resources that you may need. It may be access to computational or equipment time; it may be samples, supplies and consumables. It may be bench space to conduct the work or lab space to build a structure for your research. Determining what these resources are and their availability will involve a number of questions that your research mentor can help you to answer. These pieces of information will impact your schedule, planning, and time to degree. Student Perspective “I will be writing a substantial amount of code, and I haven’t quite de- cided if I should write it on my personal laptop in an integrated development environment or physically move myself to my oﬃce …. While working on my own computer seems “easier,” it’s probably a more eﬃcient use of time to move myself to a dedicated working environment. With a schedule and place in mind, I hope to condition myself to work well and make a consistent amount of progress on a weekly level.” The aspect of your project that is often in most short supply is time. Your project does not happen in isolation and it is not the only thing vying for your time. Early in your career you are juggling time spent on coursework with time spent on research, not to mention personal time. All are important. Certainly, the coursework and research will both have deadlines and expectations for progress associated with them. At some point in your graduate studies you will likely be done with coursework and “only” have to do your research, but at this point you are likely to have other responsibilities you are juggling too. This may involve supervising and training others in the research group for instance. You will also need to balance the time of doing the research with presenting and writing about the research for conferences, journal publications, or your thesis/dissertation. As you approach the end of your degree you will also need to devote time to ﬁnding the next position—as an undergraduate you may be applying to graduate school, as a graduate student you will be applying to postdoctoral or permanent positions in academia, government labs, or industry. The application and job search processes takes time and needs attention while you are busy ﬁnishing up the degree you are currently working on. Time—Time for coursework, research, and yourself. You need to be a healthy per- son to be an eﬀective researcher. Get enough sleep, exercise, and have time for your family, friends, and a hobby. Being your best at research will be easier if you are a healthy, happy person. You will be more easily able to achieve this if you employ some time management techniques. You also need to communicate about time with your research mentor: your work schedule, your ability to achieve deadlines, your 116 5. CONDUCTING RESEARCH need for modiﬁcation when other obligations and personal needs arise, your plans for vacation, etc. Time on task is a critical component to seeing any project through to completion. But don’t be fooled, just spending lots of time on something does not mean that you are making progress. Not only do you need to monitor the time you are spending, but also how you are spending that time, and if this time if productive. In order to do so eﬀectively, you need a good project plan to guide the use of your time and measure your progress against. Student Perspective “In my opinion, to be a successful researcher you don’t simply need to produce good research (obviously a huge plus), but you need to do it eﬃ- ciently. Splitting projects up into manageable chunks not only made it seem less daunting, but also saved me a signiﬁcant amount of time in the long run. Putting in the eﬀort to lay out a solid plan before doing the work will save a lot of time, allowing me to focus on the diﬃcult tasks. Writing down my thoughts in a notebook will save time by not having to produce the same thought twice, or completely wasting time by forgetting the thought alto- gether. Similarly, learning to be more consistent about writings will save time in the same way. Finally, as I continue to grow as a researcher, I’ll need to learn when to cut my loses and switch the direction of a project. Every re- searcher, good or bad, will reach a point where they need to change a project; a good one will be eﬃcient and not waste time trying to save the idea.” In a section titled “Professional Success: Project Management” author Prof. Mark Horen- stein of Boston University gives three “Laws of Time Estimation”4: 1. “Everything takes longer than expected.” 2. “If you’ve worked on something similar before, estimate the amount of time required to ﬁnish the task. The actual amount of time required will be about four times longer.” 3. “If you’ve never worked on something similar before, estimate the amount of time required to ﬁnish the task. The actual amount of time required will be equal to the next highest time unit. (For example, something estimated to take an hour will take a day; something estimated to take a day will take a week, etc.)” Although you might think that these “Laws” are an exaggeration, they can actually ﬁt reality better than you expect. Certainly, in research it is often true that it takes longer to ac- complish what you set out to than you would have anticipated. When by deﬁnition you are 4Horenstein, M. N., 1999. Design Concepts for Engineers, Prentice Hall, Upper Saddle River, NJ, p. 86. 5.4. PROJECT MANAGEMENT 117 doing something that has never been done before, it can be very challenging to judge how long it will take! Even for the mundane everyday tasks that you will have to handle, you probably already appreciate from experience that you have to give yourself some cushion. Back in the day when I had a paper calendar where all of my appointments, deadlines, and tasks were written, the ﬁrst page contained the following quote from an anonymous source: “WARNING—Dates in calendar are closer than they appear!!” I found it often to be true, particularly when working on an immovable deadline for a research proposal. However, this does not mean that we should throw all planning out the window. In fact, planning is what makes it all more manageable. 5.4.1 PROJECT MANAGEMENT TOOLS Often what is critical in project management is not simply understanding all the components of a project, but how they relate to and are dependent on each other. In a research setting this is important whether the work be experimental, analytical, theoretical or some combination. It may also be the case that your project is dependent on other projects or a part of a larger eﬀort involving a number of other researchers. In that case you would not be responsible for the overall project management, but you would still have to manage the aspect you are responsible for and meet the necessary deadlines so that the rest of the project can go as planned. The project must also not be over-constrained.5 In other words, the scope must be within your capabilities (or, more likely, the capabilities you will be developing); the resource require- ments must be within the budget, equipment, and facilities available; and the schedule must be reasonable, given the amount of time you are able to invest in your research. In order to fully understand your project and develop a project plan there are a some basic steps that you can take.6 1. First, clearly identify the project with a succinct problem statement. 2. Identify the tasks that will need to be accomplished in the course of the project with as much speciﬁcity as possible. Deﬁne speciﬁc milestones for the project that will allow you to measure your progress. 3. State the objective of each task so that its purpose is clearly delineated. You can think of these as deliverables. 4. Identify the people who will be involved with each task. You may perform some of them independently, but other tasks may require the participation of others (e.g., training), or rely on someone else to provide you something in order to complete the task. 5Kendrick, T., 2009. Identifying and Managing Project Risk: Essential Tool for Failure-Prooﬁng Your Project, 2nd ed., Amer- ican Management Association, New York. 6Adapted from Ullman, D. G., 2003. The Mechanical Design Process, 3rd ed., McGraw Hill, Boston, MA. 118 5. CONDUCTING RESEARCH 5. Estimate the time it will take to complete each task and identify the distribution of the time across diﬀerent phases of the project. 6. Estimate the funding, equipment, computing time, or other resources that will be required to complete each task. 7. Identify the sequence of the task, noting interdependencies between tasks (precessors and successors). Note which tasks can be done in parallel. Identify any externally imposed deadlines. A number of tools are at your disposal. The most basic is a simple timeline. You have a target end date to work toward and various milestones to meet along the way. An example is given in Figure 5.2. However, a simple timeline does not provide information about how one might be working on multiple objectives simultaneously or show how long each task will take. A Gantt Chart, like the one shown in Figure 5.3, provides additional information about when project activities are occurring and shows how they overlap. Additional modiﬁcation to the Gantt Chart can also indicate dependencies and relationships between items, e.g., data must be collected before analysis can be undertaken, but to fully explore the interdependencies, you may want to create a structure matrix like the one shown in Figure 5.4. Each task is assigned a letter name and each row of the chart identiﬁes the other tasks on which each one is dependent. At some point, however, you must stop planning and start doing. The fact is, no matter how much time and eﬀort you put into your planning, some changes will inevitably arise. Your ability to handle these changes and quickly develop a revised plan will depend on the thorough- ness of your original planning eﬀort, built in cushion within the plans, and ﬂexibility with at least one of the constraints of scope, schedule and resources. As Kendrick summarizes, “Your primary goal in managing project constraints is to remove, or at least minimize, the diﬀerences between the project objective and your project plan, in terms of scope, schedule, and resources.7” ASSIGNMENT 5-4: INDIVIDUAL ASSIGNMENT – COURSEWORK TIMELINE Create a timeline for completion of the coursework you have remaining in your degree program. 7Kendrick, T., 2009. Identifying and Managing Project Risk: Essential Tool for Failure-Prooﬁng Your Project, 2nd ed., Amer- ican Management Association, New York, p. 128. 5.4. PROJECT MANAGEMENT 119 Figure 5.2: A simple timeline identifying critical milestones in a ﬁctitious Master’s degree re- search project. September, Year 1• Identify a research project• Complete training on necessary equipment/software• Complete design of test rig• All test rig components on site and construction underway• All design modiﬁcations complete• Validation experiments on test rig complete• All data collection runs and analysis complete• First run of data collected• Data analysis complete• Update literature search• First draft of thesis handed to research advisor• Revisions of thesis complete• Thesis provided to committee members• Oral thesis defense• Written thesis document deposited• First literature search complete• Provide project proposal outline to research mentorNovember, Year 1December, Year 1February, Year 1April, Year 1June, Year 1February, Year 2March, Year 2April, Year 2May, Year 2July, Year 1August, Year 1120 5. CONDUCTING RESEARCH Figure 5.3: A Gantt Chart showing when activities in the time line are occurring. Year 1Year 2MonthASONDJFMAMJJASONDJFMAMIdentify a research projectLiterature searchProvide project proposal outline to research mentorTraining on necessary equipment/ softwareDesign rest rigOrder test rig componentsAll test rig components on site and construction underwayDesign modiﬁ cationsValidation experiments on test rigFirst run of data collectedData analysis on ﬁ rst runRemaining data collection runs and analysisUpdate literature searchTh esis writingFirst draft of thesis to research advisorTh esis revisionsTh esis provide to committee memberOral thesis defenseWritten thesis document deposited5.5. SCHEDULING COMMITTEE MEETINGS 121 Figure 5.4: A structure matrix showing the interdependencies of project tasks. ASSIGNMENT 5-5: INDIVIDUAL ASSIGNMENT – RESEARCH PROJECT GANTT CHART Develop a Gantt Chart that will help you to plan and complete your research project by the deadline you have chosen. Consider all competing demands on your time, such as your course- work requirements. Consult your research mentor with a draft version and seek input about whether or not your planning is reasonable. 5.5 SCHEDULING COMMITTEE MEETINGS It’s likely that you have a busy schedule on a day-to-day basis given your courses, research, and other personal obligations. The faculty members you interact with also have busy schedules and are usually quite busy at just the time of year that you may need their time and attention most. With your research mentor it is ideal to have regular times when you have the opportunity to interact so that you do not need to schedule each individual meeting that you two will have. Your interactions with other faculty will require individual scheduling of meetings and in the case of a committee meeting, it will require juggling the availability of multiple very busy people. In these cases, it is critical to plan ahead. If you know you will need to give an oral presentation to your committee in order to complete your degree requirements in the last two weeks of the semester, then you should start the planning process more than a month in advance so that you are certain you can ﬁnd a time when everyone can meet. There are a variety of strategies to go about this planning process, but I think the smoothest interactions take place using the following steps. • Consult any degree deadlines that apply and ensure that you know when the latest acceptable meeting date will be. TASKABCDEFGDesign test rigAAOrder test rig componentsBXBXTest rig constructionCXXCDesign modiﬁ cationsDXDXValidation experiments on test rigEXXEFirst run of data collectedFXFData analysis on ﬁ rst runGXG122 5. CONDUCTING RESEARCH • With the guidance of your research mentor, determine what weeks would be appropri- ate for the meeting/presentation and identify the length of time that you will need to schedule (this could be anywhere from 1–3 hour time block depending on the speciﬁc circumstances). • Contact the individuals on your committee independently (by email or a personal visit to their oﬃce) to determine which dates they will be in town and generally available during the target time frame that you are interested in. • Compare their availability to your own and make a list of all the potential time blocks that ﬁt all the criteria. • Using a scheduling tool such as Doodle or WhenIsGood can be helpful in narrowing down workable options. Alternatively, you can list the potential day/date/times in an email and request they respond with all options that will work for their schedule. • The above steps should be undertaken as quickly as possible because as time passes more and more obligations will ﬁll up your research mentor’s and committee members’ calendars. If someone does not respond to an email request, go to their oﬃce to ask about their availability. • If your scheduling attempt does not work the ﬁrst time, you will have to start over again and identify diﬀerent dates with your research mentor. If that is not an option, it may be possible to have one member join the meeting by phone or video conference call if they are out of town, or have you meet with them independent from the remainder of the committee. If none of these options work you may have to determine if a committee member can be substituted with a diﬀerent person. For all these reasons, it is a very good idea to start the scheduling process early. 5.6 NAVIGATING ROADBLOCKS AND OBSTACLES Inevitably there will be roadblocks and setbacks. I can’t think of a single research project that did not have at least small issues arise. It is the fundamental nature of research, particularly as you investigate areas that are at the cutting edge of a ﬁeld. You may ﬁnd it helpful to not only keep your overall research goal in mind, but also to break this large goal down into smaller sub-goals that you can more easily focus on when you run into bumps and hurdles. Research can create more unknowns in the initial planning process and therefore more points at which the plan must be revised. In some cases, the constraints are quite hard. For example, when working on a research contract, certain deliverables are expected within a speciﬁc time frame. The time frame might be modiﬁable, but usually the deliverables are quite ﬁxed in nature. In other more open-ended research projects, there may be more room for modiﬁcation of the research objectives, particularly if preliminary ﬁndings uncover what has the potential to 5.6. NAVIGATING ROADBLOCKS AND OBSTACLES 123 be a more fruitful line of inquiry. Even if you are not able to pursue these new ideas right away, it is helpful to write them down so you can explore some of them later or use one as a basis for a new research proposal. It is important to always be open to opportunities, especially when faced with challenges. “Opportunity management also may result in a more interesting, more motivating project….8” Student Perspective “My proposal had very lofty goals, and I knew that from the outset. I was upset on my progress at ﬁrst, but now I realize that for every problem I run into, I’m learning more and more about the subject matter. The whole “if at ﬁrst you don’t succeed…” motto has some clear consequences …. I know now that the full scope of my proposal will not be represented in my ﬁnal product.” In some cases, you will have to re-propose or re-negotiate your project with your research mentor, but you can do so in a way that sets you up for success. To do so, you must develop a revised plan with an appropriate scope, resources, and schedule which will allow you to accom- plish the research. Before deciding to simply reduce the scope, think creatively about how the scope might be shifted to take advantage of what you now know about the project. If reducing the scope is still required, determine the essential outcomes of the research before making any cuts. When considering resources, think creatively about what other resources might be avail- able to you. Examples range from applying for a small seed grant to ﬁnding an assistant to take some of the work burden. Schedule modiﬁcation will require a careful analysis of critical path activities and interdependencies in the project. Additional aspects of the project may need to be conducted in parallel and/or some time frames tightened up to allow for more ﬂexibility in a diﬀerent part of the schedule. Research is inherently challenging because you are trying to do something that has not been done before. You will inevitably run into roadblocks and obstacles and have to think of creative ways to get around, over, or through them. This is fundamentally a part of the process and sometimes these obstacles can be the very thing that lead you to an unexpected and fruitful outcome. Student Perspective “The most surprising thing that I learned about research this year was that research could be easily delayed by sudden problems in the laboratory. One of the largest aspects that research deals with is getting the research systems to not only work, but to work continuously over a certain period of 8Kendrick, T., 2009. Identifying and Managing Project Risk: Essential Tool for Failure-Prooﬁng Your Project, 2nd ed., Amer- ican Management Association, New York, p. 133. 124 5. CONDUCTING RESEARCH time. Working in a research lab on campus has shown me the multitude of failures in machinery, computer code, and other systems that can slow down the eﬃciency of a lab and delay the research mission. A failure in a critical system of the experiment could stop work in the entire laboratory until the problem with that one system is addressed. I believe that a lot of people have misconceptions about the research process, and they believe that scientists and engineers just turn buttons inside of a control room and research hap- pens. Being exposed to research on campus, has shown me the “dirty” side of research, where hours upon hours are spent ﬁxing machine failures, de- signing new systems to replace faulty processes, and brainstorming how to ﬁx a problem that you encounter that you originally thought not possible…. While, these problems can prove detrimental to the research mission, I be- lieve that experiencing and overcoming these problems is one of the general responsibilities of being an engineer in research. Encountering problems al- low you to design new more eﬃcient systems; as well as take a step back and think about your research in a diﬀerent way.” Consider the following challenge as an example that came up in my own research group a few years ago. The supplier we had used previously to make a photolithographic master changed its focus and was no longer supplying what we needed. Having a new master was a key compo- nent that we required in order to test out a new design critical to the successful completion of our project. We had to look for options and develop a plan to ﬁnd a way to have a new master made and do the experiments we had planned. In our lab we use the photolithographic master to make polydimethylsiloxane (PDMS) stamps that can transfer a protein pattern onto a substrate. This allows us to seed and culture cells in speciﬁc pattern designs. The basics of the process are illustrated in Figure 5.5. How could we get a new photolithographic master made? First, we considered both oﬀ- campus and on-campus sources. We looked for a new commercial supplier—a Google search can be helpful if you know the right words to search on, but it can also be helpful to look at recently published journal articles using the same technique to determine who their supplier was. We quickly found two potential commercial options and began to make inquiries about whether they could meet our speciﬁcations and how much the cost would be. While doing this, we also wondered if there was another lab on campus using the same method. We turned to the professional network of our research group to see if one of us knew someone who could help. It turned out that one of my students knew a student in another lab who was doing something similar—their research mentor was a colleague of mine, so it was easy to ask for advice. They made something similar in their lab and oﬀered to try to make what we needed. Additionally, we thought about whether this was something we could easily make ourselves. There are methods 5.6. NAVIGATING ROADBLOCKS AND OBSTACLES 125 Figure 5.5: Use of a photolithographic master to create patterned stamps for protein transfer onto a substrate and subsequent cell growth on the protein. Figure 5.6: Do-it-yourself approach to creating a photolithographic master. published in the literature and we could purchase the photolithographic master solutions. A sketch of our do-it-yourself approach is shown in Figure 5.6. We quickly ended up with several options: two potential commercial suppliers, a colleague willing to try to help us out, and a method for how to approach it if we decided to make it ourselves. What had seemed like a big obstacle—the loss of a supplier for a critical research component—had turned into a solvable problem! In the end we tried one from our colleague’s lab, but it did not quite work with our subsequent processing steps, so we used one of the other SiWaferPolymerize PDMS on top of patternPDMSStampProteinStampSubstrate totransfer proteinSeed cells ontop of protein patternμ scale patternsSiWaferdevelopphotoresistPhotoresistUse a commercial printerto make a high-restransparency1,000 dpiSpin coat photoresistto desired thicknesstRPMUVDIY126 5. CONDUCTING RESEARCH commercial suppliers and the roadblock was cleared. There are several lessons to take away from this example: there is often more than one solution to a problem; there is often more help with an issue than you might have initially suspected; and pursuing multiple paths simultaneously may produce alternatives for you to choose from. ASSIGNMENT 5-6: GROUP DISCUSSION – FINDING THE RESOURCES YOU NEED You have discovered that the key to your research is getting access to a “Widget Measurement Device.” It is critical to the successful completion of your project but your research group does not have one. Develop a plan to ﬁnd such a device and get the measurements you need. Consider the following questions. • How would you go about ﬁnding such a device? • How can you get access? • What if it does not exist on campus? • If you have to borrow someone else’s widget, what can you give in return? ASSIGNMENT 5-7: INDIVIDUAL ASSIGNMENT – OPPORTUNITY MANAGEMENT Reconsider your research plan in light of an actual or imagined roadblock and look for alternate opportunities. 5.7 RESEARCH ETHICS (ERROR, NEGLIGENCE, MISCONDUCT) Research is conducted by human beings, so human failings inevitably enter into the picture. Sometimes the failing at play is simply error: people make mistakes. The deﬁning moment is when you discover the error and decide what to do about it. Unfortunately, sometimes an other- wise honest person might be inclined to hide the error, which is the big mistake. The temptation to hide it may come from feelings of shame or concern over the repercussions but hiding an er- ror crosses the line between making a mistake and being dishonest. In my own research group, I stress with students that it is critical for them to let me know when they make a mistake or discover an error. The sooner we know about it, the sooner we can resolve things. For instance, 5.7. RESEARCH ETHICS (ERROR, NEGLIGENCE, MISCONDUCT) 127 if a piece of equipment gets broken accidentally, we want to know right away so we can repair it before it is needed again, and we’d like to determine what went wrong so we can prevent it from happening again. If the error occurred in how an experiment was run for instance, we want to know as soon as that comes to light so that we can determine the best course of action mov- ing forward, e.g., repeating the experiment using the correct protocol and revising our training procedures so that this type of error does not happen in the future. If the error ends up not getting caught until after publication of the results, there is still an opportunity to ﬁx things. Journals publish errata to correct errors discovered after publication and corrigenda to correct errors made in the publication process (like a typographical error in an equation). In the most extreme cases, when the results and conclusions are signiﬁcantly altered by the issue, the article may be withdrawn from publication if the editor(s) agree that this is the best course of action. You may think this is a horrid outcome, but your scientiﬁc colleagues would rather know that the error exists than to base their ongoing work on something that is ﬂawed. It will waste your time and waste the funding supporting your research if you pursue a path that someone has discovered is wrong but has not made the eﬀort to report it. When Prof. Pamela Ronald discovered that two papers had incorrect data and conclusions because of lab errors associated with the mislabeling of a bacterial strain and an unreliable protein assay, she decided to announce it publicly at a Keystone Symposia Meeting and retract the papers.9 Her colleagues applauded her forthrightness about the issue. Honest mistakes happen, and they should be acknowledged when they are discovered. “Scientists who make such acknowledgments promptly and openly are rarely condemned by colleagues.10” In the hierarchy of bad things happening, negligence falls somewhere between error and misconduct. Haste, carelessness, and inattention must be treated more harshly than an error. In the case of negligence someone is cutting corners. This is not good science, and the outcomes may have very negative ramiﬁcations for engineering research broadly. Money, structures, and people’s lives may be put at risk. On the professional side, not only is the negligent individual placing their own reputation at risk but they can also damage the reputations of their colleagues and researchers as a whole. Further, “By introducing preventable errors into science, sloppy or negligent research can do great damage—even if it is eventually uncovered and corrected.11” Sometimes we don’t realize that there was a problem until we try to repeat the work later. In an anonymous survey of National Institutes of Health researchers, 6% of the respondents admitted to “Failing to present data that contradict one’s own previous research.12” This is really problem- atic. Even though you and others are reading the literature critically, everyone is relying on that prior research so that they can build upon it. 9Grens, K., 2015. Self correction: What to do when you realize your publication is fatally ﬂawed. The Scientist, December, 29(12). 10On Being a Scientist: Responsible Conduct in Research. National Academies Press, 1995. 11On Being a Scientist: Responsible Conduct in Research, National Academies Press, 1995. 12Martinson, B. C., Anderson, M. S., and De Vries, R. 2005. Scientists behaving badly. Nature, 435.7043, 737. 128 5. CONDUCTING RESEARCH Misconduct is when the action crosses into the realm of intentionally deceptive. “Making up data (fabrication), changing or misreporting data or results (falsiﬁcation), and using the ideas or words of another person without giving appropriate credit (plagiarism)—all strike at the heart of values on which science is based.13” A meta-analysis conducted by Daniele Fanelli “…found that, on average, about 2% of scientists admitted to have fabricated, falsiﬁed or modiﬁed data or results at least once—a serious form of misconduct by any standard [10,36,37]—and up to one third admitted a variety of other questionable research practices including ‘dropping datapoints based on a gut feeling,’ and ‘changing the design, methodology or results of a study in response to pressures from a funding source.’14” So why do people do it? The heart of the matter is that research can involve “…intense competition, and is further burdened by diﬃcult, sometimes unreasonable, regulatory, social, and managerial demands.15” But the consequences of succumbing to the temptation can be severe. In many of the public cases reports, careers have been ruined. In some cases people have even gone to prison.16 For students, I ﬁnd that their choice to undertake an act of misconduct is frequently an issue of time. Things don’t go as planned, it takes longer than anticipated, deadlines are ap- proaching, graduation is near, a job is waiting……. then someone gives into the temptation to cut corners by fabricating, falsifying, or plagiarizing. Maybe they did it before and got away with it the ﬁrst time, or even the second time, but at some point these indiscretions will get caught. What then? It can be career ending. Years of eﬀort invested are now wasted. As an example, discovering plagiarism in one Mechanical Engineering master’s thesis, led to Ohio University to conduct a broader investigation and ultimately “…taking action against 39 mechanical en- gineering graduates…. It has ordered them to address plagiarism allegations involving theses dating back 20 years or risk having their degrees revoked.17” In some cases, the consequences can be absolutely tragic. The work and research that engineers do is intrinsically connected to society and often directly related to safety, healthy, and environmental issues. 13On Being a Scientist: Responsible Conduct in Research, National Academies Press, 1995. 14Fanelli, D., 2009. How many scientists fabricate and falsify research? A systematic review and meta-analysis of survey data. PloS One, 4(5):e5738. 15Martinson, B. C., Anderson, M. S., and De Vries, R., 2005. Scientists behaving badly. Nature, 435.7043, 737. 16Rogers, G., 2014. Former ISU scientist who faked AIDS research indicted, Des Moines Register. https://www.desmoinesregister.com/story/news/crime-and-courts/2014/06/19/former-isu-scientist- who-faked-aids-research-indicted/10881781/. 17Tomsho, R., 2006. Student Plagiarism Stirs Controversy At Ohio University, Wall Street Journal. https://www.wsj.com/articles/SB115560632839035809. 5.7. RESEARCH ETHICS (ERROR, NEGLIGENCE, MISCONDUCT) 129 Most engineering professional organizations have a code of conduct for their members. The National Society of Professional Engineers (NSPE) Code of Ethics for Engineers includes the following Fundamental Canons.18 “Engineers, in the fulﬁllment of their professional duties, shall: • Hold paramount the safety, health, and welfare of the public. • Perform services only in areas of their competence. • Issue public statements only in an objective and truthful manner. • Act for each employer or client as faithful agents or trustees. • Avoid deceptive acts. • Conduct themselves honorably, responsibly, ethically, and lawfully so as to enhance the honor, reputation, and usefulness of the profession.” These seem sensible. Engineers should make the world around them a better and safer place for the beneﬁt of society. If you keep this underlying motivation in mind as you conduct your engineering research, you will be much more able to do it in an ethical manner. 5.7.1 MISCONDUCT CASE STUDIES AND THE D.I.S.O.R.D.E.R. FRAMEWORK Lisa Newton, Professor of Philosophy and author of Ethics in America proposes a decision pro- cedure for dealing with ethical dilemmas that I ﬁnd very useful in applying to both case studies and real-life situations. The basic approached is summarized.19 “…as participants and decision makers, we should organize our options in the situation—what alternatives are really open to us? and note the probable outcomes of each. What, in this situation, is it possible, and reasonable, for us to do? And what will be the likely results of each of those choices? Which of the outcomes on the list are totally unacceptable? They should be eliminated, and the rest left for further consideration at a later stage.” The acronym developed by Newton is D.I.S.O.R.D.E.R. where we: Deﬁne the dilemma we are trying to address, investigate or identify the necessary information, identify all of the stakeholders that are impacted by the dilemma, explore the options available to us, spend time considering the rights and rules associated with the issue and the individuals involved, make a 18National Society of Professional Engineers, “Code of Ethics,” http://www.nspe.org/resources/ethics/code- ethics. 19Newton, L. H., 2002. Doing Good and Avoiding Evil, Part I. Principles and Reasoning. http://www.rit.edu/ \simw-ethics/resources/manuals/dgae1p6.html. 130 5. CONDUCTING RESEARCH decision or determination about what actions should be taken, then evaluate the eﬀects that will likely be a consequence of that decision, and at the end take time to review and reconsider to make sure we have made a decision that is reasonable. The D.I.S.O.R.D.E.R. frameworks provides a logical and yet ﬂexible decision making procedure that can be used in a variety of situations. In applying the disorder framework we focus on the options available, the rights and responsibilities of the parties involved, making a preliminary decision, considering what the eﬀects of that decision will be, and then reconsidering. It is intentionally an iterative process that asks you to do the thought experiment of what will happen as a consequence of the decisions that you take, and then to reconsider the situation with those ideas in mind. Once you have been through the O.R.D.E.R. portion of the framework at least twice you have probably gotten to the point where you have settled on a reasonable course of action where the probable results are in alignment with the ethical quandary being and dealt with. Let’s practice by considering a simple case example that came up a number of years ago in a class I taught. The students were assigned to write a review paper. The ﬁrst draft went through a peer review process with the other student colleagues in the class serving as the reviewers. When reading the paper he was assigned to review, one of the students went to Wikipedia to read some more background on the topic because it was unfamiliar to him. However, in the process he discovered that two paragraphs of the paper’s introduction were directly copied from Wikipedia by the author of the paper. Quotations were not used and Wikipedia was not cited. Let’s apply the D.I.S.O.R.D.E.R. framework to this case. First, what is the student’s dilemma? He suspects plagiarism and must decide what to do. He’s eﬀectively already done part of the investigation by determining that there was copying from Wikipedia, but he might also want to check the syllabus and/or the University deﬁnition of plagiarism to see if this situation ﬁts. In this case it certainly ﬁts the deﬁnition of plagiarism without question—the paper’s author has tried to pass oﬀ the work of someone else as their own. It does not matter if it is freely available on the internet, the author did not use quotes or paraphrase the source by putting it in their own words, and author did not cite the source. Who are the stakeholders? Clearly the author of the draft that is being reviewed is a key stakeholder, but so is the student who has identiﬁed the suspected plagiarism. The instructor for the course is an obvious stakeholder, but also the other students taking the course are stakeholders too because they are all expected to do the same assignment. More broadly, you would consider the University as one of the stakeholders as well. The student who discovered the plagiarism has a few options available—say nothing, say something to the author, or say something to the instructor. If he looks into the University of Wisconsin-Madison policy that spells out the rules associated with academic integrity, he will see that the University states that “Students are expected to uphold the core values of academic 5.7. RESEARCH ETHICS (ERROR, NEGLIGENCE, MISCONDUCT) 131 integrity which include honesty, trust, fairness, respect, and responsibility.20” With this in mind, the “say nothing” option could potentially jeopardize him, so that does not seem like a good op- tion. Alternatively, he could decide to talk with the author and clarify the University policies on plagiarism, but this is not really his job and it could result in a backlash from the other student that may be challenging to handle. In fact, the University website on “Academic Integrity” goes on to say that “As a member of the UW-Madison community, it is your responsibility to help up- hold the integrity of the university. If you suspect a classmate is cheating or committing another type of academic dishonesty, notify your instructor, professor, or teaching assistant. Remember that it is not your responsibility to investigate this. It is the job of the instructor to determine if misconduct occurred. All you need to do is report what you heard or saw.” After reviewing and reconsidering the options, the student who conducted the review decided that the best course of action was to contact the instructor who then went on to take actions in accordance with University policy. ASSIGNMENT 5-8: GROUP ACTIVITY – AN ETHICS CASE STUDY ON DATA FABRICATION Consider another case study that will allow you to further apply the D.I.S.O.R.D.E.R. frame- work. Many years ago a colleague contacted me about one of their students asking for my thoughts on what actions they could and should take in a suspected research misconduct case. My colleague had a student who was working to ﬁnish their Ph.D. and had given a draft chap- ter of their dissertation to my colleague, their advisor, for review. Some of the data presented in the chapter looked odd and drew the suspicion of my colleague. He decided to take a look at the raw data ﬁles that are kept by the instrument that was used to take the measurements in question. Upon investigation he found that although the instrument ﬁles corresponded to some of the data presented in the chapter, large portions of the data had no corresponding ﬁles on the instrument. He suspected that some of the data presented in the chapter had been fabricated. Apply the D.I.S.O.R.D.E.R. framework to this situation. The dilemma is deﬁned as data fabrication. The advisor has already found some information about the extent of the data fabri- cation, but more information is needed about the potential ramiﬁcations associated with what the student has done. Begin by determining your institution’s rules about research misconduct, in particular, data fabrication. Assume that the research was conduced with federal funding, choose an agency (such as the National Institutes of Health or the National Science Founda- tion) and determine what their relevant policies say. Continue through the D.I.S.O.R.D.E.R. framework by identify all of the stakeholders and exploring the options, being sure to pay at- tention to the rights of the student and rules of the institution and agency involved. Once you 20Oﬃce of Student Conduct and Community Standards, University of Wisconsin-Madison, “Academic Integrity,” https://conduct.students.wisc.edu/academic-integrity/. 132 5. CONDUCTING RESEARCH have all of this information, make a decision about what actions should be taken, then evaluate the eﬀects that will likely be a consequence of that decision. You may ﬁnd the that outcome is more severe or more lax than you expected. This is the time to review and reconsider so you can make sure that you have come to a decision that is reasonable. Repeat the O.R.D.E.R. portion of the framework and settle on a reasonable course of action. 5.7.2 OTHER RESOURCES ON RESEARCH ETHICS Although this chapter touches on some key issues of research ethics, this is a broad ﬁeld of study and one that entire books are devoted to. For additional reading on research ethics, the following references are suggested. National Academy of Sciences, N. A., 2009. On Being a Scientist: A Guide to Responsible Conduct in Research. National Academies Press (U.S.). Shamoo, A. E., and Resnik, D. B., 2009. Responsible Conduct of Research. Oxford Uni- versity Press. Lipson, C., 2019. Doing Honest Work in College: How to Prepare Citations, Avoid Pla- giarism, and Achieve Real Academic Success. University of Chicago Press. 5.8 SAFETY From the basic ergonomics of your work environment to the issues that arise from the need to use dangerous substances, safety is a critical issue in your research environment. Even if you are not conducting experimental work yourself, it is likely that there are labs down the hall, on the next ﬂoor, or someplace in the buildings you frequent. Make sure that you know how to respond when something dangerous occurs that may impact your own safety and the safety of others. Basic building safety features are the ﬁrst thing to become acquainted with. You should determine where the emergency exits are located, where to go in the case of a ﬁre, how to respond in the case of a natural disaster, and what actions your campus recommends in the case of an active shooter. Pay attention to drills and take part in training opportunities. Be observant about the spaces that you inhabit—read the signage and identify safety equipment that is readily available (e.g., ﬁre extinguishers, automated external deﬁbrillators, emergency sowers, eye wash stations, etc.). You may not be using chemicals, operation lasers, or interacting with radiation sources, but this might be a regular activity in a lab down the hall, so be sure to note any signage about hazards near your work environment. Identify the location of phones for emergency calls—your cell phone may be most accessible but if a land line is readily available, use it. The location of the call can be more easily identiﬁed. In the realm of experimental research, the potential dangers are myriad: chemical splashes, particle inhalation, burns from heat sources, etc. If your research is conducted in a laboratory or ﬁeld environment, you will be required to take part in standard training associated with the 5.8. SAFETY 133 common safety hazards and you will likely receive speciﬁc training on procedures you will use so that you understand and can handle the speciﬁc safety hazards. Training is essential and should occur BEFORE you begin in the research so that you know how to protect yourself and others, prevent hazardous situations from arising, and respond appropriately if a safety issue occurs. If you are not oﬀered training, you should request it. If for some reason it is not readily available, seek out the information and educate yourself. One of the keys to keeping a safe work environment is to ensure that the entire environ- ment is a safe one, not just the area and materials that are directly your responsibility. If you see something, say something. If you notice another person in the lab doing something that puts them or others in danger, talk to them immediately. If you see a way to improve safety around a piece of equipment or standard procedure, talk to your research mentor or the laboratory man- ager. You should also make sure you know who to call if you see an unexpected problem, e.g., water leaking from under the door across the hall, or a noxious smell emanating from another laboratory. On most campuses each building will have a building manager or safety oﬃcer. Labs will have an emergency contact sheet on the door that also includes contact information. But, if in doubt, call emergency services using 911. There are even health concerns sitting at your desk. You may spend much of your research time in front of a computer—coding, collecting data, analyzing data, and writing. It is important to have a setup that is ergonomic so that you do not develop issues over time—such as back or neck pain, carpel tunnel syndrome, etc. Maintaining the health of your eyes is also important. Eye strain is also something to guard against if your time in front of a screen is lengthy. ASSIGNMENT 5-9: INDIVIDUAL ASSIGNMENT – YOUR OWN SAFETY Determine the three main safety issues relevant to your daily workspace. Investigate them in more detail to determine: What protections have been put in place to mitigate the safety haz- ards? What are your responsibilities with relationship to these safety issues? How can safety be improved and what actions can you take to suggest these improvements or make these improve- ments yourself? 134 5. CONDUCTING RESEARCH ASSIGNMENT 5-10: INDIVIDUAL ASSIGNMENT – CASE STUDY Instructions: Read the brief case description provided. Reread while noting the important information, and questions that are raised in your mind about the information provided, the individuals in- volved, and their situation. Determine both the basic issues and any deeper underlying issues at play. Consider the questions posed at the end of the case and how you would respond to these questions as well as other questions that could be asked of this case. Write a one-page response that includes a brief summary of the case and its issues, your answer to the questions posed, and recommendations based on your understanding of the situation posed in the case. Case description: Mary has done an excellent job in navigating the safety issues associated with her research project and is recognized in her research group for being adept with the logistics of handling both the day-to-day safety issues and the associated campus requirements. She is also a student member of a newly formed safety committee in her department which meets several hours every month. Her work on the committee has been helpful to her research group because Mary makes sure that they all stay up to date on the safety issues relevant to their work. Dr. Smith, her research mentor, has recently taken on a new project and has already in- dicated that Jonah, a ﬁrst year graduate student, will use this project for his thesis. The project is a very interesting one, but it will involve some new safety requirements and consultation with campus safety experts before it can be started. However, instead of having Jonah coordinate the safety requirements of the new project, Dr. Smith has asked Mary to take the lead. Questions to consider: Is it reasonable for Mary to take on this duty? Is it possible for Mary to say “No” in the situation? Will Jonah’s lack of involvement have the potential to compromise safety? How might Mary work with Jonah to get safety issues of the new project coordinated without overloading herself? C H A P T E R 6 135 Documenting Your Research Findings 6.1 KEEPING A RESEARCH NOTEBOOK Several decades ago, when I worked in the medical device industry, the engineers spent the end of each day signing and dating their lab notebook pages and proving witness signatures as a cognizant individual on the notebooks of other engineers. When your notebook was full you turned it back to the company librarian and were assigned a new one. If you needed to reference one of your old notebooks you could check it back out again. These procedures were in place for data management and patent protection. Your clever ideas could result in patentable work and the signed, witnessed, and dated pages of your lab notebook might be used to prove that you were the ﬁrst to come up with the invention. In 2013 a new patent law change went into eﬀect in the U.S., moving patent priority from ﬁrst-to-invent to ﬁrst-to-ﬁle, however well-kept research documentation is still critically important today. These lab notebooks, or research notebooks as I will call them, are an important tool for every researcher, whether an experimentalist, computationalist, or theoretician. The research notebook provides a place for you to document your thinking, your results, and your conclusions. These days your notebook make take the traditional form of a bound paper laboratory notebook or it may be an electronic document (or some hybrid form). If you have joined a research group, ﬁnd out the practices of the group. The researcher in charge of the project (i.e., the principal investigator, or PI) may provide you with a physical notebook or give you an account to an electronic notebook. If not, it may be up to you to decide what format works best for you. Student Perspective “I work mainly on the computer and did not really understand how I could possibly keep track of anything outside of the digital medium. Af- ter looking at examples of lab notebooks in class and discussing what makes a good lab notebook I realized that my thought process and various other things to organize my thoughts and results could ﬁnd a place in my note- book.” Ultimately though, it is common practice that the notebook will stay with the research group when you move on to your next position. This may be a requirement of the funding agency 136 6. DOCUMENTING YOUR RESEARCH FINDINGS supporting the research on which you are working or an aspect of a broader data management plan of the research group or institution. You may be allowed to keep a copy for yourself (for instance a scan or photocopy of a paper notebook or a duplicate copy of an electronic notebook). The obvious exception to this would be if you are working on a classiﬁed project or working for a company where the intellectual property is owned by the company. Although you are likely the primary person who will read this notebook other than your research mentor, keep in mind that it needs to be readable by others and this must be kept neatly and completely. Others should be able to reproduce your work based on what they read in your notebook. For instance, there might a student who follows on in your research area after you have left the research group. So, you should keep in mind that you are not the only person you are writing for. Your research notebook should be clear and understandable to someone working in the area. The basic content of your notebook should do all of the following in order to create a traceable record of research progress/ﬁndings in one place where it can be easily accessed. • Describe your research goal(s). • Identify methods used. • Support methods chosen with literature references. • • • Include original raw data/images (or references to e-data). Include procedures/designs/programs/calculations (or references to e-ﬁles). Include ﬁnal results and their interpretation. • Attach print screens of e-data ﬁle directory hierarchies where applicable. • Provide documentation that others can follow with enough detail that they could recre- ate the work. • Describe thought processes, hypotheses, and outcomes. • Plan future research activities. • Write out steps to possible solutions for problems encountered. Beyond the research itself, your notebook is a good place to record other research-related interactions and information. It is an excellent place to keep notes from lab meeting discussions, agendas for meetings with your research mentor along with the comments/suggestions made during those meetings, and a summary of research seminars that you have attended. Being able to refer back to these additional notes at a later time will become invaluable. 6.1. KEEPING A RESEARCH NOTEBOOK 137 Student Perspective “The longer that I continue to do research, the more pertinent that it is to have a good notebook, as I ﬁnd myself looking back at certain past experiments and trying to evaluate where we’ve been, thus helping determine a plan forward.” You can also use your research notebook as a project management tool. Minimally it should describe the research goal or hypothesis you are currently testing. You can also use it as a roadmap for what comes next. This can be particularly valuable if there is a time lag and you will not be able to get back to your research to make further progress right away. Student Perspective “Documenting research properly and storing ﬁles in a way that makes sense has also been a skill I’ve had to develop over the past year. My lab notebook entries now are more helpful than they were at the start of the project. At some point I started ending each one with a list of immediate next steps, and I have found that really helpful, especially during the school year when I can’t work on the project every day and need my notebook to remind me where I left oﬀ. I have gotten better about naming and storing ﬁles in a way that makes them easy to ﬁnd again, which is important because as the project has gone on, I’ve collected a lot of ﬁles.” It may seem like a lot of work to keep a good research notebook and it is. However, doing so will pay oﬀ in a multitude of ways over time. Sometimes it is possible to make keeping a good research notebook faster and easier by creating procedures that you write once and then refer to (noting any modiﬁcations that you make over time) or making ﬁll-in-the-blank tables for things that you do routinely. Before starting your research notebook for a mentored project, talk to your research men- tor. Your mentor may have expectations about what type of notebook is kept and what informa- tion must be kept in it. Additionally, if a federal agency or foundation is funding the research project, they may have requirements of their own (for example, the Nuclear Energy Univer- sity Program funded by the Department of Energy put out a document titled “Proper Use and Maintenance of Laboratory Notebooks” with expectations for all the funded projects). 6.1.1 DOCUMENTING YOUR RESEARCH IN A PAPER LABORATORY NOTEBOOK The lab notebook in its paper form has been used for hundreds of years. There are good reasons for this, other than calamities like a ﬁre, they are long-lived documents. For example, we still 138 6. DOCUMENTING YOUR RESEARCH FINDINGS have Leonardo Da Vinci’s notebooks to look at today! Paper continues to be the way to record information for many. Some basic expectations for a paper notebook are as follows. • Use a permanently bound notebook with numbered pages. • Ensure researcher name, contact information, and research group are prominently vis- ible. • Develop a table of contents as research is documented. • Include a key to abbreviations used and naming conventions of samples/ﬁles. • Date and sign each page. • Write neatly in pen with lined through corrections; X any skipped/unused pages. • Secure all additions with tape and signed/dated over edges (no loose pages, no staples). Plan ahead with a numbering system for each notebook so you can reference between them. For instance my lab notebooks at the University of Wisconsin–Madison started with UWL1. If you are working on multiple large projects it may work better to devote diﬀerent notebooks to diﬀerent projects. Hopefully you have developed some practice though laboratory classes you have taken in high school or as an undergraduate, but a research notebook is more than just the entries about experimental procedures/protocols and results. The research notebook is often the key place where everything gets tied together. For an experimentalist, this includes the reason why you are conducting the experiment, details about or references to protocols/procedures used, names of raw data ﬁles and output ﬁles from analysis, a plot of the results to date, the name of the folder containing relevant image ﬁles, and methods gleaned from a literature citation. Many computationalists keep notebooks in addition to commenting their code so they can track their broader thinking about their research beyond the changes in functionality of a component of the code, along with version number of the code or output ﬁle name. Theorists keep notebooks to track their thought process, identify where ideas are built oﬀ of a literature citation, and capture their evolution in thinking about a topic. In addition to notes about the research you undertake, you should also capture information about meetings you take part in, the seminars you attend, and key journal articles you read. It may seem onerous at ﬁrst, but the more you capture in you research notebook along the way, the easier your later work will be. You will ﬁnd that a well-kept research notebook is particularly helpful in writing a paper or thesis. You will thank yourself later for developing good documentation habits early! You will also want to regularly back up your research notebook. If it is kept on paper, this simply means making a photocopy or scan of the pages every month (or more frequently). For an 6.1. KEEPING A RESEARCH NOTEBOOK 139 electronic notebook you can export ﬁle or make an electronic duplicate that is kept on a diﬀerent server (or alternate storage device) and in a diﬀerent building. You have to think about the worst- case scenario—what if there is a ﬁre in the building, or what if you backpack is stolen—it would be bad enough to lose a month of data but horrible to lose it all. Unfortunately, there are actual instances of this happening. Make sure you are not the star of the next cautionary tale! 6.1.2 DOCUMENTING YOUR RESEARCH IN AN ELECTRONIC RESEARCH NOTEBOOK Some campuses, research institutions, and companies provide access to electronic lab notebook software. In some cases the use of a speciﬁc electronic lab notebook software may be required. These products are reasonably new and have varied levels of adoptions in diﬀerent places. There are also a variety of diﬀerent styles, including blogs, wikis, note taking software, and document management systems. As people have become more comfortable taking notes directly on an electronic device, electronic lab notebook products have seen increasing adoption. The advanced search functions and data management capabilities make these software options very attractive. Some of this software can also provide you with added ease in connecting from a variety of devices over the Internet and sharing with other research group members and collaborators. There can also be added beneﬁts in electronic signing, ﬁle versioning, and activity tracking. As with all software however, there are some lingering concerns over long term accessi- bility with software changes or a software company no longer providing updates to make the product compatible with new operating systems. Data security can also be a concern. Look into the software that your campus recommends or supports. As discussed above, before you decide on how you will record your research activity, check with your research mentor about the practices and requirements of the research group. 6.1.3 REGULAR EVALUATION OF YOUR RESEARCH NOTEBOOK Checkups are important and will help you to maintain a good level of completeness with your documentation of research. Some funding agencies will go so far as to require the researcher in charge of the project (i.e., the principal investigator, or PI) to regularly review your research notebook. Ideally this should take place regardless of such requirements. However, even if your research mentor is not doing regular reviews, it is good practice to periodically review it yourself. Use the activities below to do so. You can also ask your research mentor for guidance, by asking them to review your research notebook and provide you with feedback. 140 6. DOCUMENTING YOUR RESEARCH FINDINGS ASSIGNMENT 6-1: INDIVIDUAL ASSIGNMENT – SELF-EVALUATION OF YOUR RESEARCH NOTEBOOK Assess the last several months of your research documentation with the rubric below. Check your PAPER research notebook for the following items: (cid:3) Name and contact information on the beginning of the notebook. (cid:3) Date and initial each page. (cid:3) Write in pen; cross out mistakes (but leave them legible); do not erase; do not tear out pages. (cid:3) Write neatly (so anyone can read it); leave space between things—do not crowd. (cid:3) No blank pages between entries. (cid:3) No loose pages; tape additions to a page. Check your ELECTRONIC research notebook for the following items: (cid:3) Name and contact information on the beginning of the notebook. (cid:3) Logical naming system for each entry/ﬁle. (cid:3) Date and name on each entry/ﬁle. (cid:3) Electronic lock (i.e., archiving) activated on past entries/ﬁles. Consider the following best practices for documenting research. Check the: (cid:3) Recording thoughts and ideas consistently. (cid:3) Statement of objective and description of speciﬁc work to be performed, or reference to an approved planning document or implementing document that addresses those topics. (cid:3) Identiﬁcation of method(s) and computer software used. (cid:3) Identiﬁcation of any samples, test equipment, and characterization equipment used. (cid:3) Description of the work as it was performed and results obtained, including names of individuals performing the work, and dated initials or signature, as appropriate, of other individuals making the entries. 6.2. DATA STORAGE AND BACKUP 141 (cid:3) Methods and procedures described in detail and updated as needed. (cid:3) Description of any problems encounter and their resolution described. (cid:3) Entries clear enough so that the ideas can be reconstructed at a later date if necessary. (cid:3) Suﬃcient detail provided to retrace the investigations and conﬁrm the results or re- peat the investigation and achieve comparable results independent of the individual investigator. What are you doing well? What needs improvement? Describe what action steps you will take in the next month to improve your documentation of research. ASSIGNMENT 6-2: INDIVIDUAL ASSIGNMENT – USING YOUR RESEARCH NOTEBOOK Give an example of how you have used information that was previously recorded in your research notebook or in someone else’s research notebook. How did you ﬁnd that prior work? How was it helpful to you? Were you able to save time by having access to good documentation of prior work in a research notebook? DATA STORAGE AND BACKUP 6.2 What would happen if your laptop was stolen or your hard drive crashed and the data was unrecoverable? Is that the only location your ﬁles are stored? If so, the thought should send you into a panic and make you immediately seek a method for backing up your data. In research your data is not just yours. You are responsible for the data and its loss could negatively impact not just you, but also your research mentor, any peers and collaborators you are working with, and the scientiﬁc community as a whole. Funding agencies recognize this and many require a Data Management Plan to be developed and submitted with the proposal for funding. This Data Management Plan will include a description of the types of data to be collected (even ﬁle format types in some cases) and how that data will be managed and preserved. Not only backup systems to avoid any data loss but also how data will be shared with other researchers. The National Science Foundation expects the following items to be addressed1: 1National Science Foundation, “Grant Proposal Guide,” Chapter II.C.2.j, https://www.nsf.gov/pubs/policydocs/ pappguide/nsf15001/gpg_2.jsp#IIC2j. 142 6. DOCUMENTING YOUR RESEARCH FINDINGS 1. the types of data, samples, physical collections, software, curriculum materials, and other materials to be produced in the course of the project; 2. the standards to be used for data and metadata format and content (where existing stan- dards are absent or deemed inadequate, this should be documented along with any pro- posed solutions or remedies); 3. policies for access and sharing including provisions for appropriate protection of privacy, conﬁdentiality, security, intellectual property, or other rights or requirements; 4. policies and provisions for re-use, re-distribution, and the production of derivatives; and 5. plans for archiving data, samples, and other research products, and for preservation of access to them. The research you are engaged with may have a Data Management Plan in place and/or standards within the research group for collecting, organizing, storing, and backing up data. You should begin by asking your research mentor if there are data standards for your research that you should follow. However, some groups leave much of the detail up to each individual researcher, so in that case you need to think about some of these key aspects yourself. Always keep the original is a basic rule. If you take an image you should keep an untouched original and make modiﬁcation only to copies of the image ﬁle. It’s a good idea to lock the original ﬁle so you don’t accidentally make changes to it. In some cases a publisher may want you to submit both the original image ﬁle along with the version of the image that you will be putting into the ﬁgure. The same rule applies to raw data output from an instrument or codes. Keep the original output and make a copy on which you then conduct analysis. You will obviously need your ﬁles somewhere you can easily access and work on them. This may be a laptop computer for instance. But you will also want to make sure ALL of your ﬁles are regularly backed up somewhere. This may be an external drive or cloud storage for instance. The data management professionals suggest that you have your data in three separate storage media in at least two separate locations in case one of them gets corrupted. This may mean that you have an external drive at home where you back up your ﬁles regularly and additionally you use a cloud data storage system like Box or Dropbox to keep a copy of your ﬁles in a separate location. Ideally these backups occur automatically without you having to manually initiate it, but if not, you need to get into a backup routine so that the time span between backups in minimized. Think of the worst-case scenario like your apartment building catching ﬁre in the middle of the night—you get out safely, but your laptop and external drive are destroyed. However, if you still have a recent backup in the cloud then your months or years of research work are not lost. When considering cloud data storage systems look into what is available through your institution. It is likely free to you and the institution has negotiated a license agreement that takes into account security and issues surrounding sensitive. It is also likely that you can easily 6.2. DATA STORAGE AND BACKUP 143 share data with your research collaborators and reassign ownership of the folder to your research mentor when you graduate and leave the institution. Before you have too many ﬁles to deal with, step back and decide how you could best provide organization for your data. You will want to develop a logical folder system so that all the ﬁles are not jumbled into one place. They should also be named clearly and succinctly. Keep in mind that this collection of ﬁles will likely be accessed by someone else—maybe after you graduate—in order to extend and build upon your research. You need the structure to be logical and intuitive. A text README.txt ﬁle at the top of the ﬁle structure can help you to describe how things are organized and keep a list of key data attributes that will be helpful not only to other but to yourself. Here is a simple ﬁle structure to illustrate these ideas: Creep Crack Growth README.txt Equipment Drawings Images Quotes Validation Experiments CCGProcedures CCGTesting Alloy617 Analysis CrackGrowthData Microscopy Alloy800H Analysis CrackGrowthData Microscopy HeatTreatCharacterization Analysis RawData Publications ExpMech-TechniquesPaper Drafts Figures FinalSubmission MetMatTransE-CCGPaper Drafts Figures 144 6. DOCUMENTING YOUR RESEARCH FINDINGS FinalSubmission SEM-ConfProc Reports AnnualReports FinalReport Having an agreed upon naming convention for experiments or version control system for software is especially important when you are working collaboratively. If each part of the name for the folder/ﬁle is deﬁned and everyone has this shared information then a sample with the name U4-H9P63Y98-PS12-PS20-L30-PDMS5M-D4-1Hz8V-D19 will tell everyone what it was part of experiment U4 that involved a speciﬁc protocol of that number, and that the cell type used was H9 passage 63 with a yield purity of 98%. The sample was pre-seeded on day 12 which ended on day 20 when the cells were put on lanes of 30 micron width using a PDMS substrate with Young’s modulus of 5 kPa and an extracellular matrix of Matrigel. Pacing was then begun on day 4 in the lanes at 1 Hz frequency at 8 volts and ended on day 19. This experiment has a page-long README ﬁle that provides detailed information about the naming system so every researcher on the project knows what is happening at each stage of the experiment and can add to the naming string as appropriate when they take data after doing the next step of the protocol with the samples. Software version control allows you to track how software changes over time and keep old archival versions to return to as needed. Versioning is also critical so that you know what results were created by which version of code and that multiple people can work on a code simultane- ously. Platforms like GitHub allow individuals and groups to deposit their code. Similar to the README ﬁle, a wiki within the shared resource provides people with information about the code, how to use it, etc. This would be overarching information beyond what would already be included in the comments within the code. Student Perspective “I’ve collected a lot of ﬁles. I started using GitHub for my code, not because I have to share it with anyone, but because I ﬁnd it’s helpful for keeping track of what version is the most current, and I think it’s a good idea to have a backup copy of it somewhere other than my laptop hard drive. I should be better about keeping other particularly important ﬁles in the cloud as well, so if my laptop were to die, it wouldn’t be as big of a problem (I do keep my laptop backed up using an external hard drive, so my ﬁles would not be permanently gone, but in the short term, ﬁles there wouldn’t be as easily accessible as ﬁles stored somewhere in the cloud).” There a number of resources available on best practices for data management.2 Your cam- pus will likely have an oﬃce of Research Data Services or librarians who can help you with campus-speciﬁc resources and practices. 6.3. AVOIDING DATA MANIPULATION 145 6.3 AVOIDING DATA MANIPULATION We may not often think about it, but there are some important ethics issues when it comes to handling data, ﬁgures, and images. As discussed in the previous chapter, this begins by avoiding error, negligence, and misconduct. As discussed above, the ﬁrst step is to collect and retain all original output, raw data, and image ﬁles. The original version should be locked and left untouched. A copy should be made when the ﬁle is needed for further analysis. Obviously, fabricating data is wrong, but sometimes it is more fuzzy when considering falsiﬁcation. For instance, you may have what you believe to be outlier data points. If there is a documented reason (for instance a comment in your lab notebook about high room temperature due to broken HVAC in the building, a sample contamination, or a power ﬂuctuation during data collection), then it is reasonable to exclude those data points. However, if you do not have a known reason for exclusion, you will need to report all the data points. In some cases, you may be able to show statistically that the outliers do not fall within the data population, but even in this case you would report any statistical exclusions that you made when writing about your results. There are also subtle ethics of presenting data in best light vs. manipulating the presen- tation of the data to make a false impression. For instance, you may see a small trend in your data ranging between 90 and 100 that is interesting. However, if presented on an axis scaled between 80 and 100 this will exaggerate the trend to a reader who is not scrutinizing the graph carefully. When you present your data, you want to do so in a way that is honest and discloses the full picture. It’s ﬁne to focus in on the small trend, just be sure to do so in a way that is not misleading. With the advent of digital images and the capability to manipulate them, a few ethical lapses in data manipulation have been made very public. Because of this, some journals regularly screen submitted images to guard against image manipulation and publish standards of practice.3 There are some general guidelines that you can follow when handling images with software packages, like PhotoShop and ImageJ, that will keep you on the side of good ethics.4 To start with, keep an archival copy of every image you generate that you never manipulate. If you need to crop or change contrast for example, then, work on a copy of the original image and log every change that you make to that image either in your research notebook or a text ﬁle stored 2See for instance, DataONE. A collaborative project on data management funded by the National Science Foundation (NSF). https://www.dataone.org/. 3“Image integrity and standards,” Nature Research, Springer Nature Limited. https://www.nature.com/nature- research/editorial-policies/image-integrity. 4Hendrickson, M., 2010. “Digital Images,” a talk presented in “Optical Microscopy Course,” W. M. Keck Laboratory for Biomedical Imaging, University of Wisconsin-Madison. 146 6. DOCUMENTING YOUR RESEARCH FINDINGS with the image(s). If you have made any manipulations beyond simple cropping and changes in brightness or contrast, then describe what you have done when you present the image. This can be described in the ﬁgure caption or the methods section of your paper. You should avoid things like modiﬁcation of a part of an image, aggressive cropping of an image, using extreme or nonlinear adjustments in intensity, and digital ﬁltering of an image. Furthermore, you should always present representative examples of the results you have observed. If a particular image was an outlier, then it must be described as such if you want to present it. C H A P T E R 7 147 Sharing Your Research via Oral Communication 7.1 INFORMAL CONVERSATIONS WITH OTHER RESEARCHERS This chapter discusses a variety of diﬀerent ways in which researchers need to communicate their work orally. It is an important skill to develop so that you can comfortably talk about your research with a range of diﬀerent audiences, at diﬀerent levels of technical depth, and with diﬀerent levels of formality. Student Perspective “I was very surprised that the researchers have to care a lot about com- municating with diﬀerent groups of people, like the general public, reporters, students, colleague, and etc. A stereotype of a mad scientist who does not communicate with other people at all is actually not possible in reality.” One of the most important audiences with which you will need to communicate are the other researchers in your ﬁeld. These may be people you work with every day, a research men- tor you communicate with regularly, collaborators you communicate with periodically, or other engineers and scientists that you interact with at meetings and conferences. It may be tempting to shy away from these sorts of communication initially, but they are truly critical both to your personal development as a researcher and to the research project you are undertaking. Even if it pushes you outside your comfort zone a bit, you need to engage in these conversations. Student Perspective “Overall, I have learned that perseverance, conﬁdence, and communi- cation are the most important skills that a researcher can possess. In order to have a successful project, one must communicate with other scientists to resolve problems in an appropriate and timely manner as well as be able to resolve issues when help is not available.” 148 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION ASSIGNMENT 7-1: INDIVIDUAL ASSIGNMENT – RESEARCH MEETING UPDATE Each research group has its own style and practices involving meetings, but at some point you can expect that you will need to talk about your work in front of others in your research group. This may be more or less formal and may or may not involve preparing presentation slides. Your assignment is to present short research talk of 5–8 minutes in duration. The talk must be relevant to your research topic but may range in content from a review of a paper to an explanation of some aspect of your ongoing research. Formal slides are not required but you may use them if it is customary in your research group. 7.2 INFORMAL CONVERSATIONS WITH NONSPECIALIST AUDIENCES It is frequently the case that we have the need or desire to talk about our research with people who are not specialists in the ﬁeld or even comfortable with technical subject matter. It may be important for us to convey the purpose of our speciﬁc research project and/or the motivation behind the general area in which we are doing research. Communicating with people outside your research group might originate from a need to write a cover letter to a journal editor about a manuscript you are submitting, discuss your research with a program manager or funder of your research group, prepare for a job interview, or communicate with the general public about policy decisions related to your research.1 Certainly, developing these non-specialist communication skills are to your own advan- tage when it comes to getting your research funded and published or landing a new job when you complete your degree, but these skills are also important because of their societal beneﬁt. Your ability and willingness to explain your research has the beneﬁt of promoting a scientiﬁcally literate society, so that people who have an opportunity to inﬂuence the paths of future research and technological uses are doing so with a basic understanding of the related research. Scientists and engineers also have an obligation to report back to the taxpayers who fund their work. To do this type of communication eﬀectively you need to invest time in ﬁguring out what it is you want to convey and the best way to go about doing it. Depending on the speciﬁc audience you will have to change the amount of depth and technical detail you discuss, eliminate the jargon you might normally use with colleagues, provide more background about the subject area, and shift your emphasis from details of project to a more general discussion of its potential applications. When you engage with other researchers in your area you have the opportunity to use jar- gon to speed up the transfer of information in conversations. However, you need to be sure that 1Baron, N., 2010. Escape from the Ivory Tower: A Guide to Making your Science Matter. Island Press. 7.2. INFORMAL CONVERSATIONS WITH NONSPECIALIST AUDIENCES 149 you know what this jargon means to others so that you don’t have a problematic miscommu- nication. Some junior researchers try to hide their limited understanding behind jargon—this may seem to work, but if you really don’t know what you are taking about the improper use of jargon will soon give you away. When you communicate with nonspecialists you need to remove the jargon, and this forces you to really understand what’s underneath these words. The order in which you talk about things will also need to change. The big idea, or headline, needs to come at the beginning to keep the listener engaged. Narrow the key points that you will make to only those that are essential for the particular audience you have in mind. Include some relevant and memorable facts or theories related to each key takeaway message. When you actually talk to people, don’t be afraid to repeat yourself—the main message should be touched on multiple times throughout. Several proponents of informal science communication focus on story telling as a way to convey research concepts to general audiences.2 This can be particularly eﬀective when commu- nicating to public audiences. Traditionally, stories that people tell have a hero and a goal. The “hero” can be a person (you) or a thing (like a technology) and the goal should be something we care about (such as an outcome that will make people’s lives better). Like any good story, there are obstacles along the way that the hero must overcome to succeed. As you tell the story, your goal is to engage the listener so they want to know what happens next. However, success is not a requirement for every story… sometimes it is a “tragedy”… for example, the equipment broke! Even these sorts of stories are important ones to tell, it’s one of the realities of research that people don’t often understand. Although you may not want to craft an entire talk to ﬁt a traditional narrative story arc, an anecdote can help to “seduce” your audience into paying attention. The key is to make sure that your anecdote oﬀers a concrete example that is representative of the research.3 ASSIGNMENT 7-2: INDIVIDUAL ASSIGNMENT – HONING YOUR MESSAGE Identify a topic area—either a current research project or a topic related to your research interests—and craft talking points that you would want to convey if you had ﬁve minutes to convince someone to fund this type of research. Don’t think of this as preparing a speech, but rather as preparing for a conversation in which you want to make some key points and be able to respond to anticipated questions. Develop a topical “headline” and 3–4 main messages with 1–2 pieces of supporting evidence. Develop a brief closing summary statement that links back to the headline captures themes brought up in your main message. 2Miller, T., 2015. Muse of Fire: Storytelling and The Art of Science Communication, https://www.spokenscience.com/ publications/. Olson, R., 2018. Don’t be such a Scientist: Talking Substance in an Age of Style. Island Press. 3Laszlo, P., 2007. Communicating Science: A Practical Guide, Springer Science & Business Media. 150 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION Headline Main Message 1 Supporting Evidence Main Message 2 Supporting Evidence Main Message 3 Supporting Evidence Closing Summary Statement For example, below is a brief example of once main message on the topic of graduate education: Main Message: Graduate education is integral to university-wide goals Evidence: Grad students are essential in research and undergrad education Evidence: Grad students increase the diversity of the campus community Relevant data would also be identiﬁed on the number of research and teaching assistantships that graduate students hold and the national and international diversity statistics of the graduate student population at the institution. ASSIGNMENT 7-3: INDIVIDUAL ASSIGNMENT – MESSAGE BOX You can use the Message Box4 shown below as a graphical method (Figure 7.1) to aid in honing your message. The Message Box is a communication tool developed by Nancy Baron, who has worked in science outreach with Seaweb and COMPASS.5 It was created for scientist so that they can prepare for interactions with the media and policy makers, but it is a generally applicable communication tool to organize the main points surrounding a technical topic in preparation for a discussion with a non-expert. The Message Box helps you to create “talking points,” or key points that you believe are important to cover in a conversation about your topic. You can use this framework to explain what you do to those who know little about your area of expertise. It is a ﬂexible tool that can be used not only to prepare for a verbal conversation but also for written communication, such as a cover letter, press release, or website. The Message Box itself is a tool for you to use to organize your thinking. Using a piece of paper or a PowerPoint slide, divide the page into four quadrants with the Issue in the middle. Create a list of 2–4 talking points around the Problem, So What, Solutions, and Beneﬁt. Although 4Baron, N. and Weiss, K., 2007. “The message box” preparation for talking with the media, seminar given on September 21. 21. 5Baron, N. and Weiss, K., 2007. “The message box” preparation for talking with the media, seminar given on September 7.2. INFORMAL CONVERSATIONS WITH NONSPECIALIST AUDIENCES 151 Figure 7.1: Technical presentation of information (left) vs. Message Box (right). Consider your audience when you translate into Message Box talking points. it might be helpful to show it to your research mentor for feedback, it is not something you would show to someone you are speaking with about your research. It is a tool for your to facilitate your communication. ASSIGNMENT 7-4: INDIVIDUAL ASSIGNMENT – VIDEO COMMUNICATION PRACTICUM It is often useful to have practice presenting in front of a camera so you can see how you sound and critique your own presentation. This assignment will give you an opportunity to gain expe- rience talking in front of a video camera in a low risk setting. Find a place where you can be undisturbed and use your phone or computer to capture the video. There are a number of questions you can choose to address during your video session. Ideally, you should focus on 1–2 questions because the total time of the video should be approx- imately ﬁve minutes. Although you should prepare some talking points in advance, it is best if you do not read oﬀ of notes. Questions to consider. Why should someone consider (or not) entering your major? Why should someone consider (or not) going to graduate school? What have you learned about the process of research? What strategies would you suggest for ﬁnding a research project and research mentor? What tips would you give someone just beginning their research project? What tips would you give to someone about staying on track with research progress? What advice would you give to someone preparing an oral presentation? AbstractBackgroundMethodsResultsDiscussionConclusionProblem?Solutions?Beneﬁt?IssueSo What?AUDIENCE152 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION Review the video after you have recorded it. Identify things you have done well and things you would like to improve. 7.3 ENGINEERING OUTREACH One speciﬁc type of nonspecial communication comes in the form of “outreach”—those events that campuses and communities hold to engage the public with science and engineering topics. Often these are targeted to the K-12 age group and frequently involve some type of hands- on activities. Even if your campus does not hold an Engineering Expo type of event, there are frequently opportunities for undergraduate and graduate students to interact with kids about engineering through K-12 schools and after school programs. Ideally, you pick a topic to present that you are interested in, maybe even something re- lated to your research. Engaging more of the senses will make their experience memorable. It is particularly helpful if people can get their hands into and onto an experiment or demonstration materials. You may be able to help a group experienced with outreach who already has activities developed. If not, there are numerous resources available which can provide you with content that you can use and adapt. If the professional society in your discipline does not already have materials available, try looking at places like TryEngineering.org or volunteer.asee.org. Although precocious middle and high school students who voluntarily come to campus for a science or engineering outreach event can surprise you with the level of their knowledge about technical topics, many people understand less about basic science concepts than you might expect. For example, “four out of ﬁve Americans do not understand the concept of a scientiﬁc study suﬃciently well enough to provide a short sentence or two of explanation.6” Because of this you need to think about ways to engage with people to understand what they already know before you begin an explanation. You can do this more readily by asking questions and interacting with them about the topic area. Ideally, you do this in a fun an engaging way, rather than making the person feel like they are taking a quiz. Student Perspective Student Perspective “In short, I learned it is better to teach someone something simple well than it is to teach them something more complicated badly.” When presenting, it is important not to overload people with too much information. You don’t want to talk down to them, but you need to simplify the ideas that you are trying to get across without introducing errors or creating misconceptions. Often you must adjust as you are interacting with people based on how they are responding. It’s like running an ongoing 6Knight-Williams, V., Santigian, L., and Williams, D., 2005. An overview and annotated bibliography of the use of analogies, hands-on activities, models, simulations, and metaphors: Part III of front-end analysis in support of nanoscale informal science education network. (Knight–Williams Research Communications.). experiment! You may have to try diﬀerent things to see what’s most eﬀective and be willing to modify your original plans. 7.3. ENGINEERING OUTREACH 153 Student Perspective “[Doing outreach] turned out to be a good practice exercise for me, because I hadn’t anticipated that most of the people that came to the exhibit were people that had never taken a chemistry class. So for the ﬁrst hour or so, I found myself struggling to keep people interested in the topic simply be- cause I was out of practice explaining things that I wrongly assumed were common knowledge. For example, many people didn’t understand atoms bond to one another. This is actually a fairly complex concept for people who haven’t had a science heavy education like me. Through this, I learned the miracle of teaching through visual aids. The molecular model kits that we had were really useful for those complex yet basic concepts that I needed to explain, especially when I was speaking to younger patrons. I learned that I really need to improve on how I present technical topics to younger people and people who are less interested in science in general. Part of it is a matter of using the right amount of scientiﬁc detail, but a lot of it has to do with how engaging I can make the topic seem as a presenter.” Below are some basic tips to think about before you interact with the public about a science our engineering topic in an informal science education setting.7 • Know the intended audience. • Deﬁne a limited set of learning goals (2–3 at most). • Be aware of the length and attention span of the audience. • Use multiple modalities to address a range of learning styles. • Don’t assume prior knowledge. • Deﬁne terms and avoid jargon. • Avoid graphs, especially multidimensional graphs and log scales. • Explain what you see in scientiﬁc images and diagrams. • Use metaphors and analogies that explain and enlighten. • Include personal aspects of the story, not just the scientiﬁc facts. 7Crone, W. C., 2006. Bringing nano to the public: A collaboration opportunity for researchers and museums, S. E. Koch, Ed., Nanoscale Informal Science Education Network, Science Museum of Minnesota, St. Paul, MN. 154 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION • Repeat the message, explaining it in multiple ways, but be concise. • Provide clear directions for an activity. • Encourage visitor conversation. • Test for misconceptions. • Evaluate at every stage. The arts can also be used to engage public audiences with engineering topics and employed as an entry point for those who might not be as intrinsically interested in science and engineer- ing topics. For example, in collaboration with professional artists and science museum exhibit designers I have worked with other engineers and scientists to engage audiences by using silver and gold nanoparticles suspended in polymers to make “stained glass” artwork with the public. It’s amazing what creative minds can come up with! The most important thing I learned when working with museum exhibit developers was that you have to make it fun. If it is not fun people can just walk away or walk on by. This gives you an opportunity to be creative! For example, I worked with a balloon artist several years ago to develop an interactive balloon model for a carbon nanotube structure that we could build with kids visiting outreach events. It was a huge success and the activity is now being used by outreach presenters all over the world. Hopefully you will engage in outreach yourself at some point if you have not already done so. Being the presenter can be fun and it will likely remind you of why you got excited about your area of study in the ﬁrst place. ASSIGNMENT 7-5: INDIVIDUAL ASSIGNMENT – EXPLANATION FOR AN 8-YEAR-OLD • Pick a topic that you will explain to a group of 8-year-olds (e.g., rainbow, ﬂuorescent light bulb, hibernation). • Develop a 30-second explanation (oral, written, movement, and/or illustration). • Be prepared to share your explanation. 7.4 POSTER PRESENTATIONS The research poster is a common form of communication, both on campus and in poster sessions held at research conferences. The poster size is usually designated but is often somewhere be- 80; a size large enough to enable viewing by someone standing a few feet tween 30 (cid:2) 40 and 40 (cid:2) 7.4. POSTER PRESENTATIONS 155 away. In some cases, the poster content and organization are prescribed, but more commonly they simply follow the general organization of a research article. The poster title, authors, and their aﬃliations usually appear across the top, with the title in a larger font (72–100 point font is common for a title). The content sections of the poster usually feature an abstract, background, methods, results, and conclusion (the body text is usually 24–32 point font, with larger font for section headings). References and acknowledgments are usually at the bottom of the poster, often below the conclusion. The layout should progress logically from left to right and top to bottom. Above all, a poster should be designed to be visually appealing, with graphics, ﬁgures, and images as a key focus and large in size. The overall design and color scheme should be harmo- nious. You can use boxes and borders to set apart diﬀerent sections of the content. Although it is important to include some text, it should be carefully chosen to be both informative and brief. Black or very dark text on a white background is easy to read. You may want to think of the poster as an advertisement or announcement of your work—thus “It needs good copy.8” Make “headlines” and easily readable text to go along with great visuals. In many circumstances, you will accompany the poster to provide a verbal explanation. Student Perspective “Through the creation of a [conference] poster… I learned much about scientiﬁc communication. First, many basic skills were cultivated through this poster designing process such as making something readily understandable, uses of bullets highlights and bold, use of white space, and knowing your own poster. Second, I learned that the number one priority when creating a poster is, making it simple to understand for the audience and aiding in breaking down any barriers which might have confused yourself. In addition, the honing of the elevator speech was a process. There was a large amount learned on what not to say (diﬃcult or misleading concepts) and what to say (most widely appealing/relevant virtues of my work).” When preparing a poster, it is critical to determine the requirements before you begin. If it will be presented in a conference venue, then the conference organization will provide guidelines. It is essential that you ﬁnd out the size restrictions and whether the poster will be displayed in a portrait or landscape format. It is also important to determine what printing process you will be using so that you can ﬁnd out if there are restrictions on the size, how much whitespace should be left around the edges, and how much advance time will be needed to get the poster printed. You do not want to print out the poster only to have the last three inches cut oﬀ, forcing you to both revise your poster in a hurry and spend money to print it twice. Carefully proofread your poster before it is printed. Also determine how you will transport the poster—with some 8Laszlo, P., 2007. Communicating Science: A Practical Guide, Springer Science & Business Media. 156 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION printing processes you can fold the material and pack it in a suitcase, but if it is printed on paper you will need a poster tube (be sure to label the tube with your name, address and phone number). You must also consider the verbal part of the poster session. You need to have your talk- ing points thought out in advance and designed to augment the poster content. As with non- specialist audiences you need to engage in a conversation and be prepared to discuss your work at the appropriate level of detail for the people you are discussing it with. This means that you might actually have two (or more) levels of explanation based on whether you are talking to a specialist who works in an area close to your own or someone who is interested in the work but not an expert in your technical specialty. Practice what you will say out loud before the big day. Ideally, you will do this with your research mentor and/or members of your research group who can give you feedback on both the poster content and your accompanying explanation. During the poster session, be open to a conversation as you are getting across your main points. Ideally, a poster session is an opportunity to engage in discussions that will help you to move your research to the next stage and you may even have great questions posed by non- experts that help you to think about your research in new ways. If you are nearing a junction in your academic career (i.e., applying to graduate schools or job hunting), you should let that be known in the conversation. You can even bring along business cards and copies of your resume in case an appropriate opportunity arises. 7.5 THE RESEARCH TALK Presenting your research may feel overwhelming at ﬁrst, but it will get easier the more times you do it, both in terms of the time it takes to prepare your talk and how comfortable you will feel in giving the talk in front of an audience. When preparing a research talk, the ﬁrst thing to determine is who your audience will be. Your research mentor should be able to tell you the kinds of people who are expected to attend. This will help you understand the level of jargon that can be used and how thoroughly you will need to discuss the background for your topic. The second thing to know is the time limit on the talk. In many cases the amount of time you will have to present will be quite ridged. Conference talk slots are usually somewhere in the range of 12–18 minutes, whereas a seminar talk could be 50 minutes. Be certain to ask if the time you are being given is inclusive of questions so that you know whether you need to make your talk a bit shorter to allow time for questions. With these two pieces of information you will be able to determine the scope of your talk. You will likely need to pick and choose what you talk about from the research you have done—don’t try to cram everything in. Develop an outline for your talk and select the key visuals that will accompany it. Often the ﬂow of a talk is similar to a paper with background, methods, results/discussion, and conclusion. If you have already submitted an abstract to a conference then your topic will be somewhat ﬁxed, but you may need to do more thinking about how you will motivate the work and what 7.5. THE RESEARCH TALK 157 background you need to provide so the audience understands where your research ﬁts into the ﬁeld. Showing that you know the context of your research and have read the related literature is an important aspect of the talk and will help to convince the audience of the knowledge you have developed. As with writing, your presentation will also need to give credit to others where appropriate. This means that you will include the names and/or references to the work of other researchers/groups on your slides (as well as in the words that you say). In addition to a title slide at the beginning that may include information about co-authors and funding, you will also include an acknowledgments slide at the end. Be certain to include your research group, other collaborators, and all of the funding that supported the research. Emphasize the visuals in your talk and add a few key phrases or bullet points on each slide. You will use your spoken words to ﬁll in the details. Having less text will also prevent you from falling in the trap of simply reading the slides to the audience. You can use ﬁgures and images from the literature as long as you give credit to the original source. This is best done with the citation information on the slide where it appears (rather than a number and a reference list at the end). You will also be presenting ﬁgures, graphs, images, and/or videos about your results, but you may ﬁnd that you need to supplement these with additional images, animations, and graphics that ﬁll in the gaps and visually explain your approach and methods. Discuss your outline or draft slides with your research mentor early so that you can de- termine if you are on the right track. Once you have developed a complete draft of the talk, practice it independently and in front of others. Many research groups will have practice talks in their regular group meeting as a conference approaches, but if this is not planned then ask your research mentor and others in your research group if they would be willing to watch a practice talk and give you feedback. Be sure to organize this far enough in advance so that you can make changes and implement the feedback thoroughly. Practice the revised talk again before the big day. When you speak, do so facing the audience. If you plan to use a pointer, practice using it so that you hand is steady. Speak with a volume that will be heard by everyone in the room. If you will have a microphone, determine how to turn it on an oﬀ and check what position will pick up your voice clearly. As you give your talk be sure to actually explain your slides to the audience. Although you are very familiar with your research, your audience will need to be oriented so that they can understand them too. This means that you will need to take time to point out the axes on a graph, the color coding for a ﬁgure, or the deﬁnition of the symbols that appear in equations. During your practice session, be certain to ask for questions that you might get from the real audience. This will help you to practice thinking on your feet and constructing some of the responses you might use. For obvious questions that you just don’t have time to address in detail in the main talk, you might prepare a few backup slides that you can place at the end of your talk and refer to as needed. During your actual presentation, it may happen that you get a question you don’t know how to respond to. Don’t panic. You can reply gracefully with “Thank you for that 158 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION question. I’m not certain of the answer at the moment, but that is something I will look into.” If you get a more aggressive question that calls the underlying basis of your work into question and you are not certain how to deal with it, you can reply “That is a much broader discussion than we have time for now, but I would be happy to talk with you in more detail after the session.” Of course, then you will need to be certain to track down this person after the session and have that diﬃcult discussion, but at least you can have the discussion without a large audience. Student Perspective “Another thing that my research project has helped me improve on has been my presentation skills. I’ve given short presentations about my project, or topics closely related to it, a number of diﬀerent times…. I’ve gotten bet- ter at putting slides together that are clear and informative, and at judging how much material I should have for a presentation that is to last a speci- ﬁed amount of time. I’ve also gotten better at explaining my project in a way that makes sense to people outside the … ﬁeld. Increased familiarity with the ﬁeld has helped me be better able to explain it as well. Practice presenting to people is also always helpful for improving my presentation skills. Every time I present I am less nervous about it, and I think in general my presentations have gotten better over time.” Whether you plan to give your talk from your own laptop, submit the ﬁle in advance to conference organizers, have it on a ﬁle sharing system, or external memory device, be certain to have it available in more than one place just in case the primary source does not work for some reason. Some conferences have a speaker prep room set aside where you can check to make sure your talk is working correctly and run through it one last time. Make sure that any videos or animations you are have included are functioning properly. If possible, especially for something like an oral proposal talk or thesis defense talk, practice the talk in the room you will be using so that you can be one familiar and comfortable with the space. At a bare minimum, make sure that the technology will work in advance of your talk. Whether the talk will be given in a class or a conference, arrive early so you won’t feel rushed. Make sure the host, instructor, or session chair knows that you are there. Ask if there are any timing signals that they plan to provide. If not, you can ask a colleague to give you a discreet wave when you are within a minute of the end time. Running long is considered rude so you should avoid doing so. Take a deep calming breath, release it in a slow steady exhale, and then give a great talk! 7.5. THE RESEARCH TALK 159 ASSIGNMENT 7-6: INDIVIDUAL ASSIGNMENT – THE FLASH TALK Sometimes it is actually easier to give a long talk than a short talk, but in some circumstances you will be given a tight time limit. In a recent conference I attended, the graduate students either presented their research in either a “ﬂash talk” or a traditional poster session. The ﬂash talk had a strict 3 minute time limit—exactly 180 seconds. These short format presentations vary, but they are designed to give a large number of speakers time to share a glimpse of their work, usually prior to some time frame in which people will be able to mingle and follow up with speakers whose research interested them. Essentially this talk is an advertisement for your work, so you want to get across a few key items to encourage follow-up. Be sure to include your name, institution, and email address. After mentioning the topic, which should be succinctly summarized by the title of your talk, begin with a brief motivation for the work. Discuss the method of research you are using to approach the problem. Present a summary of your most important results. Sum up with conclusions you have been able to draw from the work you have done. In some cases you may be talking about work in progress. If so, the ﬁrst half of the talk stays the same. If you have preliminary results to share, you can include those. You will wrap up with your plans for future work. Hone your slides to get across key visual information with your talk. There are several strategies for doing this eﬀectively. One strategy is to use a single slide layout (see quad chart format below). This gives the speaker a chance to talk without worrying about changing slides on the computer and allows the audience to look through all the information over the 3-minute time frame. Alternatively you can break up the information in a traditional slide format—title slide, motivation, methods, results, conclusions—no more than 5 slides can be reasonably covered in 3 minutes. Ideally you should condense it to fewer if possible (for instance: title and motivation, methods, results, conclusions). Once you have the draft talk prepared, do a practice run and time yourself. It is likely you will have to adjust both the slides and what you say. Practice several times to get your talk to be exactly 180 seconds. You may want to use an audio recorder so you can listen to your talk and make adjustments after listening to it critically. You may also want to practice in front of someone. You may ﬁnd that you tend to talk faster or slower in front of an audience and it is important to know this in advance. 160 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION ASSIGNMENT 7-7: INDIVIDUAL ASSIGNMENT – THE QUAD CHART Another term you will sometimes hear regarding short presentations of research is the “quad chart.” Sometimes this is intended to be a standalone entity and other times it is used as a back- drop to a short presentation. It is somewhat reminiscent of a poster in that all of the information is contained in one view. It is often created using PowerPoint and usually intended as something that is projected on a screen all at once or printed on a single page. Funding agency program managers may request a quad chart be produced for a research project that is underway, or it might be used to summarize a completed project. It might seem a bit reminiscent of the Message Box discussed earlier but the Message Box is a tool for you to use and is not shown to someone you are speaking with, whereas the quad chart is the main product being delivered. Although there is some overlap in the content between a quad chart and the Message Box, the audience and intent is usually quite diﬀerent. There is no single format for a quad chart other than that it is usually broken into four quadrants. The quad chart is intended for a technical audience and it shares many features with a poster. It also has the formality of a title, authors (e.g., research project participants), and funding acknowledgments. Usually speciﬁc instructions are given by the requester (often a funding agency program manager) about what is to be included. One common format is to use the following content in the quadrants: (1) an image or graphic that depicts the overall project; (2) a statement about the objective(s) of the research; (3) a description of the approach being taken to reach the objec- tive(s); and (4) a timeline that lists milestones and progress to date. When engaged in a Department of Energy research project several years ago, we were asked to provide a quad chart for a progress report meeting that involved the principal investi- gators (PIs) of all the research projects being funded by the program. The instructions were very explicit about what exactly was to be included in each quadrant, but it basically boiled down to the following key elements.9 1st quadrant: Purpose/Objective—“A short description of the major contribution envisioned from the project.” 2nd quadrant: Importance/Relevance—“Highlight the relevance of the research being conducted.” 9Nuclear Energy University Program, Department of Energy, https://neup.inl.gov. 7.5. THE RESEARCH TALK 161 Figure 7.2: Sample quad chart format. Impact Areas—“Identify the areas of impact from the successful completion of the project. These should provide a broad view of the project’s scope as opposed to the more technical ‘Purpose/Objective’ section.” 3rd quadrant: Tools/Methods/Facilities—“Include the details of the various specialized set of tools/methods and facilities that are being used/developed as part of the project.” 4th quadrant: Sample Results—“Highlight the key result obtained from the work done to date. A ﬁgure should be included along with a caption that explains the key ﬁndings.” Status of Deliverables—“Include the list of the deliverables submitted in the project proposal and indicate the status of each deliverable.” For this individual assignment, use the quad chart format in Figure 7.2 to summarize the status of the project you are currently working on. TitleAuthors/Project ResearchersInstitution(s)/Aﬃliation(s)Purpose/Objective: Importance/Relevance:Tools/Methods/Facilities: Sample Results: Status of Deliverables:Citations/References:Acknowledgments/Funding:162 7. SHARING YOUR RESEARCH VIA ORAL COMMUNICATION ASSIGNMENT 7-8: INDIVIDUAL ASSIGNMENT – CASE STUDY Instructions: Read the brief case description provided. Reread while noting the important information, and questions that are raised in your mind about the information provided, the individuals in- volved, and their situation. Determine both the basic issues and any deeper underlying issues at play. Consider the questions posed at the end of the case and how you would respond to these questions as well as other questions that could be asked of this case. Write a one-page response that includes a brief summary of the case and its issues, your answer to the questions posed, and recommendations based on your understanding of the situation posed in the case. Case description: Fan has been a graduate student in the Hoﬀman research group for four years. Her progress as a graduate student is going very well. She has successfully passed her qualifying exams and preliminary exam and her research project has been producing excellent results. However, she’s beginning to feel invisible and worries that no one recognizes her research accomplish- ments. In the weekly research group meeting, Prof. Hoﬀman always asks for a volunteer to give a more detailed presentation in the following week. Fan faithfully gives her brief research update, but she never volunteers to give the more detailed presentation. People frequently ask her to repeat herself when she gives her updates, which makes her self-conscious about her English proﬁciency. This week in the research group meeting several other graduate students in the research group are presenting draft abstracts for the upcoming annual conference in the ﬁeld, but Fan’s advisor did not ask her to prepare one even though Fan thinks her research is ready. In previous years when other students have come back from the conference, she hears about the interesting talks they attended, how well received their own talk was, and senses that they come back even more energized about their research projects. Fan is beginning to get worried that she will never get a chance to go to a conference and present her research. Fan is friendly with Susan, another graduate student in the group who started at the same time as her. She asks Susan to help her to make a case with Prof. Hoﬀman about giving her the change to attend the annual conference. Questions to consider: What might Susan suggest that Fan do to get an opportunity to attend the conference? What other assistance can Fan seek from campus resources to improve her presentation skills? 7.6. RESOURCES ON ORAL COMMUNICATION 163 7.6 RESOURCES ON ORAL COMMUNICATION Although this chapter touches on some key issues related to oral communication, this is a broad topic that entire courses and books are devoted to. For additional content, the following refer- ences are suggested. Baron, N., 2010. Escape from the Ivory Tower: A Guide to Making your Science Matter. Island Press. Hayes, R. and Grossman, D., 2006. A Scientist’s Guide to Talking with the Media: Prac- tical Advice from the Union of Concerned Scientists. Rutgers University Press. Humphrey, J. D. and Holmes, J. W., 2008. Style and ethics of communication in sci- ence and engineering. Synthesis Lectures on Engineering, 3(1):1–140. Miller, T., 2015. Muse of Fire: Storytelling and The Art of Science Communication, https://www.spokenscience.com/publications/ Olson, R., 2018. Don’t be Such a Scientist: Talking Substance in an Age of Style. Island Press. Vernon, B., 1993. Communicating in Science: Writing a Scientiﬁc Paper and Speaking at Scientiﬁc Meetings. Cambridge University Press. C H A P T E R 8 165 Sharing your Research via Written Communication Although writing might not be the ﬁrst thing you think of when you imagined the sorts of things you would do as an engineer, it is an essential aspect of nearly every engineering position and a skill that you can develop to maximize your career outcomes. In engineering research, the ability to share your methods and ﬁndings with others via written communication is essential. 8.1 TRANSLATING TECHNICAL TOPICS IN WRITTEN FORMATS Before delving into technical writing, it is helpful to begin by translating technical topics into more general explanations. This will allow you to use your prior writing experience and help you hone your explanation skills. Much of this approach echoes the early sections of the previous chapter. Your goal in writing about technical topics for nonspecialists is to translate the technical so that it is more broadly understandable. Initially, this can also be a very helpful way for you to develop a deeper understanding of a new research area you are engaging with. In the long run you will also need to be able to translate your own research so that broader audiences can understand what you have done or what you plan to do. This comes up in a variety of contexts, but commonly it ties into funding your research. Working in industry you would need to be able to write a memo about your research/development work so that your boss’ boss can understand its importance and how it impacts the company and its products. Working in an academic institution often requires communicating with the public through press releases and updates to both alumni and donors. Many funding agencies also require you to write a “lay abstract” about your research proposals and often expect short research updates that are understandable for public consumption. As discussed earlier, you will need to tailor the depth and technical detail depending on the speciﬁc audience you want to communicate with. You will also need to provide a more gen- eral discussion of the research, avoid the details, and focus on the potential applications. In some cases, you will have the beneﬁt of working with a professional communications specialist, but often we are left to our own devices to ﬁgure this out. One way to be successful is to see how others have done it so you can emulate their approach. The experts in this area are sci- ence writers, and you can ﬁnd their work in print and online. Look for good science writing 166 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION in places like the Science section of the New York Times, National Geographic Magazine, Wired, DiscoverMagazine.com, ScientificAmerican.com, and the news written about research at your own institution by the university communications writers. ASSIGNMENT 8-1: INDIVIDUAL ASSIGNMENT – LABORATORY-TO-POPULAR-PRESS1 Current scientiﬁc research is often covered by the popular press. What happens to a scientiﬁc idea as it travels from the lab to the newspaper, news blog, or web magazine? How is scientiﬁc information “translated” by the press for the general public? Is press coverage accurate, objective, and complete? Look for recent media coverage of research in your area of interest. Sources might include the business/technology section of a print newspaper, popular science magazines, web mag- azines, or science news blogs (for example: DiscoverMagazine.com, ScientificAmerican. com, EurekAlert.com Spectrum.IEEE.org). After ﬁnding an article of interest, use your lit- erature search skills to ﬁnd the peer-reviewed journal paper related to this article that has been published by the researcher(s) in the scientiﬁc literature. Write a 2-page paper about the original research and the media coverage. Begin your paper with a brief summary of the research and the results based on the journal article. After this summary, critically consider mass media reporting of the research described in the journal article. What aspect of the research was emphasized? Was anything important omitted? Were the results accepted uncritically? Were conﬂicting opinions discussed? ASSIGNMENT 8-2: INDIVIDUAL ASSIGNMENT – SEMINAR PRESS RELEASE Attend a research seminar and write a summary in the style of a short “press release” for a general audience. Summarize the seminar talk in 250–500 words using the following structure. • Include a short and enticing title. • Use the ﬁrst few sentences to introduce the speaker, their university aﬃliation, the date and title of the talk, and the seminar forum (e.g., the Mechanics Seminar Series at UW-Madison). 1Adapted from Caitilyn Allen, Department of Plant Pathology, University of Wisconsin–Madison. • A short description of the main ﬁnding(s) and relevance of the work should appear 8.2. BASIC PRINCIPLES OF TECHNICAL WRITING 167 early in the summary. • The remainder of the “press release” should provide additional information about the ﬁndings presented, including context for the work that was presented, how the work advances the ﬁeld through new advances, new methodologies, or reinforcement of prior work. • Minimize the amount of jargon you use and if you must include a technical term be certain to explain what it means. • Do not write about the miniscule details for the research presented and use active voice. • Include a quote from the speaker if appropriate. BASIC PRINCIPLES OF TECHNICAL WRITING 8.2 Technical writing, which would include writing of a thesis, technical report, or engineering journal article, is diﬀerent in structure, tone, and format from other types of writing. Initially, it may be challenging and awkward for you to write in this style. Two styles of the same events are described below—the ﬁrst in a “normal” description that I might write down as a description of something that happened in my day in a diary, the second in a style more appropriate for a technical journal. I came home from work and was greeted at the door by my chatty cat, Marty. Her insistent meowing made me realize that her food bowl was empty. After setting down my backpack, I ﬁlled her bowl and she immediately began to eat, inhaling half of what I had fed her. At 6:20 pm, a vocalization from feline subject #1 (female) was noted upon initial interaction. Within one minute, 0.5 cups of Cat Chow (Indoor Dry Cat Food, Pu- rina) was dispensed into the feeding bowl positioned at ground level. The subject commenced ingestion within 5 seconds, and 0.3 cups was consumed by 6:34 pm. Occasionally students will question why they must write in a particular style. It is a good question to pose, because certainly information can be eﬀectively communicated with a variety of writing styles. However, you will notice in the simple examples above there is more speciﬁc information available. If I gave you the second example and asked you to take care of my cat because I was unexpectedly called away from home, you would know that my cat expects to eat a little after 6 pm, how much to feed her, where to place the bowl, and what kind of cat food to buy if none was left. An engineering researcher must be able to master technical communi- cation techniques to provide the detail necessary to fully describe their research so that it can be replicated and do it in such a way that their work will be accepted and acknowledged by the ﬁeld. 168 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION Every discipline has its standards and forms that it uses. You must know how to play by these rules before you can consider bending or breaking them. For example, if you were an aspiring screenwriter trying to launch your career in Hollywood, you will want to write it in the customary format so that your ideas are presented in a familiar way and the producer does not discard it as amateurish before even reading it. Once you have hit the big time, and written several blockbusters, you can choose to write in a diﬀerent style, but the likelihood is that by then you will have discovered why the standard style has evolved for this discipline and writing in that style will no longer feel foreign to you. Whether you are an aspiring screenwriter or engineer the style in which the people in that ﬁeld communicate will seem foreign at ﬁrst, but ultimately you will learn how to write in that style eﬀectively and it will become more natural. 8.2.1 DEALING WITH WRITER’S BLOCK Whether a seasoned writer or a novice, nearly everyone gets stuck at some point and ﬁnds it hard to either start writing or make progress on writing. Before launching into the particulars of speciﬁc types of technical writing, it is useful to have some strategies to employ if you run into a snag with the writing itself. Here are some suggestions that you might try. • You don’t have to start at the beginning, and usually the abstract is what gets written last anyway. Try starting with the section that you ﬁnd easiest ﬁrst so that you can gain some momentum. • Make appointments with yourself for writing. This is very useful when you have a large writing project that you need to accomplish over a period of time. At the time you have designated on your calendar, you must write, no excuses. • Create the diagrams/charts/ﬁgures you believe tell the story of your work, put them in a logical order, and then go about describing them. Describe the methods used to acquire the data found in your ﬁgures, what the reader should see when they look at the ﬁgure, and what conclusions can be drawn from the ﬁgure. This text will likely end up in diﬀerent sections of the paper (Methods, Results, Discussion), but sometimes it is easier to write about a ﬁgure and move the text that you generate to the appropriate section at a later time. • Some people ﬁnd that developing a progressively more detailed outline is a fruitful strategy. In this case you would begin with a skeleton outline, then add detailed bullet points to it until you can eventually turn the bullets into sentences and the sentences into paragraphs, ultimately ﬂeshing out each section of the paper. • Try “free writing” where you just capture your stream of consciousness. This means that you don’t edit along the way or search for just the right word. You don’t even worry about sentence structure and punctuation, you just get the ideas captured. Later 8.3. STANDARD FORMATS IN TECHNICAL WRITING 169 you can go back to the product of your free writing and begin editing and sculpting these ideas into the appropriate format. • Talk to a friend about your work and record the conversation. Encourage them to ask you probing questions about your research. Afterward, review the audio ﬁle and type the pieces that seem useful, adding more to the verbal description as you are transcrib- ing it. 8.3 STANDARD FORMATS IN TECHNICAL WRITING There are several basic mechanisms of communications in the world of research, and in written communications there are a number of standard formats that are used. Writing can be used for very diﬀerent purposes, so it is important to understand both the purpose, and the audience for whom you are writing. Initially your writing may be intended solely for your research mentor. As time progresses, however, you may begin writing for venues in which other researchers in your ﬁeld will be the primary audience. Who your audience is will have an impact on a variety of diﬀerent aspects of your writing. When writing to be read by members of your research community you can use more technical jargon, however, it is critical that you understand this jargon rather than hide behind it. Any missteps in the use of jargon will be quickly identiﬁed by experts in the ﬁeld. When writing to a more general audience, or a broader technical audience who are not members of your speciﬁc subspecialty area, you will need to be much more limited in your use of technical terms and jargon. Choose a few of the most important technical terms, and make sure that you clearly deﬁne them through your writing. The layering on additional jargon should be avoided if at all possible. 8.3.1 ABSTRACTS The abstract is likely the most ubiquitous format in technical writing. For instance, you may want to submit your work to a conference for a poster or oral presentation; in most cases this will require you to provide an abstract that summarizes the work you will present. Abstracts are also commonly used at the beginning of longer forms of writing such as technical reports, proposals, theses, and journal articles. A good abstract will provide motivation for the work, information about the approach taken in the research, and a summary of the key ﬁndings. Ideally, as part of the abstract you will also indicate how the research ﬁndings impact the ﬁeld. Commonly the abstract will include: the context for the research, a description of the methods used, the important results/ﬁndings, and the impact/importance of these results. Depending on the context, the length of the abstract may be prescribed. Commonly abstracts fall in the range of 200–300 words, although an “extended abstract” will be the longer in length. In general, it is not appropriate to include citations and abbreviations in an abstract. 170 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION Take some time to read abstracts in your discipline area that have been written for a similar purpose to your current writing task. For example, if you are writing a conference abstract, then look at example abstracts from the previous conference year. If you are writing an abstract for a journal article or research paper, then look at the abstracts of recent journal publications in your discipline. While reviewing these example abstracts, think about the type of information that is being conveyed by each sentence. Dissecting what others have included in their abstract will help you decide what readers will expect to see in yours.2 Some publications require what is referred to as a “structured abstract” which includes speciﬁc subheadings.3 This began in ﬁelds of health and medicine to assist clinicians for quickly identifying methodology and results in journal articles, but this format is being adopted by more science and engineering journals because it helps the reader to quickly identify relevant content. Subheading may include some or all of the following: Introduction, Objectives, Methods, Re- sults, Discussion, Conclusion. Each subheading will usually have 1–3 sentences of concisely written content that the reader can easily understand. As a reader of journal articles we usually begin with the abstract, but as a writer of a manuscript to be submitted as a report or journal article you will generally ﬁnd it easiest to write the abstract last (or at least after you have completed a substantial amount of the other writing involved in your manuscript). These sentences maybe the ones you spend the most time crafting in the entire manuscript! ASSIGNMENT 8-3: INDIVIDUAL ASSIGNMENT – ABSTRACT DISSECTION Identify a journal paper of importance to your research area, preferably one that is considered to be an inﬂuential paper or has been highly cited. Begin by reading the abstract, then read the rest of the paper. Return to the abstract again and dissect each sentence by identifying how it addresses one or more of the four components below: • Motivation/objectives • Approach/methods • Results/ﬁndings • Impact/signiﬁcance 2“Writing an Abstract for Your Research Paper,” UW-Madison Writer’s Handbook, The Writing Center, Uni- versity of Wisconsin–Madison. https://writing.wisc.edu/handbook/assignments/writing-an-abstract-for- your-research-paper/. 3National Library of Medicine, “Structured Abstracts,” https://www.nlm.nih.gov/bsd/policy/structured_ abstractsabstracts.html. 8.3. STANDARD FORMATS IN TECHNICAL WRITING 171 8.3.2 REPORTS The technical report is a common form of writing for engineers. This may be required within your research group as a standard mechanism of keeping your research mentor updated, or as an expectation of research funding. If you hold a fellowship you may be required to provide a report at the end of the fellowship year, for instance. Many federal agencies, private foundations, and industry contracts that provide funding to support research activity also expect regular reports on the progress being made. These reports may be expected monthly, quarterly, or annually. Although your particular research contributions may only be a portion of the reported activity, you will likely be responsible for providing not only data and results, but also a written summary of the work to date. Student Perspective “I had to write quarterly and annual reports for my portion of the project and was involved in the discussion of how we were going to proceed with the project for renewal in funding.” Before you begin your writing, determine the required format and expected detail. Often, your research mentor or other research group members will be able to provide you with this type of background information. As you embark on your writing, focus on presenting information in a logical order, using clear sentence structure. Consider whether ﬁgures and tables will assist you in presenting the information more eﬀectively. Relevant ﬁgures might include a schematic diagram of a process, a photograph of an experimental setup, a graphical depiction of results, and/or a micrograph. ASSIGNMENT 8-4: INDIVIDUAL ASSIGNMENT – WRITTEN RESEARCH UPDATE Some research mentors expect students to provide weekly or monthly written reports, but even if that is not the case for you on a regular basis there may be the need for you to occasionally provide a written research update (e.g., when travel prevents your usual face-to-face meeting). If your research mentor has asked for a speciﬁc format of update, you should provide feedback in that format. If a speciﬁc format is not required, then present your update in a logical manner broken down by project and objectives. Provide actions taken since the last meeting/report, results obtained, next steps planned, and questions that need to be addressed. In preparation for your next interaction with you research mentor, draft a written report. 172 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION 8.3.3 TECHNICAL WRITING FOR A PROPOSAL, THESIS, OR JOURNAL ARTICLE Entire courses and books are written on the topic of technical writing alone.4;5;6 In this section we will focus on some key highlights and strategies you can use to help improve your writing. In addition to this content, you may also want to avail yourself of other resources such as textbooks on the subject and campus resources (e.g., your university’s Writing Center). For most formal writing, there are standard format requirements, or at least a few options for acceptable formats. Begin your writing process by understanding the format expectations. In the case of a thesis, there may be detailed guidelines provided by your program or institution on both the structure and layout out of the document. If you are writing a journal article, then you will need to consult the guide for authors that the journal publishes (usually on its web site). Depending on the journal they will be more or less prescriptive. Regardless, these author instructions should be followed to the letter. If the macro-scale organization of the document is not predetermined, then you will need to work with your research mentor to develop the basic outline. This will usually include: abstract, introduction, methods, results, discussion, conclusion, acknowledgments, references. It is also the case that within the discipline a certain style oﬀ writing is expected. As discussed above, you will need to become aware of those stylistic expectations and to use them in your writing. This is oftentimes easiest to do by looking at examples of prior writing in that style. Remember that there are both good examples and bad examples available to you, so you may want to ask for advice about which examples are the ones you should use to guide your writing. Whether it be a proposal, thesis, or journal article, you must convince the reader to in- vest their time in what you have written. Having it clearly written, well organized, and visually appealing is essential. You also have to anticipate that the reader may not actually read the doc- ument in the order that you have presented it. For example, if I am deciding whether to invest time in reading a journal article, I’ll ﬁrst read the abstract. If the abstract looks worthwhile, then I’ll glance through ﬁgures and jump to the conclusion to see what the key ﬁndings were. If my interest is piqued, then I will invest more time in reading everything in between. For the actual writing process that you will undertake, you will actually write the abstract and conclusion sec- tion LAST because these get written after you know everything you want to say. You will likely spend far more time per word writing and rewriting these sections of the paper, so that they are as clearly and compellingly written as possible. 4Humphrey, J. D. and Holmes, J. W., 2008. Style and ethics of communication in science and engineering. Synthesis Lectures on Engineering, 3.1, 1–140. 5Northey, M. and McKibbin, J., 2009. Making Sense: A Student’s Guide to Research and Writing. Oxford University Press. 6Day, R. A. and Gastel, B. How to Write and Publish a Scientiﬁc Paper. Cambridge University Press. 8.4. REFINING YOUR WRITING 173 8.3.3.1 Persuasive Writing Although it must always be scientiﬁc and objective, technical writing should also be considered persuasive writing. This is obvious in the case of a proposal where you are trying to pitch an idea and potentially convince someone to fund that idea, but it is also true for technical writing in general. You must always persuade your reader of the merits of your work with logical argument, compelling evidence, and engaging language. You may also need to consider addressing any counter arguments in order to deal with common objections preemptively. Choose an introductory paragraph from a prior writing assignment that you have com- pleted and rewrite it while focusing on persuasion. The original paragraph should be from a technical writing topic, although it does not have to be related to your research. Include both the original and revised paragraph in your assignment. 8.4 REFINING YOUR WRITING Diﬀerent people vary in their writing speed and eﬀectiveness, but I have never met someone who was able to sit down and write the ﬁnal version of their paper on the ﬁrst try. As Paul Silvia, professor of psychology, puts it: “Writing productively is a skill, not a genetic gift, and you can learn how to do it.7” Good writing requires reworking and editing what you have written (sometimes dozens of drafts are required). Additionally, when writing with the input of your research mentor or coauthors for a journal publication, you will need to seek their feedback and incorporate modiﬁ- cations. The process can sometimes be long and frustrating, but the outcome will be substantially improved. Student Perspective “I suppose I was under the assumption that good experiments and more so good researchers are those who can ﬁnish projects as quickly as possible. After what I know now, this seems to be true and false at the same time. On one side, researchers are undoubtedly judged by how many published papers they have produced, which is directly related to how quickly they can start and ﬁnish projects. But, on the other hand, they are also judged by the substance of their publications, which could be related to how slowly and carefully they start and ﬁnish projects. It seems that there is a very ﬁne line between this race to produce as many published papers as you can and trying to maintain a standard of quality of information being produced.” Ideally, the process of writing will start well before the research has been completed. There are a number of ways to go about writing productively while you are conducting research. 7Silvia, P. J., 2007. How to Write a Lot: A Practical Guide to Productive Academic Writing. American Psychological Asso- ciation. 174 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION • When you read an important journal article that you expect to cite, take some time to write about the key aspects of the article. You may be able to use the notes section of your citation management system to capture this type of writing. • As the methodology that you are using to conduct your research becomes solidiﬁed, it is an opportune time to begin crafting your methods section. • Writing about your results as they begin to accumulate allows you to organize this information more eﬀectively and this practice can be helpful in identifying previously unanticipated gaps that you will need to ﬁll. It is important to work far enough ahead of your deadline to give enough time for you and the others invested in your writing to make the needed iterations. In the case of a thesis you may also be expected to provide a complete draft weeks in advance of your defense date. Writing does not have to be done in isolation. You will likely have peers who are also in the process a writing (or should be) at the same time you are. Even if it is not helpful for you to write in the same physical space, it can be helpful to set writing goals that you hold each other to and provide each other with feedback periodically. 8.4.1 WRITING WORKSHOPS In some course settings you may be asked to review the written work of a peer in your class and provide constructive feedback. Ideally you will be given some instruction and a rubric to do so. If not, the guidance in this section should be helpful to you. Keep in mind that the author will be reading your review, so you should take pains be constructive in your criticism and to state the positives with the negatives. Every author, whether a classmate or a seasoned researcher, is a person just like you and me! They will be more open to the criticism and making changes to their writing based on your comments if they are framed constructively. When giving feedback you might ask the receiver if they want constructive criticism, and how it can be best delivered. This will show that you are willing to adjust how you provide the feedback and it will allow the recipient to reﬂect on how they can best receive it. Bradley Hughes, Director of the University of Wisconsin–Madison Writing Center, helped me to develop guidelines for writing workshops that we hold twice a semester in our research course sequence. Over the years I have asked students for feedback on how to improve these guidelines for responding to writing on engineering research topics. The resulting sugges- tions below can be used in a writing workshop forum or when exchanging your writing with a peer for feedback. Some Suggestions for Responding to a Colleague’s Draft8 8.4. REFINING YOUR WRITING 175 Before reading the draft– 1. Find out what the writer is intending to do in the document and who the intended audience is. 2. Find out what the writer wants from you as a reviewer at this stage of their writing and use that information to prioritize your feedback. When reading and responding– 3. Read the entire draft before commenting. 4. Praise what works well in the draft; point to speciﬁc passages; explain why these passages work well. PICK AT LEAST ONE THING to compliment and begin your response with that. 5. Describe what you found to be the main point of the draft so that the author can determine if their intent has been achieved. (a) Try describing what you see in the draft. (b) What you see as the main point? (c) What you see as the organizational pattern? 6. When providing criticism, be honest (but polite and constructive) in your response. Try responding as a reader, in the ﬁrst person (e.g., “I like _____.” “I got lost here …” “I think you could help readers follow this if ___________”). 7. Time is limited (for your response and for the author’s revision), so concentrate on the most important ways the draft could be improved. Comment on large issues ﬁrst. Consider the following questions. (a) Is the purpose of the document clear to a reader? Does the draft achieve its purpose? i. Is the writing accessible to a scientiﬁcally literate audience with some background in your area of research? ii. Are ideas presented in an interesting manner? iii. Can the reader infer what the speciﬁc aim of the research is? Are the goals clearly stated? 8Adapted with permission from Bradley Hughes with modiﬁcations and edits from Engineering Physics majors at UW- Madison. See “Peer Reviews,” UW-Madison Writer’s Handbook, The Writing Center, University of Wisconsin–Madison, https://writing.wisc.edu/handbook/process/peerreview/. 176 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION iv. Is the scope of the project clear? What are the deliverables of the research? v. For a proposal: A. Does the writer propose the research is such a way that it appeals both to a general technical audience and members of the author’s speciﬁc research ﬁeld? B. Does the writing provide a compelling argument for the signiﬁcance of the proposed research? vi. For a report, manuscript, or thesis: A. Is enough background given so the reader understands how the data was collected, or how a theory was developed? B. Is the draft convincing in its argument to support the conclusions? Are the results clearly documented? Is evidence used properly? (b) Are ideas adequately developed? i. Are the important ideas of the work presented? Is there a clear focus? ii. Is the draft eﬀectively organized? Is the sequence of points logical? iii. Is there an appropriate balance between major and minor points? iv. Do the author’s ideas ﬂow logically from one paragraph to the next? v. Were there any paragraphs within the author’s draft that seemed out of place? vi. Are the transitions between sections strong? Is material from earlier in the doc- ument built upon and referred to clearly in later sections? (c) Is prior published work on the topic described in suﬃcient detail to give context to the current work? Are the references clearly cited? (d) Are the ﬁgures/tables/equations clear and appropriate? i. Do the ﬁgure captions provide appropriate detail? ii. Do the ﬁgures/tables support the claims that are made in the text? iii. Are the mathematical equations understandable? 8. Be speciﬁc in your response (explain where you get stuck, what you don’t understand) and in your suggestions for revision. And as much as you can, explain why you’re making particular suggestions. 9. Identify what’s missing, what needs to be explained more fully. Also identify what can be cut. 10. Engage in a discussion, but refrain from arguing with the author or with other respondents. 11. Mark proofreading edits (awkward or confusing sentences, style, grammar, word choice, proofreading) on a printout to hand it to the author rather than spending time on these details in the discussion. 8.4. REFINING YOUR WRITING 177 ASSIGNMENT 8-5: GROUP ACTIVITY – WRITING WORKSHOP If you do not already participated in a class or research group that holds Writing Workshops, you can form your own writing group with peers at your institution. A group of 4–6 people is ideal. You will need to agree on the frequency of your meetings, how long you will meet, and what deadlines you will pose on sharing your writing prior to the workshop. A suggested format follows. Writing Workshop Group You will each need to produce a piece of writing by midnight on Monday for the writing work- shop you will be participating on Wednesday. Provide a copy of your written piece, including the cover page information discussed below, to all of the other workshop members. Before meeting, everyone must read the written pieces of all the other group members and come to the workshop prepared to discuss the writings. Bring a copy of your own written piece and cover page as well so that you can reference it and make notes. Writing Assignment Choose a research report, journal article manuscript, research proposal, or thesis you are working on as the subject of your writing piece. Provide 3–5 pages of new writing to your Writing Work- shop group members. Figures and tables (if needed) as well as references should be attached to the end and should NOT be counted toward the 3–5 pages. Include an outline of the overall piece with a description of where this writing will be incorporated. If you are not actively writing at this time, ask your research mentor to identify a “good” thesis in the same general ﬁeld as your research topic. Read this thesis and write a 1-page re- ﬂection commenting on the organization of the thesis, what you learned about thesis writing through your reading of this “good” example, what was done well by the author, and what mod- iﬁcations you would suggest to improve the thesis. Writing Workshop Cover Page The following questions should be addressed in the cover page of the writing piece. 1. What part of your proposal/thesis is this draft (for example, the introduction to my thesis; or the review of technical literature; or the ﬁrst part of the results section …)? 2. What are your main points in this section? 3. What speciﬁcally are you happy with and do you think is working well in this section? 4. What speciﬁcally would you especially like some feedback on or help with in this draft? 178 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION 5. Anything else your readers should know to read this draft in a way that will be helpful to you? ASSIGNMENT 8-6: INDIVIDUAL ASSIGNMENT – WRITING WORKSHOP REFLECTION Reﬂect on the Writing Workshop activity. Discuss the parts of the process that worked well and what could be improved. Consider “Suggestions for Responding to a Colleague’s Draft” in Section 8.4.1 and how it can be reﬁned for technical writing. What are speciﬁc critical questions that must be asked for the type of writing you reviewed? Should the questions diﬀer when considering a journal article manuscript vs. a research proposal vs. a thesis? 8.5 ISSUES SURROUNDING AUTHORSHIP Who is included as an author and the order of the authors can become a contentious subject because it involves both getting credit for the work and taking responsibility for the work. To avoid or at least minimize such problems, it can be helpful to talk about authorship when you are embarking on the research, well before you get to the stage of writing. As an early stage researcher, it is a natural topic for you to bring up for discussion with your research mentor so that you better understand the norms within your research area. Shamoo and Resnick suggest beginning the determination of authorship by identifying the ways in which individuals have contributed to a research project. They identify the following areas of research contribution9: • Deﬁning problems • Proposing hypotheses • Summarizing background literature • Designing experiments • Developing methodology • Collecting and recording data • Providing data • Managing data 9Shamoo, A. E. and Resnik, D. B., 2009. Responsible Conduct of Research. Oxford University Press. 8.5. ISSUES SURROUNDING AUTHORSHIP 179 • Analyzing data • Interpreting results • Assisting in technical aspects of research • Assisting in logistical aspects of research • Applying for grant/obtaining funding • Drafting and editing manuscripts Who appears on the author list can be more complex, particularly in a larger project that has involved a number of people at diﬀerent stages of the work. In some cases, the journal will identify the criteria authorship. The medical community has spent time wrestling with this issue as a result of some historical problems where individuals were included on the author list although they did not contribute to the work. The International Committee of Medical Journal Editors (ICMJE) proposes the following criteria for inclusion as an author on a journal publication10: • substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND • drafting the work or revising it critically for important intellectual content; AND • ﬁnal approval of the version to be published; AND • agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. You will notice here that the last bullet explicitly deals with the authors taking responsi- bility for the work that is published. In large collaborative projects, and particularly as a junior colleague, it is diﬃcult for you to know about the details of every aspect of the work. Certainly, you have responsibility for the aspects of the research and writing that you were directly involved with, thus you can ensure that those parts are conducted in the most ethical manner possible. And, if for some reason the publication is called into question, you have the responsibility to provide information related to the research. Disciplines and sub-disciplines have diﬀerent ways of determining author order: whose name goes ﬁrst on the author list, whose name goes last, and in what order others appear. In some disciplines, it is simply alphabetical. In many disciplines, the principal investigator of a research project is usually the last author. The student or researcher who conducted the majority 10International Committee of Medical Journal Editors (ICMJE), 2019. Deﬁning the Role of Authors and Con- tributors, http://www.icmje.org/recommendations/browse/roles-and-responsibilities/defining-the-role- of-authors-and-contributors.html#two. 180 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION work and wrote the majority of the paper is usually the ﬁrst author. A paper that coincides with a chapter or more of the student’s thesis will usually list student’s name ﬁrst, with other individuals such as the research mentor on the author list. ASSIGNMENT 8-7: INDIVIDUAL ASSIGNMENT – AUTHOR ORDER IN YOUR DISCIPLINE Identify three journal articles published by your research group and look at the individuals in the author list. Using the author aﬃliation information given in the journal article and your per- sonal knowledge about your research group, identify the roles that each author holds in research group or in other collaborating research groups (e.g., undergraduate student, graduate student, postdoctoral researcher, scientist, principal investigator, etc.). Make an appointment with your research mentor to discuss the common practices of authorship in your discipline. Using the journal articles that you have identiﬁed, discuss author order on these examples in the context of common practice within your discipline. 8.6 PUBLISHING YOUR RESEARCH The ﬁrst question to consider is whether or not your research can be published in a journal. In some cases, research is done that can’t be published openly or its publication has to be delayed for some period of time (often referred to as an embargo period). These publication restrictions usually only come up if you are working on classiﬁed research or working under a non-disclosure agreement. As a student this is not a desirable circumstance because you need to publish your work to build your resume. If you believe this may be the case with your research, it is important to talk to you research mentor about what aspects of the work will be publishable, and how you will be able to build your credentials so that you are ready for the job market when you complete your degree. For the majority of work conducted at university campuses, external presentation and publication restrictions are seldom an issue. However, you and your research mentor may decide to delay dissemination of your work because of a desire to patent. If this is the case, you will be working with your campus research oﬃce to determine the patentability and submit a patent application. They will help you determine the appropriate timing the public disclosure of your research (e.g., a conference presentation or journal article submission). Aside from the cases above, journal publication is the primary outcome of the engineering research that you will do (as well as conference proceedings publications in some ﬁelds). This allows other researchers, and people interested in the ﬁeld, to learn from and use your ﬁndings. Adding to the body of knowledge in the open literature helps everyone to move the ﬁeld forward, and often enables future advances in technology and products that beneﬁt society. 8.6. PUBLISHING YOUR RESEARCH 181 The point at which the research is ready for publication is a judgment call that your re- search mentor will help you determine. But often, there is a desire to get your work published sooner rather than later, especially if you are working in a fast moving and competitive ﬁeld of research. You would also prefer to have publications listed on your resume when you apply for a job, so it is in your best interest to help get the research completed and the manuscript submitted for publication. However, in the end, it will be up to your research mentor (or the principal investigator of the project) to make the determination of when the research is ready for dissemination. Student Perspective “My previous understanding about publication of research was that is important but not essential. I thought that getting published was not a necessary condition for career advancement. I thought that other methods of disseminating information like conferences, colloquia, and informal group meetings and conversations with other institutions were of equal importance to being published. I assumed that conferences were the best way of spreading ideas, since those ideas are being told by the originator with the opportunity for immediate questions and/or feedback. Conferences are important, but the most important way of spreading information and ideas is through journal publications.” Publishers use similar review processes for evaluating manuscripts that they receive. The schematic11 in Figure 8.1 gives the general ﬂow of the decision-making process—both from the journal’s perspective and the options you and your co-authors have once a decision has been rendered. Your research mentor will likely provide guidance on both choosing an appropriate journal to submit your work to, and the details of how to go about submission. It is essential to keep in mind that for a coauthored paper everyone must agree on the ﬁnal version prior to it being submit it. Although the review process can seem adversarial, the ultimate goal is to assure that the research being published has been rigorously conducted, well documented, and written about in a clear manner. Usually the comments that come back from a reviewer will help you to improve the writing and clarify what you have done and the conclusions you have drawn from your outcomes. Sometimes the review may identify additional work that should be completed prior to publication, e.g., an additional control experiment or a validation run that was missing. Other times the reviewer may ask for something that is out of scope of this manuscript or it may seem that the reviewer does not understand the fundamentals of the work you are doing. When this happens, it is possible to write a rebuttal to the editor asking that a particular review or portions of the review be set aside. You will need to work with your coauthors to determine the best 11Adapted from: Barker, k., 2006. At the Bench: A Laboratory Navigator, Updated Edition, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY. 182 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION Figure 8.1: Flow of the review and decision-making process in taking a manuscript to journal publication. course of action once you receive your reviews. It is important to act quickly though, often the response to reviews must be submitted within a deadline period. Student Perspective “The process of getting published involves a fairly rigorous (when done correctly, anyway) peer review process. The data is scrutinized, the ideas an- alyzed, and conclusions examined before the information is ever released to the scientiﬁc community. This generally prevents bad data and poor science from being published, thus preventing wasted time and funds by other sci- entists attempting to build on others’ work.” Because the process is rigorous, depending on many people doing a variety of diﬃcult tasks, and involves multiple levels of communication, the publication process is time consuming. Doing the research and writing the manuscript are certainly the majority of the work and time SubmissionPublisherChoose a publisher where your work will have a good ﬁt.Write a compelling coverletter describing the strengthsof your manuscript.Identify the editor or associateeditor most relevant to your topic.Use the constructive criticismprovided by the reviewers toimprove your work.Consider trying to persuadethe editor of the manuscript’sstrengths. Does the publisher allow you (orrequire you) to provide a listof suggested reviewers?EditorReviewersEditorManuscript AcceptedPublicationAre there other publishers where your work will have a better ﬁt?Revise and ResubmitManuscript Acceptedwith RevisionSubmit Manuscript toa Diﬀerent PublisherManuscript RejectedRewritespent, but completing the manuscript submission, responding to reviews, and making revisions will take weeks or months. You need to be prepared for this additional work. 8.6. PUBLISHING YOUR RESEARCH 183 Student Perspective “I was very surprised to ﬁnd out how long it takes for a journal to ac- cept and publish an article. After submitting an article for publication, it can take months to hear back on whether your article was accepted or not. Then, if your article does get accepted, it can take even longer for it to actually be published. The longest wait I was able to ﬁnd when looking through papers this semester was around 13 months, which might have been the most sur- prising thing I learned all semester. But, with a little more searching I found that many journals are starting to post accepted articles online before their actual publication in the journal. I think this is a step in the right direction, as it will deﬁnitely help get published articles to the community faster…” For nearly every journal you will need to do some writing beyond the manuscript itself. The guide to authors published on the journal’s website will detail the additional items required for submission. Often a cover letter to the editor is expected—the journal may prescribe the contents, but it often is expected to include information about the importance of your ﬁndings, how your work ﬁts into the scope of the journal, the most appropriate associate editor to handle your manuscript, and assurances that the manuscript is not under consideration with another journal. The response to reviewer stage of the process will also require writing—usually this includes a letter that only the editor sees, as well as a detailed written accounting of how you are responding to each of the reviewers’ points that is usually seen by both the editors and reviewers. Because the reviewers will also have access to this written response to the reviews, it is critical to be respectful and use carefully crafted language when you are in disagreement with a reviewer’s point. ASSIGNMENT 8-8: INDIVIDUAL ASSIGNMENT – WHERE TO PUBLISH Identify potential journals where you might publish the research you are currently working on. Begin by looking at the papers that you are currently citing, and journals that they are published in. Also consider other key journals in your research area that you may be familiar with, or that your research mentor has mentioned. Determine whether your topic area is a good ﬁt for aims and scope for these journals. Identify the Impact Factor of these journals and other relevant statistics provided, such as the timeframe between submission and publication. Look at each of the journal’s web pages and identify the information/guide for authors. 184 8. SHARING YOUR RESEARCH VIA WRITTEN COMMUNICATION After you have considered several journals, identify the top three candidates and summa- rize why you think these journals would be a good ﬁt for your research. 8.7 RESOURCES ON WRITTEN COMMUNICATION Although this chapter touches on some key issues related to written communication, this is a broad topic that entire courses and books are devoted to. For additional content, the following references are suggested. Humphrey, J. D. and Holmes, J. W., 2008. Style and ethics of communication in sci- ence and engineering. Synthesis Lectures on Engineering, 3(1):1–140. Northey, M. and Jewinski, J., 2012. Making Sense in Engineering and the Technical Sci- ences: Making Sense in Engineering and the Technical Sciences: A Student’s Guide to Research and Writing. OUP Canada. Day, R. A. and Gastel, B., 2006. How to write and publish a scientiﬁc paper. Cam- bridge University Press. Silvia, P. J., 2007. How to Write a Lot: A Practical Guide to Productive Academic Writing. American Psychological Association. Sternberg, D., 2014. How to Complete and Survive a Doctoral Dissertation. St. Martin’s Griﬃn. Luey, B., 2002. Handbook for Academic Authors. Cambridge University Press. C H A P T E R 9 185 Safeguarding Your Personal Health and Happiness 9.1 THE CHALLENGES YOU MAY FACE IN GRADUATE SCHOOL Life brings us diﬀerent challenges at diﬀerent times. Some of us live many years or even the bulk of our lives without experiencing much diﬃculty in our personal relationships, work, or health. For others, hardship is something that comes earlier, and potentially, more often. Regardless of your level of experience with adversity, each experience sharpens your ability to overcome obstacles and brings new opportunities for learning about yourself. For the average person, the speed of everyday life has quickened to a frenzy. Many of us are continuously digitally connected with seemingly endless new information being thrown at us. IFLScience reports that “Ninety percent of the data in the world today has been created in the last two years alone.1” Exposure to the bombardment of information leads to distraction and mind wandering that can negatively impact our attention and our day-to-day fulﬁllment.2 On top oﬀ all the usual stuﬀ that the average person has to deal with, graduate school makes things a bit more ampliﬁed, with higher stress levels associated with education-related deadlines and expectations.3 The next few paragraphs are going to dwell on the negatives of graduate school, but I’d like to pause here and give advance notice that there are concrete steps you can take to mitigate and even eliminate these issues. In fact, if you are already well aware of the issues, please feel free to skip ahead to the next section! Graduate study is diﬀerent from undergraduate study and requires a student to make a transition in their approach to education and scholarship. Your experience will become more centered on your research activities, particularly as you progress in a Ph.D. program. It is also common for a graduate student’s experience in their program to be punctuated with critical deadlines and exams that have broader career implications with limited opportunities for a “do- 1IFLScience, “How Much Data Does The World Generate Every Minute?” http://www.iflscience.com/ technology/how-much-data-does-the-world-generate-every-minute/. 2Killingsworth, M. A. and Gilbert, D. T., 2010. A wandering mind is an unhappy mind. Science, 330.6006, 932–932. 3Hyun, J. K., Quinn, B. C., Madon T., and Lustig, S., 2006. Graduate student mental health: Needs assessment and utilization of counseling services. Journal of College Student Development, 47(3):247–66. 186 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS over.” These exams can produce high levels of stress that have measurable biological impacts on your body.4 Although over 80% of Ph.D. students who are enrolled full time are funded by an assis- tantship in engineering disciplines, these are not high-paid positions. Additionally, part-time students may be part time simply because they can’t secure an assistantship. For these reasons, ﬁnancial pressures can be another source of stress for graduate students. Because graduate school is generally attended by individuals in their prime child-bearing years, often graduate students have partners, spouses, and children. In combination with a lower income and a demanding program of scholarship, family responsibilities can be challenging to juggle. Sometimes our families and friends may not be as supportive as we would like, often this is rooted in a lack of understanding about what we are doing in graduate school and what we are trying to achieve. The graduate student experience often has similar traits to an apprenticeship. There can be negatives that arise from having strong or even singular ties to one individual research advisor.5 Occasionally the student’s committee can help to buﬀer the situation, but strong committee engagement is not always present for students. Furthermore, during the course of their graduate studies, a student should undergo a transition to a junior colleague. For a variety of reason’s this transition may be arrested, and the student may be trapped in a role where they have little or no say over their activities even though they have established signiﬁcant expertise. As a result, having a low level of autonomy can be a big source of dissatisfaction. 9.1.1 GRADUATE STUDENT MENTAL HEALTH Engineering Ph.D. students spend an average of 6.7 years in graduate school to complete their degree.6 It is a long and intellectually strenuous process. Students sometimes experience “slumps” that can lead to depression. Research published in Nature Biotechnology reported that “…graduate students are more than six times as likely to experience depression and anxiety as compared to the general population.7” There has been quite a bit of research on the topic of depression in graduate school and some ﬁndings point to causes such as “..social isolation, the often abstract nature of the work and feelings of inadequacy…8” If you are dealing with mental health issues it is important to seek out help sooner rather than later. 4Lacey, K., Zaharia, M., Griﬃths, J., Ravindran, A., Merali, Z., and Anisman, H., 2000. A prospective study of neu- roendocrine and immune alterations associated with the stress of an oral academic examination among graduate students. Psychoneuroendocrinology, 25(4):339–56. 5Martin, M. M., Goodboy, A. K., and Johnson, Z. D., 2015. When professors bully graduate students: Eﬀects on student interest, instructional dissent, and intentions to leave graduate education. Communication Education, 64(4):438–54. 6National Science Board, “Science and Engineering Indicators 2018,” https://www.nsf.gov/statistics/2018/ nsb20181/. 7Evans, B., Gastelum, B., and Weiss, V., 2018. Evidence for a mental health crisis in graduate education, Nature Biotech- nology, 36, 282–284. 8Flaherty, C., 2018. Mental health crisis for grad students, Inside Higher Education. 9.2. STEPS YOU CAN TAKE TO BE HEALTHIER AND HAPPIER 187 Perfectionism can also be an issue that some struggle with, particularly because of the need for validation and fear of criticism that can go along with it. Perfectionism can manifest itself diﬀerently9: As a personal demand and expectation of oneself, as a perception that others expect perfection in you, and as an expectation that others perform to unreasonably high standards. For graduate studies, the issue of “self-oriented perfectionism” can cause a number of problems that can interfere with progress. Certainly holding yourself to high standards is good, but when those high standards require you to always portray an image of perfection to others, concealing prob- lems and struggles that you may be having, and being unwilling to ask for help when you need it, then it is a detriment to being successful. Some graduate students suﬀer from the “imposter syndrome,” the feeling that someone made a mistake by letting them into graduate school and at any moment they will be found out as a fraud. This can lead to the need to appear perfect to others and conceal and ﬂaws or perceived inadequacies. A recent research study of graduate students showed that “…avoiding outward displays of imperfection was the strongest and most consistent predictor of academic problems….10” Whether independently or with the help of counselling, if you consider yourself a perfectionist or identify with the imposter syndrome, you need to accept the reality that everyone is imperfect. Ask for the help you need, so that you can be successful. These previous paragraphs may sound dismal, but it is important to recognize that if you are experiencing issues you are not the only one.11 If you ﬁnd at some point in your graduate career that you are struggling—facing one or more of the above issues—it is important to seek out help. Not only will you ﬁnd that other graduate students experience similar issues, but there are also people, strategies, and resources available to you, if you are willing to reach out for some help. Because universities now better recognize the issues faced by students at the undergraduate and graduate levels, there are often campus resources available. You may have a university health services that you can turn to, and you are likely to have a graduate school or dean of graduate studies oﬃce on your campus that can help you to identify the resources that are available on campus. 9.2 STEPS YOU CAN TAKE TO BE HEALTHIER AND HAPPIER The challenging aspects of graduate school can have a detrimental eﬀect on you as a person, but you have control over more than you may think. In particular, you have the ability to organize 9Hewitt, P. L., Flett, G. L., Sherry, S. B., Habke, M., Parkin, M., Lam, R. W., McMurtry, B., Ediger, E., Fairlie, P., and Stein, M. B., 2003. The interpersonal expression of perfection: Perfectionistic self-presentation and psychological distress. Journal of Personality and Social Psychology, 84(6):1303. 10Cowie, M. E., Nealis, L. J., Sherry, S. B., Hewitt, P. L., and Flett, G. L., 2018. Perfectionism and academic diﬃculties in graduate students: Testing incremental prediction and gender moderation. Personality and Individual Diﬀerences, 123, 223– 228. 11Evans, T. M., Bira, L., Gastelum, J. B., Weiss, L. T., and Vanderford, N. L., 2018. Evidence for a mental health crisis in graduate education. Nat. Biotechnol., 36(3):282. 188 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS your schedule and set priorities so that you have the opportunity to be both healthy and happy as you pursue your graduate studies. For graduate students, just like other professionals, “Work—life balance is associated with physical and mental well-being…12 The next several sections identify some of these work-life balance topics—such as getting exercise and eating healthy—and the strategies that can help you achieve your goals—such as mindfulness practice and time management. Some of what you need to do is simple. In Claire Potter’s essay outlining “The Ten Com- mandments of Graduate School13” her second commandment, after “Thou shalt no rack up unnecessary credit card debt,” advises that you not neglect your dental and health care. If you move to a new location for graduate school, you will need to set up new doctors and dentists for yourself. Determine what your insurance beneﬁts are—at some institutions you will have coverage—and ﬁnd out who the providers are. Don’t wait until you have a crisis, get established with a new doctor and a new dentist early. Additionally, there are numerous campus resources that can help you to navigate speciﬁc health issues that you are already aware of, or may arise in the future. Part of your baseline for happiness in graduate school is the people who you interact with on a day-to-day basis. Recall back to Chapter 2 on Finding the Right Research Position for You. It has been shown that having a “…strong, supportive and positive mentoring relationships between graduate students and their PI/advisors correlate signiﬁcantly with less anxiety and depression.14” Knowing that is helpful for making a good choice at the start, but even if you ﬁnd that you don’t have the kind of relationship you would have wished for with your research mentor, it is not the end of hope. Focus on broadening your constellation of mentors to ﬁnd the support you need to succeed. On occasion, however, some graduate students ﬁnd themselves in a position that is negative and destructive, and a change of research mentor is needed. If the relationship is one that you need to remove yourself from, it does not mean that you have to give up your goals for achieving your Ph.D. Work with trusted colleagues on your campus to help you identify a better path forward (for instance, many campuses have an Ombudsperson who you can consult with conﬁdentially). Changing Course I have had at least one case in my research group where in the process of mentoring we discovered that the alignment between the student’s newly reﬁned goals and the research that was being conducted in my lab were not as good as we once thought they were. In this case, I helped the student to identify the new direction that they would like to take and assisted them in 12Evans, B., Gastelum, B., and Weiss, V., 2018. Evidence for a mental health crisis in graduate education, Nature Biotech- nology, 36, 282–284. 13Potter, C., 2013. The ten commandments of graduate school, Chronicle of Higher Education. 14Flaherty, C., 2018. Mental health crisis for grad students, Inside Higher Education. 9.3. GETTING SLEEP 189 getting to where they wanted to be. Although this is a problem in the short term for me, and a loss because I have invested both time and funding into their training, I have found that in the long run it’s best for both the people and the project to make the change. I know that changing research groups was a diﬃcult conversation for my student to initiate with me. Part of what helped to make it work was their willingness to help us complete our short-term goals on the research project while we were looking for a better long-term path for the student. ASSIGNMENT 9-1: INDIVIDUAL ASSIGNMENT – IDENTIFYING SUPPORT RESOURCES Nearly every graduate school in the U.S. has support resources that their graduate students can take advantage of.15 This may include access to workshops on stress management, child care sharing groups, individual mental health counselling sessions, support groups or boot camps on dissertation writing, athletic facilities, non-credit classes oﬀered by the union or continuing studies, just to name a few. Investigate the resources available to you on your campus (use websites, graduate student coordinators, and fellow students). Identify at least two resources that you would ﬁnd personally beneﬁcial immediately, and two additional resources that you could envision beneﬁt- ing from in the future when you are at a diﬀerent stage in your graduate career or experiencing a speciﬁc struggle. Choose one of these resources that you can utilize this week and make an appointment and/or schedule time for it in your calendar. 9.3 GETTING SLEEP It’s easy to let the end of the term, a looming deadline, or an important degree program exam, get your schedule out of whack. But that’s actually the worst time to get less sleep. Having a consistent sleep routine and sleep schedule are important for both your physical and mental health. Lacey et al. found that “…during the course of lengthy anticipatory periods preceding a scheduled oral examination, graduate students reported more frequent malaise (e.g., headaches, sore throat, fatigue) than did controls.” Furthermore, “…anticipation of an imminent oral aca- 15Bird, L. T. and Sheryl, A. Principles of Good Practice in Dealing with Students in Distress: Council of Graduate Schools. Available from: http://cgsnet.org/principles-good-practice-dealing-students-distress-0. 190 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS demic examination was also associated with increased cortisol levels16”—a hormone that regu- lates important bodily functions like metabolism and immune system response. Even pulling one all-nighter or getting minimal sleep before an exam can be detrimental. Alterations of immune function occur after only a modest loss of sleep.17 Good “sleep hygiene” begins with taking care of your body during the day and allowing your brain to cool down before you turn oﬀ the light to go to sleep. You have likely heard much of this advice before, but it is important to avoid caﬀeine in the later part of the day and alcohol before bedtime. You also need to put away the screens and do a relaxing activity like meditation, journaling, or reading (from paper) before you turn oﬀ the lights. Make sure your sleeping sit- uation is comfortable, dark, and quiet (if not, an eye mask and earplugs can be helpful). Once you have developed a routine stick with it. Some people have no trouble going to sleep at the beginning of the night but can’t get a full night’s sleep because they wake before they intend to and have diﬃculty going back to sleep. If this happens to you and your mind is racing, it may be helpful to keep a notepad by your bedside to write down what you are thinking about so you can let go of it for now and get back to sleep. You might also ﬁnd that re-engaging with aspects of your bedtime routine, like meditation of reading, may help you to return to restful sleep. ASSIGNMENT 9-2: INDIVIDUAL ASSIGNMENT – PERSONAL SLEEP LOG You may not realize how irregular your sleep pattern is if you are not attuned to the issue. Place a paper calendar and pencil next your bedside. Each morning jot down the approximate time you fell asleep the previous night, the time at which you woke up, the total hours of sleep, and a quality rating of your sleep between 1 and 10. Do this during a representative week of the semester. For the next week identify a target time at which you will go to bed every night and try to maintain that nighttime routine while continuing to record data. At the end of the second week identify whether your sleep quality improved. Use subsequent weeks to experiment with other sleep improvement techniques, such as limiting exposure to TV/computer/phone screens before bedtime, making modiﬁcations to your sleep environment to ensure that it is dark and quiet, and avoiding caﬀeine during the second half of the day.18 16Lacey, K., Zaharia, M., Griﬃths, J., Ravindran, A., Merali, Z., and Anisman, H., 2000. A prospective study of neu- roendocrine and immune alterations associated with the stress of an oral academic examination among graduate students. Psychoneuroendocrinology, 25(4):339–56. 17Irwin, M., Mcclintick, J., Costlow, C., Fortner, M., White, J., and Gillin, J. C., 1996. Partial night sleep deprivation reduces natural killer and cellular immune responses in humans. FASEB 10, 643–653. 18Mayo Clinic, “Sleep tips: 6 steps to better sleep,” https://www.mayoclinic.org/healthy-lifestyle/adult- health/in-depth/sleep/art-20048379. 9.4 GETTING EXERCISE 9.4. GETTING EXERCISE 191 It’s important to get exercise, particularly if your coursework and research keep you pinned at a desk most of the day. In addition to being good for your body, exercise can help you reduce stress and can be beneﬁcial for your brain. Depending on what you decide to do for exercise, it also the potential to help you meet new people beyond your research group and graduate program and develop new friendships. These can be a valuable support network for you. If you have moved to a new location for your graduate studies, the types of exercise you used to rely may not be as readily available because of a diﬀerent climate or access to facilities. Take the opportunity to expand your horizons—try out new sports, identify clubs, and test diﬀerent activities. Many campuses have club sports, leagues, and even non-credit classes that can help you to test out something new and develop skills. Minimally, most campuses have some sort of gym/pool access available to students. Think broadly about what might be available locally: running and/or biking trails, hik- ing trails, ice skating, cross-country ski trails, downhill skiing, sailing, rowing, kayaking, rock climbing, swimming, dancing, etc. Consider club and sport teams like baseball/softball, volley- ball, lacrosse, kickball, and even quidditch. For some people exercise is already a part of their daily routine, but for others it is some- thing we have to push ourselves to do regularly. If you are in the second category, there are a number of strategies that might work for you. Try scheduling exercise into your calendar just like you would do for a course, sign up for a non-credit class that meets regularly, or ﬁnd an “exercise buddy” who will help you get out to exercise regularly. If you’re starting a new exercise routine or sport, start out realistically and slowly ramp up to a level that is healthy and sustainable. If you have concerns about how exercise may impact past injury or other health condition, consult with your physician before embarking on anything strenuous. ASSIGNMENT 9-3: INDIVIDUAL ASSIGNMENT – CAMPUS SPORT AND RECREATION RESOURCES Access your institution’s website and determine what campus resources are available to you for getting/staying ﬁt. Search on terms like “recreational sports” and “club teams.” Identify several that would be of interest to you and choose one to check out in person. Get a facility tour or meet with someone who will provide you with an orientation. 192 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS EATING HEALTHY 9.5 One of the challenges of being a student, particularly if you live on or near campus, is ﬁnding ways to consistently eat healthy. Pizza deliveries, fast food restaurants, and sandwich shops are readily available, but these do not generally provide the kind of food that will help you stay healthy and fuel your brain eﬀectively. Unfortunately, many campuses meet the deﬁnition of a food desert, thus it is diﬃcult to easily obtain healthy, fresh food. In response some campuses have welcomed area farmers to hold small farmer’s markets on campus during the growing sea- son, this can be a great way to insert more fresh produce into your diet. In some areas of the country, community-supported agriculture (CSA) provides a way for you to both support a local farm by buying directly from them and receive a box of fresh produce weekly during the growing season. Depending on the particular CSA you join, you may be able to choose the size of box, delivery frequency, and even the choice of items. Some farms have drop oﬀ locations on university campuses. There may also be opportunities to buy fresh ingredients for healthier eating just a bus ride away. Look into the areas grocery stores that are available and the public transportation options that are connected to campus. If you are on a land-grant campus or a university with a large agricultural program you may also have the opportunity to buy food from campus sources. At the University of Wisconsin- Madison for instance, the Meat Sciences Laboratory has Bucky’s Butchery shop (an under- graduate operated store that sells meat one day a week), the Babcock Dairy Store has award- winning cheese (and phenomenal ice cream), and the UW Poultry Science Club sells turkeys each Thanksgiving. Take a look into what your campus has to oﬀer, you might be surprised at what you ﬁnd. You may have to do a bit of internet sleuthing, but there are likely some good options to help you eat healthy that are more easily accessible than you might have initially appreciated! ASSIGNMENT 9-4: INDIVIDUAL ASSIGNMENT – HEALTHY FOOD EXPLORATION Identify a fresh vegetable available to you locally that you have never tried before or don’t nor- mally eat. Use this vegetable as a search term in your favorite cookbook or in an online recipe resource (e.g., www.allrecipes.com). Find a recipe that looks appealing, buy the ingredients, and give it a try. CREATIVE OUTLETS 9.6 The creative nature of engineers enables their ability to innovate and discover. To imagine what might be possible. 9.6. CREATIVE OUTLETS 193 Engineers often express their creativity in a number of ways outside of their engineering practice. If you ask your engineering colleagues you may ﬁnd that you are among musicians, dancers, writers, painters, potters, woodworkers, and more. If you are one of these engineer artists, be sure to allow time for your creativity both inside and outside of engineering. Not only is it a good stress relief, you may ﬁnd that is a helpful way to practice achieving a state of immersion that you also need to be productive with your engineering data analysis, technical writing, etc. Your arts practice may also ultimately link with your engineering work in ways you may not have initially anticipated.19 The more you focus on observing, the more you will see. Your thinking and skills and creativity will be enhanced not only by improving your math skills and your language skills, but also your perceptual skills.20 For example, engagement with visual representation has been crucial aspect of my profes- sional career. My training as a visual artist has been essential skill building that has helped me to understand and interpret the images obtained from a variety of microscopy instrumentation. The ability to see detail and attend to subtle changes in images is critical to my engineering research. I believe that these skills are enhanced by my artistic practice with painting. In my teaching, I use visual representations of engineering elements and concepts. They are integrated throughout the courses that I teach at the undergraduate and graduate levels to provide learners with additional ways of interacting with complex concepts. The Pause that Refreshes I have always enjoyed art as a hobby and had taken painting and sculp- ture classes prior to attending graduate school. During my Ph.D. program I enrolled in a ceramics class oﬀered through the Art Department (it was pretty intense, so I chose the pass/fail option for the course even though I probably could have earned a good grade). After taking the class I realized that being able to immerse myself in art periodically was reducing my stress overall and helping me to be more focused when I came back to my engineering studies and research. I discovered that the campus student union also had non-credit classes and you could have access to the studio, pottery wheels, and kilns by paying a small fee even if you were not enrolled in a class. In the studio I bumped into a fellow graduate student studying chemistry who enjoyed ce- ramics as well. She and I began meeting regularly at the studio to work on our pottery. It was a wonderful complement to my engineering work that I continued throughout my Ph.D. program. 19Walesh, S. G., 2019. Can creating art make you a more eﬀective engineer?, PE Magazine, National Society of Profes- sional Engineers, pp. 24–27. 20Edwards, B., 2008. Drawing on the Artist Within, Simon and Schuster. 194 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS 9.7 EMPLOYING MINDFULNESS PRACTICES There is ample scientiﬁc research that the use of regular mindfulness practices, such as medita- tion, can have a positive impact on our body and make changes in how our mind works.21 What are mindfulness practices? “An operational working deﬁnition of mindfulness is: the awareness that emerges through paying attention on purpose, in the present moment, and nonjudgmentally to the unfolding of experience moment by moment.22” One way to achieve the qualities of attention and awareness, thought of as being characteristic of mindfulness, is the practice of meditation. Historically, meditation has been connected to Hinduism and Buddhism, but more recently it has been Westernized and converted into a secular practice. Mindfulness practices involve two basic components: “The ﬁrst component involves the self-regulation of attention so that it is maintained on immediate experience, thereby allow- ing for increased recognition of mental events in the present moment. The second component involves adopting a particular orientation toward one’s experiences in the present moment, an orientation that is characterized by curiosity, openness, and acceptance.23” Mindfulness prac- tices are broader than just meditation. Other mindfulness practices you might be familiar with include yoga and Tai Chi. There is mounting scientiﬁc evidence that regular mindfulness practice such as meditation can change your brain and your body. Studies that ask participants to employ daily meditation show that individuals can manage chronic pain, reduce stress hormones, and improve their re- silience. There is a growing literature showing that activities like Tai Chi, Qigong, yoga, and meditation can alter inﬂammatory gene expression and change cellular markers of inﬂamma- tion, even after just 6–8 weeks of training and practice.24 You should not feel that a major lifestyle change is required to achieve some beneﬁt. Small amounts of regular meditation can also be helpful to reduce stress and improve your capacity for creative thinking.25 One simple mindfulness practice is a focus on the breath. For example: Sitting in a comfortable position, you close your eyes and notice your breath. It is sometimes easier to focus by using a count with your breathing. Breath in counting to one, and breath out to one, breath in counting to two and breath out to two, breath in counting to three and breath out three, and so on. There will be a point where you ﬁnd the count length to be uncomfortable, so then reverse your count until you 21Davidson, R. J. and Begley, S., 2012. The Emotional Life of Your Brain: How Its Unique Patterns Aﬀect the Way, Your Think, Feel, and Live—and How You Can Change Them, Plume, New York. 22Kabat-Zinn, J., 2003. Mindfulness-based interventions in context: past, present, and future. Clinical Psychology: Science and Practice, 10(2), 144–156. 23Bishop, S. R., Lau, M., Shapiro, S., Carlson, L., Anderson, N. D., Carmody, J., Segal, Z. V., et al., 2004. Mindfulness: A proposed operational deﬁnition. Clinical Psychology: Science and Practice, 11(3):230–241. 24For example: Ader, R., Cohen, N., and Felten, D. L., 1987. Brain, behavior, and immunity. Brain, Behavior, and Im- munity 1(1):1–6. And Bower, J. E. and Irwin, M. R., 2016. Mind—body therapies and control of inﬂammatory biology: a descriptive review. Brain, Behavior, and Immunity, 51, 1–11. 25Schootstra, E., Deichmann, D., and Dolgova, E., 2017. Can ten minutes of mediation make your more creative? Harvard Business Review. 9.8. MAKING TIME FOR IT ALL 195 ﬁnd a comfortable count length for your breath and continue breathing in and out at this comfortable rate. As you continue to breath in and out, things will pop into your mind and that’s ok. Just take note of it, let the idea pass without dwelling on it, and then refocusing your mind on your breath. When you feel you are ready to stop, simply open your eyes. This sort of practice allows you to enhance your focus, select what you choose to focus on in the moment, and build the ability to notice your thoughts objectively without further elaboration. There are a wide range of skills and techniques that you can use to build mindfulness into your everyday life. I highly recommend that students consider getting training in one or more mindfulness techniques. There are often opportunities available on or near university campuses, as well as a plethora of online resources26 and aps that you can use.27 ASSIGNMENT 9-5: INDIVIDUAL ASSIGNMENT – MINDFUL RESET, MINDFUL RECHARGE, MINDFUL REFRESH Use brief mindfulness activities during your day to reduce your stress and increase your produc- tivity. Make a copy of the activity chart (Table 9.1). Cut along the lines and place the pieces in an envelope. The next time you are feeling stuck, or stressed, or just need a break, pick an activity card at random from the envelope and spend some time practicing your mindfulness skills with the activity described. 9.8 MAKING TIME FOR IT ALL In Chapter 5 we discussed strategies for project management as it relates to your research. For some of us it might be helpful to employ project management tools with aspects of your personal life too. 26For example: Center for Healthy Minds, University of Wisconsin–Madison (resources on cultivating wellbeing and relieving suﬀering (cid:15) through a scientiﬁc understanding of the mind, including some guided practices): http://centerhealthyminds.org/join-the-movement/workplace Center for Advanced Studies in Business, University of Wisconsin–Madison (guided audio practices): (cid:15) http://www.uwcultivatingwellbeing.com/guided-audio-practices Inner Sense Consulting, Bev Hays (guided mindfulness meditations): http://www.innersenseconsulting.com/meditations.html. 27Two of my current favorites: Simply Being Stop, Breathe and Think (cid:15) (cid:15) 196 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS Table 9.1: Mindful Reset, Mindful Recharge, Mindful Refresh Activities (Continues.) MeditateMeditate for 10 minutes on the present moment. Find a comfortable position, sitting upright if possible, and bring yourself into stillness. Pay close attention to your breath. Note, but don’t dwell on, the thoughts, emotions, and sensations that occur.SenseTranslate music into drawing. Listen to a piece of music that you enjoy. Translate the feeling that music gives you into a drawing – abstract or realism.DrawFind an object in your environment that is familiar to you. While looking at the object, do a line drawing of the object while NOT looking at the paper. Imagine that your pencil or pen is actually touching the contour of the object as you draw.JournalTh ink about ways in which you are committed to the common good. Choose one of these and write about what you will do in the future to advance that common good.ExerciseWalk 5+ ﬂ ights of stairs. Count each step.(Pay attention to your body and stop if you feel pain.)MeditateClose your eyes, take slow deep breaths, and count 20 of them. If your mind wanders, take note of what you were thinking about, and then bring yourself gently back to focus on your breath.JournalWrite about 3 things that give you a genuine smile.ConnectSpend some time talking to someone you have not spoken to in a while.JournalWrite down 20 things that you are grateful for.DrawFill an entire piece of paper with repetitions of a shape or pattern.JournalWhat was the best thing that happened to you today? Take a few minutes to write about it.SenseEat a healthy snack while giving the experience your full attention. Focus on the taste, texture, and aroma.Table 9.1: (Continued.) Mindful Reset, Mindful Recharge, Mindful Refresh Activities 9.8. MAKING TIME FOR IT ALL 197 ConnectSend a brief note/message of appreciation to a colleague, friend, or family member.SenseTake a walk in nature. Find a small space or a large expanse where you can observe the ﬂ ora and fauna around you.JournalWhen did you feel the most proud of yourself today? Take a few minutes to write about it.MeditateTake a mindful walk in a safe place. Walk a bit slower than your usual pace. Focus your awareness on your movements, balance, and the rhythm of your steps. If your mind wan-ders, take note of what you were thinking about, and then bring yourself gently back to focusing on your walk.ComposeCreate a theme song for your day. Consider which word or topics repeat as you think about the positive ways in which you would like your day to progress.Use these words or topics to create a chorus for your theme song.ExerciseDo sitting isometric exercises. For instance, while sitting and keeping your knees bent at a right angle, pick up one foot oﬀ the ﬂ oor for a count of 10. Switch and lift the other foot for a count of 10. Pay atten-tion to your body during each exercise and stop if you feel pain.ComposeTranslate feeling into rhythm. Compose a short rhythm expressing a feeling you have chosen. Express it with ﬁ nger snapping, toe tapping, tongue clicking, etc.JournalTh ink of a time when you were resilient in the face of adversity, small or large. Focus on that resiliency and write about how you can use this resiliency in the future.SenseFind a pleasant scent in your environment. Close your eyes and inhale deeply. Concen-trate on the sensations and thoughts that spring to mind.SenseFind something that feels cool or warm to the touch. Place your hands on the object. Close your eyes and engage in the moment.DrawDo a sketch of something in your ﬁ eld of view. Focus on the energy or mood of what you are drawing.ExerciseDo yoga stretches for 5 min-utes. Th ree poses.(Pay attention to your body and stop if you feel pain.)198 9. SAFEGUARDING YOUR PERSONAL HEALTH AND HAPPINESS Diﬀerent people have diﬀerent challenges when it comes to making time for it all. For some of us we have too little “me time” and for others there is too much “play time.” All of us need a balance. You need to devote substantial time to making progress in your graduate education, and you will be able to more eﬀectively do so, if you have a healthy mind and body. It is also important to resist making comparisons between yourself and other students in your degree program. Each person’s path is a unique one. Your goal is to ﬁnd the most eﬀective and eﬃcient path for yourself, that allows you to achieve your goals while also being a well-balanced individual over time. ASSIGNMENT 9-6: INDIVIDUAL ASSIGNMENT – PLANNING YOUR WEEK In reality, every week of your life will be diﬀerent from the next and you will have to be ﬂexible as a deadline or special event approaches. However, you can develop some principles that you would like to follow in managing your time on a regular basis. Begin by creating a list of the major activities that you undertake regularly, e.g., coursework, if you are taking classes, research activities, including writing, personal time that includes exercise, and other activities that make you either relaxed or energized, social/family time, and sleep. Now set out goals for the number of hours a week you feel you should devote to each activity. Schedule how this should look on a weekly calendar for the “average” week (Table 9.2). Now plan your actual calendar for the coming week. Live your life, do your work, and at the end of each day jot down the number of hours you spent on each activity category. At the end of the week total up how you spent your time and compare it to your goals. You may ﬁnd that you have not set your goals realistically, or you may ﬁnd that this week had unexpected events. Respond to this by balancing out how you spend your time in the following week. Continue this planning activity for four weeks. This process is designed to help you ﬁnd a routine that includes all of the activities you should spend time on, and a suﬃcient amount of time on them to make progress and meet your deadlines. Be sure you have not eliminated sleep, personal, and social/family time to make time for everything else—without balance you will be less productive overall. 9.8. MAKING TIME FOR IT ALL 199 Table 9.2: Weekly calendar used to set goals for the number of hours planned for each activity and actual time spent on each activity daily Planned ActualResearchCourse/TeachingCommunication/Networking/ServiceRelax/Exercise/Recharge ActivitiesFamily/Personal ResponsibilitiesSleepMondayTuesdayWednesdayTh ursdayFridaySaturdaySundayTotalAfterword 201 This book is based on my experiences as a research mentor, graduate advisor, instructor, and administrator in the Graduate School of the University of Wisconsin–Madison. I am grate- ful to all of the undergraduate and graduate research assistants who have worked with me over the years, not only for their research contributions, but also for how they helped me to develop and learn as a mentor. My teaching in the Engineering Physics undergraduate program and the phenomenal undergraduate honors students I have worked with have helped me to better understand what novice researchers want and need to know as they begin their research career. I also had the pleasure of serving in several diﬀerent administrative roles in the University of Wisconsin–Madison Graduate School for ﬁve years, where I provided leadership for all aspects of the graduate student experience, including admissions, academic services, academic analysis, funding, professional development, and diversity. I learned an immense amount from my col- leagues in the Graduate School and my faculty and staﬀ colleagues across the University who devote time and energy to graduate education. Those experiences and interactions also allowed me to see graduate education from a broader perspective, beyond that of the graduate programs in the College of Engineering where I serve as a graduate advisor and research mentor. This book draws from this range of experiences and oﬀers guidance and advice to those entering engineering research as an undergraduate or a new graduate student. Author’s Biography 203 WENDY C. CRONE Wendy C. Crone is the Karen Thompson Medhi Professor in the Department of Engineering Physics, with aﬃliate faculty appointments in the Department of Biomedical Engineering and the Department of Materials Science and Engineering, and she holds the honor of Discovery Fellow with the Wis- consin Institute for Discovery at the University of Wisconsin– Madison. Her research is in the area of solid mechanics, and many of the topics she has investigated are connected with nanotech- nology and biotechnology. She has applied her technical ex- pertise to improving fundamental understanding of mechani- cal response of materials, enhancing material behavior through surface modiﬁcation and nanos- tructuring, exploring the interplay between cells and the mechanics of their surroundings, and developing new material applications and medical devices. Her research has been funded by the National Institutes of Health, National Science Foundation, Department of Energy, Air Force Oﬃce of Scientiﬁc Research, and Whitaker Foundation. She teaches courses in the areas of engineering mechanics, engineering physics, and in- formal science education. Over the last two decades, Prof. Crone has trained over two dozen graduate students and postdocs in engineering mechanics, materials science, biomedical engi- neering, and engineering education. Her former students hold positions in academia, national laboratories, and industry. Prof. Crone has received awards for research, teaching, and mentoring. In addition to numerous peer reviewed journal publications, dozens of explanatory education products, and four patents, she is the author of the book Survive and Thrive: A Guide for Untenured Faculty. She has also served in several leadership roles over the course of her career, including Interim Dean and Associate Dean of the Graduate School at UW-Madison and President of the Society for Experimental Mechanics. 205 Index abstracts, 89, 162, 169 authorship, 178 corresponding author, 78 bias and research, 60 working to avoid, 60 careers, research, 3, 10, 46, 69, 100 citation, 78, 92 and plagiarism, 100 citation management, 93 crediting others, 99 formats for, 92 collaboration, 48 interdependencies, 56 with diverse team, 58 communication, oral, 147 and jargon, 148 engineering outreach, 152 ﬂash talk, 159 informal research interactions, 147 poster presentations, 154 quad chart, 160 research talk, 156 with nonspecialists, 148 communication, written, 165 abstracts. See abstracts email, 13 for nonexpert audiences, 165 journal articles. See journal articles persuasive writing, 173 popular press, 166 press release, 166 proposals. See proposals providing feedback to others, 174 publishing, 180 revising and editing, 173 technical reports, 171 technical writing, 167 thesis/dissertation. See thesis/dissertation writers block, 168 writing workshops, 174 conferences, research and networking, 67 corresponding author, 78 data management plan, 141 data, research, 141 backup, 142 data management plan, 141 ﬁle naming, 144 manipulation, 145 organization, 143 original archival copy, 142 security, 142 storage, 142 version control, 144 dissertation. See thesis/dissertation diversity and research, 58 206 INDEX doctor of philosphy, Ph.D., See graduate National Academy of Engineering, 7 school ethics, 2, 126 data manipulation, 145 D.I.S.O.R.D.E.R. framework, 129 misconduct, 127 negligence, 127 plagiarism. See plagiarism Evaluation of Research Progress and Researcher Development rubric, 48, 54 expertise, developing, 41, 43 evaluation of progress, 48 Individual Development Plan, 46 SMART Goal Strategy, 46 tracking progress of, 45 fellowships, 29 application, 32 ﬁnances funding, 29 student loans, 31, 114 funding of research, 28 proposals, 108 global competency, 62 International Experience Indicators rubric, 64–66 graduate school, 4, 19 and mental health, 186 and personal health, 185 application, 20, 22 application timeline, 21 committee, 114, 121 ﬁt, 19, 20, 24 funding for, 24, 29 getting accepted, 27 visiting prospective programs, 24 grand challenges for engineering, 7 health and wellbeing challenges, 185 creative outlets, 192 eating healthy, 192 excercise, 191 mental health, 185 mindfulness practices, 194 sleep, 189 strategies to support, 188 support resources, 189 time management, 195 identity as a researcher, 43 impact factor, 73 Individual Delopment Plan (IDP). See expertise, developing International Experience Indicators rubric, 64–66 intuition, developing, 43 journal articles, 73, 74 abstract, 77 acknowledgments, 80 authorship, 178 citation management. See citation citation. See citation citing, 76 evaluating, 97 guide to authors, 183 journal club, 83 journal review process, 181 literature search, 87 organization of, 79 publishing, 180 reading, 75, 77 reading critically, 84 review articles, 89 reviewing, 95 submission, 181 supplemental materials, 81 types of, 74 writing, 172 journal club, 82 laboratory notebook. See research notebook literature, 73, 74 citation, 92 citation. See citation dissertations, 91 governments reports, 91 indexing databases, 87 patents, 90 review, 95 search, 87 search strategies, 89 see also journal articles, 73 manuscript. See journal article, 201 master’s degree, MS. See graduate school meetings leading, 57 preparation for, 37 scheduling, 121 mental health, 186 mentor(s), 35 and time, 28, 56 choosing, 10 constellation of mentors, 11, 69, 188 expectations, 40 ﬁt, 10 identifying, 8, 14 meetings with, 37 mentoring up, 36 multiple perspectives, 69 non-faculty, 1 peer mentoring, 72 mentoring. See mentor(s) mindfulness practices, 194 INDEX 207 network, professional, 67 and conferences, 67 peer mentoring group, 72 strategies for building, 68 networking. See network, professional peer mentoring group, 72 plagiarism, 100, 128 poster presentations, 154 principal investigator (PI), 35 project management, 113 resources, 114 timeline, 118 tools, 118 proposals, 106 hypothesis, 108 research plan, 107 submission, 109 writing, 172 research assistantships, 30 research group, 32, 35 collaboration, 56 data practices, 142 inclusive stragegies for, 61 interactions, 56 meetings, 32 research notebook, 135 and project management, 137 bound paper notebook, 137 contents, 135, 136 electronic notebook, 139 evaluation, 139 ownership, 135 research project changing, 10 choosing, 8 ﬁt, 8, 9 getting started, 110 208 INDEX identifying, 8 making progress, 112 navigating obstacles, 122 scheduling time to work, 110 staying motivated, 112 research, engineering, 1, 2 and global competency, 62 and scientiﬁc method, 103 and undergraduates, 15 careers, 3 data. See data, research documentation. See research notebook ethics. See ethics funding of, 28 misconduct, 127 project management. See project management publishing. See journal articles research group. See research group safety, 132 societal needs, 129 teams, 58 responsible conduct of research. See ethics safety, 132 scientiﬁc method, 103 self authorship, 44 and global competency, 63 skills, developing, 43 Evaluation of Research Progress and Researcher Development rubric, 49–55 tracking of, 48 societal needs, engineering and, 7 software version control, 144 summer undergraduate research programs, 17 teaching assistantships, 30 thesis/dissertation and literature search, 91 defense talk, 156, 158 proposal, 106 writing, 172 undergraduate research experience, 14 identifying opportunities, 15 professionalism, 18 summer programs, 18 writers block, 168 writing workshops, 174, 177 providing feedback in, 174
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813191.pdf&bkn=6813190&pdfType=book	MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 Essentials of Applied Mathematics for Scientists and Engineers MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 Copyright © 2007 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts www.morganclaypool.com ISBN: 1598291866 paperback ISBN: 9781598291865 paperback ISBN: 1598291874 ISBN: 9781598291872 ebook ebook DOI 10.2200/S00082ED1V01Y200612ENG003 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING SEQUENCE IN SERIES #3 Lecture #3 Series ISSN: 1559-811X print Series ISSN: 1559-8128 electronic First Edition 10 9 8 7 6 5 4 3 2 1 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts Tulane University SYNTHESIS LECTURES ON ENGINEERING SEQUENCE IN SERIES #3 M&C M o r g a n & C l a y p o o l P u b l i s h e r s MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 iv ABSTRACT This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering ﬁelds as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, ﬂuid ﬂow, mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms. KEYWORDS Engineering mathematics, separation of variables, orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms, differential equations. MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 v Contents 1. 2. Partial Differential Equations in Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introductory Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The Heat Conduction (or Diffusion) Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Rectangular Cartesian Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 Cylindrical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Spherical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 The Laplacian Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.4 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 1.4 The Vibrating String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.1 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 1.5 Vibrating Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 Longitudinal Displacements of an Elastic Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 The Fourier Method: Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Scales and Dimensionless Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 2.1.3 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.4 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.5 Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Scales and Dimensionless Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.6 2.1.7 Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.8 Choosing the Sign of the Separation Constant . . . . . . . . . . . . . . . . . . . . . . 17 2.1.9 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.10 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.11 Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.12 Scales and Dimensionless Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 vi ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 2.1.13 Getting to One Nonhomogeneous Condition . . . . . . . . . . . . . . . . . . . . . . 20 2.1.14 Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.15 Choosing the Sign of the Separation Constant . . . . . . . . . . . . . . . . . . . . . . 21 2.1.16 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.17 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.18 Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1.19 Scales and Dimensionless Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1.20 Relocating the Nonhomogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.21 Separating Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.22 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.23 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.24 Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2 Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Scales and Dimensionless Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.2 2.2.3 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.4 Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 3. Orthogonal Sets of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 Orthogonality of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.2 Orthonormal Sets of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.1 Orthonormal Sets of Functions and Fourier Series . . . . . . . . . . . . . . . . . . 32 3.2.2 Best Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.3 Convergence of Fourier Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 3.2.4 Examples of Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Sturm–Liouville Problems: Orthogonal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3.1 Orthogonality of Eigenfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.3 4. Series Solutions of Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1 General Series Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 CONTENTS vii 4.1.1 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1.2 Ordinary Points and Series Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.3 Lessons: Finding Series Solutions for Differential Equations with Ordinary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.4 Regular Singular Points and the Method of Frobenius . . . . . . . . . . . . . . . 49 4.1.5 Lessons: Finding Series Solution for Differential Equations with 4.2.1 Regular Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.6 Logarithms and Second Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Solutions of Bessel’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Here are the Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Fourier–Bessel Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3 Legendre Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.4 Associated Legendre Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.2.2 5. 6. Solutions Using Fourier Series and Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1 Conduction (or Diffusion) Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.1 Time-Dependent Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2 Vibrations Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Fourier Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Integral Transforms: The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.1 The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Some Important Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2 6.2.1 Exponentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Shifting in the s -domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2.2 Shifting in the Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2.3 6.2.4 Sine and Cosine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2.5 Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Powers of t: tm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2.6 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 viii ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 6.2.7 Heaviside Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.2.8 The Dirac Delta Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2.9 Transforms of Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2.10 Laplace Transforms of Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2.11 Derivatives of Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.3 Linear Ordinary Differential Equations with Constant Coefﬁcients . . . . . . . . . 102 Some Important Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.4 Initial Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.4.1 Final Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.4.2 6.4.3 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.5.1 Nonrepeating Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.5.2 Repeated Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.5.3 Quadratic Factors: Complex Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.5 7. Complex Variables and the Laplace Inversion Integral . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.1.1 Limits and Differentiation of Complex Variables: Analytic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.1.2 The Cauchy Integral Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8. 9. Solutions with Laplace Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.1 Mechanical Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.2 Diffusion or Conduction Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 8.3 Duhamel’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Sturm–Liouville Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.1 A Preliminary Example: Fourier Sine Transform . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.2 Generalization: The Sturm–Liouville Transform: Theory . . . . . . . . . . . . . . . . . . 143 9.3 The Inverse Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 CONTENTS ix 10. Introduction to Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 10.1 Examples from Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 10.1.1 Regular Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 10.1.2 Singular Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Appendix A: The Roots of Certain Transcendental Equations . . . . . . . . . . . . . . . . . . 159 Appendix B: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Author Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6 book Mobk070 March 22, 2007 11:7 1 C H A P T E R 1 Partial Differential Equations in Engineering INTRODUCTORY COMMENTS 1.1 This book covers the material presented in a course in applied mathematics that is required for ﬁrst-year graduate students in the departments of Chemical and Mechanical Engineering at Tulane University. A great deal of material is presented, covering boundary value problems, complex variables, and Fourier transforms. Therefore the depth of coverage is not as extensive as in many books. Our intent in the course is to introduce students to methods of solving linear partial differential equations. Subsequent courses such as conduction, solid mechanics, and fracture mechanics then provide necessary depth. The reader will note some similarity to the three books, Fourier Series and Boundary Value Problems, Complex Variables and Applications, and Operational Mathematics, originally by R. V. Churchill. The ﬁrst of these has been recently updated by James Ward Brown. The current author greatly admires these works, and studied them during his own tenure as a graduate student. The present book is more concise and leaves out some of the proofs in an attempt to present more material in a way that is still useful and is acceptable for engineering students. First we review a few concepts about differential equations in general. FUNDAMENTAL CONCEPTS 1.2 An ordinary differential equation expresses a dependent variable, say u, as a function of one independent variable, say x, and its derivatives. The order of the differential equation is given by the order of the highest derivative of the dependent variable. A boundary value problem consists of a differential equation that is deﬁned for a given range of the independent variable (domain) along with conditions on the boundary of the domain. In order for the boundary value problem to have a unique solution the number of boundary conditions must equal the order of the differential equation. If the differential equation and the boundary conditions contain only terms of ﬁrst degree in u and its derivatives the problem is linear. Otherwise it is nonlinear. book Mobk070 March 22, 2007 11:7 2 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS (cid:1) A partial differential equation expresses a dependent variable, say u, as a function of more than one independent variable, say x, y, and z. Partial derivatives are normally written as ∂u/∂ x. This is the ﬁrst-order derivative of the dependent variable u with respect to the independent variable x. Sometimes we will use the notation u x or when the derivative is an ordinary derivative . Higher order derivatives are written as ∂ 2u/∂ x2 or u xx. The order of the differential we use u equation now depends on the orders of the derivatives of the dependent variables in terms of each of the independent variables. For example, it may be of order m for the x variable and of order n for the y variable. A boundary value problem consists of a partial differential equation deﬁned on a domain in the space of the independent variables, for example the x, y, z space, along with conditions on the boundary. Once again, if the partial differential equation and the boundary conditions contain only terms of ﬁrst degree in u and its derivatives the problem is linear. Otherwise it is nonlinear. A differential equation or a boundary condition is homogeneous if it contains only terms involving the dependent variable. Examples Consider the ordinary differential equation a(x)u (cid:1)(cid:1) + b(x)u = c (x), 0 < x < A. Two boundary conditions are required because the order of the equation is 2. Suppose u(0) = 0 and u(A) = 1. (1.1) (1.2) The problem is linear. If c (x) is not zero the differential equation is nonhomogeneous. The ﬁrst boundary condition is homogeneous, but the second boundary condition is nonhomogeneous. Next consider the ordinary differential equation a(u)u (cid:1)(cid:1) + b(x)u = c 0 < x < A (1.3) Again two boundary conditions are required. Regardless of the forms of the boundary condi- tions, the problem is nonlinear because the ﬁrst term in the differential equations is not of ﬁrst since the leading coefﬁcient is a function of u. It is homogeneous only if degree in u and u c = 0. (cid:1)(cid:1) Now consider the following three partial differential equations: u x u xx uu x + u xx + u y y + u y y + u xy + u zz = 1 = 1 = 0 (1.4) (1.5) (1.6) book Mobk070 March 22, 2007 11:7 PARTIAL DIFFERENTIAL EQUATIONS IN ENGINEERING 3 The ﬁrst equation is linear and nonhomogeneous. The third term is a mixed partial derivative. Since it is of second order in x two boundary conditions are necessary on x. It is ﬁrst order in y, so that only one boundary condition is required on y. The second equation is linear and homogeneous and is of second order in all three variables. The third equation is nonlinear because the ﬁrst term is not of ﬁrst degree in u and u x. It is of order 1 in x and order 2 in y. In this book we consider only linear equations. We will now derive the partial differential equations that describe some of the physical phenomena that are common in engineering science. Problems Tell whether the following are linear or nonlinear and tell the order in each of the independent variables: (cid:1)(cid:1) + xu u tan(y)u y tan(u)u y (cid:1) + u2 = 0 + u y y = 0 + 3u = 0 + u = 0 u y y y + u y x THE HEAT CONDUCTION (OR DIFFUSION) EQUATION 1.3 1.3.1 Rectangular Cartesian Coordinates The conduction of heat is only one example of the diffusion equation. There are many other important problems involving the diffusion of one substance in another. One example is the diffusion of one gas into another if both gases are motionless on the macroscopic level (no convection). The diffusion of heat in a motionless material is governed by Fourier’s law which states that heat is conducted per unit area in the negative direction of the temperature gradient in the (vector) direction n in the amount ∂u/∂n, that is q n = −k∂u/∂n (1.7) where q n denotes the heat ﬂux in the n direction (not the nth power). In this equation u is the local temperature and k is the thermal conductivity of the material. Alternatively u could be the partial fraction of a diffusing material in a host material and k the diffusivity of the diffusing material relative to the host material. Consider the diffusion of heat in two dimensions in rectangular Cartesian coordinates. Fig. 1.1 shows an element of the material of dimension (cid:2)x by (cid:2)y by (cid:2)z. The material has a speciﬁc heat c and a density ρ. Heat is generated in the material at a rate q per unit volume. Performing a heat balance on the element, the time (t) rate of change of thermal energy within the element, ρc (cid:2)x(cid:2)y(cid:2)z∂u/∂t is equal to the rate of heat generated within the element book Mobk070 March 22, 2007 11:7 4 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FIGURE 1.1: An element in three dimensional rectangular Cartesian coordinates (cid:1)(cid:1)(cid:1)(cid:2)x(cid:2)y(cid:2)z minus the rate at which heat is conducted out of the material. The ﬂux of heat q conducted into the element at the x face is denoted by q x while at the y face it is denoted by q y . At x + (cid:2)x the heat ﬂux (i.e., per unit area) leaving the element in the x direction is q x + (cid:2)q x while at y + (cid:2)y the heat ﬂux leaving in the y direction is q y + (cid:2)q y . Similarly for q z. Expanding xx((cid:2)x)2 the latter three terms in Taylor series, we ﬁnd that q x + (cid:2)q x = q x + q x x + terms of order ((cid:2)x)3 or higher order. Similar expressions are obtained for q y + (cid:2)q y and q z + (cid:2)q z Completing the heat balance (cid:2)x + (1/2)q x ρc (cid:2)x(cid:2)y(cid:2)z∂u/∂t = q (cid:1)(cid:1)(cid:1)(cid:2)x(cid:2)y(cid:2)z + q x(cid:2)y(cid:2)z + q y (cid:2)x(cid:2)z − (q x + q x (cid:2)x + (1/2)q x x − (q y + q y (cid:2)y + (1/2)q y y − (q z + q z (cid:2)z + (1/2)q z z xx((cid:2)x)2 + · · · )(cid:2)y(cid:2)z y y ((cid:2)y)2 + · · · )(cid:2)x(cid:2)z zz((cid:2)z)2 + · · · )(cid:2)x(cid:2)y (1.8) The terms q x(cid:2)y(cid:2)z, q y (cid:2)x(cid:2)z, and q z(cid:2)x(cid:2)y cancel. Taking the limit as (cid:2)x, (cid:2)y, and (cid:2)z approach zero, noting that the terms multiplied by ((cid:2)x)2, ((cid:2)y)2, and ((cid:2)z)2 may be neglected, dividing through by (cid:2)x(cid:2)y(cid:2)z and noting that according to Fourier’s law q x = −k∂u/∂ x, q y = −k∂u/∂ y, and q z = −k(∂u/∂z) we obtain the time-dependent heat conduction equation in three-dimensional rectangular Cartesian coordinates: ρc ∂u/∂t = k(∂ 2u/∂ x2 + ∂ 2u/∂ y 2) + q (1.9) The equation is ﬁrst order in t, and second order in both x and y. If the property values ρ, c and k and the heat generation rate per unit volume q are independent of the dependent book Mobk070 March 22, 2007 11:7 PARTIAL DIFFERENTIAL EQUATIONS IN ENGINEERING 5 FIGURE 1.2: An element in cylindrical coordinates variable, temperature the partial differential equation is linear. If q is zero, the equation is homogeneous. It is easy to see that if a third dimension, z, were included, the term k∂ 2u/∂z2 must be added to the right-hand side of the above equation. 1.3.2 Cylindrical Coordinates A small element of volume r (cid:2)(cid:4)(cid:2)r (cid:2)z is shown in Fig. 1.2. The method of developing the diffusion equation in cylindrical coordinates is much the same as for rectangular coordinates except that the heat conducted into and out of the element depends on the area as well as the heat ﬂux as given by Fourier’s law, and this area varies in the r -direction. Hence the heat conducted into the element at r is q r r (cid:2)(cid:4)(cid:2)z, while the heat conducted out of the element at r + (cid:2)r is q r r (cid:2)(cid:4)(cid:2)z + ∂(q r r (cid:2)(cid:4)(cid:2)z)/∂r ((cid:2)r ) when terms of order ((cid:2)r )2 are neglected as (cid:2)r approaches zero. In the z- and θ -directions the area does not change. Following the same procedure as in the discussion of rectangular coordinates, expanding the heat values on the three faces in Tayor series’, and neglecting terms of order ((cid:2)(cid:4))2 and ((cid:2)z)2 and higher, ρc r (cid:2)θ (cid:2)r (cid:2)z∂u/∂t = −∂(q r r (cid:2)θ (cid:2)z)/∂r (cid:2)r − ∂(q θ (cid:2)r (cid:2)z)/∂θ (cid:2)θ − ∂(q zr (cid:2)θ (cid:2)r )/∂z(cid:2)z + qr (cid:2)θ (cid:2)r (cid:2)z (1.10) book Mobk070 March 22, 2007 11:7 6 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FIGURE 1.3: An element in spherical coordinates Dividing through by the volume, we ﬁnd after using Fourier’s law for the heat ﬂuxes ρc ∂u/∂t = (1/r )∂(r ∂u/∂r )/∂r + (1/r 2)∂ 2u/∂θ 2 + ∂ 2u/∂z2 + q (1.11) 1.3.3 Spherical Coordinates An element in a spherical coordinate system is shown in Fig. 1.3. The volume of the element is r sin θ (cid:2)(cid:6)(cid:2)r r (cid:2)θ = r 2 sin θ (cid:2)r (cid:2)θ (cid:2)(cid:6). The net heat ﬂows out of the element in the r , θ , and (cid:6) directions are respectfully q r r 2 sin θ (cid:2)θ (cid:2)(cid:6) θ r sin θ (cid:2)r (cid:2)(cid:6) (cid:6) r (cid:2)θ (cid:2)r q q It is left as an exercise for the student to show that ρc ∂u/∂t = k[(1/r 2)∂/∂r (r 2∂u/∂r ) + (1/r 2 sin2 θ )∂ 2u/∂(cid:6)2 + (1/r 2 sin θ )∂(sin θ ∂u/∂θ )/∂θ + q (1.12) (1.13) (1.14) (1.15) The Laplacian Operator The linear operator on the right-hand side of the heat equation is often referred to as the Laplacian operator and is written as ∇ 2. book Mobk070 March 22, 2007 11:7 PARTIAL DIFFERENTIAL EQUATIONS IN ENGINEERING 7 1.3.4 Boundary Conditions Four types of boundary conditions are common in conduction problems. a) Heat ﬂux prescribed, in which case k∂u/∂n is given. b) Heat ﬂux is zero (perhaps just a special case of (a)), in which case ∂u/∂n is zero. c) Temperature u is prescribed. d) Convection occurs at the boundary, in which case k∂u/∂n = h(U − u). Here n is a length in the direction normal to the surface, U is the temperature of the ﬂuid next to the surface that is heating or cooling the surface, and h is the coefﬁcient of convective heat transfer. Condition (d) is sometimes called Newton’s law of cooling. THE VIBRATING STRING 1.4 Next we consider a tightly stretched string on some interval of the x-axis. The string is vibrating about its equilibrium position so that its departure from equilibrium is y(t, x). The string is assumed to be perfectly ﬂexible with mass per unit length ρ. Fig. 1.4 shows a portion of such a string that has been displaced upward. We assume that the tension in the string is constant. However the direction of the tension vector along the string varies. The tangent of the angle α(t, x) that the string makes with the horizontal is given by the slope of the wire, ∂ y/∂ x, V (x)/H = tan α(t, x) = ∂ y/∂ x (1.16) If we assume that the angle α is small then the horizontal tension force is nearly equal to the magnitude of the tension vector itself. In this case the tangent of the slope of the wire FIGURE 1.4: An element of a vibrating string book Mobk070 March 22, 2007 11:7 8 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS at x + (cid:2)x is V (x + (cid:2)x)/H = tan α(x + (cid:2)x) = ∂ y/∂ x(x + (cid:2)x). (1.17) The vertical force V is then given by H∂ y/∂ x. The net vertical force is the difference between the vertical forces at x and x + (cid:2)x, and must be equal to the mass times the acceleration of that portion of the string. The mass is ρ(cid:2)x and the acceleration is ∂ 2 y/∂t2. Thus ρ(cid:2)x∂ 2/∂t2 = H[∂ y/∂ x(x + (cid:2)x) − ∂ y/∂ x(x)] (1.18) Expanding ∂ y/∂ x(x + (cid:2)x) in a Taylor series about (cid:2)x = 0 and neglecting terms of order ((cid:2)x)2 and smaller, we ﬁnd that ρytt = Hyxx which is the wave equation. Usually it is presented as ytt = a 2 yxx where a 2 = H/ρ is a wave speed term. (1.19) (1.20) Had we included the weight of the string there would have been an extra term on the right-hand side of this equation, the acceleration of gravity (downward). Had we included a damping force proportional to the velocity of the string, another negative term would result: ρytt = Hyxx − byt − g (1.21) 1.4.1 Boundary Conditions The partial differential equation is linear and if the gravity term is included it is nonhomo- geneous. It is second order in both t and x, and requires two boundary conditions (initial conditions) on t and two boundary conditions on x. The two conditions on t are normally specifying the initial velocity and acceleration. The conditions on x are normally specifying the conditions at the ends of the string, i.e., at x = 0 and x = L. VIBRATING MEMBRANE 1.5 The partial differential equation describing the motion of a vibrating membrane is simply an extension of the right-hand side of the equation of the vibrating string to two dimensions. Thus, ρytt + byt = −g + ∇ 2 y (1.22) In this equation, ρ is the density per unit area and ∇ 2 y is the Laplacian operator in either rectangular or cylindrical coordinates. book Mobk070 March 22, 2007 11:7 PARTIAL DIFFERENTIAL EQUATIONS IN ENGINEERING 9 LONGITUDINAL DISPLACEMENTS OF AN ELASTIC BAR 1.6 The longitudinal displacements of an elastic bar are described by Eq. (1.20) except the in this case a 2 = E/ρ, where ρ is the density and E is Young’s modulus. FURTHER READING V. Arpaci, Conduction Heat Transfer. Reading, MA: Addison-Wesley, 1966. J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems. 6th edition. New York: McGraw-Hill, 2001. P. V. O’Neil, Advanced Engineering Mathematics. 5th edition. Paciﬁc Grove, CA: Brooks/Cole- Thomas Learning, 2003. book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 11 C H A P T E R 2 The Fourier Method: Separation of Variables In this chapter we will work through a few example problems in order to introduce the general idea of separation of variables and the concept of orthogonal functions before moving on to a more complete discussion of orthogonal function theory. We will also introduce the concepts of nondimensionalization and normalization. The goal here is to use the three theorems stated below to walk the student through the solution of several types of problems using the concept of separation of variables and learn some early lessons on how to apply the method without getting too much into the details that will be covered later, especially in Chapter 3. We state here without proof three fundamental theorems that will be useful in ﬁnding series solutions to partial differential equations. Theorem 2.1. Linear Superposition: If a group of functions un, n = m through n = M are all solutions to some linear differential equation then M(cid:1) n=m c nun is also a solution. Theorem 2.2. Orthogonal Functions: Certain sets of functions (cid:8) possess the property that n deﬁned on the interval (a, b) b(cid:2) a b(cid:2) a (cid:8) (cid:8) md x = constant, n = m n (cid:8) (cid:8) md x = 0, n (cid:3)= m n book Mobk070 March 22, 2007 11:7 12 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS These are called orthogonal functions. Examples are the sine and cosine functions. This idea is discussed fully in Chapter 3, particularly in connection with Sturm–Liouville equations. Theorem 2.3. Fourier Series: A piecewise continuous function f (x) deﬁned on (a, b) can be represented by a series of orthogonal functions (cid:8) n(x) on that interval as ∞(cid:1) f (x) = (cid:8) n(x) An n=0 where (cid:3) = (cid:3) An b x=a f (x)(cid:8) b n(x)(cid:8) (cid:8) x=a n(x)d x n(x)d x These properties will be used in the following examples to introduce the idea of solution of partial differential equations using the concept of separation of variables. 2.1 HEAT CONDUCTION We will ﬁrst examine how Theorems 1, 2, and 3 are systematically used to obtain solutions to problems in heat conduction in the forms of inﬁnite series. We set out the methodology in detail, step-by-step, with comments on lessons learned in each case. We will see that the mathematics often serves as a guide, telling us when we make a bad assumption about solution forms. Example 2.1. A Transient Heat Conduction Problem Consider a ﬂat plate occupying the space between x = 0 and x = L. The plate stretches out in the y and z directions far enough that variations in temperature in those directions may be neglected. Initially the plate is at a uniform temperature u0. At time t = 0 the wall at x = 0 is raised to u1 while the wall at x = L is insulated. The boundary value problem is then + 0 < x < L t > 0 = ku xx ρc ut u(t, 0) = u1 u x(t, L) = 0 u(0, x) = u0 (2.1) (2.2) 2.1.1 Scales and Dimensionless Variables When it is possible it is always a good idea to write both the independent and dependent variables in such a way that they range from zero to unity. In the next few problems we shall show how this can often be done. book Mobk070 March 22, 2007 11:7 We ﬁrst note that the problem has a fundamental length scale, so that if we deﬁne another space variable ξ = x/L, the partial differential equation can be written as THE FOURIER METHOD: SEPARATION OF VARIABLES 13 ρc ut = L −2kuξ ξ 0 < ξ < 1 t < 0 (2.3) Next we note that if we deﬁne a dimensionless time-like variable as τ = αt/L2, where α = k/ρc is called the thermal diffusivity, we ﬁnd uτ = uξ ξ (2.4) We now proceed to nondimensionalize and normalize the dependent variable and the boundary conditions. We deﬁne a new variable U = (u − u1)/(u0 − u1) (2.5) Note that this variable is always between 0 and 1 and is dimensionless. Our boundary value problem is now devoid of constants. Uτ = Uξ ξ U (τ, 0) = 0 Uξ (τ, 1) = 0 U (0, ξ ) = 1 (2.6) (2.7) All but one of the boundary conditions are homogeneous. This will prove necessary in our analysis. 2.1.2 Separation of Variables Begin by assuming U = (cid:11)(τ )(cid:6)(ξ ). Insert this into the differential equation and obtain Next divide both sides by U = (cid:6)(cid:11), (cid:6)(ξ )(cid:11)τ (τ ) = (cid:11)(τ )(cid:6)ξ ξ (ξ ). (cid:11)τ (cid:11) = (cid:6)ξ ξ (cid:6) = ±λ2 (2.8) (2.9) The left-hand side of the above equation is a function of τ only while the right-hand side is a function only of ξ . This can only be true if both are constants since they are equal to each other. λ2 is always positive, but we must decide whether to use the plus sign or the minus sign. We have two ordinary differential equations instead of one partial differential equation. Solution for (cid:11) gives a constant times either exp(−λ2τ ) or exp(+λ2τ ). Since we know that U is always between 0 and 1, we see immediately that we must choose the minus sign. The second ordinary book Mobk070 March 22, 2007 11:7 14 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS differential equation is and we deduce that the two homogeneous boundary conditions are (cid:6)ξ ξ = −λ2(cid:6) (cid:6)(0) = 0 (cid:6)ξ (1) = 0 Solving the differential equation we ﬁnd (cid:6) = A cos(λξ ) + B sin(λξ ) (2.10) (2.11) (2.12) where A and B are constants to be determined. The ﬁrst boundary condition requires that A = 0. The second boundary condition requires that either B = 0 or cos(λ) = 0. Since the former cannot be true (U is not zero!) the latter must be true. ξ can take on any of an inﬁnite number = (2n − 1)π/2, where n is an integer between negative and positive inﬁnity. of values λ n Equation (2.10) together with boundary conditions (2.11) is called a Sturm–Liouville problem. The solutions are called eigenfunctions and the λ n are called eigenvalues. A full discussion of Sturm–Liouville theory will be presented in Chapter 3. Hence the apparent solution to our partial differential equation is any one of the following: Un = Bn exp[−(2n − 1)2π 2τ/4)] sin[π (2n − 1)ξ/2]. (2.13) 2.1.3 Superposition Linear differential equations possess the important property that if each solution Un satisﬁes the differential equation and the boundary conditions then the linear combination ∞(cid:1) n=1 Bn exp[−(2n − 1)2π 2τ/4] sin[π (2n − 1)ξ/2] = ∞(cid:1) n=1 Un (2.14) also satisﬁes them, as stated in Theorem 2. Can we build this into a solution that satisﬁes the one remaining boundary condition? The ﬁnal condition (the nonhomogeneous initial condition) states that 1 = ∞(cid:1) n=1 Bn sin(π (2n − 1)ξ/2) (2.15) This is called a Fourier sine series representation of 1. The topic of Fourier series is further discussed in Chapter 3. book Mobk070 March 22, 2007 11:7 THE FOURIER METHOD: SEPARATION OF VARIABLES 15 2.1.4 Orthogonality It may seem hopeless at this point when we see that we need to ﬁnd an inﬁnite number of constants Bn. What saves us is a concept called orthogonality (to be discussed in a more general way in Chapter 3). The functions sin(π (2n − 1)ξ/2) form an orthogonal set on the interval 0 < ξ < 1, which means that 1(cid:2) 0 sin(π (2n − 1)ξ/2) sin(π (2m − 1)ξ/2)d ξ = 0 when m (cid:3)= n (2.16) = 1/2 when m = n Hence if we multiply both sides of the ﬁnal equation by sin(π (2m − 1)ξ/2)d ξ and integrate over the interval, we ﬁnd that all of the terms in which m (cid:3)= n are zero, and we are left with one term, the general term for the nth B, Bn 1(cid:2) Bn = 2 sin(π (2n − 1)ξ/2)d ξ = 4 π (2n − 1) 0 (2.17) Thus U = ∞(cid:1) n=1 4 π (2n − 1) exp[−π 2(2n − 1)2τ/4] sin[π (2n − 1)ξ/2] (2.18) satisﬁes both the partial differential equation and the boundary and initial conditions, and therefore is a solution to the boundary value problem. 2.1.5 Lessons We began by assuming a solution that was the product of two variables, each a function of only one of the independent variables. Each of the resulting ordinary differential equations was then solved. The two homogeneous boundary conditions were used to evaluate one of the constant coefﬁcients and the separation constant λ. It was found to have an inﬁnite number of values. ξ are called eigenfunctions. Linear These are called eigenvalues and the resulting functions sinλ superposition was then used to build a solution in the form of an inﬁnite series. The inﬁnite series was then required to satisfy the initial condition, the only nonhomogeneous condition. The coefﬁcients of the series were determined using the concept of orthogonality stated in Theorem 3, resulting in a Fourier series. Each of these concepts will be discussed further in Chapter 3. For now we state that many important functions are members of orthogonal sets. n book Mobk070 March 22, 2007 11:7 16 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS The method would not have worked had the differential equation not been homoge- neous. (Try it.) It also would not have worked if more than one boundary condition had been nonhomogeneous. We will see how to get around these problems shortly. Problems 1. Equation (2.9) could just as easily have been written as (cid:11)τ (cid:11) = (cid:6)ξ ξ (cid:6) = +λ2 Show two reasons why this would reduce to the trivial solution or a solution for which (cid:11) approaches inﬁnity as τ approaches inﬁnity, and that therefore the minus sign must be chosen. 2. Solve the above problem with boundary conditions Uξ (τ, 0) = 0 and U (τ, 1) = 0 using the steps given above. Hint: cos(nπ x) is an orthogonal set on (0, 1). The result will be a Fourier cosine series representation of 1. 3. Plot U versus ξ for τ = 0.001, 0.01, and 0.1 in Eq. (2.18). Comment. Example 2.2. A Steady Heat Transfer Problem in Two Dimensions Heat is conducted in a region of height a and width b. Temperature is a function of two space dimensions and independent of time. Three sides are at temperature u0 and the fourth side is at temperature u1. The formulation is as follows: ∂ 2u ∂ y 2 ∂ 2u ∂ x2 (2.19) = 0 + with boundary conditions u(0, x) = u(b, x) = u(y, a) = u0 u(y, 0) = u1 (2.20) 2.1.6 Scales and Dimensionless Variables First note that there are two obvious length scales, a and b. We can choose either one of them to nondimensionalize x and y. We deﬁne ξ = x/a and η = y/b (2.21) so that both dimensionless lengths are normalized. book Mobk070 March 22, 2007 11:7 THE FOURIER METHOD: SEPARATION OF VARIABLES 17 To normalize temperature we choose U = u − u0 − u0 u1 The problem statement reduces to (cid:4) Uξ ξ + (cid:5) 2 Uηη = 0 a b U (0, ξ ) = U (1, ξ ) = U (η, 1) = 0 U (η, 0) = 1 (2.22) (2.23) (2.24) 2.1.7 Separation of Variables As before, we assume a solution of the form U (ξ, n) = X(ξ )Y (η). We substitute this into the differential equation and obtain Y (η)Xξ ξ (ξ ) = −X(ξ ) (cid:5) 2 (cid:4) a b Yηη(η) (2.25) Next we divide both sides by U (ξ, n) and obtain (cid:5) (cid:4) a b In order for the function only of ξ on the left-hand side of this equation to be equal to the function only of η on the right-hand side, both must be constant. 2 Ynn Y Xξ ξ X = ±λ2 (2.26) = − 2.1.8 Choosing the Sign of the Separation Constant However in this case it is not as clear as the case of Example 1 what the sign of this constant must be. Hence we have designated the constant as ±λ2 so that for real values of λ the ± sign determines the sign of the constant. Let us proceed by choosing the negative sign and see where this leads. Thus or Xξ ξ = −λ2 X Y (η)X(0) = 1 Y (η)X(1) = 0 X(0) = 1 X(1) = 0 (2.27) (2.28) book Mobk070 March 22, 2007 11:7 18 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and Yηη = ∓ (cid:7) 2 (cid:6) b a λ2Y X(ξ )Y (0) = X(ξ )Y (1) = 0 Y (0) = Y (1) = 0 The solution of the differential equation in the η direction is Y (η) = A cosh(bλη/a) + B sinh(bλη/a) (2.29) (2.30) (2.31) Applying the ﬁrst boundary condition (at η = 0) we ﬁnd that A = 0. When we apply the boundary condition at η = 1 however, we ﬁnd that it requires that 0 = B sinh(bλ/a) (2.32) so that either B = 0 or λ = 0. Neither of these is acceptable since either would require that Y (η) = 0 for all values of η. We next try the positive sign. In this case Xξ ξ = λ2 X (cid:6) Yηη = − (cid:7) 2 b a λ2Y with the same boundary conditions given above. The solution for Y (η) is now Y (η) = A cos(bλη/a) + B sin(bλη/a) The boundary condition at η = 0 requires that 0 = A cos(0) + B sin(0) so that again A = 0. The boundary condition at η = 1 requires that 0 = B sin(bλ/a) Since we don’t want B to be zero, we can satisfy this condition if λ n = anπ/b, n = 0, 1, 2, 3, . . . Thus Y (η) = B sin(nπ η) (2.33) (2.34) (2.35) (2.36) (2.37) (2.38) (2.39) book Mobk070 March 22, 2007 11:7 THE FOURIER METHOD: SEPARATION OF VARIABLES 19 Solution for X(ξ ) yields hyperbolic functions. X(ξ ) = C cosh(λ ξ ) + D sinh(λ n ξ ) n The boundary condition at ξ = 1 requires that 0 = C cosh(λ n) + D sinh(λ n) or, solving for C in terms of D, C = −D tanh(λ n) One solution of our problem is therefore (2.40) (2.41) (2.42) Un(ξ, η) = Kn sin(nπ η)[sinh(anπξ/b) − cosh(anπξ/b) tanh(anπ/b)] (2.43) 2.1.9 Superposition According to the superposition theorem (Theorem 2) we can now form a solution as U (ξ, η) = ∞(cid:1) n=0 Kn sin(nπ η)[sinh(anπξ/b) − cosh(anπξ/b) tanh(anπ/b)] (2.44) The ﬁnal boundary condition (the nonhomogeneous one) can now be applied, 1 = − ∞(cid:1) n=1 Kn sin(nπ η) tanh(anπ/b) (2.45) 2.1.10 Orthogonality We have already noted that the sine function is an orthogonal function as deﬁned on (0, 1). Thus, we multiply both sides of this equation by sin(mπ η)d η and integrate over (0, 1), noting that according to the orthogonality theorem (Theorem 3) the integral is zero unless n = m. The result is 1(cid:2) η=0 1(cid:2) sin(nπ η)d η = −Kn sin2(nπ η)d η tanh(anπ/b) η=0 1 nπ [1 − (−1)n] = −Kn tanh(anπ/b) = − 2[1 − (−1)n] nπ tanh(anπ/b) Kn 1 2 (2.46) (2.47) (2.48) book Mobk070 March 22, 2007 11:7 20 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS The solution is represented by the inﬁnite series ∞(cid:1) U (ξ, η) = 2[1 − (−1)n] nπ tanh(anπ/b) sin(nπ η) n=1 × [cosh(anπξ/b) tanh(anπ/b) − sinh(anπξ/b)] (2.49) 2.1.11 Lessons The methodology for this problem is the same as in Example 1. Example 2.3. A Steady Conduction Problem in Two Dimensions: Addition of Solutions We now illustrate a problem in which two of the boundary conditions are nonhomogeneous. Since the problem and the boundary conditions are both linear we can simply break the problem into two problems and add them. Consider steady conduction in a square region L by L in size. Two sides are at temperature u0 while the other two sides are at temperature u1. u xx + u y y = 0 (2.50) We need four boundary conditions since the differential equation is of order 2 in both inde- pendent variables. u(0, y) = u(L, y) = u0 u(x, 0) = u(x, L) = u1 (2.51) (2.52) 2.1.12 Scales and Dimensionless Variables The length scale is L, so we let ξ = x/L and η = y/L. We can make the ﬁrst two bound- ary conditions homogeneous while normalizing the second two by deﬁning a dimensionless temperature as Then U = u − u0 − u0 u1 Uξ ξ + Uηη = 0 U (0, η) = U (1, η) = 0 U (ξ, 0) = U (ξ, 1) = 1 (2.53) (2.54) (2.55) (2.56) 2.1.13 Getting to One Nonhomogeneous Condition There are two nonhomogeneous boundary conditions, so we must ﬁnd a way to only have one. Let U = V + W so that we have two problems, each with one nonhomogeneous boundary book Mobk070 March 22, 2007 11:7 condition. THE FOURIER METHOD: SEPARATION OF VARIABLES 21 Wξ ξ + Wηη = 0 W(0, η) = W(1, η) = W(ξ, 0) = 0 W(ξ, 1) = 1 Vξ ξ + Vηη = 0 V (0, η) = V (1, η) = V (ξ, 1) = 0 V (ξ, 0) = 1 (2.57) (2.58) (2.59) (2.60) (It should be clear that these two problems are identical if we put V = W(1 − η). We will therefore only need to solve for W.) 2.1.14 Separation of Variables Separate variables by letting W(ξ, η) = P (ξ )Q(η). Pξ ξ P = − Qηη Q = ±λ2 (2.61) 2.1.15 Choosing the Sign of the Separation Constant Once again it is not immediately clear whether to choose the plus sign or the minus sign. Let’s see what happens if we choose the plus sign. Pξ ξ = λ2 P The solution is exponentials or hyperbolic functions. P = A sinh(λξ ) + B cosh(λξ ) (2.62) (2.63) Applying the boundary condition on ξ = 0, we ﬁnd that B = 0. The boundary condition on ξ = 1 requires that A sinh(λ) = 0, which can only be satisﬁed if A = 0 or λ = 0, which yields a trivial solution, W = 0, and is unacceptable. The only hope for a solution is thus choosing the minus sign. If we choose the minus sign in Eq. (2.61) then with solutions Pξ ξ = −λ2 P Qηη = λ2 Q P = A sin(λξ ) + B cos(λξ ) (2.64) (2.65) (2.66) book Mobk070 March 22, 2007 11:7 22 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and Q = C sinh(λη) + D cosh(λη) (2.67) respectively. Remembering to apply the homogeneous boundary conditions ﬁrst, we ﬁnd that for W(0, η) = 0, B = 0 and for W(1, η) = 0, sin(λ) = 0. Thus, λ = nπ , our eigenvalues cor- responding to the eigenfunctions sin(nπ ξ ). The last homogeneous boundary condition is W(ξ, 0) = 0, which requires that D = 0. There are an inﬁnite number of solutions of the form P Qn = Kn sinh(nπ η) sin(nπ ξ ) (2.68) 2.1.16 Superposition Since our problem is linear we apply superposition. W = ∞(cid:1) n=1 Kn sinh(nπ η) sin(nπ ξ ) Applying the ﬁnal boundary condition, W(ξ, 1) = 1 1 = ∞(cid:1) n=1 Kn sinh(nπ ) sin(nπ ξ ). (2.69) (2.70) 2.1.17 Orthogonality Multiplying both sides of Eq. (2.70) by sin(mπ ξ ) and integrating over the interval (0, 1) 1(cid:2) 0 sin(mπ ξ )d ξ = ∞(cid:1) n=0 1(cid:2) Kn sinh(nπ ) sin(nπ ξ ) sin(mπ ξ )d ξ (2.71) 0 The orthogonality property of the sine eigenfunction states that Thus, and 1(cid:2) 0 sin(nπ ξ ) sin(mπ ξ )d ξ = 0, m (cid:3)= n 1/2, m = n Kn = 2/ sinh(nπ ) W = ∞(cid:1) n=0 2 sinh(nπ ) sinh(nπ η) sin(nπ ξ ) (2.72) (2.73) (2.74) book Mobk070 March 22, 2007 11:7 Recall that THE FOURIER METHOD: SEPARATION OF VARIABLES 23 V = W(ξ, 1 − η) and U = V + W 2.1.18 Lessons If there are two nonhomogeneous boundary conditions break the problem into two problems that can be added (since the equations are linear) to give the complete solution. If you are unsure of the sign of the separation constant just assume a sign and move on. Listen to what the mathematics is telling you. It will always tell you if you choose wrong. Example 2.4. A Non-homogeneous Heat Conduction Problem Consider now the arrangement above, but with a heat source, and with both boundaries held at the initial temperature u0. The heat source is initially zero and is turned on at t = 0 . The exercise illustrates the method of solving the problem when the single nonhomogeneous condition is in the partial differential equation rather than one of the boundary conditions. + ρc ut = ku xx + q u(0, x) = u0 u(t, 0) = u0 u(t, L) = u0 (2.75) (2.76) 2.1.19 Scales and Dimensionless Variables Observe that the length scale is still L, so we deﬁne ξ = x/L. Recall that k/ρc = α is the diffusivity. How shall we nondimensionalize temperature? We want as many ones and zeros in coefﬁcients in the partial differential equation and the boundary conditions as possible. Deﬁne U = (u − u0)/S, where S stands for “something with dimensions of temperature” that we must ﬁnd. Dividing both sides of the partial differential equation by q and substituting for x L2Sρc Ut q = k SUξ ξ q + 1 (2.77) Letting S = q /k leads to one as the coefﬁcient of the ﬁrst term on the right-hand side. Choosing the same dimensionless time as before, τ = αt/L2 results in one as the coefﬁcient of book Mobk070 March 22, 2007 11:7 24 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS the time derivative term. We now have Uτ = Uξ ξ + 1 U (0, ξ ) = 0 U (τ, 0) = 0 U (τ, 1) = 0 (2.78) (2.79) 2.1.20 Relocating the Nonhomogeneity We have only one nonhomogeneous condition, but it’s in the wrong place. The differential equation won’t separate. For example if we let U (ξ, τ ) = P (ξ )G(τ ) and insert this into the partial differential equation and divide by P G, we ﬁnd G (cid:1) (τ ) G = P (cid:1)(cid:1) (ξ ) P + 1 P G (2.80) The technique to deal with this is to relocate the nonhomogenous condition to the initial condition. Assume a solution in the form U = W(ξ ) + V (τ, ξ ). We now have Vτ = Vξ ξ + Wξ ξ + 1 (2.81) If we set Wξ ξ = −1, the differential equation for V becomes homogeneous. We then set both W and V equal to zero at ξ = 0 and 1 and V (0, ξ ) = −W(ξ ) and The solution for W is parabolic Wξ ξ = −1 W(0) = W(1) = 0 Vτ = Vξ ξ V (0, ξ ) = −W(ξ ) V (τ, 0) = 0 V (τ, 1) = 0 W = 1 2 ξ (1 − ξ ) (2.82) (2.83) (2.84) (2.85) (2.86) book Mobk070 March 22, 2007 11:7 2.1.21 Separating Variables We now solve for V using separation of variables. THE FOURIER METHOD: SEPARATION OF VARIABLES 25 V = P (τ )Q(ξ ) Pτ = Qξ ξ Q P = ±λ2 (2.87) (2.88) We must choose the minus sign once again (see Problem 1 above) to have a negative exponential for P (τ ). (We will see later that it’s not always so obvious.) P = exp(−λ2τ ). The solution for Q is once again sines and cosines. Q = A cos(λξ ) + B sin(λξ ) (2.89) The boundary condition V (τ, 0) = 0 requires that Q(0) = 0. Hence, A = 0. The boundary condition V (τ, 1) = 0 requires that Q(1) = 0. Since B cannot be zero, sin(λ) = 0 so that our eigenvalues are λ = nπ and our eigenfunctions are sin(nπ ξ ). 2.1.22 Superposition Once again using linear superposition, V = ∞(cid:1) n=0 Bn exp(−n2π 2τ ) sin(nπ ξ ) Applying the initial condition ξ (ξ − 1) = 1 2 ∞(cid:1) n=1 Bn sin(nπ ξ ) (2.90) (2.91) This is a Fourier sine series representation of 1 2 ξ (ξ − 1). We now use the orthogonality of the sine function to obtain the coefﬁcients Bn. 2.1.23 Orthogonality Using the concept of orthogonality again, we multiply both sides by sin(mπ ξ )d ξ and integrate over the space noting that the integral is zero if m is not equal to n. Thus, since 1(cid:2) 0 sin2(nπ ξ )d ξ = 1 2 1(cid:2) = Bn ξ (ξ − 1) sin(nπ ξ )d ξ 0 (2.92) (2.93) book Mobk070 March 22, 2007 11:7 26 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 2.1.24 Lessons When the differential equation is nonhomogeneous use the linearity of the differential equation to transfer the nonhomogeneous condition to one of the boundary conditions. Usually this will result in a homogeneous partial differential equation and an ordinary differential equation. We pause here to note that while the method of separation of variables is straightforward in principle, a certain amount of intuition or, if you wish, cleverness is often required in order to put the equation and boundary conditions in an appropriate form. The student working diligently will soon develop these skills. Problems 1. Using these ideas obtain a series solution to the boundary value problem = u xx ut u(t, 1) = 0 u(t, 0) = 0 u(0, x) = 1 2. Find a series solution to the boundary value problem + x = u xx ut u x(t, 0) = 0 u(t, 1) = 0 u(0, x) = 0 VIBRATIONS 2.2 In vibrations problems the dependent variable occurs in the differential equation as a second- order derivative of the independent variable t. The methodology is, however, essentially the same as it is in the diffusion equation. We ﬁrst apply separation of variables, then use the boundary conditions to obtain eigenfunctions and eigenvalues, and use the linearity and orthogonality principles and the single nonhomogeneous condition to obtain a series solution. Once again, if there are more than one nonhomogeneous condition we use the linear superposition principle to obtain solutions for each nonhomogeneous condition and add the resulting solutions. We illustrate these ideas with several examples. Example 2.5. A Vibrating String Consider a string of length L ﬁxed at the ends. The string is initially held in a ﬁxed position y(0, x) = f (x), where it is clear that f (x) must be zero at both x = 0 and x = L. The boundary book Mobk070 March 22, 2007 11:7 value problem is as follows: THE FOURIER METHOD: SEPARATION OF VARIABLES 27 = a 2 yxx ytt y(t, 0) = 0 y(t, L) = 0 y(0, x) = f (x) yt(0, x) = 0 (2.94) (2.95) 2.2.1 Scales and Dimensionless Variables The problem has the obvious length scale L. Hence let ξ = x/L. Now let τ = ta/L and the equation becomes yτ τ = yξ ξ (2.96) One could now nondimensionalize y, for example, by deﬁning a new variable as f (x)/ fmax, but it wouldn’t simplify things. The boundary conditions remain the same except t and x are replaced by τ and ξ . 2.2.2 Separation of Variables You know the dance. Let y = P (τ )Q(ξ ). Differentiating and substituting into Eq. (2.96), Pτ τ Q = P Qξ ξ (2.97) Dividing by P Q and noting that Pτ τ /P and Qξ ξ /Q cannot be equal to one another unless they are both constants, we ﬁnd Pτ τ /P = Qξ ξ /Q = ±λ2 (2.98) It should be physically clear that we want the minus sign. Otherwise both solutions will be hyperbolic functions. However if you choose the plus sign you will immediately ﬁnd that the boundary conditions on ξ cannot be satisﬁed. Refer back to (2.63) and the sentences following. The two ordinary differential equations and homogeneous boundary conditions are Pτ τ + λ2 P = 0 Pτ (0) = 0 (2.99) book Mobk070 March 22, 2007 11:7 28 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and The solutions are Qξ ξ + λ2 Q = 0 Q(0) = 0 Q(1) = 0 P = A sin(λτ ) + B cos(λτ ) Q = C sin(λξ ) + D cos(λξ ) (2.100) (2.101) (2.102) The ﬁrst boundary condition of Eq. (2.100) requires that D = 0. The second requires that = nπ . The boundary condition at τ = 0, that C sin(λ) be zero. Our eigenvalues are again λ Pτ = 0 requires that A = 0. Thus n P Qn = Kn sin(nπ ξ ) cos(nπ τ ) The ﬁnal form of the solution is then y(τ, ξ ) = ∞(cid:1) n=0 Kn sin(nπ ξ ) cos(nπ τ ) 2.2.3 Orthogonality Applying the ﬁnal (nonhomogeneous) boundary condition (the initial position). f (ξ ) = ∞(cid:1) n=0 Kn sin(nπ ξ ) In particular, if f (x) = h x, 0 < x < 1/2 1(cid:2) 0 and = h(1 − x), 1/2 < x < 1 1/2(cid:2) 1(cid:2) f (x) sin(nπ x)d x = h x sin(nπ x)d x + h(1 − x) sin(nπ x)d x 0 = 2h n2π 2 sin (cid:5) (cid:4) nπ 2 1/2 = 2h n2π 2 (−1)n+1 1(cid:2) 0 Kn sin2(nπ x)d x = Kn /2 (2.103) (2.104) (2.105) (2.106) (2.107) (2.108) book Mobk070 March 22, 2007 11:7 so that THE FOURIER METHOD: SEPARATION OF VARIABLES 29 y = 4h π 2 ∞(cid:1) n=1 (−1)n+1 n2 sin(nπ ξ ) cos(nπ τ ) (2.109) 2.2.4 Lessons The solutions are in the form of inﬁnite series. The coefﬁcients of the terms of the series are determined by using the fact that the solutions of at least one of the ordinary differential equations are orthogonal functions. The orthogonality condition allows us to calculate these coefﬁcients. Problem 1. Solve the boundary value problem = u xx utt u(t, 0) = u(t, 1) = 0 u(0, x) = 0 ut(0, x) = f (x) Find the special case when f (x) = sin(π x). FURTHER READING V. Arpaci, Conduction Heat Transfer. Reading, MA: Addison-Wesley, 1966. J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems. 6th edition. New York: McGraw-Hill, 2001. book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 31 C H A P T E R 3 Orthogonal Sets of Functions In this chapter we elaborate on the concepts of orthogonality and Fourier series. We begin with the familiar concept of orthogonality of vectors. We then extend the idea to orthogonality of functions and the use of this idea to represent general functions as Fourier series—series of orthogonal functions. Next we show that solutions of a fairly general linear ordinary differential equation—the Sturm–Liouville equation—are orthogonal functions. Several examples are given. VECTORS 3.1 We begin our study of orthogonality with the familiar topic of orthogonal vectors. Suppose u(1), u(2), and u(3) are the three rectangular component vectors in an ordinary three-dimensional space. The norm of the vector (its length) \|\|u\|\| is \|\|u\|\| = [u(1)2 + u(2)2 + u(3)2]1/2 (3.1) If \|\|u\|\| = 1, u is said to be normalized. If \|\|u\|\| = 0, u(r ) = 0 for each r and u is the zero vector. A linear combination of two vectors u1 and u2 is u = c 1u1 + c 2u2 , The scalar or inner product of the two vectors u1 and u2 is deﬁned as (u1 , u2) = 3(cid:1) r =1 u1(r )u2(r ) = (cid:6)u1 (cid:6)(cid:6)u2 (cid:6) cos θ 3.1.1 Orthogonality of Vectors If neither u1 nor u2 is the zero vector and if (u1 , u2) = 0 then θ = π/2 and the vectors are orthogonal. The norm of a vector u is \|\|u\|\| = (u, u)1/2 (3.2) (3.3) (3.4) (3.5) book Mobk070 March 22, 2007 11:7 32 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS \|\| has magnitude unity, and if u1 and u2 are orthogonal then (cid:1) = un 3.1.2 Orthonormal Sets of Vectors The vector (cid:1) (cid:1) /\|\|un 2 are orthonormal and their inner product is m) = δ ((cid:1) n , (cid:1) n nm = 0, m (cid:3)= n = 1, m = n 1 and (3.6) where δ nm is called the Kronecker delta. If (cid:1) 2, and (cid:1) 1, (cid:1) vector in three-dimensional space can be written as a linear combination of (cid:1) that is, 3 are three vectors that are mutually orthogonal to each other then every 2, and (cid:1) 3; 1, (cid:1) f (r ) = c 1 Note that due to the fact that the vectors (cid:1) (cid:1) + c 2 (cid:1) 2 + c 3 (cid:1) 3 1 n form an orthonormal set, (f , (cid:1) 1) = c 1 , (f , (cid:1) 2) = c 2 , (f , (cid:1) 3) = c 3 Simply put, suppose the vector f is f = 2(cid:1) 1 + 4(cid:1) 2 + (cid:1) . 3 (3.7) (3.8) (3.9) Taking the inner product of f with (cid:1) (f , (cid:1) and according to Eq. (3.8) c 1 1 we ﬁnd that 1) + 4((cid:1) 1 = 4 and c 3 1) = 2((cid:1) 1 = 2. Similarly, c 2 , (cid:1) , (cid:1) 2) + ((cid:1) = 1. , (cid:1) 3) (3.10) 1 FUNCTIONS 3.2 3.2.1 Orthonormal Sets of Functions and Fourier Series Suppose there is a set of orthonormal functions (cid:6) √ ( deﬁned as one whose inner product, deﬁned as n(x) deﬁned on an interval a < x < b 2 sin(nπ x) on the interval 0 < x < 1 is an example). A set of orthonormal functions is (cid:3) b x=a m(x)d x, is n(x)(cid:6) (cid:6) b(cid:2) ((cid:6) n , (cid:6) m) = (cid:6) n (cid:6) m d x = δ nm x=a Suppose we can express a function as an inﬁnite series of these orthonormal functions, f (x) = ∞(cid:1) n=0 (cid:6) n c n on a < x < b (3.11) (3.12) Equation (3.12) is called a Fourier series of f (x) in terms of the orthonormal function set (cid:6) n(x). book Mobk070 March 22, 2007 11:7 ORTHOGONAL SETS OF FUNCTIONS 33 If we now form the inner product of (cid:6) m with both sides of Eq. (3.12) and use the deﬁnition of an orthonormal function set as stated in Eq. (3.11) we see that the inner product of f (x) and (cid:6) n(x) is c n. b(cid:2) c n (cid:6)2 n(ξ )d ξ = c n = x=a b(cid:2) x=a f (ξ ) (cid:6) n(ξ )d ξ (3.13) In particular, consider a set of functions (cid:8) n that are orthogonal on the interval (a, b) so that b(cid:2) (cid:8) n(ξ )(cid:8) m(ξ )d ξ = 0, m (cid:3)= n where (cid:6)(cid:8) n (cid:6)2 = (cid:3) b x=a x=a (cid:6)2 , m = n n (ξ )d ξ is called the square of the norm of (cid:8) = (cid:6)(cid:8) n (cid:8)2 (cid:8) (cid:6)(cid:8) n n (cid:6) = (cid:6) n n. The functions (3.14) (3.15) then form an orthonormal set. We now show how to form the series representation of the function f (x) as a series expansion in terms of the orthogonal (but not orthonormal) set of functions (cid:8) n(x). f (x) = ∞(cid:1) n=0 (cid:8) (cid:6)(cid:8) n n b(cid:2) (cid:6) ξ =a f (ξ ) n(ξ ) (cid:8) (cid:6)(cid:8) (cid:6) d ξ = n ∞(cid:1) n=0 b(cid:2) (cid:8) n f (ξ ) ξ =a (cid:8) (cid:6)(cid:8) n(ξ ) (cid:6)2 d ξ n (3.16) This is called a Fourier series representation of the function f (x). As a concrete example, the square of the norm of the sine function on the interval (0, π ) is π(cid:2) (cid:6) sin(nx)(cid:6)2 = sin2(nξ )d ξ = ξ =0 π 2 so that the corresponding orthonormal function is (cid:8) (cid:6) = 2 π sin(nx) A function can be represented by a series of sine functions on the interval (0, π ) as f (x) = ∞(cid:1) n=0 π(cid:2) sin(nx) ς =0 sin(nς ) (cid:9) π 2 f (ς )d ς This is a Fourier sine series. (3.17) (3.18) (3.19) book Mobk070 March 22, 2007 11:7 34 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 3.2.2 Best Approximation We next ask whether, since we can never sum to inﬁnity, the values of the constants c n in Eq. (3.13) give the most accurate approximation of the function. To illustrate the idea we return to the idea of orthogonal vectors in three-dimensional space. Suppose we want to approximate a three-dimensional vector with a two-dimensional vector. What will be the components of the two-dimensional vector that best approximate the three-dimensional vector? Let the three-dimensional vector be f = c 1 (cid:1) (cid:1) 2 2. We wish to minimize \|\|k − f \|\|. + a2 + c 2 vector be k = a1 (cid:1) (cid:1) 1 1 + c 3 (cid:1) 3. Let the two-dimensional \|\|k − f \|\| = − c 1)2 + (a2 − c 2)2 + c 2 3 (cid:10) (a1 (cid:11) 1/2 (3.20) It is clear from the above equation (and also from Fig. 3.1) that this will be minimized when a1 = c 1 and a2 = c 2. Turning now to the orthogonal function series, we attempt to minimize the difference between the function with an inﬁnite number of terms and the summation only to some ﬁnite value m. The square of the error is b(cid:2) E2 = ( f (x) − Km(x))2d x = x=a b(cid:2) x=a (cid:12) (cid:13) f 2(x) + K 2(x) − 2 f (x)K (x) d x (3.21) where and f (x) = ∞(cid:1) n=1 (cid:6) c n n(x) = Km m(cid:1) n=1 (cid:6) an n(x) (3.22) (3.23) FIGURE 3.1: Best approximation of a three-dimensional vector in two dimensions book Mobk070 March 22, 2007 11:7 Noting that ORTHOGONAL SETS OF FUNCTIONS 35 m(cid:1) m(cid:1) m(x)d x = K 2 b(cid:2) ana j (cid:6) n(x)(cid:6) j (x)d x = n=1 j =1 x=a m(cid:1) n=1 a 2 n = a 2 1 + a 2 2 + a 2 3 + · · · + a 2 m (3.24) b(cid:2) x=a and b(cid:2) x=a ∞(cid:1) m(cid:1) f (x)K (x)d x = b(cid:2) c na j (cid:6) n(x)(cid:6) j (x)d x j =1 x=a c nan = c 1a1 + c 2a2 + · · · + c mam (3.25) = n=1 m(cid:1) n=1 b(cid:2) E2 = f 2(x)d x + a 2 1 + · · · + a 2 m − 2a1c 1 − · · · − 2amc m (3.26) x=a Now add and subtract c 2 1 , c 2 2 , . . . , c 2 m. Thus Eq. (3.26) becomes E2 = b(cid:2) x=a f 2(x)d x − c 2 1 − c 2 2 − · · · − c 2 m + (a1 − c 1)2 + (a2 − c 2)2 + · · · + (am − c m)2 which is clearly minimized when an = c n. (3.27) 3.2.3 Convergence of Fourier Series We brieﬂy consider the question of whether the Fourier series actually converges to the function f (x) for all values, say, on the interval a ≤ x ≤ b. The series will converge to the function if the value of E deﬁned in (3.19) approaches zero as m approaches inﬁnity. Sufﬁce to say that this is true for functions that are continuous with piecewise continuous ﬁrst derivatives, that is, most physically realistic temperature distributions, displacements of vibrating strings and bars. In each particular situation, however, one should use the various convergence theorems that are presented in most elementary calculus books. Uniform convergence of Fourier series is discussed extensively in the book Fourier Series and Boundary Value Problems by James Ward Brown and R. V. Churchill. In this chapter we give only a few physically clear examples. book Mobk070 March 22, 2007 11:7 36 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 3.2.4 Examples of Fourier Series Example 3.1. Determine a Fourier sine series representation of (0, 1). The series will take the form f (x) = x on the interval x = ∞(cid:1) j =0 c j sin( j π x) (3.28) since the sin( j π x) forms an orthogonal set on (0, 1), multiply both sides by sin(kπ x)d x and integrate over the interval on which the function is orthogonal. 1(cid:2) x=0 x sin(kπ x)d x = 1(cid:2) ∞(cid:1) k=0 x=0 c j sin( j π x) sin(kπ x)d x (3.29) Noting that all of the terms on the right-hand side of (2.20) are zero except the one for which k = j , 1(cid:2) x=0 After integrating we ﬁnd Thus, 1(cid:2) x sin( j π x)d x = c j sin2( j π x)d x (3.30) x=0 (−1) j +1 j π = c j 2 x = ∞(cid:1) j =0 (−1) j +1 j π 2 sin( j π x) (3.31) (3.32) This is an alternating sign series in which the coefﬁcients always decrease as j increases, and it therefore converges. The sine function is periodic and so the series must also be a periodic function beyond the interval (0, 1). The series outside this interval forms the periodic continuation of the series. Note that the sine is an odd function so that sin( j π x) = − sin(− j π x). Thus the periodic continuation looks like Fig. 3.2. The series converges everywhere, but at x = 1 it is identically zero instead of one. It converges to 1 − ε arbitrarily close to x = 1. book Mobk070 March 22, 2007 11:7 ORTHOGONAL SETS OF FUNCTIONS 37 1 -1 1 2 3 FIGURE 3.2: The periodic continuation of the function x represented by the sine series Example 3.2. Find a Fourier cosine for f (x) = x on the interval (0, 1). In this case x = ∞(cid:1) n=0 c n cos(nπ x) (3.33) Multiply both sides by cos(mπ x)d x and integrate over (0, 1). 1(cid:2) x=0 x cos(mπ x)d x = ∞(cid:1) 1(cid:2) c n n=0 x=0 cos(mπ x) cos(nπ x)d x (3.34) and noting that cos(nπ x) is an orthogonal set on (0, 1) all terms in (2.23) are zero except when n = m. Evaluating the integrals, = [(−1)2 − 1] (nπ )2 There is a problem when n = 0. Both the numerator and the denominator are zero there. (3.35) c n 2 However we can evaluate c 0 by noting that according to Eq. (3.26) 1(cid:2) x=0 xd x = c 0 = 1 2 and the cosine series is therefore x = 1 2 + ∞(cid:1) n=1 [(−1)n − 1] (nπ )2 2 cos(nπ x) (3.36) (3.37) The series converges to x everywhere. Since cos(nπ x) = cos(−nπ x) it is an even function and its periodic continuation is shown in Fig. 3.3. Note that the sine series is discontinuous at x = 1, while the cosine series is continuous everywhere. (Which is the better representation?) book Mobk070 March 22, 2007 11:7 38 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 1 -1 1 2 3 FIGURE 3.3: The periodic continuation of the series in Example 3.2 It should be clear from the above examples that in general a Fourier sine/cosine series of a function f (x) deﬁned on 0 ≤ x ≤ 1 can be written as f (x) = c 0 2 + ∞(cid:1) n=1 c n cos(nπ x) + ∞(cid:1) n=1 bn sin(nπ x) (3.38) where (cid:3) (cid:3) = c n = bn Problems 1. Show that 1 1 x=0 f (x) cos(nπ x)d x (cid:3) x=0 cos2(nπ x)d x 1 x=0 f (x) sin(nπ x)d x (cid:3) x=0 sin2(nπ x)d x 1 n = 0, 1, 2, 3, . . . n = 1, 2, 3, . . . (3.39) π(cid:2) x=0 sin(nx) sin(mx)d x = 0 when n (cid:3)= m. 2. Find the Fourier sine series for f (x) = 1 − x on the interval (0, 1). Sketch the periodic continuation. Sum the series for the ﬁrst ﬁve terms and sketch over two periods. Discuss convergence of the series, paying special attention to convergence at x = 0 and x = 1. 3. Find the Fourier cosine series for 1 − x on (0, 1). Sketch the periodic continuation. Sum the ﬁrst two terms and sketch. Sum the ﬁrst ﬁve terms and sketch over two periods. Discuss convergence, paying special attention to convergence at x = 0 and x = 1. book Mobk070 March 22, 2007 11:7 ORTHOGONAL SETS OF FUNCTIONS 39 3.3 STURM–LIOUVILLE PROBLEMS: ORTHOGONAL FUNCTIONS We now proceed to show that solutions of a certain ordinary differential equation with certain boundary conditions (called a Sturm–Liouville problem) are orthogonal functions with respect to a weighting function, and that therefore a well-behaved function can be represented by an inﬁnite series of these orthogonal functions (called eigenfunctions), as in Eqs. (3.12) and (3.16). Recall that the problem Xxx + λ2 X = 0, X(0) = 0, X(1) = 0 0 ≤ x ≤ 1 (3.40) has solutions only for λ = nπ and that the solutions, sin(nπ x) are orthogonal on the interval (0, 1). The sine functions are called eigenfunctions and λ = nπ are called eigenvalues. As another example, consider the problem with boundary conditions Xxx + λ2 X = 0 X(0) = 0 X(1) + H Xx(1) = 0 The solution of the differential equation is X = A sin(λx) + B cos (λx)) (3.41) (3.42) (3.43) The ﬁrst boundary condition guarantees that B = 0. The second boundary condition is satisﬁed by the equation A[sin(λ) + Hλ cos(λ)] = 0 Since A cannot be zero, this implies that − tan(λ) = Hλ. (3.44) (3.45) The eigenfunctions are sin(λx) and the eigenvalues are solutions of Eq. (3.45). This is illustrated graphically in Fig. 3.4. We will generally be interested in the fairly general linear second-order differential equation and boundary conditions given in Eqs. (3.46) and (3.47). (cid:14) (cid:15) + [q (x) + λp(x)]X = 0 a ≤ x ≤ b r (x) d X d x d d x a1 X(a) + a2d X(a)/d x = 0 b1 X(b) + b2d X(b)/d x = 0 (3.46) (3.47) book Mobk070 March 22, 2007 11:7 40 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FIGURE 3.4: Eigenvalues of − tan(λ) = Hλ Solutions exist only for discrete values λ are the eigenfunctions. n the eigenvalues. The corresponding solutions Xn(x) 3.3.1 Orthogonality of Eigenfunctions Consider two solutions of (3.46) and (3.47), Xn and Xm corresponding to eigenvalues λ λ m. The primes denote differentiation with respect to x. n and (r X (r X (cid:1) m) (cid:1) n) (cid:1) + q Xm (cid:1) + q Xn = −λ m p Xm = −λ n p Xn Multiply the ﬁrst by Xn and the second by Xm and subtract, obtaining the following: (cid:1) (r Xn X m − r Xm X (cid:1) n) (cid:1) = (λ n − λ m) p Xm Xn Integrating both sides (3.48) (3.49) (3.50) r (X (cid:1) m Xn − X (cid:1) n Xm)b a = (λ n − λ m) b(cid:2) a p(x)Xn Xmd x (3.51) Inserting the boundary conditions into the left-hand side of (3.51) (cid:1) (cid:1) m(a)Xn(a) − X m(b)Xn(b) − X X = − b1 b2 Xm(b)Xn(b) + a1 a2 Xm(a)Xn(a) − a1 a2 (cid:1) n(b)Xm(b) + X (cid:1) n(a)Xm(a) Xn(a)Xm(a) + b1 b2 Xm(b)Xn(b) = 0 (3.52) book Mobk070 March 22, 2007 11:7 ORTHOGONAL SETS OF FUNCTIONS 41 Thus b(cid:2) (λ n − λ m) p(x)Xn Xmd x = 0, m (cid:3)= n (3.53) a Notice that Xm and Xn are orthogonal with respect to the weighting function p(x) on the interval (a, b). Obvious examples are the sine and cosine functions. Example 3.3. Example 2.1 in Chapter 2 is an example in which the eigenfunctions are sin(λ and the eigenvalues are (2n − 1)π/2. ξ ) n Example 3.4. If the boundary conditions in Example 2.1 in Chapter 2 are changed to (cid:6)(cid:1) (0) = 0 (cid:6)(1) = 0 we note that the general solution of the differential equation is (cid:6)(ξ ) = A cos(λξ ) + B sin(λξ ) (3.54) (3.55) The boundary conditions require that B = 0 and cos(λ) = 0. The values of λ can take on any of the values π/2, 3π/2, 5π/2, . . . , (2n − 1)π/2. The eigenfunctions are cos(λ ξ ) and the eigenvalue are λ n = (2n − 1)π/2. n Example 3.5. Suppose the boundary conditions in the original problem (Example 1, Chapter 2) take on the more complicated form (cid:6)(0) = 0 (cid:6)(1) + h(cid:6)(cid:1) (1) = 0 (3.56) The ﬁrst boundary condition requires that B = 0. The second boundary conditions require that sin(λ n) + hλ n cos(λ n) = 0, or λ n = − 1 h tan(λ n) (3.57) (3.58) which is a transcendental equation that must be solved for the eigenvalues. The eigenfunctions are, of course, sin(λ nx). Example 3.6. A Physical Example: Heat Conduction in Cylindrical Coordinates The heat conduction equation in cylindrical coordinates is ∂u ∂t = ∂ 2u ∂r 2 + 1 r ∂u ∂r 0 < r < 1 (3.59) with boundary conditions at R = 0 and r = 1 and initial condition u(0, r ) = f (r ). book Mobk070 March 22, 2007 11:7 42 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Separating variables as u = R(r )T(t), 1 T d T d t = 1 R d 2 R dr 2 + 1 r R d R dr = −λ2 0 ≤ r ≤ 1, 0 ≤ t (3.60) (Why the minus sign?) The equation for R(r ) is (cid:1) (r R (cid:1) + λ2r R = 0, ) (3.61) which is a Sturm–Liouville equation with weighting function r. It is an eigenvalue problem with an inﬁnite number of eigenfunctions corresponding to the eigenvalues λ n. There will be two solutions R1(λ n. The solutions are called Bessel functions, and they will be discussed in Chapter 4. nr ) for each λ nr ) and R2(λ Rn(λ nr ) = An R1(λ nr ) + Bn R2(λ nr ) (3.62) The boundary conditions on r are used to determine a relation between the constants A and B. For solutions R(λ nr ) and R(λ mr ) 1(cid:2) 0 r R(λ nr )R(λ mr )dr = 0, n (cid:3)= m (3.63) is the orthogonality condition. The solution for T(t) is the exponential e −λ2 nt for all n. Thus, the solution of (3.60), because of superposition, can be written as an inﬁnite series in a form something like u = ∞(cid:1) n=0 Kne −λ2 n R(λ nr ) (3.64) and the orthogonality condition is used to ﬁnd Kn as 1(cid:2) 1(cid:2) = Kn f (r )R(λ nr )r dr/ f (r )R2(λ nr )r dr (3.65) r =0 r =0 Problems 1. For Example 2.1 in Chapter 2 with the new boundary conditions described in Example 3.2 above, ﬁnd Kn and write the inﬁnite series solution to the revised problem. book Mobk070 March 22, 2007 11:7 ORTHOGONAL SETS OF FUNCTIONS 43 FURTHER READING J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems, 6th edition. New York: McGraw-Hill, 2001. P. V. O’Neil, Advanced Engineering Mathematics. 5th edition. Brooks/Cole Thompson, Paciﬁc Grove, CA, 2003. book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 45 C H A P T E R 4 Series Solutions of Ordinary Differential Equations 4.1 GENERAL SERIES SOLUTIONS The purpose of this chapter is to present a method of obtaining solutions of linear second-order ordinary differential equations in the form of Taylor series’. The methodology is then used to obtain solutions of two special differential equations, Bessel’s equation and Legendre’s equation. Properties of the solutions—Bessel functions and Legendre functions—which are extensively used in solving problems in mathematical physics, are discussed brieﬂy. Bessel functions are used in solving both diffusion and vibrations problems in cylindrical coordinates. The functions R(λ nr ) in Example 3.4 at the end of Chapter 3 are called Bessel functions. Legendre functions are useful in solving problems in spherical coordinates. Associated Legendre functions, also useful in solving problems in spherical coordinates, are brieﬂy discussed. 4.1.1 Deﬁnitions In this chapter we will be concerned with linear second-order equations. A general case is Division by a(x) gives a(x)u (cid:1)(cid:1) + b(x)u (cid:1) + c (x)u = f (x) (cid:1)(cid:1) + p(x)u (cid:1) + q (x)u = r (x) u (4.1) (4.2) Recall that if r (x) is zero the equation is homogeneous. The solution can be written as the sum of = 0. The nature a homogeneous solution u h (x) and a particular solution u p(x). If r (x) is zero, u p of the solution and the solution method depend on the nature of the coefﬁcients p(x) and q (x). If each of these functions can be expanded in a Taylor series about a point x0 the point is said to be an ordinary point and the function is analytic at that point. If either of the coefﬁcients is not analytic at x0, the point is a singular point. If x0 is a singular point and if (x − x0) p(x) and (x − x0)2q (x) are analytic, then the singularities are said to be removable and the singular point is a regular singular point. If this is not the case the singular point is irregular. book Mobk070 March 22, 2007 11:7 46 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 4.1.2 Ordinary Points and Series Solutions If the point x0 is an ordinary point the dependent variable has a solution in the neighborhood of x0 of the form u(x) = ∞(cid:1) n=0 c n(x − x0)n (4.3) We now illustrate the solution method with two examples. Example 4.1. Find a series solution in the form of Eq. (4.3) about the point x = 0 of the differential equation (cid:1)(cid:1) + x2u = 0 u (4.4) The point x = 0 is an ordinary point so at least near x = 0 there is a solution in the form of the above series. Differentiating (4.3) twice and inserting it into (4.4) (cid:1) = u (cid:1)(cid:1) = u ∞(cid:1) n=0 ∞(cid:1) n=0 nc nxn−1 n(n − 1)c nxn−2 ∞(cid:1) n=0 n(n − 1)c nxn−2 + ∞(cid:1) n=0 xn+2c n = 0 (4.5) Note that the ﬁrst term in the u series are zero. We can shift the indices in both summations so that the power of x is the same in both series by setting n − 2 = m in the ﬁrst series. series is zero while the ﬁrst two terms in the u (cid:1) (cid:1)(cid:1) ∞(cid:1) n=0 n(n − 1)c nxn−2 = ∞(cid:1) m=−2 (m + 2)(m + 1)c m+2xm = ∞(cid:1) m=0 (m + 2)(m + 1)c m+2xm (4.6) Noting that m is a “dummy variable” and that the ﬁrst two terms in the series are zero the series can be written as ∞(cid:1) n=0 (n + 2)(n + 1)c n+2xn In a similar way we can write the second term as ∞(cid:1) n=0 c nxn+2 = ∞(cid:1) n=2 c n−2xn (4.7) (4.8) book Mobk070 March 22, 2007 11:7 We now have SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 47 ∞(cid:1) n=0 (n + 2)(n + 1)c n+2xn + ∞(cid:1) n=2 c n−2xn = 0 (4.9) which can be written as 2c 2 + 6c 3x + ∞(cid:1) n=2 [(n + 2)(n + 1)c n+2 + c n−2]xn = 0 (4.10) Each coefﬁcient of xn must be zero in order to satisfy Eq. (4.10). Thus c 2 and c 3 must be zero and c n+2 = −c n−2 /(n + 2)(n + 1) (4.11) while c 0 and c 1 remain arbitrary. Setting n = 2, we ﬁnd that c 4 , c 7 , c 10 c 3 are zero, so are c 6 = −c 0 /12 and setting n = 3, c 5 , c 11, etc. Also, c 8 = −c 4 /(8)(7) = c 0 = −c 1 /(4)(3)(8)(7) and /20. Since c 2 and c 9 = −c 5 /(9)(8) = c 1 /(5)(4)(9)(8). The ﬁrst few terms of the series are u(x) = c 0(1 − x4/12 + x6/672 + · · · ) + c 1(1 − x5/20 + x9/1440 + · · · ) (4.12) The values of c 0 and c 1 may be found from appropriate boundary conditions. These are both alternating sign series with each term smaller than the previous term at least for x ≤ 1 and it is therefore convergent at least under these conditions. The constants c 0 and c 1 can be determined from boundary conditions. For example if u(0) = 0, c 0 + c 1 = 0, so c 1 = −c 0. If u(1) = 1, c 0[−1/12 + 1/20 + 1/672 − 1/1440 + · · · ] = 1 Example 4.2. Find a series solution in the form of Eq. (4.3) of the differential equation (cid:1)(cid:1) + xu (cid:1) + u = x2 u (4.13) valid near x = 0. Assuming a solution in the form of (4.3), differentiating and inserting into (4.13), ∞(cid:1) n=0 (n − 1)nc nxn−2 + ∞(cid:1) n=0 nc nxn + ∞(cid:1) n=0 c nxn − x2 = 0 (4.14) book Mobk070 March 22, 2007 11:7 48 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Shifting the indices as before ∞(cid:1) n=0 (n + 2)(n + 1)c n+2xn + ∞(cid:1) n=0 nc nxn + ∞(cid:1) n=0 c nxn − x2 = 0 (4.15) Once again, each of the coefﬁcients of xn must be zero. Setting n = 0, we see that n = 0 : 2c 2 n = 1 : 6c 3 n = 2 : 12c 4 n > 2 : c n+2 + c 0 + 2c 1 + 3c 2 = c n n + 2 c 2 = 0, = 0, − 1 = 0, /2 = −c 0 /3 = −c 1 c 3 = (1 + 3c 0 c 4 /2)/12 The last of these is called a recurrence formula. Thus, u = c 0(1 − x2/2 + x4/8 − x6/(8)(6) + · · · ) + c 1(x − x3/3 + x5/(3)(5) − x7/(3)(5)(7) + · · · ) + x4(1/12 − x2/(12)(6) + · · · ) (4.16) (4.17) Note that the series on the third line of (4.17) is the particular solution of (4.13). The constants c 0 and c 1 are to be evaluated using the boundary conditions. 4.1.3 Lessons: Finding Series Solutions for Differential Equations with Ordinary Points If x0 is an ordinary point assume a solution in the form of Eq. (4.3) and substitute into the differential equation. Then equate the coefﬁcients of equal powers of x. This will give a recurrence formula from which two series may be obtained in terms of two arbitrary constants. These may be evaluated by using the two boundary conditions. Problems 1. The differential equation (cid:1)(cid:1) + xu (cid:1) + xu = x u has ordinary points everywhere. Find a series solution near x = 0. 2. Find a series solution of the differential equation near x = 0 and identify the particular solution. (cid:1)(cid:1) + (1 + x2)u = x u book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 49 3. The differential equation (1 − x2)u (cid:1)(cid:1) + u = 0 has singular points at x = ±1, but is analytic near x = 0. Find a series solution that is valid near x = 0 and discuss the radius of convergence. 4.1.4 Regular Singular Points and the Method of Frobenius If x0 is a singular point in (4.2) there may not be a power series solution of the form of Eq. (4.3). In such a case we proceed by assuming a solution of the form u(x) = ∞(cid:1) n=0 c n(x − x0)n+r (4.18) (cid:3)= 0 and r is any constant, not necessarily an integer. This is called the method of in which c 0 Frobenius and the series is called a Frobenius series. The Frobenius series need not be a power series because r may be a fraction or even negative. Differentiating once and differentiating again (cid:1) = u ∞(cid:1) n=0 (n + r )c n(x − x0)n+r −1 (cid:1)(cid:1) = u ∞(cid:1) n=0 (n + r − 1)(n + r )c n(x − x0)n+r −2 (4.19) (4.20) These are then substituted into the differential equation, shifting is done where required so that each term contains x raised to the power n, and the coefﬁcients of xn are each set equal to zero. The coefﬁcient associated with the lowest power of x will be a quadratic equation that can be solved for the index r . It is called an indicial equation. There will therefore be two roots of this equation corresponding to two series solutions. The values of c n are determined as above by a recurrence equation for each of the roots. Three possible cases are important: (a) the roots are distinct and do not differ by an integer, (b) the roots differ by an integer, and (c) the roots are coincident, i.e., repeated. We illustrate the method by a series of examples. Example 4.3 (distinct roots). Solve the equation x2u (cid:1)(cid:1) + x(1/2 + 2x)u (cid:1) + (x − 1/2)u = 0 The coefﬁcient of the u (cid:1) term is p(x) = (1/2 + 2x) x (4.21) (4.22) book Mobk070 March 22, 2007 11:7 50 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and the coefﬁcient of the u (cid:1)(cid:1) term is q (x) = (x − 1/2) x2 (4.23) Both have singularities at x = 0. However multiplying p(x) by x and q (x) by x2 the singularities are removed. Thus x = 0 is a regular singular point. Assume a solution in the form of the Frobenius series: u = n=0 c nxn+r , differentiate twice and substitute into (4.21) obtaining (cid:16)∞ ∞(cid:1) n=0 (n + r )(n + r − 1)xn+1 + ∞(cid:1) n=0 1 2 (n + r )c nxn+r + ∞(cid:1) n=0 2(n + r )c nxn+r +1 + ∞(cid:1) n=0 c nxn+r +1 − ∞(cid:1) n=0 1 2 c nxn+r = 0 (4.24) The indices of the third and fourth summations are now shifted as in Example 4.1 and we ﬁnd (cid:14) r (r − 1) + 1 2 r − 1 2 (cid:15) c 0xr + (cid:14) (n + r )(n + r − 1) + 1 2 ∞(cid:1) n=1 (cid:15) (n + r ) − 1 2 c nxn+r + ∞(cid:1) n=1 [2(n + r − 1) + 1]c n−1xn+r = 0 (4.25) Each coefﬁcient must be zero for the equation to be true. Thus the coefﬁcient of the c 0 term must be zero since c 0 itself cannot be zero. This gives a quadratic equation to be solved for r , and this is called an indicial equation (since we are solving for the index, r ). r (r − 1) + 1 2 r − 1 2 = 0 (4.26) with r = 1 and r = −1/2. The coefﬁcients of xn+r must also be zero. Thus [(n + r )(n + r − 1) + 1/2(n + r ) − 1/2]c n + [2(n + r − 1) + 1]c n−1 = 0 . (4.27) The recurrence equation is therefore = − c n For the case of r = 1 2(n + r − 1) + 1 (n + r )(n + r − 1) + 1 2 (n + r ) − 1 2 c n−1 (4.28) c n = − 2n + 1 (cid:17) n + 3 n 2 (cid:18) c n−1 (4.29) book Mobk070 March 22, 2007 11:7 Computing a few of the coefﬁcients, SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 51 c 1 c 2 c 3 = − 3 5 2 c 0 = − 6 5 c 0 c 1 = − 5 7 = − 7 c 2 27 2 c 0 = − 6 7 = − 4 9 c 0 etc. and the ﬁrst Frobenius series is (cid:6) (cid:7) u1 = c 0 x − 6 5 x2 + 6 7 x3 − 4 9 x4 + · · · (4.30) Setting r = −1/2 in the recurrence equation (4.26) and using bn instead of c n to distinguish it from the ﬁrst case, bn = − 2n − 2 (cid:17) n − 3 n 2 (cid:18) bn−1 (4.31) Noting that in this case b1 series has only one term: b0x = 0, all the following bns must be zero and the second Frobenius −1/2. The complete solution is (cid:6) x − 6 5 x2 + 6 7 x3 − 4 9 x4 + · · · + b0x (4.32) −1/2 (cid:7) u = c 0 Example 4.4 (repeated roots). Next consider the differential equation There is a regular singular point at x = 0, so we attempt a Frobenius series around x = 0. x2u (cid:1)(cid:1) − xu (cid:1) + (x + 1)u = 0 (4.33) Differentiating (4.17) and substituting into (4.30), (n + r − 1)(n + r )c nxn+r − ∞(cid:1) n=0 (n + r )c nxn+r + ∞(cid:1) n=0 c nxn+r + ∞(cid:1) n=0 c nxn+r +1 = 0 (4.34) ∞(cid:1) n=0 or [r (r − 1) − r + 1]c 0xr + ∞(cid:1) n=1 [(n + r − 1)(n + r ) − (n + r ) + 1]c nxn+r + where we have shifted the index in the last sum. The indicial equation is r (r − 1) − r + 1 = 0 ∞(cid:1) n=1 c n−1xn+r = 0 (4.35) (4.36) book Mobk070 March 22, 2007 11:7 52 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and the roots of this equation are both r = 1. Setting the last two sums to zero we ﬁnd the recurrence equation and since r = 1, = − c n 1 (n + r − 1)(n + r ) − (n + r ) + 1 c n−1 = − c n 1 n(n + 1) − (n + 1) + 1 c n−1 c 1 = −c 0 (4.37) (4.38) = c 2 = c 3 c 1 −1 6 − 3 + 1 −1 12 − 4 + 1 c 2 c 0 = 1 4 −1 9 = = c 1 −1 36 c 0 etc. The Frobenius series is (cid:6) (cid:7) u1 = c 0 x − x2 + 1 4 x3 − 1 36 x4 + . . . (4.39) In this case there is no second solution in the form of a Frobenius series because of the repeated root. We shall soon see what form the second solution takes. Example 4.5 (roots differing by an integer 1). Next consider the equation x2u (cid:1)(cid:1) − 2xu (cid:1) + (x + 2)u = 0 (4.40) There is a regular singular point at x = 0. We therefore expect a solution in the form of the Frobenius series (4.18). Substituting (4.18), (4.19), (4.20) into our differential equation, we obtain ∞(cid:1) ∞(cid:1) ∞(cid:1) ∞(cid:1) (n + r )(n + r − 1)c nxn+r − 2(n + r )c nxn+r + 2c nxn+r + c nxn+r +1 = 0 n=0 n=0 n=0 n=0 Taking out the n = 0 term and shifting the last summation, ∞(cid:1) n=1 [r (r − 1) − 2r + 2]c 0xr + + ∞(cid:1) n=1 c n−1xn+r = 0 [(n + r )(n + r − 1) − 2(n + r ) + 2]c nxn+r (4.41) (4.42) book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 53 The ﬁrst term is the indicial equation. There are two distinct roots, r1 = 2 and r2 = 1. However they differ by an integer. r (r − 1) − 2r + 2 = 0 (4.43) r1 − r2 = 1. Substituting r1 = 2 into (4.39) and noting that each coefﬁcient of xn+r must be zero, [(n + 2)(n + 1) − 2(n + 2) + 2]c n + c n−1 = 0 (4.44) The recurrence equation is = c n = c 1 = c 2 = c 3 −c n−1 (n + 2)(n − 1) + 2 −c 0 2 −c 1 6 −c 2 12 c 0 12 −c 0 144 = c 0 = The ﬁrst Frobenius series is therefore (cid:14) (cid:15) u1 = c 0 x2 − 1 2 x3 + 1 12 x4 − 1 144 x5 + . . . (4.45) (4.46) We now attempt to ﬁnd the Frobenius series corresponding to r2 we ﬁnd that = 1. Substituting into (4.44) [n(n + 1) − 2(n + 1) + 2]c n = −c n−1 (4.47) When n = 1, c 0 must be zero. Hence c n must be zero for all n and the attempt to ﬁnd a second Frobenius series has failed. This will not always be the case when roots differ by an integer as illustrated in the following example. Example 4.6 (roots differing by an integer 2). Consider the differential equation x2u (cid:1)(cid:1) + x2u (cid:1) − 2u = 0 (4.48) You may show that the indicial equation is r 2 − r − 2 = 0 with roots r1 roots differ by an integer. When r = 2 the recurrence equation is = 2, r2 = −1 and the c n = − n + 1 n(n + 3) c n−1 (4.49) book Mobk070 March 22, 2007 11:7 54 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS The ﬁrst Frobenius series is (cid:14) (cid:15) u1 = c 0x2 1 − 1 2 x + 3 20 x2 − 1 30 x3 + . . . When r = −1 the recurrence equation is [(n − 1)(n − 2) − 2]bn + (n − 2)bn−1 = 0 (4.50) (4.51) When n = 3 this results in b2 = 0. Thus bn = 0 for all n ≥ 2 and the second series terminates. (cid:6) (cid:7) u2 = b0 1 x − 1 2 (4.52) 4.1.5 Lessons: Finding Series Solution for Differential Equations with Regular Singular Points 1. Assume a solution of the form u = ∞(cid:1) n=0 c nxn+r , c 0 (cid:3)= 0 (4.53) Differentiate term by term and insert into the differential equation. Set the coefﬁcient of the lowest power of x to zero to obtain a quadratic equation on r . If the indicial equation yields two roots that do not differ by an integer there will always be two Frobenius series, one for each root of the indicial equation. 2. If the roots are the same (repeated roots) the form of the second solution will be u2 = u1 ln(x) + ∞(cid:1) n=1 bnxn+r1 (4.54) This equation is substituted into the differential equation to determine bn. 3. If the roots differ by an integer, choose the largest root to obtain a Frobenius series for u1. The second solution may be another Frobenius series. If the method fails assume a solution of the form u2 = u1 ln(x) + ∞(cid:1) n=1 bnxn+r2 (4.55) This equation is substituted into the differential equation to ﬁnd bn. This is considered in the next section. book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 55 4.1.6 Logarithms and Second Solutions Example 4.7. Reconsider Example 4.4 and assume a solution in the form of (4.54). Recall that in Example 4.4 the differential equation was x2u (cid:1)(cid:1) − xu (cid:1) + (1 + x)u = 0 (4.56) and the indicial equation yielded a double root at r = 1. A single Frobenius series was u1 = x − x2 + x3 4 − x4 36 + · · · Now differentiate Eq. (4.54). (cid:1) 2 u = u (cid:1) 1 ln x + 1 x + u1 ∞(cid:1) n=1 (n + r )bnxn+r −1 (cid:1)(cid:1) 2 u = u (cid:1)(cid:1) 1 ln x + 2 x (cid:1) 1 u − 1 x2 u1 + ∞(cid:1) n=1 (n + r − 1)(n + r )bnxn+r −2 (4.57) Inserting this into the differential equation gives (cid:1)(cid:1) 1 − xu (cid:1) 1 + (1 + x)u1] + 2(xu (cid:1) 1 − u1) ln(x)[x2u ∞(cid:1) + [bn(n + r − 1)(n + r )xn+r − bn(n + r )xn+r + bnxn+r ] n=1 ∞(cid:1) n=1 + bnxn+r +1 = 0 (4.58) The ﬁrst term on the left-hand side of (4.52) is clearly zero because the term in brackets is the original equation. Noting that r = 1 in this case and substituting from the Frobenius series for u1, we ﬁnd (c 0 can be set equal to unity without losing generality) (cid:14) −x2 + x3 3 2 − x4 12 (cid:15) + · · · + ∞(cid:1) n=1 [n(n + 1) − (n + 1) + 1]bnxn+1 + ∞(cid:1) n=2 bn−1xn+1 = 0 or −2x2 + x3 − x4 6 + · · · + b1x2 + n2bn + bn−1 (cid:13) xn+1 = 0 ∞(cid:1) (cid:12) n=2 Equating coefﬁcients of x raised to powers we ﬁnd that b1 = 2 (4.59) (4.60) book Mobk070 March 22, 2007 11:7 56 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS For n ≥ 2 etc. + b1 = 0 b2 1 + 4b2 − 1 6 + 9b3 + b2 = 0 = −3/4 = 11 108 b3 (cid:6) (cid:7) u2 = u1 ln x + 2x2 − 3 4 x3 + 11 108 x4 − · · · The complete solution is u = [C1 + C2 ln x] u1 + C2 (cid:14) 2x2 − 3 4 x3 + 11 108 (cid:15) x4 − · · · (4.61) (4.62) Example 4.8. Reconsider Example 4.5 in which a second Frobenius series could not be found because the roots of the indicial equation differed by an integer. We attempt a second solution in the form of (4.55). The differential equation in Example 4.5 was x2u (cid:1)(cid:1) − 2xu (cid:1) + (x + 2)u = 0 and the roots of the indicial equation were r = 2 and r = 1, and are therefore separated by an integer. We found one Frobenius series = x2 − 1 2 x4 − 1 144 x3 + 1 12 x5 + · · · u1 for the root r = 2, but were unable to ﬁnd another Frobenius series for the case of r = 1. Assume a second solution of the form in Eq. (4.55). Differentiating and substituting into (4.40) (cid:1) + (x + 2)u] ln(x) + 2xu (cid:1) − 3u1 (cid:1)(cid:1) − 2xu 1 ∞(cid:1) bn[(n + r )(n + r − 1) − 2(n + r ) + 2]xn+r [x2u + + n=1 ∞(cid:1) n=1 bnxn+r +1 = 0 Noting that the ﬁrst term in the brackets is zero, inserting u1 and u that r2 = 1 x2 − 3 2 x3 + 5 12 x4 − 7 144 x5 + . . . + b0x2 + ∞(cid:1) n=2 {[n(n − 1)]bn + bn−1 }xn+1 = 0 (4.64) (4.63) (cid:1) 1 from (4.50) and noting book Mobk070 March 22, 2007 11:7 Equating x2 terms, we ﬁnd that b0 = −1. For higher order terms SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 57 Taking b1 = 0, 3 2 = 2b2 + b1 = 2b2 + b1 b2 = 3 4 − 5 12 = 6b3 + b2 = 6b3 + 3 4 b3 = − 7 36 The second solution is (cid:6) (cid:7) u2 = u1 ln(x) − x − 3 4 x3 + 7 36 x4 − . . . The complete solution is therefore u = [C1 + C2 ln x] u1 − C2 (cid:14) x − 3 4 x3 + 7 36 (cid:15) x4 − · · · Problems 1. Find two Frobenius series solutions x2u (cid:1)(cid:1) + 2xu (cid:1) + (x2 − 2)u = 0 2. Find two Frobenious series solutions x2u (cid:1)(cid:1) + xu (cid:1) + (cid:6) (cid:7) x2 − 1 4 u = 0 3. Show that the indicial equation for the differential equation (cid:1)(cid:1) + u (cid:1) + xu = 0 xu (4.65) (4.66) has roots s = −1 and that the differential equation has only one Frobenius series solution. Find that solution. Then ﬁnd another solution in the form u = ln ∞(cid:1) n=0 c nxn+s + ∞(cid:1) m=0 anxs +m where the ﬁrst summation above is the ﬁrst Frobenius solution. book Mobk070 March 22, 2007 11:7 58 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS BESSEL FUNCTIONS 4.2 A few differential equations are so widely useful in applied mathematics that they have been named after the mathematician who ﬁrst explored their theory. Such is the case with Bessel’s equation. It occurs in problems involving the Laplacian ∇ 2u in cylindrical coordinates when variables are separated. Bessel’s equation is a Sturm–Liouville equation of the form ρ2 d 2u dρ2 + ρ d u dρ + (λ2ρ2 − ν2)u = 0 Changing the independent variable x = λρ, the equation becomes x2u (cid:1)(cid:1) + xu (cid:1) + (x2 − ν2)u = 0 (4.67) (4.68) 4.2.1 Solutions of Bessel’s Equation Recalling the standard forms (4.1) and (4.2) we see that it is a linear homogeneous equation with variable coefﬁcients and with a regular singular point at x = 0. We therefore assume a solution of the form of a Frobenius series (4.17). u = ∞(cid:1) j =0 c j x j +r (4.69) Upon differentiating twice and substituting into (4.68) we ﬁnd ∞(cid:1) j =0 [( j + r − 1)( j + r ) + ( j + r ) − ν2]c j x j +r + (cid:1) j =0 c j x j +r +2 = 0 (4.70) In general ν can be any real number. We will ﬁrst explore some of the properties of the solution when ν is a nonnegative integer, 0, 1, 2, 3, . . . . First note that ( j + r − 1)( j + r ) + ( j + r ) = ( j + r )2 (4.71) Shifting the exponent in the second summation and writing out the ﬁrst two terms in the ﬁrst (r − n)(r + n)c 0 ∞(cid:1) + (r + 1 − n)(r + 1 + n)c 1x + [(r + j − n)(r + j + n)c j + c j −2]x j = 0 (4.72) j =2 In order for the coefﬁcient of the x0 term to vanish r = n or r = −n. (This is the indicial = 0. For each term in the equation.) In order for the coefﬁcient of the x term to vanish c 1 book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 59 summation to vanish −1 (r + j − n)(r + j + n) c j = c j −2 = This is the recurrence relation. Since c 1 convenient to write j = 2k and note that −1 j (2n + j ) = 0, all c j c j −2 , r = n j = 2, 3, 4, · · · (4.73) = 0 when j is an odd number. It is therefore so that = c 2k −1 22k(r + k) c 2k−2 = c 2k (−1)k k!(n + 1)(n + 2) . . . (n + k)22k c 0 The Frobenius series is (cid:19) u = c 0xn 1 + ∞(cid:1) k=1 (−1)k k!(n + 1)(n + 2) . . . .(n + k) (cid:20) (cid:5) 2k (cid:4) x 2 (4.74) (4.75) (4.76) Now c 0 is an arbitrary constant so we can choose it to be c 0 equation reduces to = 1/n!2n in which case the above J n = u = ∞(cid:1) k=0 (−1)k k!(n + k)! (cid:4) x 2 (cid:5) n+2k (4.77) The usual notation is J n and the function is called a Bessel function of the ﬁrst kind of order n. Note that we can immediately conclude from (4.77) that J n(−x) = (−1)n J n(x) Note that the roots of the indicial equation differ by an integer. When r = −n (4.72) does not yield a useful second solution since the denominator is zero for j = 0 or 2n. In any case it is easy to show that J n(x) = (−1)n J −n, so when r is an integer the two solutions are not independent. A second solution is determined by the methods detailed above and involves natural (4.78) logarithms. The details are very messy and will not be given here. The result is (cid:21) Yn(x) = 2 π J n(x) (cid:4) (cid:22) ln x 2 (cid:5) (cid:23) + γ + ∞(cid:1) k=1 (−1)k+1[φ(k) + φ(k + 1)] 22k+n+1k!(k + n)! x2k+n − 2 π n−1(cid:1) k=0 (n − k − 1)! 22k−n+1k! x2k−n (cid:24) (4.79) In this equation (cid:6)(k) = 1 + 1/2 + 1/3 + · · · + 1/k and γ is Euler’s constant 0.5772156649 . . . . . . book Mobk070 March 22, 2007 11:7 60 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FIGURE 4.1: Bessel functions of the ﬁrst kind Bessel functions of the ﬁrst and second kinds of order zero are particularly useful in solving practical problems (Fig. 4.1). For these cases and J 0(x) = ∞(cid:1) k=0 (cid:5) 2k (−1)k (k!)2 (cid:4) x 2 Y0 = J 0(x) ln(x) + ∞(cid:1) k=1 (−1)k+1 22k(k!)2 φ(k)x2k (4.80) (4.81) The case of ν (cid:3)= n. Recall that in (4.70) if ν is not an integer, a part of the denominator is (1 + ν)(2 + ν)(3 + ν) . . . (n + ν) (4.82) We were then able to use the familiar properties of factorials to simplify the expression for J n(x). If ν (cid:3)= n we can use the properties of the gamma function to the same end. The gamma function is deﬁned as ∞(cid:2) (cid:11)(ν) = ν−1e −td t t 0 (4.83) book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 61 ∞(cid:2) (cid:11)(ν + 1) = ν −td t e t 0 (4.84) Note that and integrating by parts (cid:11)(ν + 1) = [−t νe −t] ∞ 0 + ν ∞(cid:2) 0 ν−1e −td t = ν(cid:11)(ν) t (4.85) and (4.82) can be written as (1 + ν)(2 + ν)(3 + ν) . . . .(n + ν) = (cid:11)(n + ν + 1) (cid:11)(ν + 1) so that when ν is not an integer J ν(x) = ∞(cid:1) n=0 (−1)n 22n+νn!(cid:11)(n + ν + 1) x2n+ν (4.86) (4.87) Fig. 4.3 is a graphical representation of the gamma function. Here are the rules 1. If 2ν is not an integer, J ν and J −ν are linearly independent and the general solution of Bessel’s equation of order ν is u(x) = A J ν(x) + B J −ν(x) (4.88) 2. 3. where A and B are constants to be determined by boundary conditions. If 2ν is an odd positive integer J ν and J −ν are still linearly independent and the solution form (4.88) is still valid. If 2ν is an even integer, J ν(x) and J −ν(x) are not linearly independent and the solution takes the form u(x) = A J ν(x) + BY ν(x) (4.89) Bessel functions are tabulated functions, just as are exponentials and trigonometric functions. Some examples of their shapes are shown in Figs. 4.1 and 4.2. Note that both J ν(x) and Yν(x) have an inﬁnite number of zeros and we denote them as λ j , j = 0, 1, 2, 3, . . . book Mobk070 March 22, 2007 11:7 62 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FIGURE 4.2: Bessel functions of the second kind FIGURE 4.3: The gamma function Some important relations involving Bessel functions are shown in Table 4.1. We will derive only the ﬁrst, namely d d x d d x ν (x J ν(x)) = x ν ν (x J ν(x)) = d d x J ν−1(x) (cid:19) ∞(cid:1) n=0 (−1)n 22n+νn!(cid:11)(n + ν + 1) x2n+2ν (cid:20) (4.90) (4.91) book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 63 TABLE 4.1: Some Properties of Bessel Functions ν −ν J ν(x)] J ν(x)] J ν+1(x) J ν−1(x) −ν (cid:1) = x ν 1. [x (cid:1) = −x 2. [(cid:10)x 3. J ν−1(x) + J ν+1(x) = 2ν/x[J ν(x)] 4. Jν−1(x) − J ν+1(x) = 2J ν(x)(cid:1) J ν−1(x)d x = x 5. −ν J ν+1(x)d x = x 6. J v+ constant −ν x x (cid:3) (cid:3) ν ν J ν(x) + constant = ∞(cid:1) n=0 ν = x (−1)n2(n + ν) 22n+νn!(n + ν)(cid:11)(n + ν) ∞(cid:1) (−1)n 22n+ν−1n!(cid:11)(n + ν) n=0 x2n+2ν−1 x2n+2ν−1 = x ν J ν−1(x) (4.92) (4.93) These will prove important when we begin solving partial differential equations in cylindrical coordinates using separation of variables. Bessel’s equation is of the form (4.138) of a Sturm–Liouville equation and the func- tions J n(x) are orthogonal with respect to a weight function ρ (see Eqs. (3.46) and (3.53), Chapter 3). Note that Bessel’s equation (4.67) with ν = n is ρ2 J (cid:1)(cid:1) n + ρ J (cid:1) n + (λ2ρ2 − n2)J n = 0 d dρ (ρ J (cid:1) n)2 + (λ2ρ2 − n2) d dρ J 2 n = 0 (4.94) (4.95) which can be written as Integrating, we ﬁnd that (cid:1) [(ρ J )2 + (λ2ρ2 − n2)J 2] 1 0 − 2λ2 ρ J 2dρ = 0 (4.96) ρ=0 1(cid:2) Thus, 1(cid:2) 2λ2 ρ J 2 n dρ = λ2[J (cid:1) n(λ)]2 + (λ2 − n2)[J n(λ)]2 (4.97) ρ=0 book Mobk070 March 22, 2007 11:7 64 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Thus, we note from that if the eigenvalues are λ condition is, according to Eq. (3.53) in Chapter 3 j , the roots of J ν(λ ρ) = 0 the orthogonality j 1(cid:2) 0 ρ J n(λ j ρ)J n(λ k ρ)dρ = 0, j (cid:3)= k On the other hand, if the eigenvalues are the roots of the equation = 1 2 [J n+1(λ j )]2, j = k (4.98) H J n(λ j ) + λ j J (cid:1) n(λ j ) = 0 ρ J n(λ j ρ)J n(λ k ρ)dρ = 0, j (cid:3)= k 1(cid:2) 0 (λ2 j = − n2 + H2)[J n(λ 2λ2 j j )]2 , j = k (4.99) Using the equations in the table above and integrating by parts it is not difﬁcult to show that x(cid:2) s =0 s n J 0(s )d s = xn J 1(x) + (n − 1)xn−1 J 0(x) − (n − 1)2 s n−2 J 0(s )d s (4.100) x(cid:2) s =0 4.2.2 Fourier–Bessel Series Owing to the fact that Bessel’s equation with appropriate boundary conditions is a Sturm– Liouville system it is possible to use the orthogonality property to expand any piecewise continuous function on the interval 0 < x < 1 as a series of Bessel functions. For example, let f (x) = ∞(cid:1) n=1 An J 0(λ nx) (4.101) Multiplying both sides by x J 0(λ k x)d x and integrating from x = 0 to x = 1 (recall that the weighting function x must be used to insure orthogonality) and noting the orthogonality property we ﬁnd that f (x) = ∞(cid:1) j =1 (cid:3) 1 x=0 x f (x)J 0(λ (cid:3) x=0 x[J 0(λ j x)d x j x)]2d x 1 J 0(λ j x) (4.102) book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 65 Example 4.9. Derive a Fourier–Bessel series representation of 1 on the interval 0 < x < 1. We note that with J 0(λ j ) = 0 and Thus 1(cid:2) x=0 x[J 0(λ j x)]2d x = 1 2 [J 1(λ j )]2 1(cid:2) x=0 x J 0(λ j x)d x = J 1(λ j ) 1 = 2 ∞(cid:1) j =1 J 0(λ j x) j J 1(λ λ j ) (4.103) (4.104) (4.105) Example 4.10 (A problem in cylindrical coordinates). A cylinder of radius r1 is initially at a temperature u0 when its surface temperature is increased to u1. It is sufﬁciently long that variation in the z direction may be neglected and there is no variation in the θ direction. There is no heat generation. From Chapter 1, Eq. (1.11) α = (r ur )r ut r u(0, r ) = u0 u(t, r1) = u1 (4.106) u is bounded (4.107) The length scale is r1 and the time scale is r 2 1 normalizes the problem is (u − u1)/(u0 /α. A dimensionless dependent variable that − u1) = U . Setting η = r/r1 and τ = tα/r 2 1 , Uτ = 1 η (ηUη)η U (0, η) = 1 U (τ, 1) = 0 U is bounded (4.108) (4.109) Separate variables as T(τ )R(η). Substitute into the differential equation and divide by T R. Tτ T = 1 Rη (η Rη)η = ±λ2 (4.110) book Mobk070 March 22, 2007 11:7 66 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS where the minus sign is chosen so that the function is bounded. The solution for T is exponential and we recognize the equation for R as Bessel’s equation with ν = 0. 1 η (η Rη)η + λ2 R = 0 The solution is a linear combination of the two Bessel functions of order 0. C1 J 0(λη) + C2Y0(λη) (4.111) (4.112) Since we have seen that Y0 is unbounded as η approaches zero, C2 must be zero. Furthermore, the boundary condition at η = 1 requires that J 0(λ) = 0, so that our eigenfunctions are J 0(λη) and the corresponding eigenvalues are the roots of J 0(λ n) = 0. Un = Kne −λ2 n τ J 0(λ n η), n = 1, 2, 3, 4, . . . (4.113) Summing (linear superposition) Using the initial condition, U = ∞(cid:1) n=1 Kne −λ2 n τ J 0(λ n η) 1 = ∞(cid:1) n=1 Kn J 0(λ n η) (4.114) (4.115) Bessel functions are orthogonal with respect to weighting factor η since theyare solutions to a Sturm–Liouville system. Therefore when we multiply both sides of this equation by η J 0(λ η)d η m and integrate over (0, 1) all of the terms in the summation are zero except when m = n. Thus, 1(cid:2) η=0 J 0(λ n η)ηd η = Kn 1(cid:2) η=0 0 (λ J 2 n η)ηd η (4.116) but 1(cid:2) η=0 1(cid:2) η=0 η J 2 0 (λ n 1 (λ η)d η = J 2 n) 2 η J 0(λ n η)d η = 1 λ n J 1(λ n) (4.117) book Mobk070 March 22, 2007 11:7 Thus SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 67 U (τ, η) = ∞(cid:1) n=0 2 n J 1(λ λ n) −λ2 n τ e J 0(λ n η) (4.118) Example 4.11 (Heat generation in a cylinder). Reconsider the problem of heat transfer in a long cylinder but with heat generation and at a normalized initial temperature of zero. uτ = 1 r (r ur )r + q0 u(τ, 1) = u(0, r ) = 0, u bounded (4.119) (4.120) Our experience with the above example hints that the solution maybe of the form u = ∞(cid:1) j =1 A j (τ )J 0(λ jr ) (4.121) This equation satisﬁes the boundary condition at r = 1 and A j (τ ) is to be determined. Substi- tuting into the partial differential equation gives ∞(cid:1) ∞(cid:1) (cid:15) (cid:14) (cid:1) j (τ )J 0(λ j ) = A j =1 j =1 A j (τ ) 1 r d dr r d J 0 dr + q0 (4.122) (4.123) (4.124) In view of Bessel’s differential equation, the ﬁrst term on the right can be written as ∞(cid:1) j =1 −λ2 j J 0(λ jr )A j (τ ) The second term can be represented as a Fourier–Bessel series as follows: q0 = q0 ∞(cid:1) j =1 2J 0(λ j J 1(λ λ jr ) j ) as shown in Example 4.9 above. Equating coefﬁcients of J 0(λ jr ) we ﬁnd that A j (τ ) must satisfy the ordinary differential equation (cid:1) A (τ ) + λ2 j A(τ ) = q0 2 j J 1(λ λ j ) with the initial condition A(0) = 0. Solution of this simple ﬁrst-order linear differential equations yields A j (τ ) = 2q0 j J 1(λ λ3 j ) + C exp(−λ2 j τ ) (4.125) (4.126) book Mobk070 March 22, 2007 11:7 68 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS After applying the initial condition A j (τ ) = 2q0 j J 1(λ λ3 j ) (cid:12) (cid:13) 1 − exp(−λ2 j τ ) The solution is therefore u(τ, r ) = ∞(cid:1) j =1 (cid:12) 2q0 j J 1(λ λ3 j ) 1 − exp(−λ2 j τ ) (cid:13) J 0(λ jr ) (4.127) (4.128) Example 4.12 (Time dependent heat generation). Suppose that instead of constant heat generation, the generation is time dependent, q (τ ). The differential equation for A(τ ) then becomes (cid:1) A (τ ) + λ2 j A(τ ) = 2q (τ ) j J 1(λ λ j ) (4.129) An integrating factor for this equation is exp(λ2 j τ ) so that the equation can be written as (cid:12) d d τ A j exp(λ2 j τ ) (cid:13) = 2q (τ ) j J 1(λ λ j ) exp(λ2 j τ ) (4.130) Integrating and introducing as a dummy variable t A j (τ ) = 2 j J 1(λ λ j ) τ(cid:2) t=0 q (t) exp(−λ2 j (τ − t))d t (4.131) Problems 1. By differentiating the series form of J 0(x) term by term show that (cid:1) 0(x) = −J 1(x) J 2. Show that (cid:2) x J 0(x)d x = x J 1(x) + constant 3. Using the expression for (cid:3) x s =0 s n J 0(s )d s show that x(cid:2) s 5 J 0(s )d s = x(x2 − 8)[4x J 0(x) + (x2 − 8)J 1(x)] s =0 4. Express 1 − x as a Fourier–Bessel series. book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 69 LEGENDRE FUNCTIONS 4.3 We now consider another second-order linear differential that is common for problems involv- ing the Laplacian in spherical coordinates. It is called Legendre’s equation, (1 − x2)u (cid:1)(cid:1) − 2xu (cid:1) + ku = 0 (4.132) This is clearly a Sturm–Liouville equation and we will seek a series solution near the origin, which is a regular point. We therefore assume a solution in the form of (4.3). u = ∞(cid:1) j =0 c j x j (4.133) Differentiating (4.133) and substituting into (4.132) we ﬁnd ∞(cid:1) j =0 or [ j ( j − 1)c j x j −2(1 − x2) − 2 j c j x j + n(n + 1)c j x j ] (4.134) ∞(cid:1) {[k − j ( j + 1)]c j x j + j ( j − 1)c j x j −2} = 0 (4.135) j =0 On shifting the last term, ∞(cid:1) j =0 {( j + 2)( j + 1)c j +2 + [k − j ( j + 1)]c j }x j = 0 (4.136) The recurrence relation is c j +2 = − j ( j + 1) − k ( j + 1)( j + 2) c j (4.137) There are thus two independent Frobenius series. It can be shown that they both diverge at x = 1 unless they terminate at some point. It is easy to see from (4.137) that they do in fact terminate if k = n(n + 1). Since n and j are integers it follows that c n+2 , c n+6, etc. are all zero. Therefore the solutions, which depend on n (i.e., the eigenfunctions) are polynomials, = 0 and the solution is a constant. If series that terminate at j = n. For example, if n = 0, c 2 = 0 and consequently c n+4 book Mobk070 March 22, 2007 11:7 70 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS n = 1 c n (cid:14) u = Pn(x) = c n = 0 when n ≥ 1 and the polynomial is x. In general xn − n(n − 1) 2(2n − 1) (2n − 2k)! (n − 2k)!(n − k)! (−1)k k! = 1 2k xn−2k m(cid:1) xn−2 + n(n − 1)(n − 2)(n − 3) 2(4)(2n − 1)(2n − 3) k=0 (cid:15) xn−4 − . . . (4.138) where m = n/2 if n is even and (n − 1)/2 if n is odd. The coefﬁcient c n is of course arbitrary. It turns out to be convenient to choose it to be c 0 c n = 1 = (2n − 1)(2n − 3) · · · 1 n! (4.139) the ﬁrst few polynomials are P0 = 1, P1 = x, P2 = (3x2 − 1)/2, P3 = (5x3 − 3x)/2, P4 = (35x4 − 30x2 + 3)/8, Successive Legendre polynomials can be generated by the use of Rodrigues’ formula For example Pn(x) = 1 2nn! d n d xn (x2 − 1)n P5 = (63x5 − 70x3 + 15x)/8 Fig. 4.4 shows graphs of several Legendre polynomials. (4.140) FIGURE 4.4: Legendre polynomials book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 71 The second solution of Legendre’s equation can be found by the method of variation of parameters. The result is Qn(x) = Pn(x) (cid:2) d ζ n (ζ )(1 − ζ 2) P 2 (4.141) It can be shown that this generally takes on a logarithmic form involving ln [(x + 1)/(x − 1)] which goes to inﬁnity at x = 1. In fact it can be shown that the ﬁrst two of these functions are Q0 = 1 2 ln 1 + x 1 − x and Q1 = x 2 ln 1 + x 1 − x − 1 Thus the complete solution of the Legendre equation is u = APn(x) + B Qn(x) (4.142) (4.143) where Pn(x) and Qn(x) are Legendre polynomials of the ﬁrst and second kind. If we require the solution to be ﬁnite at x = 1, B must be zero. Referring back to Eqs. (3.46) through (3.53) in Chapter 3, we note that the eigenvalues λ = n(n + 1) and the eigenfunctions are Pn(x) and Qn(x). We further note from (3.46) and (3.47) that the weight function is one and that the orthogonality condition is 1(cid:2) −1 Pn(x)Pm(x)d x = 2 2n + 1 δ mn (4.144) where δ mn is Kronecker’s delta, 1 when n = m and 0 otherwise. Example 4.13. Steady heat conduction in a sphere Consider heat transfer in a solid sphere whose surface temperature is a function of θ , the angle measured downward from the z-axis (see Fig. 1.3 Chapter 1). The problem is steady and there is no heat source. ∂ 2 r ∂r 2 (r u) + 1 sin θ u(r = 1) = f (θ ) (cid:7) (cid:6) ∂ ∂θ sin θ ∂u ∂θ = 0 (4.145) u is bounded book Mobk070 March 22, 2007 11:7 72 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Substituting x = cos θ , ∂ 2 ∂r 2 (r u) + ∂ ∂ x r (cid:14) (1 − x2) (cid:15) ∂u ∂ x = 0 (4.146) We separate variables by assuming u = R(r )X(x). Substitute into the equation and divide by RX and ﬁnd r R (r R) (cid:1)(cid:1) = − [(1 − x2)X (cid:1) (cid:1) ] = ±λ2 X or (cid:1)(cid:1) ∓ λ2 R = 0 (cid:1) r (r R) [(1 − x2)X (cid:1) ± λ2 X = 0 ] (4.147) (4.148) The second of these is Legendre’s equation, and we have seen that it has bounded solutions at r = 1 when λ2 = n(n + 1). The ﬁrst equation is of the Cauchy–Euler type with solution R = C1r n + C2r −n−1 (4.149) Noting that the constant C2 must be zero to obtain a bounded solution at r = 0, and using superposition, u = ∞(cid:1) n=0 Knr n Pn(x) (4.150) and using the condition at fr = 1 and the orthogonality of the Legendre polynomial π(cid:2) θ=0 f (θ )Pn(cos θ )d θ = π(cid:2) θ=0 Kn P 2 n (cos θ )d θ = 2Kn 2n + 1 (4.151) ASSOCIATED LEGENDRE FUNCTIONS 4.4 Equation (1.15) in Chapter 1 can be put in the form (cid:25) 1 α ∂u ∂t = ∂ 2u ∂r 2 + 2 r ∂u ∂r (cid:26) + 1 r 2 ∂ ∂µ (cid:25) (1 − µ2) (cid:26) ∂u ∂µ + 1 r 2(1 − µ2) ∂ 2u ∂(cid:6)2 (4.152) by substituting µ = cos θ . book Mobk070 March 22, 2007 11:7 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 73 We shall see later that on separating variables in the case where u is a function of r, θ, (cid:6), and t, we ﬁnd the following differential equation in the µ variable: (cid:26) (cid:25) (cid:26) (cid:25) (1 − µ2) d d µ d f d µ + n(n + 1) − m2 1 − µ2 f = 0 (4.153) We state without proof that the solution is the associated Legendre function P m associated Legendre polynomial is given by n (µ). The P m n = (1 − µ2)1/2m d m d µm Pn(µ) The orthogonality condition is and 1(cid:2) −1 [P m n (µ)]2d µ = 2(n + m)! (2n + 1)(n − m)! 1(cid:2) −1 n P m P m n(cid:1) d µ = 0 (cid:1) n (cid:3)= n (4.154) (4.155) (4.156) The associated Legendre function of the second kind is singular at x = ±1 and may be computed by the formula n (x) = (1 − x2)m/2 d m Qn(x) Qm d xm (4.157) Problems 1. Find and carefully plot P6 and P7. 2. Perform the integral above and show that and that x(cid:2) Q0(x) = C P0(x) ξ =0 d ξ (1 − ξ 2)P0(ξ ) = C 2 ln (cid:7) (cid:6) 1 + x 1 − x x(cid:2) Q1(x) = C x ξ =0 d ξ ξ 2(1 − ξ 2) = C x 2 ln (cid:7) (cid:6) 1 + x 1 − x − 1 3. Using the equation above ﬁnd Q0 0(x) and Q1 1(x) book Mobk070 March 22, 2007 11:7 74 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS FURTHER READING J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems. New York: McGraw-Hill, 2001. C. F. Chan Man Fong, D. DeKee, and P. N. Kaloni, Advanced Mathematics for Engineering and Science. 2nd edition. Singapore: World Scientiﬁc, 2004. P. V. O’Neil, Advanced Engineering Mathematics. 5th edition. Brooks/Cole Thompson, Paciﬁc Grove, CA, 2003. book Mobk070 March 22, 2007 11:7 75 C H A P T E R 5 Solutions Using Fourier Series and Integrals We have already demonstrated solution of partial differential equations for some simple cases in rectangular Cartesian coordinates in Chapter 2. We now consider some slightly more complicated problems as well as solutions in spherical and cylindrical coordinate systems to further demonstrate the Fourier method of separation of variables. CONDUCTION (OR DIFFUSION) PROBLEMS 5.1 Example 5.1 (Double Fourier series in conduction). We now consider transient heat con- duction in two dimensions. The problem is stated as follows: ut = α(u xx + u y y ) u(t, 0, y) = u(t, a, y) = u(t, x, 0) = u(t, x, b) = u0 u(0, x, y) = f (x, y) (5.1) That is, the sides of a rectangular area with initial temperature f (x, y) are kept at a constant temperature u0. We ﬁrst attempt to scale and nondimensionalize the equation and boundary conditions. Note that there are two length scales, a and b. We can choose either, but there will remain an extra parameter, either a/b or b/a in the equation. If we take ξ = x/a and η = y/b then (5.1) can be written as (cid:6) (cid:7) a 2 α ut = uξ ξ + a 2 b 2 uηη (5.2) The time scale is now chosen as a 2/α and the dimensionless time is τ = αt/a 2. We also choose a new dependent variable U (τ, ξ, η) = (u − u0)/( fmax − u0). The now nondimensionalized system is Uτ = Uξ ξ + r 2Uηη U (τ, 0, η) = U (τ, 1, η) = U (τ, ξ, 0) = U (τ, ξ, 1) = 0 U (0, ξ, η) = ( f − u0)/( fmax − u0) = g (ξ, η) (5.3) book Mobk070 March 22, 2007 11:7 76 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS We now proceed by separating variables. Let U (τ, ξ, η) = T(τ )X(ξ )Y (η) Differentiating and inserting into (5.3) and dividing by (5.4) we ﬁnd (cid:1) T T = X (cid:1)(cid:1) X (cid:1)(cid:1) Y + r 2Y XY (5.4) (5.5) where the primes indicate differentiation with respect to the variable in question and r = a/b. Since the left-hand side of (5.5) is a function only of τ and the right-hand side is only a function of ξ and η both sides must be constant. If the solution is to be ﬁnite in time we must choose the constant to be negative, –λ2. Replacing T (cid:1)/T by –λ2 and rearranging, (cid:1)(cid:1) (cid:1)(cid:1) −λ2 − X X = r Y Y (5.6) Once again we see that both sides must be constants. How do we choose the signs? It should be clear by now that if either of the constants is positive solutions for X or Y will take the form of hyperbolic functions or exponentials and the boundary conditions on ξ or η cannot be satisﬁed. Thus, (cid:1) T T (cid:1)(cid:1) X X (cid:1)(cid:1) r 2 Y Y = −λ2 = −β 2 = −γ 2 (5.7) (5.8) (5.9) Note that X and Y are eigenfunctions of (5.8) and (5.9), which are Sturm–Liouville equations and β and γ are the corresponding eigenvalues. Solutions of (5.7), (5.8), and (5.9) are T = A exp(−λ2τ ) X = B1 cos(βξ ) + B2 sin(βξ ) Y = C1 cos(γ η/r ) + C2 sin(γ η/r ) (5.10) (5.11) (5.12) = 0. Applying the ﬁrst homogeneous boundary condition, we see that X(0) = 0, so that B1 = 0. Applying the third homogeneous boundary condition we see that Y (0) = 0, so that C1 The second homogeneous boundary condition requires that sin(β) = 0, or β = nπ . The last homogeneous boundary condition requires sin(γ /r ) = 0, or γ = mπr . According to (5.6), λ2 = β2 + γ 2 . Combining these solutions, inserting into (5.4) we have one solution in the book Mobk070 March 22, 2007 11:7 SOLUTIONS USING FOURIER SERIES AND INTEGRALS 77 form Umn(τ, ξ, η) = Knme −(n2π 2+m2π 2r 2)τ sin(nπ ξ ) sin(mπ η) (5.13) for all m, n = 1, 2, 3, 4, 5, . . . Superposition now tells us that ∞(cid:1) ∞(cid:1) n=1 m=1 Knme −(n2π 2+m2π 2r 2)τ sin(nπ ξ ) sin(mπ ) Using the initial condition g (ξ, η) = ∞(cid:1) ∞(cid:1) n=1 m=1 Knm sin(nπ ξ ) sin(mπ η) (5.14) (5.15) We have a double Fourier series, and since both sin(nπ ξ ) and sin(mπ η) are members of orthogonal sequences we can multiply both sides by sin(nπ ξ )sin(mπ η)dξ dη and integrate over the domains. 1(cid:2) 1(cid:2) ξ =0 η=0 g (ξ, η) sin(nπ ξ ) sin(mπ η)d ξ d η sin2(nπ ξ )d ξ sin2(mπ η)d η = Knm 1(cid:2) (cid:2) 1 η=0 ξ =0 = Knm 4 1(cid:2) (5.16) Our solution is 1(cid:2) ∞(cid:1) ∞(cid:1) 4 g (ξ, η) sin(nπ ξ ) sin(mπ η)d ξ d η e −(n2π 2+m2π 2r 2)τ sin(nπ ξ ) sin(mπ η) (5.17) n=1 m=1 ξ =0 η=0 Example 5.2 (A convection boundary condition). Reconsider the problem deﬁned by (2.1) in Chapter 2, but with different boundary and initial conditions, = u(0, x) u(t, 0) = u0 ku x(t, L) − h[u1 − u(t, L)] = 0 (5.18) (5.19) The physical problem is a slab with conductivity k initially at a temperature u0 suddenly exposed at x = L to a ﬂuid at temperature u1 through a heat transfer coefﬁcient h while the x = 0 face is maintained at u0. book Mobk070 March 22, 2007 11:7 78 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS The length and time scales are clearly the same as the problem in Chapter 2. Hence, τ = tα/L2 and ξ = x/L. If we choose U = (u − u0)/(u1 − u0) we make the boundary condition at x = 0 homogeneous but the condition at x = L is not. We have the same situation that we had in Section 2.3 of Chapter 2. The differential equation, one boundary condition, and the initial condition are homogeneous. Proceeding, we ﬁnd Uτ = Uξ ξ U (τ, 0) = U (0, ξ ) = 0 Uξ (τ, 1) + B[U (τ, 1) − 1] = 0 (5.20) where B = h L/k. It is useful to relocate the nonhomogeneous condition as the initial condition. As in the previous problem we assume U (τ, ξ ) = V (τ, ξ ) + W(ξ ). Vτ = Vξ ξ + Wξ ξ W(0) = 0 Wξ (1) + B[W(1) − 1] = 0 V (τ, 0) = 0 Vξ (τ, 1) + BV (τ, 1) = 0 V (0, ξ ) = −W(ξ ) Set Wξ ξ = 0. Integrating twice and using the two boundary conditions on W, W(ξ ) = Bξ B + 1 The initial condition on V becomes V (0, ξ ) = −Bξ/(B + 1) . (5.21) (5.22) (5.23) Assume V (τ, ξ ) = P (τ )Q(ξ ), substitute into the partial differential equation for V , and divide by P Q as usual. (cid:1) P P (cid:1)(cid:1) = Q Q = ±λ2 We must choose the minus sign for the solution to be bounded. Hence, −λ2τ P = Ae Q = C1 sin(λξ ) + C2 cos(λξ ) (5.24) (5.25) book Mobk070 March 22, 2007 11:7 SOLUTIONS USING FOURIER SERIES AND INTEGRALS 79 FIGURE 5.1: The eigenvalues of λ = −B tan(λ n) n Applying the boundary condition at ξ = 0, we ﬁnd that C2 condition on V at ξ = 1, = 0. Now applying the boundary or C1 λ cos(λ) + C1 B sin(λ) = 0 λ = −B tan(λ) (5.26) (5.27) This is the equation for determining the eigenvalues, λ n. It is shown graphically in Fig. 5.1. Example 5.3 (Superposition of several problems). We’ve seen now that in order to apply separation of variables the partial differential equation itself must be homogeneous and we have also seen a technique for transferring the inhomogeneity to one of the boundary conditions or to the initial condition. But what if several of the boundary conditions are nonhomogeneous? We demonstrate the technique with the following problem. We have a transient two-dimensional problem with given conditions on all four faces. + u y y = u xx ut u(t, 0, y) = f1(y) u(t, a, y) = f2(y) u(t, x, 0) = f3(x) u(t, x, b) = f4(x) u(0, x, y) = g (x, y) (5.28) book Mobk070 March 22, 2007 11:7 80 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS + u5. The problem can be broken down into ﬁve problems. u = u1 + u3 + u4 + u2 + u1y y = u1xx u1t u1(0, x, y) = g (x, y) u1 = 0, all boundaries = 0 + u2y y u2xx u2(0, y) = f1(y) u2 = 0 on all other boundaries = 0 + u3y y u3xx u3(a, y) = f2(y) u3 = 0 on all other boundaries = 0 + u4y y u4xx u4(x, 0) = f3(x) u4 = 0 on all other boundaries = 0 + u5y y u5xx u5(x, b) = f4(x) u5 = 0 on all other boundaries (5.29) (5.30) (5.31) (5.32) (5.33) 5.1.1 Time-Dependent Boundary Conditions We will explore this topic when we discuss Laplace transforms. Example 5.4 (A ﬁnite cylinder). Next we consider a cylinder of ﬁnite length 2L and radius r1. As in the ﬁrst problem in this chapter, there are two possible length scales and we choose r1. The cylinder has temperature u0 initially. The ends at L = ±L are suddenly insulated while the sides are exposed to a ﬂuid at temperature u1. The differential equation with no variation in the θ direction and the boundary conditions are α r = (r ur )r + u zz ut u z(t, r, −L) = u z(t, r, +L) = 0 kur (r1) + h[u(r1) − u1(r1)] = 0 u(0, r, z) = u0 u is bounded (5.34) book Mobk070 March 22, 2007 11:7 SOLUTIONS USING FOURIER SERIES AND INTEGRALS 81 If we choose the length scale as r1 then we deﬁne η = r/r1 normalized temperature can be chosen as U = (u − u1)(u0 , ζ = z/L, and τ = αt/r 2 − u1). With these we ﬁnd that 1 . The (cid:4) (cid:5) 2 Uς ς r1 L Uτ = 1 η (ηUη)η + Uς (ς = ±1) = 0 Uη(η = 1) + BU (η = 1) = 0 U (τ = 0) = 1 where B = hr1 /k. Let U = T(τ )R(η)Z(ζ ). Insert into the differential equation and divide by U . (cid:1) T T = 1 η R (η R (cid:1) ) (cid:1) + (cid:4) r1 L (cid:5) (cid:1)(cid:1) 2 Z Z (5.35) (5.36) Zς (ς = ±1) = 0 Rη(η = 1) + B R(η = 1) = 0 U (τ = 0) = 1 Again, the dance is the same. The left-hand side of Eq. (5.36) cannot be a function of η or ζ so each side must be a constant. The constant must be negative for the time term to be bounded. (cid:1)(cid:1)/Z must be a negative constant because otherwise Z would be exponential functions and we could not simultaneously satisfy the boundary conditions at ζ = ±1. Thus, we have Experience tells us that Z T η2 R (cid:1) = −λ2T (cid:1) + β 2η2 R = 0 (cid:1)(cid:1) + η R (cid:6) (cid:7) (cid:1)(cid:1) = −γ 2 Z L r1 with solutions 2 Z −λ2t T = Ae Z = C1 cos(γ Lς/r1) + C2 sin(γ Lς/r1) R = C3 J 0(βη) + C4Yo (βη) (5.37) (5.38) It is clear that C4 must be zero always when the cylinder is not hollow because Y0 is unbounded when η = 0. The boundary conditions at ς = ±1 imply that Z is an even function, so that C2 book Mobk070 March 22, 2007 11:7 82 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS must be zero. The boundary condition at ζ = 1 is Zζ = −C1(γ L/r1) sin(γ L/r1) = 0, or γ L/r1 = nπ (5.39) The boundary condition at η = 1 requires (cid:1) 0 (β) + B J 0(β)] = 0 or C3[J B J 0(β) = β J 1(β) which is the transcendental equation for ﬁnding β m. Also note that λ2 = γ 2 n + β 2 m (5.40) (5.41) By superposition we write the ﬁnal form of the solution as U (τ, η, ς) = ∞(cid:1) ∞(cid:1) n=0 m=0 −(γ 2 n +β2 m )τ Knme J 0(β m η) cos(nπ ς ) (5.42) Knm is found using the orthogonality properties of J 0(β condition. m η) and cos(nπ ζ ) after using the initial 1(cid:2) r =0 1(cid:2) r J 0(β m η)d η cos(nπ ς )d ς = Knm ς =−1 1(cid:2) r =0 1(cid:2) r J 2 0 (β m η)d η cos2(nπ ς )d ς (5.43) ς =−1 Example 5.5 (Heat transfer in a sphere). Consider heat transfer in a solid sphere whose surface temperature is a function of θ , the angle measured downward from the z-axis (see Fig. 1.3, Chapter 1). The problem is steady and there is no heat source. Substituting x = cos θ , (cid:7) (cid:6) sin θ ∂u ∂θ = 0 ∂ 2 ∂r 2 (r u) + 1 r sin θ u(r = 1) = f (θ ) ∂ ∂θ u is bounded ∂ 2 ∂r 2 (r u) + ∂ ∂ x r (cid:14) (1 − x2) (cid:15) ∂u ∂ x = 0 (5.44) (5.45) We separate variables by assuming u = R(r )X(x). Substitute into the equation, divide by RX and ﬁnd r R (r ) (cid:1)(cid:1) = − [(1 − x2)X (cid:1) (cid:1) ] = ±λ2 X (5.46) book Mobk070 March 22, 2007 11:7 or SOLUTIONS USING FOURIER SERIES AND INTEGRALS 83 (cid:1)(cid:1) ∓ λ2 R = 0 r (r R) [(1 − x2)X (cid:1) (cid:1) ± λ2 X = 0 ] (5.47) The second of these is Legendre’s equation, and we have seen that it has bounded solutions at r = 1 when ±λ2 = n(n + 1). The ﬁrst equation is of the Cauchy–Euler type with solution R = C1r n + C2r −n−1 (5.48) Noting that the constant C2 must be zero to obtain a bounded solution at r = 0, and using superposition, ∞(cid:1) u = Knr n Pn(x) n=0 and using the condition at f (r = 1) and the orthogonality of the Legendre polynomial π(cid:2) θ=0 f (θ )Pn(cos θ )d θ = Kn = 2n + 1 2 π(cid:2) θ=0 π(cid:2) θ=0 Kn P 2 n (cos θ )d θ = 2Kn 2n + 1 f (θ )Pn(cos θ )d θ (5.49) (5.50) (5.51) VIBRATIONS PROBLEMS 5.2 We now consider some vibrations problems. In Chapter 2 we found a solution for a vibrating string initially displaced. We now consider the problem of a string forced by a sine function. Example 5.6 (Resonance in a vibration problem). Equation (1.21) in Chapter 1 is ytt = a 2 yxx + A sin(ηt) (5.52) Select a length scale as L, the length of the string, and a time scale L/a and deﬁning ξ = x/L and τ = ta/L, yτ τ = yξ ξ + C sin(ωτ ) (5.53) where ω is a dimensionless frequency, ηL/a and C = AL2a 2. The boundary conditions and initial velocity and displacement are all zero, so the bound- ary conditions are all homogeneous, while the differential equation is not. Back in Chapter 2 we book Mobk070 March 22, 2007 11:7 84 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS saw one way of dealing with this. Note that it wouldn’t have worked had q been a function of time. We approach this problem somewhat differently. From experience, we expect a solution of the form (cid:1)(cid:1)(cid:1) y(ξ, τ ) = ∞(cid:1) n=1 Bn(τ ) sin(nπ ξ ) (5.54) where the coefﬁcients Bn(τ ) are to be determined. Note that the equation above satisﬁes the end conditions. Inserting this series into the differential equation and using the Fourier sine series of C C = ∞(cid:1) n=1 (cid:1)(cid:1) n (τ ) sin(nπ ξ ) = B ∞(cid:1) n=1 ∞(cid:1) 2C[1 − (−1)n] nπ sin(nπ ξ ) [−(nπ )2 Bn(τ )] sin(nπ ξ ) (5.55) n=1 + C ∞(cid:1) n=1 2[1 − (−1)n] nπ sin(nπ ξ ) sin((cid:24) τ ) (5.56) Thus (cid:1)(cid:1) B n = −(nπ )2 Bn + C 2[1 − (−1)n] nπ sin((cid:24) τ ) (5.57) subject to initial conditions y = 0 and yτ = 0 at τ = 0. When n is even the solution is zero. That is, since the right-hand side is zero when n is even, But since both Bn(0) and B Bn = C1 cos(nπ τ ) + C2 sin(nπ τ ) = C2 (cid:1) n(0) are zero, C1 = 0. When n is odd we can write (5.58) (cid:1)(cid:1) 2n−1 B + [(2n − 1)π ]2 B2n−1 4C = (2n − 1)π sin(ωτ ) n. The homogeneous solution of the above (5.59) (2n − 1)π is the natural frequency of the system, ω equation is B2n−1 = D1 cos(ω n τ ) + D2 sin(ω n τ ) . To obtain the particular solution we assume a solution in the form of sines and cosines. BP = E1 cos(ωτ ) + E2 sin(ωτ ) Differentiating and inserting into the differential equation we ﬁnd (5.60) (5.61) −E1 ω2 cos(ωτ ) − E2 ω2 sin(ωτ ) + ω2 n[E1 cos(ωτ ) + E2 sin(ωτ )] = 4C ω n sin(ωτ ) (5.62) book Mobk070 March 22, 2007 11:7 Equating coefﬁcients of sine and cosine terms SOLUTIONS USING FOURIER SERIES AND INTEGRALS 85 Thus E1(ω2 n E2(ω2 n − ω2) cos(ωτ ) = 0 − ω2) sin(ωτ ) = 4C ω n ω (cid:3)= ω n sin(ωτ ) E1 = 0 = E2 ω 4C n(ω2 n − ω2) ω (cid:3)= ω n Combining the homogeneous and particular solutions B2n−1 = D1 cos(ω n τ ) + D2 sin(ω n τ ) + 4C n(ω2 n − ω2) ω sin(ωτ ) The initial conditions at τ = 0 require that D1 D2 = 0 = − 4C(ω/ω n(ω2 ω n n) − ω2) (5.63) (5.64) (5.65) (5.66) The solution for B2n−1 is B2n−1 = 4C n(ω2 − ω2 n) ω (cid:6) ω ω n (cid:7) sin(ω n τ ) − sin(ωτ ) , ω (cid:3)= ω n (5.67) The solution is therefore y(ξ, τ ) = 4C ∞(cid:1) n=1 sin(ω ξ ) n n(ω2 − ω2 n) ω (cid:6) ω ω n (cid:7) sin(ω n τ ) − sin(ωτ ) (5.68) When ω = ω n the above is not valid. The form of the particular solution should be chosen as BP = E1 τ cos(ωτ ) + E2 τ sin(ωτ ) (5.69) Differentiating and inserting into the differential equation for B2n−1 [E1 τ ω2 n + 2E2 ω n − E1 τ ω2 n] cos(ω n τ ) + [E2 τ ω2 n − E2 τ ω2 n − 2E1 ω n] sin(ω n Thus E2 = 0 E1 = − 4C 2ω2 n τ ) = 4C ω n sin(ω n τ ) (5.70) (5.71) book Mobk070 March 22, 2007 11:7 86 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and the solution when ω = ω n is B2n−1 = C1 cos(ω n τ ) + C2 sin(ω n τ ) − 2C ω2 n τ cos(ω τ ) n (5.72) The initial condition on position implies that C1 velocity is zero gives = 0. The initial condition that the initial ω nC2 − 2C ω2 n = 0 The solution for B2n−1 is Superposition now gives B2n−1 = 2C ω3 n [sin(ω n τ ) − ω n τ cos(ω n τ )] (5.73) (5.74) y(ξ, τ ) = ∞(cid:1) n=1 2C ω3 n sin(ω n ξ )[sin(ω n τ ) − ω n τ cos(ω n τ )] (5.75) An interesting feature of the solution is that there are an inﬁnite number of natural frequencies, η = a L [π, 3π, 5π, . . . , (2n − 1)π, . . .] (5.76) If the system is excited at any of the frequencies, the magnitude of the oscillation will grow (theoretically) without bound. The smaller natural frequencies will cause the growth to be fastest. Example 5.7 (Vibration of a circular membrane). Consider now a circular membrane (like a drum). The partial differential equation describing the displacement y(t, r, θ ) was derived in Chapter 1. (cid:6) (cid:7) ∂ 2 y ∂t2 a −2 = 1 r = 0. The Suppose it has an initial displacement of y(0, r, θ ) = f (r, θ ) and the velocity yt displacement at r = r1 is also zero and the displacement must be ﬁnite for all r, θ , and t. The length scale is r1 and the time scale is r1 = η and ta/r1 + 1 r 2 /a. r/r1 (5.77) = τ . r ∂ ∂r ∂ y ∂r ∂ 2 y ∂θ 2 We have ∂ 2 y ∂τ 2 = 1 η ∂ ∂η (cid:7) (cid:6) η ∂ y ∂η + 1 η2 ∂ 2 y ∂θ 2 (5.78) book Mobk070 March 22, 2007 11:7 Separation of variables as y = T(τ )R(η)S(θ ), substituting into the equation and dividing by TRS, SOLUTIONS USING FOURIER SERIES AND INTEGRALS 87 (cid:1)(cid:1) T T = 1 η R (η R (cid:1) ) (cid:1) + 1 η2 (cid:1)(cid:1) S S = −λ2 The negative sign is because we anticipate sine and cosine solutions for T. We also note that λ2η2 + η R (η R (cid:1) ) (cid:1)(cid:1) (cid:1) = − S S = ±β 2 (5.79) (5.80) To avoid exponential solutions in the θ direction we must choose the positive sign. Thus we have T (cid:1)(cid:1) = −λ2T (cid:1)(cid:1) = −β 2S S (cid:1) + (η2λ2 − β 2)R = 0 η(η R (cid:1) ) The solutions of the ﬁrst two of these are T = A1 cos(λτ ) + A2 sin(λτ ) S = B1 cos(βθ ) + B2 sin(βθ ) (5.81) (5.82) = 0. β must be an integer so The boundary condition on the initial velocity guarantees that A2 that the solution comes around to the same place after θ goes from 0 to 2π . Either B1 and B2 can be chosen zero because it doesn’t matter where θ begins (we can adjust f (r, θ )). T(τ )S(θ ) = AB cos(λτ ) sin(nθ ) (5.83) The differential equation for R should be recognized from our discussion of Bessel functions. The solution with β = n is the Bessel function of the ﬁrst kind order n. The Bessel function of the second kind may be omitted because it is unbounded at r = 0. The condition that mn) = 0. The solution can now be completed R(1) = 0 means that λ is the mth root of J n(λ using superposition and the orthogonality properties. y(τ, η, θ ) = ∞(cid:1) ∞(cid:1) n=0 m=1 Knm J n(λ mn η) cos(λ mn τ ) sin(nθ ) (5.84) Using the initial condition f (η, θ ) = ∞(cid:1) ∞(cid:1) n=0 m=1 Knm J n(λ mn η) sin(nθ ) (5.85) book Mobk070 March 22, 2007 11:7 88 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and the orthogonality of sin(nθ ) and J n(λ mn η) 2π(cid:2) (cid:2) 1 η=0 θ=0 f (η, θ )η J n(λ mn η) sin(nθ )d θ d η = Knm sin2(nθ )d θ 2π(cid:2) θ=0 1(cid:2) r =0 = Knm 4 n+1(λ J 2 mn) η J 2 n (λ mn η)d η (5.86) = Knm 4 n+1(λ J 2 nm) 2π(cid:2) (cid:2) 1 η=0 θ=0 f (η, θ )η J n(λ nm η) sin(nθ )d θ d η (5.87) Problems 1. The conduction equation in one dimension is to be solved subject to an insulated surface at x = 0 and a convective boundary condition at x = L. Initially the temperature is u(0, x) = f (x), a function of position. Thus = α u xx ut u x(t, 0) = 0 ku x(t, L) = −h[u(t, L) − u1] u(0, x) = f (x) First nondimensionalize and normalize the equations. Then solve by separation of variables. Find a speciﬁc solution when f (x) = 1 − x2. 2. Consider the diffusion problem + q (x) = α u xx ut u x(t, 0) = 0 u x(t, L) = −h[u(t, L) − u1] u(0, x) = u1 Deﬁne time and length scales and deﬁne a u scale such that the initial value of the dependent variable is zero. Solve by separation of variables and ﬁnd a speciﬁc solution for q (x) = Q, a constant. Refer to Problem 2.1 in Chapter 2. book Mobk070 March 22, 2007 11:7 3. Solve the steady-state conduction SOLUTIONS USING FOURIER SERIES AND INTEGRALS 89 = 0 + u y y u xx u x(0, y) = 0 u(a, y) = u0 u(x, 0) = u1 u y (x, b) = −h[u(x, b) − u1] Note that one could choose a length scale either a or b. Choose a. Note that if you choose U = u − u1 − u1 u0 there is only one nonhomogeneous boundary condition and it is normalized. Solve by separation of variables. FOURIER INTEGRALS 5.3 We consider now problems in which one dimension of the domain is inﬁnite in extent. Recall that a function deﬁned on an interval (−c , c ) can be represented as a Fourier series f (x) = 1 2c c(cid:2) ς =−c f (ς )d ς + 1 c + 1 c c(cid:2) ∞(cid:1) n=1 ς =−c f (ς ) sin c(cid:2) ∞(cid:1) ς =−c n=1 (cid:6) nπ ς c f (ς ) cos (cid:5) (cid:4) nπ ς c d ς cos (cid:5) (cid:4) nπ x c (cid:7) d ς sin (cid:5) (cid:4) nπ x c (5.88) which can be expressed using trigonometric identities as f (x) = 1 2c c(cid:2) ς =−c f (ς )d ς + 1 c We now formally let c approach inﬁnity. If (cid:2)α = π/c . Then c(cid:2) ∞(cid:1) (cid:14) f (ς ) cos (cid:15) (ς − x) d ς (5.89) ς =−c n=1 (cid:3) ∞ ς =−c f (ς )d ς exists, the ﬁrst term vanishes. Let nπ c f (x) = 2 π c(cid:2) ∞(cid:1) n=1 ς =0 f (ς ) cos[n(cid:2)α(ς − x)d ς (cid:2)α (5.90) book Mobk070 March 22, 2007 11:7 90 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS or, with we have c(cid:2) gc (n(cid:2)α, x) = f (ς ) cos[n(cid:2) α(ς − x)]d ς (5.91) ς =0 f (x) = ∞(cid:1) n=1 gc (n(cid:2)α, x)(cid:2)α (5.92) As c approaches inﬁnity we can imagine that (cid:2)α approaches dα and n(cid:2)α approaches α, whereupon the equation for f (x) becomes an integral expression f (x) = 2 π ∞(cid:2) ∞(cid:2) ς =0 α=0 f (ς ) cos[α(ς − x)]d ς d α (5.93) which can alternatively be written as ∞(cid:2) f (x) = [A(α) cos α x + B(α) sin α x]d α (5.94) where and α=0 A(α) = 2 π B(α) = 2 π ∞(cid:2) ς =0 ∞(cid:2) ς =0 f (ς ) cos ας d ς f (ς ) sin ας d ς (5.95) (5.96) Example 5.8 (Transient conduction in a semi-inﬁnite region). Consider the boundary value problem (x ≥ 0, t ≥ 0) = u xx ut u(0, t) = 0 u(x, 0) = f (x) (5.97) This represents transient heat conduction with an initial temperature f (x) and the boundary at x = 0 suddenly reduced to zero. Separation of variables as T(t)X(x) would normally yield a book Mobk070 March 22, 2007 11:7 SOLUTIONS USING FOURIER SERIES AND INTEGRALS 91 solution of the form Bn exp(−λ2t) sin (cid:7) (cid:6) λx c for a region of x on the interval (0, c ). Thus, for x on the interval 0 ≤ x ≤ ∞ we have B(α) = 2 π ∞(cid:2) ς =0 f (ς ) sin ας d ς (5.98) (5.99) and the solution is Noting that and that we have u(x, t) = 2 π ∞(cid:2) λ=0 ∞(cid:2) exp(−λ2t) sin(λx) f (s ) sin(λs )d s d α (5.100) s =0 2 sin α s sin α x = cos α (s − x) − cos α(s + x) (5.101) exp(−γ 2α) cos(γ b)d γ = 1 2 (cid:8) π α exp (cid:7) (cid:6) − b 2 4α ∞(cid:2) 0 u(x, t) = 1 √ 2 π t ∞(cid:2) (cid:25) (cid:14) f (s ) exp (cid:15) − (s − x)2 4t − exp (cid:15)(cid:26) (cid:14) − (s + x)2 4t d s 0 Substituting into the ﬁrst of these integrals σ 2 = (s −x)2 4t and into the second integral σ 2 = (s + x)2 4t u(x, t) = 1√ π ∞(cid:2) f (x + 2σ √ −σ 2 d σ t)e −x/2 √ t ∞(cid:2) − 1√ π √ x/2 t f (−x + 2σ √ −σ 2 d σ t)e (5.105) (5.102) (5.103) (5.104) book Mobk070 March 22, 2007 11:7 92 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS In the special case where f (x) = u0 u(x, t) = 2u0√ π √ t(cid:2) x/2 exp(−σ 2)d σ = u0 erf 0 (cid:6) (cid:7) x √ t 2 (5.106) where erf( p) is the Gauss error function deﬁned as erf ( p) = 2√ π p(cid:2) 0 exp(−σ 2)d σ (5.107) Example 5.9 (Steady conduction in a quadrant). Next we consider steady conduction in the region x ≥ 0, y ≥ 0 in which the face at x = 0 is kept at zero temperature and the face at y = 0 is a function of x: u = f (x). The solution is also assumed to be bounded. = 0 + u y y u xx u(x, 0) = f (x) u(0, y) = 0 (5.108) (5.109) (5.110) −αy sin α x, which is, according to our Since u(0, y) = 0 the solution should take the form e experience with separation of variables, a solution of the equation ∇ 2u = 0. We therefore assume a solution of the form ∞(cid:2) u(x, y) = B(α)e −α y sin α xd α (5.111) with 0 B(α) = 2 π The solution can then be written as ∞(cid:2) u(x, y) = 2 π f (ς ) sinας d ς (5.112) ∞(cid:2) 0 ∞(cid:2) f (ς ) −α y sin α x sin α ς d α d ς e (5.113) ς =0 α=0 Using the trigonometric identity for 2 sin a x sin aς = cos a(ς − x) − cos a(ς + x) and noting that ∞(cid:2) 0 −α y cos aβ d α = e y β 2 + y 2 (5.114) book Mobk070 March 22, 2007 11:7 we ﬁnd SOLUTIONS USING FOURIER SERIES AND INTEGRALS 93 u(x, y) = y π ∞(cid:2) (cid:14) f (ς ) 0 1 (ς − x)2 + y 2 − 1 (ς + x)2 + y 2 (cid:15) d ς (5.115) Problem Consider the transient heat conduction problem ut = u xx + u y y x ≥ 0, 0 ≤ y ≤ 1, t ≥ 0 with boundary and initial conditions u(t, 0, y) = 0 u(t, x, 0) = 0 u(t, x, 1) = 0 u(0, x, y) = u0 and u(t, x, y) is bounded. Separate the problem into two problems u(t, x, y) = v(t, x)w(t, y) and give appropriate boundary conditions. Show that the solution is given by u(t, x, y) = 4 π erf (cid:14) x √ t 2 (cid:15) ∞(cid:1) n=1 sin(2n − 1)π y 2n − 1 exp[−(2n − 1)2π 2t] FURTHER READING V. Arpaci, Conduction Heat Transfer. Reading, MA: Addison-Wesley, 1966. J. W. Brown and R. V. Churchill, Fourier Series and Boundary Value Problems. 6th edition. New York: McGraw-Hill, 2001. book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 95 C H A P T E R 6 Integral Transforms: The Laplace Transform Integral transforms are a powerful method of obtaining solutions to both ordinary and partial differential equations. They are used to change ordinary differential equations into algebraic equations and partial differential into ordinary differential equations. The general idea is to multiply a function f (t) of some independent variable t (not necessarily time) by a Kernel function K (t, s ) and integrate over some t space to obtain a function F(s ) of s which one hopes is easier to solve. Of course one must then inverse the process to ﬁnd the desired function f (t). In general, b(cid:2) F(s ) = K (t, s ) f (t)d t t=a (6.1) THE LAPLACE TRANSFORM 6.1 A useful and widely used integral transform is the Laplace transform, deﬁned as ∞(cid:2) L[ f (t)] = F(s ) = f (t)e −s td t (6.2) t=0 Obviously, the integral must exist. The function f (t) must be sectionally continuous and of (cid:27) (cid:27) ≤ Me kt when t > 0 for some constants M and k. For f (t) exponential order, which is to say example neither the Laplace transform of t −1 nor exp(t2) exists. (cid:27) (cid:27) The inversion formula is L −1[F(s )] = f (t) = 1 2πi lim L → ∞ γ +i L(cid:2) γ −i L F(s )e ts d s (6.3) book Mobk070 March 22, 2007 11:7 96 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS in which γ – iL and γ + iL are complex numbers. We will put off using the inversion integral until we cover complex variables. Meanwhile, there are many tables giving Laplace transforms and inverses. We will now spend considerable time developing the theory. SOME IMPORTANT TRANSFORMS 6.2 6.2.1 Exponentials First consider the exponential function: ∞(cid:2) L[e −at] = −ate −s td t = e t=0 ∞(cid:2) t=0 e −(s =a)td t = 1 s + a If a = 0, this reduces to 6.2.2 Shifting in the s-domain L[1] = 1/s ∞(cid:2) (6.4) (6.5) L[e a t f (t)] = −(s −a) t f (t)d t = F(s − a) e (6.6) t=0 6.2.3 Shifting in the time domain Consider a function deﬁned as Then f (t) = 0 t < a f (t) = f (t − a) t > a ∞(cid:2) τ =0 a(cid:2) ∞(cid:2) −s τ e f (τ − a)d τ = 0d τ + −s τ e f (τ − a)d τ τ =0 τ =a Let τ − a = t. Then ∞(cid:2) t=0 −s (t+a) f (t)d t = F(s )e −as = L[ f (t − a)] e the shifted function described above. (6.7) (6.8) (6.9) book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 97 6.2.4 Sine and cosine Now consider the sine and cosine functions. We shall see in the next chapter (and you should already know) that e ikt = cos(kt) + i sin(kt) (6.10) Thus the Laplace transform is L[e ikt] = L[cos(kt)] + i L[sin(kt)] = 1 s − ik = s + ik (s + ik)(s − ik) = s s 2 + k 2 + i k s 2 + k 2 (6.11) so L[sin(kt)] = L[cos(kt)] = k s 2 + k 2 s s 2 + k 2 6.2.5 Hyperbolic functions Similarly for hyperbolic functions L[sinh(kt)] = L (cid:14) 1 2 (e kt − e −kt) (cid:15) (cid:14) (cid:15) = 1 2(cid:1) 1 s − k − 1 s + k = k s 2 − k 2 Similarly, L[cosh(kt)] = s s 2 − k 2 6.2.6 Powers of t: tm We shall soon see that the Laplace transform of tm is L[tm] = (cid:11)(m + 1) s m+1 m > −1 Using this together with the s domain shifting results, L[tme −at] = (cid:11)(m + 1) (s + a)m+1 Example 6.1. Find the inverse transform of the function F(s ) = 1 (s − 1)3 (6.12) (6.13) (6.14) (6.15) (6.16) (6.17) book Mobk070 March 22, 2007 11:7 98 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS This is a function that is shifted in the s -domain and hence Eq. (6.6) is applicable. Noting that L −1(1/s 3) = t2/ (cid:11)(3) = t2/2 from Eq. (6.16) f (t) = t2 2 e t Or we could use Eq. (6.17) directly. Example 6.2. Find the inverse transform of the function The inverse transform of is, according to Eq. (6.11) F(s ) = 3 s 2 + 4 −s e F(s ) = 2 s 2 + 4 f (t) = 3 2 sin(2t) The exponential term implies shifting in the time domain by 1. Thus f (t) = 0, = 3 2 t < 1 sin[2(t − 1)], t > 1 Example 6.3. Find the inverse transform of F(s ) = s (s − 2)2 + 1 The denominator is shifted in the s -domain. Thus we shift the numerator term and write F(s ) as two terms F(s ) = s − 2 (s − 2)2 + 1 + 2 (s − 2)2 + 1 Equations (6.6), (6.12), and (6.13) are applicable. The inverse transform of the ﬁrst of these is a shifted cosine and the second is a shifted sine. Therefore each must be multiplied by exp(2t). The inverse transform is f (t) = e 2t cos(t) + 2e 2t sin(t) book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 99 1 k t FIGURE 6.1: The Heaviside step 6.2.7 Heaviside step A frequently useful function is the Heaviside step function, deﬁned as It is shown in Fig. 6.1. The Laplace transform is Uk(t) = 0 = 1 0 < t < k k < t L[Uk(t)] = ∞(cid:2) t=k e −s td t = 1 s e −ks (6.18) (6.19) The Heaviside step (sometimes called the unit step) is useful for ﬁnding the Laplace transforms of periodic functions. Example 6.4 (Periodic functions). For example, consider the periodic function shown in Fig. 6.2. It can be represented by an inﬁnite series of shifted Heaviside functions as follows: f (t) = U0 − 2Uk + 2U2k − 2U3k + · · · = U0 + ∞(cid:1) n=1 (−1)n2Unk (6.20) 1 -1 FIGURE 6.2: A periodic square wave book Mobk070 March 22, 2007 11:7 100 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 1 h t0-h t0 FIGURE 6.3: The Dirac delta function The Laplace transform is found term by term, L[ f (t)] = 1 s = 1 s {1 − 2e (cid:25) 1 − 2e −s k[1 − e (cid:26) −s k 1 + e −s k −s k + e (cid:6) = 1 s −3s k · · · ]} (cid:7) −2s k − e −s k 1 − e 1 + e −s k 6.2.8 The Dirac delta function Consider a function deﬁned by Ut0 lim − Ut0 h −h = δ(t0) h → 0 L[δ(t0)] = e −s t0 The function, without taking limits, is shown in Fig. 6.3. 6.2.9 Transforms of derivatives (cid:14) (cid:15) L d f d t = ∞(cid:2) t=0 d f d t ∞(cid:2) −s td t = e −s td f e t=0 (6.21) (6.22) (6.23) (6.24) and integrating by parts (cid:14) (cid:15) L d f d t = f (t)e −s t (cid:27) (cid:27)∞ 0 + s ∞(cid:2) t=0 f (t)e −s td t = s F(s ) − f (0) To ﬁnd the Laplace transform of the second derivative we let g (t) − f transform (cid:1) (t). Taking the Laplace (cid:1) L[g (t)] = s G(s ) − g (0) book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 101 and with we ﬁnd that In general G(s ) = L[ f (cid:1) (t)] = s F(s ) − f (0) (cid:15) (cid:14) L d 2 f d t2 = s 2 F(s ) − s f (0) − f (cid:1) (0) (cid:7) (cid:6) L d n f d tn = s n F(s ) − s n−1 f (0) − s n−2 f (cid:1) (0) − · · · − d n−1 f d tn−1 (0) The Laplace transform of tm may be found by using the gamma function, ∞(cid:2) L[tm] = tme −s td t and let x = s t 0 ∞(cid:2) (cid:4) L[tm] = (cid:5) m e x s −x d x s = 1 s m+1 ∞(cid:2) x=0 xme −xd x = (cid:11)(m + 1) s m+1 x=0 which is true for all m > −1 even for nonintegers. 6.2.10 Laplace Transforms of Integrals  f (τ )d τ  = L[g (t)] t(cid:2)   τ =0 L where dg /d t = f (t). Thus L[dg /d t] = s L[g (t)]. Hence  t(cid:2)   = 1 s  L f (τ )d τ τ =0 6.2.11 Derivatives of Transforms (6.25) (6.26) (6.27) (6.28) (6.29) F(s ) (6.30) ∞(cid:2) F(s ) = f (t)e −s td t t=0 (6.31) book Mobk070 March 22, 2007 11:7 102 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS so and in general For example d F d s ∞(cid:2) = − t f (t)e −s td t t=0 d n F d s n = L[(−t)n f (t)] (cid:6) (cid:7) L[t sin(kt)] = − d d s k s 2 + k 2 = 2s k (s 2 + k 2)2 (6.32) (6.33) (6.34) 6.3 LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Example 6.5. A homogeneous linear ordinary differential equation Consider the differential equation (cid:1) + 3y = 0 (cid:1)(cid:1) + 4y y y(0) = 0 (cid:1) (0) = 2 y Therefore (cid:1)(cid:1) L[y ] = s 2Y − s y(0) − y (cid:1) (0) = s 2Y − 2 (cid:1) L[y ] = s Y − y(0) = s Y (s 2 + 4s + 3)Y = 2 Y = 2 (s + 1)(s + 3) = A s + 1 + B s + 3 To solve for A and B, note that clearing fractions, A(s + 3) + B(s + 1) (s + 1)(s + 3) = 2 (s + 1)(s + 3) Equating the numerators, or A + B = 0 3A + B = 2 : A = 1 B = −1 (6.35) (6.36) (6.37) (6.38) (6.39) (6.40) (6.41) book Mobk070 March 22, 2007 11:7 and from Eq. (6.8) INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 103 Y = 1 s + 1 −t − e y = e − 1 s + 3 −3t 6.4 6.4.1 SOME IMPORTANT THEOREMS Initial Value Theorem Thus ∞(cid:2) lim s →∞ t=0 (cid:1) f (t)e −s td t = s F(s ) − f (0) = 0 s →∞ s F(s ) = lim lim t→0 f (t) (6.42) (6.43) (6.44) 6.4.2 Final Value Theorem As s approaches zero the above integral approaches the limit as t approaches inﬁnity minus f (0). Thus lim s F(s ) = lim f (t) s → 0 t → ∞ (6.45) 6.4.3 Convolution A very important property of Laplace transforms is the convolution integral. As we shall see later, it allows us to write down solutions for very general forcing functions and also, in the case of partial differential equations, to treat both time dependent forcing and time dependent boundary conditions. Consider the two functions f (t) and g (t). F(s ) = L[ f (t)] and G(s ) = L[g (t)]. Because of the time shifting feature, −s τ e G(s ) = L[g (t − τ )] = −s t g (t − τ )d t e ∞(cid:2) t=0 ∞(cid:2) F(s )G(s ) = f (τ )e −s τ G(s )d τ τ =0 (6.46) (6.47) book Mobk070 March 22, 2007 11:7 104 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS But so that ∞(cid:2) −s τ e G(s ) = −s t g (t − τ )d t e (6.48) t=0 ∞(cid:2) t(cid:2) F(s )G(s ) = −s t e f (τ )g (t − τ )d τ d t (6.49) t=0 τ =0 where we have used the fact that g (t − τ ) = 0 when τ > t. The inverse transform of F(s )G(s ) is −1[F(s )G(s )] = L t(cid:2) τ =0 f (τ )g (t − τ )d τ (6.50) PARTIAL FRACTIONS 6.5 In the example differential equation above we determined two roots of the polynomial in the denominator, then separated the two roots so that the two expressions could be inverted in forms that we already knew. The method of separating out the expressions 1/(s + 1) and 1/(s + 3) is known as the method of partial fractions. We now develop the method into a more user friendly form. 6.5.1 Nonrepeating Roots Suppose we wish to invert the transform F(s ) = p(s )/q (s ), where p(s ) and q (s ) are polynomi- als. We ﬁrst note that the inverse exists if the degree of p(s ) is lower than that of q (s ). Suppose q (s ) can be factored and a nonrepeated root is a. F(s ) = φ(s ) s − a According to the theory of partial fractions there exists a constant C such that φ(s ) s − a Multiply both sides by (s − a) and take the limit as s → a and the result is + H(s ) = C s − a C = φ(a) (6.51) (6.52) (6.53) book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 105 (6.54) (6.55) (6.56) Note also that the limit of p(s ) s − a q (s ) as s approaches a is simply p(s )/q (cid:1) (s ). If q (s ) has no repeated roots and is of the form q (s ) = (s − a1)(s − a2)(s − a3) · · · (s − an) then −1 L (cid:14) (cid:15) p(s ) q (s ) = n(cid:1) m=1 p(am) q (cid:1)(am) e am t Example 6.6. Find the inverse transform of F(s ) = 4s + 1 (s 2 + s )(4s 2 − 1) First separate out the roots of q (s ) q (s ) = 4s (s + 1)(s + 1/2)(s − 1/2) q (s ) = 4s 4 + 4s 3 − s 2 − s (cid:1) (s ) = 16s 3 + 12s 2 − 2s − 1 q Thus (cid:1) (cid:1) (cid:1) q q (0) = −1 (−1) = −3 (−1/2) = 1 (1/2) = 3 q f (t) = e q (cid:1) −t − e p(0) = 1 p(−1) = −3 p(−1/2) = −1 p(1/2) = 3 −t/2 + e t/2 − 1 Example 6.7. Solve the differential equation subject to initial conditions (cid:1)(cid:1) − y = 1 − e 3t y (cid:1) y (0) = y(0) = 0 book Mobk070 March 22, 2007 11:7 106 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Taking the Laplace transform (s 2 − 1)Y = 1 s Y (s ) = − 1 s − 3 1 s (s 2 − 1) − 1 (s − 3)(s 2 − 1) = 1 s (s + 1)(s − 1) − 1 (s − 3)(s + 1)(s − 1) First ﬁnd the inverse transform of the ﬁrst term. (cid:1) q q = s 3 − s (cid:1) = 3s 2 − 1 (0) = −1 (1) = 2 (−1) = 2 q q q (cid:1) (cid:1) p(0) = 1 p(1) = 1 p(−1) = 1 The inverse transform is Next consider the second term. −1 + 1/2e t + 1/2 e −t (cid:1) q q = s 3 − 3s 2 − s + 3 (cid:1) = 3s 2 − 6s − 1 (−3) = 44 (1) = −4 (−1) = 8 q q q (cid:1) (cid:1) p(−3) = 1 p(1) = 1 p(−1) = 1 The inverse transform is Thus 1 44 e −3t − 1 4 e t + 1 8 −t e y(t) = 1 4 e t + 5 8 e −t + 1 44 −3t − 1 e book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 107 6.5.2 Repeated Roots We now consider the case when q (s ) has a repeated root (s + a)n+1. Then = F(s ) = p(s ) q (s ) = Aa (s − a) φ(s ) (s − a)n+1 + A1 (s − a)2 n = 1, 2, 3, . . . + · · · + An (s − a)n+1 + H(s ) (6.57) It follows that φ(s ) = A0(s − a)n + · · · + Am(s − a)n−m + · · · + An + (s − a)n+1 H(s ) (6.58) By letting s →a we see that An and take the limit as s → a. = φ(a). To ﬁnd the remaining A’s, differentiate φ (n – r ) times Thus φ(n−r )(a) = (n − r )!Ar F(s ) = n(cid:1) r =0 φ(n−r )(a) (n − r )! 1 (s − a)r +1 + H(s ) (6.59) (6.60) If the inverse transform of H(s ) (the part containing no repeated roots) is h(t) it follows from the shifting theorem and the inverse transform of 1/s m that f (t) = n(cid:1) r =0 φ(n−r )(a) (n − r )!r ! tr e at + h(t) (6.61) Example 6.8. Inverse transform with repeated roots F(s ) = s (s + 2)3(s + 1) = A0 (s + 2) + A1 (s + 2)2 + A2 (s + 2)3 + C (s + 1) Multiply by (s + 2)3. s (s + 1) = A0(s + 2)2 + A1(s + 2) + A2 + C(s + 2)3 (s + 1) = φ(s ) Take the limit as s → −2, A2 = 2 book Mobk070 March 22, 2007 11:7 108 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Differentiate once φ(cid:1) = 1 (s + 1)2 −2 (s + 1)3 To ﬁnd C, multiply by (s + 1) and take s = −1 (in the original equation). (−2) = 2 = A0 (−2) = 1 = A1 φ(cid:1)(cid:1) = φ(cid:1)(cid:1) φ(cid:1) C = −1. Thus F(s ) = 2 (s + 2) + 1 (s + 2)2 + 2 (s + 2)3 − 1 (s + 1) and noting the shifting theorem and the theorem on tm, −2t + 2t2e f (t) = 2e −2t + te −2t + e −t 6.5.3 Quadratic Factors: Complex Roots If q (s ) has complex roots and all the coefﬁcients are real this part of q (s ) can always be written in the form This is a shifted form of (s − a)2 + b 2 s 2 + b 2 (6.62) (6.63) This factor in the denominator leads to sines or cosines. Example 6.9. Quadratic factors Find the inverse transform of F(s ) = 2(s − 1) s 2 + 2s + 5 = 2s (s + 1)2 + 4 − 1 (s + 1)2 + 4 Because of the shifted s in the denominator the numerator of the ﬁrst term must also be shifted to be consistent. Thus we rewrite as The inverse transform of F(s ) = 2(s + 1) (s + 1)2 + 4 − 3 (s + 1)2 + 4 2s s 2 + 4 book Mobk070 March 22, 2007 11:7 INTEGRAL TRANSFORMS: THE LAPLACE TRANSFORM 109 is and the inverse of is Thus 2 cos(2t) −3 s 2 + 4 = − 3 2 2 (s 2 + 4) − 3 2 sin(2t) f (t) = 2e −t cos(2t) − 3 2 −t sin(2t) e Tables of Laplace transforms and inverse transforms can be found in many books such as the book by Arpaci and in the Schaum’s Outline referenced below. A brief table is given here in Appendix A. Problems 1. Solve the problem (cid:1)(cid:1)(cid:1) − 2y y y(0) = y (cid:1)(cid:1) + 5y (cid:1) (0) = 0 (cid:1) = 0 (cid:1)(cid:1) (0) = 1 y using Laplace transforms. 2. Find the general solution using Laplace transforms (cid:1)(cid:1) + k 2 y = a y 3. Use convolution to ﬁnd the solution to the following problem for general g (t). Then ﬁnd the solution for g (t) = t2. 4. Find the inverse transforms. (a) (b) (cid:1) + y = g (t) (cid:1)(cid:1) + 2y (cid:1) (0) = y(0) = 0 y y F(s ) = s + c (s + a)(s + b)2 F(s ) = 1 (s 2 + a 2)s 3 book Mobk070 March 22, 2007 11:7 110 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS (c) F(s ) = (s 2 − a 2) (s 2 + a 2)2 5. Find the periodic function whose Laplace transform is −s 1 − e 1 + e −s F(s ) = 1 s 2 (cid:14) (cid:15) and plot your results for f (t) for several periods. FURTHER READING M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications, 1974. V. S. Arpaci, Conduction Heat Transfer. Reading, MA: Addison-Wesley, 1966. R. V. Churchill, Operational Mathematics, 3rd edition. New York: McGraw-Hill, 1972. I. H. Sneddon, The Use of Integral Transforms. New York: McGraw-Hill, 1972. book Mobk070 March 22, 2007 11:7 111 C H A P T E R 7 Complex Variables and the Laplace Inversion Integral BASIC PROPERTIES 7.1 A complex number z can be deﬁned as an ordered pair of real numbers, say x and y, where x is the real part of z and y is the real value of the imaginary part: z = x + iy (7.1) where i = √ −1 I am going to assume that the reader is familiar with the elementary properties of addition, subtraction, multiplication, etc. In general, complex numbers obey the same rules as real numbers. For example (x1 + iy1) (x2 + iy2) = x1x2 − y1 y2 + i (x1 y2 + x2 y1) The conjugate of z is ¯z = x − iy (7.2) (7.3) It is often convenient to represent complex numbers on Cartesian coordinates with x and y as the axes. In such a case, we can represent the complex number (or variable) z as z = x + iy = r (cos θ + i sin θ ) (7.4) as shown in Fig. 7.1. We also deﬁne the exponential function of a complex number as cos θ + i sin θ = e iθ which is suggested by replacing x in series e x = (cid:16)∞ n=0 xn n! by iθ . Accordingly, and e iθ = cos θ + i sin θ −iθ = cos θ − i sin θ e (7.5) (7.6) book Mobk070 March 22, 2007 11:7 112 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS y r x FIGURE 7.1: Polar representation of a complex variable z Addition gives and subtraction gives Note that cos θ = e iθ + e 2 −iθ = cosh(iθ ) sin θ = e iθ − e 2i −iθ = −i sinh(iθ ) (cid:18) −x−iy (cid:17) cosh z = 1 2 = e x + e 2 e x+iy + e −x = 1 2 e x − e 2 cos y + i sin y (cid:17) e x [cos y + i sin y] + e −x −x [cos y − i sin y] (cid:18) = cosh x cos y + i sinh x sin y The reader may show that sinh z = sinh x cos y + i cosh x sin y. Trigonometric functions are deﬁned in the usual way: sin z = e i z − e 2i −i z cos z = e i z + e 2 −i z tan z = sin z cos z (7.7) (7.8) (7.9) (7.10) (7.11) Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. book Mobk070 March 22, 2007 11:7 COMPLEX VARIABLES AND THE LAPLACE INVERSION INTEGRAL 113 Noting that (cid:14) z2 = r 2(cos2 θ − sin2 θ + i2 sin θ cos θ ) (1 + cos 2θ ) − 1 2 = r 2 1 2 (1 − cos 2θ ) + i sin 2θ (cid:15) = r 2[cos 2θ + i sin 2θ ] We deduce that In fact in general Example 7.1. Find i 1/2. z1/2 = r 1/2(cos θ/2 + i sin θ/2) zm/n = r m/n[cos(mθ/n) + i sin(mθ/n)] (7.12) (7.13) Noting that when z = I , r = 1 and θ = π/2, with m = 1 and n = 2. Thus i 1/2 = 11/2[cos(π/4) + i sin(π/4)] = 1√ 2 (1 + i) Note, however, that if w = cos (cid:4) π 4 (cid:5) + π + i sin (cid:5) + π (cid:4) π 4 then w2 = i. Hence 1√ 2 (−1 − i) is also a solution. The roots are shown in Fig. 7.2. i FIGURE 7.2: Roots of i 1/2 book Mobk070 March 22, 2007 11:7 114 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS -1 +1 FIGURE 7.3: The roots of 11/2 In fact in this example θ is also π/2 + 2kπ . Using the fact that z = r e −i(θ+2kπ) k = 1, 2, 3, . . . it is easy to show that √ z1/n = n r (cid:14) (cid:6) cos θ + 2π k n (cid:7) (cid:6) + i sin θ + 2π k n (cid:7)(cid:15) (7.14) This is De Moivre’s theorem. For example when n = 2 there are two solutions and when n = 3 there are three solutions. These solutions are called branches of z1/n. A region in which the function is single valued is indicated by forming a branch cut, which is a line stretching from the origin outward such that the region between the positive real axis and the line contains only one solution. In the above example, a branch cut might be a line from the origin out the negative real axis. Example 7.2. Find 11/2 and represent it on the polar diagram. 11/2 = 1 cos and since θ = 0 in this case (cid:14) (cid:6) (cid:7) (cid:6) (cid:7)(cid:15) θ 2 + kπ + i sin θ 2 + kπ 11/2 = cos kπ + i sin kπ There are two distinct roots at z = +1 for k = 0 and −1 for k = 1. The two values are 1, and an appropriate branch cut shown in Fig. 7.3. The two solutions are called branches of might be from the origin out the positive imaginary axis, leaving as the single solution 1. √ Example 7.3. Find the roots of (1 + i)1/4. Making use of Eq. (7.13) with m = 1 and n = 4, r = (cid:6) (cid:7) (cid:6) (cid:14) √ (1 + i)1/4 = ( 2)1/4 π + 2kπ 4 cos 16 + i sin π 16 + 2kπ 4 √ (cid:9) 2, θ = π 4, we ﬁnd that (cid:7)(cid:15) k = 0, 1, 2, 3 book Mobk070 March 22, 2007 11:7 COMPLEX VARIABLES AND THE LAPLACE INVERSION INTEGRAL 115 21/2 21/8 1+ i 1 16 FIGURE 7.4: The roots of (1 + i)1/4 Hence, the four roots are as follows: (cid:6) (cid:14) (1 + i)1/4 = 21/8 cos = 21/8 = 21/8 (cid:14) (cid:14) (cid:14) cos cos (cid:6) (cid:6) (cid:6) = 21/8 cos π 16 π 16 π 16 π 16 (cid:7) (cid:6) π 16 (cid:7)(cid:15) (cid:6) + i sin (cid:7) π + 2 (cid:7) + π + 3π 2 + i sin (cid:6) + i sin (cid:7) + i sin π 16 π (cid:7)(cid:15) π + 2 (cid:7)(cid:15) + π (cid:7)(cid:15) 16 (cid:6) π 16 + 3π 2 The locations of the roots are shown in Fig. 7.4. The natural logarithm can be deﬁned by writing z = r e iθ for −π ≤ θ < π and noting that ln z = ln r + iθ (7.15) and since z is not affected by adding 2nπ to θ this expression can also be written as ln z = ln r + i (θ + 2nπ) with n = 0, 1, 2, . . . (7.16) When n = 0 we obtain the principal branch. All of the single valued branches are analytic for r > 0 and θ 0 < θ < θ + 2π . 0 7.1.1 Limits and Differentiation of Complex Variables: Analytic Functions Consider a function of a complex variable f (z). We generally write f (z) = u(x, y) + iv(x, y) book Mobk070 March 22, 2007 11:7 116 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS where u and v are real functions of x and y. The derivative of a complex variable is deﬁned as follows: f f (z + (cid:2)z) − f (z) (cid:2)z (cid:1) = lim (cid:2)z → 0 or (cid:1) f (z) = lim u(x + (cid:2)x, y + (cid:2)y) + iv(x + (cid:2)x, y + (cid:2)y) − u(x, y) − iv(x, y) (cid:2)x + i(cid:2)y (cid:2)x, (cid:2)y → 0 Taking the limit on (cid:2)x ﬁrst, we ﬁnd that u(x, y + (cid:2)y) + iv(x, y + (cid:2)y) − u(x, y) − iv(x, y) i(cid:2)y (cid:1) (z) = lim f (cid:2)y → 0 and now taking the limit on (cid:2)y, f (cid:1) (z) = 1 i ∂u ∂ y + ∂v ∂ y = ∂v ∂ y − i ∂u ∂ y Conversely, taking the limit on (cid:2)y ﬁrst, u(x + (cid:2)x, y) + iv(x + (cid:2)x, y) − u(x, y) − iv(x, y) (cid:2)x (cid:1) (z) = lim j (cid:2)x → 0 ∂u ∂ x = + i ∂v ∂ x The derivative exists only if ∂u ∂ x = ∂v ∂ y and ∂u ∂ y = − ∂v ∂ x (7.17) (7.18) (7.19) (7.20) (7.21) (7.22) These are called the Cauchy—Riemann conditions, and in this case the function is said to be analytic. If a function is analytic for all x and y it is entire. Polynomials are entire as are trigonometric and hyperbolic functions and exponential functions. We note in passing that analytic functions share the property that both real and imaginary parts satisfy the equation ∇ 2u = ∇ 2v = 0 in two-dimensional space. It should be obvious at this point that this is important in the solution of the steady-state diffusion equation book Mobk070 March 22, 2007 11:7 COMPLEX VARIABLES AND THE LAPLACE INVERSION INTEGRAL 117 y 1 0 B A 1 2 x FIGURE 7.5: Integration of an analytic function along two paths in two dimensions. We mention here that it is also important in the study of incompressible, inviscid ﬂuid mechanics and in other areas of science and engineering. You will undoubtedly meet with it in some of you clurses. Example 7.4. f = z2 f = sin z f = e a z (cid:1) = 2z f (cid:1) = cos z f (cid:1) = ae a z f Integrals Consider the line integral along a curve C deﬁned as x = 2y from the origin to the point x = 2, y = 1, path OB in Fig. 7.5. (cid:2) C z2d z z2 = x2 − y 2 + 2i xy = 3y 2 + 4y 2i We can write and d z = (2 + i)d y Thus 1(cid:2) y=0 (3y 2 + 4y 2i)(2 + i)d y = (3 + 4i)(2 + i) 1(cid:2) y=0 y 2d y = 2 3 + 11 3 i book Mobk070 March 22, 2007 11:7 118 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS On the other hand, if we perform the same integral along the x axis to x = 2 and then along the vertical line x = 2 to the same point, path OAB in Fig. 7.5, we ﬁnd that 2(cid:2) x=0 x2d x + 1(cid:2) y=0 (2 + iy)2id y = 8 3 + i 1(cid:2) y=0 (4 − y 2 + 4iy)d y = 2 3 + 11 3 i This happened because the function z2 is analytic within the region between the two curves. In general, if a function is analytic in the region contained between the curves, the integral (cid:2) f (z)d z C (7.23) is independent of the path of C. Since any two integrals are the same, and since if we integrate the ﬁrst integral along BO only the sign changes, we see that the integral around the closed contour is zero. f (z)d z = 0 C (7.24) This is called the Cauchy–Goursat theorem and is true as long as the region R within the closed curve C is simply connected and the function is analytic everywhere within the region. A simply connected region R is one in which every closed curve within it encloses only points in R. The theorem can be extended to allow for multiply connected regions. Fig. 7.6 shows a doubly connected region. The method is to make a cut through part of the region and to integrate counterclockwise around C1, along the path C2 through the region, clockwise around the interior curve C3, and back out along C4. Clearly, the integral along C2 and C4 cancels, so that f (z)d z + f (z)d z = 0 C1 C3 (7.25) where the ﬁrst integral is counterclockwise and second clockwise. 7.1.2 The Cauchy Integral Formula Now consider the following integral: f (z)d z (z − z0) If the function f (z) is analytic then the integrand is also analytic at all points except z = z0. We now form a circle C2 of radius r0 around the point z = z0 that is small enough to ﬁt inside (7.26) C book Mobk070 March 22, 2007 11:7 COMPLEX VARIABLES AND THE LAPLACE INVERSION INTEGRAL 119 FIGURE 7.6: A doubly connected region FIGURE 7.7: Derivation of Cauchy’s integral formula the curve C1 as shown in Fig. 7.7. Thus we can write f (z) z − z0 C1 d z − f (z) z − z0 C2 d z = 0 (7.27) where both integrations are counterclockwise. Let r0 now approach zero so that in the second and d z = r0ie iθ d θ . The second integral is as follows: integral z approaches z0 2π(cid:2) = r0e iθ , z − z0 f (z0) r0e iθ r0ie iθ C2 d θ = − f (z0)i d θ = −2πi f (z0) θ=0 Thus, Cauchy’s integral formula is f (z0) = 1 2πi f (z) z − z0 C d z (7.28) where the integral is taken counterclockwise and f (z) is analytic inside C. book Mobk070 March 22, 2007 11:7 120 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS We can formally differentiate the above equation n times with respect to z0 and ﬁnd an extension as Problems 1. Show that f (n)(z0) = n! 2πi f (z) (z − z0)n+1 d z C (7.29) (a) sinh z = sinh x cos y + i cosh x sin y (b) cos z = cos x cosh y − i sin x sinh y and show that each is entire. 2. Find all of the values of √ (a) (−1 + i (b) 8 1 6 3 2 3) 3. Find all the roots of the equation sin z = cosh 4 4. Find all the zeros of (a) sinh z (b) cosh z book Mobk070 March 22, 2007 11:7 121 C H A P T E R 8 Solutions with Laplace Transforms In this chapter, we present detailed solutions of some boundary value problems using the Laplace transform method. Problems in both mechanical vibrations and diffusion are presented along with the details of the inversion method. 8.1 MECHANICAL VIBRATIONS Example 8.1. Consider an elastic bar with one end of the bar ﬁxed and a constant force F per unit area at the other end acting parallel to the bar. The appropriate partial differential equation and boundary and initial conditions for the displacement y(x, t) are as follows: t > 0 yτ τ = yζ ζ , 0 < ζ < 1, y(ζ, 0) = yt(ζ, 0) = 0 y(0, τ ) = 0 yς (1, τ ) = F/E = g We obtain the Laplace transform of the equation and boundary conditions as s 2Y = Yς ς Y (s , 0) = 0 Yς (s , 1) = g /s Solving the differential equation for Y (s , ζ ), Y (s ) = (A sinh ς s + B cosh ς s ) Applying the boundary conditions we ﬁnd that B = 0 and g = As cosh s s g A = s 2 cosh s Y (s ) = g sinh ς s s 2 cosh s book Mobk070 March 22, 2007 11:7 122 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Since the function 1 s sinh ς s = ς + s 2ς 3 3! + s 4ς 5 5! + . . . the function is analytic and Y (s ) can be written as the ratio of two analytic functions sinh ς s 1 s Y (s ) = 1 s sinh ς s s cosh s Y (s ) therefore has a simple pole at s = 0 and the residue there is R(s = 0) = lim s → 0 s Y (s ) = lim s → 0 + . . . ς + s 2ς 3 3! cosh s = g ς The remaining poles are the singularities of cosh s . But cosh s = cosh x cos y + i sinh x sin y, so the zeros of this function are at x = 0 and cosy = 0. Hence, s n = i(2n − 1)π/2. The residues at these points are (cid:19) (cid:20) R(s = s n) = lim s → s n g sinh ς s s d d s (s cosh s ) e s τ = g s 2 n sinh ς s n sinh s n τ e s n (n = ±1, ±2, ±3 . . .) Since we have and (cid:14) sinh i (cid:15) (π ς ) 2n − 1 2 = i sin (cid:14) 2n − 1 2 (cid:15) (π ς ) R(s = s n) = (cid:12) gi sin 2n−1 2 π (cid:13) − 2 (cid:12) 2n−1 2 i sin (cid:13) (π ς ) (cid:12) 2n−1 2 (cid:14) (cid:13) exp i π (cid:15) 2n − 1 2 π τ (cid:14) sin (cid:15) 2n − 1 s π = (−1)n+1 The exponential function can be written as 2n − 1 2 2n − 1 2 = cos exp π τ (cid:14) (cid:15) (cid:14) i (cid:15) (cid:14) π τ + i sin (cid:15) 2n − 1 2 π τ Note that for the poles on the negative imaginary axis (n < 0) this expression can be written as (cid:14) exp i 2m − 1 2 (cid:15) (cid:14) π τ = cos 2m − 1 2 (cid:15) (cid:14) π τ − i sin 2m − 1 2 π τ (cid:15) where m = −n > 0. This corresponds to the conjugate poles. book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 123 Thus for each of the sets of poles we have R(s = s n) = 4g (−1)n π 2(2n − 1)2 sin (2n − 1)π ς 2 exp (cid:15) (cid:14) (2n − 1)π τ i 2 Now adding the residues corresponding to each pole and its conjugate we ﬁnd that the ﬁnal solution is as follows: (cid:19) ς + 8 π 2 y(ς, τ ) = g ∞(cid:1) n=1 (−1)n (2n − 1)2 sin (2n − 1)π ς 2 cos (2n − 1)π τ 2 (cid:20) Suppose that instead of a constant force at ζ = 1, we allow g to be a function of τ . In this case, the Laplace transform of y(ζ , τ ) takes the form Y (ς, s ) = G(s ) sinh(ς s ) s cosh s The simple pole with residue g ζ is not present. However, the other poles are still at the same s n values. The residues at each of the conjugate poles of the function F(s ) = sinh(ς s ) s cosh s are 2(−1)n π (2n − 1) sin (2n − 1)π ς 2 sin (2n − 1)π τ 2 = f (ς, τ ) According to the convolution theorem τ(cid:2) y(ς, τ ) = y(τ − τ (cid:1) )g (τ (cid:1) )d τ (cid:1) τ (cid:1)=0 y(ς, τ ) = 4 π ∞(cid:1) n=0 (−1)n (2n − 1) sin (2n − 1)π ς 2 τ(cid:2) τ (cid:1) g (τ − τ (cid:1) ) sin (2n − 1)π τ (cid:1) 2 d τ (cid:1). In the case that g = constant, integration recovers the previous equation. Example 8.2. An inﬁnitely long string is initially at rest when the end at x = 0 undergoes a transverse displacement y(0, t) = f (t). The displacement is described by the differential book Mobk070 March 22, 2007 11:7 124 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS equation and boundary conditions as follows: = ∂ 2 y ∂ 2 y ∂t2 ∂ x2 y(x, 0) = yt(x, 0) = 0 y(0, t) = f (t) y is bounded Taking the Laplace transform with respect to time and applying the initial conditions yields s 2Y (x, s ) = d 2Y (x, s ) d x2 The solution may be written in terms of exponential functions Y (x, s ) = Ae −s x + Be s x In order for the solution to be bounded B = 0. Applying the condition at x = 0 we ﬁnd A = F(s ) where F(s ) is the Laplace transform of f (t). Writing the solution in the form Y (x, s ) = s F(s ) −s x e s and noting that the inverse transform of e −s x/s is the Heaviside step Ux(t) where Ux(t) = 0 Ux(t) = 1 t < x t > x and that the inverse transform of s F(s ) is f (cid:1) (t), we ﬁnd using convolution that t(cid:2) y(x, t) = (cid:1) f (t − µ)Ux(µ)d µ = f (t − x) x < t µ=0 = 0 x > t For example, if f (t) = sin ω t y(x, t) = sin ω(t − x) x < t = 0 x > t book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 125 Problems 1. Solve the above vibration problem when y(0, τ ) = 0 y(1, τ ) = g (τ ) Hint: To make use of convolution see Example 8.3. 2. Solve the problem ∂ 2 y ∂t2 = ∂ 2 y ∂ x2 yx(0, t) = y(x, 0) = yt(x, 0) = 0 y(1, t) = h using the Laplace transform method. 8.2 DIFFUSION OR CONDUCTION PROBLEMS We now consider the conduction problem Example 8.3. uτ = uς ς u(1, τ ) = f (τ ) u(0, τ ) = 0 u(ς, 0) = 0 Taking the Laplace transform of the equation and boundary conditions and noting that u(ς, 0) = 0, solution yields s U (s ) = Uς ς U = A sinh √ s ς + B cosh √ s ς U (0, s ) = 0 U (1, s ) = F(s ) The ﬁrst condition implies that B = 0 and the second gives and so U = F(s ) sinh sinh √ s ς √ s . F(s ) = A sinh √ s book Mobk070 March 22, 2007 11:7 126 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS If f (τ ) = 1, F(s ) = 1/s , a particular solution, V , is √ V = sinh s sinh s ς √ s where Now, v = L −1V (s ) √ s ς √ s sinh sinh ς = √ s + (ς √ √ s + ( √ s )3 3! s )3 3! + (ς √ + ( 5! s )5 5! √ s )5 + . . . + . . . and so there is a simple pole of V e s τ necessarily zero, there are simple poles at sinh s = 0 is at s = 0. Also, since when sinh s not s = 0 or s = −n2π 2. The residue at the pole s = 0, sinhς √ √ √ lim s → 0 s V (s )e s τ = ς and since V (s ) e s τ has the form P (s )/Q(s ) the residue of the pole at −n2π 2 is P (ς, −n2π 2) Q(cid:1)(−n2π 2) e −n2π 2τ = (cid:20) √ sinh ς √ √ s 2 cosh −n2π 2τ s e s + sinh √ s s =−n2π 2 = 2 sin(nπ ς ) nπ cos(nπ ) e −n2π 2τ The solution for v(ζ , τ ) is then v(ς, τ ) = ς + ∞(cid:1) n=1 2(−1)n nπ e −n2π 2τ sin(nπ ς ) The solution for the general case as originally stated with u(1, τ ) = f (τ ) is obtained by ﬁrst differentiating the equation for v(ζ , τ ) and then noting the following: and so that U (ς, s ) = s F(s ) sinh ς s sinh √ s √ s (cid:12) L (cid:13) (cid:1) (τ ) f = s F(s ) − f (τ = 0) U (ς, s ) = f (τ = 0)V (ς, s ) + L (cid:12) (cid:1) (cid:13) (s ) f V (ς, s ) book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 127 Consequently u(ς, τ ) = f (τ = 0)v(ς, τ ) + (cid:1) (τ − τ (cid:1) )v(ς, τ (cid:1) )d τ (cid:1) f τ(cid:2) = ς f (τ ) + 2 f (0) π + 2 π ∞(cid:1) n=1 (−1)n n τ (cid:1)=0 ∞(cid:1) n=1 (−1)n n e τ(cid:2) −n2π 2τ sin(nπ ς ) sin(nπ ς ) (cid:1) (τ − τ (cid:1) )e f −n2π 2τ (cid:1) d τ (cid:1) τ (cid:1)=0 This series converges rapidly for large values of τ . However for small values of τ , it converges slowly. There is another form of solution that converges rapidly for small τ . The Laplace transform of v(ζ , τ ) can be written as sinh ς s sinh √ s √ s ς −ς √ s √ √ s − e √ s − e − s ) (cid:22) √ ς s − e e (cid:22) e √ s ∞(cid:1) = e s (e ς = 1 s e = 1 s n=0 −(1+2n−ς ) = 1 √ s s e (cid:23) (cid:22) √ s −ς ς e √ s √ −ς s − e √ 1 − e −2 s √ −2 s + e (cid:23) 1 + e √ s − e −(1+2n+ς ) √ s −4 √ s + e √ (cid:23) s + . . . −6 The inverse Laplace transform of e √ s =k s is the complimentary error function, deﬁned by erfc(k/2 √ τ ) = 1 − 2√ π √ τ(cid:2) k/2 x=0 −x2 e d x Thus we have v(ς, τ ) = (cid:14) ∞(cid:1) (cid:6) erfc n=0 1 + 2n − ς √ τ 2 (cid:7) (cid:6) − erfc 1 + 2n + ς √ τ 2 (cid:7)(cid:15) and this series converges rapidly for small values of τ . Example 8.4. Next we consider a conduction problem with a convective boundary condition: uτ = uς ς u(τ, 0) = 0 uς (τ, 1) + Hu(τ, 1) = 0 u(0, ς ) = ς book Mobk070 March 22, 2007 11:7 128 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Taking the Laplace transform s U − ς = Uς ς U (s , 0) = 0 Uς (s , 1) + HU (s , 1) = 0 The differential equation has a homogeneous solution √ √ = A cosh( s ς ) + B sinh( s ς ) Uh and a particular solution = U p ς s so that U = ς s + A cosh( √ s ς ) + B sinh( s ς ) √ Applying the boundary conditions, we ﬁnd A = 0 B = − (cid:12)√ s s cosh( 1 + H √ s ) + H sinh( √ (cid:13) The Laplace transform of the solution is as follows: √ U = ς − (cid:12)√ s s (1 + H) sinh( √ s cosh( s ς ) s ) + H sinh( s ) √ (cid:13) s ) The inverse transform of the ﬁrst term is simply ζ . For the second term, we must ﬁrst ﬁnd the poles. There is an isolated pole at s = 0. To obtain the residue of this pole note that lim s → 0 − √ (1 + H) sinh ς √ s cosh √ s s + H sinh √ s e s τ = lim s → 0 √ − (1 + H)(ς √ √ s + H( √ s = x + iy. Then s + · · · ) s + · · · ) = −ς canceling the ﬁrst residue. To ﬁnd the remaining residues let (x + iy) [cosh x cos y + i sinh x sin y] + H [sinh x cos y + i cosh x sin y] = 0 Setting real and imaginary parts equal to 0 yields x cosh x cos y − y sinh x sin y + H sinh x cos y = 0 and y cosh x cos y + x sinh x sin y + H cosh x sin y = 0 book Mobk070 March 22, 2007 11:7 which yields SOLUTIONS WITH LAPLACE TRANSFORMS 129 x = 0 y cos y + H sin y = 0 The solution for the second term of U is lim s → iy (s − iy)(1 + H) sinh( (cid:12)√ √ s s cosh( s ) + H sinh s ς )e s τ (cid:13) √ s ) √ or where (cid:15) (cid:14) P (ς, s )e s τ Q(cid:1)(ς, s ) s =−y 2 cosh √ s + 1 2 sinh √ s + H √ s 2 (cid:15) √ s cosh (cid:12)√ √ Q = s √ (cid:1) = Q s cosh √ s + H sinh √ s cosh s + H sinh s + s (cid:13) √ s (cid:14) (cid:1) = Q (cid:1) = Q √ s (1 + H) 2 (cid:14) √ s (1 + H) 2 (cid:14) sinh cosh − s √ s + s 2 √ (cid:15) s 2H H(H + 1) + y 2 2H cosh (cid:15) √ s iy cos(y) 1 √ s 2 √ s (cid:1) Q (s = −y 2) = while −y 2τ un(ς, τ ) = −y 2τ ς )e P (s = −y 2) = (1 + H)i sin(yς )e −(1 + H) sin(yn (cid:22) H(H+1)+y 2 2H 2(H + 1) H(H + 1) + y 2 yn cos(yn) (cid:15) sin ς yn sin yn = (cid:14) (cid:23) = −y 2τ −2H(H + 1) sin(yn [H(H + 1) + y 2]yn cos(yn) ς )e −y 2 n τ e The solution is therefore u(ς, τ ) = ∞(cid:1) n=1 2(H + 1) H(H + 1) + y 2 sin ς yn sin yn −y 2 n τ e book Mobk070 March 22, 2007 11:7 130 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Note that as a partial check on this solution, we can evaluate the result when H → ∞ as u(ς, τ ) = ∞(cid:1) n=1 −2 yn cos yn sin ς yne −y 2 n τ = ∞(cid:1) n=1 2(−1)n+1 nπ sin(nπ ς )e −n2π 2τ in agreement with the separation of variables solution. Also, letting H → 0 we ﬁnd u(ς, τ ) = ∞(cid:1) n=1 ς ) sin(yn sin(yn) 2 y 2 n τ e y 2 n with yn = 2n−1 2 π again in agreement with the separation of variables solution. Example 8.5. Next we consider a conduction (diffusion) problem with a transient source q (τ ). (Nondimensionalization and normalization are left as an exercise.) uτ = uς ς + q (τ ) u(ς, 0) = 0 = uς (0, τ ) u(1, τ ) = 1 Obtaining the Laplace transform of the equation and boundary conditions we ﬁnd A particular solution is s U = Uς ς + Q(s ) Uς (0, s ) = 0 U (1, s ) = 1 s UP = Q(s ) s and the homogeneous solution is UH = A sinh(ς √ s ) + B cosh(ς √ s ) Hence the general solution is U = Q s + A sinh(ς √ s ) + B cosh(ς, √ s ) book Mobk070 March 22, 2007 11:7 Using the boundary conditions SOLUTIONS WITH LAPLACE TRANSFORMS 131 The poles are (with Uς (0, s ) = 0, = Q U (1, s ) = 1 s s + 1 − Q s U = Q s √ s = x + iy) √ s = 0 or (cid:6) (cid:7) 2 2n − 1 2 cosh s = − A = 0 s ) B = 1 − Q √ s cosh( s ) √ + B cosh( √ cosh(ς √ cosh( s ) s ) cos y = 0 √ s = ± 2n − 1 π i 2 π 2 = −λ2 n n = 1, 2, 3, . . . or when s = 0. When s = 0 the residue is Res = lim s → 0 s U (s )e s τ = 1 √ The denominator of the second term is s cosh s and its derivative with respect to s is √ s + cosh √ sinh s √ s 2 When s = −λ2 n, we have for the residue of the second term lim s → −λ2 n (cid:19) √ (1 − Q) cosh(ς s + √ s 2 sinh √ cosh (cid:20) s ) √ s e s τ and since and we have −1 cosh(ς s cosh L √ √ s ) s √ s = i sin sinh (cid:7) (cid:6) 2n − 1 2 π = i(−1)n+1 cosh(ς √ s ) = cos (cid:6) 2n − 1 2 (cid:7) ς π (cid:17) (cid:18) 2n−1 2 ς π π i 2(−1)n+1 e = cos (cid:18) (cid:17) 2n−1 2 2 )2π 2τ = 2(−1)n cos −( 2n−1 (cid:17) 2n−1 2 (2n − 1)π (cid:18) ς π −( 2n−1 2 )2π 2τ e book Mobk070 March 22, 2007 11:7 132 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS We now use the convolution principle to evaluate the solution for the general case of q (τ ). We are searching for the inverse transform of (cid:6) cosh(ς cosh 1 s √ s ) √ s + Q(s ) s 1 − cosh(ς cosh (cid:7) √ √ s ) s The inverse transform of the ﬁrst term is given above. As for the second term, the inverse transform of Q(s ) is simply q (τ ) and the inverse transform of the second term, absent Q(s) is (cid:17) (cid:18) 1 − 2(−1)n+1 cos 2n−1 2 (2n − 1)π ς π −( 2n−1 2 )2π 2τ e According to the convolution principle, and summing over all poles u(ς, τ ) = ∞(cid:1) n=1 (cid:18) ς π 2(−1)n+1 cos (cid:17) 2n−1 2 (2n − 1)π (cid:19) −( 2n−1 2 )2π 2τ e (cid:2) τ ∞(cid:1) + n=1 τ (cid:1)=0 (cid:17) 1 − 2(−1)n+1 cos 2n−1 2 (2n − 1)π (cid:20) (cid:18) ς π −( 2n−1 2 )2π 2τ e q (τ − τ (cid:1) )d τ (cid:1) Example 8.6. Next consider heat conduction in a semiinﬁnite region x > 0, t > 0. The initial temperature is zero and the wall is subjected to a temperature u(0, t) = f (t) at the x = 0 surface. = u xx ut u(x, 0) = 0 u(0, t) = f (t) and u is bounded. Taking the Laplace transform and applying the initial condition Thus s U = Uxx U (x, s ) = A sinh x √ s + B cosh x √ s Both functions are unbounded for x → ∞. Thus it is more convenient to use the equivalent solution U (x, s ) = Ae −x √ s + Be x √ s = Ae √ s −x in order for the function to be bounded. Applying the boundary condition at x = 0 F(s ) = A book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 133 Thus we have U (x, s ) = F(s )e √ s −x Multiplying and dividing by s gives U (x, s ) = s F(s ) √ s −x e s The inverse transform of e −x √ s /s is (cid:19) √ e −1 L (cid:20) s = erfc (cid:6) (cid:7) x √ t 2 −x s and we have seen that L{ f (cid:1)} = s F(s ) − f (0) Thus, making use of convolution, we ﬁnd u(x, t) = f (0)erfc (cid:6) x √ t 2 (cid:7) t(cid:2) + (cid:1) f (t − µ) erfc µ=0 x µ d µ √ 2 Example 8.7. Now consider a problem in cylindrical coordinates. An inﬁnite cylinder is initially at dimensionless temperature u(r, 0) = 1 and dimensionless temperature at the surface u(1, t) = 0. We have (cid:6) (cid:7) ∂u ∂r r = 1 r ∂ ∂u ∂t ∂r u(1, t) = 0 u(r, 0) = 1 u bounded The Laplace transform with respect to time yields (cid:6) (cid:7) s U (r, s ) − 1 = 1 r d dr r dU dr with U (1, s ) = 1 s book Mobk070 March 22, 2007 11:7 134 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Obtaining the homogeneous and particular solutions yields U (r, s ) = 1 s + A J 0(i √ s r ) + BY0(i √ s r ) The boundedness condition requires that B = 0, while the condition at r = 1 Thus A = − 1 √ s J 0(i s ) U (r, s ) = 1 s √ s r ) √ s ) − J 0(i s J 0(i The inverse transform is as follows: (cid:1) u(r, t) = 1 − Residues of (cid:15) (cid:14) e s t J 0(i s J 0(i √ √ s r √ s ) √ Poles of the function occur at s = 0 and J 0(i s = λ function of the ﬁrst kind order are zero. Thus, they occur at s = −λ2 s ) = 0 or i n, the roots of the Bessel n. The residues are (cid:14) lim s → 0 √ √ s r ) s ) e s t J 0(i J 0(i (cid:15) = 1 √ (cid:15) and lim s → −λ2 n (cid:15) (cid:14) √ s r ) √ s ) e s t J 0(i (cid:1) 0(i s J = lim s → −λ2 n (cid:14) e s t J 0(i √ s r ) s ) i/2 = e −λ2 nt √ s −J 1(i (cid:19) (cid:20) J 0(λ nr ) n J 1(λ λ n) − 1 2 The two unity residues cancel and the ﬁnal solution is as follows: u(r, t) = ∞(cid:1) n=1 −λ2t n e J 0(λ nr ) n J 1(λ λ n) Problems 1. Consider a ﬁnite wall with initial temperature zero and the wall at x = 0 insulated. The wall at x = 1 is subjected to a temperature u(1, t) = f (t) for t > 0. Find u(x, t). 2. Consider a ﬁnite wall with initial temperature zero and with the temperature at x = 0 u(0, t) = 0. The temperature gradient at x = 1 suddenly becomes u x(1, t) = f (t) for t > 0. Find the temperature when f (t) = 1 and for general f (t). 3. A cylinder is initially at temperature u = 1 and the surface is subject to a convective boundary condition ur (t, 1) + Hu(t, 1) = 0. Find u(t, r ). book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 135 8.3 DUHAMEL’S THEOREM We are now prepared to solve the more general problem ∂u ∂t ∇ 2u + g (r, t) = (8.1) where r may be considered a vector, that is, the problem is in three dimensions. The general boundary conditions are and ∂u ∂ni + h i u = fi (r, t) on the boundary Si u(r, 0) = F(r ) (8.2) (8.3) initially. Here theorem without proof. ∂u ∂ni represents the normal derivative of u at the surface. We present Duhamel’s Consider the auxiliary problem ∇ 2 P + g (r, λ) = ∂ P ∂t where λ is a timelike constant with boundary conditions ∂ P ∂ni + h i P = fi (r, λ) on the boundary Si and initial condition P (r, 0) = F(r ) The solution of Eqs. (8.1), (8.2), and (8.3) is as follows: u(x, y, z, t) = ∂ ∂t t(cid:2) λ=0 P (x, y, z, λ, t − λ)d λ = F(x, y, z) + t(cid:2) λ=0 (8.4) (8.5) (8.6) ∂ ∂t P (x, y, z, λ, t − λ)d λ (8.7) This is Duhamel’s theorem. For a proof, refer to the book by Arpaci. Example 8.8. Consider now the following problem with a time-dependent heat source: −t = u xx + xe ut u(0, t) = u(1, t) = 0 u(x, 0) = 0 book Mobk070 March 22, 2007 11:7 136 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS We ﬁrst solve the problem −λ = Pxx + xe Pt P (0, t) = P (1, t) = 0 P (x, 0) = 0 while holding λ constant. Recall from Chapter 2 that one technique in this case is to assume a solution of the form so that and P (x, λ, t) = X(x) + W(x, λ, t) = Wxx Wt W(0, λ, t) = W(1, λ, t) = 0 W(x, λ, 0) = −X(x, λ) −λ = 0 + xe Xxx X(0) = X(1) = 0 Separating variables in the equation for W(x, t), we ﬁnd that for W(x, λ, t) = S(x)Q(t) Qt Q = Sxx S = −β 2 The minus sign has been chosen so that Q remains bounded. The boundary conditions on S(x) are as follows: The solution gives S(0) = S(1) = 0 S = A sin(β x) + B cos(βx) Q = Ce −β t Applying the boundary condition at x = 0 requires that B = 0 and applying the boundary condition at x = 1 requires that sin(β) = 0 or β = nπ . Solving for X(x) and applying the boundary conditions gives X = x 6 (1 − x2)e −λ = −W(x, λ, 0) book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 137 The solution for W(x, t) is then obtained by superposition: W(x, t) = ∞(cid:1) n=0 Kne −n2π 2t sin(nπ x) and using the orthogonality principle −λ e 1(cid:2) x=0 x 6 (x2 − 1) sin(nπ x)d x = Kn 1(cid:2) n=0 sin2(nπ x)d x = 1 2 Kn so and W(x, t) = P (x, λ, t) = ∞(cid:1) n=1 (cid:21) x 6 −λ e 1(cid:2) x=0 x 3 (1 − x2) + (x2 − 1) sin(nπ x)d x e −n2π 2t sin(nπ x) (x2 − 1) sin(nπ x)d x sin(nπ x) e −n2π 2t −λ e (cid:24) (cid:2) ∞(cid:1) 1 n=1 x=0 x 3 P (x, λ, t − λ) = ! x 6 + " −λ (1 − x2)e (cid:2) ∞(cid:1) 1 n=1 x 3 x=0 1(cid:2) (x2 − 1) sin(nπ x)d x sin(nπ x) e −n2π 2t e n2π 2λ−λ ∂ ∂t P (x, λ, t − λ) = ∞(cid:1) n=1 n2π 2 x=0 (1 − x2) sin(nπ x)d xe −n2π 2t e (n2π 2−1)λ x 3 According to Duhamel’s theorem, the solution for u(x, t) is then u(x, t) = 1(cid:2) ∞(cid:1) n=1 x=0 x 3 (1 − x2)n2π 2 sin(nπ x)d x sin(nπ x) e −n2π 2(t−λ) −λ d λ t(cid:2) λ=0 = ∞(cid:1) n=1 n2π 2 n2π 2 − 1 1(cid:2) x=0 x 3 (1 − x2) sin(nπ x)d x [e −t − e −n2π 2t] sin(nπ x) Example 8.9. Reconsider Example 8.6 in which ut = u xx on the half space, with u(x, 0) = 0 u(0, t) = f (t) book Mobk070 March 22, 2007 11:7 138 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS To solve this using Duhamel’s theorem, we ﬁrst set f (t) = f (λ) with λ a timelike constant. Following the procedure outlined at the beginning of Example 8.6, we ﬁnd U (x, s ) = f (λ) The inverse transform is as follows: u(x, t, λ) = f (λ) erfc Using Duhamel’s theorem, √ s −x e s (cid:6) (cid:7) x √ t 2 u(x, t) = (cid:14) ∂ ∂t t(cid:2) λ=0 f (λ)erfc (cid:6) (cid:7)(cid:15) √ x t − λ 2 d λ which is a different form of the solution given in Example 8.6. Problems 1. Show that the solutions given in Examples 8.6 and 8.9 are equivalent. 2. Use Duhamel’s theorem along with Laplace transforms to solve the following conduc- tion problem on the half space: = u xx ut u(x, 0) = 0 u x(0, t) = f (t) 3. Solve the following problem ﬁrst using separation of variables: + sin(π x) = ∂ 2u ∂u ∂t ∂ x2 u(t, 0) = 0 u(t, 1) = 0 u(0, x) = 0 4. Consider now the problem ∂u ∂t = ∂ 2u ∂ x2 + sin(π x)t e −t with the same boundary conditions as Problem 7. Solve using Duhamel’s theorem. book Mobk070 March 22, 2007 11:7 SOLUTIONS WITH LAPLACE TRANSFORMS 139 FURTHER READING V. S. Arpaci, Conduction Heat Transfer, Reading, MA: Addison-Wesley, 1966. R. V. Churchill, Operational Mathematics, 3rd ed. New York: McGraw-Hill, 1972. I. H. Sneddon, The Use of Integral Transforms, New York: McGraw-Hill, 1972. book Mobk070 March 22, 2007 11:7 140 book Mobk070 March 22, 2007 11:7 141 C H A P T E R 9 Sturm–Liouville Transforms Sturm–Liouville transforms include a variety of examples of choices of the kernel function K (s , t) that was presented in the general transform equation at the beginning of Chapter 6. We ﬁrst illustrate the idea with a simple example of the Fourier sine transform, which is a special case of a Sturm–Liouville transform. We then move on to the general case and work out some examples. A PRELIMINARY EXAMPLE: FOURIER SINE TRANSFORM 9.1 Example 9.1. Consider the boundary value problem with boundary conditions and initial condition ut = u xx x ≤ 0 ≤ 1 u(0, t) = 0 u x(1, t) + Hu(1, t) = 0 u(x, 0) = 1 Multiply both sides of the differential equation by sin(λx)d x and integrate over the interval x ≤ 0 ≤ 1. 1(cid:2) x=0 sin(λx) d 2u d x2 d x = d d t 1(cid:2) x=0 u(x, t) sin(λx)d x Integration of the left hand side by parts yields 1(cid:2) x=0 d 2 d x2 [sin(λx)]u(x, t)d x + (cid:14) sin(λx) d u d x − u d d x [sin(λx)] (cid:15) 1 0 book Mobk070 March 22, 2007 11:7 142 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and applying the boundary conditions and noting that d 2 d x2 [sin(λx)] = −λ2 sin(λx) −λ2 1(cid:2) x=0 sin(λx)u(x, t)d x + [u x sin(λx) − λu cos(λx)]1 0 = −λ2U (λ, t) − u(1)[λ cos λ + H sin λ] we have Deﬁning 1(cid:2) Sλ{u(x, t)} = u(x, t) sin(λx)d x = U (λ, t) x=0 as the Fourier sine transform of u(x, t) and setting we ﬁnd whose solution is λ cos λ + H sin λ = 0 Ut(λ, t) = −λ2U (λ, t) U (λ, t) = Ae −λ2t The initial condition of the transformed function is U (λ, 0) = 1(cid:2) x=0 sin(λx)d x = 1 λ [1 − cos(λ)] Applying the initial condition we ﬁnd U (λ, t) = 1 λ [1 − cos(λ)]e It now remains to ﬁnd from this the value of u(x, t). Recall from the general theory of Fourier series that any odd function of x deﬁned on −λ2t 0 ≤ x ≤ 1 can be expanded in a Fourier sine series in the form u(x, t) = ∞(cid:1) n=1 sin(λ # # sin(λ nx) # #2 n) 1(cid:2) ξ =0 u(ξ, t) sin(λ ξ )d ξ n book Mobk070 March 22, 2007 11:7 and this is simply STURM–LIOUVILLE TRANSFORMS 143 u(x, t) = ∞(cid:1) n=1 sin(λ # # sin(λ nx) #2 U (λ # n) , t) n with λ n given by the transcendental equation above. The ﬁnal solution is therefore u(x, t) = ∞(cid:1) n=1 2(1 − cos λ n) 2 sin(2λ λ n) n − 1 sin(λ nx)e −λ2 nt 9.2 GENERALIZATION: THE STURM–LIOUVILLE TRANSFORM: THEORY Consider the differential operator D D[ f (x)] = A(x) f (cid:1)(cid:1) + B(x) f (cid:1) + C(x) f a ≤ x ≤ b (9.1) with boundary conditions of the form Nα[ f (x)]x=a Nβ[ f (x)]x=b = f (a) cos α + f = f (b) cos β + f (cid:1) (cid:1) (a) sin α (b) sin β (9.2) where the symbols Nα and Nβ are differential operators that deﬁne the boundary conditions. For example the differential operator might be D[ f (x)] = fxx and the boundary conditions might be deﬁned by the operators Nα[ f (x)]x=a = f (a) = 0 and Nβ[ f (x)]x=b = f (b) + H f (cid:1) (b) = 0 We deﬁne an integral transformation b(cid:2) T[ f (x)] = f (x)K (x, λ)d x = F(λ) (9.3) a book Mobk070 March 22, 2007 11:7 144 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS We wish to transform these differential forms into algebraic forms. First we write the differential operator in standard form. Let r (x) = exp x(cid:2) a B(ξ ) A(ξ ) d ξ p(x) = r (x) A(x) q (x) = − p(x)C(x) Then D[ f (x)] = 1 p(x) where (cid:12) is the Sturm–Liouville operator. (cid:12) (cid:1) (cid:1) − q f ) (r f (cid:13) = 1 p(x) (cid:12)[ f (x)] Let the kernel function K (x, λ)in Eq. (9.3) be K (x, λ) = p(x)(cid:6)(x, λ) (9.4) (9.5) (9.6) Then while so that b(cid:2) T[D[ f (x)]] = (cid:6)(x, λ)(cid:12)[ f (x)]d x a b(cid:2) a = f (x)(cid:12)[(cid:6)(x, λ)]d x + [((cid:6)fx − (cid:6) x f )r (x)]b a (9.7) Nα[ f (a)] = f (a) cos α + f (a) sin α (cid:17) α[ f (a)] = d N d α f (a) cos α + f (cid:1) (cid:1) (cid:18) (a) sin α = − f (a) sin α + f (a) cos α (cid:1) f (a) = Nα[ f (a)] cos α − N (cid:1) (cid:1) α[ f (a)] sin α (cid:1) α[ f (a)] cos α + Nα[ f (a)] sin α (a) = N f where the prime indicates differentiation with respect to α. (9.8) (9.9) book Mobk070 March 22, 2007 11:7 The lower boundary condition at x = a is then STURM–LIOUVILLE TRANSFORMS 145 (cid:1) (a, λ) f (a)] r (a) (a) − (cid:6)(cid:1) α[ f (a)] cos α + (cid:6)(a, λ)Nα[ f (a)] sin α − (cid:6)(cid:1) (cid:1) [(cid:6)(a, λ) f   = (cid:6)(a, λ)N +(cid:6)(cid:1) (a, λ)N (cid:1) α[ f (a)] sin α (a, λ)Nα[ f (a)] cos α   r (a) (9.10) But if (cid:6)(x, λ) is chosen to satisfy the Sturm–Liouville equation and the boundary con- ditions then and and we have Nα[(cid:6)(x, λ)]x=a Nβ[(cid:6)(x, λ)]x=b = (cid:6)(a, λ) cos α + (cid:6)(cid:1) = (cid:6)(b, λ) cos β + (cid:6)(cid:1) (a, λ) sin α (b, λ) sin β (cid:6)(a, λ) = Nα[(cid:6)(a, λ)] cos α − N (cid:6)(cid:1) (cid:1) α[(cid:6)(a, λ)] sin α (cid:1) α[(cid:6)(a, λ)] cos α + Nα[(cid:6)(a, λ)] sin α (a, λ) = N [(N (cid:1) α[(cid:6)(a, λ)] cos α + Nα[ f (a)] sin α)(Nα[(cid:6)(a, λ)] cos α + N (cid:1) − (N α[ f (a)] cos α − Nα[ f (a)] sin α)]r (a) (cid:1) α[(cid:6)(a, λ)] cos α + Nα[(cid:6)(a, λ)] sin α)(N (cid:1) α[(cid:6)(a, λ)] sin α) (9.11) (9.12) (9.13) = {N (cid:1) α[ f (a)]Nα[(cid:6)(a, λ)] − Nα[ f (a)]N (cid:1) α[(cid:6)(a, λ)]}r (a) If the kernel function is chosen so that Nα[(cid:6)(a, λ)] = 0, for example, the lower boundary condition is −Nα[ f (a)]N (cid:1) α[(cid:6)(a, λ)]r (a) (9.14) Similarly, at x = b (cid:12) (cid:6)(b, λ) f (cid:1) (b) − (cid:6)(cid:1) (cid:13) (b, λ) f (b) r (b) = −Nβ[ f (b)]N (cid:1) β[(cid:6)(b, λ)]r (b) (9.15) Since (cid:6)(x, λ) satisﬁes the Sturm–Liouville equation, there are n solutions forming a set of orthogonal functions with weight function p(x) and (cid:12)(cid:6) n(x, λ n) = −λ2 n p(x)(cid:6) n(x, λ n) (9.16) book Mobk070 March 22, 2007 11:7 146 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS so that where (cid:10) (cid:11) D[ f (x)] T = −λ2 b(cid:2) p(x) f (x)(cid:6) n(x, λ)d x + Nα[ f (a)]N (cid:1) α[(cid:6) n(a, λ)]r (a) x=a − Nβ[ f (b)]N (cid:1) β[(cid:6) n(b, λ)]r (b) λ2 n b(cid:2) a p(x) fn(x)(cid:6) n(x, λ n)d x = λ2 n Fn(λ n) (9.17) (9.18) THE INVERSE TRANSFORM 9.3 The great thing about Sturm–Liouville transforms is that the inversion is so easy. Recall that the generalized Fourier series of a function f (x) is f (x) = ∞(cid:1) (cid:6) n=1 n) n(x, λ (cid:6) (cid:6)(cid:6) n (cid:6) fn(ξ ) p(ξ ) b(cid:2) a n(ξ, λ (cid:6)(cid:6) n) (cid:6) d ξ = n ∞(cid:1) n=1 (cid:6) (cid:6)(cid:6) n(x) (cid:6)2 F(λ n) n (9.19) where the functions (cid:6) n(x, λ n)form an orthogonal set with respect to the weight function p(x). Example 9.2 (The cosine transform). Consider the diffusion equation 0 ≤ x ≤ 1 = yxx yt yx(0, t) = y(1, t) = 0 y(x, 0) = f (x) t > 0 To ﬁnd the proper kernel function K (x, λ) we note that according to Eq. (9.16) (cid:6) n(x, λ n) must satisfy the Sturm–Liouville equation (cid:12)[(cid:6) n(x, λ)] = − p(x)(cid:6) n(x, λ) where for the current problem (cid:12)[(cid:6) n(x, λ)] = d 2 d x2 [(cid:6) n(x, λ)] and p(x) = 1 along with the boundary conditions (9.11) Nα[(cid:6)(x, λ)]x=a Nβ[(cid:6)(x, λ)]x=b = (cid:6) x(0, λ) = 0 = (cid:6)(1, λ) = 0 book Mobk070 March 22, 2007 11:7 Solution of this differential equation and applying the boundary conditions yields an inﬁnite number of functions (as any Sturm–Liouville problem) STURM–LIOUVILLE TRANSFORMS 147 (cid:6)(x, λ n) = A cos(λ nx) with cos(λ n) = 0 λ n π = (2n − 1) 2 n) = cos(λ Thus, the appropriate kernel function is K (x, λ Using this kernel function in the original partial differential equation, we ﬁnd nx) with λ n = (2n − 1) π 2 . where Cλ (cid:10) (cid:11) y(x, t) = Y (t, λ d Y d t = −λ2 nY n) is the cosine transform of y(t, x). The solution gives −λ2 t Y (t, λ n) = Be and applying the cosine transform of the initial condition 1(cid:2) B = f (x) cos(λ nx)d x x=0 According to Eq. (9.19) the solution is as follows: y(x, t) = ∞(cid:1) n=0 # # cos(λ cos(λ nx) # #2 nx) 1(cid:2) x−0 f (x) cos(λ nx)d xe −λ2 n t Example 9.3 (The Hankel transform). Next consider the diffusion equation in cylindrical coordinates. (cid:6) (cid:7) Boundary and initial conditions are prescribed as ut = 1 r d dr r d u dr ur (t, 0) = 0 u(t, 1) = 0 u(0, r ) = f (r ) First we ﬁnd the proper kernel function (cid:12)[(cid:6)(r, λ n)] = d dr (cid:7) (cid:6) r n d (cid:6) dr = −λ2 n r (cid:6) book Mobk070 March 22, 2007 11:7 148 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS with boundary conditions (cid:6) , 0) = 0 r (λ n (cid:6)(λ , 1) = 0 n The solution is the Bessel function J 0(λ nr ) with λ n given by J 0(λ n) = 0. Thus the transform of u(t, r ) is as follows: (cid:11) (cid:10) u(t, r ) Hλ 1(cid:2) = U (t, λ n) = r J 0(λ nr )u(t, r )dr r =0 This is called a Hankel transform. The appropriate differential equation for U (t, λ n) is so that dUn d t = −λ2 nUn Un(t, λ n) = Be −λ2 n t Applying the initial condition, we ﬁnd 1(cid:2) B = r f (r )J 0(λ nr )dr r =0 and from Eq. (9.19) u(t, r ) = ∞(cid:1) n=0 1 (cid:3) r =0 r f (r )J 0(λ nr )dr # #2 J 0(λ nr ) # # J 0(λ nr )e −λ2 n t Example 9.4 (The sine transform with a source). Next consider a one-dimensional transient diffusion with a source term q (x): = u xx + q (x) ut y(0, x) = y(t, 0) = t(t, π ) = 0 First we determine that the sine transform is appropriate. The operator (cid:12) is such that (cid:12)(cid:6) = (cid:6) xx = λ(cid:6) book Mobk070 March 22, 2007 11:7 and according to the boundary conditions we must choose (cid:6) = sin(nx) and λ = −n2. The sine transform of q (x) is Q(λ). STURM–LIOUVILLE TRANSFORMS 149 = −n2U + Q(λ) Ut U = U (λ, t) The homogeneous and particular solutions give when t = 0, U = 0 so that where Qn is given by Un = Ce −n2t + Qn n2 C = − Qn n2 = Qn π(cid:2) x=0 q (x) sin(nx)d x Since Un = Qn n2 [1 − e −n2t] the solution is u(x, t) = ∞(cid:1) n=1 Qn n2 [1 − e −n2t] # # sin(nx) # #2 sin(nx) Note that Qn is just the nth term of the Fourier sine series of q (x). For example, if q (x) = x, = Qn π n (−1)n+1 Example 9.5 (A mixed transform). Consider steady temperatures in a half cylinder of inﬁ- nite length with internal heat generation, q (r ) that is a function of the radial position. The appropriate differential equation is ur r + 1 r ur + 1 r 2 uθθ + u zz with boundary conditions + q (r ) = 0 0 ≤ r ≤ 1 0 ≤ z ≤ ∞ 0 ≤ θ ≤ π u(1, θ, z) = 1 u(r, 0, z) = u(r, π, z) = u(r, θ, 0) = 0 book Mobk070 March 22, 2007 11:7 150 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS (cid:10) u(r, θ, z) (cid:11) = Un(r, n, z) with respect to θ Let the sine transform of u be denoted by Sn on the interval (0, π ). Then ∂ 2Un ∂r 2 + 1 r ∂Un ∂r − n2 r 2 Un + ∂ 2Un ∂z2 + q (r )Sn(1) = 0 where Sn(1) is the sine transform of 1, and the boundary conditions for u(r, θ, z) on θ have been used. Note that the operator on (cid:6) in the r coordinate direction is (cid:12) (cid:12) (cid:6)(r, µ j ) (cid:13) = 1 r d dr (cid:7) (cid:6) r d (cid:6) dr − n2 r 2 (cid:6) = −µ2 j (cid:6) With the boundary condition at r = 1 chosen as (cid:6)(1, µ (cid:6) = r J n(r, µ j ) with eigenvalues determined by J n(1, µ j ) = 0 this gives the kernel function as j ) = 0 We now apply the ﬁnite Hankel transform to the above partial differential equation and denote the Hankel transform of Un by U j n . After applying the boundary condition on r we ﬁnd, after noting that Nβ[Un(z, 1)] = Sn(1) (cid:1) β[(cid:6)(1, z)] = −µ N j J n+1(µ j ) j J n+1(µ j )Sn(1) + d 2U j n d z2 + Q j (µ j )Sn(1) = 0. Here Q j (µ j ) is the Hankel trans- + µ −µ2 j U j n form of q (r ). Solving the resulting ordinary differential equation and applying the boundary condition at z = 0, U j n(µ j , n, z) = Sn(1) Q j (µ j ) + µ µ2 j j J n+1(µ j ) [1 − exp(−µ j z)] We now invert the transform for the sine and Hankel transforms according to Eq. (9.19) and ﬁnd that Note that u(r, θ, z) = 4 π ∞(cid:1) ∞(cid:1) n=1 j =1 U j n(µ j [J n+1(µ , n, z) j )]2 J n(µ jr ) sin(nθ ) Sn(1) = [1 − (−1)n]/n book Mobk070 March 22, 2007 11:7 Problems Use an appropriate Sturm–Liouville transform to solve each of the following problems: STURM–LIOUVILLE TRANSFORMS 151 1. Chapter 3, Problem 1. 2. Chapter 2, Problem 2. 3. Chapter 3, Problem 3. 4. u(r, 0) = 0 u(1, t) = 0 u bounded ∂u ∂t = 1 r ∂ ∂r (cid:7) (cid:6) r ∂u ∂r + G(constant t) 5. Solve the following using an appropriate Sturm–Liouville transform: = ∂ 2u ∂u ∂ x2 ∂t u(t, 0) = 0 u(t, 1) = 0 u(0, x) = sin(π x) 6. Find the solution for general ρ(t): = ∂ 2u ∂ x2 ∂u ∂t u(t, 0) = 0 u(t, 1) = ρ(t) u(0.x) = 0 FURTHER READING V. S. Arpaci, Conduction Heat Transfer, Reading, MA: Addison-Wesley, 1966. R. V. Churchill, Operational Mathematics, 3rd ed. New York: McGraw-Hill, 1972. I. H. Sneddon, The Use of Integral Transforms, New York: McGraw-Hill, 1972. book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 153 C H A P T E R 10 Introduction to Perturbation Methods Perturbation theory is an approximate method of solving equations which contain a parameter that is small in some sense. The method should result in an approximate solution that may be termed “precise” in the sense that the error (the difference between the approximate and exact solutions) is understood and controllable and can be made smaller by some rational technique. Perturbation methods are particularly useful in obtaining solutions to equations that are nonlinear or have variable coefﬁcients. In addition, it is important to note that if the method yields a simple, accurate approximate solution of any problem it may be more useful than an exact solution that is more complicated. 10.1 EXAMPLES FROM ALGEBRA We begin with examples from algebra in order to introduce the ideas of regular perturbations and singular perturbations. We start with a problem of extracting the roots of a quadratic equation that contains a small parameter ε (cid:13) 1. 10.1.1 Regular Perturbation Consider, for example, the equation The exact solution for the roots is, of course, simply obtained from the quadratic formula: x2 + εx − 1 = 0 (10.1) which yields exact solutions and x = − ε 2 (cid:8) ± 1 + ε2 4 x = 0.962422837 x = −1.062422837 (10.2) book Mobk070 March 22, 2007 11:7 154 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Equation (10.2) can be expanded for small values of ε in the rapidly convergent series x = 1 − + ε 2 ε2 8 − ε4 128 + · · · (10.3) or x = −1 − ε2 ε − + ε4 − · · · (10.4) 8 To apply perturbation theory we ﬁrst note that if ε = 0 the two roots of the equation, which we will call the zeroth-order solutions, are x0 = ±1. We assume a solution of the form 128 2 x = x0 + a1 ε + a2 ε2 + a3 ε3 + a4 ε4 + · · · (10.5) Substituting (10.5) into (10.1) 1 + (2a1 + 1)ε + (cid:17) a 2 1 + 2a2 + a1 (cid:18) ε2 + (2a1a2 + 2a3 + a2)ε3 + · · · − 1 = 0 (10.6) where we have substituted x0 we ﬁnd = 1. Each of the coefﬁcients of εn must be zero. Solving for an = − 1 2 = 1 8 = 0 a1 a2 a3 so that the approximate solution for the root near x = 1 is x = 1 − + ε 2 ε2 8 + O(ε4) The symbol O(ε4) means that the next term in the series is of order ε4 (10.7) (10.8) Performing the same operation with x0 (cid:17) a 2 1 1 − (1 + 2a1)ε + − 2a2 + a1 (cid:18) ε2 + (2a1a2 = −1 Again setting the coefﬁcients of εn equal to zero a1 a2 = − 1 2 = − 1 8 a3 = 0 − 2a3 + a2)ε3 + · · · − 1 = 0 (10.9) (10.10) book Mobk070 March 22, 2007 11:7 INTRODUCTION TO PERTURBATION METHODS 155 so that the root near x0 = −1 is x = −1 − − ε 2 ε2 8 + O(ε4) (10.11) The ﬁrst three terms in (10.8) give x = 0.951249219, accurate to within 1.16% of the exact value while (10.11) gives the second root as x = −1.051249219, which is accurate to within 1.05%. Next suppose the small parameter occurs multiplied by the squared term, εx2 + x − 1 = 0 Using the quadratic formula gives the exact solution. (cid:8) x = − 1 2ε ± 1 4ε2 + 1 ε If ε = 0.1 (10.13) gives two solutions: and x = 0.916079783 x = −10.91607983 (10.12) (10.13) We attempt to follow the same procedure to obtain an approximate solution. If ε = 0 identically, x0 = 1 and substituting into (10.12) we ﬁnd = 1. Using (10.5) with x0 (1 + a1)ε + (2a1 + a2)ε2 + (cid:17) 2a2 + a 2 1 + a3 (cid:18) ε3 + · · · = 0 Setting the coefﬁcients of εn = 0 , solving for an, and substituting into (10.5) x = 1 − ε + 2ε2 − 5ε3 + · · · (10.14) (10.15) gives x = 0.915, close to the exact value. However Eq. (10.12) clearly has two roots, and the method cannot give an approximation for the second root. The essential problem is that the second root is not small. In fact (10.13) shows that as ε → 0, \|x\| → 1 2ε so that the term εx2 is never negligible. 10.1.2 Singular Perturbation Arranging (10.12) in a normal form x2 + x − 1 ε = 0 (10.12a) book Mobk070 March 22, 2007 11:7 156 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS and the equation is said to be singular as ε → 0. If we set xε = u we ﬁnd an equation for u as u2 + u − ε = 0 (10.16) With ε identically zero, u = 0 or −1. Assuming that u may be approximated by a series like (10.5) we ﬁnd that (−a1 − 1)ε + − a2 ε2 + (2a1a2 − a3)ε3 + · · · = 0 (10.17) (cid:18) (cid:17) a 2 1 a1 a2 a3 = −1 = 1 = −2 so that x = − 1 ε − 1 + ε − 2ε2 + · · · (10.18) (10.19) The three-term approximation of the negative root is therefore x = −10.92, within 0.03% of the exact solution. As a third algebraic example consider x2 − 2εx − ε = 0 (10.20) This at ﬁrst seems like a harmless problem that appears at ﬁrst glance to be amenable to a regular perturbation expansion since the x2 term is not lost when ε → 0. We proceed optimistically by taking x = x0 + a1 ε + a2 ε2 + a3 ε3 + · · · Substituting into (10.20) we ﬁnd x2 0 + (2x0a1 − 2x0 − 1)ε + (cid:17) a 2 1 + 2x0a2 − 2a1 (cid:18) ε2 + · · · = 0 from which we ﬁnd x0 = 0 − 2x0 + 2x0a2 2x0a1 a 2 1 − 1 = 0 = 0 − 2a1 (10.21) (10.22) (10.23) From the second of these we conclude that either 0 = −1 or that there is something wrong. That is, (10.21) is not an appropriate expansion in this case. Note that (10.20) tells us that as ε → 0, x → 0. Moreover, in writing (10.21) we have → constant. Let us suppose instead essentially assumed that ε → 0 in such a manner that x ε book Mobk070 March 22, 2007 11:7 INTRODUCTION TO PERTURBATION METHODS 157 that as ε → 0 We than deﬁne a new variable x(ε) ε p → constant x = ε pv(ε) such that v(0) (cid:3)= 0. Substitution into (10.20) yields ε2 pv2 − 2ε p+1v − ε = Q (10.24) (10.25) (10.26) where Q must be identically zero. Note that since Q becomes, as long as it is not identically zero. ε must also be zero no matter how small ε Now, if p > 1/2, 2 p − 1 > 0 and in the limit as ε → 0 ε2 pv(ε) − 2ε pv(ε) − 1 → −1, which cannot be true given that Q = 0 identically. Next suppose p < 1/2. Again, Q is ε2 p identically zero for all ε including the limit as ε → 0. In the limit as ε → 0, v(ε)2 − ε1− pv(ε) − ε1−2 p → v(0) (cid:3)= 0. p = 1/2 is the only possibility left, so we attempt a solution with this value. Hence Substitution into (10.20) gives x = ε1/2v(ε) v2 − 2 √ εv − 1 = 0 and this can now be solved by a regular perturbation assuming β = √ ε (cid:13) 1. Hence, v = v 0 Inserting this into (10.28) with β = β + a2 β 2 + a3 β 3 + · · · + a1 √ ε v 0 − 1 + (2v 0a1 − 2v 0)β + (cid:17) a 2 1 + 2v 0a2 − 2a1 (cid:18) β 2 + · · · = 0 Thus v 0 a1 a2 = ±1 = 1 = + 1 2 or − 1 2 (10.27) (10.28) (10.29) (10.30) (10.31) book Mobk070 March 22, 2007 11:7 158 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS Thus the two solutions are and v = √ ε + ε + 1 2 √ ε + · · · ε v = − √ ε + ε − 1 2 √ ε + · · · ε book Mobk070 March 22, 2007 11:7 159 Appendix A: The Roots of Certain Transcendental Equations TABLE A.1: The ﬁrst six roots, † α n, of C 0 0.001 0.002 0.004 0.006 0.008 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 α 1 0 0.0316 0.0447 0.0632 0.0774 0.0893 0.0998 0.1410 0.1987 0.2425 0.2791 0.3111 0.4328 0.5218 0.5932 0.6533 0.7051 0.7506 0.7910 α 2 3.1416 3.1419 3.1422 3.1429 3.1435 3.1441 3.1448 3.1479 3.1543 3.1606 3.1668 3.1731 3.2039 3.2341 3.2636 3.2923 3.3204 3.3477 3.3744 α tan α + C = 0. α α 3 4 6.2832 6.2833 6.2835 6.2838 6.2841 6.2845 6.2848 6.2864 6.2895 6.2927 6.2959 6.2991 6.3148 6.3305 6.3461 6.3616 6.3770 6.3923 6.4074 9.4248 9.4249 9.4250 9.4252 9.4254 9.4256 9.4258 9.4269 9.4290 9.4311 9.4333 9.4354 9.4459 9.4565 9.4670 9.4775 9.4879 9.4983 9’5087 α 5 12.5664 12.5665 12.5665 12.5667 12.5668 12.5670 12.5672 12.5680 12.5696 12.5711 12.5727 12.5743 12.5823 12.5902 12.5981 12.6060 12.6139 12.6218 12.6296 α 6 15.7080 15.7080 15.7081 15.7082 15.7083 15.7085 15.7086 15.7092 15.7105 15.7118 15.7131 15.7143 15.7207 15.7270 15.7334 15.7397 15.7460 15.7524 15.7587 book Mobk070 March 22, 2007 11:7 160 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS TABLE A.1: (continue) C 0.9 1.0 1.5 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 30.0 40.0 50.0 60.0 80.0 100.0 ∞ α 1 0.8274 0.8603 0.9882 1.0769 1.1925 1.2646 1.3138 1.3496 1.3766 1.3978 1.4149 1.4289 1.4729 1.4961 1.5202 1.5325 1.5400 1.5451 1.5514 1.5552 1.5708 α 2 3.4003 3.4256 3.5422 3.6436 3.8088 3.9352 4.0336 4.1116 4.1746 4.2264 4.2694 4.3058 4.4255 4.4915 4.5615 4.5979 4.6202 4.6353 4.6543 4.6658 4.7124 α tan α + C = 0. α α 3 4 6.4224 6.4373 6.5097 6.5783 6.7040 6.8140 6.9096 6.9924 7.0640 7.1263 7.1806 7.2281 7.3959 7.4954 7.6057 7.6647 7.7012 7.7259 7.7573 7.7764 7.8540 9.5190 9.5293 9.5801 9.6296 9.7240 9.8119 9.8928 9.9667 10.0339 10.0949 10.1502 10.2003 10.3898 10.5117 10.6543 10.7334 10.7832 10.8172 10.8606 10.8871 10.9956 † The roots of this equation are all real if C > 0. α 5 12.6375 12.6453 12.6841 12.7223 12.7966 12.8678 12.9352 12.9988 13.0584 13.1141 13.1660 13.2142 13.4078 13.5420 13.7085 13.8048 13.8666 13.9094 13.9644 13.9981 14.1372 α 6 15.7650 15.7713 15.8026 15.8336 15.8945 15.9536 16.0107 16.0654 16.1177 16.1675 16.2147 16.2594 16.4474 16.5864 16.7691 16.8794 16.9519 17.0026 17.0686 17.1093 17.2788 book Mobk070 March 22, 2007 11:7 APPENDIX A: THE ROOTS OF CERTAIN TRANSCENDENTAL EQUATIONS 161 TABLE A.2: The ﬁrst six roots, † α n, of C −1.0 −0.995 −0.99 −0.98 −0.97 −0.96 −0.95 −0.94 −0.93 −0.92 −0.91 −0.90 −0.85 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 α 1 0 0.1224 0.1730 0.2445 0.2991 0.3450 0.3854 0.4217 0.4551 0.4860 0.5150 0.5423 0.6609 0.7593 0.9208 1.0528 J.l656 1.2644 1.3525 1.4320 1.5044 1.5708 1.6320 1.6887 1.7414 1.7906 α 2 4.4934 4.4945 4.4956 4.4979 4.5001 4.5023 4.5045 4.5068 4.5090 4.5112 4.5134 4.5157 4.5268 4.5379 4.5601 4.5822 4.6042 4.6261 4.6479 4.6696 4.6911 4.7124 4.7335 4.7544 4.7751 4.7956 α cotα + C = 0. C α 3 7.7253 7.7259 7.7265 7.7278 7.7291 7.7304 7.7317 7.7330 7.7343 7.7356 7.7369 7.7382 7.7447 7.7511 7.7641 7.7770 7.7899 7.8028 7.8156 7.8284 7.8412 7.8540 7.8667 7.8794 7.8920 7.9046 10.9041 10.9046 10.9050 10.9060 10.9069 10.9078 10.9087 10.9096 10.9105 10.9115 10.9124 10.9133 10.9179 10.9225 10.9316 10.9408 10.9499 10.9591 10.9682 10.9774 10.9865 10.9956 11.0047 11.0137 11.0228 11.0318 α 1 14.0662 14.0666 14.0669 14.0676 14.0683 14.0690 14.0697 14.0705 14.0712 14.0719 14.0726 14.0733 14.0769 14.0804 14.0875 14.0946 14.1017 14.1088 14.1159 14.1230 14.1301 14.1372 14.1443 14.1513 14.1584 14.1654 α 2 17.2208 17.2210 17.2213 17.2219 17.2225 17.2231 17.2237 17.2242 17.2248 17.2254 17.2260 17.2266 17.2295 17.2324 17.2382 17.2440 17.2498 17.2556 17.2614 17.2672 17.2730 17.2788 17.2845 17.2903 17.2961 17.3019 book Mobk070 March 22, 2007 11:7 162 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS TABLE A.2: (continue) C 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 30.0 40.0 50.0 60.0 80.0 α 1 1.8366 1.8798 1.9203 1.9586 1.9947 2.0288 2.1746 2.2889 2.4557 2.5704 2.6537 2.7165 2.7654 2.8044 2.8363 2.8628 2.9476 2.9930 3.0406 3.0651 3.0801 3.0901 3.1028 α 2 4.8158 4.8358 4.8556 4.8751 4.8943 4.9132 5.0037 5.0870 5.2329 5.3540 5.4544 5.5378 5,6078 5.6669 5.7172 5.7606 5.9080 5.9921 6.0831 6.1311 6.1606 6.1805 6.2058 α cotα + C = 0. C α 3 7.9171 7.9295 7.9419 7.9542 7.9665 7.9787 8.0385 8.0962 8.2045 8.3029 8.3914 8.4703 8.5406 8.6031 8.6587 8.7083 8.8898 9.0019 9.1294 9.1987 9.2420 9.2715 9.3089 11.0409 11.0498 11.0588 11.0677 11.0767 11.0856 1 J.l296 1 J.l727 11.2560 11.3349 11.4086 11.4773 11.5408 11.5994 11.6532 11.7027 11.8959 12.0250 12.1807 12.2688 12.3247 12.3632 12.4124 α 1 14.1724 14.1795 14.1865 14.1935 14.2005 14.2075 14.2421 14.2764 14.3434 14.4080 14.4699 14.5288 14.5847 14.6374 14.6870 14.7335 14.9251 15.0625 15.2380 15.3417 15.4090 15.4559 15.5164 α 2 17.3076 17.3134 17.3192 17.3249 17.3306 17.3364 17.3649 17.3932 17.4490 17.5034 17.5562 17.6072 17.6562 17.7032 17.7481 17.7908 17.9742 18.1136 18.3018 18.4180 18.4953 18.5497 18.6209 3.1105 6.2211 100.0 ∞ 18.8496 † The roots of this equation are all real if C > −1. These negative values of C arise in connection with the sphere, §9.4. 15.7080 12.5664 15.5537 12.4426 18.6650 3.1416 6.2832 9.3317 9.4248 book Mobk070 March 22, 2007 11:7 APPENDIX A: THE ROOTS OF CERTAIN TRANSCENDENTAL EQUATIONS 163 TABLE A.3: The ﬁrst six roots α n, of C 0 0.01 0.02 0.04 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 30.0 40.0 50.0 60.0 80.0 100.0 ∞ α 1 0 0.1412 0.1995 0.2814 0.3438 0.3960 0.4417 0.5376 0.6170 0 7465 0.8516 0.9408 1.0184 1.0873 1.1490 1.2048 1.2558 1.4569 1.5994 1.7887 1.9081 1.9898 2.0490 2.0937 2.1286 2.1566 2.1795 2.2509 2.2880 2.3261 2.3455 2.3572 2.3651 2.3750 2.3809 2.4048 α J 1(α) − C J 0(α) = 0 α 4 α 3 7.0156 7.0170 7.0184 7.0213 7.0241 7.0270 7.0298 7.0369 7.0440 7.0582 7.0723 7.0864 7.1004 7.1143 7.1282 7.1421 7.1558 7.2233 7.2884 7.4103 7.5201 7.6177 7.7039 7.7797 7.8464 7.9051 7.9569 8.1422 8.2534 8.3771 8.4432 8.4840 8.5116 8.5466 8.5678 8.6537 10.1735 10.1745 10.1754 10.1774 10.1794 10.1813 10.1833 10.1882 10.1931 10.2029 10.2127 10.2225 10.2322 10.2419 10.2516 10.2613 10.2710 10.3188 10.3658 10.4566 10.5423 10.6223 10.6964 10.7646 10.8271 10.8842 10.9363 11.1367 11.2677 11.4221 11.5081 11.5621 11.5990 11.6461 11.6747 11.7915 α 2 3.8317 3.8343 3.8369 3.8421 3.8473 3.8525 3.8577 3.8706 3.8835 3.9091 3.9344 3.9594 3.9841 4.0085 4.0325 4.0562 4.0795 4.1902 4.2910 4.4634 4.6018 4.7131 4.8033 4.8772 4.9384 4.9897 5.0332 5.1773 5.2568 5.3410 5.3846 5.4112 5.4291 5.4516 5.4652 5.5201 α 5 13.3237 13.3244 13.3252 13.3267 13.3282 13.3297 13.3312 13.3349 13.3387 13.3462 13.3537 13.3611 13.3686 13.3761 13.3835 13.3910 13.3984 13.4353 13.4719 13.5434 13.6125 13.6786 13.7414 13.8008 13.8566 13.9090 13.9580 14.1576 14.2983 14.4748 14.5774 14.6433 14.6889 14.7475 14.7834 14.9309 α 6 16.4706 16.4712 16.4718 16.4731 16.4743 16.4755 16.4767 16.4797 16.4828 16.4888 16.4949 16.5010 16.5070 16.5131 16.5191 16.5251 16.5312 16.5612 16.5910 16.6499 16.7073 16.7630 16.8168 16.8684 16.9179 16.9650 17.0099 17.2008 17.3442 17.5348 17.6508 17.7272 17.7807 17.8502 17.8931 18.0711 book Mobk070 March 22, 2007 11:7 book Mobk070 March 22, 2007 11:7 165 Appendix B In this table q = ( p/a)1/2; a and x are positive real; α, β, γ are unrestricted; k is a ﬁnite integer; n is a ﬁnite integer or zero; v is a fractional number; 1 · 2 · 3 · · · n = n!; 1 · 3 · 5 · · · (2n − 1) = (2n − 1)!! n(cid:11)(n) = (cid:11)(n + 1) = n!; (cid:11)(1) = 0! = 1; (cid:11)(v)(cid:11)(1 − v) = π/ sin vπ ; (cid:11)( 1 2 ) = π 1/2 NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 TRANSFORM 1 p 1 p 2 1 p k 1 p 1/2 1 p 3/2 1 p k+1/2 1 p v p 1/2 p 3/2 p k−1/2 p n−v 1 p + α 1 ( p + α)( p + β) 1 ( p + α)2 FUNCTION 1 t tk−1 (k − 1)! 1 (πt)1/2 (cid:6) (cid:7) 1 2 2 t π 2k π 1/2(2k − 1)!! tk−1/2 − v−1 t (cid:11)(v) 1 2π 1/2t5/2 3 4π 1/2t5/2 (−1)k (2k − 1)!! 2k π 1/2tk+1/2 v−n−1 t (cid:11)(v − n) −α t e e −α t −β t − e α − β −α t te book Mobk070 March 22, 2007 11:7 166 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 (γ − β)e e 1 ( p + α)( p + β)( p + γ ) 1 ( p + α)2( p + β) 1 ( p + α)3 1 ( p + α)k p ( p + α)( p + β) p ( p + α)2 −γ t −βt + (β − α)e −αt + (α − γ )e (α − β)(β − γ )(γ − α) −αt[1 − (β − α)t] −βt − e (β − α)2 1 2 tk−1e −αt (k − 1)! −αt − βe α − β t2e αe −βt −αt (1 − αt)e −αt p ( p + α)( p + β)( p + γ ) α(β − γ )e −βt + γ (α − β)e −γ t −αt + β(γ − α)e (α − β)(β − γ )(γ − α) −αt − βe [β − α(β − α)t]e −βt p ( p + α)2( p + β) p ( p + α)3 α p 2 + α2 p p 2 + α2 α p 2 − α2 p p 2 − α2 −q x −q x q −q x p −q x q p −q x e e e e e p 2 −q x e p 1+n/2 (cid:6) (cid:6) (β − α)2 (cid:7) 1 − 1 2 αt t −αt e sin αt cos αt sinh αt cosh αt −x2/4αt −x2/4αt x 2(πα t3)1/2 e (cid:5) (cid:4) α π t 1/2 e (cid:14) erfc x 2(αt)1/2 (cid:15) (cid:14) (cid:15) (cid:7) 1/2 (cid:6) 2 αt π (cid:7) −x2/4αt − xerfc (cid:6) (cid:15) e (cid:14) x 2(αt)1/2 (cid:7) 1/2 t + x2 2α (γ − β)e erfc − x x 2(αt)1/2 −αt + (α − γ )e (α − β)(β − γ )(γ − α) t απ −βt + (β − α)e e −x2/4αt −γ t book Mobk070 March 22, 2007 11:7 APPENDIX B 167 −βt − e e −αt[1 − (β − α)t] (β − α)2 −αt t2e 1 2 tk−1e −αt (k − 1)! −αt − βe α − β αe −βt (1 − αt)e −αt α(β − γ )e −βt + γ (α − β)e −γ t −αt + β(γ − α)e (α − β)(β − γ )(γ − α) −αt − βe [β − α(β − α)t]e −βt (cid:6) (β − α)2 (cid:7) 1 − 1 2 αt t −αt e sin αt (cid:14) (cid:7) 1/2 (cid:6) α γ γ t 1 2 e    −x(γ /α)1/2 e erfc +e x(γ /α)1/2 (cid:15) erfc x 2(α t)1/2 x 2(α t)1/2 t + −x(γ /α)1/2 e (cid:15) erfc e x(γ /α)1/2 γ t 1 2 e   (cid:14) t − (cid:14)  +   x 2(α t)1/2 (cid:14) x 2(α t)1/2 (cid:14) x 2(α t)1/2 (cid:14) x 2(α t)1/2 erfc (cid:14) − (γ t)1/2 + (γ t)1/2 (cid:15) (cid:15)    (cid:15)   (cid:15)    (cid:15)  − (γ t)1/2 + (γ t)1/2 (cid:15) − (γ t)1/2 + (γ t)1/2 γ t e +  αβ αβ 2 − γ e −x(γ /α)1/2 α1/2 α1/2β + γ 1/2 e α1/2 α1/2β − γ 1/2 e x(γ /α)1/2 x βx+αβ2terfc 2(α t)1/2 (cid:4) (cid:12) 1/2 (cid:5) (cid:14) erfc erfc x 2(α t)1/2 (cid:14) x 2(α t)1/2 (cid:15) + β(α t)1/2 (cid:13) x t I1 2(xt)1/2 (cid:12) I0 2(xt)1/2 (cid:13) (cid:6) (cid:7) t x (v−1)/2 (cid:12) 2(xt)1/2 (cid:13) Iv−1 e −q x ( p − γ )(q + β) γ (cid:3)= αβ 2 , 1 2 − e x/ p − 1 e x/ p 1 p 1 p y e x/ p e e e −q x e p 3/4 −q x e q + β −q x q (q + β) −q x p(q + β) −q x q p(q + β) −q x q n+1(q + β) −q x (q + β)2 −q x p(q + β)2 −q x e p − γ e e e e −q x q ( p − γ ) e −q x ( p − γ )2 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 book Mobk070 March 22, 2007 11:7 168 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 49 50 51 52 53 54 55 56 K0(q x) 1 p 1/2 K2v(q x) v/2−1 Kv(q x) p v/2 Kv(q x) p (cid:12) p − ( p 2 − x2)1/2 (cid:13)v e x[( p+α)1/2−( p+β)1/2]z − 1 e x[ p−( p+α)1/2( p+β)1/2] ( p + α)1/2( p + β)1/2 e x[( p+α)1/2−( p+β)1/2]2 (cid:12) ( p + α)1/2( p + β)1/2 ( p + α)1/2 + ( p + β)1/2 (cid:13) 2v −x2/4α t 1 2t e 1 2(πt)1/2 e v−1 −vαv/22 −x28α t Kv (cid:3) ∞ x2/4α t e x (cid:7) (cid:6) x2 8α t −u u v−1d u −x2/4α t v x αv/2(2t)v+1 e v x t (cid:12) −(α+β)t/2 I1 1 v Iv(xt) t1/2(t + 4x)1/2 2 (α − β)t1/2(t + 4x)1/2 (cid:13) x(α − β)e −(α+β)(t+x)/2 I0 e v/2e −(α+β)t/2 Iv t (cid:12) (cid:12) 1 2 (α − β)t1/2(t + 2x)1/2 1 2 (α − β)t1/2(t + 4x)1/2 (α − β)v(t + 4x)v/2 (cid:13) (cid:13) book Mobk070 March 22, 2007 11:7 169 Author Biography Dr. Robert G. Watts is the Cornelia and Arthur L. Jung Professor of Mechanical Engineering at Tulane University. He holds a BS (1959) in mechanical engineering from Tulane, an MS(1960) in nuclear engineering from the Massachusetts Institute of Technology and a PhD (1965) from Purdue University in mechanical engineering. He spent a year as a Postdoctoral associate studying atmospheric and ocean science at Harvard University. He has taught advanced applied mathematics and thermal science at Tulane for most of his 43 years of service to that university. Dr. Watts is the author of Keep Your Eye on the Ball: The Science and Folklore of Baseball (W. H. Freeman) and the editor of Engineering Response to Global Climate Change (CRC Press) and Innovative Energy Strategies for CO2 Stabilization (Cambridge University Press) as well as many papers on global warming, paleoclimatology energy and the physic of sport. He is a Fellow of the American Society of Mechanical Engineers. book Mobk070 March 22, 2007 11:7
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=7042954.pdf&bkn=7042953&pdfType=book	S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G Series ISSN: 1939-5221 Series ISSN: 1939-5221 Series ISSN: 1939-5221 SERIES EDITOR: Stephen F. Barrett, University of Wyoming SERIES EDITOR: Stephen F. Barrett, University of Wyoming SERIES EDITOR: Stephen F. Barrett, University of Wyoming THE CAPTAINS OF ENERGY THE CAPTAINS OF ENERGY THE CAPTAINS OF ENERGY Systems Dynamics from an Energy Perspective Systems Dynamics from an Energy Perspective Systems Dynamics from an Energy Perspective Vincent C. Prantil, Milwaukee School of Engineering Vincent C. Prantil, Milwaukee School of Engineering Vincent C. Prantil, Milwaukee School of Engineering Timothy Decker, Milwaukee Area Technical College, University of Wisconsin Milwaukee Timothy Decker, Milwaukee Area Technical College, University of Wisconsin Milwaukee Timothy Decker, Milwaukee Area Technical College, University of Wisconsin Milwaukee In teaching an introduction to transport or systems dynamics modeling at the undergraduate In teaching an introduction to transport or systems dynamics modeling at the undergraduate In teaching an introduction to transport or systems dynamics modeling at the undergraduate level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the mathematical modeling of time-dependent system behavior offers is a venue in which students mathematical modeling of time-dependent system behavior offers is a venue in which students mathematical modeling of time-dependent system behavior offers is a venue in which students can be taught that physical analogies exist between what they likely perceive as distinct areas can be taught that physical analogies exist between what they likely perceive as distinct areas can be taught that physical analogies exist between what they likely perceive as distinct areas of study in the physical sciences. We introduce a storyline whose characters are superheroes of study in the physical sciences. We introduce a storyline whose characters are superheroes of study in the physical sciences. We introduce a storyline whose characters are superheroes that store and dissipate energy in dynamic systems. Introducing students to the overarching that store and dissipate energy in dynamic systems. Introducing students to the overarching that store and dissipate energy in dynamic systems. Introducing students to the overarching conservation laws helps develop the analogy that ties the different disciplines together under a conservation laws helps develop the analogy that ties the different disciplines together under a conservation laws helps develop the analogy that ties the different disciplines together under a common umbrella of system energy. In this book, we use the superhero cast to present the effort- common umbrella of system energy. In this book, we use the superhero cast to present the effort- common umbrella of system energy. In this book, we use the superhero cast to present the effort- flow analogy and its relationship to the conservation principles of mass, momentum, energy, flow analogy and its relationship to the conservation principles of mass, momentum, energy, flow analogy and its relationship to the conservation principles of mass, momentum, energy, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and thermal engineering systems to illustrate how to apply the analogy to arrive at governing and thermal engineering systems to illustrate how to apply the analogy to arrive at governing and thermal engineering systems to illustrate how to apply the analogy to arrive at governing differential equations describing the systems’ behavior in time. Ultimately, we show how only differential equations describing the systems’ behavior in time. Ultimately, we show how only differential equations describing the systems’ behavior in time. Ultimately, we show how only two types of differential equation, and therefore, two types of system response are possible. two types of differential equation, and therefore, two types of system response are possible. two types of differential equation, and therefore, two types of system response are possible. This novel approach of storytelling and a movie script is used to help make the mathematics of This novel approach of storytelling and a movie script is used to help make the mathematics of This novel approach of storytelling and a movie script is used to help make the mathematics of lumped system modeling more approachable for students. lumped system modeling more approachable for students. lumped system modeling more approachable for students. ABOUT SYNTHESIS ABOUT SYNTHESIS ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library This volume is a printed version of a work that appears in the Synthesis Digital Library This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original of Engineering and Computer Science. Synthesis Lectures provide concise, original of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development topics, published quickly, in digital presentations of important research and development topics, published quickly, in digital presentations of important research and development topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com and print formats. For more information visit www.morganclaypool.com and print formats. For more information visit www.morganclaypool.com w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m 9 781627 055888 9 781627 055888 9 781627 055888 ISBN: 978-1-62705-588-8 ISBN: 978-1-62705-588-8 ISBN: 978-1-62705-588-8 90000 90000 90000 P P R R A A N N T T I I L L P R A N T I L • • • D D E E C C K K E E R R D E C K E R THE CAPTAINS OF ENERGY THE CAPTAINS OF ENERGY THE CAPTAINS OF ENERGY Systems Dynamics from an Energy Perspective Systems Dynamics from an Energy Perspective Systems Dynamics from an Energy Perspective T H E C A P T A T T H H E E C C A A P P T T A A N N S S O O F F N S O F I I I E E N N E E R R G G Y Y E N E R G Y M M M O O O R R R G G G A A A N N N & & & C C C L L L A A A Y Y Y P P P O O O O O O L L L VINCENT C. PRANTIL • TIMOTHY DECKER VINCENT C. PRANTIL • TIMOTHY DECKER VINCENT C. PRANTIL • TIMOTHY DECKER S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G S Y N T H E S I S L E C T U R E S O N E N G I N E E R I N G Stephen F. Barrett, SERIES EDITOR Stephen F. Barrett, SERIES EDITOR Stephen F. Barrett, SERIES EDITOR e Captains of Energy Systems Dynamics from an Energy Perspective Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. e Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: e Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 e Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 e Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 iv A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering ermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape ermal Optimization Using Bejan’s Constructal eory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and rive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: e DG/K-Based Approach Stephen P. Radzevich 2008 v Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2015 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. e Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker www.morganclaypool.com ISBN: 9781627055888 ISBN: 9781627055895 paperback ebook DOI 10.2200/S00610ED1V01Y201410ENG024 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #24 Series ISSN Print 1939-5221 Electronic 1939-523X e Captains of Energy Systems Dynamics from an Energy Perspective Vincent C. Prantil Milwaukee School of Engineering Timothy Decker Milwaukee Area Technical College University of Wisconsin Milwaukee SYNTHESIS LECTURES ON ENGINEERING #24 CM&cLaypoolMorganpublishers&ABSTRACT In teaching an introduction to transport or systems dynamics modeling at the undergraduate level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the mathematical modeling of time-dependent system behavior oﬀers is a venue in which students can be taught that physical analogies exist between what they likely perceive as distinct areas of study in the physical sciences. We introduce a storyline whose characters are superheroes that store and dissipate energy in dynamic systems. Introducing students to the overarching conservation laws helps develop the analogy that ties the diﬀerent disciplines together under a common umbrella of system energy. In this book, we use the superhero cast to present the eﬀort-ﬂow analogy and its relationship to the conservation principles of mass, momentum, energy, and electrical charge. We use a superhero movie script common to mechanical, electrical, ﬂuid, and thermal engineering systems to illustrate how to apply the analogy to arrive at governing diﬀerential equations describing the systems’ behavior in time. Ultimately, we show how only two types of diﬀerential equation, and therefore, two types of system response are possible. is novel approach of storytelling and a movie script is used to help make the mathematics of lumped system modeling more approachable for students. KEYWORDS mathematical modeling, systems dynamics, transport modeling, lumped system anal- ysis, engineering mechanics, systems modeling, modeling approximation, energy, storage, eﬀort, ﬂow, multi-disciplinary systems Contents ix Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Language of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv e Language of Experts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv e Importance of Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi e Captains of Energy Story . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Outline of Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1 2 If You Push It, It Will Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 e Eﬀort-Flow Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 System Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 e Energy Balance Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Governing Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Deriving a Governing Diﬀerential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 e Four Casts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 System Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 3.1 3.2 3 e Electrical Cast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Eﬀort and Flow Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 Potential Energy Storage Character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Kinetic Energy Storage Character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Dissipative Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Single Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 3.4.1 RC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.2 RL Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.3 A Generalized Mathematical Form for the Single Storage Element Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 Multiple Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 x 3.5.1 Series RLC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.5.2 Parallel RLC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5.3 Idealized LC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.5.4 A Generalized Mathematical Form for the Dual Storage Element Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6 4.1 4.2 4 e Mechanical Cast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Eﬀort and Flow Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.1 Potential Energy Storage Character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.2 Kinetic Energy Storage Character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3 Dissipative Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Single Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 4.4.1 Spring-Damper Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4.2 Mass-Damper Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4.3 A Generalized Mathematical Form for the Single Storage Element Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.5 Multiple Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5.1 e Classical Mass-Spring-Damper System . . . . . . . . . . . . . . . . . . . . . . 54 4.5.2 Idealized Mass-Spring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.5.3 A Generalized Mathematical Form for the Dual Storage Element Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Rotational Mechanical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.6.1 Eﬀort and Flow Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.6.2 Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.6.3 Dissipative Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.6.4 e Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.6 4.7 5 5.1 A Common Notion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Time Domain Solutions of 1st Order Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.1.1 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.1.2 Forced Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.3 Dimensionless Solutions for 1st Order Systems . . . . . . . . . . . . . . . . . . . 80 5.1.4 Universal Truths for 1st Order System Response in the Time Domain . 81 Time Domain Solutions of 2nd Order Systems . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2 6 xi 5.2.1 Free Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.2.2 Forced Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.3 Dimensionless Solutions for 2nd Order Systems . . . . . . . . . . . . . . . . . . . 95 5.2.4 Characteristic Times for Transients in 2nd Order Systems . . . . . . . . . . . 96 5.2.5 Universal Truths for 2nd Order System Response in the Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2.6 Energy Storage and Dissipation for 2nd Order System Response in the Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.3 6.1 Going Nowhere? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Frequency Domain Solutions of 1st Order Systems . . . . . . . . . . . . . . . . . . . . . 114 6.1.1 Transfer Function Analysis for Harmonic Input . . . . . . . . . . . . . . . . . . 114 6.1.2 Steady-State Response and Bode Plot Analysis . . . . . . . . . . . . . . . . . . . 116 6.1.3 An Interpretation of Dimensionless Frequency Ratio . . . . . . . . . . . . . . 118 6.1.4 Filtering Characteristics of 1st Order Systems . . . . . . . . . . . . . . . . . . . . 120 6.1.5 Universal Truths for 1st Order Systems Subject to Harmonic Input . . 127 6.1.6 Energy Storage and Dissipation in 1st Order Systems Subject to Harmonic Input Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Frequency Domain Solutions of 2nd Order Systems . . . . . . . . . . . . . . . . . . . . 130 6.2.1 Transfer Function Analysis for Harmonic Input . . . . . . . . . . . . . . . . . . 131 6.2.2 Steady-State Response and Bode Plot Analysis . . . . . . . . . . . . . . . . . . . 132 6.2.3 Universal Truths for 2nd Order Systems Subject to Harmonic Input . . 144 Redesigning Systems for Steady-State Behaviors . . . . . . . . . . . . . . . . . . . . . . . 144 Energy Storage and Dissipation in 2nd Order Systems Subject to Harmonic Input Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.2 6.3 6.4 6.5 7.1 7 e Fluid and ermal Casts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Fluid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.1.1 Fluid Eﬀort and Flow Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.1.2 Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 7.1.3 Dissipative Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.1.4 Single Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.1.5 Multiple Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.2 ermal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 7.2.1 ermal Eﬀort and Flow Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 xii 8 7.2.2 Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.2.3 Dissipative Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.2.4 Single Storage Element Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Afterword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Preface If I make a mark in time, I can’t say the mark is mine; I’m only the underline Of the word. Like everybody else, I’m searchin’ through All I’ve heard. xiii Cat Stevens “Tuesday’s Dead” ere is a transparency to my accumulated writing. When I look deep beneath my declarations, I see the underlying thoughts of others. I realize now how much of what I have said is neither original nor unique. ought is forever being revived, recycled and renewed. Robert Fulghum Words I Wish I Wrote e technical content in this book is based on disciplinary physics whose mathematical modeling is well-known. e overarching concepts of eﬀort and ﬂow variables have been pre- sented before in a variety of ways [6–8, 18, 19]. Personally, I wish I’d been taught this way of analogical thinking in my undergraduate studies. Only recently was I taken by the power in the analogy when tasked to teach a course in systems dynamics. In the course of teaching, I developed a story to accompany the analogy. What is oﬀered here is this story. e mathematical relations are not new, but the story is. Like Cat Stevens and Robert Fulghum, I still ﬁnd value in this interpretation of “words said before.” As the physicist Joanne Lavvan admits in her interview for the book Einstein’s God [17], “I have not changed the facts; I’ve only changed the approach to the facts.” xiv PREFACE THE LANGUAGE OF MATHEMATICS Schooling, Frey asserts, discriminates against right-brained functions in favor of left-brain functions. Analogical thinking should be done BEST by right-brain-dominant individuals, but transport processes are often taught in an abstract, mathematically oriented manner. us, people who should be best able to understand transport process applications must struggle to learn them in the abstract. Arthur T. Johnson Biological Process Modeling: An Analogical Approach Mathematics is the language of modeling. Richard Feynman has called it “the language Mother Nature speaks” [5]. erefore, it does no good to try to understand her without it. In the business of mathematically modeling material behavior, it turns out that polymer transport of embedded ﬁbers, stresses in dry, densely packed granular materials, and anisotropy in crys- talline metals have something in common. Mathematical models for all of these physical phe- nomena share a common mathematical formulation based on the discipline-speciﬁc underlying physics. e ultimate commonality between diﬀerent physical systems is how they are represented mathematically. What can make studying these ﬁelds daunting is the level of abstraction in the mathematics. is mathematics can seem cumbersome, but it is also the single underlying story- line, the common thread for which each of the individual applications is but one manifestation. Mathematics can be like the DNA that is common to two people who are more alike than they appear. In using mathematics to model, we draw a unique picture of what is inherently similar about distinct scientiﬁc disciplines under a wide modeling umbrella. Previous treatments have success- fully applied the principles of mathematical modeling to draw the boundaries of this umbrella. But mathematical abstraction has often kept the umbrella at bay for those who think less “left- brained.” In today’s digital world, more and more is done on our behalf by models and simulations entrusted to the computer and crunching “big data.” Students don’t understand numbers as well as they once did. ey rely on the computer’s perfection, and they are unable to check its answers in case they type the numbers in wrong. Perhaps our society will decide that the average person does not need to understand numbers and that we can entrust this knowledge to an elite caste (the computer) [but either way] there is a catch. In order to say anything about the universe with mathematics, we have to construct a mathematical model. And models are always imperfect. ey always oversimplify reality, and every mathematical model begins with assumptions. Sometimes we forget these are only assumptions. We fall in love with our models. Major trauma ensues when we have to modify or discard them. Dana MacKenzie e Universe in Zero Words PREFACE xv Dana MacKenzie may be right that we are possibly moving to a world where mathematics may be the machine behind the curtain. But engineers will still have to build, maintain, and ultimately understand the machine. So, math matters! Ultimately what is essential for today’s engineering student is to understand the implications of mathematical simulation performed on their behalf. How that is done is not necessarily the end of the story, but it may be ﬁnding the path of least abstract resistance. We ultimately need a way to introduce the mathematics at an appropriate level for new learners. We too often trudge through a nest of complexity trying to ﬁnd the kernel of wisdom that excites. Complexity is often left to “the experts to explain.” e problem is we don’t often enough pull it oﬀ. Fortunately, complex systems have always been, on some level, simpliﬁed through the telling of stories. THE LANGUAGE OF EXPERTS Students are challenged by important aspects of engineering that can seem obvious and easy to experts, the so called “expert-blind-spot” which can impede eﬀective classroom instruction. Susan Singer and Karl Smith Understanding and Improving Learning in Undergraduate Science and Engineering Singer and Smith [13] make a salient point: that experts have too often forgotten more than students have yet to learn. We’re so far into the forest, we may have forgotten how to describe the trees. e reason some experts fail to communicate is that they’ve been trained to talk in jargon and unnecessary precision which begets complexity without understanding. is sentiment is passionately outlined by Tyler DeWitt, an MIT doctoral student in microbiology and high school teacher: that good science communication can cut through exhaustive detail by telling a good story. In the communication of science, there is this obsession with seriousness. Science communication has taken on this idea I call the tyranny of precision where you can’t just tell a story. Good storytelling is not about detail; it’s all about emotional connection! We have to convince our audience that what we’re talking about matters by knowing which details to leave out so that the main point still comes across! e great architect Mies van der Rohe said “Sometimes you have to learn to lie in order to tell the truth.” I understand the importance of detailed, speciﬁc scientiﬁc communication between experts. But not when we’re trying to teach young learners. (In this case) leave out the seriousness, leave out the jargon, leave out those annoying details, and just get to the point! Make me laugh. Make me care. How should you start? How about saying “Listen let me tell you a story”? Tyler DeWitt TED Talk: Hey Science Teachers, Make It Fun! xvi PREFACE So we set out to tell a story. A story where animation, characters, roles, and a script of- fer a less formal introduction to the common story of energy storage and loss. e way around abstraction is through metaphor and analogy. THE IMPORTANCE OF TRIANGULATION It is of ﬁrst rate importance that you know how to “triangulate” – that is, to know how to ﬁgure something out from what you already know. R.P. Feynman Tips on Physics Analogical reasoning is based on the brain’s ability to form patterns by association. A new idea is compared to an idea that is already well-understood. e brain may be able to understand (these) new concepts more easily if they are perceived as being part of a pattern. Jonah Lehrer How We Decide Educators can help students change misconceptions by using “bridging analogies” that link students’ correct knowledge with the situation about which they harbor false beliefs. Using multiple representations in instruction is one way to move students to expertise. Susan Singer and Karl Smith Understanding and Improving Learning in Undergraduate Science and Engineering e common theme of bridging disciplines shines forth. is can be accomplished pow- erfully by employing analogies. An emphasis on analogical thinking is adopted throughout this book. e concepts are not new. Only the presentation. ere is a common story, “a single script to essentially the same movie.” e movie can be set in a variety of stages: electrical current ﬂow, ﬂuid mass transport, heat ﬂow, and momentum transfer. In each of these distinct applications, we are essentially watching remakes of this same underlying movie: same script, same characters, but diﬀerent actors playing the roles. ese diﬀerent actors bring their own nuanced interpretation to the speciﬁc characters they play. If you’ve ever seen a re-make of an old movie, you’ve experienced this sort of thinking. You’ve seen the story told before through the eyes of one director and a speciﬁc cast of actors. In what follows, our pedagogical approach is simply to view the common script through the eyes of four distinct casts. We’ll see that the story told is the same, but each cast brings its own distinct feel to the common script. Also, as is the case whenever one is presented with two tellings of essentially the same story, we tend to prefer one cast. People often relate all other interpretations to this favorite telling. PREFACE xvii THE CAPTAINS OF ENERGY STORY Storytelling provides a method for scholarly discourse in engineering education to make implicit knowledge more explicit, promote reﬂective practice, and provide entry points into a community of practice. C.J. Atman, et al. Enabling Engineering Student Success is book uses storytelling to unify the concepts that underlie transport modeling, and make that modeling come alive. In IMAGINE: How Creativity Works, Jonah Lehrer [9] describes how such a premise can dramatically awaken the reader: Our breakthroughs often arrive when we apply old solutions to new situations. e best way to understand this conceptual blending is to look at the classic children’s book Harold and the Purple Crayon. e premise of the book is simple: Harold has a magic crayon. When he draws with this purple crayon, the drawing becomes real. If Harold wants to go for a walk, he simply draws a path with his crayon. But here’s the twist that makes Harold and the Purple Crayon (so) engaging: it blends together two distinct concepts of the world. Although the magic crayon is a fantastical invention Harold still has to obey the rules of reality. When Harold draws a mountain and tries to climb it, gravity still exists in the crayon universe. e book is a delicate balance of the familiar and the ﬁctional. Jonah Lehrer IMAGINE: How Creativity Works One of the problems with math is that we learn to speak the language on time scales that are not always aligned with our understanding of unifying physical concepts such as energy. Energy is a great uniﬁer of discussions on physical systems, but has not always been exploited as the storyteller that it can be. Energy illustrates a common pattern in each story. In this book, you will be introduced to the Captains of Energy who are at work in engineering systems that are excited by a world outside of themselves, a world controlled by Father Force. Father Force will deliver energy to the system. e Captains will play a game of catch with the imparted energy, a game of monkey-in-the-middle where the Evil Dr. Friction eats away at the energy cache as it is exchanged between Captains Potential and Kinetic Energy again and again. e familiar and ﬁctional are used to unify the mathematical abstraction in an exercise in conceptual blending. e purpose is to convince you that there are only three characters, four casts, one script, and only two equations you need to understand. e purple crayon is tied to reality and made familiar in an attempt to foster longer lasting learning. We script the movie and screenplay with the diﬀerent xviii PREFACE actors that appear on the mechanical, electrical, ﬂuid, and thermal stages. One important result of thinking in this way is that you can learn that “breadth at the expense of depth” has inherent advantages for life-long learning. e ability to see how “diﬀerent things look alike” will equip you with the tools that allow you to adapt to other applications whose underlying physics may be distinctly diﬀerent, but whose mathematical formulation you have “already seen” before. OUTLINE OF THE BOOK Chapter 1 addresses the overarching analogy of all systems variables as belonging to one of two categories: 1. Eﬀort variables and 2. Flow variables We introduce characters that represent the three key system elements in any transport sys- tem: inertia, stiﬀness, and friction. ereby, we cast several simple systems in this analogical framework and set the stage for the analogy’s universality among separate engineering disciplines. We summarize well-known and essential mathematical relations that correspond to each of the system elements and their respective characters. We introduce the idea that there are separate casts of players in each engineering discipline, but they play the same three roles of the system elements. e script is, in this sense, always the same. Only the actors playing the roles are diﬀer- ent. As when any movie is cast with diﬀerent actors, the same script, when played out, can have a quite diﬀerent feel, but the storyline remains unchanged. In Chapter 2, we use the mathematical relations for system elements directly in a conserva- tion principle resulting in a governing diﬀerential equation. We provide an example of how this is accomplished for an electrical system, as this is most often the discipline to which all others are made analogous. In Chapter 3, we illustrate several examples of electrical systems and derive their respective governing diﬀerential equations. We examine several possible systems, but stress the procedure more than the system speciﬁcs. We do this to emphasize that the speciﬁcs can be viewed as incidental. Here, we provide reasoning for students to understand when governing equations will be ﬁrst order and second order. We also introduce the notion of a normalized form of these equations and their solutions. Chapter 4 presents the mechanical analog of systems similar to those examined in Chap- ter 3. Actors in the mechanical cast are presented and their roles in speciﬁc systems are oﬀered as examples. We present single and dual energy character scripts that result in ﬁrst and second order diﬀerential equations, respectively. In Chapter 5, we exploit linearity to ﬁnd solutions to the normalized governing diﬀerential equations in the time domain. We oﬀer an examination of dimensionless solutions as a means to illustrate the concept of a master curve that cements the analogy mathematically. We present the PREFACE xix forms of master curves for ﬁrst and second order systems and set the stage for analogies in ﬂuid and thermal systems. In Chapter 6, we present classical solutions for systems in steady state that are excited by harmonic loads. Classically referred to as system response in the frequency domain, solutions are obtained via use of Laplace transforms and sinusoidal transform functions. It is typical to see these solutions already in dimensionless form rendering total system solutions that are entirely di- mensionless. We explain why casting models in dimensionless form is serendipitous for predictive capability. In Chapter 7, we present the system analogy for ﬂuid and thermal systems. We illustrate several examples of where ﬁrst and second order systems arise and the nonexistence of second order thermal systems. roughout this book, our intention is to provide an analogous procedure whereby students can see that deriving governing diﬀerential equations is a task accomplished always in the same manner, independent of the system’s discipline. In the Chapter Activities following Chapters 2–7, we present a small series of applications whereby the analogy can be used to construct equivalent systems that should now “look familiar.” We hope this belies a complexity that is born of speciﬁc detail, a detail which we argue does not actually exist when one approaches the mathematical model from the perspective of a common movie script merely played out by new and diﬀerent casts of actors. Vincent C. Prantil and Timothy Decker January 2015 Acknowledgments xxi We greatly appreciate the contributions of Drs. John E. Pakkala and Hope L. Weiss at the Milwaukee School of Engineering for their meticulous reviewing, prooﬁng, and vetting of this manuscript. eir perspectives bring a clarity and consistency to the presentation that it otherwise might not have found. We are grateful to them for providing a review of an earlier draft of this work which helped us to polish and reﬁne many details. From Vincent C. Prantil: I wish to dedicate this book to my uncle and life-long mentor in all things academic, Dr. Carl Calliari, retired professor of Education at Rowan University. I also wish to thank the enormous vat of patience exhibited by my partner in life and crime, Laurna, and my children, Carmen and Lorin. eir support, laughter, and love continue to carry me through my journey with more encouragement, enthusiasm, and sanity than it otherwise would possess. ey have unselﬁshly encouraged and supported the many adventures in my calling as a teacher. I would like to thank my parents, Dolores and Joseph Prantil, for rearing me in a home with much room for laughter and looking at the world in unconventional ways. ey let me ﬁnd my own way and have always been there to support even the craziest of ideas. I am grateful for the likes of Steven Strogatz, Michael Guillen, and Bill Nye of Cornell, along with Tyler DeWitt of MIT for their testimony to the art of writing beautifully about sci- ence and to the pedagogical power in making science fun. I dedicate this book to my students who adopted the energy characters as routes to analogical peg points in the mind’s eye. My students doubt, prod, question, and keep me young. We travel through the forest together. I am grateful to Sandy Haeger and her coterie at the One Way Cafe in Wauwatosa, Wisconsin. Sandy weekly allowed me to nurse a bottomless cup of coﬀee and a hard roll, the smallest tab in the Midwest, while penning these pages and perusing Tim’s drawings. I am blessed to have been provided with an amazingly understanding publisher in Joel Claypool and the ever accommodating editor, Andrea Koprowicz, whose encouragement and upbeat demeanor saved many of my faltering mo- ments. Finally, I am forever grateful to my Creator who blesses me every day with a mysterious mix of skepticism, faith, failure, humility, humor, energy, and imagination. Ego adhuc cognita. xxii ACKNOWLEDGMENTS From Timothy Decker: I dedicate this book to my son Evan, a constant source of support, strength, and hockey. He centers me and makes me remember daily what is important in life. I also dedicate this book to my many students who keep me young, and keep me guessing, laugh- ing, and learning. Vincent C. Prantil and Timothy Decker January 2015 C H A P T E R 1 1 If You Push It, It Will Flow Lenny: “What makes things move, George?” George: “Forces do, Lenny.” Lenny: “What makes things stop moving, George?” George: “Forces do, Lenny.” Leonard Susskind and George Hrabovsky e eoretical Miminum: What You Need to Know to Start Doing Physics At ﬁrst glance, it is not often evident that individual disciplines in the physical sciences exhibit a fascinating similitude. at is, behaviors in distinct ﬁelds share a unifying theme. For instance, a voltage drop across a circuit causes charge or current to ﬂow. Similarly, a temperature diﬀerence causes heat to ﬂow from hot to cold. e windfall for engineers is that the mathematical models for these transport processes, either for current or heat, are identical! Richard Feynman has said that “mathematics are the eyes with which we see physics” [3, 5]. To the more physically inclined, this may appear to be placing the cart ahead of the horse. But when we view the world this way, models allow us to “see” a unifying theme that underlies what we physically observe. Mother Nature, in her sense of orderliness, has chosen to sing a similar song in diﬀerent keys. e music is mathematics [2]. But mathematics can be a double-edged sword. While it can help us to see patterns and maybe even search for physical insight through patterns, it can be abstract and elusive for the new learner with less experience using their newly acquired tools of calculus. Here, we deﬁne a movie script that has only four character roles. ese will be a character putting energy into the system, two characters who store energy, and an energy eater. ese roles will be played by a new and diﬀerent cast in each discipline (the electrical, mechanical, ﬂuid, and thermal worlds). When a movie is remade with new actors portraying the characters, often people will take a liking to one cast over another. In other words, one particular cast of actors bring the screenplay to life in a particularly more meaningful way for them. So the relationship between voltage and current above is analogous to an identical relationship between temperature and heat ﬂow. Often engineers with a propensity for viewing the world “electrically” can translate a thermal system into an equivalent electrical one for the purposes of understanding “the movie” with a new and diﬀerent cast. e reason this is so is because there is a common framework in which current and heat ﬂow may be cast where the characters are the same; they are merely portrayed by diﬀerent actors. is analogical thinking is a formidably powerful tool for fostering learning. 2 1. IF YOU PUSH IT, IT WILL FLOW 1.1 THE EFFORT-FLOW ANALOGY All learning is by analogy. Albert Einstein No set of engineering principles is more useful or pervasive than the concepts of eﬀort variables and ﬂow variables. By analogy, these can be applied to almost any situation involving transfer of something from one location or situation to another. A.T. Johnson University of Maryland, College Park e substrate of analogical thinking involves recognizing a commonality between what, on the surface, may initially appear to be unrelated. For instance, the ﬂow of mass, momentum, heat, and electrical charge are not as independent as they may appear at ﬁrst glance. In fact, a powerful unifying theme or analogy exists linking the transport models in these otherwise distinct disciplines. Figure 1.1: A force applied to a mechanical system causes motion to occur. Force must continually be applied in the presence of friction if motion is to continue. Eﬀort variables represent the force-like quantities, forces in and on a system. Flow variables are quantities that change in response to the applied eﬀort. e eﬀort and ﬂow are called con- jugate pairs because they are necessarily married in a description of work and energy. Consider the example of a force applied to a block along a frictional surface. If there is suﬃcient force, the block will move. e block is a system characterized by its inertia and the friction between the block and the ﬂoor. A character we will call Father Force provides an externally applied eﬀort 1.1. THE EFFORT-FLOW ANALOGY 3 to the block. Father Force lives in a world outside of the system. e external force or eﬀort he supplies, if high enough to overcome the friction force, will cause a change in the block’s velocity or ﬂow. e force on the block and the resulting motion cannot be speciﬁed independently, i.e., there is an explicit relation between these two quantities. We can associate motions with requisite forces or, just the same, forces with the ensuing motion. While causality is, in some sense, in the mind of the observer, we can agree from this point on that a force applied to a system causes motion to take place. It is these quantities of force and subsequent motion that will form the basis for an elementary analogy. Consider now an electrical analog to this mechanical system. If you place a voltage diﬀerence across a resistor, current will ﬂow through the resistor. For a known amount of resistance, you cannot specify the voltage diﬀerence applied and the resulting current independently. ey are related. e electrical voltage diﬀerence acts like a net force. is net force pushes electrical charge through the resistor. e resistor represents an electrical analog to friction, if you will. And the current is a rate of change of electrical charge with time, just as the velocity of the block is a rate of change of displacement with time. What remains the same is that when you place an eﬀort diﬀerence or a net eﬀort across a system, ﬂow occurs through the system. Of Special Note In any transport process, a diﬀerence in an eﬀort variable across a small region of a system drives a transport or ﬂow of some quantity through the small region. .. So, a force diﬀerence or net force across a mass will cause a change in its momentum. A diﬀerence in electrical potential (or voltage) causes current to ﬂow. A temperature diﬀerence causes heat to ﬂow while a pressure diﬀerence causes ﬂuid to ﬂow. In a unifying template, force, voltage, temperature, and pressure play analogous roles. ey are the eﬀort driving the ﬂow of, respectively, momentum, (electrical) charge, (heat) energy, and mass. ese are the four quantities that are classically conserved or balanced in all systems. ese are four quantities you can neither create nor destroy. Eﬀort always drives ﬂow. And what ﬂows is usually related to whatever is conserved. Learn to think this way and almost everything you will learn in engineering will abide by this same set of rules wherever transport or dynamics are involved. We list the conjugate eﬀort and ﬂow variables for the four separate disciplines in Table 1.1. Here, the four disciplines have fostered models that describe how mechanical momentum, ﬂuid mass, electrical charge, and thermal heat ﬂow under the inﬂuence of force, pressure, voltage, and temperature diﬀerences respectively. In the course of your education, you may come across the nomenclature of a generalized force. A simple description in the current context is that a generalized force acts through a gen- 4 1. IF YOU PUSH IT, IT WILL FLOW Table 1.1: Eﬀort and ﬂow variables used to describe transport of momentum, mass, heat, and charge eralized displacement to produce work [16]. In a mechanical system, forces act through displace- ments to do work. In rotational mechanical systems, torque acts through an angular displacement to perform work (see Table 1.2). Note the units of force multiplied by displacement, e.g., N-m or joules, J, is the same as the product of torque and angular displacement, Nm-rad or N-m or J, units of work (and energy). In electrical systems, the product of voltage and charge is given by the product of volts and coulombs. By deﬁnition, this product is also measured in joules, J. We have chosen to associate ﬂow with the time rate of change of a displacement-like quantity, e.g., velocity, angular velocity, or current. As such, we will work with the following convention: eﬀort is a generalized force, while ﬂow is the derivative of a generalized displacement. e product of eﬀort and ﬂow will result in power or the rate at which work is performed on or energy is input to a system. Table 1.2: Concept of generalized force and motion in mechanical systems Of Special Note Because we follow the ﬂow of a conserved quantity, most often the ﬂow variable is the time rate of change of the conserved quantity. .. 1.1.1 SYSTEM ELEMENTS e screenplay of the transport process movie is written in terms of energy which is always con- served. As we will see soon, the concept of conservation plays a critical role in modeling. Since all real systems involve losses in energy, it would be more correct to say that energy is always bal- DisciplineEﬀortFlowElectricalVoltageCurrentMechanicalForceVelocityFluidPressureMassFlowRateThermalTemperatureHeatFlowRateDisciplineEﬀortFlowMechanicalGeneralizedForceGeneralizedMotionTranslationalForceVelocityRotationalTorqueAngularVelocityanced. e balance is composed of two types of stored energy pitted against the eventual losses. So our movie has two types of characters or elements: those that store energy and those that dissipate energy. Further, there are two elementary storage characters: those that store potential energy and those that store kinetic energy. 1.1. THE EFFORT-FLOW ANALOGY 5 Storage Elements e key role of the system elements or components in modeling is that they represent explicit relations between the eﬀort and ﬂow. A system element will be portrayed by a character in our movie. Any transport process can, at any moment in time, store energy by virtue of its eﬀort variable or its ﬂow variable. We call energy stored by virtue of a system’s eﬀort variable potential energy. Any system element that stores potential energy will play the role of Captain Potential Energy. is energy is locked inside a system by way of an eﬀort diﬀerence that can be relaxed to allow the energy to be released in a form evidenced by the system’s ﬂow variable. Energy stored by virtue of a system’s ﬂow variable is kinetic energy. Any system element that stores kinetic energy will play the role of Captain Kinetic Energy. In what follows, we will write mathematical expressions for the energy storage that will have analogs in each discipline of study. ey will always look the same. To plant the analogy, we choose the electrical and mechanical disciplines to demonstrate examples of the system elements or characters. We will also use these disciplinary examples to attempt to shed light on “how” potential and kinetic energy are stored and “who” stores them. Potential Energy Storage Elements ose elements of transport that store potential energy do so by virtue of building up an eﬀort diﬀerence that can be released to perform useful work. In these cases, ﬂow is always proportional to a time derivative of eﬀort: FLOW d dt / (cid:140)EFFORT(cid:141) (1.1) where the proportionality constant determines the speciﬁc amount of ﬂow released upon relax- ation of an eﬀort diﬀerence or the capacity of the process to perform work. As such, we term this constant the system capacity or capacitance, C. Of Special Note Energy stored by virtue of stored diﬀerences in eﬀort is potential energy. Characters that store potential energy follow the equation: FLOW C D d dt (cid:140)EFFORT(cid:141) (1.2) that deﬁnes the character’s capacitance. .. 6 1. IF YOU PUSH IT, IT WILL FLOW Recall that in electrical circuits, capacitors are system elements that store energy through voltage diﬀerences across dielectric plates. Upon discharge, a ﬂow of charge or current is released. For this process: i.t/ C dV .t/ dt D (1.3) Analogously, we may ask which system element stores potential energy in a mechanical system. We typically recall from elementary mechanics that this is a spring. Potential energy is stored by virtue of a stored eﬀort or mechanical force in the deformed spring. Recall that the force and displacement are related by Hooke’s law for simple, linear springs. F D kx (1.4) No diﬀerential relation is evident, so let’s examine our storage a bit more closely. Recall that the ﬂow variable is velocity, the time derivative of displacement. In fact, ﬂow variables are often related to conserved or balanced quantities. In mechanical systems, momentum is balanced. In systems where mass is constant, this implies that velocity is the appropriate ﬂow variable when linear momentum is conserved. Using the deﬁnition of velocity as the time derivative of displace- ment relates velocity to a time derivative of force: x.t/ (cid:29) ) 1 k F .t/ dx.t/ dt D D D 1 k dF .t/ dt (1.5) en, by analogy, the mechanical capacitance is given by the reciprocal of the spring stiﬀ- ness: CMECH 1 k D Generalizing, by analogy, a transport process exhibits a capacitance given by: C D 1 EFFORT Z .FLOW/ dt (1.6) (1.7) When the energy is stored by virtue of eﬀort, it is potential energy. Energy is given by an integral of power expended in a process. ereby, the potential energy stored in a capacitor would be given as: Z V .t/i.t/ dt D D Z (cid:18) 1 C Z (cid:18) 1 C Z i.t/dt (cid:19) i.t/ dt q.t/(cid:19) i.t/ dt Z (cid:18) 1 C D q(cid:19) dq 1 2 (cid:18) 1 C (cid:19) q2 D where the deﬁnition of current is: i.t/ D dq.t/ dt (1.8) (1.9) Once again, analogously in a mechanical system, the potential energy stored by a spring by virtue of the force within it is given as: 1.1. THE EFFORT-FLOW ANALOGY 7 Z F (cid:29) dt D Z .kx/ (cid:29) dt D Z .kx/ dx 1 2 kx2 D (1.10) You may recall from your elementary physics courses that this is the expression for potential energy in a deformed spring. To begin our energy story, any system element who stores potential energy is Captain Potential Energy. He possesses energy by virtue of eﬀort or the force contained in his springs! Figure 1.2: Captain Potential Energy stores energy by virtue of eﬀort in his compressed springs. e containment vessel for the eﬀort is the stiﬀness or capacitance. Captain Potential Energy is distin- guished by his possession of a system’s capacitance. Kinetic Energy Storage Elements ose elements of transport that store kinetic energy do so by virtue of their ﬂow variable. As a result, eﬀort diﬀerential is related to a time derivative of ﬂow: d dt Where the proportionality constant determines the speciﬁc amount of eﬀort diﬀerence required to cause the prescribed rate of change of ﬂow. is term is referred to as the system inductance, L. EFFORT (cid:140)FLOW(cid:141) (1.11) / 8 1. IF YOU PUSH IT, IT WILL FLOW Of Special Note Energy stored by virtue of stored ﬂow is kinetic energy. Characters that store kinetic energy follow the equation: EFFORT L d dt D (cid:140)FLOW(cid:141) (1.12) that deﬁnes the character’s inductance. .. Recall that in electrical circuits, inductors are system elements across whose terminals a voltage drop is related to a time rate of change of current. L d i.t/ dt V D (1.13) Analogously, we may ask which system element stores kinetic energy in a mechanical sys- tem. We typically recall from elementary mechanics that this is the mass or inertia of the system. is comes naturally from Newton’s Second Law relating the net force on a mass to its time rate of change of linear momentum. When mass is constant, the rate of change of momentum is proportional to the mass’s acceleration. F D ma m d (cid:29).t/ dt D (1.14) us, when a mass exhibits some non-zero speed, it possesses kinetic energy by virtue of its speed and in proportion to its mass or inertia. If there were no mass, there would be no entity to have speed! In this interesting way, we can learn to say that the mass stores the kinetic energy in the form of its speed. Because the mass stores the kinetic energy in a mechanical system, we can say that Generalizing, by analogy, a transport process exhibits an inductance given by: LMECH m D L D 1 FLOW Z .EFFORT/ dt (1.15) (1.16) With energy being an integral of power, we can work in terms of the ﬂow variable to deﬁne the kinetic energy: Z V .t/i.t/ dt Z (cid:18)L d i.t/ dt D (cid:19) i.t/ dt D Z .Li/ d i 1 2 Li 2 D (1.17) Once again, analogously in a mechanical system 1.1. THE EFFORT-FLOW ANALOGY 9 Z F (cid:29).t/ dt Z (cid:18)m d (cid:29).t/ dt (cid:19) (cid:29) dt D D Z .m(cid:29)/ d (cid:29) 1 2 m(cid:29) 2 D (1.18) is may look familiar to you as the kinetic energy in a moving mass.Continuing our energy story, any system element who stores kinetic energy is Captain Kinetic Energy. He possesses energy by virtue of ﬂow or the velocity associated with his mass or inertia! Figure 1.3: Captain Kinetic Energy stores energy by virtue of his speed. e containment vessel for the speed is the inertia or mechanical inductance. Captain Kinetic Energy is distinguished by his possession of a system’s inductance. So let’s remember that mathematically, both storage elements (or characters) relate ﬂow or eﬀort to the derivative of the other. Diﬀerential relations imply energy storage. Of Special Note Diﬀerential mathematical relationships for system elements imply energy storage. .. 10 1. IF YOU PUSH IT, IT WILL FLOW Dissipative Elements In dynamic transport, dissipative elements relate ﬂow and eﬀort strictly algebraically. Algebraic relations imply energy dissipation. Resistive elements, in principle, play a part in every disciplinary story. Flow experiences resistance under the action of any diﬀerence in eﬀort that drives it: EFFORT FLOW (1.19) / Here the proportionality constant determines the speciﬁc amount of resistance that must be overcome by a given net eﬀort to drive a given amount of ﬂow. is term is referred to as the system resistance, R. Of Special Note Characters that dissipate energy follow the equation: EFFORT R (cid:3) D FLOW (1.20) that deﬁnes the character’s resistance. .. where (cid:3) indicates multiplication. Figure 1.4: e Evil Dr. Friction dissipates energy as ﬂow occurs under the driver of an eﬀort dif- ference across some resistive element. e Evil Dr. Friction is distinguished by his possession of a system’s resistance to ﬂow. Recall that in electrical circuits, resistors are system elements across whose terminals a volt- age drop is proportional to the current ﬂowing through it as prescribed by Ohm’s law: 1.1. THE EFFORT-FLOW ANALOGY 11 Similarly in a mechanical system, force can be applied to produce motion by overcoming the eﬀects of friction. For example, when viscous forces oppose the motion, a good representation of the force required to overcome this resistance is given by: V iR D (1.21) where clearly, by analogy, Of Special Note F D b(cid:29) RMECH b D (1.22) (1.23) Algebraic mathematical relations imply energy dissipation. Often, these dissi- pative relations bear someone’s name, e.g., Ohm, Fourier, Newton, Toricelli, etc. .. Generalizing, by analogy, a transport process exhibits a resistance given by: EFFORT FLOW e energy “eaten by” any resistive element is equivalent to the work done by the dissipating agent, e.g., friction in a mechanical system. When energy is “eaten” it is no longer available to be stored in potential and/or kinetic forms. We say it is eﬀectively “lost.” e lost or dissipated energy is quantiﬁed by the work done by the force or eﬀort across the element: (1.24) D R Z d W dt dt D Z d W D Z (cid:0)i.t/2R(cid:1) dt D Z .V .t/i.t// dt Z V .q/ dq D Analogously in a mechanical system, the lost energy is given by: Z d W dt dt D Z d W D Z FFRICTION(cid:29) dt D Z FFRICTIONdx (1.25) (1.26) You may recall from undergraduate engineering dynamics that this expression is equivalent to the work done or energy dissipated by friction acting on a moving mass. As energy is trans- ported and exchanged between potential and kinetic forms, resistive agents essentially steal part of the transfer. ere is a balance between energy transferred and energy lost. e resistive element acts to transform energy to a form not useful by the particular system, i.e., resistors transform 12 1. IF YOU PUSH IT, IT WILL FLOW useful electrical energy to heat, a loss by-product of current ﬂow in a real circuit. Similarly, fric- tion in mechanical systems steals energy, transforming it to sound and heat, no longer useful for producing motion. e Evil Dr. Friction is the character who irreversibly robs energy in a system as it is being released from either potential or kinetic forms and in any transfer between the two. 1.1.2 THE ENERGY BALANCE PRINCIPLE In any given system, transport occurs when eﬀort drives ﬂow of some quantity. By deﬁning a control volume into and out of which ﬂow occurs, one can create a balance of any quantity, Q, by stating that QIN P QOUT (cid:0) P QSTORED D P (1.27) dQIN dt QIN D . As we will see, this simple balance principle is the precursor to every diﬀer- where P ential equation governing the transport of conserved or balanced quantities. Generally, input and output transport will require overcoming some resistance to ﬂow with the net inﬂow resulting in storage. C H A P T E R 2 13 Governing Dynamics Governing dynamics, gentlemen; it’s all governing dynamics John Nash In all of science we take certain axioms as given and proceed to model behavior from there. One such premise is that there is a collection of quantities whose behavior is governed by principles of conservation and balance. Among these are mass, momentum, energy, and electrical charge. We accept that these quantities can neither be created nor destroyed. erefore, the amount of any one of these quantities is a function of how much you begin with and how much is either transported to you or from you. ere can be external sources and sinks and repositories where the quantities can be stored. To write a statement that balances any conserved quantity at a point, we isolate an inﬁnitesimally small volume with inlet and exit windows through which our quantity of choice can be transported in and out. It is perhaps best at this point to proceed by example. In an attempt to be consistent with other treatments of the eﬀort-ﬂow analogy, let’s consider a volume, e.g., a bank vault, into which money may enter and exit through diﬀerent ports in the volume boundary, e.g., the bank doors. QIN In order to introduce the parameter of time, imagine that dollars enter the bank at a rate of P QOUT dollars dollars per day. Say a diﬀerent amount may be ﬂowing out of the bank at a rate of P per day. A balance principle is as simple as tallying how much money enters vs. how much exits. If the amount entering is greater than the amount exiting in any given interval of time, there is a net accrual and the amount of money in the bank increases over time. In other words, there is a net amount of storage of money in the bank. Contrarily, if the amount exiting exceeds the amount entering in any time interval, the amount of money in the bank will decrease. One can then conclude that the amount stored in this time interval is a negative value, i.e., there is a net QSTORED < 0 over this time interval. So the statement of balance (in rate loss of money when P form) is simply QIN P QOUT QSTORED D P In the absence of a storage mechanism, the amount of the quantity already stored in this volume remains constant and we say this quantity is conserved. When this is the case, any net inﬂow must be accompanied by an equal amount of outﬂow. (cid:0) P (2.1) 14 2. GOVERNING DYNAMICS Figure 2.1: A repository for a balanced quantity that allows inﬂow and exit from it through virtual windows and storage on the interior. 2.1 DERIVING A GOVERNING DIFFERENTIAL EQUATION 2.1. DERIVING A GOVERNING DIFFERENTIAL EQUATION 15 We will need to explore some of the more germane properties of diﬀerential equations here to establish the utility of our analogy. When we let the size of the volume into which a balanced or conserved quantity ﬂows shrink to a point, the balance or net storage principle becomes a diﬀer- ential equation governing the amount of the quantity present at that point at any given moment in time. Once again, to make the mathematics more approachable, let’s proceed by example. Let’s start with a simple story of a passive electrical circuit that contains an energy dissipator, the resis- tor, connected in series with an electrical potential energy storage device known as the capacitor as shown in Figure 2.2. At some point in time, a DC battery is connected across the circuit. In our cartoon version in Figure 2.3, Father Force represents an excitation from the outside world, an externally applied eﬀort. We can often understand system behavior by associating this force with a driving external agent from the outside world perturbing the system. Here, the agent of the outside world, the battery, imposes a voltage diﬀerence across the circuit. In our story, we call this agent of the outside world Father Force because he represents an externally applied eﬀort diﬀerence. He hurls electric charge at the circuit, our system. is electrical voltage diﬀerence drives electrical charge at some rate (known as current) through the resistor. e resistor is an energy dissipator, the Evil Dr. Friction in our cartoon. His snake “eats charge” and thus electrical energy. He steals it from the system. is electrical energy will be lost mostly in the form of heat. What is left exits the resistor and can be stored across the plates of an electrical capacitor. Here we see Captain Potential Energy as the storage agent in the capacitor. Figure 2.2: A series RC circuit as typically represented with a standard circuit diagram. A represen- tative volume element of the circuit is examined under the magnifying glass. Given that the circuit is grounded at the lower battery post, a voltage at the prescribed node represents the voltage drop across the capacitor, V1. At this point, we should point out that the system is deﬁned exclusively by the system element characters, i.e, one character that eats energy and one that stores energy. e battery is “the outside world.” is agent imposes a voltage diﬀerence on the circuit that causes current to +−V0CRV116 2. GOVERNING DYNAMICS Figure 2.3: A electrical eﬀort (voltage diﬀerence provided by a DC battery) throws charge ﬂow through a resistor, an energy dissipator, which eats part of the input charge only to have the amount that gets through be stored by a storage element or character. As the voltage diﬀerence across the capacitor grows storing electrical potential energy, the voltage drop across the resistor decreases and, along with it, the current in the circuit. ﬂow. Father Force lives in the outside world and delivers an input to the system whose characters are Captain Potential Energy and the Evil Dr. Friction! To derive any governing diﬀerential equation, we isolate a small part of the system. Con- sider a point in the circuit between the resistor and the capacitor (the node under the magnifying glass in Figure 2.2). is choice of representative volume element (RVE) is somewhat arbitrary. Since the only charge storage element in our example is the capacitor (and this character is outside of the RVE), the amount of charge per unit time (or current) ﬂowing into the node must exactly equal or balance the current ﬂowing out because there is no means by which to allow charge to accumulate on a wire alone. is concept must now be rendered mathematically. e current IN must equal current OUT or the current that passed through the energy dissipator must equal that ﬂowing into the energy storage element. Material laws usually govern the inﬂow and outﬂow of the balanced quantity. ese material laws are hypotheses based on observation and measurement [1, 2, 12, 14]. 2.1. DERIVING A GOVERNING DIFFERENTIAL EQUATION 17 QSTORED D P 0 D QOUT iC iC C d.V1 (cid:0) QIN P ) ) VO RC (cid:0) P iR (cid:0) iR D V1 (cid:0) R D V1 P C V1 D VREF / dt VO .t/ (2.2) where VO is the battery voltage and V1 is the voltage drop across the capacitor. Figure 2.4: e abstraction of the mathematical governing equation exhibits “sides” belonging to the system and the outside world which acts to excite the system into some manner of dynamic response. Because the reference voltage is chosen to be grounded, that is zero voltage, we say that this diﬀerential equation governs the voltage drop, V1 , across the potential energy storage device or capacitor. It is important to note that the resistor, capacitor, and the interior system voltage, V1, lie mathematically on one side of the equation while the driver from the outside world lies on the other side of the equation. e left side contains all system parameters and quantities while the right hand side represents a “forcing function” that drives the ﬂow. RC V1 P C V1 D VO .t/ (2.3) is will be a constant theme in our development. e movie characters and their behavior live “on the left” while the circumstances presented to them by the outside world (and to which they must respond) will lie “on the right” (see Figure 2.4). CRV1 + V1 =SystemOutsideWorld Vo•18 2. GOVERNING DYNAMICS 2.2 THE FOUR CASTS Movies are always open to being remade ... I think of it like the James Bond movies. Diﬀerent actors can play the same role. Steve Martin I think the movie business is all movies that you’ve seen before. Everything’s a remake; people want things that are familiar. Graydon Carter So the story of the evolution of quantity, Q, over time is governed by the balance QIN P QOUT QSTORED QPOTENTIAL QKINETIC STORED (cid:0) P D P Here, we must make a statement, though, that while it is allowable, there need not be two storage characters. Recall, the example given in Section 2.1 had only a potential energy storage element in its cast. So the transport processes of interest are those that contain: STORED C P D P (2.4) 1. Dissipative elements and a potential energy storage element 2. Dissipative elements and a kinetic energy storage element 3. Dissipative elements and both potential and kinetic energy storage elements 4. Both potential and kinetic energy storage elements and no dissipative elements It will turn out that systems with only one type of storage element character in their script are always governed by ﬁrst order ordinary diﬀerential equations in time. Alternatively, systems whose script contains two types of storage element will always be characterized by second order ordinary diﬀerential equations in time. ese are important characteristics to be aware of before we discuss the nature of their solutions. e focus of the analogical approach is its power in describing the similitude between systems transporting conserved quantities in four otherwise distinct disciplines of engineering. Dynamic diﬀerential equations are statements of how conserved quantities change in time. In electrical systems, we will always balance electrical charge; in mechanical systems, momentum; in ﬂuid systems, mass; and in thermal systems, heat energy. ese are summarized in Table 2.1. 2.3 SYSTEM ORDER In our analogy to a screenplay, we have limited our discussion to two scripts: those associated with ﬁrst order governing equations and those associated with second order governing equations. While it is seldom said in this way, the order of the governing diﬀerential equation is deﬁned as Table 2.1: Conserved quantities 2.4. LINEARITY 19 the diﬀerence between the highest order derivative appearing in the equation and the lowest order derivative appearing in the equation. It will be shown that the system order is the most important determinant of the system behavior. We will have more to say about this as we set about solving these equations in Chapters 5 and 6. 2.4 LINEARITY It will suﬃce to say that a diﬀerential equation is linear when the system variable and all its deriva- tives on the left side of the equation, i.e., those associated with the capacitor voltage, V1, in the example of the previous section, appear only to the ﬁrst power and there are no transcendental or trigonometric terms on the left side, e.g., exponential functions, natural logarithms, or periodic functions of the dependent variable. While analytical, functional solutions do exist for so-called nonlinear systems, they are mostly rare or diﬃcult. erefore, solutions to nonlinear systems of- ten require numerical solution techniques. Solutions to governing diﬀerential equations are the mathematical representations of physical system behavior. We will concern ourselves with linear systems only in this book. We can use the linear story to help us visualize and understand non- linear behavior once we master a linear understanding. When appropriate, we can then linearize nonlinear systems to ﬁnd a simpler story over a limited range of behavior. DisciplineConservedQuantityElectricalChargeTranslationalMechanicalLinearMomentumRotationalMechanicalAngularMomentumFluidMassThermalInternalEnergyC H A P T E R 3 e Electrical Cast 21 An electron’s journey through a circuit can be described as a zigzag path that results from countless collisions with the atoms of the conducting wire. Each collision results in the alteration of the path, thus leading to a zigzag type motion. While the electric potential diﬀerence across the two ends of a circuit encourages the ﬂow of charge, it is the collisions of charge carriers with atoms of the wire that discourages the ﬂow of charge. e Physics Classroom In Chapter 2, our example system was a passive RC circuit, a system whose script contains only two character “types”: a potential energy storage character and a dissipative character. In this system, the battery is an agent of the outside world that continually hurls charge through the resistive element that “eats charge” and turns its electrical energy to heat or thermal energy. It is important to note that the energy is not destroyed, but merely transformed to another form that is no longer available as electrical potential causing current ﬂow through the circuit. is represents a loss of so-called electrical energy to other non-useful forms (in terms of hurling electrons through the electrical circuit). e heat in a light bulb is a necessary loss incurred as current ﬂows through a resistive ﬁlament which produces heat AND light. Perhaps ironically, the light is a useful “by- product” of the circuit, but, from a purely electrical perspective, it represents a loss of electrical energy that forces the circuit to require constant energy input. 3.1 EFFORT AND FLOW VARIABLES If you push charge, it will ﬂow. e ﬂow of charge is, by deﬁnition, an electrical current. How you push charge is by creating a diﬀerence in electrical potential (or voltage). e electrical po- tential or voltage drop along a portion of a circuit drives the charge to ﬂow from higher to lower electrical potential. Electrical charge can be diﬃcult for mechanical engineers to grasp if we look at the world as driven by external forces that require contact to initiate motion. Electrical charge responds to force-at-a-distance, force ﬁelds that are many orders of magnitude larger than, say, gravitational forces in mechanical systems. e reason forces are not always seen as this large is that many, many positive and negative electrical charges end up cancelling each other out. It is only the sparse imbalances in charge that occasionally occur that tip the balance and end up cre- 22 3. THE ELECTRICAL CAST ating a diﬀerence in electrical potential. is diﬀerence is not an equilibrium state and charges tend to move to reduce this diﬀerence. So charge moves in response to the electromagnetic ﬁeld, a force felt by charge when all charges are not paired up [4]. But it is also a known condition that, like mass and energy, no one can create or destroy charge. Positive and negative charges exist. On the whole, they cannot be created or destroyed, but they can be collected in such states that diﬀerences in net amounts drive ﬂow of unlike charges toward one another. All governing equations are based on writing mathematical statements of this conservation of electrical charge. Given that charge is conserved, governing equations of motion arise out of balancing electrical “forces” that drive charge to move toward an equilibrium state. Table 3.1: Eﬀort, ﬂow, and conserved quantities for electrical systems 3.2 STORAGE ELEMENTS All such powered passive electrical circuits can, at most, contain three system element characters. Recall that two of the characters are capable of storing energy, one in the form of potential energy, the other in terms of kinetic energy. 3.2.1 POTENTIAL ENERGY STORAGE CHARACTER Potential energy storage devices store energy in the form of the eﬀort variable. e electrical cast member who plays the role of Captain Potential Energy is a device that stores a diﬀerential of electrical eﬀort or voltage. is is the capacitor. e potential energy storage character is described mathematically in the same way for every disciplinary system. e governing mathematical expression of the storage by virtue of eﬀort is FLOW iC C C D D d.EFFORT/ dt d.V1.t/ ; VREF/ (cid:0) dt ; where capacitance is measured in farads or ampere-seconds/volt A s : (cid:0) V f PD Conserved Quantity Units Symbol Charge Coulombs q Variable Units Effort Electrical Potential Voltage Volts V Flow Current Amperes i 3.3. DISSIPATIVE ELEMENTS 23 Figure 3.1: e electrical potential energy storage character is played by the capacitor. 3.2.2 KINETIC ENERGY STORAGE CHARACTER Kinetic energy storage devices store energy in the form of the ﬂow variable. e electrical cast member who plays the role of Captain Kinetic Energy is that device that stores energy by virtue of electrical ﬂow or current. is is the inductor. e kinetic energy storage character is described mathematically in the same way for every disciplinary system. e governing mathematical expression of the storage by virtue of ﬂow is EFFORT V1.t/ (cid:0) V2.t/ ; L L d.FLOW/ dt d.iL.t// dt ; D D where inductance is measured in henries or volt-seconds/ampere H (cid:1) D V s : (cid:0) A 3.3 DISSIPATIVE ELEMENTS Energy losses occur at the hand of a dissipative element or a character that “eats energy.” e role of the Evil Dr. Friction in the electrical script is played by the resistor. Recall, the governing mathematical expression of the dissipation is always algebraic rather than diﬀerential: EFFORT V1 V2 (cid:0) D D FLOW; R (cid:3) RiR; 24 3. THE ELECTRICAL CAST Figure 3.2: e electrical kinetic energy storage character is played by the inductor. Figure 3.3: e electrical energy dissipative character is played by the resistor. where resistance is measured in ohms or volts/ampere (cid:10) (cid:1) D V A : 3.4. SINGLE STORAGE ELEMENT SCRIPTS 25 Although there is no hard and fast rule about this, the mathematical expression governing en- ergy loss is very often characterized as “someone’s law.” Here, Ohm’s law governs the electrical energy dissipated in a resistor. Because dissipative elements result in energy losses, a requisite V2, is necessary to drive a current, iR, through the eﬀort diﬀerential, here the voltage drop, V1 element. (cid:0) A summary of the electrical cast and the roles they play is given in Figure 3.4 and a summary of the relevant system element relations is summarized in Table 3.2. Table 3.2: Relevant system element relations for electrical systems 3.4 SINGLE STORAGE ELEMENT SCRIPTS Recall, single energy storage scripts are capable of storing only one type of system energy, poten- tial or kinetic. When coupled with an energy dissipating agent, ﬁrst order ordinary diﬀerential equations are the result. ese ﬁrst order equations in time govern the system eﬀort and ﬂow behavior(s). For the electrical cast, the simplest examples are the series RC and LR circuits. 3.4.1 RC CIRCUITS In the case of the series RC circuit (Section 2.1), electrical energy is provided from “the outside world” by the electrical potential boost of the DC voltage source or battery. Some energy is lost through the resistor, yet enough gets through so that a potential diﬀerence or voltage builds up Field Effort Variable Flow Variable Electrical Voltage Current Relation Form Analogy Dissipative Material Property Law Effort = Resistance x Flow ()12VVRi−= Resistance = Resistance Energy Storage in Effort Variable Flow = Capacitance x d(Effort)/dt ()12dVViCdt−= Capacitance = Capacitance Energy Storage in Flow Variable Effort = Inductance x d(Flow)/dt ()12diVVLdt−= Inductance = Inductance 26 3. THE ELECTRICAL CAST Figure 3.4: e electrical cast of characters. 3.4. SINGLE STORAGE ELEMENT SCRIPTS 27 across the plates of the potential energy storage element thereby charging the capacitor through a diﬀerential of voltage or eﬀort. Recall, what results mathematically is a diﬀerential equation for the voltage stored across the capacitor plates that is linear and ﬁrst order. erefore, the resulting diﬀerential equation is written for the eﬀort variable. Figure 3.5: e electrical cast of characters playing out a series RC circuit. Here, the quantity RC possesses units of time. RC (cid:1) D RC (cid:1) D (cid:10)f; A V A s (cid:0) V s: (cid:1) D D It is known as the system time constant, RC (cid:28). Because time is the independent variable and all responses are time histories, it is of primary importance that the system is characterized by this special amount of time. Eﬀort (voltage) and ﬂow (current) will change over time. Because the time constant, (cid:28), enters the governing diﬀerential equation explicitly, it ﬂavors the entire system response. How fast or slow eﬀort and ﬂow evolve in time in the system will always be in quanta of time constants. at is, system variables will change explicitly in “chunks” of time of (cid:28) seconds. We will learn to talk in these terms. e amount of time it will take for any change to occur in a ﬁrst order system will be N time constants. e number, N , of course, will depend on what phenomenon we are discussing. We will call the time constant, (cid:28), the system parameter. It parameterizes how fast the system responds to external stimuli. Electrical systems, it turns out, are “mathematically versatile” in that the resulting ordi- nary diﬀerential equations will as often govern the behavior of the eﬀort variable, V1, as the ﬂow variable, i. e equation governing the capacitor voltage can be recast as a 1st order ordinary diﬀerential equation governing the system current, i. V1.t/ VO .t/ (cid:0) R i.t/: D RCV1 + V1 = VO (t)CRV1 + V1 =SystemOutsideWorld Vo•28 3. THE ELECTRICAL CAST Inverting the potential energy storage relation for the capacitor will give an expression for the voltage, V1.t/, which may be substituted into this relation: VO .t/ Z i.t/ C (cid:0) dt R i.t /R RC di.t/ dt C i.t / i.t / VO .t / Z i.t/ C (cid:0) dt C VO .t /; P D D D VO .t/ is an equivalent input signal current seen as a forcing function by the diﬀerential where C P equation governing the system current. It is associated with the time rate of change of the imposed battery voltage, VO .t/. It is important to note that the same system time constant, RC (cid:28), appears in and characterizes the solution(s) of both diﬀerential equations: those governing the capacitor voltage (eﬀort) and the circuit current (ﬂow)! D 3.4.2 RL CIRCUITS We might as easily let the current that passes through the resistor be stored in the form of electrical kinetic energy. e cast member that plays the character storing kinetic energy is the inductor. Figure 3.6: An electrical eﬀort (voltage diﬀerence) drives charge ﬂow through an energy dissipator, the resistor, only to have the amount that gets through be stored by a storage element or character, the inductor, in the form of the ﬂow variable. We are used to representing this system by a circuit diagram as in Figure 3.7. 3.4. SINGLE STORAGE ELEMENT SCRIPTS 29 Figure 3.7: An electrical RL circuit as typically represented. Upon applying the battery (an external voltage diﬀerence) across the circuit, charge will respond to the electromagnetic force and ﬂow through the circuit. At this point, we should point out that the system is deﬁned only by the element characters, i.e., the characters that eat energy and those that store energy. e battery is an agent of the outside world. is agent imposes a voltage diﬀerential, i.e., an imposed eﬀort, on the circuit that causes current to ﬂow. As in Chapter 2, let’s choose a node in the circuit between the resistor and the storage device, the inductor. Since the only charge storage element is the inductor (and this character is outside of the RVE), the current ﬂowing into the node must exactly balance the current ﬂowing out. is concept must now be rendered mathematically. e current that passed through the energy dissipater must equal that ﬂowing into the kinetic energy storage element. V1.t/ VO .t/ (cid:0) R iR.t/ D D iL.t/: We now introduce the relation corresponding to the storage of kinetic energy by virtue of ﬂow: V1.t/ VREF (cid:0) D V1.t/ L di.t/ dt : D Substituting for V1.t/ using the dissipation element relation: V1.t/ (cid:0) VREF V1.t/ D di.t/ L R i.t/ dt C VO .t/ (cid:0) i.t/R di.t/ dt D VO .t/: L 1 R D D is diﬀerential equation governs the circuit current, i. It is important to note at this point that all the resistance, inductance, and interior system current again lie mathematically on one side of 30 3. THE ELECTRICAL CAST the equation while the driver from the outside world, the battery voltage, lies on the other side of the equation. e left side contains all system parameters and quantities while the right-hand side represents a forcing function that drives the ﬂow. Figure 3.8: e electrical cast of characters playing out a series RL circuit. Of Special Note is will be a constant theme in our development. e movie characters and their behavior live “on the left” while the circumstances presented to them by the outside world will lie “on the right.” .. Here, the mathematical term on the right-hand side, 1 R VO .t/, is a ﬂow-like external signal input to the system supplied by the battery. 3.4.3 A GENERALIZED MATHEMATICAL FORM FOR THE SINGLE STORAGE ELEMENT SCRIPT If we observe the general nature of the governing diﬀerential equations for both the RC and RL circuits, there is a distinct one-to-one correspondence of terms. Single storage element scripts are characterized by 1st order ordinary diﬀerential equations in time. We further see that these equations can be cast in a form wherein: (a) Either the eﬀort or ﬂow variable appears isolated with a coeﬃcient of unity and (b) e coeﬃcient of the eﬀort or ﬂow derivative term (RC or L/R) has units of time 1()OLdiiVtRdtR+= •1RRVoI + I = SystemOutsideWorld LWe generalize the governing ODE for any single storage element script or 1st order system as: 3.4. SINGLE STORAGE ELEMENT SCRIPTS 31 (cid:28) d dt C (cid:9)O .t/ G (cid:3) D I .t/ D where (cid:28) is the system time constant and is either an eﬀort or ﬂow variable in the system. Here, we L=R. In general, the time constant will be some have already seen cases where (cid:28) RC and (cid:28) D function of the system element parameters, (cid:28) f .L; C; R/. e forcing function will be some D normalized form of the actual physical input excitation that renders an equivalent eﬀort or ﬂow driving function. e generalized forcing function is often represented as the actual physically imposed agent of excitation scaled by a factor called the static gain, G, where (cid:9)O .t/ I.t/. For the series RC circuit, we have the relations summarized in Table 3.3. D D G (cid:3) Table 3.3: Parts of 1st order governing diﬀerential equations for a series RC circuit While for the series RL circuit, we arrive at the results summarized in Table 3.4. Table 3.4: Parts of 1st order governing diﬀerential equations for a series RL circuit One of the most powerful aspects of the analogical approach is that when systems behave linearly, the solutions to any equation expressed in this generalized form are essentially equivalent, i.e., ALL linear ﬁrst order systems share inherent and important common characteristics in their system response to input or excitation from “the outside world.” We will examine these common characteristics in detail when we address time domain solutions in Chapter 5. Response Variable Capacitor Voltage, ()1Vt Circuit Current, ()it System Parameter RCτ= RCτ= External Excitation ()()OOtVtΨ= ()()OOtCVtΨ= G = 1;()()OItVt= G = CD1; ()()OItVt= 1 Here, we use the differential operator where, by example, for an arbitrary variable, p: dpDppdt≡≡ Response Variable Inductor Voltage, ()1Vt Circuit Current, ()it System Parameter LRτ= LRτ= External Excitation ??2 ()()OOVttRΨ= G = ?? ; ()??It= G = 1/R;()()OItVt= 2 These quantities will be asked of the reader in the Chapter Activities following this chapter. 32 3. THE ELECTRICAL CAST Of Special Note Universal Truths for 1st Order Systems (a) ey are comprised of system elements (or characters) that store ONLY ONE form of energy, either potential or kinetic forms of energy, but not both. (b) eir behavior is characterized by a single system parameter called the system time constant, (cid:28), where (c) (cid:28) D f .R; C / or (cid:28) g .L; R/ D .. 3.5 MULTIPLE STORAGE ELEMENT SCRIPTS e story changes when a system can store energy in more than one form. A more general circuit would be able to store electrical energy in both potential and kinetic forms as well as dissipate energy. e multiple storage element character script involves a capacitor, inductor, and resistor. 3.5.1 SERIES RLC CIRCUITS Such a system is characterized by system capacitance, inductance, and electrical resistance. Con- sider a circuit where these elements are connected in series. Figure 3.9: A series electrical RLC series circuit. Upon applying the battery to the circuit, current is driven in a clockwise sense around the circuit. In this script, the battery hurls charge at the resistor which “eats” a portion, allowing some residue of the charge through to the inductor and capacitor. Charge build-up across the capacitor provides a voltage drop whose time rate of change corresponds to a time rate of charge across the +−V0RV1LV2C3.5. MULTIPLE STORAGE ELEMENT SCRIPTS 33 capacitor plates. What occurs physically is that charge accumulates on one side of the capacitor. If the rate is suﬃcient to cause a rate of change of the voltage drop across the capacitor, charge at the other plate changes over time. Mathematically, at least, this dictates a current or eﬀective movement of charge. is charge then “gets a boost from the battery” and starts the process all over again. Focus on the voltage drop across the capacitor as the relevant system variable whose re- sponse we desire. Writing a current balance on node 2: QIN P (cid:0) P QOUT iL.t/ V2.t/ QSTORED iC .t/ D P D V1.t/ (cid:0) LD C d.V2.t/ (cid:0) dt VREF/ LC V2.t/ R C V2.t/ V1.t/: D D But we do not know the other system voltage, V1.t/. is is because there is now more than one way to store energy! erefore, we must investigate a second current (or charge) balance at node 1. QIN P (cid:0) P QOUT iR.t/ QSTORED iL.t/: D P D From the relation governing eﬀort and ﬂow through the resistor: and but so V1.t/ VO .t/ (cid:0) D RiR.t/ iR.t/ iL.t/ D iL.t/ iC .t/ C V2.t/ P D D V1.t/ VO .t/ RC V2.t/: P (cid:0) D Substituting this into the relation obtained at the ﬁrst node and rearranging terms: LC V2.t/ R C RC V2.t/ P C V2.t/ D VO .t/: Once again, all the system parameters .R; L; C / and a voltage internal to the system, V2.t/, are all on one side of the equation while the excitation “force” or eﬀort supplying charge to the system “from the outside world” appears on the other side of the equation. 34 3. THE ELECTRICAL CAST Figure 3.10: A series RLC electrical circuit character equation. 3.5.2 PARALLEL RLC CIRCUITS One may also investigate a branched loop over which the charge will “choose the path of least resistance,” or, more properly, the path of least impedance. e impedance is nothing more than a dynamic resistance. Using the deﬁnition of resistance as the ratio of eﬀort/ﬂow: For the inductor: For the capacitor: LDi.t/ (cid:1)V D RINDUCTOR DYNAMIC D CD(cid:1)V i D LD i.t/=CD (cid:1)V .t/ RCAPACITOR D DYNAMIC D 1=CD where, again, we are using the diﬀerential operator, D . / (cid:15) D / d . (cid:15) dt . Let’s next consider a parallel RLC circuit in Figure 3.11. 3.5. MULTIPLE STORAGE ELEMENT SCRIPTS 35 Figure 3.11: A parallel electrical RLC series circuit. Upon applying the battery to the circuit, current is driven in a clockwise sense around the circuit, but must now “choose the path of least impedance” at the branch point. Performing a charge balance over the system at internal node 1: QIN P (cid:0) P VO .t/ (cid:0) R QOUT iR.t/ V1.t/ D P D QSTORED iL.t/ V1.t/ LD C C D iC .t/ C V1.t/: P Applying the operator LD to both sides of the equation: LC V1.t/ R C L R P V1.t/ C V1.t/ L R P VO .t/: D All the system parameters .R; L; C / and a voltage internal to the system, V1 .t/, are all on one side of the equation while the excitation “force” supplying charge to the system “from the outside world” appears on the other side of the equation. In this script, the battery hurls charge at the resistor (Evil Dr. Friction). Evil Dr. Friction eats some charge allowing less out which then is stored in the system inductor (in the form of electrical kinetic energy) and/or the capacitor (in the form of electrical potential energy). How much is stored in each of these storage elements depends on their impedance or instantaneous (dynamic) electrical resistance with more energy being stored in the path with least impedance. When the storage characters dominate over friction, they will pass energy back and forth with friction eating away at each transfer. In Figure 3.13, a system imparted with potential energy +−V0CRV1L36 3. THE ELECTRICAL CAST Figure 3.12: A parallel electrical RLC series circuit character equation. (A) will pass it on to Captain Kinetic Energy. Dissipation is eating energy during this transfer as evidence by Evil Dr. Friction ﬁghting Captain Kinetic Energy (B). Dissipation continues to degrade the energy cache during each subsequent exchange back to Captain Potential Energy (C) and back to Captain Kinetic Energy (D) until all the electrical energy has been consumed. In the case where an input signal delivers energy continually to the system, eventually the amount stored in potential and kinetic forms reaches a steady state while the energy losses continue to accrue with time. V1 + V1 =SystemOutsideWorld V1+RCLVo···RLL3.5. MULTIPLE STORAGE ELEMENT SCRIPTS 37 Figure 3.13: A second order system with dissipation results in energy being “consumed” within each exchange from kinetic to potential and back to kinetic. 3.5.3 IDEALIZED LC CIRCUITS Consider the ﬁrst series RLC circuit. In the limit as the resistance vanishes, the diﬀerential equa- tion for the capacitor voltage becomes: LC V2.t/ R C V2.t/ D VO .t/: In this script, the battery provides a voltage or eﬀort diﬀerence that drives charge at the inductor. A charge diﬀerence causes a rate of change of current passing through the inductor. is process creates kinetic energy that is present in the system owing to the presence of the inductor. Be- DCBA38 3. THE ELECTRICAL CAST cause charge must be conserved, the rate of change of current in the inductor results in a charge diﬀerence across the capacitor that varies in time, i.e., changes in stored potential energy in the capacitor. Charge diﬀerences that change in time across the plates of the capacitor result in a ﬂow of charge. is charge ﬂows back to the battery for “a boost” from the “outside world.” e electrical energy is simply transferred from kinetic to potential and back with no dissipation ad inﬁnitum. We will “see” this behavior in the structure of the mathematical solutions described in Chapter 5. is system is a simple frictionless harmonic oscillator where the harmonic response occurs in the system voltage or eﬀort variable as well as the current or ﬂow variable. is is analo- gous to motion in a simple, frictionless pendulum where a similar simple harmonic motion results for the angular velocity and position (ﬂow variables). We can also show that harmonic variation also occurs in the component of the gravitational force that produces the internal torque driving the system back again. Figure 3.14: A second order system without dissipation results in energy simply being transferred between potential and kinetic forms, but otherwise being conserved in total. e simple pendulum is an analog to the LC circuit in the absence of any electrical resistance. 3.5.4 A GENERALIZED MATHEMATICAL FORM FOR THE DUAL STORAGE ELEMENT SCRIPT If we examine the governing ordinary diﬀerential equations for the system voltages in Sec- tions 3.5.1, 3.5.2, and 3.5.3, we see that dual storage element scripts are always characterized by 2nd order ordinary diﬀerential equations in time. We can further see that the resulting gov- erning diﬀerential equations can be cast in a form where: (a) the eﬀort or ﬂow variable appears isolated with a coeﬃcient of unity on “the system side” of the ODE, (b) the coeﬃcient of the eﬀort or ﬂow derivative term (RC or L/R) has units of time, and (c) the coeﬃcient of the eﬀort or ﬂow second derivative term (LC) has units of (cid:140)T (cid:141)2 3.5. MULTIPLE STORAGE ELEMENT SCRIPTS 39 One can then generalize the governing ODE for any dual storage element script or 2nd order system as: 1 !2 N d dt C 2(cid:16) !N d dt C (cid:9)O .t/ G (cid:3) D I .t/ ; D where !N is the system natural frequency, (cid:16) is the dimensionless system damping ratio, and is either an eﬀort or ﬂow variable in the system. Here, we have already seen a similar situation when the equation is 1st order. In this case, we saw the (cid:28) L=R. For 2nd order systems, there are two system parameters: the natural frequency and damping ratio will be functions of the f .L; C; R/. e forcing function will be some normal- system element parameters, ized form of the actual physical input excitation that renders an equivalent eﬀort or ﬂow driving function. e generalized forcing function is often represented as the actual physically imposed agent of excitation scaled by a factor called the static gain, G, where (cid:9)O .t/ For the second order RLC circuits, the results obtained are summarized in Table 3.5. RC or (cid:28) !N ; (cid:16) I.t/. g D D D D G (cid:3) f Table 3.5: Parts of 2nd order governing diﬀerential equations for series and parallel RLC circuits Of Special Note Universal Truths for 2nd Order Systems (a) ey are comprised of system elements (or characters) that store BOTH potential AND kinetic forms of energy (b) eir behavior is characterized by a pair of system parameters, !N ; (cid:16) f g , where (c) !N D f .L; C / and (cid:16) g .L; C; R/ D .. RLC Circuits Series Circuit Parallel Circuit Response Variable Capacitor Voltage, ()2Vt Capacitor/Inductor Voltage, ()1Vt System Parameter 1;2NRCLLCωζ== 11;2NLRCLCωζ== External Excitation ()()OOtVtΨ= ()()OOLtVtRΨ= G = 1;()()OItVt= G = LD/R; ()()OItVt= 40 3. THE ELECTRICAL CAST One of the most powerful aspects of the analogical approach is that when systems behave linearly, the solutions to any equation expressed in this generalized form are essentially equivalent, i.e., ALL linear second order systems share inherent and important common characteristics in their system response to input or excitation from “the outside world.” We will examine these common characteristics in detail when we address time domain solutions in Chapter 5. 3.6 CHAPTER ACTIVITIES Problem 1 Perform a charge balance over an appropriate circuit node in the series RC circuit in Figure 2.2 to derive a governing diﬀerential equation for the circuit’s current (ﬂow variable) instead of the circuit voltage drop across the capacitor (eﬀort variable). Problem 2 Perform a charge balance over an appropriate circuit node in the RL circuit in Fig- ure 3.7 to derive a governing diﬀerential equation for the circuit’s voltage drop (eﬀort vari- able) across the inductor instead of the circuit current (ﬂow variable). Fill in the missing normalized excitation signal input in Table 3.3. Problem 3 Recast the nodal balance over the representative circuit nodes in the series RLC circuit to derive a governing diﬀerential equation for the circuit’s current (ﬂow variable) instead of the system voltage drop across the capacitor (eﬀort variable). Problem 4 Recast the nodal balance over the representative circuit nodes in the parallel RLC circuit in to derive a governing diﬀerential equation for the circuit’s current (ﬂow variable) instead of the system voltage drop across the inductor/capacitor pair (eﬀort variable). Problem 5 Consider the series circuit for which the capacitor and resistor are swapped resulting in a series CR circuit shown here: Perform a charge balance at an appropriate node and derive the diﬀerential equation gov- erning the voltage drop across the resistor. +−V0V1CRProblem 6 An actual inductor will often contain non-negligible resistance because it is a long coiled piece of wire. For this more realistic version of the parallel RLC circuit shown here: 3.6. CHAPTER ACTIVITIES 41 perform a charge balance at an appropriate node and re-derive the governing diﬀerential equation for the voltage drop across the capacitor. Problem 7 Consider the circuit shown with parallel system capacitors. At t V0, is applied to the circuit by connecting it suddenly across a battery: D 0, a step voltage, e0 0/ D D 12 V 40 milliamps: iR.t D (a) On the circuit diagram label the relevant nodes and apply the necessary conservation principles to derive the diﬀerential equation governing the response of the voltage drop across the pair of capacitors in the circuit. +−V0CR1R2V1L+−RC1C2V1V042 3. THE ELECTRICAL CAST (b) What order is the equation? Use the potential energy storage system element equation to ﬁnd the relevant initial condition or initial conditions for the system eﬀort variable. (c) Compare the governing equation with that from the simple series RC circuit in Fig- ure 2.2. What conclusion can you draw about the eﬀective capacitance of a pair of capacitors in parallel? C H A P T E R 4 43 e Mechanical Cast A body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed. Sir Isaac Newton is transfer of knowledge from one branch of science, electrical network theory, to another branch of science dealing with mechanical structures is one of a long line of such interchanges (that are) made possible by fundamental analogies which rest ﬁnally on that fact that electrical and mechanical motions satisfy the same type of diﬀerential equations. Since these interchanges have been going on for hundreds of years, it seems worthwhile to examine their foundation and development. W.P. Mason “Electrical and Mechanical Analogies” Bell System Technical Journal In Chapter 1, we examined the concepts of eﬀort and ﬂow which continue to guide and build our analogy between diﬀerent disciplines. Recall that we posited that force acts as an eﬀort to cause motion. ereby, the ﬂow variable can be represented by either the displacement or velocity variable depending on whether one wishes to choose the motion variable or its rate of change in time as the pertinent ﬂow variable. With these choices made, rectilinear forces that act on a mass cause changes to the directional momentum of the mass. As per Newton, the net force acting on a mass equals the net change in momentum. In the absence of a net force, the linear momentum of a mass or particle is conserved. 4.1 EFFORT AND FLOW VARIABLES If you push inertia, it will ﬂow. e ﬂow of mass is, by our deﬁnition, velocity. How you push a mass is by creating a force diﬀerential or a net force across the mass. is is clearly evidenced in a free body diagram. According to Newton’s second law of motion, the net force applied to an inertial element results in a time rate of change in its linear momentum. is is a statement of the balance of linear momentum, as summarized in Table 4.1. 44 4. THE MECHANICAL CAST Table 4.1: Eﬀort, ﬂow, and conserved quantities for translational mechanical systems 4.2 STORAGE ELEMENTS It is now time to identify the mechanical cast that will play the roles of energy storage and dis- sipation in mechanical systems. Typically, the motion can be separated into translational and rotational components. ese can be analyzed separately in linear systems. 4.2.1 POTENTIAL ENERGY STORAGE CHARACTER e mechanical cast member who plays the role of Captain Potential Energy is that device that stores a force internally that may, at some later time, be released to perform useful mechanical work on the system. is potential energy storage character is played by the simple spring. Figure 4.1: e mechanical potential energy storage character is played by the spring. It embodies the mechanical capacitance of the system. Conserved Quantity Units Symbol Linear momentum kg-m/s p Variable Units Effort Force N ; lb F Flow Velocity m/s ; ft/s υ e governing mathematical expression of the storage by virtue of eﬀort is 4.2. STORAGE ELEMENTS 45 FLOW (cid:29) CMECH CMECH D D d.EFFORT/ dt d.FNET / dt : Integrating both sides over time results in an expression for the mechanical analog to an electrical system’s capacitance 1 CMECH Z (cid:29).t /dt CMECH FNET kx D 1 k : D (cid:17) 4.2.2 KINETIC ENERGY STORAGE CHARACTER Using the rate form, we address the ﬂow rate of position or velocity. e mechanical cast member who plays the role of Captain Kinetic Energy is that device that stores energy by virtue of its ﬂow or velocity. e mechanical actor who stores kinetic energy by virtue of velocity is the system’s inertia. Figure 4.2: e mechanical kinetic energy storage character is played by the system’s inertia. Inertia is embodied in a system’s mass. e governing mathematical expression of the storage by virtue of ﬂow is EFFORT FNET D D L d.FLOW/ dt d (cid:29) dt D LMECH ma: 46 4. THE MECHANICAL CAST Since this relation gives us Newton’s second law of motion, one concludes that the mechanical analog to an electrical system’s inductance is the inertia or mass of the mechanical system 4.3 DISSIPATIVE ELEMENTS LMECH m: (cid:17) e role of the Evil Dr. Friction in a mechanical script is played by the physical presence of friction. Friction, in a sense, eats energy, reducing the amount available to produce motion. Figure 4.3: e mechanical energy character that dissipates energy is played by any form of friction. Here the friction acts physically along the surface of some inertia with the ﬂoor on which it is sliding. Father Force performs work on the mass which it can store as kinetic energy of motion thwarted by the Evil Dr. Friction who eats a portion of the input work done by Father Force. e governing mathematical expression of the dissipation is always algebraic rather than diﬀerential. If we consider the source of the friction to be viscous friction as, say, would result from a thin layer of viscous oil between the box and the ﬂoor. Alternatively, the same force would result in a mechanical damper in which the same shear force is developed in a cylindrical dashpot. e viscous force resisting the relative motion of the ends of the dashpot is proportional to the relative velocity FNET b(cid:29): D 4.4. SINGLE STORAGE ELEMENT SCRIPTS 47 Figure 4.4: e friction force is modeled by the net force across a mechanical dashpot; this viscous force is proportional to the relative velocity. For many applications, a viscous representation of friction may suﬃce. e resistive eﬀort ﬂow relation is also algebraic EFFORT FNET D D R FLOW (cid:3) RMECH(cid:29): is relation dictates that the mechanical analog to the electrical system’s resistance is the viscous friction or damping coeﬃcient, b RMECH b: (cid:17) Alternatively, the friction could result from other physical sources such as dry friction, often termed Coulomb friction. Many systems, however, have friction forces that may be described as viscous-like in nature, enough so that the algebraic relation between the dissipation and ﬂow holds. A summary of the mechanical cast and the roles they play is given in Figure 4.5. A list of corresponding system element equations is given in Table 4.2. 4.4 SINGLE STORAGE ELEMENT SCRIPTS 4.4.1 SPRING-DAMPER SYSTEMS An idealized case often studied is that of the mass-less spring-damper system. is represents the bound on behavior of a system with negligible inertia that is dominated by its elasticity and friction. In the case of the spring-damper system, mechanical energy is lost through the damper while the residue is stored by virtue of a net force inside the spring. 48 4. THE MECHANICAL CAST Figure 4.5: e mechanical cast of characters. Table 4.2: Relevant system element relations for translational mechanical systems 4.4. SINGLE STORAGE ELEMENT SCRIPTS 49 Figure 4.6: An idealized mass-less spring-damper system under the inﬂuence of an externally applied force, F .t/. In order to balance linear momentum of the inertia-less plate, we perform a force balance on a representative piece of the system, i.e., the plate. For mechanical systems, this part of the system is that on which all forces act, the mass. e result is a free body diagram (FBD). Field Effort Variable Flow Variable Mechanical Force Velocity Relation Form Analogy Dissipative Material Property Law Effort = Resistance x Flow ()21Fbxx=− Resistance = Friction; Damping coefficient, b Energy Storage in Effort Variable Flow = Capacitance x d(Effort)/dt 1dFkdtυ= Capacitance = 11kstiffness= Energy Storage in Flow Variable Effort = Inductance x d(Flow)/dt dFmdtυ= Inductance = Mass/Inertia, m bkxF(t)50 4. THE MECHANICAL CAST Figure 4.7: Free body diagram (FBD) for a mass-less spring-damper system. Of Special Note Free body diagrams are the representative volume elements (RVE) for all me- chanical systems. .. Summing all forces and assuming the mass is constant: QOUT QIN P FO .t/ (cid:0) (cid:0) P kx b x P (cid:0) QSTORED D P dp dt D D m d (cid:29) dt D 0: Rearranging terms results in the diﬀerential equation governing position of the plate b x C P b x k P kx x C FO .t/ 1 k FO .t/ D D is diﬀerential equation is linear and ﬁrst order. Appealing to our analogy with electrical systems: b x k P x C D b 1 x k P x C D RMECHCMECH x x P C D 1 k FO .t/ D CMECHFO .t/ where A similar system character equation results analogous to the electrical RC circuit in Figure 4.8. RMECH CMECH b 1=k: D D F(t) kx bv 4.4. SINGLE STORAGE ELEMENT SCRIPTS 51 Figure 4.8: e mass-less spring-damper mechanical system is a purely mechanical analog to the series RC circuit as evidenced by the character equation. Unlike electrical systems, mechanical systems’ diﬀerential equations are not typically “mathematically versatile” in that they will almost exclusively appear with the ﬂow variable as the dependent variable. e equation governing the plate displacement could be re-cast in terms of the reaction force necessary to cause a given displacement, but this is often relegated to post- processing the displacement solution, i.e., one typically does NOT see diﬀerential equations for the force stored in or transmitted by the spring where force is solved as the primary variable. In most, if not all, mechanical systems, the primary solution variable is the ﬂow variable. 4.4.2 MASS-DAMPER SYSTEMS What if we wanted to examine a system that stored its energy solely in kinetic form? e alter- native two-character script with a single energy storage character would involve Captain Kinetic Energy battling the Evil Dr. Friction! Consider a parachutist diving out of an airplane and sud- denly pulling their chute cord. ey’re subject to a step input force from gravity. Father Force is instantaneously pulling them toward the Earth, as illustrated in Figure 4.9. e Evil Dr. Friction is also pushing back the parachute with a drag force due to the air in the parachute. In this case, one may argue that friction is not so evil as it ﬁghts gravity. But if we view motion of the mass as giving the system kinetic energy, then friction continues to eat that energy away from the diver. In this case, friction happens to be our friend (if we desire a safe landing), but it is still the enemy of speed. Aerodynamic drag forces are always functions of the skydiver’s downward velocity. For b1kx + x = •1kFOSystemOutsideWorld 52 4. THE MECHANICAL CAST simplicity, let’s say the drag force is linearly proportional to the velocity. We begin modeling this system with a free body diagram shown in Figure 4.9. Figure 4.9: Upon diving from an airplane, a skydiver experiences a sudden step input force exerted by gravity. e parachute provides a velocity-dependent drag force opposing the gravitational force. e net force results in the diver’s acceleration. At this point, we should point out that the system is deﬁned only by the element characters. Father Force is Planet Earth, providing a driving eﬀort that is an energy supply to the system from the outside world. Normally this energy would turn entirely into kinetic energy of the skydiver with potentially fatal results. But the Evil Dr. Friction consumes part of the energy. e rest is stored by way of velocity in the mass of the diver by Captain Kinetic Energy. Each system element character exhibits its own characteristic eﬀort-ﬂow equation. So by balancing linear momentum: QIN P QOUT (cid:0) P b D P QSTORED dp.t/ d (cid:29).t/ mg x.t/ P x.t/ P Recognizing that this diﬀerential equation is actually ﬁrst order in velocity x.t/ R x.t/ R dt D dt D mg: D D C m m m (cid:0) b m b R m b P x.t/ (cid:29).t/ x.t/ C P (cid:29).t/ C D D 1 b 1 b mg mg D D (cid:29)TERMINAL (cid:29)TERMINAL: 4.4. SINGLE STORAGE ELEMENT SCRIPTS 53 is diﬀerential equation governs the system ﬂow variable or velocity of the mass, (cid:29). e left side contains all system parameters and variables while the right-hand side represents a scaled forcing function that drives the ﬂow to its steady-state value, the so-called terminal velocity! So we don’t need to solve the equation to see where it’s heading. e equation can be written in an eﬀectively identical form to that governing the electrical RL circuit in Figure 3.10. m b d (cid:29).t / dt C (cid:29).t/ 1 b D FO .t/: is equation, in fact, takes on a form identical to the RL circuit when the analogous mechanical parameters are introduced LMECH RMECH d .FLOW/ dt C FLOW FO .t/ 1 RMECH EXTERNAL EFFORT RMECH D D FLOW SS: D Figure 4.10: e skydiving mass-damper mechanical system is a purely mechanical analog to the series RL circuit as evidenced by the character equation. 4.4.3 A GENERALIZED MATHEMATICAL FORM FOR THE SINGLE STORAGE ELEMENT SCRIPT If we observe the governing diﬀerential equations for both the spring-damper and mass-damper mechanical systems, we see that single storage element scripts are characterized by the same 1st order ordinary diﬀerential equations in time as 1st order electrical systems: (cid:28) d .t/ dt C .t/ (cid:9)O .t/ G (cid:3) D I.t/ D 54 4. THE MECHANICAL CAST where (cid:28) is the system time constant and is either an eﬀort or ﬂow variable in the system. e forcing function will be some normalized form of the actual physical input excitation that renders an equivalent eﬀort or ﬂow driving function. For the parallel spring-damper system, the ﬁrst order time constant and signal excitation are summarized in Table 4.3. Table 4.3: Parts of 1st order governing diﬀerential equations for a parallel k–b system While for the mass-damper system, an analogous set of relations is summarized in Ta- ble 4.4. Table 4.4: Parts of 1st order governing diﬀerential equations for a mass-damper system One of the most powerful aspects of the analogical approach is that when systems behave linearly, the solutions to any equation in this generalized form are essentially equivalent, i.e., ALL linear ﬁrst order systems share inherent characteristics in their system response to input or excitation from “the outside world.” 4.5 MULTIPLE STORAGE ELEMENT SCRIPTS 4.5.1 THE CLASSICAL MASS-SPRING-DAMPER SYSTEM Introducing non-negligible inertia to the platform in Section 4.3, the two-storage-element- character script now has the ability to store kinetic as well as potential energy as depicted in Figure 4.11. Response Variable Platform Position, ()xt System Parameter MECHMECHbRCkτ== External Excitation ()()OOFttkΨ= G = 1/k ; ()()OItFt= Response Variable Platform Position, ()xt System Parameter MECHMECHLmbRτ== External Excitation ()()OOFtmgtbbΨ== G = 1/b ; ()()OItFtmg== 4.5. MULTIPLE STORAGE ELEMENT SCRIPTS 55 Figure 4.11: A parallel m–k–b mechanical system. Upon applying the external force to the inertial element, ﬂow or motion of the mass is driven. Writing a linear momentum balance on the mass: QOUT QIN P FO .t/ (cid:0) kx.t/ (cid:0) P b (cid:0) x.t/ P D P QSTORED dp.t/ D dt D m d (cid:29).t/ dt D m x.t/: R Rearranging terms and normalizing the equation x.t/ P After scaling the entire equation by the stiﬀness to normalize the ﬂow variable term x.t/ R FO .t/: kx.t/ C C D m b m k R x.t/ C b k P x.t/ C x.t/ 1 k D FO .t/: Using the mechanical analogs for the electrical system element parameters LMECHCMECH x.t/ R C RMECHCMECH x.t/ P C x.t/ D 1 k FO .t/ where LMECH CMECH RMECH m 1=k b: D D D In this script, the external excitation provided by Father Force translates into a change of mo- mentum of the inertia in the system. e resistance acting against the mass in the form of the Evil Dr. Friction eats some work performed on the block with the residual work being stored as potential energy that stretches the spring and kinetic energy stored by virtue of the velocity of the mass. bkxF(t)m56 4. THE MECHANICAL CAST Figure 4.12: A classical mass-spring-damper system is equivalent to the series RLC circuit when placed in the form of a character equation. 4.5.2 IDEALIZED MASS-SPRING SYSTEMS An idealized case can be illustrated when the resistance becomes “inﬁnitesimally small” and ALL of the energy input by the driving force is stored as potential energy in the spring and kinetic energy in the mass. is is the idealized case of a system without losses. In this case: m x.t/ 1 k R LMECHCMECH C x R FO .t/ 1 k CMECHFO .t/: x.t/ x C D D In this script, the external force drives a momentum change in the mass which is slowed down by the spring opposing its motion. As the kinetic energy imparted to the mass by the force is reduced, an equivalent amount of potential energy is stored in the spring. e mechanical energy is simply transferred from kinetic to potential and back with no dissipation ad inﬁnitum. In this sense, Captain Potential Energy and Captain Kinetic Energy “have a catch” with a ball of energy while the Evil Dr. Friction gets none. is is the translational mechanical analog to the equivalent LC electrical circuit. Recall, we made an appeal to our intuition about a simple frictionless pendulum system at the end of Chapter 3. e frictionless pendulum is a rotational mechanical analog of the simple mass-spring harmonic oscillator discussed here and the idealized LC circuit of Section 3.5.3. It is now a natural excursion to relate the eﬀort-ﬂow story for such rotational mechanical systems in Section 4.6. 4.5. MULTIPLE STORAGE ELEMENT SCRIPTS 57 Figure 4.13: e simple frictionless pendulum is an analog system to the LC circuit in the absence of any electrical resistance. Table 4.5: Parts of a 2nd order governing diﬀerential equation for a classical m–k–b system 4.5.3 A GENERALIZED MATHEMATICAL FORM FOR THE DUAL STORAGE ELEMENT SCRIPT All mechanical scripts in which two distinct energy storage characters appear are always char- acterized by the same 2nd order ordinary diﬀerential equations in time as electrical 2nd order systems: 1 !2 N d .t / dt C 2(cid:16) !N d .t/ dt C .t/ (cid:9)O .t/ G (cid:3) D I .t/ D where !N is the system natural frequency, (cid:16) is the dimensionless system damping ratio, and f .L; C; R/. e dependet variable, , is either an eﬀort or ﬂow variable in the system. !N ; (cid:16) f e forcing function will be some normalized form of the actual physical input excitation that renders an equivalent eﬀort or ﬂow driving function. g D Table 4.5 summarizes the results for the second order mechanical systems discussed so far. Mechanical Systems Classical m-k-b System Response Variable Position, ()xt System Parameter ;2Nkbmkmωζ== External Excitation ()()OOFttkΨ= G = 1/k ;()()OItFt= 58 4. THE MECHANICAL CAST 4.6 ROTATIONAL MECHANICAL SYSTEMS One example is torque, moment of inertia, angular momentum, vs force, mass and momentum. e possible undistinguishability of translation and rotation would seem to indicate that they are really two guises for the same set of phenomena. e Physics Stack Exchange 4.6.1 EFFORT AND FLOW VARIABLES If you push a mass with a rectilinear or translational force, translational velocity will evolve over time as the mass accelerates. You push a mass by creating a diﬀerence in rectilinear force across the mass, i.e., applying a net force. It is precisely analogous to note that if you twist a rotational inertia, such as a massive disk, for example, it will develop an angular velocity. To do this, you need to apply a net rotational force or a net torque. All governing equations are based on writing mathematical statements of the conservation of angular momentum as summarized in Table 4.6. Table 4.6: Eﬀort, ﬂow, and conserved quantities for rotational mechanical systems So, for rotational mechanical systems, one still draws an appropriately labeled free body diagram, only now one must sum the external torques and relate this to a net change in angular momentum according to Newton’s laws. is is done in a manner strictly analogous with trans- lational mechanical systems. 4.6.2 STORAGE ELEMENTS e energy storage occurs through the same actors: springs for potential energy and masses for kinetic energy, but these must now be an angular or torsional spring, (cid:20), and a measure of inertial resistance to angular motion or a mass moment of inertia, J . Conserved Quantity Units Symbol Angular momentum kg-m2/s L Variable Units Effort Torque Nm ; ft-lb T Flow Angular velocity rad/s ω 4.6. ROTATIONAL MECHANICAL SYSTEMS 59 Potential Energy Storage Character e torsional potential energy storage devices store energy in the form of the eﬀort variable or torque. e mechanical cast member who plays the role of Captain Potential Energy is that device that stores a torque internally that may, at some later time, be released to perform useful rotational form of mechanical work on the system. is potential energy storage character is played by the torsional spring. Figure 4.14: e rotational mechanical potential energy storage character is played by the torsional spring. It embodies the rotational mechanical capacitance of the system. e mathematical expression of the storage by virtue of eﬀort is FLOW !.t/ D D CROT_MECH CROT_MECH d.EFFORT/ dt d TNET .t/ dt : Integrating both sides results in an expression for a rotational mechanical analog to electrical capacitance 1 CROT_MECH Z !.t/dt CROT_MECH D (cid:17) TNET .t/ (cid:20)(cid:18).t/ D 1 (cid:20) : Kinetic Energy Storage Character e mechanical cast member who plays the role of Captain Kinetic Energy is that device that stores energy internally by virtue of its rotational speed. is potential energy storage character is played by the rotational or mass moment of inertia. You may recall from your undergraduate dynamics course that the rotational form of New- ton’s Second Law states that a net torque applied to a system is equal to the time rate of change 60 4. THE MECHANICAL CAST Figure 4.15: e rotational mechanical kinetic energy storage character is played by the system’s rotary or mass moment of inertia. Inertia is embodied in a system’s mass weighted by the square of its distance about the axis of rotation. of the system’s angular momentum, H . e mathematical expression of the storage by virtue of ﬂow is EFFORT TNET .t/ D D L d.FLOW/ dt dH dt D d.J !.t// dt D LROT_MECH d!.t/ dt D J(cid:11).t/ J R(cid:18).t/: D Again, applying the eﬀort-ﬂow analogy, one observes that the mass moment of inertia is the mechanical analog of an electrical inductance LROT_MECH J (cid:17) (cid:17) Z r 2d m: 4.6.3 DISSIPATIVE ELEMENTS e role of the Evil Dr. Friction in our rotational mechanical script is played by any physical presence of friction about the axis of rotation. Let’s consider the source of the friction to be viscous friction as would result from a thin layer of viscous oil between two rotational elements as in a sleeve bearing. 4.6. ROTATIONAL MECHANICAL SYSTEMS 61 Figure 4.16: e friction force is modeled by the net torque across a mechanical cylindrical dash- pot; this viscous force is proportional to the relative angular velocity. For many applications, a viscous representation of friction may suﬃce. For which EFFORT TNET RROT_MECH D D (cid:17) R FLOW (cid:3) RROT_MECH!.t/ (cid:12) (cid:12)!.t/ D where (cid:12) is a torsional damping coeﬃcient relating the torque necessary to sustain an angular velocity diﬀerential across a rotational frictional element. A summary of the rotational mechan- ical cast and the roles they play is given in Figure 4.17. A list of corresponding system element equations is given in Table 4.7. 4.6.4 THE SIMPLE PENDULUM Consider the swinging pendulum shown in Figure 4.18. If we perform an angular momentum balance about the pivot point: QIN P QOUT (cid:0) P TO .t/ (cid:0) mgL sin (cid:18).t/ (cid:12) P(cid:18).t/ (cid:0) D P QSTORED dH.t/ D dt D J d!.t/ dt D J(cid:11).t/ J R(cid:18).t/: D Assuming small angles of rotation linearizes the system sin (cid:18).t/ (cid:18).t/ J R(cid:18).t/ (cid:12) P(cid:18).t/ C C ) (cid:25) mgL(cid:18).t/ TO .t/: D 62 4. THE MECHANICAL CAST Figure 4.17: e rotational mechanical cast of characters. Table 4.7: Relevant system element relations for rotational mechanical systems 4.6. ROTATIONAL MECHANICAL SYSTEMS 63 Rearranging terms and normalizing by the eﬀective torsional stiﬀness J (cid:20)EFF R(cid:18) (cid:12) (cid:20)EFF P(cid:18) (cid:18) C mgL: C (cid:20)EFF D 1 (cid:20)EFF D TO .t/ All the system parameters .J; (cid:12); (cid:20)EFF/ and a ﬂow variable internal to the system, (cid:18), are all on one side of the equation while the excitation eﬀort, now an applied torque, appears on the other side. If we scale the entire equation by the torsional stiﬀness to normalize the ﬂow variable term LROT_MECHCROT_MECH R(cid:18).t/ C RROT_MECHCROT_MECH P(cid:18).t/ (cid:18).t/ C 1 (cid:20)EFF D TO .t/: Note that while you might not see a torsional spring here, there is one! By virtue of hanging from a cable of length, L, in a gravitational ﬁeld, the mass may store maximum potential energy at the ends of each swing where height of the mass provides potential energy due to the work of the gravitational ﬁeld. Gravity is our spring! Possible sources of damping are provided by air resistance during the swing and friction at the pivot. Rotational inertia is provided by the mass being lumped a ﬁnite distance from the pivot, the center of rotation. is is illustrated in Figure 4.18. Here, Father Force provides the eﬀort or torque to drive the swinging angular motion. At the ends of the swing, all energy is potential in form. As the bob gains speed on the downswings, the system Field Effort Variable Flow Variable Mechanical Torque Angular velocity Relation Form Analogy Dissipative Material Property Law Effort = Resistance x Flow ()21Tβωω=− Resistance = Friction; Damping coefficient, β Energy Storage in Effort Variable Flow = Capacitance x d(Effort)/dt 1dTdtωκ= Capacitance = 11stiffnessκ= Energy Storage in Flow Variable Effort = Inductance x d(Flow)/dt dTJdtω= Inductance = Rotary Mass/Inertia, J 64 4. THE MECHANICAL CAST Figure 4.18: THE rotational pendulum. gains rotational kinetic energy at the expense of potential energy. All the while, the Evil Dr. Friction, acting in the air ﬂowing around the bob and in resistance at the pivot, eats away at each exchange. 4.7 CHAPTER ACTIVITIES Problem 1 It is somewhat intriguing and not often discussed what the mechanical system analo- gous to the parallel RLC circuit (discussed in Section 3.4.2) would be. Identify this mechan- ical system whose governing diﬀerential equation would be analogous with that obtained for the parallel RLC circuit. Draw the system elements and their relative connectivity and derive the governing diﬀerential equation. 4.7. CHAPTER ACTIVITIES 65 Problem 2 Consider the plate damper, mechanical system from which the spring has been re- moved. e system is turned vertically and subject to a step input gravitational force as shown: 0 m from rest, write the diﬀerential equation If the mass is dropped from the position xO D governing the system plate velocity. What order is the equation (and system)? What system parameter(s) characterize the system? Problem 3 You’re escaping the East India Trading Company in your trusty vessel “e Black Pearl.” e Pearl’s sails generate thrust in the following relationship: FSail D CS .VW Vp/ (cid:0) where VP is the velocity of the Pearl, VW is the velocity of the wind, and CS is a constant. e drag on the Pearl’s hull is linearly proportional to her velocity: where CD and the Pearl’s mass, m, are constant. FDrag D CDVP xmgTwo, thin, viscous fluid layersresulting in a total dampingcoefficient = b66 4. THE MECHANICAL CAST Use an appropriately labeled free body diagram to derive the diﬀerential equation governing the Pearl’s velocity. Determine an algebraic expression for the Pearl’s terminal, i.e., steady state, velocity. Identify the time constant, (cid:28), for the ship’s velocity response. Problem 4 Consider the mass-spring-damper system subjected to a ramp input platform dis- placement, y.t/ 5t as shown: D (a) Draw an appropriately labeled free body diagram and derive the governing diﬀerential equation for the displacement of the mass. (b) What order are the equation and the system? (c) What is/are the relevant system parameter(s)? Problem 5 Consider the downhill skier pictured here: kmxby4.7. CHAPTER ACTIVITIES 67 e total drag on the skier, FD, is a combination of man-made-snow surface resistance and * V aerodynamic drag resulting in the following relationship for the drag force: * F D CD * V is the velocity of the skier down the inclined slope, and constant. Draw an appropriately labeled free body diagram and derive the equation where CD is the coeﬃcient of drag, CD governing the skier’s velocity. Determine the relevant system parameter(s) for the model. D D Problem 6 A pressure compensating hydraulic spool valve consists of a bar-bell-like mass in a cylindrical sleeve (shown below). e valve is moved horizontally by a solenoid that applies a step input force to the mass. A spring at the far end provides an opposing force. Hydraulic ﬂuid in a tight clearance of width, h, provides a viscous friction force resisting the motion and given by the relation: where C is a constant. F(cid:29) D C (cid:29) h Show that a balance of forces in the horizontal direction gives: m d 2x dt2 D F .t/ kx (cid:0) (cid:0) C (cid:29) h : is equation physically represents a statement of what balance principle? Write algebraic expressions for the system natural frequency and damping ratio in terms of the provided quantities. 68 4. THE MECHANICAL CAST Problem 7 Consider the angular position of a 100 kg winter Olympic snowboarder on a circular pipe of radius, R. e total drag on the snowboarder, FD, is a combination of man-made- snow surface resistance and aerodynamic drag resulting in the following relationship for the * V where CD is the coeﬃcient of drag and * V is the tangential velocity * FD drag force: of the snowboarder and CD CD D constant. Use I D mR2. D Using an appropriately labeled free body diagram and applying a balance of torques, show that the diﬀerential equation governing the angular position of our snowboarder with re- spect to time is given by mR2 CDR2 P(cid:18) C If the skier could enter the pipe at an angle of 30 degrees and remain at angles equal to or lower than this, linearize the equation to obtain a linear, ordinary diﬀerential equation governing the skier’s angular position. mgR sin (cid:18) C D 0: R(cid:18) Problem 8 Consider the mass-less-platform-spring-damper system subjected to a ramp input platform displacement, y.t/ 5t as shown: D kbyx(a) Draw an appropriately labeled free body diagram and derive the governing diﬀerential 4.7. CHAPTER ACTIVITIES 69 equation for the displacement of the mass. (b) What order are the equation and the system? (c) What is/are the relevant system parameter(s)? C H A P T E R 5 A Common Notion 71 Euclid’s ﬁrst common notion is this: things that are equal to the same thing are equal to each other. at’s a rule of mathematical reasoning. It’s true because it works. Has done and always will do. Euclid says this truth is self-evident. You see … there it is, even in that 2000 year old book of mechanical law. It is a self-evident truth that things which are equal to the same thing are equal to each other. Abraham Lincoln quoting Euclid’s Book of Common Notions I understand what an equation means if I have a way to ﬁgure out the characteristics of its solution without solving it. Richard P. Feynman quoting Paul Dirac Mr. Lincoln read Euclid wisely: two things equal to the same thing are equal to each other. is basic premise lies at the notion of a common solution for linear ordinary diﬀerential equa- tions. What we will learn here is that all solutions for ﬁrst order systems look like “the same thing.” is will also hold for all 2nd order systems. In Chapters 2 and 3, we motivated the independent physical principles of inertia, stiﬀness, and friction (or alternatively inductance, capacitance, and resistance) by linking them with a cartoon-like characterization in an attempt to illustrate the analogous roles these play in mechanical and electrical systems. We further made this charac- terization to create a mnemonic device by which the abstract mathematics used to model such systems may be more approachable and less daunting. In fact, because the mathematics is essen- tially “always the same thing,” the analogy serves to teach us that there’s less to learn than we might otherwise have thought. We further associated principles of inertia, stiﬀness, and friction with their physical roles as agents of storage of kinetic energy, potential energy, and the dissipation of energy, respectively. We then followed a universal principle of balancing or conserving a basic quantity entering and leaving a volume element of the system. When we introduce mathematical relations for Captains Potential and Kinetic Energy and the Evil Dr. Friction using eﬀort and ﬂow variables, it is a relatively painless procedure to write a governing ordinary diﬀerential equation for a system. So far, the common axioms of systems in diﬀerent disciplines are: (a) Each system contains elements represented by characters that: 72 5. A COMMON NOTION (a) Store kinetic energy, e.g., inertia or inductance (b) Store potential energy, e.g., stiﬀness or capacitance (c) Dissipate energy, e.g., friction or electrical resistance. (b) e governing diﬀerential equation results from expressing conservation or balance of ele- mental quantities, e.g., momentum in a mechanical system, or change through a represen- tative electrical circuit node, and (c) Very speciﬁc and critically important quantities called system parameters arise out of various ratios, products, and sums of the system elements, e.g., (a) e time constant, (cid:28), for linear, 1st order, ordinary diﬀerential equations (b) e natural frequency, !N , and the damping ratio, (cid:16), for linear, 2nd order, ordinary diﬀerential equations. What makes these quantities so crucial is that they characterize everything interesting about the mathematical solutions. In the following sections, we will discuss and dissect these solutions for linear, ﬁrst and second order diﬀerential equations in terms of the system parameters. Re- member, the speciﬁc mathematical form of the system parameters, the time constant, natural frequency, and damping ratio, arise from the individual discipline-speciﬁc actors playing out a common movie script. 5.1 TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS Consider the movie scripts we discussed in Chapter 2 that correspond to 1st order systems. First order systems result when the script involves a single type of storage element or character (either potential or kinetic energy storage) along with dissipative elements. Note there may be multiple agents of storage, but they must store only one type of energy. So far, we’ve been introduced to: (a) A single electrical capacitor with a resistor, e.g., a series RC circuit with battery (b) A single electrical inductor with a resistor, e.g., a series RL circuit with battery (c) A single mechanical spring with a dashpot or friction element arranged in parallel, e.g., the idealized, mass-less spring-dashpot system (d) A single mechanical inertia with a friction element, e.g., the parachutist in free-fall. In all these cases, the governing diﬀerential equation has the form shown in Section 3.4.3: d .t/ (cid:28) dt C 0/ D D O .t .t/ D (cid:9) .t/ Table 5.1: Relation of the system time constant to the system element parameters 5.1. TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 73 where is either eﬀort or ﬂow that is stored in the system and the time constant, (cid:28), depends on the individual inertial, stiﬀness, or friction quantities. erefore, one needs only identify the storage and dissipative elements and their structural arrangement to conclude the relevant time constant. Recall, this is illustrated in Figure 2.4. e system response for .t/ is then driven by the system’s initial condition and the forcing function or signal input, (cid:9) .t /. For linear systems, solutions for .t/ may be obtained by either use of Laplace transforms in the complex plane or a superposition of homogeneous and complimentary solutions in the time domain. Laplace transform solutions are available in a number of good texts on systems dynamics [10, 11, 19]. For the purposes of physical interpretation, we choose here to restrict ourselves to solutions strictly in the time domain. By doing this, we hope to replace the mathematical jargon with the physical meaning underlying the math. From courses in elementary diﬀerential equations, we recall that any linear, ordinary, ﬁrst order diﬀerential equation in a single independent variable exhibits a solution that can be posed as the sum of the response, h .t/, to the corresponding homogeneous diﬀerential equation (cid:28) d h.t/ dt C h.t/ 0 D and the particular response, p .t/, to the diﬀerential equation driven by the external signal input or forcing function, (cid:9) .t/: where the total solution, via linear superposition, is given by: (cid:28) d p.t/ dt C p.t/ (cid:9) .t/ D .t/ h .t/ C D p .t/ : You probably were shown this in your earlier courses in diﬀerential equations. e homogeneous solution is often referred to as the natural or free response as this portion of the solution solves the equation where only the system parameters appear and there is no forcing function or agent of change from the outside world. Father Force is AWOL in this part of the response. It’s all System Time Constant Electrical Analogy Series RC Circuit RC Series RL Circuit L/R Massless Spring Dashpot b/k Product MECHMECHRC Freefall Parachutist m/b Ratio /MECHMECHLR 74 5. A COMMON NOTION about the system on the left side of the equation. Recall this from the illustration given by the character equation in Figure 2.4 for the RC circuit. is part of the solution prescribes how the system will react when free of external forces or inputs, i.e., how a system responds essentially to initial conditions. erefore, the natural response will be a function of the system parameters ONLY, i.e., in the case of a ﬁrst order system, the time constant, (cid:28). e portion of the solution that responds directly to the excitation from the outside world is the so-called particular solution. An agent external to the system is forcing the system to respond to it. We can understand this distinction even more clearly once we have solved both diﬀerential equations. 5.1.1 TRANSIENT RESPONSE Mathematicians postulate forms for solutions to diﬀerential equations … well, let’s face it, they guess. P.E. Wellstead Introduction to Physical System Modeling While there is, of course, more to it than that, we, as engineers, rather than mathemati- cians, are happy to take the nod on the form of the solution. Many real physical systems exhibit exponential behavior. ey can be modeled as ﬁrst order ordinary diﬀerential equations because an exponential solution works to “solve” it. D where the unknown quantity, (cid:21), results from satisfying the homogeneous form of the governing diﬀerential equation: h .t/ Ae(cid:21)t Dividing through by Ae(cid:21)t renders the characteristic equation: (cid:28)A(cid:21)e(cid:21)t Ae(cid:21)t C 0: D So solutions like h .t/ D (cid:28)(cid:21) 1 D Ae(cid:21)t work when (cid:21) C 0 (cid:21) ) D (cid:0) 1=(cid:28): 1=(cid:28). So we have D (cid:0) h .t/ Ae(cid:0) 1=(cid:28) : D e value of the constant, A, is determined by applying system’s initial conditions after the com- plete or total solution is found. e natural response is an exponential decay over the dimensionless time, t=(cid:28), and represents the part of the solution that responds to the system’s initial conditions. 5.1. TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 75 Of Special Note e free response is a response to initial conditions in the absence of any external forcing from the outside world. We can associate this response with the transient response of the system. As it is purely exponential in nature, it “dies out” in a ﬁnite amount of time we call the settling time. .. 5.1.2 FORCED RESPONSE e mathematical particular solution, p .t / , responds directly to the forcing function imposed by the outside world. e proper form for this response is a function that is, in some sense, the most general form of the function driving the system. Some familiar forms of input excitations are shown in Table 5.2. Table 5.2: General forms of particular solutions corresponding to a variety of polynomial input exci- tations We can more clearly show the physical interpretation of the forced response by performing a full solution for a few simple examples. Step Input Consider the example of the mass-less plate discussed in Section 4.3 wherein a constant force is instantaneously applied to the plate and maintained: (cid:21) for which the appropriate forced response is a constant: F0 .t/ (cid:26) 0 D P t t < 0 0 p .t/ K D D constant: Input Excitation General Form of ()ptψ Step Constant: K Ramp or Step-Ramp Linear: Ct + K Polynomial Similar Order Polynomial ()1NNptAtBtCtKψ−=++++ Harmonic ()()cosOINtAtψωα=+ Harmonic()()cospOUTtAtψωαϕ=++ Arbitrary Function Truncated Polynomial Taylor Series 76 5. A COMMON NOTION is function must now satisfy the inhomogeneous or forced version of the diﬀerential equation (cid:28) d dt .K/ C K K D D P =k P =k: So the particular solution is that amount of deformation the spring would experience under a (cid:14)STATIC. e forced system response is then simply the static purely static load P , i.e., P =k deﬂection of the spring alone. To understand this in more detail, let’s compose the total solution for the position of the plate D Ae(cid:0) t=(cid:28) P =k x .t/ x.0/ A ) D D D xh .t/ x0 x0 D (cid:0) xp .t/ P =k D C A C P =k or x.t/ .x0 (cid:0) D P =k/ e(cid:0) t=(cid:28) P =k: C Notice that since the transient, by deﬁnition, decays away at long times compared with the system time constant, (cid:28), the particular solution must represent that part of the solution that remains at long times or the steady state. is solution is shown graphically in Figure 5.1. We learn several interesting characteristics from this response that, it turns out, are char- acteristic of all ﬁrst order responses. Since for our case: x.0/ x .t 4(cid:28)/ (cid:21) 2 m x0 D P =k x.t/ .x0 (cid:0) D (cid:25) D xSS D D P =k/ e(cid:0) 12 m t=(cid:28) P =k: C P =k e response to the step input force proceeds exponentially from the initial value of 2 meters to the ﬁnal value of xSS (cid:14)STATIC in approximately four time constants. As engineers, we choose a somewhat arbitrary datum for the time at which the exponential decay is suﬃciently complete. Here, we adopt as a reference point the time by which 98% of the change from the initial value to the steady-state value takes place. is is four time constants because 98% of the exponential decay has occurred within this time frame: D D t=(cid:28) e(cid:0) 4(cid:28)=(cid:28) e(cid:0) 4 e(cid:0) D D D 0:018 0:02: (cid:25) We often refer to this regime as the transient because the plate position is changing throughout this time range. ereafter the response is in the steady-state at a value equaling that given by the static deﬂection of the spring alone because the plate is eﬀectively no longer moving and the internal force in the damper has decayed to some negligibly small value. 5.1. TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 77 Figure 5.1: e response of a mass-less plate with spring and damper to a step input force of 60 N 2 seconds. e response 10 Ns/m). e time constant is given by b=k (x0 is characterized by an exponential approach from an initial value to a ﬁnal value of (cid:14)STATIC 5 N/m; b 2 m; k P =k. D D D D D Of Special Note e forced response is a response speciﬁcally to the external forcing from the out- side world. is response is present long after the transient or free response has decayed away. For this reason, the forced response is often referred to as the steady-state response. .. When one examines these regimes along with the mathematics of the homogeneous and particular solutions, one can list several observations that are universally true for all ﬁrst order systems. 01234567891024681012Time (s)Plate Position (m)63%86.5%95%98%SteadyStateTransient78 5. A COMMON NOTION Of Special Note Observations regarding solutions to all 1st order diﬀerential equations (a) e homogenous solution responds to the initial conditions and repre- sents the mathematical structure of the physical transient from initial to steady-state values. (b) e particular solution responds speciﬁcally to the forcing function im- posed upon the system by some external agent. It is the only portion of the solution that survives after the exponential decay of the transient. As such, p .t/ represents the response of the system in steady state. (c) In the parlance of a movie script, from beginning (initial) to end (steady state) values, the transient part of the movie lasts roughly 4 time con- stants. Admittedly, this number is somewhat arbitrary and can be ad- justed to please the precision with which one needs to attain steady state. What doesn’t change is that the steady state is eﬀectively attained in quanta of time constants (d) Lastly, the entire response can be cast in dimensionless form. is is al- ways an appealing feature in predictive models because it points toward physically motivated model parameters. In this language, the steady state is generally a function of time when the input signal is time-dependent. .. To see this last point, one can reformulate the solution to take the form of a dimensionless response variable, O .t/ where .t/ O D .t/ 0 SS (cid:0) SS D (cid:0) e(cid:0)O t where t (cid:28) t O D which is plotted in Figure 5.2. Often, students will only ﬁrst see this dimensionless form of solu- tions to ﬁrst order diﬀerential equations in their undergraduate heat transfer courses. As you may SS is the not have yet had such a course, what is important to point out is that the term .t/ driving agent that causes the variable .t/ to change over time. When the variable eventually reaches its steady-state value, this driving agent vanishes and the transient is complete. So the main “take away” concept here is that the driver for dynamic response is the measure by which the current value of the variable is diﬀerent from its eventual steady-state value. It is precisely this diﬀerence in values that actually exponentially decays away in time. Because all systems, regard- less of their initial conditions or forcing function, can be cast in this form, we can refer to this dimensionless form as a master curve for ﬁrst order systems. A master curve is a function onto (cid:0) 5.1. TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 79 which all solutions fall when appropriately normalized or non-dimensionalized. Master curves are appealing in predictive mathematical modeling because of the physical interpretation given to the normalizing quantities. Here, these are the diﬀerence between the value of the dependent system variable and its eventual steady-state value, i.e., the driving force, and the system time constant. Figure 5.2: e response of a mass-less plate with spring and damper to a step input force in dimen- sionless form. e diﬀerence between a system response variable, .t/, and its value in steady state is the driver causing the dynamic response. As for most meaningful dimensionless parameters in models, .t/ represents a ratio between two physical quantities: the ratio of the current driving agent to O the initial driving agent. erefore, this particular ratio of diﬀerences always decays exponentially in ﬁrst order systems over time regimes measured in quanta of system time constants. Ramp Input We can maintain that the generalization holds when the system is exposed to a time-dependent forcing function. Consider the ramp input signal: F0 .t/ (cid:26) 0 10 t D t < 0 0 t (cid:21) 00.511.522.533.544.5500.10.20.30.40.50.60.70.80.91Dimensionless TimeDimensionless PositionSteadyState63%86.5%95%98%Transient80 5. A COMMON NOTION for which the appropriate normalized signal input in our example is F .t/=k general form of a linear function is then presumed for the particular solution: D 10t=k. e most p .t/ C t K: C D Substituting this into the diﬀerential equation and upon setting like terms equal to one another: (cid:28) C K C C C t D .10=k/t (cid:28) C K C C C t C 0 K D D D .10=k/t 10=k C (cid:28) K C C (cid:28) D (cid:0) D 10 (cid:0) k (cid:28) or p .t/ 10 k (cid:28) C 10 k t D 10 k D (cid:0) (cid:28) / : .t (cid:0) It is important to note that while the forcing function is a straight line with zero intercept the eventual steady-state solution has an intercept. is implies there is an oﬀset in time between the forcing function and the steady response. is steady solution given by p .t/ (cid:28)/ is the straight dotted line in Figure 5.3. 10 k .t D (cid:0) Compiling the total solution and applying the initial conditions: x .t/ x.0/ x.t/ D D D xh .t/ x0 D .x0 C xp .t/ D 10(cid:28)=k C A (cid:0) 10(cid:28)=k/ e(cid:0) t=(cid:28) Ae(cid:0) 10.t C (cid:0) (cid:28)/=k t=(cid:28) 10.t C (cid:0) (cid:28)/=k which is plotted in Figure 5.3 for several distinct initial displacements along with the asymptotic steady-state line. 5.1.3 DIMENSIONLESS SOLUTIONS FOR 1st ORDER SYSTEMS We note that even when the steady state is time-dependent, the entire response can still, for every ﬁrst order system, be cast in dimensionless form: .t/ O D .t/ 0 SS .t/ (cid:0) SS .0/ D (cid:0) e(cid:0)O t where t (cid:28) : t O D is dimensionless solution is plotted in Figure 5.4. Note the form is identical with that in Fig- ure 5.2. 5.1. TIME DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 81 Figure 5.3: e response of a mass-less plate with spring and damper to a step input force in dimen- sional form. e response is characterized by an exponential approach or transient from an initial value to a ﬁnal value that, like the forcing function, increases linearly in time. 5.1.4 UNIVERSAL TRUTHS FOR 1st ORDER SYSTEM RESPONSE IN THE TIME DOMAIN We can now add several observations to our list of universal truths that always characterize how 1st order systems respond to their environment. We note that 1st order systems always approach a steady-state response monotonically from their initial condition, and the response never over- shoots this steady response. e steady response behaves like “a fence” that bounds the total response. is total response approaches the steady solution “from one side” where the initial conditions reside, as observed in Figure 5.3 for the ramp input example. We also note that even when the steady-state solution is time-dependent, the appropriate non-dimensionalization de- livers a master curve that is identical for all initial conditions, or starting points, and steady-state solutions or ending points as shown in Figure 5.4. 012345678910-20-15-10-505101520Time (s)Platform Position (m)TransientSteady State82 5. A COMMON NOTION Figure 5.4: e response of a mass-less plate with spring and damper to a ramp input force in dimen- sionless form. Of Special Note Universal Truths for 1st Order Systems (a) ey are comprised of system elements (or characters) that store only a single form of energy, either potential or kinetic energy (but not both). (b) eir behavior is characterized by a single system parameter called the system time constant, (cid:28), where f1 .R; C / (cid:28) D D f2 .b; k/ or (cid:28) g1 .L; R/ D D g2 .m; b/ : (c) e system is identiﬁed with one characteristic time given by the time constant. (d) e system transient decays away in a multiple number of system time constants. (e) e system response approaches steady state monotonically from one side. (f ) e system is never capable of overshooting the eventual steady-state response. (g) e system response can be universally placed in a dimensionless form normalized by the driving agent (cid:0) SS, and the characteristic time constant, (cid:28). .. 00.511.522.533.5400.10.20.30.40.50.60.70.80.91Dimensionless TimeDimensionless Position5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 83 5.2 TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS Again, as discussed in detail in Chapter 2, 2nd order systems result when the script involves both distinct types of storage character, i.e., both potential and kinetic energy storage. Note there may be multiple agents of storage, but they must be capable of storing both types of energy. So far, we’ve been introduced to: (a) An electrical capacitor and inductor with a resistor, e.g., series or parallel RLC circuits with an external passive power supply, i.e., battery. (b) An electrical capacitor and inductor with no systemic damping, e.g., a series/parallel LC circuit with an external passive power supply, i.e., battery. (c) A mass with mechanical spring and dashpot connected in series or parallel, e.g., the ideal- ized, mass-spring-dashpot system. (d) An idealized, undamped mass-spring harmonic oscillator. In these cases, the normalized governing diﬀerential equation has the form: 1 !2 N d 2 .t/ dt2 C 2(cid:16) !N d .t/ dt C .t/ D (cid:9) .t/ where reresents the dependent eﬀort or ﬂow variable in the system and the system is charac- , where each terized by a pair of parameters: the damping ratio and natural frequency, depends on the individual inertial, stiﬀness, or friction quantities. Examining the systems in Sec- tions 3.5 and 4.5, we arrived at the results summarized in Table 5.3. (cid:16); !N g f When viewed from the perspective of the eﬀort-ﬂow analogy with electrical systems, i.e., considering the system damping ratio and natural frequency, a parallel mass-spring-damper sys- tem should behave similarly to the series RLC circuit (see Table 5.3). erefore, one need only identify the storage and dissipative elements and how they are structured in the system to know that the relevant natural frequency and damping ratio are particular products and/or ratios of the respective system element parameters. Recall, this is illustrated in Tables 3.3 and 3.4 for 1st order electrical systems. e system response for .t/ is driven by one or both of the system’s initial conditions and the forcing function or signal input, (cid:9) .t/. e corresponding transient and steady-state parts of the solution satisfy: and 1 !2 N d 2 h.t/ dt2 C 2(cid:16) !N d h.t/ dt C h.t/ 0 D 1 !2 N d 2 p.t/ dt2 C 2(cid:16) !N d p.t/ dt C p.t/ (cid:9) .t/ D 84 5. A COMMON NOTION Table 5.3: Analogous representations for system natural frequency and damping ratio respectively, where the total solution, via linear superposition, is given by: .t/ h .t/ C D p .t/ : e transient response will be a function of the system parameters only, i.e., the system natural frequency, !N , and system damping ratio, (cid:16), and is that portion of the solution that responds directly to the initial conditions. e portion of the solution that responds directly to the excitation from the outside world is the particular solution, p .t/. 5.2.1 FREE RESPONSE Similar to ﬁrst order equations, exponential functions also satisfy the second order equation: where the unknown exponents result from satisfying the ODE: h .t/ D Ae(cid:21)t 1 !2 N A(cid:21)2e(cid:21)t 2(cid:16) !N C A(cid:21)e(cid:21)t Ae(cid:21)t 0: D C Dividing through by Ae(cid:21)t renders the characteristic equation for the ODE: 1 !2 N (cid:21)2 C 2(cid:16) !N (cid:21) 1 C D 0 ) two solutions, (cid:21)1;2: Because this equation is quadratic, it exhibits two roots, (cid:21)1;2. Depending on the sign of the dis- criminant, pairs of roots to this equation correspond to three distinctly diﬀerent physical regimes of behavior as in Table 5.4. System Natural Frequency (rad/s) Electrical Analogy Damping Ratio Electrical Analogy Series RLC Circuit 1NLCω= 2RCLζ= Parallel RLC Circuit 1NLCω= 12LRCζ= Parallel Mass-Spring-Damper Nkmω= 1NMECHMECHLCω= 2bkmζ= 2MECHMECHMECHRCLζ= Parallel Mass-Spring Nkmω= 1NMECHMECHLCω= 0ζ= 0ζ= Table 5.4: e three physical scenarios for transient solutions of second order systems 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 85 Underdamped Systems For the ﬁrst scenario, the system is under-damped. Mathematically, these result when the damp- ing ratio, (cid:16), is less than one. Physically, this happens when elasticity and inertia dominate friction b=2pkm. If the stiﬀness and inertia, pkm dominate in a system (see Figure 5.5). Recall, (cid:16) relative to dissipation, b, then (cid:16) < 1. Energy storage, in some sense, is strong enough to overcome energy dissipation allowing for a transfer back and forth between potential and kinetic forms of energy in the system. D Figure 5.5: Strength of energy characters in an under-damped 2nd order system. is is rendered mathematically by the solutions of the characteristic equation. e tran- sient solution is given by: h .t/ D C1e(cid:21)1t C2e(cid:21)2t C where C1 and C2 are constants to be determined later by imposing the initial conditions. When the roots are complex, they contain a negative real portion corresponding to the exponential de- cay caused by the energy dissipating character, and a purely imaginary portion that corresponds to a harmonic oscillation that occurs “inside the decaying envelope” of the exponential part of the solution. ese are the energy storage characters transferring energy back and forth between Scenario ζ Nature of roots Roots Physical Regime 1 1ζ< Pair of complex conjugate roots 21,21NNjλζωωζ=−±− Under Damped 2 1ζ= Pair of two real, equal roots 12Nλλζω==− Critically Damped 3 1ζ> Pair of two real, distinct roots 21,21NNλζωωζ=−±− Over Damped 86 5. A COMMON NOTION potential and kinetic forms. Algebraic manipulation results in a solution of the form h .t/ D e(cid:0) (cid:16)!N t (cid:140)A cos .!d t/ B sin .!d t/(cid:141) C (cid:0) D !N p1 (cid:16)2 is the damped natural frequency, and A and B are constants determined where !d by applying the initial conditions. e system will oscillate in the transient with this characteristic frequency in the presence of energy dissipation. And the natural response decays away exponen- tially in a time frame prescribed by the system damping ratio and natural frequency. ere is no time constant, per se, for a second order system. e constants, A and B, are determined by applying the system’s initial conditions. e under-damped transient response is an exponentially decaying harmonic that decays over the dimensionless time, t=.1=(cid:16)!N /. t O D Of Special Note It is interesting to note that while resistance is fairly straightforward to quantify in electrical systems, damping coeﬃcients in mechanical systems have a somewhat higher degree of uncertainty associated with them. You will not ﬁnd a value for the damping coeﬃcient stamped on the container for a damping element. Friction always has an inherent uncertainty about its actual mathematical representation. Because of this, and because it is the damping ratio, (cid:16), and not the damping coeﬃcient, b, that matters in our solutions, we point out that there is a straightforward way to determine the damping ratio directly from experimental data. For this purpose, imagine that you perturb an under-damped second order system from rest with an initial displacement and let the system’s free response decay away from the rest. It is easy to show that the ratio of successive peaks is given by: xN 1 C xN D (cid:16) !N Td e(cid:0) ln (cid:18) xN C xN 1 (cid:19) (cid:14) (cid:17) D (cid:16)!N Td 2(cid:25)(cid:16) D p1 (cid:0) : (cid:16)2 ereby, the log decrement, (cid:14), a quantity readily measured from experiment, is a func- tion solely of the system’s damping ratio. Inverting this relation (cid:16) D (cid:14) p4(cid:25) 2 : (cid:14)2 C So the damping ratio is easily determined by measuring the log decrement, (cid:14), or loga- rithm of ratios of successive peaks. e damped period of the free decaying oscillation is also easy to measure. With the period known, it is straightforward to compute the .. system’s natural frequency: 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 87 !N D 2(cid:25)=Td p1 (cid:16)2: (cid:0) So the system parameters can be computed directly from simple experimental measure- ments. .. Critically Damped Systems e second scenario is basically a fence between the 1st and 3rd scenarios. e system is called critically damped. Physically, this corresponds to a system where the energy storage and dissipa- 2pkm (see Figure 5.6). e ability of the system’s tion “have equal strength,” if you will, and b elasticity and inertia to store potential and kinetic energy, respectively, is “equal,” in some sense, to the ability of the system to dissipate energy. Energy storage, then, just rivals energy dissipation. In this limit, there is just enough friction or dissipation to prevent anything other than a single transfer of energy between the kinetic and potential forms. As such, there is suﬃcient enough energy dissipation to just prevent oscillatory response from occurring. D Figure 5.6: Strength of energy characters in a critically damped 2nd order system. e solutions contain two negative, equal real parts, (cid:21)1 (cid:16)!N , corresponding to the exponential decay caused by the energy dissipating characters. e transient solution is given by: D (cid:0) (cid:21)2 D D (cid:21) h .t/ C1e(cid:21)t C2te(cid:21)t C1e(cid:0) (cid:16)!N t C2te(cid:0) (cid:16)!N t : D C D e constants, C1 and C2, are determined by the system’s initial conditions. e critically damped t=.1=(cid:16)!N /. As transient response is a pure exponential decay over the dimensionless time, we will soon observe, this decay is the fastest decay that does not allow for oscillatory behavior in the transient. is makes the critically damped response case an important limit solution for engineering design as there are a number of physical situations in which one desires as fast a decay C D t O 88 5. A COMMON NOTION as possible without oscillation from a given prescribed set of initial conditions, e.g., response of a mass-spring-damper automobile strut to an imposed initial compression. Overdamped Systems Physically, the ﬁnal scenario corresponds to a system where the energy dissipation dominates the response at the expense of the ability of the system’s elasticity and inertia to store potential and kinetic energy respectively. Mathematically, b > 2pkm (cid:16) > 1. In this limit, there is more energy dissipation than is necessary to prevent oscillatory response from occurring (see Figure 5.7). ) Figure 5.7: Strength of energy characters in an overdamped 2nd order system. is is rendered mathematically by the solutions of the characteristic equation: two nega- !N p(cid:16)2 tive, and distinct real parts, (cid:21)1;2 1 corresponding to two distinct rates of exponential decay caused by the energy dissipating characters. e transient solution is given by: (cid:16)!N D (cid:0) (cid:6) (cid:0) h .t/ D C1e(cid:21)1t C2e(cid:21)2t C D (cid:16) (cid:0) C1e (cid:16)!N C !N p(cid:16) 2 1(cid:17)t (cid:0) (cid:16) (cid:0) C2e (cid:16) !N (cid:0) !N p(cid:16) 2 1(cid:17)t : (cid:0) C e constants, C1 and C2, are determined by the system’s initial conditions. e critically damped transient response is a pair of pure exponential decays over two distinct dimensionless times: t1 O D t= (cid:16)1= (cid:16) (cid:0) (cid:16)!N C !N p(cid:16)2 (cid:0) 1(cid:17)(cid:17) and t2 O D t= (cid:16)1= (cid:16) (cid:0) (cid:16)!N (cid:0) !N p(cid:16)2 1(cid:17)(cid:17) : (cid:0) e over damped response is identiﬁed by two physical time scales for decay: (a) one decay time that is larger than that in the critically damped case (b) a distinct second decay time that is smaller than that in the critically damped case. us, superposing both solutions results in an overall decay time longer than that observed in the critically damped case. e more damping or friction added to a system beyond this limit, the slower the decay to steady state. 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 89 5.2.2 FORCED RESPONSE e handling of the mathematical particular solution, p .t/, is no diﬀerent than that for 1st order systems. e solution to the inhomogeneous diﬀerential equation responds directly to the forcing function. e form for this response is the most general form of the function driving the system as outlined in Table 5.2. Again, the physical interpretation of the forced response is best shown by performing several simple examples. Step Input to an Underdamped System Consider the example of the parallel mass-spring-damper discussed in Section 4.4 wherein a constant force is instantaneously applied. e classic step input signal is simply a constant input suddenly applied: for which the appropriate forced response is F0 .t / D (cid:26) 0 P t t < 0 0 (cid:21) is function must now satisfy the inhomogeneous or forced version of the ODE p .t/ K D D constant: 1 !2 N K R C 2(cid:16) K !N P C K K D D P k P =k D (cid:14)STATIC: e forced system response is then simply the static deﬂection of the spring alone. To understand this in more detail, let’s compose the total solution for the position of the plate x .t/ D xh .t/ C xp .t/ D e(cid:0) (cid:16)!N t (cid:140)A cos .!d t/ B sin .!d t/(cid:141) P =k: C C Applying the initial conditions: x.0/ x.0/ P D D x0 (cid:29)0 ) ) A B D D x0 (cid:29)0 (cid:0) C P =k (cid:16)!N .x0 !N p1 P =k/ : (cid:0) (cid:16)2 (cid:0) Finally, upon substitution (cid:16)!N t " x.t/ e(cid:0) D .x0 (cid:0) P =k/ cos .!d t/ (cid:29)0 C C (cid:16)!N .x0 !N p1 (cid:0) P =k/ (cid:0) (cid:16)2 # sin .!d t/ P =k: C is solution is shown graphically in Figure 5.8 for several sets of initial displacements. is response exhibits several features characteristic of all under-damped 2nd order re- sponses: an exponentially decaying, oscillatory, harmonic response that overshoots the eventual 90 5. A COMMON NOTION Figure 5.8: e response of a lumped mass with parallel spring and damper to a step input force of 60 N (x1;2;3 10 Ns/m). e response is characterized by a decaying oscillation from an initial value that overshoots its steady-state value. It oscillates about and ultimately decays to the steady-state value of (cid:14)STATIC 2 m, 8 m, 14 m; (cid:29)0 5 N/m; b 0 m/s; k F0=k. D D D D 0 D steady-state solution at xSS (cid:14)STATIC. is eventual steady state is then reached in ap- proximately four characteristic decay times parameterized by !N , and (cid:16). is is the transient regime where the response is characterized by two characteristic times: the decay time of the envelope bounding the oscillations and the period of the oscillations as outlined in Table 5.5. F0=k D D Table 5.5: Characteristic transient time scales for under-damped second order systems Following the exponential decay, the response is in the steady state at a value equaling that given by the static deﬂection of the spring alone because the inertial mass is eﬀectively no longer moving and the internal force in the damper has decayed to some negligibly small value. Again, precisely as for ﬁrst order systems, we observe characteristics common to the solutions of all 2nd order systems. 0102030405060708024681012141618Time (s)Position (m)Solution Feature Characteristic Time Exponential decay 1Nζω Period of damped harmonic response 2221dNππωωζ=− 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 91 Of Special Note Observations regarding solutions to all 2nd order diﬀerential equations (a) e homogenous solution responds to the initial conditions and represents the mathematical structure of the physical transient from initial to steady-state values. (b) e particular solution responds speciﬁcally to the signal input or forcing function imposed upon the system by some external agent, i.e., the outside world. It is the only portion of the solution that survives after the exponential decay of the transient. As such, p .t / represents the response of the system in steady state. (c) In the parlance of a movie script, from beginning (initial) to end (steady-state) values, the movie lasts eﬀectively 4 characteristic decay times as prescribed in Ta- ble 5.5. So the steady state is eﬀectively attained in quanta of exponential decay times. (d) Lastly, the entire response can, for every second order system, be cast in dimen- sionless form. .. To see this last point, one can reformulate the solution to take the form of a dimensionless response variable, O .t/ where .t/ O D .t/ 0 SS (cid:0) SS D (cid:0) Ge(cid:0)O t1 cos 2(cid:25) t2 O (cid:0) tan(cid:0) )! 1 ( (cid:16).(cid:17) p1 1/ (cid:16)2 C (cid:0) (cid:0) C s 1 2(cid:17)(cid:16)2 1 (cid:29)0 (cid:16)!N .x0 (cid:0) t= .1=(cid:16)!N / t= .2(cid:25)=!d / G (cid:17) t1 O t2 O D D D D (cid:17)2(cid:16)2 C (cid:16)2 xSS/ t=Td D which is plotted in Figure 5.9. Because all systems, regardless of their initial conditions or forcing function, can be cast in this form, we can refer to the function in Figure 5.9 as a master curve for under-damped second order systems. e diﬀerence between the current system response variable, .t/, and its value in steady .t/ represents the ra- state is the driver causing the dynamic response. In dimensionless form, O tio of the current driving agent to the initial driving agent. e master curves are representative for any initial displacement, any set of system parameters for which the system remains under- damped, and any step input force. is master representation shows explicitly that with a suﬃcient 92 5. A COMMON NOTION Figure 5.9: e response of a lumped mass with parallel spring and damper to a step input force from rest. e curves that are distinct in Figure 5.5 all collapse to the same curve (Curve 1). e rest of the curves correspond to increasing amounts of viscous damping in the system. amount of damping, any second order system’s response will be nearly indistinguishable from a corresponding ﬁrst order-like response. Further, since there are two initial conditions necessary for second order systems, there xSS/ such that the response is (cid:16)!N .x0 is a natural scaling of the initial velocity with (cid:29) (cid:3) D characterized by a dimensionless form of the initial velocity: (cid:0) (cid:29)0 O D (cid:29)0=(cid:29) (cid:3) D (cid:29)0=(cid:16)!N .x0 xSS/ : (cid:0) e response of the original system is plotted in dimensionless form for a variety of initial velocities in Figure 5.10. Ramp Input to an Over-damped System We can maintain that the generalization holds when the system is exposed to a time-dependent forcing function. Consider the ramp input signal: F0 .t/ (cid:26) 0 Dt D t < 0 0 t (cid:21) : e most general form of a linear function is then presumed for the particular solution: p .t/ K D C C t: 00.511.522.533.54-0.6-0.4-0.200.20.40.60.81Dimensionless Decay TimeDimensionless PositionIncreasing damping ratio First order-like responseCurve 15.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 93 Figure 5.10: e response of a lumped mass with parallel spring and damper to a step input force for a variety of initial velocities. Substituting this into the diﬀerential equation and setting like terms equal to one another: 1 !2 N .0/ C 2(cid:16) !N C K C C C t ) C 0 K Dt k D=k K C 2(cid:16) !N C D D D .2(cid:16)=!N / D (cid:0) D k or p .t/ 2(cid:16) !N D k C D k t D (cid:18)t D k (cid:0) (cid:19) : 2(cid:16) !N D (cid:0) Compiling the total solution and applying the initial conditions: x .t/ D D xh .t/ xp .t/ C (cid:16)!N (cid:16) C1e (cid:0) !N p(cid:16) 2 1(cid:17)t (cid:0) C C (cid:16) (cid:0) C2e (cid:16)!N (cid:0) !N p(cid:16) 2 1(cid:17)t (cid:0) D k .t (cid:0) C .2(cid:16)=!N // : Applying initial conditions: x.0/ x.0/ P D D x0 x0 ) ) x0 x0 D D C1 C C1 (cid:16) C2 (cid:0) (cid:16)!N (cid:0) 2D(cid:16)=k!N !N p(cid:16)2 1(cid:17) (cid:0) C C2 (cid:16) (cid:0) (cid:16)!N (cid:0) !N p(cid:16)2 C 1(cid:17) (cid:0) C D k : 00.511.522.533.54-0.6-0.4-0.200.20.40.60.81Dimensionless TimeDimensionless Position0.81Dimensionless TimeDimensionless Position94 5. A COMMON NOTION Figure 5.11: e response of an over-damped mass-spring-damper system to a ramp input force in dimensional form. e response is characterized by an exponential approach or transient from an initial value at rest to a ﬁnal value that, like the forcing function, increases linearly in time. Figure 5.12: e response of an overdamped mass-spring-damper system to a ramp input force in dimensional form. With increasing values for the damping ratio, the response eventually appears ﬁrst- order-like. 0510152025303540-300-200-1000100200300400Time (s)Position (m)Steady State01020304050607080-400-2000200400600800Time (s)Position (m)1020200Time (s)Position (m)Increasing damping ratio5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 95 After resolving the values of C1 and C2, we plot the total response in Figure 5.3 for several distinct initial displacements. As for the under-damped case, systems with increasing damping ratios eventually respond in a manner that “looks” ﬁrst-order-like (see Figure 5.12). Finally, solving the constants C1 and C2 for various initial velocities gives the responses shown in Figure 5.13. Figure 5.13: e response of an overdamped mass-spring-damper system to a step input force for various values of the initial velocity. 5.2.3 DIMENSIONLESS SOLUTIONS FOR 2nd ORDER SYSTEMS Again, even when the steady state is time-dependent, the entire response can still, for every second order system, be cast in dimensionless form: .t/ O D .t/ 0 SS .t/ (cid:0) SS .0/ D = (cid:0) t1; (cid:0)O t2(cid:1) O D 8 (cid:136)< (cid:136): e(cid:0)O t1 (cid:2)A cos (cid:0)2(cid:25) t Ae O t1 Ae(cid:0)O t2(cid:1) O C C t2(cid:1)(cid:3) O B sin (cid:0)2(cid:25) C t B te O O t2 Be(cid:0)O (cid:16) < 1 (cid:16) 1 D (cid:16) > 1 where the respective characteristic times are given in Table 5.6. ese solutions for the under and overdamped systems, respectively (in Section 5.2.2) are plotted in dimensionless form in Figure 5.14. Note the limit behaviors of under-damped and damped systems. 0510152025303540-150-100-50050100150200250300350Time (s)Position (m)96 5. A COMMON NOTION Figure 5.14: e response of a mass-spring-damper to an arbitrary input force in dimensionless form. 5.2.4 CHARACTERISTIC TIMES FOR TRANSIENTS IN 2nd ORDER SYSTEMS e characteristic time for transients in any ﬁrst order system corresponds directly with its system parameter, (cid:28). Alternatively, the characteristic times associated with the transient response in 2nd order systems are functions of its system parameters as outlined in Table 5.6. 5.2.5 UNIVERSAL TRUTHS FOR 2nd ORDER SYSTEM RESPONSE IN THE TIME DOMAIN We can now add several observations to our list of universal truths that always characterize how 2nd order systems respond to their environment. We note that 2nd order systems always ap- proach a steady-state response from their initial state, and the response overshoots this steady re- sponse for under-damped systems and does not overshoot for over-damped systems. e steady response behaves like “a fence” that bounds the total response only when the system is over- damped. is over-damped response approaches the steady solution “from one side” as observed in Figure 5.11 for the ramp input example. We also note that even when the steady-state so- lution is time-dependent, the appropriate non-dimensionalization delivers a master curve that is identical for all initial conditions, i.e., starting points, and steady-state solutions, i.e., ending points. 00.511.522.533.54-0.6-0.4-0.200.20.40.60.81Dimensionless TimeDimensionless PositionOverdamped systemUnderdamped systemTable 5.6: Characteristic times for transient solutions of second order systems 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 97 Of Special Note Universal Truths for 2nd Order Systems (a) ey are comprised of system elements (or characters) that store both potential and kinetic forms of energy !N ; (cid:16) f g g2 .m; k; b/ (b) eir behavior is characterized by a pair of system parameters, , where (c) !N D f1 .L; C / D f2 .m; k/ and (cid:16) g1 .L; C; R/ D D (d) e system transients are identiﬁed by two characteristic times (e) e system, when underdamped, is capable of overshooting the eventual steady- state response. (f ) With an appropriate amount of damping, the system response is nearly indistin- guishable from that of an appropriately parameterized ﬁrst order system (g) e system response can be universally placed in dimensionless form, normalized by two characteristic times. .. Scenario ζ Physical Regime Characteristic Times 1 1ζ< Under Damped 1Nζωexponential decay 221Nπωζ− damped period 2 1ζ= Critically Damped 1Nζωexponential decay 3 1ζ> Over Damped ()211NNζωωζ+− first exponential decay ()211NNζωωζ+−− second exponential decay 98 5. A COMMON NOTION 5.2.6 ENERGY STORAGE AND DISSIPATION FOR 2nd ORDER SYSTEM RESPONSE IN THE TIME DOMAIN Let’s continue with the example of the mass-spring-damper system. e system stores both ki- netic and potential energy. Now that we have resolved the resultant motion and velocity of the lumped mass analytically in Section 5.2.2, we may compute the energy partition that results from an imposed step input force applied to the mass when the system is underdamped (Figure 5.15). e early transient behavior shows clearly that peak potential energy caches coincide with the absence of kinetic energy when the mass is at rest at peak values of displacement as shown in Figure 5.16. Behavior in the steady state shows the continued decay to a state of steady potential energy corresponding to the spring extended to its static deﬂection where motion ceases and kinetic energy decays to zero as shown in Figure 5.17. All the energy is eventually stored in the spring as the displacement converges on the static value. All the while, an order of magnitude more energy is dissipated in the damper throughout the transient as evidenced in Figure 5.18. Note that the dissipated energy only ever increases. e work done by friction, as plotted in Figure 5.18, can never decrease and only ever accumulates. is is perhaps more evident in an under-damped system that is given an initial displace- ment and released from rest. Here the entire response is simply a transient decay from the initial conditions. Recall from our discussion in Chapter 3 that in this case of a damped harmonic os- cillator, the kinetic and potential caches are passed back and forth to one another while friction eats away during each transfer as shown in Figure 5.19. e energy story for each of the three characters (inertia, stiﬀness, and friction) is shown for a typical case in Figure 5.20. In the resulting free response, energy is “consumed” within each exchange from kinetic to potential and back to kinetic. With each “pass of the energy ball” the total amplitude of stored energy is decreased by precisely the amount eaten away by friction as shown in Figure 5.21. Neg- ligible energy is dissipated as the potential energy peaks, i.e., where the kinetic energy (and, therefore, velocity) is minimal. Most of the energy is dissipated where the kinetic energy (and velocity) reach their respective maxima. Finally, consider the case of the over-damped system subjected to a ramp input. We solved the inertial displacement and velocity in Section 5.2.2. Here, owing to the slope of the ramp input force, the net kinetic energy stored plateaus at a relatively small value while the spring continues to stretch storing the lion’s share of the imparted energy as potential. e dissipated energy also accounts for a substantial energy cache. ese are shown in the early transient in Figure 5.19. Later, in the steady state the displacement becomes linear in time resulting in a potential energy cache that accumulates quadratically in time. e friction work is the integral of an F-v curve in the damper when the force approaches a constant value. In this case, the friction work increases linearly over long times. e stored kinetic energy plateaus along with the velocity at long times. Here, we recognize features of the solution without showing its explicit functional form. As Feynman correctly noted, “(We can) understand what an equation means if (we) have a way to ﬁgure out the characteristics of its solution without solving it.” 5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 99 Figure 5.15: Energy partition for a mass-spring-damper system subject to a step input force of 60 N (x0 125 N=m 5 Ns=m 30 kg). 2 m (cid:29)0 m k b D I 0 m=s I D D I D I D Figure 5.16: Energy partition for a mass-spring-damper system subject to a step input force of 60 N (x0 125 N=m 5 Ns=m 30 kg). 2 m (cid:29)0 m k b D I 0 m=s I D D I D I D 0510152025050100150200250Time (s)Stored System Energy (J)Total Stored EnergyStored Potential EnergyStored Kinetic Energy051015050100150200250Time (s)Stored ystem Energy (J)Potential EnergyKInetic Energy100 5. A COMMON NOTION Figure 5.17: Steady-state energy partition for a mass-spring-damper system subject to a step input force of 60 N (x0 125 N=m 5 Ns=m 30 kg). 0 m=s 2 m (cid:29)0 m k b D I D I D I D I D Figure 5.18: Total energy and dissipated energy for a mass-spring-damper system subject to a step input force. 20253035404550556005101520253035Time (s)Stored and Dissipated Energy (J)Kinetic energyTotal and Potential energies converge0510152025303540050100150200250Time (s)Stored and Dissipated Energy (J)Total EnergyDissipated Energy5.2. TIME DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 101 Figure 5.19: e second order free response is the story of an energy catch between Captains Potential and Kinetic Energy while the Evil Dr. Friction “steals away” energy with each transfer. Figure 5.20: A second order system with dissipation is excited by an initial displacement from rest with no external forces applied. 01234567891000.511.522.533.544.55Time (s)Energies (J)Potential EnergyKinetic EnergyDissipated Energy102 5. A COMMON NOTION Figure 5.21: In the free response of an under-damped second order system with dissipation, with each “pass of the energy ball” the total amplitude of stored energy is decreased by precisely the amount eaten away by friction. Figure 5.22: An over-damped second order system with ramp input experiences a continual intro- duction of energy to the system. 7.67.888.28.48.68.899.22.12.22.32.42.52.62.72.82.93Time (s)Energies (J)Dissipated EnergyKinetic EnergyPotential Energy0246810121416182000.511.522.5x 105Time (s)Stored & Dissipated Energy (J)Input EnergyPotential EnergyDissipated EnergyKinetic Energy5.3. CHAPTER ACTIVITIES 103 Figure 5.23: An over-damped second order system with ramp input as it enters steady state. Here, one can reason the forms of the steady dependence of energy dissipation (linear) and storage (quadratic) without actually solving the explicit equations. 5.3 CHAPTER ACTIVITIES Problem 1 Consider the plate damper, mechanical system shown: If the mass is initially moving to the right with a velocity of 1 m/s from the position x0 D 2 m and a constant, horizontal force is suddenly applied to the mass, as shown, write the (cid:0) diﬀerential equation governing the system plate displacement. What are the system’s natural frequency and damping ratio? Sketch the system position response as a function of time. Be sure to speciﬁcally label initial conditions, steady-state response, transient response, and 0102030405060708000.511.522.5x 106Time (s)System Element Energies (J)Total Input EnergyPotential EnergyDissipated EnergyKinetic Energy104 5. A COMMON NOTION the settling time with numerical values where possible. Use m 6 Ns=m. 0:1 kg I k D D 40 N=m b I D Plot time histories for the system potential and kinetic energy caches as well as the energy dissipated over time. Problem 2 Consider the plate damper, mechanical system from which the spring has been re- moved. e system is turned vertically and subject to a step input gravitational force as shown: If the mass is dropped from the position x0 0 m from rest, write the diﬀerential equation D governing the system plate velocity. Sketch the system response as a function of time. Be sure to speciﬁcally label initial conditions, steady-state response, transient response, and the settling time with numerical values where possible. Use m 10 m=s. 4 kg I 6 Ns=m D (cid:25) D g b I Problem 3 Consider the mass-spring-damper system shown subject to a ramp input displacement of y .t/ 5t: D xmgTwo, thin, viscous fluid layersresulting in a total dampingcoefficient = b5.3. CHAPTER ACTIVITIES 105 Derive the governing diﬀerential equation for the displacement of the mass. Solve the equa- 25 Ns=m. Plot the response, labeling the transient tion using m and steady regimes. Plot the displacement response in dimensionless form and compare with Figure 5.11. 40 N=m 10 kg D D D k b I I Problem 4 Consider the downhill skier pictured here: e total drag on the skier, FD, is a combination of man-made-snow surface resistance and * V aerodynamic drag resulting in the following relationship for the drag force: * F D CD * V is the velocity of the skier down the inclined slope and constant. Draw an appropriately labeled free body diagram and derive the equation where CD is the coeﬃcient of drag, CD governing the skier’s velocity. D D If the skier jumps out a gate and starts ideally from rest, determine: (a) the skier’s eventual terminal downhill velocity (b) how long it will take to eﬀectively attain this speed. kmxby106 5. A COMMON NOTION Use m system over a relevant time scale. What story do they tell? 16 Ns=m 80 kg D D (cid:25) g b I I 10 m=s. Plot the energy stored and dissipated in the Problem 5 Consider the idealized windshield wiper mechanism illustrated here. 1=2mR2 for the disk A mass-less blade is rigidly attached to the disk of radius R. Use I and wiper blade assembly for all calculations. Assuming the angular rotation of the disk remains “small,” derive the diﬀerential equation governing the sweep of the wiper blade. Based on your diﬀerential equation, derive theoretical expressions for the system’s natural frequency and damping ratio. What damping coeﬃcient is required to critically damp the system? (cid:25) Solve for the total response when the platform is subject to a step input displacement of R y.t/ 1:2 inches using: YIN 1:2 inches 0:5 inches 1 lb=ft k I D I D D 0:01 slug I b D m D D 0:25 lb-s/ft. Problem 6 Consider the angular position of a 100 kg winter Olympic snowboarder on a circular pipe of radius, R. e total drag on the snowboarder, FD, is a combination of man-made- snow surface resistance and aerodynamic drag resulting in the following relationship for the MRkby(t)* drag force: F D of the snowboarder and CD CD D constant. D * V where CD is the coeﬃcient of drag and * V is the tangential velocity 5.3. CHAPTER ACTIVITIES 107 Use I mR2; R 10 m; g 10 m=s2 for all calculations. D D D Assuming that the snowboarder enters the pipe at an initial position of (cid:18) 30(cid:14) and begins his angular descent from rest, show that the diﬀerential equation governing the angular position of our snowboarder with respect to time is given by D P(cid:18) C Consider that the small angle approximation is valid and that on two successive passes ﬁve seconds apart, the maximum angular values are: mgR sin (cid:18) D C 0: R(cid:18) mR2 CDR2 and (cid:18)N (cid:18)N 1 C D D 30(cid:14) 25(cid:14): Using the log decrement, compute the system’s natural frequency and damping ratio. Make a theoretically informed estimate of the drag coeﬃcient, CD, based on these measurements. From an initial angular entry point at (cid:18)0 30(cid:14), how long would it take the snowboarder to eﬀectively come to rest? Present your solution in dimensionless form and compare a graph of the dimensionless position with Figure 5.11. D Problem 7 You’re escaping the East India Trading Company in your trusty vessel “e Black Pearl.” e Pearl’s sails generate thrust in the following relationship: FSail D CS .VW VP / (cid:0) where VP is the velocity of the Pearl, VW is the velocity of the wind, and CS is a constant. e drag on the Pearl’s hull is linearly proportional to her velocity: where CD and the Pearl’s mass, m, are constant. FDrag D CDVP 108 5. A COMMON NOTION Use an appropriately labeled free body diagram to derive the diﬀerential equation governing the Pearl’s velocity. Determine an algebraic expression for the Pearl’s terminal, i.e., steady state, velocity. Determine an algebraic expression for how long it will take the Pearl to “eﬀectively” attain its terminal velocity. Write out a functional solution for the velocity of the Pearl. Assume the initial velocity is given by VPO. Sketch the solution for the Pearl’s velocity. Identify the time constant, (cid:28), and the corresponding terminal velocity, (cid:29)SS, on the graph. Problem 8 A pressure-compensating hydraulic spool valve consists of a bar-bell-like mass in a cylindrical sleeve (shown below). e valve is moved horizontally by a solenoid that applies a step input force to the mass. A spring at the far end provides an opposing force. Hydraulic ﬂuid in a tight clearance of width, h, provides a viscous friction force resisting the motion and given by the relation: F(cid:29) D C (cid:29) h where C is a constant. A balance of forces in the horizontal direction gives: m d 2x dt2 D F .t/ kx (cid:0) (cid:0) C (cid:29) h : 5.3. CHAPTER ACTIVITIES 109 F .t / m k h D D D D (cid:26) 0 t < 0 0 (cid:21) 1 N t 0:01 kg 100 N=m 10(cid:0) 20 (cid:3) 6 m Upon step-input application of the solenoid force, the valve is designed to move horizontally as fast as possible to its equilibrium position without overshooting it and without oscillating. (a) e governing equation m d 2x what balance principle? dt2 D F .t/ kx (cid:0) (cid:0) C (cid:29) h physically represents a statement of (b) What value of C must be used for the steady-state amount of valve travel to be achieved in the minimum time without oscillation? (c) What is the steady-state amount of horizontal travel realized by the valve under this step input force? (d) Roughly how long will it take for the valve to travel to its equilibrium position? (e) Plot the system’s total energy stored and dissipated over time. (f ) Often hydraulic ﬂuid becomes contaminated as wear particles accumulate in the clear- ance between the spool and its housing. Such particles often jam in the clearance ef- fectively reducing the clearance width. Using arguments supported by the form of the solution for the valve motion, explain the eﬀect the particulate contamination will have on the time necessary to move the valve to its steady-state position. (g) If the value of the oil drag coeﬃcient, C , used in part (a), were reduced to half its original value, would the system overshoot and oscillate about its eventual steady state? If so, with what frequency would it do so? Problem 9 Consider the circuit shown with parallel system capacitors. At t V0, is applied to the circuit by connecting it suddenly across a battery: D 0, a step voltage, 110 5. A COMMON NOTION V0 D iR .t 12 V 0/ D D 40 mil liamps On the circuit diagram label the relevant nodes and apply the necessary conservation princi- ples to derive the diﬀerential equation governing the response of the voltage drop across the pair of capacitors in the circuit. Use the potential energy storage system element equation to ﬁnd the relevant initial condition or initial conditions for the system eﬀort variable. Sketch the system response as a function of time, labeling the output variable (on verti- cal axis), and the transient and steady-state regimes of behavior using R 25 (cid:22)f 100 (cid:22)f. 100 (cid:10) C1 D D C2 I I D Problem 10 Consider the system presented below in which the cord is wrapped around a solid disc with mass moment of inertia, 1 2 M R2. e cord sticks to the disc without slipping. e disc At, applied about the ﬁxed pivot at its center. is subjected to a ramp input torque, T .t/ e disc starts from rest at (cid:18).0/ 0 rad. Assume the disk rotation remains “small” and use an appropriately labeled free body diagram to derive the diﬀerential equation governing the disc’s angular position, (cid:18).t/. Solve for the functional form of the disc position. At what time will the assumption of “small” angles break down? Assume angles of 30 degrees or less are reasonably “small.” Express your answer in terms of M; R; A; k1, and k2. D D +−RC1C2V1V05.3. CHAPTER ACTIVITIES 111 Problem 11 Consider the situation of drug absorption into a human being. e human body is your system and a drug is administered by the outside world at a rate given by f .t/. For such a case, the diﬀerential equation governing the amount of medicine in the blood stream, m, is given by: d m dt C rm D f .t/ t in hours where r D 0:0833 hr(cid:0) 1. e drugs are to be administered by injection which may be modeled as a non-zero initial condition: f .t/ 0, and m .t 7 mg. m0 0/ D D D D (a) Compute the solution for the presence of drug in the body over a representative time scale. (b) What is the settling time for the drug to wear oﬀ? (c) How many drug storage agent types are present in the system? Why? (d) How many drug dissipation agent types are present in the system? Why? Problem 12 Consider the mechanical system of the idealized building model below: MRθk1k2112 5. A COMMON NOTION D 0:5 slug I Take m at rest at the position x.0/ to the right, as shown D k D 8 lb=ft b 1 lb 32 lb. If the mass is initially D 0 ft and a constant, horizontal 32 lb. force is suddenly applied F .t/ s=ft F0 D D (cid:0) I I (a) What are the system’s natural frequency and damping ratio? (b) Sketch the system response as a function of time. Be sure to speciﬁcally label initial conditions, steady-state response, transient response, and the settling time with nu- merical values where possible. (c) What internal damping coeﬃcient would be needed in the column walls to “just” make the building’s lateral motion response behave “1st -order-like”? kkx(t)F(t)mRigidFloorMasslesscolumnsC H A P T E R 6 Going Nowhere? 113 Going from home to work to home to work, I am moving, but in the end I haven’t gone anywhere … vibrating strings move but go nowhere … drawers open, close, open, close—all that motion and nothing to show for it. Oscillatory motion is interesting. Doing the same thing over and over and going nowhere is pretty important. e Physics Hypertext Book e conversion of circular motion into sine waves is a pervasive part of our daily lives. Sine waves are the atoms of structure. ey’re nature’s building blocks. Primordial sine waves spanned the stuﬀ of the cosmos. e ripples of a pond and the ridges of sand dunes are manifestations of the emergence of sinusoidal structure from a background of bland uniformity. ere’s something almost spiritual about them. Steven Strogatz e Joy of X We’ve examined polynomial functions as input signals to dynamic systems. e category of harmonic functions is a special class unto itself and deserves individual treatment. Going to work and returning home, swinging on a swing in a playground, rotating a drum in a washing machine, spinning tires on an automobile—all are pervasive manifestations of periodicity in the world around us. And while one can admit the nature of periodicity is that one “goes nowhere,” the energy story tells us something diﬀerent. ere is “something to show for it” in the energy tale. Response of a building to earthquake loading easily reminds us that only in one peculiar sense does the building “go nowhere.” e ability of the building to absorb, store, or dissipate the input energy convinces us there is another side of the story. ere are myriad examples of periodic input that excite dynamics. Because the periodicity appears in the forcing function or excitation, we are interested in the steady-state solution long after the transient has decayed away. Normally such treatments are referred to as the frequency response of systems because the response is dependent on the frequency of the input excitation relative to the system. ese solutions naturally appear in terms of the system parameters, where the speciﬁc mathematical form of the system parameters arises from the individual movie script. 114 6. GOING NOWHERE? 6.1 FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS First order systems result when the script involves a single type of storage element or character: either Captain Potential Energy or Captain Kinetic Energy. ere may be multiple storage ele- ments, but they must store only one type of energy. ere can only be one storage superhero. In these cases, the governing diﬀerential equation has the form: (cid:28) d dt C (cid:9)0.t/ D D (cid:9)IN.t / D (cid:9)IN cos.!t /: In the time domain, we used the superposition of homogeneous and complimentary solutions to determine a total solution composed of both transient and steady state. For the unique case of periodic loading, the input excitation “never goes away.” erefore, one must be cognizant of the nature of the steady-state solution because it is the speciﬁc response to this ever-present input. e nature of the steady-state response to periodic input is captured in three characteristics: (a) the solution to a periodic excitation of frequency, !, is also a periodic function with the same frequency, ! (b) the magnitude of the steady-state solution is a scale multiple of the input magnitude of the excitation and (c) the solution is shifted in time from the input signal. As such, the steady-state solution is always of the form: SS.t/ D (cid:9)OUT cos.!t ’/ C and we need only determine the magnitude, (cid:9)OUT pletely determine the periodic steady-state response of the system. D A(cid:9)IN, and phase shift, ’, in order to com- 6.1.1 TRANSFER FUNCTION ANALYSIS FOR HARMONIC INPUT Consider the case where the magnitude of the excitation, (cid:9)IN, is constant, i.e., it is not a func- tion of the excitation frequency. Because the steady state has no memory of the system’s initial conditions, we assume zero initial conditions and apply the Laplace operator: .t/ (cid:9)0.t/ d .t/ L (cid:26)(cid:28) dt C (cid:9) .s/ C 1/(cid:9) .s/ D (cid:9)IN.s/ D (cid:9)IN.s/: D (cid:28)s(cid:9) .s/ .(cid:28)s C (cid:9)IN.t/ D D (cid:9)IN cos.!t/(cid:27) D 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 115 Since (cid:9) .s/ represents the total output of the system when subject to input (cid:9)IN.s/, we do not lose any generality by referring to it as (cid:9)OUT .s/ giving .(cid:28) s C G.s/ 1/(cid:9)OUT .s/ (cid:9)OUT .s/ (cid:9)IN.s/ D D D (cid:9)IN.s/ 1 (cid:28) s C 1 ) : e parameter s is a quantity in the complex plane where s j!. In the case where the time domain function is periodic and representable by trigonometric functions, the real portion of s dictates the exponential rate of decay for constant magnitude input. Since there is no decay in a 0. e complex part remaining for the steady state is then simply pure sinusoid, in our case a s j!. Using this simpliﬁcation, we arrive at what is often called the sinusoidal transfer function (STF). For the remainder of this chapter, we will conﬁne our discussions to STF’s only. Making this substitution: C D D D a G.s j!/ D (cid:9)OUT .j!/ (cid:9)IN .j!/ D 1 D 1 (cid:28) !j C : Now the STF is a function whose numerator and denominator, in general, can be thought of as vectors in the complex plane G.s j!/ D D Bj Ej A C C C D D 0; C 1; B 1; E where A (cid:28)! for a ﬁrst order system subject to constant magnitude peri- odic input. e STF can be used to easily compute the magnitude and phase shift of the resultant periodic response. e numerator and denominator vectors of the STF can be represented graph- ically in the complex plane (Figure 6.1), where: D D G.s j!/ D N D A C A C C C C C D D D and N D N ej(cid:11) Dej(cid:12) Bj Ej D Bj Ej D D N (cid:11) D (cid:12) D D D D pA2 tan(cid:0) B 2 C 1 .B=A/ pC 2 tan(cid:0) E2 C 1 .E=C / : 116 6. GOING NOWHERE? Figure 6.1: Graphical representation of the numerator and denominator vectors of the STF in the complex plane. Now we may illustrate the utility of the Laplace approach for periodic input excitations. e STF, G.j!/ in this form can be used to readily obtain the magnitude and phase shift: G .j!/ (cid:9)OUT .j!/ (cid:9)IN.j!/ ) D 8 (cid:136)(cid:136)(cid:136)< (cid:136)(cid:136)(cid:136): From this result: (cid:9)OUT (cid:9)IN D (cid:9)OUT .j!/ (cid:9)IN.j!/ k k N D D pA2 pC 2 D B 2 E 2 D A C C : k k ’ D (cid:134) (cid:9)OUT .j!/ (cid:0) (cid:134) (cid:9)IN .j!/ N D (cid:134) D (cid:11) (cid:12) (cid:0) D (cid:0) (cid:134) SS.t/ (cid:9)OUT cos.!t ’/ A(cid:9)IN cos.!t ’/ C where, A, the ampliﬁcation ratio, and ’, the phase shift, of the response relative to the input excitation are given above as functions of the excitation frequency, !, and the system parameters (here, (cid:28)). C D D 6.1.2 STEADY-STATE RESPONSE AND BODE PLOT ANALYSIS Frequency response is entirely characterized by the degree to which the output response is am- pliﬁed and the degree to which the output response lags the input signal. Let’s examine how this plays out for the simple case of the series RC circuit. Recall this circuit in Figure 6.2. Consider the case where the input battery voltage or eﬀort diﬀerential placed on the system constant, such that is periodic with input magnitude, VIN D V0.t/ D VIN cos .!t/ 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 117 Figure 6.2: e series RC circuit and its governing diﬀerential equation. where the magnitude VIN ⁄ f .!/. en, following the development of Section 6.1.1, L (cid:26)(cid:28) d V1.t/ dt C V1.t/ VIN cos.!t/(cid:27) D V1.s/ (cid:28)sV1.s/ .(cid:28)s C 1/V1.s/ C D D VIN.s/ D VIN.s/: ) Since V1.s/ represents the output voltage of the system, we can refer to it as VOUT .s/ giving .(cid:28)s C G.s/ D 1/VOUT .s/ VOUT .s/ VIN.s/ D D VIN.s/ 1 (cid:28) s 1 C which results in a sinusoidal transfer function G.s j!/ D VOUT .j!/ VIN .j!/ D 1 D 1 (cid:28) !j C : From here, it is straightforward to calculate the ampliﬁcation ratio A D VOUT .j!/ k VIN .j!/ k k k p12 D q12 C 02 C .(cid:28)!/2 D 1 q1 C .(cid:28)!/2 and the phase shift N .j!/ ’ D (cid:134) (cid:0) (cid:134) D .j!/ 0 (cid:0) D tan(cid:0) 1 .(cid:28)!/ RCV1 + V1 = VO (t)●+−V0CRV1118 6. GOING NOWHERE? of the system response V1SS.t/ D AVIN cos.!t ’/ C VIN D q1 .(cid:28) !/2 C cos (cid:0)!t (cid:0) tan(cid:0) 1 .(cid:28)!/(cid:1) : Note that all characteristics of the steady solution are only functions of the dimensionless quantity, (cid:28)!. Plots of the ampliﬁcation ratio (or alternatively the output response magnitude) and the phase shift as functions of the dimensionless quantity, (cid:28)!, are known as the Bode plots. ese are shown in Figures 6.3 and 6.4, respectively, below. 6.1.3 AN INTERPRETATION OF DIMENSIONLESS FREQUENCY RATIO Often Bode plots are presented simply as a function of the dimensionless parameter, (cid:28)!, which is sometimes referred to as the dimensionless frequency ratio. Whenever dimensionless parameters appear in a model, such parameters can often be placed in the form of a ratio of two physical quantities at play in the model. Let’s examine how one may ascribe a physical interpretation to this dimensionless frequency ratio. Consider the dimensionless parameter written as a ratio (cid:28)! D ! 1=(cid:28) D input excitation frequency equivalent system frequency : e input signal excites the system at an imposed frequency, !. Alternatively, the “outside world” !=2(cid:25) cycles of input per sec- bombards the system with an imposed eﬀort or ﬂow at a rate of f ond. is excitation is characterized by a characteristic time called its period, T 2(cid:25)=!. So we see that the frequency can be interpreted as the reciprocal of the characteristic time. e larger the input signal frequency, the smaller its characteristic time. A similar interpretation can be had for the system. Since the system is characterized by its time constant, one can understand the time constant to be a measure of the system’s response time, the time it takes the system to respond to external stimuli. 1=f D D D Now the dimensionless parameter, (cid:28)!, as written above can be physically interpreted as a dimensionless frequency ratio: the ratio of the input excitation frequency to the frequency with which the system can respond to any input. When the excitation frequency is large compared to the frequency to which the system is capable of responding, then the excitation frequency is termed “high” in this relative sense. When the equivalent system frequency is large compared to the frequency imposed on it by “the outside world,” then the excitation frequency is considered “low.” When the ratio is of order unity, the frequency can be termed “moderate.” Summarizing (cid:28)! D ! 1=(cid:28) D 8 (cid:136)< (cid:136): (cid:29) (cid:25) (cid:28) 1 1 1 ) ) ) high excitation frequency moderate excitation frequency low excitation frequency: 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 119 Figure 6.3: Ampliﬁcation ratio as a function of dimensionless frequency ratio. Figure 6.4: Phase shift as a function of dimensionless frequency ratio. 10-310-210-110010110210300.10.20.30.40.50.60.70.80.91Dimensionless Frequency Ratio Dimensionless Amplification Ratio10-310-210-1100101102103-1.6-1.4-1.2-1-0.8-0.6-0.4-0.20Dimensionless frequency ratioPhase angle (radians)120 6. GOING NOWHERE? Similarly, consider the dimensionless parameter written as a ratio (cid:28)! (cid:28) D 1=! D system characteristic time input excitation characteristic time : e system time constant is the characteristic response time of the system to external stimuli. e !=2(cid:25) cycles of input signal bombards the system with an imposed eﬀort or ﬂow at a rate of f 2(cid:25)=!. If 1=f input per second or one dose every T seconds, where T is the input period, T we consider the input excitation characteristic time to be a scaled quantity, 1=!, we see that the excitation characteristic time can be interpreted as the reciprocal of the imposed frequency. e larger the input signal frequency, the smaller its characteristic time. D D D Now the dimensionless parameter, (cid:28) !, as written above can be physically interpreted as a dimensionless characteristic response time ratio: the ratio of the time it takes the system to respond to an external stimulus to the characteristic time over which that stimulus is delivered by some external agent. When the system time constant is large compared to this characteristic time over which an excitation is delivered, the system is considered “slow to respond” or alternatively, the input is “coming at the system” faster than it can respond! When the system time constant is small compared to this characteristic time over which an excitation is delivered, then the system response time is small relative to how often the stimulus is delivered. In this limit, the system is considered “fast to respond” or alternatively, the input is “coming at the system” slower than that rate at which the system can respond! When the ratio is of order unity, the system can respond on time scales commensurate with those over which the excitation is being delivered. Summarizing (cid:28)! (cid:28) D 1=! D 8 (cid:136)< (cid:136): (cid:29) (cid:25) (cid:28) 1 1 1 ) ) ) FAST system relative to the “outside world” system is of similar relative “speed” as the “outside world” : SLOW system relative to the “outside world”´ ese interpretations are summarized in Table 6.1. 6.1.4 FILTERING CHARACTERISTICS OF 1st ORDER SYSTEMS In the classic sense of a frequency response, Bode plots show an inﬁnite number of potential steady-state solutions each at a diﬀerent imposed excitation frequency. e plots, because they are characterized by the dimensionless parameter, (cid:28)!, exhibit unique behavior in the relatively low, moderate, and high frequency regimes. Low Pass Filters For the series RC circuit, the Bode plots are illustrated in Figures 6.3 and 6.4. In the low frequency regime, the amplitude ratio approaches unity and the output is negligibly shifted in time. In other words, the magnitude of the output voltage across the capacitor is nearly the same value as that Table 6.1: Physical interpretations of the dimensionless frequency ratio, (cid:28)! 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 121 input to the system by the external battery. In this limit, the steady-state output precisely mimics the input signal as shown in Figure 6.5. For moderate excitation frequencies, the amplitude ratio approaches and p2 the phase shift approaches 45 degrees as shown in Figure 6.6. In the high frequency regime, the amplitude ratio approaches zero and the phase shift approaches 90 degrees making the output a sine wave response to a cosine input. e output has negligible magnitude and lags the input signal as much as possible as shown in Figure 6.7. e series RC circuit passes through all of the input excitation to the system at low in- put frequencies and passes none of the input signal and lags as much as possible at high input frequencies. For this reason the system is referred to as a low pass ﬁlter. High Pass Filters at the series RC circuit happened to behave as a low pass ﬁlter is entirely a result of its transfer function. It depends on both the nature of the excitation, the numerator in the transfer function, and the system itself, the denominator in the transfer the function. Change either the system, its elements or their structure or the nature of the input excitation and you necessarily change the transfer function, the representative Bode plots, and the ﬁltering characteristics of the excited system. So let’s consider an alternate mechanical system with a mass-less platform sandwiched between a linear spring and damper as shown in Figure 6.8. Dimensionless Frequency Ratio High Input Excitation Frequency Low Input Excitation Frequency 1ωτωτ= 1ωτ>> 1ωτ<< Dimensionless Characteristic Time Ratio Fast System Response Slow System Response 1ττωω= 1τω<< 1τω>> 122 6. GOING NOWHERE? Figure 6.5: Series RC circuit response to low frequency excitation. is system is characterized by a time constant of 1 second and a transient of approximately 4 seconds after which time the response is predominantly steady state. Figure 6.6: Series RC circuit response to moderate frequency excitation. Once again, the system settling time is roughly 4 seconds. 050100150-10-8-6-4-20246810Time (s)System and Excitation Voltages (V)Excitation SignalSystem Capacitor VoltageTransient0510152025-10-8-6-4-20246810Time (s)System and Excitation Voltages (V)Excitation SignalSystem CapacitorVoltage6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 123 Figure 6.7: Series RC circuit response to high frequency excitation. Figure 6.8: e mechanical spring-damper system with an interposed mass-less platform. 00.511.522.5-10-8-6-4-20246810Time (s)System and Excitation Voltages (V)Excitation SignalSystem CapacitorVoltagey()y()+=+=mechmechmechmechbbxxtkkRCxxRCtkbyx124 6. GOING NOWHERE? Operating on the governing diﬀerential equation with the Laplace operator L (cid:26)(cid:28) dx.t/ dt C x.t / (cid:27) dy.t/ dt (cid:28) D X.s/ (cid:28)sX.s/ (cid:28)sY .s/: C We understand the input to the system is the displacement of the end of the damper, Y.s/, and the output is the displacement of the mass-less platform, X.s/, giving D D .(cid:28) s C G.s/ 1/XOUT .s/ XOUT .s/ YIN.s/ D D D Calculating the ampliﬁcation ratio (cid:28) sYIN.s/ (cid:28) s : (cid:28)s 1 C A D XOUT .j!/ YIN .j!/ k k k k q02 D q12 C C .(cid:28) !/2 .(cid:28) !/2 D (cid:28)! q1 C .(cid:28) !/2 and the phase shift D (cid:134) the system response is given by ’ N .j!/ D .j!/ (cid:0) (cid:134) (cid:25) 2 (cid:0) D tan(cid:0) 1 .(cid:28) !/ XSS.t/ D A YIN cos.!t ’/ C (cid:28)!YIN D q1 .(cid:28)!/2 C cos (cid:16)!t (cid:25) 2 C (cid:0) tan(cid:0) 1 .(cid:28)!/(cid:17) : Again, all characteristics of the steady solution are only functions of the dimensionless quan- tity, (cid:28)!. Plots of the ampliﬁcation ratio and the phase shift are shown in Figures 6.9 and 6.10, respectively, below. e mass-less platform exhibits quite diﬀerent behavior. Here it is in the high frequency regime that the amplitude ratio approaches unity and the phase shift approaches zero degrees. In other words, the steady-state platform displacement precisely mimics the input signal as shown in Figure 6.11. It is good to ask what is happening physically in this limit. When the right end of the damper is displaced at very high frequency, one is essentially applying a large periodic velocity here. When a large velocity diﬀerential is applied across a damper, it locks up and behaves as if it is rigid. e displacement time histories of both the input excitation and the platform motion should be identical in this limit. Alternatively, when the damper’s right end is harmonically displaced at extremely low fre- quency, it is the same as applying an inﬁnitesimal velocity diﬀerential across the damper or negli- gible force. In this limit, the lion’s share of the displacement across the damper occurs at the right 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 125 Figure 6.9: Ampliﬁcation ratio as a function of dimensionless frequency ratio. Figure 6.10: Phase shift as a function of dimensionless frequency ratio. 10-310-210-110010110210300.10.20.30.40.50.60.70.80.91Dimensionless Frequency RatioDimensionless Amplification Ratio10-310-210-110010110210300.20.40.60.811.21.41.6Dimensionless frequency ratioPhase angle (radians)126 6. GOING NOWHERE? Figure 6.11: Mass-less platform response to high frequency excitation. e settling time for this system is approximately 2.5 seconds. Figure 6.12: Mass-less platform response to low frequency excitation. 00.511.522.533.544.55-20-15-10-50510Time (s)Rxternally Imposed and System Platform Displacements (in) Imposed damper displacementSystem platform displacementTransient050100150-10-8-6-4-20246810Time (s)Externally Imposed and System Platform Displacement (in)System platform displacement Imposed damper displacement6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 127 end while the magnitude of displacement of the system platform is negligible. Also the platform displacement lags the input displacement history by “as much as possible” or 90 degrees resulting in a platform displacement that is a sine wave response to a cosine input as shown in Figure 6.12. Because this mechanical system passes all of the input excitation to the system at high input frequencies and passes none of the input signal and lags as much as possible at low input frequencies, the system is referred to as a high pass ﬁlter. 6.1.5 UNIVERSAL TRUTHS FOR 1st ORDER SYSTEMS SUBJECT TO HARMONIC INPUT Of Special Note For all ﬁrst order systems, certain steady-state behaviors are characteristic of all systems: (a) eir steady-state behavior is a function of a single dimensionless parameter, (cid:28)! (b) Dimensionless ampliﬁcation ratios can never exceed a value of unity (c) Phase shifts can never exceed 90 degrees (d) Bode plots contain, at most, a single inﬂection point: (a) Order 1 equation ) (b) One inﬂection point increase or decrease with (cid:28)!. ) 1 inﬂection point ampliﬁcation ratio and phase monotonically either (e) Systems may only ever be low-pass or high-pass ﬁlters. .. 6.1.6 ENERGY STORAGE AND DISSIPATION IN 1st ORDER SYSTEMS SUBJECT TO HARMONIC INPUT EXCITATION Let’s continue with the example of the mass-less spring-damper system discussed in Section 6.1.4. Because the idealized platform has negligible mass, no kinetic energy can be stored by the system. We know that energy can only be stored in the form of potential energy in the spring or dissipated by the damper. Now that we have resolved the resultant motion and velocity of the platform, we may compute the energy partition that results from an imposed harmonic input to the damper. 128 6. GOING NOWHERE? For zero initial conditions, the total platform displacement can be written as xTRANSIENT .t/ C xSS_0/ e(cid:0) x.t/ D D D .x0 .x0 (cid:0) (cid:0) xSS_0/ e(cid:0) t=(cid:28) xSTEADY STATE.t/ t=(cid:28) C AYIN cos.!t (cid:28)!YIN C p1 .(cid:28) !/2 C ’/ C cos (cid:16)!t (cid:25) 2 C (cid:0) tan(cid:0) 1.(cid:28)!/(cid:17) : e potential energy is simply VSYSTEM.t/ 1 2 D kx2: While the energy dissipated in the damper is equal to the friction work performed by the damper WFRICTION.t/ t t Z D 0 Z D 0 FFRICTION.t/dx b. y.t/ P x.t//2dt: (cid:0) P ese quantities are shown graphically in Figures 6.13 and 6.14, respectively. e energy story tells an interesting tale that is potentially belied by the frequency response alone. At low input frequency, there is negligible movement of the platform. While the platform displacement is relatively low compared with the damper stroke displacement, it is not zero. As a result, the spring potential energy, is relatively speaking, low. e relative velocity over the damper, however, results in energy dissipation that dominates the energy story. It is nearly two orders of magnitude larger than the potential energy stored in the system. At high frequency, the damper appears eﬀectively locked, but there remains a relative ve- locity over the damper that can be relatively large owing to the high frequency of the damper stroke displacement. erefore, the energy dissipated in the damper still dominates, only now it is only half an order of magnitude larger. e relative amount of energy stored has increased compared with the case at low frequency. It is important that this result explicitly depends on the values of spring constant and damp- ing coeﬃcient and not simply their ratio, the time constant. erefore, the energy story of two systems with the same time constant will not necessarily be the same as is the story for eﬀort and ﬂow. But the relative amounts of energy stored and spent will potentially be a deciding factor in system design. is is an important issue not often discussed in elementary courses in systems dynamics. It plays a signiﬁcant role in that while one needs to know the ﬂow variables of velocity and displace- ment to calculate the kinetic and potential energies stored by the system, it may be the energy storage versus dissipation that is the deciding factor in the feasibility of the design. An analo- gous issue arises in ﬁnite element analysis where the primary solution variables are a set of nodal point displacements in a loaded structure. While this is true, it is often the internal stresses that 6.1. FREQUENCY DOMAIN SOLUTIONS OF 1st ORDER SYSTEMS 129 Figure 6.13: Energy partition for a mass-less platform response for low input frequency excitation. Figure 6.14: Energy partition for a mass-less platform response for high input frequency excitation. 01020304050600500100015002000250030003500Time (s)Energy stored and dissipated in spring-damper-platform system (J)Total energyEnergy dissipated in damperPotential energy in spring00.511.522.533.544.5500.511.522.533.5x 104Time (s)Energy stored and dissipated in spring-damper-platform system (J)Total EnergyEnergy dissipated in damperPotential energy in spring130 6. GOING NOWHERE? are the determining factor in design. e internal stresses are calculated by using displacements to compute strains and strains to compute stresses. at is, the displacements or ﬂow variables, by themselves, are incidental. e corresponding transmitted forces or eﬀort variables internal to the system and energies stored are primary factors in system design. In engineering system design, engineers often redesign systems to lower transmitted forces or internally stored energy. is is accomplished by either altering the geometric structure of the system, i.e., whether system elements are connected in series or parallel, or by altering the material properties, i.e., the sys- tem capacitances, inductances, or resistances in any given geometric conﬁguration. It’s not unlike playing with Lego bricks. ey can be put together in an inﬁnite number of ways and we can choose diﬀerent sizes of bricks. When the spring and damper are placed on either side of the platform and the outside world is stroking the damper, as shown here, the requisite energy losses are substantial. As we will see, such is not always the case. 6.2 FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS If you wish to understand the universe, think of energy, frequency, and vibration. Nikola Tesla Second order systems result when the script involves multiple types of storage elements or characters, i.e., Captains Potential and Kinetic Energy both appear in the movie. Note there may be many storage elements, but they must collectively store both types of energy. In these cases, the governing diﬀerential equation has the form: 1 !2 N d 2 .t/ d t 2 C 2(cid:16) !N d .t/ dt C .t/ D (cid:9)0.t/ D (cid:9)IN.t/ D (cid:9)IN cos.!t/ where represents the pertinent eﬀort or ﬂow variable that characterizes the system and !N and (cid:16) are the system natural frequency and damping ratio, respectively. Again, for periodic load- ing, the input excitation “never goes away.” e steady-state solution is a response speciﬁcally to this omnipresent input excitation. Just as with 1st order systems, the nature of the steady-state response to periodic input is captured in three characteristics: (a) the solution to a periodic excitation of frequency, !, is also a periodic function with the same frequency, ! (b) the magnitude of the steady-state solution is a scale multiple of the input magnitude of the excitation and (c) the solution is shifted in time from the input signal 6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 131 erefore, the steady-state solution is always of the form: SS.t / D (cid:9)OUT cos.!t ’/ C and we need only to determine the magnitude, (cid:9)OUT A(cid:9)IN, and phase shift, ’, in order to completely determine the periodic steady-state response of the system. Because the steady-state solution has no memory of the system’s initial conditions, we, again, use Laplace transforms to examine a system’s steady-state response to periodic input. D 6.2.1 TRANSFER FUNCTION ANALYSIS FOR HARMONIC INPUT Consider the case where the magnitude of the excitation, (cid:9)IN, is constant, i.e., it is not a function of the excitation frequency. Again, assuming zero initial conditions and applying the Laplace operator to the diﬀerential equation: L (cid:26) 1 !2 N 1 !2 N (cid:18) 1 !2 N d 2 dt 2 C 2(cid:16) !N d dt C 2(cid:16) !N (cid:9)0.t/ D (cid:9)IN.t/ D (cid:9)IN cos.! t/(cid:27) D (cid:9)IN.s/ D D s2(cid:9) .s/ C 2(cid:16) !N s2 C s C s(cid:9) .s/ (cid:9) .s/ C 1(cid:19) (cid:9)OUT .s/ (cid:9)IN.s/ D G.s/ (cid:9)OUT .s/ (cid:9)IN.s/ D D 1 (cid:18) 1 !2 N s2 C 2(cid:16) !N s C : 1(cid:19) For periodic input, s D j!, rendering the second order sinusoidal transfer function: G.s j!/ D (cid:9)OUT .j!/ (cid:9)IN .j!/ D D 1 (cid:19) : 2(cid:16) !N !j C (cid:18)1 !2 !2 N (cid:0) Now G.s j!/ D D Bj Ej A C C C where A 1; B 0; C D magnitude periodic input. D D (cid:18)1 !2 !2 N (cid:0) (cid:19) ; E 2(cid:16) !N D for a second order system subject to constant 132 6. GOING NOWHERE? e ampliﬁcation ratio and phase shift follow: G .j!/ (cid:9)OUT .j!/ (cid:9)IN.j!/ D 8 < : ) (cid:9)OUT (cid:9)IN D k k (cid:9)OUT .j!/ (cid:9)OUT .j!/ (cid:9)IN .j!/ k D k (cid:9)IN .j!/ N D D (cid:0) (cid:134) D (cid:134) pA2 pC 2 N B 2 E2 D D (cid:11) D A (cid:12) (cid:0) C C (cid:0) (cid:134) ’ D (cid:134) and SS.t / where A and ’ are functions of !N and (cid:16). (cid:9)OUT cos.!t D ’/ C D A(cid:9)IN cos.!t ’/ C 6.2.2 STEADY-STATE RESPONSE AND BODE PLOT ANALYSIS For second order systems, the concept of a frequency ratio is explicit as the system is characterized by its natural frequency as opposed to a time parameter as in ﬁrst order systems. Again, the speciﬁc instances of periodic signal inputs are best shown by speciﬁc examples. Periodic Input Signal of Constant Magnitude Consider the classical mass-spring-damper system from Section 4.4.1 and illustrated in Fig- ure 4.12. Let’s restrict ourselves to the case where the externally applied input force or eﬀort placed FIN cos .!t/ on the system is periodic with input magnitude, FIN where the magnitude FIN f .!/. en, following the development of Section 6.1.1, constant, such that F0.t/ D D ⁄ (cid:18) 1 !2 N G.s/ s2 C 2(cid:16) !N X.s/ 1(cid:19) X.s/ s C D FIN.s/ 1 k 1 D FIN.s/=k D (cid:18) 1 !2 N s2 C 2(cid:16) !N s C 1(cid:19) which results in a sinusoidal transfer function G .j!/ XOUT .j!/ FIN.j!/=k D D 1 (cid:19) : 2(cid:16) !N C !j (cid:18)1 (cid:0) !2 !2 N e resulting ampliﬁcation ratio is given by: A D XOUT .j!/ k k FIN.j!/=k k k p12 02 C 2 (cid:19) D s(cid:18)1 !2 !2 N (cid:0) 2 D (cid:19) q.1 (cid:18)2(cid:16) ! !N C 1 r 2/2 (cid:0) .2(cid:16)r/2 C where r D is given by: 6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 133 !=!N is known as the dimensionless frequency ratio. e corresponding phase shift N .j!/ ’ D (cid:134) (cid:0) (cid:134) D .j!/ 0 (cid:0) D tan(cid:0) 1 (cid:0)2(cid:16)r=.1 r 2/(cid:1) : (cid:0) So, ﬁnally, in steady state XSS.t/ A FIN k D cos.!t ’/ C D q.1 FIN=k r 2/2 C (cid:0) .2(cid:16)r/2 cos (cid:0)!t (cid:0) tan(cid:0) 1 (cid:0)2(cid:16)r=.1 r 2/(cid:1)(cid:1) : (cid:0) Note that all characteristics of the steady solution are only functions of the dimensionless quanti- ties, (cid:16) and r. Plots of the ampliﬁcation ratio and the phase shift as functions of the dimensionless quantities, (cid:16) and r, are known as the Bode plots or surfaces for second order systems. ese are shown in Figures 6.15 and 6.16, respectively, for the case of constant magnitude input signal. We should note several observations for this speciﬁc case of a constant force amplitude periodic signal input to a parallel mass-spring-damper system: (a) at low frequency ratio, all of the signal input is passed onto the system with an ampliﬁcation of zero and zero phase shift. (b) At frequency ratios near unity, where the input signal frequency equals the system natural frequency, the ampliﬁcation ratio can become much larger than one. For an undamped system, the output system response magnitude will grow unbounded at r 1. is is known as resonance. D (c) At high frequency ratio, the ampliﬁcation ratio falls oﬀ monotonically and asymptotically to zero at suﬃciently high frequency ratio. (d) e ampliﬁcation ratio always decreases with increasing damping for all frequency ratios. (e) At suﬃciently high damping ratio, the system appears ﬁrst-order-like and behaves like a low pass ﬁlter. In most cases, one cannot make generalizations about the behavior of any one system from a diﬀerent system. To see how any periodically excited system behaves in the steady state, one must derive the transfer function and examine the behavior in the Bode plots. e transfer function depends both on the system parameters and features of the forcing function. Whenever either is altered, the transfer function and steady-state behavior can be altered. Each system under speciﬁc signal inputs must be examined on its own merits. Considering a second example will make this point unambiguous. Periodic Input Signal from a Rotating Imbalance When rotating machinery is submitted to an imbalance about the axis of rotation, such as happens when wet clothes shift to one side of a spinning basin in a washing machine, the washing machine 134 6. GOING NOWHERE? Figure 6.15: Ampliﬁcation ratio as a function of frequency and damping ratios. 01234500.20.40.60.81012345Frequency ratioDamping ratioAmplification ratio00.511.522.533.544.5500.511.522.53Frequency ratioAmplification ratioIncreasing damping ratio6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 135 Figure 6.16: Phase shift as a function of frequency and damping ratios. 00.511.522.533.544.5500.511.5-3.5-3-2.5-2-1.5-1-0.50Frequency ratioDamping ratioPhase angle (rad)00.511.522.533.544.55-3.5-3-2.5-2-1.5-1-0.50Frequency ratioPhase angle (rad)Increasing damping ratio136 6. GOING NOWHERE? is excited into motion. Similarly, an automobile exhibiting a wheel imbalance will have observable and detrimental vibration imparted to the car axle and frame. A simple lumped model of such an inertial imbalance is illustrated in Figure 6.17. Figure 6.17: A second order system subject to a rotating imbalance. e system is characterized by some frictional losses that we assume can be modeled ef- fectively as viscous dissipation with damping coeﬃcient, b, and a system stiﬀness, k, whereby the system stores potential energy. e relatively small imbalance .m M / is spinning about a frame rigidly attached to the mass, M , at constant angular velocity, !. e imbalance, m, is spinning at a prescribed rotational speed, thus imparting an eccentric load on the inertial mass, M , that is sinusoidal with a magnitude that is dependent on the spinning speed. Because the spinning speed is prescribed, the system has only a single degree of freedom. is is often called a classical rotating imbalance. Consider the location of the mass imbalance relative to the center of the lumped system mass to be given by a vector, R .t/ j where R is O j / the magnitude of the eccentricity of the imbalance. If the block is constrained in the vertical . O direction, a free body diagram on the inertial block renders the following governing diﬀerential equation for the horizontal motion of the mass, M : R cos !t R sin !t (cid:28) C D i O M d 2x.t/ dt2 C b dx.t/ dt C kx.t/ m R.t/ R D D (cid:0) mR!2 cos.!t/: Normalizing the equation by the system stiﬀness, k, and assuming M m, d 2x.t/ M k d 2x.t/ dt2 C dt2 C 1 !2 N b k dx.t/ dt C x.t/ 2(cid:16) !N dx.t/ dt C x.t/ mR!2 k mR!2 M!2 N D D cos.!t/ D cos.!t/: (cid:29) mR!2 M!2 N cos.!t/ Note here that the magnitude of the forcing function is dependent on the frequency of rotation of the imbalance. e magnitude of the imbalance increases as the square of the spinning frequency. bkx(t)mRωM6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 137 We will see that this is a crucial feature of this excitation. Applying the Laplace operator to the diﬀerential equation: L (cid:18) M k d 2x.t/ dt2 C b k dx.t/ dt C x.t / R.t /(cid:19) m k R D (cid:0) (cid:18) 1 !2 N s2 C 2(cid:16) !N s C 1(cid:19) X.s/ m (cid:0) k D s2R.s/ M (cid:0) k m M D s2R.s/ ms2 (cid:0) M!2 N D R.s/ G.s/ X.s/ R.s/ D D ms2=M!2 N (cid:0) s2 (cid:18) 1 !2 N 2(cid:16) !N s C 1(cid:19) C which results in a sinusoidal transfer function G .j!/ XOUT .j!/ RIN.j!/ D D (cid:18)1 and ampliﬁcation ratio m!2=M!2 N 2(cid:16) !N !2 !2 N C (cid:19) (cid:0) !j A k D M XOUT .j!/ k mRIN .j!/ k k D s(cid:18)1 N (cid:1) (cid:0)!2=!2 2 !2 !2 N A .r; (cid:16)/. (cid:0) (cid:19) C (cid:18)2(cid:16) ! !N 2 D (cid:19) q.1 (cid:0) r 2 r 2 /2 .2(cid:16)r/2 C where r !=!N , and, again, A D D e corresponding phase shift is given by: N .j!/ ’ D (cid:134) (cid:0) (cid:134) D .j!/ 0 (cid:0) D tan(cid:0) 1 (cid:0)2(cid:16)r= (cid:0)1 r 2(cid:1)(cid:1) : (cid:0) So, ﬁnally XSS.t/ A mRIN M D cos.!t ’/ C D .mRIN=M / r 2 r 2 /2 .2(cid:16)r/2 (cid:0) C q.1 cos (cid:0)!t (cid:0) tan(cid:0) 1 (cid:0)2(cid:16)r= (cid:0)1 r 2(cid:1)(cid:1)(cid:1) : (cid:0) While the phase shift is identical to that for the constant magnitude forcing function, the presence of r 2 in the numerator changes the ampliﬁcation ratio in signiﬁcant ways. e resultant Bode plot of the ampliﬁcation ratio is shown in Figure 6.18. For the speciﬁc case of a periodic signal input from a rotating imbalance to a parallel spring- damper—mass system: (a) at low frequency ratio, none of the signal input is passed onto the system with an ampliﬁ- cation of zero and zero phase shift. 138 6. GOING NOWHERE? Figure 6.18: Ampliﬁcation ratio for a rotating imbalance. 01234500.20.40.60.81012345Frequency ratioDamping ratioAmplification ratio00.511.522.533.544.5500.511.522.53Frequency ratioAmplification RatioIncreasing damping ratio6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 139 (b) At near resonant frequencies, the ampliﬁcation ratio can become much larger than one. For an undamped system, the output system response magnitude will grow unbounded at r 1. D (c) At high frequency ratio, the ampliﬁcation ratio converges to a value of one. (d) e ampliﬁcation ratio always decreases with increasing damping for all frequency ratios. (e) At suﬃciently high damping ratio, the system appears ﬁrst-order-like and behaves like a high pass ﬁlter. Signiﬁcant changes are evidenced here at both high and low input frequencies when compared with the steady-state behavior of the system whose excitation magnitude is independent of fre- quency. In fact, the limit behavior is opposite for both systems at both low and high frequency. Periodic Input Signal from a Base Excitation When a system is subject to forces that are applied through its internal elements, i.e., springs and dampers by the motion of an external agent, the imposed forces are still applied by virtue of an external agent. Consider the case of an idealized model of an automobile suspension. Here, the inertial lumped mass represents the mass of a 1=4 model of an automobile comprised of a 1=4 of the chassis/frame, a single suspension strut, and one tire. e model stiﬀness, k, lumps together the stiﬀness of the suspension strut and the rubber tire while the damper primarily represents the viscous dissipation in the suspension strut. Figure 6.19: A second order system subject to excitation of its base. e vertical motion, y.t/, is provided by a sinusoidal road proﬁle with wavelength, (cid:21), traversed by a vehicle with speed, (cid:29): y.t/ D Y0 cos !t kbmxyv140 6. GOING NOWHERE? and ! D 2(cid:25)(cid:29) (cid:21) : A free body diagram on the inertial block renders the following governing diﬀerential equation for the horizontal motion of the mass: X F k .y.t / D d 2x.t/ m (cid:0) dx.t/ b dt2 C dt C x.t // b . y.t / P C (cid:0) P x.t// m x.t/ R kx.t / ky.t / b C D D dy.t/ dt : Where the terms on the right-hand side of the equation are external forces provided by virtue of the tire motion imposed by the road proﬁle and speed of the vehicle. Again, normalizing the governing diﬀerential equation by the system stiﬀness, k: m k d 2x.t/ dt 2 C b k dx.t/ dt C x.t/ D y.t/ b k dy.t/ dt C or, in terms of the system parameters 1 !2 N d 2x.t/ dt2 C 2(cid:16) !N dx.t/ dt C x.t/ y.t/ D 2(cid:16) !N dy.t/ dt : C Applying the Laplace operator to the normalized diﬀerential equation: (cid:18) 1 !2 N s2 C 2(cid:16) !N s C 1(cid:19) X.s/ (cid:18)1 2(cid:16) !N C D s(cid:19) Y .s/ G.s/ X.s/ Y .s/ D D (cid:16)1 (cid:18) 1 !2 N s2 C C 2(cid:16) !N s(cid:17) 2(cid:16) !N s C 1(cid:19) which results in a sinusoidal transfer function G .j!/ XOUT .j!/ YIN .j!/ D D (cid:16)1 (cid:18)1 (cid:0) C !2 !2 N 2(cid:16) ! !N j (cid:17) (cid:19) C 2(cid:16) !N !j D .1 .1 (cid:0) C r 2 / 2(cid:16)rj / 2(cid:16)rj C and ampliﬁcation ratio A D XOUT .j!/ YIN .j!/ k k k k q1 D q.1 (cid:0) where r D !=!N , and, again, A A .r; (cid:16)/. D .2(cid:16)r/2 C r 2/2 .2(cid:16)r/2 C 6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 141 e corresponding phase shift is given by: ’ N .j!/ D (cid:134) D .j!/ D (cid:0) (cid:134) tan(cid:0) 1 .2(cid:16)r/ tan(cid:0) 1 (cid:0)2(cid:16)r=.1 r 2/(cid:1) : (cid:0) (cid:0) So, ﬁnally XSS.t/ D A YIN cos.!t YIN q1 C r 2 /2 D q.1 (cid:0) ’/ C .2(cid:16)r/2 .2(cid:16)r/2 C cos (cid:0)!t C tan(cid:0) 1 .2(cid:16)r/ tan(cid:0) 1 (cid:0)2(cid:16)r=.1 r 2/(cid:1)(cid:1) : (cid:0) (cid:0) e resultant Bode plot of the ampliﬁcation ratio and phase shifts are shown in Figures 6.20 and 6.21, respectively. For periodic signal input from a base excitation to a parallel mass-spring-damper system: (a) at low frequency ratio, all of the signal input is passed onto the system with an ampliﬁcation of unity and zero phase shift. (b) At near resonant frequencies, the ampliﬁcation ratio can become much larger than one. For an undamped system, the output response magnitude will grow unbounded at r 1. D (c) At the peculiar frequency ratio of r of damping ratio. D p2, the ampliﬁcation ratio becomes unity irrespective (d) At high frequency ratio, the ampliﬁcation ratio converges to zero. (e) e ampliﬁcation ratio no longer decreases with increasing damping ratio for all frequency ratios! p2, is is true only for frequency ratios less than r increasing the amount of damping actually increases the ampliﬁcation ratio. is may seem counterintuitive, but the mathematics, i.e., our “eyes with which we see physics,” says it is true, and experiments verify this reality! p2. For ratios higher than r D D (f ) At suﬃciently high damping ratio, the system behaves like an all pass ﬁlter, i.e., the ampli- ﬁcation ratio converges to unity for all frequency ratios. Signiﬁcant changes are evidenced here: increasing friction enhances ampliﬁcation for r > p2 eventually ending up allowing all of the external excitation to be seen in the steady state at all frequencies when the friction is suﬃciently high. 142 6. GOING NOWHERE? Figure 6.20: Ampliﬁcation ratio for base excitation of a 2nd order system. 01234500.20.40.60.810123456Frequency ratioDamping ratioAmplification ratio00.511.522.533.544.5500.511.522.53Frequency ratioAmplification ratioIncreasing damping ratio6.2. FREQUENCY DOMAIN SOLUTIONS OF 2nd ORDER SYSTEMS 143 Figure 6.21: Phase shift for base excitation of a 2nd order system. 01234500.20.40.60.81-3-2.5-2-1.5-1-0.50Frequency ratioDamping ratioPhase angle00.511.522.533.544.55-2.5-2-1.5-1-0.50Frequency ratioPhase angleIncreasing damping ratio144 6. GOING NOWHERE? 6.2.3 UNIVERSAL TRUTHS FOR 2nd ORDER SYSTEMS SUBJECT TO HARMONIC INPUT Of Special Note For all second order systems: (a) eir steady-state behavior is a function of a two dimensionless parameters: the !=!N , and the damping ratio, (cid:16). frequency ratio, r D (b) Ampliﬁcation ratios can exceed a value of unity, particularly near resonant fre- quencies. (c) Phase shifts can exceed 90 degrees. (d) Bode plots contain, at most, two inﬂection points allowing for peaks at interme- diate frequency ratios. (a) Order 2 equation (b) 2 inﬂection points ampliﬁcation ratio and phase can increase and then decrease (or vice versa) with dimensionless frequency ratio, r. 2 inﬂection points ) ) (e) Systems can be low-pass, high-pass, mid-band pass, or all-pass ﬁlters. .. 6.3 REDESIGNING SYSTEMS FOR STEADY-STATE BEHAVIORS One thing to note in second order systems is that resonance can be a particularly interesting case as ampliﬁcation can be quite large. So we might want to design systems that are not capable of meandering into any troublesome regimes. Let’s say, for instance, in the case of a constant force magnitude periodic input to a second order mass-spring-damper system, one wished to never see output dynamic position amplitudes greater than half the static deﬂection. Being interested in this limit, let’s say we wish to dictate that the dynamic output be precisely half the static deﬂection. Recall, the ampliﬁcation depicted in Figure 6.15 is a function of two parameters, the frequency ratio, r !=!N , and the damping ratio, (cid:16). If we limit the ampliﬁcation to be precisely 1=2, then we have a unique relationship between the frequency and damping ratios shown in Figure 6.22. is ﬁgure is a cut parallel to the r–(cid:16) plane elevated to a height of A 1=2. D ere are now several interesting observations one can make regarding possibilities for ob- taining the design condition A pairs to the left of the cut have ampliﬁcation greater than 1=2 while all pairs to the right have ampliﬁcation less than 1=2. On the curve separating the two regions, the ampliﬁcation precisely equals 1=2. If we desire 1=2. In Figure 6.22, all r; (cid:16) f r; (cid:16) f D g g D 6.3. REDESIGNING SYSTEMS FOR STEADY-STATE BEHAVIORS 145 Figure 6.22: A curve }.r; (cid:16)/ for which A mass-spring-damper system. D 1=2 for constant force magnitude periodic input to a A f f g g g g D r; (cid:16) r; (cid:16) 1; 1 g D f r; (cid:16) f m; k; b pair, say 1; 1 f 1=2, we can choose any . What speciﬁc triple pair on this curve. e number of possibilities? Yes, inﬁnity. Further, as engineers, we don’t swap out parts with natural frequencies and damping ratios. We specify spring stiﬀnesses, damping coeﬃcients, and inertial masses. Well, let’s pick one of the inﬁnity of solutions for a particular corre- ? Well, there are, again, an inﬁnite number of such triples that determine sponds to pairs, there is yet another a single dimensionless pair. So, for every one of the inﬁnity of 2 possible solutions. Of course, one will inﬁnity of need to consider cost, weight, availability, and other factors as constraints to fence in a reasonable solution, but there are still often a large number of potential candidates for a redesigned solution. ere are a wealth of solutions at our disposal because the second order system is characterized by two independent dimensionless parameters. In ﬁrst order systems, only the time constant can be changed to alter the steady-state behavior. But typically this single parameter is a product or ; . ere remain an inﬁnite num- ratio of system parameters pairs: g g ber of solutions for these pairs of system elements that will deliver the requisite time constant for a suﬃcient redesign of the steady-state amplitude or phase shift. triples! On some scale, there are R; L f R; C f m; b f m; k; b r; (cid:16) f k; m 1 g f g g f f g g ; ; Note also that within any order system, the possibilities for redesign are dictated by the transfer function and are, therefore, dependent upon the details of the system and how it is excited by external agents. Consider that you wanted to limit the ampliﬁcation ratio to a value of 1=2 for a system exhibiting a rotating imbalance. In this case, taking the appropriate slice through the 2 three-dimensional Bode surface results in the section shown in Figure 6.23. ere are still 1 146 6. GOING NOWHERE? Figure 6.23: A curve input to a second order mass-spring-damper system. .r; (cid:16)/ for which A D = 1=2 for a frequency dependent magnitude periodic force potential solutions. Note that unlike the case of constant magnitude periodic force, however, now as one increases the damping ratio, the frequency ratio must increase rather than decrease in order to maintain a level ampliﬁcation ratio of 1=2. e frequency content in the magnitude of the force imbalance alters redesign scenarios in a signiﬁcant way. If one increased the damping ratio along with the frequency ratio in the case where periodic force magnitude is constant, one would climb the ampliﬁcation surface to values in excess of the desired design value of 1=2. One must move, in some sense, in the opposite direction in one case than the other to achieve the desired results. erefore, accurately modeling the system and transfer function characteristics is crucial when redesigning such dynamic systems. 6.4 ENERGY STORAGE AND DISSIPATION IN 2nd ORDER SYSTEMS SUBJECT TO HARMONIC INPUT EXCITATION Again, system ﬂow or eﬀort variables solutions are calculated as primary variables. e transmitted forces and stored energies tell a part of the story not addressed by ﬂow variables alone. For this reason, we consider the classic case of the second order mass-spring-damper subject to a constant amplitude periodic force excitation. And we will examine the energy stored by the system when the excitation frequency is low, moderate (near resonance), and high as depicted in Figure 6.24. 6.4. ENERGY STORAGE AND DISSIPATION IN 2nd ORDER SYSTEMS 147 Figure 6.24: Low, resonant, and high frequency constant magnitude periodic input forces to second order system. Figure 6.25: Low frequency response for position and energy in an underdamped 2nd order system subject to periodic force input of constant magnitude. 0200400600800100012001400160018002000-1.5-1-0.500.511.5Time (s)Position (m) & Energy (J)PositionPotential EnergyKinetic Energy148 6. GOING NOWHERE? Figure 6.26: High frequency response for position and energy in an underdamped 2nd order system subject to periodic force input of constant magnitude. Figure 6.27: Resonant frequency response for position and energy in an underdamped 2nd order system subject to periodic force input of constant magnitude. 0Time (s)Position (m) and Energy (J)PositionKinetic EnergyPotential Energy020406080100120-1001020304050Time (s)Position (m) and Energy (J)PositionKinetic EnergyPotential Energy6.5. CHAPTER ACTIVITIES 149 Because steady-state solutions are sinusoidal functions, speed is proportional to frequency. At low frequency, this minimizes the kinetic energy, leaving the lion’s share of energy stored as potential energy (see Figure 6.25). Conversely, for high frequency input, the system amplitude approaches zero, leaving minimal potential energy storage. High frequency imparts high velocities and the kinetic energy is the prime storage mechanism at high frequencies (see Figure 6.26). At near resonant frequencies, both the steady-state amplitude and speed grow to large values. Here the stored energy cache takes on large values that alternate between potential and kinetic forms as shown in Figure 6.27. 6.5 CHAPTER ACTIVITIES Problem 1 Consider the circuit pictured below, in which the bulb acts a resistor. At t 0, a pe- riodic voltage, V0, is applied to the circuit by connecting it suddenly across a frequency modulated battery: D e diﬀerential equation governing current response of the circuit is given by: L R diL dt C iL D V0.t/ R iL.t 0/ D D 0 amps (a) Derive the amplitude ratio I E0=R . (b) When R 1000 (cid:10), and L 125 mH is the electrical circuit current response fast or slow given the forcing function? Explain your answer. D D (c) Redesign the series LR circuit so that the steady-state circuit current has a magnitude 55 cos.0:002t/ V. of 40 milliamps when driven by the periodic circuit voltage V0.t/ D 0()cos(0.002)55OOVtEtEV== 150 6. GOING NOWHERE? Problem 2 Consider the mass-less spring-damper mechanical system: where b 250 Ns/m; k 125 N/m; F .t/ F0 cos.0:25t/; F0 100 N. D e diﬀerential equation governing the position of the mass-less platform is given by: D D D b k dx dt C (a) Derive the transfer function F .t/ k x D XOUT F0=k x.t 0/ D D 0 m (b) Redesign the spring-damper system by changing out the spring so that the steady-state output magnitude is 0.40 m when driven by the force F .t/ 100 cos.0:25t/ N. D Problem 3 Consider a bell is modeled as a cone as shown here: In large bells, the clapper is motor controlled at the pivot. Consider the case where the motor provides a torque given by: T D 45 cos t Nm bkxF(t)LT(t)mθα6.5. CHAPTER ACTIVITIES 151 and there is a torsional spring with negligible damping at the pivot. Assume m L 100 Nm/rad; (cid:11) 1 m; (cid:20) 30(cid:14). 25 Kg; D D D D (a) Assuming the mass of the rod holding the clapper is negligible, determine if the steady- state motion of the clapper will ring the bell. If yes, why? If no, why not? Assume that the shape of the bell is a cone. (b) For what clapper mass would the steady-state motion of the clapper just barely reach the conical bell to ring it? Problem 4 Consider the lumped rotational mechanical system consisting of a point mass, m, sus- pended at the end of a long, thin bar whose mass is lumped entirely with the point mass a distance L away from a frictionless pivot. A translational spring and dashpot are attached to the mass a distance L away from the same pivot as shown: Use m D 0:1 kg; k D 40 N/m; b D 3 N-s/m; L 1 m. D (a) Derive the diﬀerential equation governing the angular motion of the system as a func- tion of time. Assume “small” angles to linearize the system. (b) What are the system’s natural frequency and damping ratio? (c) Derive the system transfer function, is applied at the pivot point, P . (cid:2)OUT T0=(cid:20) , if a driving torque of T0 15 cos.5t/ Nm D (d) Identify for what non-zero input frequency, !, the transfer function equals unity . 1/, i.e., the dynamic steady amplitude of angular vibration just equals the static angular deﬂection or “you get out precisely what you put in.” D kmbθL152 6. GOING NOWHERE? Problem 5 Consider the situation of drug absorption into a human being as mentioned in Prob- lem 11 in Chapter 5. e human body is your system and a drug is administered by the outside world at a rate given by f .t/. For such a case, the diﬀerential equation governing the amount of medicine in the bloodstream, M is given by: dM dt C rM D f .t/ t in hours where r D 0:0833 hr(cid:0) 1. ere are two means of drug delivery: (i) by injection or (ii) a periodic dosage of so many pills per day, i.e., a periodic input. For the case of an injection of 7 mg of drugs, we have f .t/ 0 and M.t 7 mg. e pill dosage can be modeled by a periodic input: M0 0/ D D D 3r cos (cid:0) (cid:25) D 4 t(cid:1) mg/hr (t in hours), and M.t f .t / 8r D C 0/ D D M0 D 0 mg. (a) Compute the total solution for the amount of drug in the body over time for the in- jection and the periodic pill dosage. (b) Compare the two solutions graphically. What amount of injection may deliver an equivalent amount of drug dosage as the pill prescription over time? (c) In this system are you supposedly “in control” of the system variables or the outside world? Problem 6 Consider the windshield wiper mechanism illustrated here. e mass-less blade is mR2 for the disk and wiper blade as- rigidly attached to the disk of radius R. Use I sembly for all calculations. (cid:25) (a) Assuming the angular rotation of the disk remains “small,” derive the diﬀerential equa- tion governing the sweep of the wiper blade. (b) Based on your diﬀerential equation, compute theoretical expressions for the system’s natural frequency and damping ratio. (c) Specify the damping coeﬃcient “b” necessary if you desire the steady-state wiper blade sweep to be (cid:1)(cid:18) 45(cid:14). D (cid:6) 6.5. CHAPTER ACTIVITIES 153 6 rad/s; R D 0:5 inches; k 1 lb/ft; m D D 0:02 slug. For all calculations, use: YIN 0:25 inches; ! D D Problem 7 Consider the parallel RLC electrical circuit shown below: MRθbky(t) = y0cos(ωt)+−V0CRV1L154 6. GOING NOWHERE? e governing diﬀerential equation for the capacitor voltage can be shown to be: LC V1 R C L V1 R P V1 C D L R P V0: Consider that the system is excited by a frequency modulated input voltage, V0.t/ E0 cos !t. D (a) Derive the transfer function for V1.s/=V0.s/ as a function of the relevant system pa- rameters and the frequency of excitation, !. (b) Using the transfer function, derive an expression for the amplitude ratio V1=E0. (c) Describe the behavior of the magnitude of the voltage across the capacitor at low fre- quency, resonance and high frequency? (d) At resonance, for what damping ratio will the amplitude ratio, V1=E0, fall below unity? (e) When the damping ratio (cid:16) shown here: D 1=2, a plot of ampliﬁcation ratio vs. frequency ratio is For this level of damping, determine for what input frequency ranges the output signal voltage drops below 20% of the input battery voltage if the system has a natural frequency of 2000 rad/s. What ﬁltering characteristics would you say this system exhibits? Describe whether a ﬁrst order system could exhibit such characteristics. If so, why? If not, why not? Problem 8 Consider a downhill skier skiing down a series of moguls wherein the angle of incli- nation of the skier varies harmonically such that 00.511.522.533.544.5500.10.20.30.40.50.60.70.80.91Frequency ratioAmplification ratio6.5. CHAPTER ACTIVITIES 155 (cid:18)0.t/ D 0:35 cos 2(cid:25) t radians: e ODE governing the skier’s velocity was given by: m v P C bv D mg sin (cid:18)0: Assuming the angle of inclination remains small, and invoking the small angle approxima- tion: m v P C bv D F .t/ D mg sin (cid:18)0.t/ mg(cid:18)0.t/ (cid:25) D 0:35mg cos 2(cid:25) t: (a) Derive the transfer function V .s/ .F .s/=b/ . (b) What is the steady-state magnitude of the skier’s downhill velocity? (c) With m 80 kg, and b D 1/, intermediate .(cid:28)! (cid:25) 16 Ns/m, classify the mogul gravity loading as low .(cid:28)! 1/. D 1/, or high frequency .(cid:28)! (cid:29) (cid:28) (d) Show that for a “very heavy” skier, their steady-state velocity magnitude would be: VSS D 0:35g 2(cid:25) i.e., that the steady-state velocity magnitude of the skier is independent of the skier’s mass. Is the skier described in part (c) “heavy” in steady state, dynamically speaking? Problem 9 Consider the translational series mass-spring-damper mechanical system shown below forced by excitation of the damper y.t/ YIN cos.!t/: D 156 6. GOING NOWHERE? (a) Show that the governing diﬀerential equation is given by: m x R b x P C C kx b y P D (b) Using the transfer function, derive an expression for the amplitude ratio XOUT YIN in terms of the damping ratio and the dimensionless frequency ratio. Describe, in words, the 1/, and high behavior of the ampliﬁcation ratio at low .r .r 1/, intermediate .r 1/ frequencies. (cid:28) (cid:25) (cid:29) (c) Is this system analogous to any of the electrical circuits you have experienced thus far? If so, describe the analogous system elements for each. (d) If the damper is pumped at a frequency p2 times the system’s resonant frequency, 4 cos p2!N t and the damping ratio for the system is 1=2, determine the output, steady-state motion of the mass, m, as a function of YIN cos p2!N t D D i.e., y.t/ (cid:24) D time. (e) At resonance, for what damping ratio will the amplitude ratio, XOUT YIN , fall below unity? Problem 10 Consider the regenerative braking lumped model illustrated here. Pumping the brake pedal eﬀectively acts as a base excitation on a damper linked to the brake disk of diameter, D, and mass, m 0:25 slugs. D 4 lb/ft; b k D D 20 lb-s/ft; D 1 ft; J D D 1 2 mR2; y.t/ D 0:5 cos.20t/ ft. kmxby6.5. CHAPTER ACTIVITIES 157 Show that, when the angular motion of the disk remains small, the governing ODE for the angular motion of the disk is given by: J R(cid:18) C bR2 P(cid:18) C 2kR2(cid:18) Rb y P D where J 1 2 mR2. D (a) Derive the transfer function for (cid:2)OUT YIN=D . (b) Using k 4 lb/ft; b 20 lb-s/ft; D 1 ft; m 0:25 slugs; y.t/ what is the steady-state angular motion amplitude, (cid:2)OUT? D D D D 0:5 cos.20t/ ft. D (c) Redesign the dashpot to reduce the steady-state amplitude to 0.25 radians. MRθk1k2by(t)C H A P T E R 7 159 e Fluid and ermal Casts Finally, we introduce two last casts of characters telling the story of eﬀort and ﬂow in ﬂuid and thermal systems. 7.1 FLUID SYSTEMS e ﬂow of ﬂuids fascinates everybody. We watch streams, waterfalls, whirlpools, and we are fascinated by this substance which seems almost alive relative to solids. Richard P. Feynman e Feynman Lectures on Physics e hydraulic analogy compares electric current ﬂowing through circuits to water ﬂowing through pipes. When a pipe is ﬁlled with hair, it takes a larger pressure to achieve the same ﬂow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push or voltage drop to drive the same ﬂow or electric current. Wikipedia Have you ever wondered why water is stored in high towers or standpipes? By virtue of their height, towers storing ﬂuid produce hydrostatic pressure suﬃcient to drive the ﬂuid out into distribution systems such as pipes for homes and businesses. Fluid ﬂows out of the tank under the gravitational force of its own weight. e ﬂuid eﬀort across a volume of contained ﬂuid pushes the ﬂuid which then responds by ﬂowing. Again, your intuition helps in this telling of the story. 7.1.1 FLUID EFFORT AND FLOW VARIABLES What pushes ﬂuid is a pressure diﬀerential across, say, a length of pipe. is drives a volume ﬂow rate of ﬂuid, Q, through the pipe. At their essence, ﬂuid systems are special cases of mechanical systems in general. As with mechanical systems, when the ﬂuid is incompressible, this volume ﬂow rate directly implies a mass ﬂow rate. m P D dm dt D (cid:26)Q: 160 7. THE FLUID AND THERMAL CASTS Table 7.1: Eﬀort, ﬂow, and conserved quantities for ﬂuid systems 7.1.2 STORAGE ELEMENTS e ﬂuid cast is capable of storing energy in both potential and kinetic forms. e ﬂuid system is nearly always a circuit of containment vessels that deliver ﬂuid from one location to another. Potential Energy Storage Character Potential energy storage in ﬂuid systems takes place when the ﬂuid stores a large eﬀort or pressure diﬀerential in a ﬂuid circuit. e ﬂuid cast member who plays the role of Captain Potential Energy is a storage tank. By virtue of a height or head of ﬂuid, a large static pressure diﬀerential is built up due to gravitational loading. Let’s now imagine: what factors will determine the amount of potential energy that a tank can store? It seems intuitive that the volume of ﬂuid may matter. But ﬂuid volume in, say, a cylindrical tank is a product of its area and height. It is a result from ﬂuid statics that the pressure at the bottom of a column of ﬂuid is determined solely by the height of ﬂuid in the column. Often pressure is measured in pressure head or the height of liquid of a given density that produces a given pressure. Pressure and height are, in this sense, both equally interchangeable eﬀort variables. Since pressure, and not force, drives the ﬂuid mass, what properties of a storage tank make for a ﬂuid system having the capacity to drive ﬂow of ﬂuid mass? First, let’s follow the mathematical relation for storage of potential energy of water kept in a tank of cross-sectional area, A. As we have already mentioned, the pressure at the bottom of the tank will be related to the height of water in the tank. So pressure and height are inter- changeable eﬀort variables. For the moment, let’s focus on pressure itself. Since you have not had a course in ﬂuid mechanics yet, let’s practice letting the mathematics and our analogy guide us. e mathematical expression of the storage by virtue of eﬀort is In this way, we have FLOW CFLUID D d.EFFORT/ dt : CFLUID Q D dp=dt D dV=dt dp=dt D dV dp : Here, the ﬂuid capacitance, CFLUID, is a rate of change of ﬂuid volume corresponding to a rate of change in applied pressure. Fluid dynamicists refer to this quantity as the ﬂuid compliance. en Conserved Quantity Units Symbol Fluid mass kg m Variable Units Effort Pressure N/ m2 ; lb/ft2 p Flow Volume flow rate m3/s ; ft3/s dVQdt= 7.1. FLUID SYSTEMS 161 Figure 7.1: e ﬂuid potential energy storage character is played by the storage tank. It stores energy in potential form in accordance with increased height of mass in the tank and storage of a pressure diﬀerential across the height of the tank. the analogy with mechanical systems comes full circle because in mechanical systems, the inverse of a substance’s stiﬀness is its compliance So analogously for ﬂuid systems d (cid:18) mg ATANK dp D CMECH k(cid:0) 1: D (cid:19) g ATANK D dm D g ATANK d .(cid:26)V / (cid:26)g ATANK dV D CFLUID dV dp D ATANK (cid:26)g (cid:17) where the ﬂuid capacitance is measured in CFLUID (cid:1) D m4s2=kg: Kinetic Energy Storage Character When considering energy storage via ﬂow, ﬂuid systems are directly analogous with translational mechanical ﬂow. e ﬂuid cast member who plays the role of Captain Kinetic Energy is that device that stores energy by virtue of its volume ﬂow rate. Consider the case of a ﬂuid that is incompressible. e volume ﬂow rate in a cylindrical pipe is determined directly by the ﬂuid velocity along the pipe. Kinetic energy is stored by virtue of ﬂuid velocity that is, in the strictest sense of our analogy, stored by a measure of the ﬂuid inertia. In ﬂuid systems, this is often referred to as the ﬂuid inertance. Again, without a physical intuition or feel for inertance, let’s allow the analogy to guide us mathematically. is may seem abstract, at the moment, but the analogous behavior, in the 162 7. THE FLUID AND THERMAL CASTS Figure 7.2: e ﬂuid kinetic energy storage character is played by the system’s inertia. Fluid inertance is embodied in a ﬂuid system’s mass. end, will hopefully bolster our physical feel once we undertake a course in ﬂuid mechanics and dynamics. e mathematical expression of the storage by virtue of ﬂow is EFFORT p L d.FLOW/ dt L dQ dt : D D Understanding that ﬂuids are a special case of mechanical systems m d (cid:29) dt : F D Using F pA, m D D (cid:26)A‘ and Q A(cid:29) D pA D (cid:26)A‘ d (cid:29) dt D (cid:26)‘ dQ dt or for ﬂuid, say, ﬂowing in a pipe of length, ‘PIPE p D ) dQ dt D (cid:26)‘ A LPIPE FLUID D L dQ dt (cid:26)FLUID ‘PIPE=APIPE where the ﬂuid inertance is measured in LFLUID (cid:1) D kg m4 : Many ﬂuid systems are designed for steady ﬂow purposes, e.g., hoses, faucets, pipelines. Transients occur when such systems are turned on and shut oﬀ, but for most of the operating time, the ﬂow is 0. In these instances, inertia plays a negligible role in the energy storage Q steady and P and the inertance is then neglected. d (cid:29)=dt (cid:25) / 7.1. FLUID SYSTEMS 163 7.1.3 DISSIPATIVE ELEMENTS Energy dissipation in ﬂuid systems results from any element in the ﬂuid circuit that impedes ﬂuid ﬂow rate. e role of the Evil Dr. Friction in the ﬂuid ﬂow script is played by the physical presence of friction acting against the ﬂow of ﬂuid. Two salient examples are pipe friction and losses exhibited in ﬂow of ﬂuid through valves or constrictions. Figure 7.3: e friction force is modeled by the net viscous force that is proportional to a pressure diﬀerence in the ﬂuid circuit. e governing mathematical expression of the dissipation is algebraic and often bears some- one’s name! Let’s consider an incompressible, viscous ﬂuid undergoing slow, laminar ﬂow in a pipe. For such conditions, the Hagen-Poiseuille law relates volume ﬂow rate, Q, of the ﬂuid to the pressure diﬀerence applied across the section of pipe driving the ﬂow And the Hagen-Poiseuille ﬂow law is given by RQ p D ) R D p=Q: p(cid:25)RD4=128(cid:22)‘ Q D where (cid:22) is the viscosity of the ﬂuid, and D and ‘ are the diameter and length of the pipe re- spectively. e viscocity is a ﬂuid property that quantiﬁes a ﬂuid’s material resistance to ﬂow. It is measured in poises: 1 poise (cid:1) D 0:1 Ns=m2: 164 7. THE FLUID AND THERMAL CASTS Using our analogy for resistance: and for Hangen-Poiseuille ﬂow EFFORT p R (cid:3) RQ D D FLOW p D ) 128(cid:22)‘ (cid:25)D4 Q RPIPE FLUID D 128(cid:22)‘ (cid:25)D4 : e resistance to ﬂow will increase linearly with the pipe length and ﬂuid viscosity. e resistance will also decrease as the pipe radius is increased, but this dependence is to the fourth power! e ﬂuid resistance is measured in RFLUID (cid:1) D Ns m2 (cid:3) m=m4 kg m4s : (cid:1) D Flow resistances from higher velocity ﬂows must account for turbulence. ese resistances are almost always nonlinear and will not be considered explicitly here. Table 7.2: Relevant system element relations for ﬂuid systems Field Effort Variable Flow Variable Fluid Pressure Mass flow rate Relation Form Analogy Dissipative Material Property Law Effort = Resistance x Flow Linear ()12ppRQ−= Resistance = Laminar Pipe Flow Linear Resistance = 4128LDµπ Energy Storage in Effort Variable Flow = Capacitance x d(Effort)/dt AdpQgdtρ= Fluid Capacitance = Compliance FLUIDACgρ= Energy Storage in Flow Variable Effort = Inductance x d(Flow)/dt dQpdt= Fluid Inductance = Inertance PIPEFLUIDPIPEFLUIDPIPEAρ== 7.1. FLUID SYSTEMS 165 Figure 7.4: e ﬂuid system cast of characters. 166 7. THE FLUID AND THERMAL CASTS 7.1.4 SINGLE STORAGE ELEMENT SCRIPTS An idealized case often studied is that of the storage tank draining out of an aperture cut below the ﬂuid surface or into an exterior pipe. Here, we might be asking how much time it takes to ﬁll or drain the tank. Or we might be interested in calculating the height of ﬂuid in the tank under steady ﬂow conditions. e system is comprised of the standing tank acting as the ﬂuid capacitor, and the draining pipe which is the ﬂuid resistor. You may ask why the tank’s resistance is not considered. It is, after all, a sort of “short” pipe with a rather large diameter. But consider the ratio of the tank’s eﬀective length to its diameter to the fourth power. When this value is negligible compared to that of the drainpipe, then the resistance of the pipe dominates over that of the tank and it may be reasonable to neglect the ﬂow resistance of the tank. We perform a force balance on a representative control volume of ﬂuid in the pipe. Father Force, pictured on the ladder in Figure 7.5, provides a supply of water from the outside world. Let’s presume he turns on an input tap that provides a ﬂuid volume ﬂow rate of QIN. e pressure Figure 7.5: e classic problem of the draining tank. diﬀerence across the pipe created by the weight of ﬂuid in the tank drives the outgoing ﬂow in the drainpipe. e pressure at the free surface in the tank and the outﬂow of the pipe is atmospheric. If we use this value as a reference eﬀort value, or alternatively use the so-called gauge pressure, we can set these reference values of pressure to zero. en the operative pressure diﬀerence across the pipe is illustrated in Figure 7.6. 7.1. FLUID SYSTEMS 167 Figure 7.6: Mass ﬂow rate over a control volume of ﬂuid in the draining pipe. From the eﬀort ﬂow analogy QIN QOUT CFLUID dp dt : D e input volume ﬂow rate is externally provided by “the outside world,” aka Father Force. e output volume ﬂow rate depends on the resistance of the pipe while the capacity to maintain a driving pressure diﬀerence is determined by the characteristics of the storage tank. Using the corresponding system element equations corresponding to Dr. Friction and Captain Potential (cid:0) 168 7. THE FLUID AND THERMAL CASTS Energy, respectively, QIN p=RPIPE FLUID D (cid:0) CFLUID d .p/ dt RPIPE FLUIDC TANK FLUID dp dt C p D RPIPE FLUIDQIN: is is a diﬀerential equation for the pressure at the bottom of the tank or entry to the pipe, the system eﬀort variable. is is also linearly related to the height of ﬂuid in the tank, often called the pressure head. Performing a change of variable from pressure to pressure head p D (cid:26)Ahg=A (cid:26)gh: D RPIPE FLUIDC TANK FLUID d .(cid:26)gh/ (cid:26)gh dt C dh dt C h RPIPE FLUIDQIN RPIPE FLUIDQIN=(cid:26)g: D D RPIPE FLUIDC TANK FLUID When there is no source from the outside world, the equation will be homogeneous. e solution of the homogeneous equation is the sole transient and the steady state is an empty tank with zero height of ﬂuid and zero gauge pressure. When there is an external ﬂow source, the steady-state height of ﬂuid in the tank will coincide with the condition that dh=dt 0 D ) hSS D RPIPE FLUIDQIN=(cid:26)g: e time constant is given by the classical RC expression using the hydraulic analogy to electrical systems RPIPE FLUIDC TANK FLUID D 128(cid:22)‘PIPEATANK (cid:26)g(cid:25)D4 PIPE (cid:28): D Note that (cid:28) turns out to have units of time, as we expect from the analogy: (cid:28) (cid:17) RPIPE FLUIDC TANK FLUID (cid:1) D (cid:18) kg m4s (cid:19) m4s2=kg (cid:1) D s: Recall that the governing equations for electrical systems typically appear in terms of eﬀort and/or ﬂow while mechanical systems are most often in terms of ﬂow. Steady incompressible ﬂuid systems are most often written in terms of eﬀort, either the ﬂuid pressure or pressure head. 7.1.5 MULTIPLE STORAGE ELEMENT SCRIPTS A multiple storage script must involve ﬂuid kinetic energy as well as ﬂuid potential energy. An illustrative case is that of the U-tube manometer. Fluid in static equilibrium in a vertical U-tube will contain as much ﬂuid mass or climb as high in the left tube as the right tube as shown in Figure 7.7. If an external pressure were applied to the free surface in the left tube, a relative ﬂuid height would develop as the ﬂuid originally in the left tube is displaced into the right tube. If the pressure were then released, this displaced ﬂuid would then be driven by a net gravitational loading until it moved back into the left tube. is motion would resemble that of a pendulum released from a given initial angle. 7.1. FLUID SYSTEMS 169 Figure 7.7: A classical U-tube manometer ﬂuid pendulum. If the tube friction is not suﬃcient to prevent it, the ﬂuid will overshoot the original equi- librium position by virtue of the kinetic energy of ﬂow. en it will climb up the left tube and “swing” back and forth as a ﬂuid pendulum. Friction between the ﬂuid and the tube walls will pro- vide damping and the transfer of potential energy to kinetic energy and back will be accompanied by losses that cause the ﬂuid pendulum swing to eventually cease (see Figure 7.8). Writing a momentum balance on a representative ﬂuid control volume, one can show that the diﬀerential equation governing the relative height of ﬂuid in the manometer is given by: RFLUIDA2 dh 2(cid:26)gAh AP .t/ (cid:26)AL dt C D d 2h dt2 C where P .t/ is an externally imposed gauge pressure at one ﬂuid surface. If we scale the entire equation to normalize the eﬀort variable term of pressure head, one can show that (see Chapter Activities Problem 2): C where the system element equation for the capacitance of a U-tube manometer is D C LFLUIDCFLUID Rh RFLUIDCFLUID Ph h HO .t/ and the pressure head forcing function is CFLUID D A=2(cid:26)g D You should take note that the coeﬃcient of the head, h, is already unity. As such, we have: H0 .t/ P .t/=2(cid:26)g: LFLUIDCFLUID (cid:1) D kg m4 m4s2 kg s2 (cid:1) D Cross-sectional area, A2hlength, L170 7. THE FLUID AND THERMAL CASTS Figure 7.8: e energy catch with losses in a U-tube manometer ﬂuid pendulum. which exhibits units of 1=!2 N and which exhibits units of 2(cid:16)=!N . RFLUIDCFLUID (cid:1) D s In this script, the externally applied pressure drives the ﬂuid mass which is initially opposed by a gravitational spring and tube friction. As the kinetic energy imparted to the mass by the pressure is reduced, an equivalent amount of potential energy is stored in the spring or height in Free Response Displacement HistoryTime, th(t1)h(t2)h(t3)TADCBABDCthe remaining tube. e ﬂuid system energy is simply transferred from kinetic to potential and back with dissipation provided by the tube walls. Once again, Captain Potential Energy and Captain Kinetic Energy “have a catch” with a ball of energy while the Evil Dr. Friction takes a bite at each pass. 7.2. THERMAL SYSTEMS 171 Figure 7.9: A dynamic second order system energy exchange with dissipation. 7.2 THERMAL SYSTEMS ere is apparently no thermal element which displays an energy storage mechanism which is complementary to the ﬂow store. Paul E. Wellstead Introduction to Physical System Modeling But as sure as you’re born … you’re never gonna see no unicorn. Shel Silverstein “e Unicorn” Finally, we introduce our last cast of characters telling the thermal story of eﬀort and ﬂow. e eﬀort-ﬂow analogy holds only in part for thermal systems because Captain Kinetic Energy does not exist! ere is no storage nor balance of a momentum-like quantity in any thermal system. ermal kinetic energy is a unicorn. In other words, you won’t ﬁnd one! 172 7. THE FLUID AND THERMAL CASTS 7.2.1 THERMAL EFFORT AND FLOW VARIABLES In thermal systems, your intuition will again serve you well. You already know that a temperature diﬀerence across an element will cause heat to ﬂow from hot to cold. erefore, temperature plays the role of eﬀort while heat ﬂow rate is the ﬂow variable. Table 7.3: Eﬀort, ﬂow, and conserved quantities for thermal systems 7.2.2 STORAGE ELEMENTS e single most interesting characteristic of thermal systems is, arguably, that they can store only one type of energy, namely potential. is is the main and a crucial diﬀerence between thermal and all other systems. As such, thermal systems can only ever be governed by ﬁrst order diﬀerential equations in time. Let’s examine the potential energy character in detail. Potential Energy Storage Character ermal capacitance is deﬁned as the capacity to store an eﬀort diﬀerential across an element. Here that translates into a temperature diﬀerence. e energy stored per unit temperature dif- ference is a measure of the capacitive strength. e thermal cast member who plays the role of Captain Potential Energy is the mass which provides material-speciﬁc heat capacity. e mathematical expression of the storage by virtue of eﬀort is FLOW CTHERM D d.EFFORT/ dt which can then be written for thermal systems q q CTHERM D D ) (cid:17) mcP d.(cid:1)T / dt d.T CTHERM mcP : TREF/ (cid:0) dt mcP D d T dt Here, our thermal capacitor represents the potential for a thermal system to store thermal heat energy by virtue of a temperature diﬀerence contained in the element. A material’s ability to store Conserved Quantity Units Symbol Heat energy Joules J Variable Units Effort Temperature OC ; OF T Flow Heat flow rate Watt = J/s; BTU/hr q 7.2. THERMAL SYSTEMS 173 Figure 7.10: e thermal potential energy storage character is played by the heat capacity carried by the system mass. It embodies the thermal capacitance of the system. heat energy for every degree of rise in its temperature is referred to as its heat capacity, cP . mcP d.(cid:1)T / dt d.T CTHERM q q D D TREF/ (cid:0) dt mcP D dT dt where the quantity mcP .T capacitance is the total thermal heat capacity (cid:0) TREF/ is referred to as the internal energy of the system. e thermal CTHERM mcP : (cid:17) e heat capacity is an extensive quantity and is proportional to the system’s thermal mass. It is a measure of how much energy can be stored in a mass before its temperature will increase a single degree: mcP (cid:1) D kg kg : J (cid:0) (cid:14)C Kinetic Energy Storage Character In Shel Silverstein’s words, “you’re never gonna see no unicorn.” us, is the thermal kinetic energy storage character. Kinetic energy elements that store energy by virtue of the ﬂow variable simply do not exist. Ergo, Paul Wellstead’s notion that “apparently, there are none.” Captian Kinetic Energy is AWOL! is has tremendous implications for thermal system dynamics. Namely, because both Captain Potential Energy and Captain Kinetic Energy must be present and accounted for in order to have a second order system, all thermal systems are necessarily governed by ﬁrst order equations in time. 174 7. THE FLUID AND THERMAL CASTS Figure 7.11: e thermal kinetic energy storage character does not exist!! 7.2.3 DISSIPATIVE ELEMENTS Dissipation in thermal systems is provided by physical agents that impede heat ﬂow. Heat ﬂow is impeded diﬀerently in solid, ﬂuid, and a vacuum. Heat ﬂows through a solid by means of conduction, through ﬂuids by means of convection, and through a vacuum by radiation. Radiative heat ﬂow is highly nonlinear and will not be addressed here. Conductive Resistance to Heat Flow Heat ﬂows through solids by conduction, a process in which heat thermally agitates the solid atoms in their lattice. e solid lattice impedes the ﬂow of heat. A temperature diﬀerence must be imposed across a solid to drive heat ﬂow through it. By virtue of their lattice structure, solids that are conducting heat provide a thermal resistance to heat ﬂow. Here, Fourier’s law of heat conduction provides a relationship between a temperature dif- ference across a solid of constant thickness and the resulting heat ﬂow rate by virtue of a material property known as the thermal conductivity, k. Fourier said that the heat ﬂux through a solid is proportional to the local temperature gradient through the thermal conductivity qCOND kA dT dx : D (cid:0) Consider once more that in deriving a diﬀerential equation for heat ﬂow, we balance heat into and out of a small representative control volume in the system. If the control volume is suﬃciently small, any temperature distribution will “look linear” and we can model the temperature gradient as a ﬁnite diﬀerence qCOND kA dT dx (cid:25) (cid:0) kA (cid:1)T (cid:1)x D (cid:0) kA T2 x2 D (cid:0) T1 x1 D T1 kA T2 (cid:0) L (cid:0) (cid:0) where L is some representative distance across which conduction is taking place through “a win- dow” of cross-sectional area, A, and at whose ends the temperatures are T1 and T2, respectively. 7.2. THERMAL SYSTEMS 175 Figure 7.12: Solids provide thermal resistance to heat ﬂow by the energy lost through thermal agita- tion of strongly bonded solid lattice networks. We are now able to relate the temperature diﬀerence necessary to drive heat ﬂow through a re- sistive element T1 T2 (cid:0) D L kA qCOND D RCOND THERMqCOND where we can now apply the system analogy EFFORT RCOND D THERM (cid:17) RCOND L=kA THERM (cid:3) FLOW where the units of thermal resistance are given by L=kA (cid:1) D m= m W (cid:0) (cid:14)C m2 (cid:14)C W (cid:1) D and heat ﬂow rate is measured in watts W Watt (cid:1) D (cid:17) J s : Convective Resistance to Heat Flow Alternatively, heat ﬂow is impeded in a diﬀerent manner when being transferred through a ﬂuid. Heat ﬂows through a ﬂuid medium by a process known as convection, and the ﬂuid provides a thermal resistance as heat convects through the ﬂuid under the inﬂuence of an imposed temper- ature diﬀerence. 176 7. THE FLUID AND THERMAL CASTS Figure 7.13: Fluid media provide thermal resistance to heat ﬂow by the energy lost through thermal agitation of loosely bound ﬂuid molecules. Convective heat ﬂow is governed by Newton’s Law of Cooling whereby a solid at tempera- , will result in heat transferred ture, T , surrounded by a large reservoir of ﬂuid at temperature, T through the ﬂuid given by 1 qCONV hA .T T / hA(cid:1)T (cid:0) where h is referred to as the heat transfer or ﬁlm coeﬃcient and A is the area through which the heat is ﬂowing. Inverting this relationship, the resulting temperature diﬀerence between the solid surface and the ﬂuid becomes D D 1 (cid:1)T 1 hA D qCONV D RCONV THERMqCONV and invoking the eﬀort-ﬂow analogy RCONV 1= hA THERM (cid:3) FLOW EFFORT RCONV D THERM (cid:17) (cid:14)C W (cid:1) D m2 . W m2 (cid:14)C where RCONV THERM (cid:17) 1= hA (cid:1) D 1= A list of thermal system element equations is given in Table 7.4. A summary of the thermal cast and the roles they play is given in Figure 7.14. 7.2.4 SINGLE STORAGE ELEMENT SCRIPTS An idealized case often studied is that of conduction through a solid, insulated wall. e solid is characterized by a capacity to retain heat measured by its temperature. Father Force is now temperature. e heat capacity of the wall allows it to store thermal energy by virtue of its tem- perature. is is referred to as the solid wall’s internal energy. e heat capacity of the wall is 7.2. THERMAL SYSTEMS 177 Figure 7.14: e thermal system cast of characters. 178 7. THE FLUID AND THERMAL CASTS Table 7.4: Relevant system element relations for thermal systems likened to a thermal spring being pushed by Father Force as shown in Figure 7.15. is illustrates the capacity of the wall to remain at an elevated temperature and store thermal energy in a form measurable by its eﬀort variable. e solidly bonded molecules of the insulating layer provide resistance to heat ﬂowing through them to the outside, TOUT < T . In order to balance heat ﬂow rate through the insulation, we perform a thermal heat energy balance on a representative control volume in the insulation. qOUT 0 (cid:0) D CTHERM dT dt D mcP d .T / dt where T is the temperature of the wall. If the dominant temperature diﬀerence is that between the wall and the temperature outside of the insulating layer, TOUT, then we can represent the heat Field Effort Variable Flow Variable Thermal Temperature Heat flow rate Relation Form Analogy Dissipative Material Property Law Effort = Resistance x Flow ()12TTRq−= Convective Resistance = 1hA Conductive Resistance = LkA Energy Storage in Effort Variable Flow = Capacitance x d(Effort)/dt PdTqmcdt= Capacitance = Thermal Heat Capacity THERMPCmc= Energy Storage in Flow Variable Effort = Inductance x d(Flow)/dt Not Applicable Inductance = There is no thermal equivalent or analog for inductance 7.2. THERMAL SYSTEMS 179 mcP d .T / dt Figure 7.15: Heat ﬂow through a control volume across a solid wall. ﬂowing out through the insulation as kA(cid:1)T =L (cid:0) D (cid:0) TOUT / =RINSULATION .T (cid:0) RCOND THERMCTHERM ) CONDUCTION D dT dt C D T TOUT 180 7. THE FLUID AND THERMAL CASTS resulting in RCOND THERMCTHERM dT dt C T D TOUT : e excitation from the outside world is provided by the external temperature. e solution of this equation is a temperature changing monotonically from T .0/ to TOUT in roughly four time constants. e time constant is given by the classical RC expression using the analogy to electrical systems Note that the units of the time constant are: RCOND THERMCTHERM mcP L D kA D (cid:28): RCOND THERMCTHERM (cid:28) mcP L kA (cid:1) D J (cid:14)C (cid:14)C W s (cid:1) D (cid:17) or units of time. e analogy delivers a parameter known to characterize all ﬁrst order systems in time as we’ve described them. (cid:17) Alternatively, a simple illustration of convective heat transfer occurs during quenching: when a hot, small solid object is transferred to a large cooling bath (Fig. 7.16). In order to balance Figure 7.16: Heat ﬂow through a control volume contained in a ﬂuid surrounding an object from which heat is being transferred. heat ﬂow rate in the ﬂuid surrounding the quenched sphere, we perform a heat energy balance on a representative control volume in the ﬂuid reservoir. qSTORED qOUT (cid:0) hA .T qIN 0 (cid:0) D T (cid:0) / 1 D mcP dT dt D CTHERM dT dt : TTOUT7.3. CHAPTER ACTIVITIES 181 Invoking the eﬀort-ﬂow analogy 0 (cid:0) 1 RCONV THERM .T T / 1 (cid:0) D mcP dT dt D CTHERM dT dt : Rearranging RCONV THERMCTHERM dT dt C T : T 1 D e excitation from the outside world is provided by the quench tank ﬂuid reservoir temperature. e solution of this equation is a temperature changing monotonically from T .0/ to T in roughly four time constants. e time constant is given by the classical RC expression using the analogy to electrical systems 1 RCONV THERMCTHERM D 7.3 CHAPTER ACTIVITIES mcP hA D (cid:28): Problem 1 A U-tube manometer is a relatively simple device used to measure pressure. When the ﬂuid level is displaced as shown above and released, the following oscillation in relative ﬂuid height is observed: When a periodic pressure is applied at one end, a force and mass balance on the system gives the following governing diﬀerential equation for the ﬂuid height, h.t/: R(cid:26)A2 dh dt C 2(cid:26)gAh D PA cos 4t d 2h dt2 C 0/ D 0/ D D (cid:26)AL h.t dh dt D .t 5 cm 0 cm=s where (cid:26) is the ﬂuid density, A 1 cm2, and L 5 cm. D D Free Response Displacement HistoryTime, th(t1)h(t2)h(t3)TCross-sectional area, A2hlength, L182 7. THE FLUID AND THERMAL CASTS (a) Using representative analogies in Table 7.2, show that the diﬀerential equation gov- erning the height, h, can be written as: RFLUIDCFLUID Ph h C D H0.t/ LFLUIDCFLUID Rh H0.t/ D CFLUID C P .t/=2g(cid:26) A=2(cid:26)g: D it is critically damped. Assume the acceleration due to gravity is given by g (b) Write an algebraic expression for the ﬂuid inertance, i.e., the ﬂuid inertia. (c) Calculate the natural frequency and the ﬂuid resistance, R, in this pendulum system if 10 m/s2. (d) What periodic pressure magnitude, P , needs to be applied to obtain a steady-state output height of 2 cm (an amount that will just cause liquid to spill out of the U- tube). D (e) What are the characteristic times for the system in part (d)? (f ) If the tube resistance is removed, i.e., R 0 1=m D the ﬂuid height, h.t/, as a function of time. (cid:0) s. Compute the total solution for Problem 2 e height of ﬂuid in a tank with two outlet pipes, one at the bottom of the tank and one 2 meters directly above it, is given by the following governing diﬀerential equation: 1 R2 H / .h (cid:0) D QIN P g A g Ph A H R1 R2 D D h C 1 R1 C 20 m2 2 m 2 1=ms 2 1=ms 30 m3=s D D D 10 m=s2 QIN P g (cid:25) hH(a) What are the conserved quantity, and the eﬀort and ﬂow variables? (b) Sketch the response for the height of ﬂuid in the tank. Assume the initial height is 5 7.3. CHAPTER ACTIVITIES 183 meters. (c) Assume the system has already come to steady state. From this new initial state, what is the new steady-state height of ﬂuid in the tank if the top outlet pipe is suddenly lowered 1 m, i.e., H 1 m? D (d) How long will it take to attain this new steady-state height? Problem 3 e diﬀerential equation governing heat transfer in the thermocouple probe quenched suddenly in a ﬂuid bath maintained at T 1 is given by mcP dT dt D hA .T 1 (cid:0) T / where m is the mass of thermocouple bead, cp is its speciﬁc heat per unit mass, h is the heat transfer coeﬃcient of still air, and AS is the surface area of the thermocouple bead. Supposed it is known that the time constant for an experiment is 3 minutes from which it is determined that the heat transfer coeﬃcient of still air is h (cid:0)(cid:14)C . If you know the heat transfer coeﬃcient of still ice water is h (cid:0)(cid:14)C , roughly how long will it take for the thermocouple bead to reach steady-state when the probe is re-immersed quickly into the ice water? 3600 W 15 W m2 D D m2 Problem 4 For the thermocouple probe quenched in Problem 3, the temperature, T .t/, is gov- erned by the following 1st order ODE plunged suddenly in boiling water from standing air: mcP hAS .T D dT dt C 0/ D 100 T D 20 (cid:14)C (a) Sketch the dynamic thermal response of this ﬁrst order system of a room temperature mass suddenly placed in boiling water. (b) Consider that at the same time, you have a second mass with double the heat capacity of the original mass, cP , that is at an initial temperature of 150 degrees C when it is placed suddenly in a reservoir of liquid with a heat transfer coeﬃcient 40% of that for water. On the same graph, sketch the response of this second mass. (c) Write the functional form of the temperature solution for the second mass. Problem 5 Consider an electrical analogy to a human artery provided by the 4-element Wind- kessel model. e capacitor represents the elasticity of the arterial wall, i.e., ranges of this value can model hardening of the arteries. e resistance to blood ﬂow is determined by the 184 7. THE FLUID AND THERMAL CASTS viscosity of blood, i.e., a dehydrated patient will exhibit more viscous blood and a higher resistance to ﬂow. An inductor is said to simulate inertia of the blood, i.e., it can model the density of blood changing as when its iron content becomes depleted. P .t/ 25 cos !t V R1 R2 C L D 1000 (cid:10) 1000 (cid:10) D D :002 f 40 H D D In this analogy, the current represents the blood ﬂow rate, the applied voltage source rep- resents the eﬀort variable of blood pressure, and the frequency of the input excitation is the heart rate or pulse (where it is understood that rad/s correlates with beats-per-minute). e governing diﬀerential equation for the system blood ﬂow rate (current in the model) is given by: LC d 2iC dt2 C (cid:18)R1C L R2 C (cid:19) diC dt C (cid:18)1 (cid:19) iC R1 R2 C P .t/ R2 C C dP dt D where R1 R2 D D R: Consider that the so-called inertia of the ﬂuid is small, but not zero. Mathematically, this implies (cid:28) (a) Make a mathematically convincing argument, i.e., back it up with the necessary equa- tions/relationships, to show that as the heart rate increases dramatically, a condition LC RC 7.3. CHAPTER ACTIVITIES 185 known as tachycardia, the blood ﬂow rate decreases for a given constant blood pres- sure. Assume any response to initial conditions has decayed away and the system is in steady state. HINT: Consider the transfer function for I =.P =R/ when formulating your answer! (b) Describe, in words, the behavior of the ampliﬁcation ratio, I =.P =R/, at low .r << 1/, !=!N . 1/, and high .r >> 1/ normalized frequencies where r intermediate .r (cid:25) D (c) For the given input magnitude blood pressure of 25 V, if a life-viable cutoﬀ blood ﬂow rate in steady state is 4 milli-amperes, at what heart rate, !, will the patient expire? Problem 6 Consider an older weightlifter who loves sausage and whose diet has hardened his arteries. An electrical 4-element Windkessel model identical in structural form to that for Problem 5 may be used. For such an analogous electrical heart, the governing diﬀerential equation and corresponding transfer function for the weightlifter’s blood ﬂow rate are given by: (cid:18)1 R1 R2 C (cid:19) I.t/ L R2 P I .t/ C LC I .t/ R C D 1 R2 P .t/ C P .t/ P C IOU T .PIN=.R1 C R2// D .1 1 (cid:0) C r 2/ r 2(cid:16) j 2(cid:16)rj C Assume: L 40 H C I 100 (cid:22)f I R1 D D D 9000 (cid:10) R2 I D 1000 (cid:10) P .t/ I D 1000 cos.50t/ V. (a) For these conditions, what is the steady-state amplitude of blood ﬂow rate (current)? (b) If the inductance is increased 5 fold to 200H and the capacitance is further reduced 5 fold to 20 (cid:22)f (i.e., the arteries continue to harden), to what extent will this change the steady-state blood ﬂow rate amplitude? (c) Find an expression for the ampliﬁcation ratio, A, as a function of damping ratio, (cid:16), at resonance (r 1). D Problem 7 Consider the electrical circuit analog for a quenched solid in an insulating jacket as shown here: 186 7. THE FLUID AND THERMAL CASTS e resulting governing diﬀerential equation for the solid’s temperature is given by: (cid:26)V cP dT dt C (cid:18) 1 R1 C (cid:19) T 1 R2 1 R1 D TBATH cos.!t/ T T (a) When forced by a periodic input at low frequency, the amplitude ratio approaches what value? Give your answer as an algebraic expression in terms of R1 and R2. 1 (b) What does the amplitude ratio T T 1 approach for high frequency input? Problem 8 Before insulating materials were readily available, buildings were thermally insulated by endowing their walls with suﬃciently large thermal time constants. When driven by the daily solar thermal ﬂuctuation, the diﬀerential equation governing (cid:18), the ﬂuctuation in wall temperature above and below its average daily value, is given by: 4 P(cid:18) (cid:18) C D 12 cos (cid:16) (cid:25) 12 t(cid:17) (cid:14)F where the time, t, is measured in hours. (a) What is the amplitude of the steady-state thermal ﬂuctuation of the wall (in (cid:14)F)? (b) For what value of the thermal time constant will the amplitude of the steady-state 7.3. CHAPTER ACTIVITIES 187 thermal wall ﬂuctuation drop to 2(cid:14)F, eﬀectively insulating the building? (cid:6) (c) How would you re-design the wall so that the steady-state response is reached in ap- proximately 6 hours? You may state your answer in terms of the characteristic time or times of the system response. (d) Draw an analogous electrical circuit whose behavior would be equivalent in some sense to this thermal problem. Label all the analogous electrical system elements correspond- ing to each of the thermal elements and describe the relevant input forcing function to the electrical circuit. Problem 9 Consider omas Jeﬀerson’s home at Monticello, built before insulation was avail- able. In the 18th century, buildings were thermally insulated by endowing their walls with suﬃciently large thermal time constants. When driven by the daily solar thermal ﬂuctuation, the diﬀerential equation governing (cid:18), the ﬂuctuation in wall temperature above and below its average daily value, is given by: mcp P(cid:18) C kA L (cid:18) D 40kA L cos (cid:16) (cid:25) 12 t(cid:17) (cid:14)C where the time, t, is measured in hours, and: kA L D mcp D 100 Jm=hr (cid:14)C 0:25 m 1600 J=(cid:14)C D e dimensionless Biot number, Bi hL k D D RCOND RCONV quantiﬁes the relative magnitudes of conductive and convective resistances in a thermal system. e wall here is designed such that its Biot number is very large so that convection to the air surrounding the walls can be neglected. 188 7. THE FLUID AND THERMAL CASTS (a) What is the amplitude of the steady-state thermal ﬂuctuation of the wall (in (cid:14)C)? (b) For what value of the thermal time constant will the amplitude of the steady-state thermal wall ﬂuctuation drop to 5(cid:14)C, eﬀectively insulating the building? (cid:6) (c) Re-design the wall by altering its thickness only so that the time constant obtained in part (b) can be obtained? (d) With the time constant from part (c), how many hours will any transient now last en route to steady state? (e) Draw an analogous electrical circuit whose behavior would be equivalent to this ther- mal problem. NOTE: You must draw the actual circuit and then label all the analogous electrical system elements corresponding to each of the thermal elements and describe the relevant input forcing function to the electrical circuit. C H A P T E R 8 Summary 189 e rules that describe nature seem to be mathematical. It is not a characteristic necessity of science that it be mathematical. It just turns out you can state mathematical laws which work to make powerful predictions. Why nature is mathematical is, again, a mystery. Richard Feynman e Meaning of It All Fortunately, today’s online world, with its advances in video and animation, oﬀers several underused opportunities for the informal dissemination of mathematical ideas. Perhaps the most essential message to get across is that with math you can reach not just the sky or the stars or the edges of the universe, but timeless constellations of ideas that lie beyond. Manil Suri How to Fall in Love With Math A la Suri [15], what we’ve sought to oﬀer here is a digestible version of building govern- ing diﬀerential equations from the cartoon building blocks of characters with whom are associ- ated fundamental relations from the eﬀort-ﬂow analogy. We’ve presented an animated storyline wherein Captains Potential Energy and Kinetic Energy store system energy while the Evil Dr. Friction ﬁnds ways to steal it. We motivate these characters as roles in a common movie script about energy transfer in systems dynamics. We’ve then introduced the mechanical, electrical, ﬂuid, and thermal casts that play these energy roles in the separate system disciplines. It has been our intention to simply provide a mnemonic device to remember that separate physical actors always play the same roles in this movie. We also associate with these roles in the script equations relating eﬀort and ﬂow. Simple conservation balances then hopefully provide a more straightforward way to remember how to derive a governing diﬀerential equation for the system. We have also provided the story to show how features of our superheroes characterize the solutions to these equations. More than half of the students taught with these character rep- resentations of the eﬀort-ﬂow analogy claim these stories made coming to terms with systems dynamics more fun and the concepts more memorable. Learning can be fun. Even learning math can be fun! 190 8. SUMMARY Figure 8.1: e cast of the movie script for systems dynamics: Father Force, Captains Potential and Kinetic Energy, and the “not always Evil” Dr. Friction! Afterword 191 is book has been written to present multi-disciplinary systems in a common light with an encompassing story focused on energy storage and dissipation. Based on our experience teaching the eﬀort-ﬂow analogy with these energy superheroes, we have found that the mnemonic of char- acters performing a common script played by discipline-speciﬁc actors helps students more clearly identify with the theme common to these dynamic systems. We have chosen a variety of chapter activities that illustrate this common behavior across engineering disciplines. After reading this manuscript, if you have comments on the presentation of the storyline or the orchestration of the chapter activities and examples or wish to suggest additional examples that emphasize system similitude across disciplines, feel free to contact the authors at [email protected].ank you, in advance, for any input you have. Bibliography 193 [1] Dym, C. (2004). Principles of Mathematical Modeling. Academic Press. 16 [2] Feynman, R. P. (1998). e Meaning of It All: oughts of a Citizen-Scientist. Perseus Books. 1, 16 [3] Feynman., R., Gottlieb, A., and Leighton, R. (2006). Tips on Physics:. Pearson Addison Wesley. 1 [4] Feynman, R. (2009). Richard Feynman on Electricity. https://www.youtube.com/watc h?v=kS25vitrZ6g. 22 [5] Feynman, R. (2012). What is the relationship between mathematics, science and na- http://www.researchgate.net/post/What_is_the_relationship_between ture? _Mathematics_Science_and_Nature. xiv, 1 [6] Jensen, B. D. and McLain, T. W. (2012). System Dynamics. http://twmclasses.group s.et.byu.net/lib/exe/fetch.php?media=483:335notes.pdf. xiii [7] Johnson, A. T. (1998). Biological Process Engineering: An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems. Wiley-Interscience. [8] Johnson, A. T. (2001). Teaching by analogy: e use of eﬀort and ﬂow variables. Proceed- ings of the 2001 American Society of Engineering Education Annual Conference & Exposition, Session 2973:1–3. xiii [9] Lehrer, J. (2012). IMAGINE: How Creativity Works. Houghton Miﬄin. xvii [10] Ogata, K. (2003). Systems Dynamics. Prentice Hall. 73 [11] Palm, W. (2013). Systems Dynamics. McGraw Hill-Engineering-Math. 73 [12] Public Broadcasting System–NOVA (1993). e Best Mind Since Einstein - Richard Feyn- man Biography. Television Production. 16 [13] Singer, S. and Smith, K. A. (2013). Discipline-based education research: Understanding and improving learning in undergraduate science and engineering. Journal of Engineering Education, 00:1–4. DOI: 10.1002/sce.21091. xv 194 BIBLIOGRAPHY [14] Soﬁa, J. W. (1995). e fundamentals of thermal resistance measurement. Technical report, Analysis Tech. 16 [15] Suri, M. (2013). How to Fall in Love With Math. http://www.nytimes.com/2013/09/ 16/opinion/how-to-fall-in-love-with-math.html. 189 [16] Susskind, L. and Hrabovsky, G. (2013). e eoretical Minimum: What You Need to Know to Start Doing Physics. Basic Books. 4 [17] Tippett, K. (2010). Einstein’s God. Penguin Books. xiii [18] Wellstead, P. E. (2000). Introduction to Physical System Modelling. www.control-systems- principles.co.uk. xiii [19] Woods, R. L. and Lawrence, K. L. (1997). Modeling and Simulation of Dynamic Systems. Prentice Hall. xiii, 73 Authors’ Biographies 195 VINCENT C. PRANTIL Vincent C. Prantil earned his B.S., M.S., and Ph.D. in Mechanical Engineering from Cornell University where he was awarded the Sibley Prize in Mechanical Engineering and held an An- drew Dickson White Presidential Fellowship. He was a Senior Member of Technical Staﬀ at Sandia National Laboratories California in the Applied Mechanics and Materials Modeling Di- rectorates for eleven years. He joined the faculty in the Department of Mechanical Engineering at the Milwaukee School of Engineering in September 2000 where he presently specializes in ﬁnite element model development, numerical methods, and dynamic systems modeling. Since joining academia, he has become interested in the use of animation to both engage students and as a suggestive tool for students to use as a mnemonic device to enhance long-lasting learning. In addition to working with Tim Decker in Milwaukee, he has teamed up with colleagues at North- ern Illinois University and Rutgers University in their eﬀorts to showcase the power of video simulation for teaching undergraduate engineering concepts in dynamic modeling and controls theory. TIMOTHY DECKER Timothy Decker has played an important role in educational engagement over the past several decades. With extensive experience in game animation, character design and children’s television, Tim has been an Animation Supervisor for Disney Interactive, lead animator for Knowledge Ad- venture, and layout artist/animator for the award-winning television series “e Simpsons” as well as Teenage Mutant Ninja Turtles, Alvin and Chipmunks, and the Critic. He has also appeared on many episodes of the “Imagination Station” as a guest artist inspiring children in the art of anima- tion and cartooning. He has extensive experience directing animation in Canada, India, Korea, and the United States. roughout his career, Tim has won numerous gaming awards from PC Magazine, Communication Arts Magazine, Family Magazine and the Academy of Arts and Sci- ences. Tim has been awarded three regional Emmy awards for his participation with Milwaukee Public Television. Tim holds a Bachelor’s degree in Character Animation and Film from Califor- nia Institute of the arts (CalArts) and an Associates degree in Illustration from Rocky Mountain College of Art and Design. Tim is enjoying his second career as a Lecturer at Peck School of the Arts at the University of Wisconsin–Milwaukee and Milwaukee Area Technical College. Tim teaches animation, character development, puppetry, claymation, and drawing for animation. His students are major participants in many national and international ﬁlm festivals.Tim believes 196 AUTHORS’ BIOGRAPHIES that immersive virtual environments are advantageous for communicating complex ideas, and that animation has the ability to support the telling of scientiﬁc stories in medical, engineering, and applied sciences.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8355742.pdf&bkn=8355741&pdfType=book	Series ISSN: 2327-6738 Series Editor: Robert Beitle, Jr., University of Arkansas Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw, Bahir Dar University, Ethiopia This book is designed to be used in an introductory sophomore-level undergraduate course in chemical engineering, civil engineering, industrial engineering, chemistry, and/or industrial chemistry. Senior-level students in resource development, soil science, and geology might also find this book useful. In addition, it is our hope that even advanced mathematics-oriented high school seniors might find the material easy to master as well. This book emphasizes concepts, definitions, chemical equations, and descriptions with which some chemical science professionals struggle. It stresses the importance of maintaining uniformly high standards in pure chemical science and manufacturing technology while still keeping in mind that procedures that might seem strange also yield results that prove effective. ABOUT THE AUTHOR Tadele Assefa Aragaw is a lecturer in Chemistry and Environmental Engineering, a Researcher, and a Facility Manager in the Chemical and Food Engineering at the Bahir Dar Institute of Technology. Since 2017 he has been involved in a research project in the area of Ethiopian kaolin characterization for different industrial applications as well as an indigenous microalgae investigation from wastewater for biodiesel production. In 2012, Tadele received his B.S. in Chemistry from the University of Gondar. In 2014, he started studying for his master’s degree in Environmental Engineering while also teaching an Analytical Chemistry and Environmental Engineering course for Chemical Engineering students. He received his M.Sc. in Environmental Engineering in 2016 from the Bahir Dar Institute of Technology, Bahir Dar University. Tadele has published articles in the field of his profession, Environmental Engineering. About SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis books provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. store.morganclaypool.com A R A G A W C O N C I S E I N T R O D U C T I O N T O C E M E N T C H E M I S T R Y A N D M A N U F A C T U R I N G M O R G A N & C L A Y P O O L Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw Concise Introduction to Cement Chemistry and Manufacturing Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw 2018 Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi 2018 Empowering Professional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimizaton, Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 iii The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 iv Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 v Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2018 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw www.morganclaypool.com ISBN: 9781681733234 ISBN: 9781681733241 ISBN: 9781681733258 paperback ebook hardcover DOI 10.2200/S00839ED1V01Y201803ENG031 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Series ISSN Print 1939-5221 Electronic 1939-523X Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw Bahir Dar University, Ethiopia SYNTHESIS LECTURES ON ENGINEERING #31 CM&cLaypoolMorganpublishers&ABSTRACT This book is designed to be used in an introductory sophomore-level undergraduate course in chemical engineering, civil engineering, industrial engineering, chemistry, and/or industrial chemistry. Senior-level students in resource development, soil science, and geology might also ﬁnd this book useful. In addition, it is our hope that even advanced mathematics-oriented high school seniors might ﬁnd the material easy to master as well. This book emphasizes concepts, deﬁnitions, chemical equations, and descriptions with which some chemical science professionals struggle. It stresses the importance of maintaining uniformly high standards in pure chemical science and manufacturing technology while still keeping in mind that procedures that might seem strange also yield results that prove eﬀective. KEYWORDS cement chemistry, cement production, clinkerization, dry process, manufacturing, Portland cement, wet process Contents ix Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 2 3 4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Classiﬁcation of Cements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Raw Materials and Their Components for Cement Production . . . . . . . . . . . . . . 3 2.1 The Raw Material Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Mode of Formation of Limestones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Carbonate Associations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Additives and Corrective Materials in Cement Production . . . . . . . . . . . . . . . . . 7 Exploration of Raw Materials for Cement Manufacturing . . . . . . . . . . . . . . . . . . 9 4.1 Signiﬁcance of Raw Materials Exploration in Cement Making . . . . . . . . . . . . . 9 4.2 Objectives of Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 The Composition of Portland Cement and Production Process . . . . . . . . . . . . . 11 5.1 Clinkerization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.1.1 Clinker Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.1.2 Clinkerization Phenomenon vis-à-vis Clinker Characteristics . . . . . . . 14 5.2 Raw Materials for Cement Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.3 Chemical Composition of Raw Mixes and Compositional Compatibility . . . 16 5.3.1 Module Values of Raw Mixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.3.2 Eﬀect of Chemical Composition on the Reactivity and Burnability of Raw Mixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.4 Particle Size of Ground Materials in Raw Mixes and Physical Properties of Clays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 x 6 Burnability and Clinkerization of Cement Raw Mixes . . . . . . . . . . . . . . . . . . . . 23 6.1 6.2 6.3 Burnability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Reaction Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 7 Manufacturing Portland Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.1 Dry Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Wet Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 8 9 Testing Portland Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.1 Samples for Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.2 Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8.3 Fineness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 8.4 Consistency of Standard Cement Paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Soundness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 8.5 8.6 Setting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 8.7 Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 8.8 Hydration of Portland Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 10 Diﬀerent Kinds of Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 10.1 Rapid Hardening or High Early Strength Cement . . . . . . . . . . . . . . . . . . . . . 41 10.2 High Alumina Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 10.3 Quick Setting Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 10.4 Portland Slag Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 10.5 Low Heat Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 10.6 Air Entraining Portland Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 10.7 White Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 10.8 Colored Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 10.9 Portland Pozzolana Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 10.10 Chemically Inert (Acid-resistant) Cements . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 11 Storage of Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 xi 12 Technical Analysis of Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 12.1 Solution Preparation and Apparatus/Reagents Used . . . . . . . . . . . . . . . . . . . . 50 12.2 Sample Analysis and Their Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 12.2.1 Experiment No. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 12.2.2 Experiment No. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 12.2.3 Experiment No. 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 12.2.4 Experiment No. 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 12.2.5 Experiment No. 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 12.2.6 Experiment No. 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 12.2.7 Experiment No. 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 12.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 xiii Preface This book deals with the chemistry of the principal silicate and aluminate cements used in build- ing and civil engineering. Emphasis is placed throughout on the underlying science and manu- facturing process but detail practical applications which are well covered in other works. In order to help the readers understand the context in which this book has been darted for chemical engineering, civil engineering, industrial chemistry, chemistry, soil science, and geology disciplines, the book represents a summary information collected from limited number of sources and written by the author’s understanding the science behind cement chemistry and manufacturing. The information provided in this book is intended to be used as an input to the determinations of the principles of production and chemistry of cement in speciﬁc areas. The rest of this section describes the type of information that is provided in each chapter of the book. Chapters 1, 2, and 3 provide general information on cement production in the world, together with its marketing, classiﬁcation, and type of cements, chemistry, and raw material, the formation of limestone, additives, and pozzolan materials in cement processing. Chapters 4, 5, 6, and 7 describe in more detail the mining of raw materials and com- position; clinkerization and production processes of cement including the advantages and dis- advantages of the dry and wet production mechanisms with quality and economic aspect; its burnability. Chapters 8, 9, 10, and 11 present the testing of the produced cement materials with certain parameters; hydration eﬀects of Portland cement for the cement strength; diﬀerent types of cement and storage mechanisms. Chapter 12 describes the technical analysis of basic cement quality parameters with a detailed laboratory procedure. It is therefore of the utmost importance that the information contained in this book is fully take into account the best available techniques that change over time. This book will be reviewed and updated as appropriate. Tadele Assefa Aragaw April 2018 Acknowledgments xv There are far too many people to thank for their contributions to this book. Whether it was help with the chemical equations, the writing of the text, preparation of illustrations, or overall understandability, all contributions are greatly appreciated. I would also like to thank the reviewers, Dr. Molla Bahiru, University of Gondar and Dr. Belete Asefa Aragaw, Bahir Dar University, for their many helpful comments and sugges- tions. Tadele Assefa Aragaw April 2018 C H A P T E R 1 Introduction 1 World cement [3] production has registered more than a nine-fold increase over the last three and a half decades—from 133 million tons in 1950 to 860 million tons in 1979 to 1 billion tons in 1985. At the same time, there has been tremendous technological progress in the ce- ment manufacturing process, which is being continuously updated through the introduction of new technological advances for capacity enhancement as well as by various devices for energy economy and conservation. Such developments during the past few decades have inevitably im- posed greater responsibility on the geologists and mining engineers engaged in exploration and exploitation of raw materials for cement manufacture. Cement is the name given to mineral powders which when mixed with water form a plastic body that easily can be shaped and that hardens after some time to yield a strong, stone hard body. Cement is used for making building and plastering mixes (lime), structural and decorative articles (Plaster of paris and magnesia cements), prefabricated concrete and reinforced concrete structural items, underground and hydraulic structures, etc. As can be understood from the uses, the production of cement in a country, particularly a developing one such as Ethiopia, has to be given great importance. 1.1 CLASSIFICATION OF CEMENTS Depending on their uses and properties, cements are divided into three main groups. 1. Air cements: harden and retain their strength in air. They include: air lime, gypsum, and magnesium cements. These materials are used for making buildings and plastering (lime) and structural and decorative articles (Plaster of Paris and magnesia cements). 2. Hydraulic cements: harden and retain their strength in water. They include: hydraulic lime, Roman cement, Portland cement, and cement with various admixtures (Pozzolan cement, Portland slag cement), alumina cements, etc. Hydraulic cements are more important than air cements and are used for making prefabricated concrete and reinforced-concrete struc- tural items and parts of buildings as well as underground and hydraulic structures. 3. Acid-resistant cements: hardening withstands the action of mineral acids such as H2SO4, HNO3, HCl, etc. In building practices, cements are used in the form of structural pastes of several types: grouts (i.e., a mixture of cement with water, mortars, mixtures of cement with water and ﬁne ag- 2 1. INTRODUCTION gregate (sand)), and concrete mix containing cement, water ﬁne, and coarse aggregate (cement, gravel, crushed stone). The hardened mix is called concrete, and concrete embedded with steel is known as rein- forced concrete. C H A P T E R 2 3 Raw Materials and Their Components for Cement Production The raw materials for making cement are naturally occurring materials as well as some in- dustrial waste products. The naturally occurring materials include: gypsum minerals (gypsum CaSO4.2H2O, anhydrite CaSO4), limestone minerals (limestone, chalk, dolomites), and clay minerals (clays and marbles, silica sand, bauxites). The industrial waste minerals used for making cements include: metallurgical slag, the nepheline sludge of the alumina manufacturing industry, and the sodium hydroxide production sludge, which contains CaCO3, pyrite cinder, etc. The raw-meal feed for cement making basically contains four types of compounds: carbon- ates aluminosilicates, iron components, aluminum compounds (oxide), and minor constituents. Out of these, the ﬁrst three are very important in the formation of cement clinker, while the fourth aﬀects the manufacturing process (mainly burning, stabilization of the kiln, and pre- heated performance) depending upon the type and quantity of the minor constituents present. The three main components should satisfy among themselves the compositional compatibility, thermal combinability, and physical amenability (responsibility) to production processes (crash- ing, grinding and homogenization, burning and clinker formation). 2.1 THE RAW MATERIAL COMPONENTS The calcareous component of the cement raw meal is usually any rock containing CaCO3. Limestone is the most commonly available calcium carbonate rock. Besides CaCO3 present as calcite or aragonite, these rocks also contain various quantities of impurities like: quartz, clay, phosphates, opal (SiO2), pyrite (FeS2), siderite (FeCO3), qoethite (FeO.OH), dolomite (CaMg(CO3)2), magnetite, gypsum (CaSO4.2H2O), ﬂuorite (CaFe2), bituminous impurities, etc. The type of limestone is characteristic of its mode of origin and has deﬁnite implication for cement making as well as for various production processes. The mode of origin has also profound eﬀects on the mineral form, degree of crystalline, grain size, cementing medium, degree of com- paction, mode, and mineral form of occurrence of the impurities in the limestone and controls its physical, technological, dissociation, and combinability properties. Each of these properties has 4 2. RAW MATERIALS AND THEIR COMPONENTS FOR CEMENT PRODUCTION signiﬁcant bearing in the process control and optimization in cement manufacture. The mode of origin controls the association of various rocks, found interbedded, or as intercalations (anything out of ordinary course), gradations, or impurities in limestone. Study of this factor is important for regional prospecting and delineation of the rock types. The environments of deposition control the chemical (major and minor constituents) composi- tion and their variations account for the direct suitability of the rock. The details of the physic- chemical environment and its variations control the mineralogical composition, degree of crysa- tallinity, grain size, nature, and extent of cementing material in the rock. The ﬁrst three factors primarily control the reactivity and thermal combinability of the ﬁne raw meal obtained from the rock, while the last three control the amenability of the rock to ﬁne grinding for raw, meal preparation. At the same time, the reactivity and burnability of a raw meal depends upon its ﬁneness. Present-day cement manufacture in large plants is based on the advanced technology of process optimization in which energy conservation is the main constituting factor. Fuel used for raw-material burning and electrical energy used for crushing, grinding, and homogenization, also primarily based on fuel as source, can be eﬀectively conserved through a proper under- standing of the behavior of the raw materials to size reduction and burning processes. It is therefore apparent that a knowledge about the diﬀerent modes of formation of lime- stones, the geological and structural peculiarities, and the lithological association with diﬀerent other rock types is therefore an essential prerequisite for regional prospecting and exploration for selecting an appropriate deposit while detailed study of the mineralogical association, textural, structural, and granulometric characteristics of the deposit is essential to understand and control its behavioral pattern in cement manufacture. 2.2 MODE OF FORMATION OF LIMESTONES Wide compositional, textural, and granulometric variations among limestones and their fre- quent intimate associations with clays, dolomites, and other rock types reﬂect their varied mode of formation. A brief appraisal of diﬀerent environments and physical-chemical factors control- ling carbonate formation is helpful in limestone prospecting as well as in their quality evaluation. Carbonate rocks are mainly the products of deposition in shallower marine environments. 1. Mechanism and Process of Formation The majority of carbonates is of sedimentary origin and is formed by: (a) crystallization of calcium carbonate as an initial solid material by both organic and inorganic precipitation or by a combination of both; (b) chemical and/or mechanical breakdown of pre-existing rocks, transportation of the products either as detrital particles or in chemical solution, and the deposition or precipitation in standing bodies of water in a layered sequence; 2.3. CARBONATE ASSOCIATIONS 5 (c) lithiﬁcation of calcium carbonate sediments under low-temperature, low-pressure conditions which include various steps beginning with the change of grain miner- alogy, addition of coatings to grains, selective dissolution of matrix and/or grains, precipitation of mineral cement in pores, recrystallization, etc.; and (d) replacement of calcium sulphate or quartz by calcium carbonate under the eﬀect of sulphate reducing bacteria, by ammoniﬁcation or nitrate reduction. This is a less com- mon process. CaSO4+8H+H2O+CO2 2(NH4) OH+CaH(CO3)2 H) H) CaCO3+4H2O+H2S CaCO3 + (NH4)2CO3 +2H2O 2. Chemical Precipitates These may be biogenic or inorganically precipitated rocks. The deposits may be well- bedded, thick, and uniform and may have aphonic, cryptocrystalline, or ﬁne-grained gran- ulometry. The rocks are usually dense with low porosity and extensively uniform lamina- tions. 3. Detrial Carbonates These consist of gravel, sand, or clay-sized fragments derived from other carbonate rocks. The detrial fragments constituting the framework are cemented by normal precipitates, which may be microcrystalline calcite (micrite) or sparry calcite cement (sprite) and other post-depositional replacement or recrystallization minerals. Such limestones are usually hard, compact, and show high compressive strength and diﬃcult grindability. 2.3 CARBONATE ASSOCIATIONS Calcium occupies a unique position in its ionic radius (0.99 Å) which is intermediate between small and large cations. It can form either rhombohedra (calcite) or orthorhombic (aragonite) carbonates. Other calcite-type rhombohedra carbonates include MgCO3, and FeCO3. Arago- nite type includes SrCO3, BaCO3, and PbCO3. Iron-containing carbonates dissociate at lower temperatures and are comparatively more reactive than pure or siliceous limestones. Aragonite- type minerals show preferential substitution with larger cations, while surface conditions, calcite, aragonite, and dolomite are the common carbonate minerals. C H A P T E R 3 7 Additives and Corrective Materials in Cement Production Additives are naturally occurring rocks or industrial wastes which are added to a raw mix to com- pensate its compositional deﬁciency for cement making or to correct marginal deviations from the desired composition. For a very pure limestone, additives may be generally distinguished as argillaceous components and corrective materials are ferruginous components. The role of either may be reversible, signiﬁcant, or minor depending upon the compositional characteristics of the limestone. Various admixtures are introduced to the cements to give them the required properties and also to reduce manufacturing costs. Hydraulic admixtures: containing alumina, which increase the resistance of cements to the eﬀects of water and aid hardening under water; plasticizing agents: surface-active substances which increase the elasticity and bonding properties of the cement paste: Inert aggregates (sand, limestone, dolomite), acid-resistant admixtures (andesite, beschfaunite, granite), etc. Besides chemical composition, one important aspect in the choice of additives and cor- rective materials with respect to a particular limestone is the compatibility among their physical, mineralogical, and thermal combinability characteristics, which control, respectively, eﬀective grinding and homogenization, dissociation, and clinkerization. C H A P T E R 4 9 Exploration of Raw Materials for Cement Manufacturing 4.1 SIGNIFICANCE OF RAW MATERIALS EXPLORATION IN CEMENT MAKING 1. Large limestone deposits need be prospected for increasingly larger capacity of individual plants. 2. Depletion of large, good-quality, and favorably located deposits through exploitation ne- cessitated falling back upon inferior-grade and less favorably accessible deposits. 3. More rigid implementation of statutory regulations on noise and dust control excludes use of many good deposits located near habitations. 4. Higher capital investment on cement plants because of both rising costs and higher ca- pacity installations intensiﬁes the need for greater reliability in raw material proving to minimize the entrepreneurial risk. 5. The increasingly rigorous demands on better cement quality impose more rigid require- ments on raw material quality. 6. The rapid switch-over to the energy-saving dry process of cement manufacture with sus- pension preheaters calls for: (a) thorough homogenization or raw meal for better reactivity, where compatibility of physical and technological properties of the raw meal constituents is a primary pre- requisite, and (b) a lesser permissible limit for deleterious minor constituents in raw materials and ce- ment. 4.2 OBJECTIVES OF EXPLORATION 1. Location of cement plant, taking into consideration the principal factors, i.e., location of the raw-material deposits, availability of infrastructural facilities, such as power, transport and communication, and nearness to the marketing region. 10 4. EXPLORATION OF RAW MATERIALS FOR CEMENT MANUFACTURING 2. Optimum size and working life of a plant based on raw material availability; market con- ditions guided by the scope and extent of capital investment and the risk factor involved. 3. Choice of manufacturing process. Dry, semi-dry, or wet process of manufacture, depending upon moisture content, minor constituents present in raw material, cost and availability of solid (coal), liquid (oil products), and gaseous fuels. 4. Quality of the product and scope of manufacture of diﬀerent types of cement. The quality of raw materials controls that of clinker, its speciﬁc quality characteristics and availability of other subordinate raw materials, or industrial wastes deﬁnes the scope of manufacturing ordinary Portland cement, white cement, Portland pozzolana cement, etc. 5. System design in the cement manufacturing process. The crushability and grindability of limestone and the raw mix components decides the types of crushers and mills; the degree of uniformity inequality or raw material deposits dictates the need or otherwise for pre-blending or homogenization installations; and the type and quality of harmful minor constituents decides the design of the preheater and the extent of bypass of kiln exit gases. 6. Mine planning and quarry layout. The geographic geologic characteristics of the raw- material deposit, such as terrain condition, over burden, mode of occurrence, and structural features determine the mine layout, the number and height of benches, direction of mining and scope of selective quarrying for uniform mine output, etc.; the lithologic, i.e., textural, structural, and fracturing (strength) properties of the rock decides upon the choice of min- ing method, by drilling and blasting or ripping. The quarry layout, distance from plant, and topography of the region decide the choice of loading and transport machineries, their number and capacity, i.e., shovels, excavators, dragline, etc., for transport to the crusher or plant. C H A P T E R 5 11 The Composition of Portland Cement and Production Process Portland cement was ﬁrst introduced in 1824 by Joseph Aspdin, a brick layer from Leeds, Eng- land [5]. On setting, the color of cement resembles the color of rocks near Portland, England, hence the name. Approximate composition of raw material used for manufacturing ordinary Portland ce- ment is: clinker (percent by weight) varies within the limits shown in Table 5.1. Table 5.1: Chemical compositions of cement All the above compounds undergo some chemical combinations during the process of burning and fusion. Main constituents of cement are: 3CaO.SiO2, 2CaO.SiO2, 3CaO.Al2O3. Tri-calcium silicate is the best cementing material and the more it is present in cement the better the cement is. In a properly burnt clinker, 3CaO.SiO2 should be about 40%. In a properly burnt clinker it shall have less of 3CaO.SiO2 and more of free lime. After the addition of water to cement it sets and hardens due to the hydration and hydrol- ysis of the above three compounds which act as a glue. The aluminates are the ﬁrst to set and harden. Trisilicate is slower, and disilicate is the slowest. As such, the initial setting of cement is due to Trisilicate. Disilicate takes 14–18 days to add the strength. All three compounds in their action with water give out heat. Maximum heat giving compound is the aluminates which is responsible for most of the undesirable properties of concrete. Cement having lesser aluminates shall have less initial strength but higher intimate strength. Also, there will be less generation of heat, more volumetric stability, less cracking, and more resistance to acid attacks. Incomplete Calcium Oxide (CaO) 60–65%Silica (SiO2)20–25%Aluminum Oxide (Al2O3)4–8%Ferrous Oxide (Fe2O3)2–4%Magnesium Oxide (MgO)1–3%12 5. THE COMPOSITION OF PORTLAND CEMENT AND PRODUCTION PROCESS burning of clinker leaves free lime in it. This free lime causes expansion and disruption of con- crete after use. The silicates form a gel with water. The gel ﬁlls the pores of cement there by making it impervious. The gel later on crystallizes and ﬁrmly binds the particles. According to IS 269-1975, composition of ordinary Portland cement shall satisfy the fallowing conditions. 1. Ratio of the percentage of lime to that of silica, alumina, and iron oxide when calculated by the formula CaO 0:75O3 (cid:0) 1:2Al2O3 0:65Fe2O3 2:8SiO2 C shall not be less than 0.66 and not more than 1.02. C 2. Ratio of percentage of alumina to that of iron oxide shall not be less than 0.66. 3. Weight of insoluble residue shall not be less than 2%. 4. Weight of magnesia shall not be more than 6%. 5. Total sulphur contents calculated as SO3 (sulphuric anhydride) shall not be more than 2.75%. 6. Total loss on ignition shall not be more than 4%. In commercial practice the charge composition is calculated on the basis of the required percentage ratio of the basic oxides in the clinker. These ratios are called modules, the silicate module “n” and the alumina module “p”: %Fe2O3 %SiO2 C %Al2O3 %Al2O3 %Fe2O3 .CaO overall \ P KS D D D (cid:0) CaO free) .1:65Al2O3 0:35Fe2O3 (cid:0) 2:8.SiO2 overall C SiO2 free/ (cid:0) 0:7SO3/ : C The basic characteristics describing the mineral composition of Portland cement clinker is the coeﬃcient of saturation of the silica with lime, KS, expressing the ratio of the amount of lime re- maining in the clinker after formation of 2CaO.SiO2, 3CaO.Al2O3, and CaSO4 to the amount of lime necessary for combining with the silica to form 3CaO.SiO2. Using given values of modules and KS and also data obtained by chemical analysis of the raw materials, limestone, and clay, their ratio by weight in the charge is computed. For Portland cement the coeﬃcient of saturation lies between 0.8 and 0.95. The lower the KS value, the higher the content of 2CaO.SiO2 in the clinker and lower the activity of the cement. 5.1. CLINKERIZATION PROCESS 13 In the manufacturing of Portland cements the properties of the ﬁnal products owe their origin to clinker and gypsum and other additives that are introduced during the process of grind- ing, and changes that place during the process of grinding and subsequent storage. Any consid- eration of the characteristics of raw materials requires a basic understanding of the factors that control the clinker quality and the clinkerization process. 5.1 CLINKERIZATION PROCESS 5.1.1 CLINKER CHARACTERISTICS The clinker characteristics that are signiﬁcant in achieving a quality product can be summarized as follows: 1. appropriate bulk chemical composition; 2. formation of hydraulically active phases; 3. optimum grain growth; 4. optimum proportion of diﬀerent phases; and 5. proper microstructural development. A quality clinker can be produced if the following measures are adopted. 1. Achieving the bulk chemical composition of clinker in the following range: CaO (C) 63–67% Al2O (A) Fe2O3 (F) 4–7% 2.4% SiO2 (S) 21–24% C A F S C C D C 98–93 to 93–91 MgO K2O SO3 C C C P2OS C TiO2 D 2–3 to 7–9% 2. Stabilizing the hydraulically active clinker phases including the high-temperature poly- morphic forms of alite (Ca3SiO3) and belite (B-Ca2SiO4). 3. Optimizing the proportions of the major phases in a clinker, where the alite content should be aimed as high as possible, preferably in the range of 55–65%, and aluminates and ferrite phase in the range 9–11% and 12%, respectively, the balance being made up of belite. 4. Keeping the average grain size of the clinker minerals around 30 (cid:22)m and raising the max- imum crystal size of alite grains even higher to the extent possible but not exceeding the range 70–100 (cid:22)m. 14 5. THE COMPOSITION OF PORTLAND CEMENT AND PRODUCTION PROCESS 5. Forming monadoblastic texture, i.e., a microstructure in which there is little clustering of grains with alite and belie crystals being well distributed over the entire clinker volume as independent grains having well-crystallized aluminates and ferrite phase in the interstices. 5.1.2 CLINKERIZATION PHENOMENON VIS-À-VIS CLINKER CHARACTERISTICS It is well known that the above measures adopted to achieve clinker quality are realized through the clinkerzation process which can be represented in a simpliﬁed form by the reaction steps given in Fig. 5.1. Figure 5.1: Approximate reaction sequence in clinkerization. It is evident from this summary diagram that the clinkerization phenomenon is strongly dependent on the reactivity (signifying the achievable rate of diﬀerent reactions at respective temperature within practical time limits) and burnability (signifying the overall measure of ease or diﬃculty of burning under practical operating conditions) or raw mixes, which, in turn, de- pend on the intrinsic characteristics of the constituent raw materials. In this context it should be kept in mind that the burning process (Fig. 5.2) has several interdependent and interrelated controlling factors, which means that knowledge of the raw material characteristics is necessary to match the need of systems design and operation. Dehydration and DehydroxylationDecarbonationBreakdown of AluminosilicatesSolid State ReactionsLiquid Phase SinteringCooling27°C55°C550°C1280°C1280°C1450°C600°C660°C950°C1000°C1000°C1300°CMelt FormationH2OCaO<2%CaO ---17%Al2O3 + SiO2 + Fe2O3C3S + C2S + meltC3S + C3A + C2S + C4AFC2S + CA + C12A7 + Ferrite + CaOOH5.2. RAW MATERIALS FOR CEMENT MAKING 15 Figure 5.2: Major factors controlling the burning operations. 5.2 RAW MATERIALS FOR CEMENT MAKING The common raw materials for cement making have been classiﬁed and categorized in Tables 5.2 and 5.3. It is well known that the dispersed raw meal feed for cement manufacture basically consists of two components—calcium carbonate and aluminosilicates—that are complementary in nature. Table 5.2: Raw materials in combined methods of manufacture of cement BurningOperation andControlBurning Conditions CoolingSchedule Clinker EnvironmentClinker Output and QualityBurnability ofRaw MixRaw MaterialsCharacteristicsLiquid PhaseVolatiles Coal AshReactionSystemDesignPrincipal raw materialSourceProductsBlast-furnace slag Blast furnace of iron and steel industry Clinker, slag cement, road ballast slag wool, slag bricks, lightweight aggregate Calcium sulphate Natural gypsum chemical gypsum Cement sulphuric acidCalcium silicate Nepheline wasteCement, alumina, fertilizers Salt brine and limestone Soda manufacturing industry Caw tic soda, white cement Dolomite Natural Cement, magnesiaCement raw materials and rhyolitic tuﬀ rocks Natural Cement, fertilizers 16 5. THE COMPOSITION OF PORTLAND CEMENT AND PRODUCTION PROCESS Table 5.3: Raw materials for Portland cement industry 5.3 CHEMICAL COMPOSITION OF RAW MIXES AND COMPOSITIONAL COMPATIBILITY 5.3.1 MODULE VALUES OF RAW MIXES The composition of Portland cement clinker is represented by four major oxides. A combination of their ratios known as module values (Table 5.4) is used for the control of bulk chemical composition of clinkers. For convenience, these module values are extended to raw mixes as well. As a broad guideline the fallowing rational limits have been proposed to the soviet cement industry for clinkers and corresponding raw mixes with coal ash inﬂuence. CategoryNatureMaterials in useMaterials for Clinker ProductionPrincipalCarbonates Limestone, chalk, marble, sea shell, moral, carbonate sludge of paper, sugar, and fertil-izer industries Aluminosilicates Clay, soil, shale, phyllites, slate, and volcanic rocks. Fly ash from thermal power stations Lime-silicates Wollaston tic rocks, metallurgical silages, wastes of aluminum industry SupplementaryCorrective materialsSand and sandstones, buxite, iron are later-ite, pyrite cinders from chemical industry Special AdditivesGrinding acids, etc.Surface active agents like triethnolamine sulphate lye, sodium paly phosphate, etc. Slurry thinners, etc.Surface active agents Granulation Activators Min-eralizes Chemical reagents like Na2CO3, CaF2, Na2SiF6, Ca3(PO4)3, CaSO4, 2H2O, etc.Materials for Converting Clinker into CementPrincipalSet retarderNatural gypsum, chemical gypsumSupplementaryHydraulic blending materialsMaterials with lime reactivity, such as natural pozzolanic rocks, burnt days, blast furnace slag, ﬂ y ash Special AdditivesGrinding acids, Hydrophobic agents, pigments 5.3. CHEMICAL COMPOSITION OF RAW MIXES AND COMPOSITIONAL COMPATIBILITY 17 Table 5.4: Module value used for clinker and raw mix (S=SiO2, A= Al2O3, F= Fe2O3, C=CaO, M= MgO, S= SO3)Silica Modulus (Ms) = S A+FAlumina Modulus (MA) = A FHydraulic Modulus (MH) = C S+A+FLime saturation factor (LSF) = 100C 2.8S+1.1A+0.7F(when MA<0.64)Lime saturation factor (LSF) = 100C 2.8S+1.65A+0.35F(when MA>0.64)Lime saturation factor (LFSB) = C-0.7s 2.8S+1.2A+0.65FLime Standard (Ls) II = 100C 2.8S+1.18A+0.65FLime Standard (Ls) II = 100(C +0.75M) 2.8S+1.18A+0.65F(when MgO<2%)Lime Saturation III = 100(C+0.75M) 2.8S+1.18A+0.65F(when MgO>2%)Lime – Saturation factor (LSFR) = C-(1.65A+0.35F+0.7s) 2.8s(when MA >0.64)∆= 100 2.8s+1.65A+0.35F-C 2.8S+A+F+C18 5. THE COMPOSITION OF PORTLAND CEMENT AND PRODUCTION PROCESS 5.3.2 EFFECT OF CHEMICAL COMPOSITION ON THE REACTIVITY AND BURNABILITY OF RAW MIXES There are limitations; nevertheless, some of the eﬀects of compositional variations are high- lighted as follows. 1. Other conditions remaining the same, with increase in LSF, both reactivity and burnability of raw mixes are decreased at temperatures below the liquid formation, whereas above this temperature (1300(cid:14)C) only burnability is decreased and reactivity is practically not aﬀected. On the other hand, increase in silica modulus aﬀects reactivity at all temperatures, while increase in alumina modulus get reﬂected primarily in harder burning. 2. In actual practice, one unit of LSF is regarded as equivalent of 20(cid:14)C rise in burning tem- perature. 3. Alumina modulus is particularly critical in liquid phase sintering. In this context the points in Table 5.5 are of practical signiﬁcance. Table 5.5: Alumina modulus is particularly critical in liquid phase sintering 4. For the same silica modules, the maximum formation of liquid at minimum temperature corresponds to the alumina modulus 1.38 or 1.63, depending on the MgO saturation, and for the same alumina modulus, the amount of liquid increases with decrease of silica modulus. 5. The general relationship of raw mix burnability with module value is illustrated in Fig. 5.3. The reactivity of raw mixes is a resultant eﬀect of • dissociation of the mineral species into reacting oxides/complexes, • transformation of the decomposed phases into a reactive stats, and • combination reactions. SystemLiquid Formation Temperature °CA/F Ratio for theEutectic CompositionFluxing OxideC-A-F-S13381.38Al2O3,when A/F<1.38Fe2O3,when A/F>1.38C-A-F-S-M13011.63Al2O3, when A/F<1.63Fe2O3,when A/F>1.635.4. PARTICLE SIZE OF GROUND MATERIALS IN RAW MIXES AND PHYSICAL PROPERTIES OF CLAYS 19 Figure 5.3: Eﬀect of module values clinkering temperature and burnability. 5.4 PARTICLE SIZE OF GROUND MATERIALS IN RAW MIXES AND PHYSICAL PROPERTIES OF CLAYS The particle size of raw mix is important for the very basic reason that the sintering rate is roughly proportional to the inverse of particle size. In general, the ﬁneness of raw mixes varies in the range 3000–5000 cm2/g with about 9–22% particles or more than 0.07–0.09 mm and 0–5% over 0.2 mm size. Properties like plasticity, speciﬁc surface, water requirement, suspension stability, coag- ulation of clay particles, swelling, etc. are of considerable importance in raw meal preparation, particularly in the wet process. Clays with at least 7–15 plasticity index and having 10% particles 0:08 mm size with CEC 11–12 mg/100 g 0:2 mm size and cumulative 20% particles of of are reportedly regarded as cement making variety. C C 5.5 SUMMARY AND CONCLUSIONS 1. The characterization and evaluation of raw materials for the manufacture of Portland ce- ment have to be done necessarily in relation to the requirements of the manufacturing process and product quality, and their interrelation can be conceived as depicted in Fig. 5.4. 2. Although a wide varity of raw materials is used in cement industry, future trends would seem to use industrial wastes and to establish industrial complexes, based on a single set of raw material of another. 3. A limestone with a minimum 44–45% CaO and maximum 3–3.5% MgO, 0.6% k2O, 0.6–0.8% SO3, 0.25% P2O5, 0.5% Mn2O3, 1.3% TiO2, and 0.015–0.02% Cl is regarded as a cement-grade limestone, provided its SiO2, Al2O3, and Fe2O3 contents satisfy the ultimate module values of raw mixes. The compositional ranges of alumniofersilicate ma- terials cannot be deﬁned rigidly as they have to match the principal carbonate component. In general, a clay with more than 3% K2O and 1% SO3 may be considered, primafacie, Modulus of SilicaModulus of AluminaTemperature °C1440140013601320(a)(b)20 5. THE COMPOSITION OF PORTLAND CEMENT AND PRODUCTION PROCESS Figure 5.4: Interrelation of processing steps, characterization features, and basic properties of raw mixes in cement making. unsuitable. For most of the minor constituents 0.5% is found to be a safe limit, in excess of which a special examination is called for. 4. To arrive at a desirable raw-mix composition, clinker module ranges like 0.92–0.95 for LSF, 2.0–2.5 for Ms, and 1.4–1.6 for MA may provide a rational guide. 5. The thermal behavior of raw materials primarily depends on the activity state of the min- eral species present in them. The temperature, rate, and activation energy of limestone dissociation depend on its mineralogy and microstructure. The rates of clinker formation reactions are also dependant on the mineral forms of the aluminoferrosilicate components of a kiln feed. The concurrence of carbonate dissociation and thermal demolition of alu- minoferrosilicate component is considered a basic necessity for proper burning. 6. The amenability of limestones to size reduction process is apparently controlled by the free and ﬁxed silica content and the grain size variations of calcite and quartz, although a host of other factors also have a role to play. RawMaterialsParticulateSolidsClinkerMiningCrushingGrindingHandlingHomogenizationDryingBurningGrindingwithGypsumFinishedProductwith SellingPropertiesCementCompositionalCompatibilityBasic PropertiesRequired in a Row MixSteps inCementManufactureCharacterizationFeaturesThermalCombinaibilityChemicalCompositionMineralCompositionMicrostructure(GrainCharacteristics)Size andSurface ofParticulateSolidsPhysical Amenabilityto ProductionProcesses likeCrushing, Grinding5.5. SUMMARY AND CONCLUSIONS 21 7. The particle size distribution in ground raw mixes is critical both for burnability and clinker granulometry. The mineralogy of the coarser fractions of raw mixes is particularly signiﬁ- cant for measure of their burnability. The limiting particle size for diﬀerent mineral forms in raw mixes has already been evolved for easy burning. 8. Properties of the clay component are as important in cement making as those of the car- bonate rocks. Since the clay composition is widely variable and its mineralogy is complex, the choice of clay is done more on the basis of its Si: (A, F) ratio, fusibility, and physical characteristics like plasticity granulometry, cation exchange capacity, etc. C H A P T E R 6 23 Burnability and Clinkerization of Cement Raw Mixes 6.1 BURNABILITY Burnability of raw mixes has been a matter of great importance in cement technology. The be- havior of a raw mix during its sintering process is greatly inﬂuenced by its chemical, mineralog- ical and granulometeric compositions, variation in these aﬀect kiln operation, refractory lining, fuel consumption, and clinker quality. Each cement raw mix burns in its own way resulting in variation of clinker quality. The burnability of a cement raw mix conceptually denotes the amount of mass transfer of its constituents with ease or diﬃculty to the clinker phases. By convention, burnability is measured by determining the CaOf (free) after burning the raw mix for a certain time ((cid:18)) at a certain temperature (T ), i.e., CaOf F .(cid:18); T /, above 1300(cid:14)C when melt is formed, burn ability D decreases by increasing this parameter. Burnability is generally expressed by either of the following two quantities. 1. Measure of CaOf of a pseudo-isochrones ((cid:18) constant) at a given temperature. Increas- ing values of CaOf correspond to decreasing burnability. D 2. Measure of time ((cid:18)/ of pseudo-isotherm (T corresponds to decreasing burnability. D constant) for CaOf 2%, increasing of (cid:18) (cid:20) The following are the important parameters which aﬀect the burnability of a raw mix to a great extent. 1. Raw mix-mineralogical composition: • Lime components: consisting mainly of CaCO3 and very small quantity of the fol- lowing in order S-M-R:F:S:N:K. • Clay components: consisting mainly of SiO2 with considerable amount of the fol- lowing in the order R:F:C-M-S-N-K. • Corrective ingredients: consisting mainly of other of any main oxides (C/A/S/F). • Modiﬁers: consisting of diﬀerent inorganic compounds which accelerate the clinkiza- tion reactions. 24 6. BURNABILITY AND CLINKERIZATION OF CEMENT RAW MIXES 2. Raw mix-chemical composition: • Main component oxides are: C, A, S, and F. • Minor volatiles are: K, N, S, P, F, Cl, and H. • Minor non-volatiles are: Sf , M, Ti, Mn, Sr, and Cr. Each component of the raw mix has individual and combined (Ms, MA, LSF, and Ms) eﬀect on burnability. 3. Raw mix–granulometric composition: ﬁneness and particle size, distributions, homogene- ity, and compaction. • The more ﬁne grained, the greater surface area a raw mix has, the easier it is to sinter and the lower the sintering temperature. Homogenization of kiln feed is a major operation in cement manufacturing as it aﬀects the quality of clinker, burning process, and fuel consumption. Fluctuation of the kiln feed measured as % CaCO3 should not be more than 0.2 from the holding point. An in- crease of 1% CaCO3 will increase the C3S by 13% and reduce C2S by about 11.5%. The ultimate homogeneity depends on the physical-chemical characters, ﬁneness and particle size distributions, method of mixing, and eﬃciency of the blending system. (cid:6) 4. Raw mix–thermal treatment: Firing temperature: in clinker the temperature must be fairly enough for the formation of alite phase. Burning of the raw mix is generally carried out at 1450–1500(cid:14)C. Excessively high burning temperature results in a great stress on the kiln and the refractory lining, more fuel consumption, reduction in cement strength, and larger alite crystals. Increase in burning temperature from 1360–1420(cid:14)C results in lowering the burning period by half. Maximum ﬁring temperature was determined by a multiple regression analysis of raw meal containing only the four main oxides as given below: (cid:14)C 1300 4:51 C3S 3:74C3A 12:64C4AF: (cid:0) (a) Holding time: on increasing holding time, the following changes may be observed. C D (cid:0) i. C3A content decreases and C4AF content increases. ii. C2S decreases and C3S increases. iii. Higher mechanical strength at later ages and lower at early ages. iv. Heat of hydration at early ages decreases. v. Unburnt clinker can produce high-quality cement even in presence of high CaOf . (b) Burning rate: rapid burning is always favored for the following reasons. i. More coarse-grained materials can be charged. 6.1. BURNABILITY 25 ii. Materials diﬀering by their degree of ﬁneness can be charged. iii. Five grains of C2S formed which accelerate the interaction of C2S, CaOf and liquid. (c) Burning activation: thermal activation may be enhanced by either accompaniment with mechanical (vibratory mill) or chemical (mineralizer) activation. Mechanical activation gives better results than chemical. 5. Liquid phase formation: appearance temperature, amount, viscosity, surface tension, ionic mobility: A, F, M, minor volatile and non-volatile components generally govern the amount of liquid formed, its appearance, temperature, viscosity, surface tension, and ionic mobility in the clinkerization process. The range of clinker composition may be fairly wide if the amount of liquid phase increases slowly. A clinker with about 25% liquid phase form a raw mix is generally considered an ideal raw mix for kiln lining, fuel saving, rapid C3S formation through dissolution of phase at 1450(cid:14)C is usually calculated by 3:0A 8:5A 2:28F 5:22F N N K K C C C C C C M M (cid:0) (cid:0) when MA > 1:38 when MA < 1:38 6. Clinker quality: silicate phase, alumina-ferrite phases. It has been seen that the burnability becomes worse as the potential C3S content increases, at the expense of other clinker constituents, while increasing C3A and C4AF content, the burnability improves, and the C4AF is signiﬁcantly more eﬀective in this respect. 7. Coal ash: amount absorbed, composition, ﬁneness. When coal is used as the fuel for clinker-making, its ash quantity, composition, and ﬁne- ness aﬀect the burnability. Generally, the composition of coal ash varies within the limits: S-35-60%, A-15-35%, F-5-20%, C-0-10%, and M, S and alkalis are often present in the ash is small amounts. In general, the ash composition shows a very high S/C ratio and moderately high A/F ratio. 8. Kiln atmosphere: oxidation, reduction. Reducing conditions during cement clinker burning substantially aﬀect the color of the clinker by producing Ferrous oxide, accelerate the setting by enhancing C3A content at expense of C4AF, and reduce the strength by breaking down C3S during clinker coaling. Therefore, oxidizing conditions (0-1-2 vol. % in exist gas) should be maintained in the kiln for better clinker quality. 26 6. BURNABILITY AND CLINKERIZATION OF CEMENT RAW MIXES 6.2 REACTIVITY Reactivity of a raw mix is deﬁned by the overall chemical reactions among the represented con- stituents of the raw mix, attained on burning it at a certain temperature for a certain time, i.e., F .T; (cid:18) /, above 1300(cid:14)C when melt is formed, this parameter, however, has no eﬀect on Rm D reactivity. Factors Aﬀecting Reactivity 1. Physical-chemical, mineralogical, and granulometric composition. 2. Chemical process of clinker mineral formation. 6.3 REACTION SEQUENCE The course of reaction inside a rotary kiln has been of great interest to the cement technolo- gists since the kiln is controlled by computer and, obviously, a mathematical model to explain the reaction process is to be constructed in order to ﬁnd a logical relation between the process variables. Table 6.1: Zone temperature range 0(cid:14)C and reaction proﬁle The experimental observations revealed the following phenomena. 1. The ﬁrst aluminate phase “CA” is formed at lower temperatures (550–600(cid:14)C) which, in turn, combine with free CaO resulting in the formation of an intermediate phase C12A7 and ﬁnally it converts into C3A above 900(cid:14)C. 2. The formation of C2AS as an intermediate phase is likely but dependent on the nature of raw materials used. 3. The ultimate formation of C4AF at higher temperature (1300–1440(cid:14)C) is consecutively followed by the appearance of ferrite phase (CF and C2F) at lower temperature (800– 900(cid:14)C). Parallel observations, which conﬁrmed the above items. IUp to 200Evaporation (slurry drying) preheating (dehydration, dehydroxylation, and ﬁ rstappearance new phases). Decarbonization (calcinations) exothermic reactions sintering cooling II200–800III800–1100IV1100–1300V1300–1450–1300VI1300–10006.3. REACTION SEQUENCE 27 1. The reaction sequence of raw mixes is almost identical in dry, semi-dry, and wet kiln. 2. The dissociation and decarbonation of raw-mix components start at 550–600(cid:14)C. The CaO formed during decarbonation reacts with other components simultaneously in such a way that about 2% CaOf at 800(cid:14)C and about 17% at complete decarbonation temperature (1000(cid:14)C) remain unreacted. 3. The ﬁrst detectable phases CA C2S were noticed at 7000(cid:14)C. The amount of these phase increase with temperature up to 900–1000(cid:14)C, when poorly detectable C3S and some C4AF/C2F are traced. C12A7 C C 4. In some other investigations, the ﬁrst phases detected are CF CS which are sub- sequently converted into clinker phases with rise of temperature in accordance with the following scheme: CA C C CA________ C12A7__________C3A CF ________ C2F____________C4AF CS ________ C3S ____________C2S 5. X-Fe, FeO, and Fe2O3 along with the temperature of x-wolestonite almost concurrently with B-C2S are detected from a series of charge samples. 6. Extensive study made after comparing ﬁve kiln charges coating a reaction sequence was derived accordingly, as shown in Fig. 6.1, which further conﬁrmed the above observations. Figure 6.1: Reaction sequence in cement rotary kiln. QuartzB-C2SC3SC3ACaOfC4A3SC4AFC4AFC12A7CaOAnhydriteGehleniteMagneio-ferriteMgO/FeO.Fe2OSpurrite2(C2S).CaCO3CaCO3ClaysB-C2S28 6. BURNABILITY AND CLINKERIZATION OF CEMENT RAW MIXES 7. The solid reactions are almost complete at a temperature of about 1300(cid:14)C and a melt phase appears. The melt phase contains a complete melting of C3A C4AF and partial melting of C2S and CaO with incorporation of such constituents as R2O, MgO. The formation of C3S is activated through clinker phases appear with the formation C3A, C4AF, C2S, C3S, MgO, and glass after crystallization of the residual liquid. C C H A P T E R 7 29 Manufacturing Portland Cement The manufacture of cement [2] is composed of two independent processes. Fabrication of the intermediate product—the clinker, which includes preparation of the raw mixture and ﬁring of it and the grinding of the clinker together with the admixtures, storing and packing of the Portland cement. There exist two methods for preparing raw mixture: a wet method and a dry method. Both are outlined in this chapter. 7.1 DRY PROCESS The speciﬁc feature of this process is that the raw materials are ground and mixed in the dry state. In this process, limestone and clay are ground separately to ﬁne powders and then mixed together in the desired proportions. Water is then added to it so as to get a thick paste of which cakes are then made, dried, and burnt in kilns. To the clinker obtained after burning is added 3–4% of gypsum and ground to very ﬁne powder. This powder is cementing ready for use. This process is slow, costly, and also diﬃcult to have the correct proportion of constituents; to do so is a cumbersome operation. The quality of cement is not as good as that of the one manufactured by wet process. This method has therefore become obsolete. 7.2 WET PROCESS The speciﬁc feature of this process is that the raw materials are prepared in water. The ﬂow diagram of the wet process for manufacturing Portland cement is given in Fig. 7.1. Mixing: The limestone is ﬁrst broken up in crushers (2), and a liquid mass from clay mixer (1), which are in desired proportions are fed into ball mill (raw-material mill (3)), and are simulta- neously ground to very ﬁne powder and water is added to it. Ball mill (shown in Fig. 7.2) is a rotating steel cylinder in which there are hardened steel balls. When the mill rotates the steel balls pulverize the raw materials which form into a solution with water. This liquid mixture is known as a slurry. This slurry is then passed into storage tanks known as silos (correcting slurry basin (4)), where it is stirred with agitators or by pneumatic mixing. The slurry is passed to horizontal basin (5), where the proportioning is ﬁnally adjusted to ensure the correct chemical 30 7. MANUFACTURING PORTLAND CEMENT Figure 7.1: Flow diagram of Portland cement manufacturing by wet process: (1) clay mixer, (2) hammer crusher, (3) raw material mill, (4) correcting slurry basin, (5) horizontal slurry basin, (6) rotary drum furnace, (7) grate cooler, (8) storage, (9) cement mill, and (10) cement silos. (Hand-drawn by the author.) composition, and to obtain the necessary ratio of compounds (components). Composition of raw mix in the wet process can be better controlled than in dry process. The corrected slurry is then fed into the rotary kiln for burning. Burning: The corrected slurry is fed at the higher end of the inclined rotary kiln (rotary drum furnace (6)) shown in Fig. 7.2, whereas from the lower end of the kiln a ﬂame is produced (using combustion products) by injecting pulverized coal with a blast of air, and that moves through it in a counter current of hot gaseous. The rotary kiln is a steel tube lined inside with ﬁre bricks. It goes to 120 m long and from 2.5–3.5 m in diameter. The kiln is mounted on rollers at a gradient of 1 in 25 to 1 in 30 and rotating once in every minute. The slurry interaction results in the successive processes of water evaporation, mineral dehydration, dissociation of limestone, and chemical reactions between the basic oxides, CaO, which is formed, and the 7.2. WET PROCESS 31 Figure 7.2: Cross section of a ball mill and rotary kiln. (Hand-drawn by the author.) components of the clay SiO2, Al2O3, Fe2O3, and ﬁnally small lumps or “nodules” are ﬁrmed. The nodules gradually roll down passing through zones of rising temperature until them rich burning (sintering) zone where they are ﬁnally burnt at 1500–1650(cid:14)C. At this temperature “nodules” changes to clinkers. The clinker is cooled with cold air in grate type cooler (7), to temperature of 50–60(cid:14)C. In these coolers, which are located below the kiln, the air is passed up through a bed of clinker particles uniformly distributed on a bar grating. Grinding: The clinker is transferred from the coolers to the storehouse (8), where it is kept for a certain length of time for quenching (hydration) of free lime. The cured clinker together with hydraulic or inert admixtures and gypsum, which is adds to control the setting time, is ground in tubular cement mills (9). The cement is stored in reinforced concrete silos (10), through the bottom of which air is forced when the cement is being discharged to loosen it. Cement is delivered to consumers in automobile or railway cement tanks in bulk or in paper multilayer bags. 32 7. MANUFACTURING PORTLAND CEMENT Figure 7.3: Flow diagram of cement manufacture (wet process). Argillaceous MaterialWashing with WaterStored in BasinCalcareous MaterialCrushingStored in SilosChannelsGrinding in the Ball Mills or Tube MillsCorrection BasinStorage BasinC H A P T E R 8 33 Testing Portland Cement 8.1 SAMPLES FOR TESTING Each sample for testing shall consist of an intimate mixture of approximately equal portions selected from at least 12 diﬀerent bags or packages when then the cement is not loose or 12 diﬀerent position in the heap or heaps when the cement is loose. Selection of samples shall be done in such a manner so as to obtain a fair average sample. The sample taken will be stored in an airtight container until the time of the test. 8.2 CHEMICAL COMPOSITION Loss of ignition: Heat 1.00 g of the sample for 15 m in a platinum crucible (or for 1 h in porcelain crucible) at a temperature of 900–1000(cid:14)C. Cool and weightloss on ignition should not be more than 4%. Insoluble residue: Boil for 10 m a well-stirred mixture of 1 g cement, 40 cc of water and 10 cc concentrated hydrochloric acid (sp.gr.1.18). Filter the solution and rinse the container ﬁve times and wash the ﬁlter ten times with hot water. Wash the residue on a ﬁlter with hot water and boil for 10 min with Na2CO3 solution (2N). Filter the solution again through the same ﬁlter paper and wash ﬁve times with water. It is now washed with HCl (2N) and ﬁnally with water until it is free from chlorides. The ﬁlter paper should be dried ignited and weighed to give the insoluble residue. The insoluble residue should not be more than 1.5%. Lime and alumina: The percentage of lime to silica, alumina, and iron oxide when calculated by the formula CaO 0:7SO3 (cid:0) 1:2Al2O3 0:65Fe2O3 C 2:8SiO2 C should not be greater than 1.02 nor less than 0.66. The ratio of the parentage of alumina to that of iron oxide shall not be less than 0.66. An excess of free lime will cause unsoundness of cement. Magnesia: If free magnesia exceeds 5% then it makes the cement unsound. 34 8. TESTING PORTLAND CEMENT 8.3 FINENESS Finer cements react quicker with water and develop early strength, although the ultimate strength is not aﬀected. However, ﬁner cements increase the shrinkage and cracking of con- crete. The ﬁneness is tested by either one of the following two methods. 1. By sieve analysis: break with hands any lumps present in 100 g of cement placed in a sieve No. 9, and sieve it by gentle motion of the wrist for 15 m continuously. The residue when weighed should not exceed 10% by weight of the cement sample. 2. By speciﬁc surface: will not be less than 2250 cm2/g as found by Wagner’s turbidmeter method. 8.4 CONSISTENCY OF STANDARD CEMENT PASTE The following physical test should be carried out, whenever possible, between the temperate range of 25–29(cid:14)C. This test is performed to ﬁnd out the correct amount of water to be added to a given quantity of cement so as to get a paste of normal consistency. This test precedes the test of cement for soundness, setting time, and tensile strength or for compressive strength. This test can do with the help of vicat’s apparatus having the frame movable rod, as shown in Fig. 8.1. Diameter of the rod mostly is 1 cm and is 5 cm long. At its lower end is attached a detachable needle 1 mm square or 1.3 mm in diameter and 5 cm long. There is a vertical sale graduated from 0–40 mm in either direction to measure the vertical movement of the rod. To start with 25% of clean water is mixed with about 300 g of neat cement in a crucible. The mixing can be done with a standard spatula shown. After about 30 s it is thoroughly mixed with hands for at least 1 min. The kneaded paste is tossed about six times from one hand to the other and pressed into the hard rubber mold through its bigger end. Fill the mold completely with paste and remove the extra paste by a single movement of the palm. Place the inverted mold (with larger end on glass plate) and slice oﬀ extra paste from top by a single movement of trowel. Place to mold resting on glass plate under the needle. Bring 1 cm diameter end of needle in touch with the paste and release it without any jerk or force and note the penetration. The time taken from adding of water in cement to ﬁlling of mold should be between 3–5 min. Repeat experiment with trial pastes made with varying percentages of water. The paste giving a penetration of 33–35 mm is said to be of normal consistency. The amount of water mixed is expressed as a percentage by the weight of dry cement. This is usually in the neighborhood of 30% for a paste or normal consistency. 8.5. SOUNDNESS 35 Figure 8.1: Vicat apparatus. 8.5 SOUNDNESS It is essential that cement concrete does not undergo large changes in volume after setting. This change in volume is known as unsoundness and may cause cracks, distortion, and disintegration of concrete. The test is carried out with the help of Le Chevalier’s apparatus shown in Fig. 8.2. It consists of a split brass cylinder 30 mm high, 30 mm internal diameter, and 0.5 mm thick. Two pointers AA, 165 cm in length up to the axis of cylinder, are attached to the cylinder, one on each side of the split. Cement paste prepared with 0.78 times the water required preparing a paste of normal consistency and 100 g of cement is ﬁlled in the mold resting on a glass plate. Another glass plate is placed on the mold and weighed down. The whole is immediately placed 36 8. TESTING PORTLAND CEMENT in a water bath maintained at a temperature of 27–32(cid:14)C after 24 h the distance between the pointers is measured and the mold is transferred to a beaker of water heated to the boiling point in 25–30 m and kept at this temperature for one hour. After cooling the increase is distance. Between the pointers is noted. The increase in this distance should not be more than 5 mm for cement that had been aerated for 7 days in a humidity of 50–80% before test or 10 mm if the cement had been kept in airtight containers. Figure 8.2: (a) Le Chevalier’s apparatus and (b) briquettes of standard dimension. (Hand-drawn by the author.) 8.6 SETTING TIME To enable the concrete to be laid in position properly the initial setting of cement should not start too quickly. Once the concrete has been laid it should harden rapidly so that the structure could be put to use early. The initial setting of cement is that stage in the process of hardening after which any cracks that may appear do not reunite. Final setting is that when it has attained suﬃcient strength and hardness. Vicat apparatus shown in Fig. 8.1 is used to ﬁnd the setting time for cement. The paste of 300 g cement made with 0.85 times the amount of water required for paste of normal consistency 8.7. COMPRESSIVE STRENGTH 37 is ﬁlled in the mold at the lower end of the rod is ﬁtted with a 1 mm square needle. This needle is brought in contact with the surface of paste and released. The initial set is said to have taken place when the needle fails to penetrate beyond a point 5 mm above the glass plate. The time taken from the instant can added to cement to the moment when the needle fails to penetrate 5 mm before the glass plate is known as it should not be less than 30 m for ordinary Portland cement. For ﬁnding out the ﬁnal setting time the 1 mm square needle is replaced by the other needle. This needle has an annular attachment around 1 mm square needle and projecting by 0.5 mm below it. To ﬁnd ﬁnal setting time the needle shall be brought in touch with the paste in the mold and released instantly. The ﬁnal set shall be considered as having taken place when the attachment fails to make any impression on the surface of paste whereas the needle makes one. The time from the moment water was added to make impression on the surface of cement paste is known as ﬁnal setting time. For ordinary Portland cement the ﬁnal setting time should not be more than 10 h. The test should be performed in an air-conditioned room with 90% humidity and at a temperature between 25–29(cid:14)C. 8.7 COMPRESSIVE STRENGTH The compressive strength of cement is judged by ﬁnding the compressive strength of cement and sand mortar. For the purpose on part by the weight of cement is mixed dry with three parts by weight of IS sand. To this dry mixture of cement and sand is added water given by the following formula: P n 4 C where P is the % of water by weight of dry materials and P n is the % of water required for making a cement paste of normal consistency. 3:5; D P Cement sand and water shall be intimately mixed to give the paste of uniform color but the mixing should be intimately mixed to give the paste a uniform color but the mixing should not be for more than 3–4 min. Cubes of 7.06 cm sides are then molded out of this paste and are kept in an atmosphere to 90% humidity and 25–29(cid:14)C temperature for 24 h. They are then removed from the molds and kept submerged in clean water until the time of the test and should not be allowed to dry. Three webs each are tested in a compression testing machine after 3 days and 7 days. Compressive strength of ordinary Portland cement should not be less than the following values: After 3 days After 7 days 115 kg/cm2 175 kg/cm2 38 8. TESTING PORTLAND CEMENT 8.8 TENSILE STRENGTH Tensile strength of cement sand mortar is tested to judge the tensile strength of cement. To do so briquettes of standard dimensions are prepared. Briquettes have a uniform thickness of 25.1 mm and a minimum sectional area of 645 mm2 at the central section. For preparing briquettes one part by weight of cement and three parts by weight of water are mixed with the quantity of water found from the following formula, P D 0:2P n 2:5: C Cement sand and water are mixed intimately so as to get a uniform of the mortar. A small heap of mortar is placed on a briquette mold and ﬁlled as usual. It is then beaten down with the standard spatula until water appears on the surface. The mold is now turned upside down and as before again a small heap of mortar is placed and beaten down. The surfaces are smoothed with the blade of a trowel. The briquettes are taken out of moulds after keeping them in an atmosphere of 90% humidity and temperature of 25–29(cid:14)C for 24 h. Six such specimens each are tested in a briquette testing machine after 3 days and 7 days. Tensile strength for good Portland cement should be as follows: After 3 days not less than 20 kg/sq cm After 7 days not less than 25 kg/sq cm C H A P T E R 9 39 Hydration of Portland Cement The hydration behavior of Portland cement [4] encompasses that of its constituent minerals, but care must be taken in translating their functioning to that of practical Portland cement sys- tems. While a number of studies have tended to approximate, the hydrations of alite with that of Portland cement, many additional criteria are involved. Not least of these are interactive rela- tionships between the principal hydrating minerals C3S, C2S, C3A, and C4AF. None of these phases is pure; each contains a large number of elements in small quantities in solid solution. Alkalis can and do aﬀect the course of the reaction, whether percent as water-soluble sulphate or incorporated in the constituent phases initially with exsolution occurring during hydration. The products formed (C-S-H, ettringite (the reaction product of C3A with gypsum), mono sulphate- C4AH13, Calcium hydroxide, etc.) are also impure. Analytical electron microscopy of cement pastes has shown that C-S-H incorporates signiﬁcant amounts of aluminum, iron, and sulphur, while the ettringite and MonoSulphate phases contain signiﬁcant amounts of silicon, and even the calcium hydroxide contains small quantities of foreign ions chieﬂy silicate. There is no pure saturated solution of calcium hydroxide, for instance a whole host of other cations and anions in diﬀerent quantities (mostly small) are also present. The permutation and combination of what can and does occur in practice are, of course, inﬁnite and it must not be forgotten that hydrating Portland cements are exceedingly complex systems with many interactive possibilities. In the processes for shortening the hardening time can be classiﬁed as follows. 1. The use of quicker hardening cements such as high early strength cement. 2. Heat treatment methods. 3. The use of electromagnetically treated mixing water. 4. The use of chemical additive as hardening accelerators. 5. The use of pressure. For optimum eﬀects the magnetizing parameter, such as the magnetic ﬁeld strength, the ﬂow rate of the water and the period of inﬂuence of the ﬁeld on the water must be accurately determined. C H A P T E R 10 41 Diﬀerent Kinds of Cement The following are some of the important kinds of cements manufactured to suit the diﬀerent requirements. 10.1 RAPID HARDENING OR HIGH EARLY STRENGTH CEMENT This cement gains strength faster than the ordinary Portland cement. Its initial and ﬁnal setting times are the same as those of ordinary cement. It contains more of tri-calcium silicate and is more ﬁnely ground. It gives out more heat while setting and is as such unsuitable for mass concreting. It is used for such structures as are to be subjected to loads early, e.g., repair of bridges and roads, etc.; it is more costly than the ordinary cement. It is manufactured by burning at clinkering temperature an intimate mixture of calcareous and argillaceous materials and grinding the resultant clinker without the addition of gypsum and not more than 1% air entraining agents. The average compressive strength of at least three mortar cubes (area of face 50 cm2) com- 3 percent (of combined posed of one part cement and three parts standard sand by mass p/4 mass of cement and sand) water, shall be as under: C After 24 h After 72 h not less than 160 kg/cm2 not less than 275 kg/cm2 P is the % of water required to prepare a paste of standard consistency. 10.2 HIGH ALUMINA CEMENT It is manufactured by fusing together a mixture of bauxite and limestone in correct proportion and at high temperatures. The resulting product is ground ﬁnely. It develops strength rapidly and is of black color and resists well the attack of chemicals especially of suphates seawater. Its ultimate strength is much higher than that of ordinary cement. Its initial setting time is more than 2 h and the ﬁnal set takes place immediately thereafter. Most of the heat is given out by it in the ﬁrst 10 h as a result of which it can be conveniently used in freezing temperatures but it used in thin layers in normal temperatures. 42 10. DIFFERENT KINDS OF CEMENT 10.3 QUICK SETTING CEMENT It sets faster than the ordinary Portland cement. Its initial setting time is 5 m and the ﬁnal setting time is 30 m. It is used for making concrete that required setting early, as for laying under water or in running water. Initial setting time being very little there is always the danger of concrete having undergone initial setting during mixing and placing as such this cement is used only in exceptional circumstances. 10.4 PORTLAND SLAG CEMENT It is obtained by mixing Portland cement clinker, gypsum, and granulated slag in proper pro- portion and grinding it ﬁnely. This cement has properties very much similar to those of ordinary Portland cement with the following improvements. 1. It has less heat of hydration. 2. It has better resistance to soils, sulphates of alkali metals, alumina, and iron. 3. It has better resistance to acidic waters. This cement can advantageously be used in marine work. Manufacture of Portland slag cement is aimed primarily at proﬁtably utilizing blast furnace slag—a waste product from blast furnaces 10.5 LOW HEAT CEMENT Heat generated by cement while setting may cause the structure to crack in case of concrete. Heat generation is controlled by keeping the percentage of tri-calcium aluminates and tri-calcium silicate low. Its initial and ﬁnal setting times are nearly the same as those of ordinary cement but the rate of its developing strength is very slow. It is not very suitable for use in ordinary structures, when not only the use of structures shall be delayed but also the shuttering shall have to be kept for long and curing will be prolonged. 10.6 AIR ENTRAINING PORTLAND CEMENT It is ordinary Portland cement mixed with small quantities of air entraining materials used are: resin, vinsol resin, oils, fats, and fatty acids. Vinsol resin and darex are most commonly used. These materials have the property of entraining air in the form of ﬁne air bubbles in concrete. These bubbles render the concrete more plastic, more workable and more resistant to freezing. However, because of air entraining the strength of concrete reduces and as such the quantity of air so entrained should not exceed 5%. 10.7 WHITE CEMENT It is cement with pure white color and having the same properties as those of ordinary Portland cement. Grayish color of ordinary cement is due to iron oxide, as such white cement is manu- factured from white chalk and clay free from iron oxide. Oil fuel and not the coal are used for the burning of this cement. It much more costly than ordinary cement. 10.7. WHITE CEMENT 43 10.8 COLORED CEMENT By mixing suitable pigments ordinary Portland cement could be given a red or brown color. For other colors, 5–10% of desired pigments are ground with white cement. Pigments used in cement should be chemically inert and durable so as to fade due to the eﬀect of light or weather. 10.9 PORTLAND POZZOLANA CEMENT Portland pozzolana cement is produced either by grinding together Portland cement clinker and pozzolana (porous volcanic rock) or by intimately and uniformly blending Portland cement and ﬁne pozzolana. This cement has properties similar to those of ordinary Portland cement, and can therefore be used for all general purposes where the latter is employed, with no change in the proportion of coarse or ﬁne aggregates and cement. Gypsum can be added in both cases. Portland pozzolana cement produces less heat of hydration and oﬀers greater resistance to the attack of aggressive waters or cuspate-bearing soils than ordinary Portland cement. It also reduces leaching of calcium hydroxide liberated during the setting and hydration of cement. Consequently, Portland pozzolana cements concrete structures. Pozzolana cement takes a little longer than ordinary Portland cement to gain strength. It is recommended that when pozzolana cement is used in reinforced concrete, the centering be left in position a little longer than would be the case with ordinary Portland cement. Ultimate strength of this cement is more than that of ordinary Portland cement but initial and ﬁnal setting times are the same. 10.10 CHEMICALLY INERT (ACID-RESISTANT) CEMENTS It can be divided into acid-resistant cements, concretes, and putties. Acid-resistant cement is made without ﬁring from silicate or soluble glass (an aqueous solution ion of the silicates of alkali metals with a common formula Ck, Na2O.nSiO2), ﬁnely ground acid-resistant aggregates (andesine, diabase, quartz), and sodium ﬂuosilicate Na2SiF6. Depending on the aggregate used acid-resistant cements are called quartz cement, landsite cement, etc. Cement powder consists of a mixture of pulverized aggregate and sodium ﬂuosilicate. When this mixture is combined with liquid glass, the mass formed soon sets and then rapidly hardens. Setting and hardening take place as a result of the reaction between the liquid glass and 44 10. DIFFERENT KINDS OF CEMENT sodium ﬂuosilicate leading to formation of silicon acid gel (H4SiO4) which possess bonding properties. Acid-resistant cements are used for lining chemical equipment and for preparing mortar and concretes. When a piece of equipment (acid-storage.vat acid absorption tower, reactor, etc.) is lined, polyisobutylene or rubber is glued on to the shell walls and the acid-resistant lining is applied on top of this ﬁlm to provide complete tightness of the lining. Acid-resistant putties, used in assembling chemical apparatus, are also made from acid-resistant cements. C H A P T E R 11 Storage of Cement 45 Portland cement is a ﬁnely ground material. It therefore readily absorbs moisture even from the atmosphere. It is therefore essential to protect it from dampness during storage. Lack of proper care may cause setting of cement or reduction in its strength due to partial setting. Following precautions must as such be taken in storing cement. 1. Walls, roof, and ﬂoor of the building in which cement is to be stored should be completely waterproof. 2. In case the cement store is newly constructed then its interior should have been thoroughly dried before cement is stored on it. 3. Doors and windows should be properly titted and should be kept shut. 4. Except in the case of dry concrete ﬂoor the cement bags should be stacked on wooden planks. 5. The bags should be stacked away from walls. A space of 25 cm all around should be left between the exterior walls and the piles. 6. Bags should be piled close together. 7. Bags should be piled in header stretcher fashion and not more than 15 bags high. 8. While removing cement from store do not take out bags from one tier only. Step back two or three tiers. 9. Each incoming consignment should be stacked separately and a placard bearing the date of arrival of the consignment should be pinned to it. This would help in using cement in the same order as it arrives thereby avoiding dead storage, that is a stack remaining in position for a long time while other consignments of cement come in and go out. 10. For temporary storage of cement at the site of work, bags should not be stacked on the ground. A minimum number of bags needed should be piled upon a raised, dry platform and covered with tarpaulins. C H A P T E R 12 47 Technical Analysis of Cement Cement has to be produced in quantity to meet the need it has to have standard quality [1]. Cement analysis is mainly done to control its quality. Various constituents aﬀect the quality of cement (cement has an ideal composition). The following formula can be used to calculate the percentage or kg wt. of constituent provided the rest are as follows. Given: where K D a.b .b (cid:0) (cid:0) c/ d / ; kg of calcined limestone kg of clinker to be made percent of CaO in clinker percent of CaO in calcined limestone percent of CaO in ignited shale K a c d b D D D D D Example: Suppose that a calcined limestone contains 96% CaO, ignites shale contains 4% CaO, and the desired clinker is 65% CaO. If 100 kg of clinker is to be made, what amount of calcined limestone and ignited shale are required? a.b .b c/ d / (cid:0) (cid:0) K D Solution: Given: a b c d Then, D D D D 100 kg 4% 65% 96% D D D 0.04 0.65 0.96 K D 100.0:04 .0:04 (cid:0) 0:65/ (cid:0) 0:96/ D 66:3 kg of calcined. Limestone: Since the clinker is calcined limestone plus ignited shale, the amount of ignited shale required is: 100 33:7 kg. 66:3 (cid:0) D 48 12. TECHNICAL ANALYSIS OF CEMENT Within certain deﬁnite limitation in composition of cement, the mixture behaves satis- factorily in kilns and produces good cement; outside of these limits it is also shown that trouble in burning may result or the cement may be of inferior quality. There are possible defects arising from unbalanced composition. For instance; if the lime content is too high, the extra lime does not come in to combination, and this may cause ex- pansion and cracking of the mortar or concrete. Silica, alumina, and ferric oxide are likewise limited. If the lime content is ﬁxed, and silica becomes too high, which may be accompanied by a decrease in alumina and ferric oxide, the temperature of burning will be raised and the special inﬂuence of the high lime is lost. If the lime is too low which means an increase in the alumina ferric oxide, the cement may become quick-setting and contain larger amount of alu- mina compounds which appear to be of little value for their cementing qualities. The magnesia (MgO) content is limited, not to exceed 5% because higher magnesia may be dangerous to the soundness of cement, especially at the later ages. The customary method for expressing the relations is by means of ratios of the several ox- ides. Some of these values are based only on empirical results of experience, some on theoretical ideal composition in terms of the probable compounds formed. Ordinary or Portland cement, technically, is a greenish-grey active, impalpable powder made by burning to a high tempera- ture in a rotary kiln, a pulverized mixture containing deﬁnite proportions of oxides of calcium, silicon, aluminum, and iron and grinding the resultant clinker. 2–6% gypsum (CaSO4. 2H2O) by weight (based on maximum limit of 2–2.5% of SO3 in the cement) is added during grinding of clinker to control setting time. Lime in cement has maximum limit. This can be expressed in terms of ratios of the ox- ides. In this instance, the molecular ratio of CaO/SiO2 <3, since the tricalcium silicate is the most basic of the silicates in cement, which can be seen from the following reaction of cement formation. Formation of cement take place by the reaction in the solid state to a great extent. 49 Firing reaction: CaCO3 Clay >500(cid:14)C Dehydrated clay And then CaO Al2O3 C CaO C SiO2 (or dehydrate clay CaO C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! >500(cid:14)C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! H2O (cid:0) 650(cid:14)C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! >650(cid:14)C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! CaO C CO2 dehydrated clay a mixture of Al2O3SiO2 CaO.Al2O3 2CaO.SiO2 CaO.Al2O3 2CaO.SiO2 C Finally, 2CaO CaO.Al2O3 C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! 3CaO.Al2O3 CaO C 2CaO.SiO2 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! 3CaO.SiO2 (cement resistant to sulphate-containing water should not contain 3CaO.Al2O3 but only 4CaO.Al2O3.Fe2O3). When excess of lime is present, the compounds formed are 3CaO.SiO2 and 3CaO.Al2O3, thus the upper limit for CaO is expressed by: CaO SiO2 C C MgO Al2O3 D 3: If CaO decreases beyond a certain limit, 2CaO.SiO2 (dicalcium silicate) appears which disin- tegrates spontaneously and non-hydraulic. The lower limit for CaO (lime), in which tricalcium silicate (3CaO.SiO2) will fail to appear is CaO MgO C .Al2O3 SiO2 (cid:0) Fe2O3 D C not less than 3. If this ratio fails below 3, then the undesirable 2CaO.Al2 CaO.SiO2 will be formed. Experiments suggest that 3CaO.SiO2 and 2CaO Al2CaO.Al2O3 is the best. But Portland clinker consists of tricalcium silicate (3CaO.SiO2), and beta dicalcium silicate ((cid:12)-2CaO.SiO2) as principal constituents together with lesser and variable quantities of tricalcium aluminates (3CaO.Al2O3), tetra calcium alumino ferrite (4CaO.Al2O3:Fe2O3), or some solid solution of iron—phase, periclase (MgO), free lime (CaO), and trace amounts of many other compounds. Cement has to be hydraulic. This is expressed by the ratio of wt. percentage of their four major constituents (SiO2, Al2O3, Fe2O3, CaO). The hydraulic modulus (Hm) D SiO2 C CaO Al2O3 Fe2O3: C 50 12. TECHNICAL ANALYSIS OF CEMENT The hydraulic modulus should be between 1.8 and 2.2. When SiO2 is too high, (Al2O3 Fe2O3) is decreased and the temperature of burning is raised, the inﬂuence of the lime is also lost. An expression for this is: C the silicate modulus (Sm) SiO2 D Al2O3 Fe2O3 C .%wt.:/ The value should be in the range of 2.0–2.5. Cement with high silicate modulus hardens slowly; that with low silicate modulus set rapidly. 12.1 SOLUTION PREPARATION AND APPARATUS/REAGENTS USED 150 ml beakers, stirrer, watch glass, white band ﬁlter paper, red band ﬁlter paper, conical ﬂasks, funnel, porcelain (evaporating dish), crucible tongue, grinding mortar, glass pistle, drying oven, igniting furnace, analytical balance, cooling desiccators, burette distilled water, heater (stove) measuring cylinders, and sand bath are used for the analysis. Reagent Used • HCl of d 1:19 or 1.185 D • AgNO3 solution • 10% Na2CO3 dissolving in 10% HCl • 40% HF • Cone H2SO4 of d 1:84 5% H2SO4 D • HNO3 of d 1:19 D • NH4O4 of 25%, 10%, 2.5% • Na2HPO4 of 50%, 5% • 3% NH4NO3 • Saturated (NH4)2 C2O4, 0.1% (NH4)2C2O4 • 0.01% methyl orange solution • 0.1N KMnO4 12.1. SOLUTION PREPARATION AND APPARATUS/REAGENTS USED 51 Preparation of Reagent Value of reagents in laboratory and value of reagents to be used are calculated by the formula: C1 d1 V 1 C 2 d2 V 2: D 1. HCl of 37%: d HCl of 10%: d D D 1:185, N 12:5 D 1:0475 is required to be prepared 10 V1 D (cid:2) 37 1:0475 (cid:2) 1:185 (cid:2) 50 11:9 D D 12 ml 12 ml of 37% is diluted with distilled water to 50 ml to give 10% HCl. 2. H2SO4 of 96%: d 1:84, N D D 36 is present in laboratory H2SO4 of 5%: d D 1:0325 is required to be prepared. 5 (cid:2) V1 D 1:0325 96 (cid:2) 1:84 (cid:2) 200 5:845 D D 5:85 ml 5.85 ml of 96% is diluted with water to 200 ml to give 5%. H2SO4 3. HNO3 of 70.5%: d 1:4225, N 16:14 D D HNO3 of 31.47%: d D 1:19 required to be prepared V1 D 31:47 70:5 50 1:19 (cid:2) 1:4225 D (cid:2) (cid:2) 18:67 D 19 ml 19 ml of 70.5% is diluted with water to 50 ml to give d 1:19 HNO3. D 4. NH4OH of 28%: d (a) NH4OH of D D 25%: d 0:898, N 14:76 D 0:907 is required to be prepared D V1 D 25 (cid:2) 28 0:907 50 (cid:2) 0:898 D (cid:2) 45 ml 45 ml of 28% is diluted with water to 50 ml to give 25% NH4OH. (b) NH4OH of 10%: d D 0:957 is required to be prepared V1 D 10 0:957 200 (cid:2) 28 (cid:2) 0:898 D 76:12 76 ml D (cid:2) 76 ml of 28% is diluted with water to 200 ml to give 10% NH4OH. 52 12. TECHNICAL ANALYSIS OF CEMENT (c) NH4OH of 2.5%: d D 0:987 is required to be prepared V1 D 2:5 (cid:2) 28 0:987 50 (cid:2) 0:898 D 4:9 D 5 ml (cid:2) 5 ml of 28% is diluted with water to 50 ml to give 2.5% NH4OH. 10% NaCO3 10 g is dissolved with distilled water up to 10 ml 3% NH4NO3 3 g is dissolved with distilled water up to 10 ml 50% Na2HPO4 50 g is dissolved with distilled water up to 10 ml 5% Na2HPO4 5 g is dissolved with distilled water up to 10 ml 0.1%(NH4)2C2O4 0.1 g is dissolved with distilled water up to 10 ml 0.01% methyl orange 0.01 g is dissolved with distilled water up to 10 ml • (NH4)2C2O4 is dissolved in water until it is saturated. • 40% HF Solution is prepared • 0.1N KMnO4 is prepared by standardizing it with Na2C2O4 as follows: KMnO4 m D D 0:1 (cid:2) 31:6 1000 (cid:2) 150 D 0:47415 g • 0.47415 g KMnO4 is dissolved in water to 150 ml to give 0:1 N D Na2C2O4 m D D 0:1 (cid:2) 67 (cid:2) 1000 100 D 0:67 g • 0.67 g Na2C2O4 is dissolved in water to 100 ml to give 0.1 N Na2C2O4 m 0:1 67 (cid:2) (cid:2) D D 100 D 0:67 g • 0.67 g Na2O4 is dissolved in water to 100 ml to give 0.1 N • The aliquant part (25 ml) of Na2C2O4 is put into conical Flask and acidiﬁed with a small amount of HCl and tittered with KMnO4, until the apple (pink) color of KMnO4 appears with one drop of it. • Volume of KMnO4 used for titration D • Volume of Na2C2O4 taken for titration 26 ml 25.0 ml D • Normality of Na2C2O4 0:1 N D 12.2. SAMPLE ANALYSIS AND THEIR REPORT 53 • Normality of KMnO4 ? Na2C2O4 V1N1 D D KMnO4 V2N2 0:25 0:1 (cid:2) NKMnO4 26:9 (cid:3) (cid:2) 0:1 0:25 D (cid:2) 0:0929 D 26.9 12.2 SAMPLE ANALYSIS AND THEIR REPORT 12.2.1 EXPERIMENT NO. 1 Determination of Moisture Content Procedure: • 2.00 g of cement sample was weighed on analytical balance and put into reweighed crucible of known constant weight. • Then it was dried in a drying oven at temperature of 110(cid:14)C for 3 h. • Next the crucible with content is put into a desiccator and cooled for 20 min and weighed. • Again, it was dried for 1 h, then cooled and weighed. Date obtained and calculation 1. Constant weight of crucible 7.05800 g. D 2. Wt. of crucible cement sample 9.05800 g. D C 3. Wt. of cement sample (b–a) 2:00000 g. D 4. Wt. of crucible cement sample after drying for 3 h in 110(cid:14)C C After drying for 1 h 9.03865 g. D 9.03900 g. D 5. Wt. of sample after drying (d–a) 9:03865 7:05800 (cid:0) D 1:98065 g: 6. Wt. of moisture loss (c–e) 0.01935 g. D 7. Wt. of moisture loss in percentage f 100 (cid:2) C 0:01935 2 (cid:2) D 100 D 0:9675%: 54 12. TECHNICAL ANALYSIS OF CEMENT 12.2.2 EXPERIMENT NO. 2 Determination of Loss of Substance After Ignition Procedure: • 2.00 g of cement sample was put into crucible of known constant weight. • Next it was dried in a drying oven for 30 min at 110(cid:14)C and then ignited in the furnace at 1000(cid:14)C for 1 h. • Then it was cooled in a desiccator for 20 min and weighed. Data obtained and calculation 1. Constant wt. of crucible 6.90700 g. D cement sample 8.90700 g. D 2. Wt. of crucible C 3. Wt. sample (b–a) 4. Wt. of crucible furnace (d–a). C 2.00000 g. D sample after drying for 30 min in the oven, and igniting it for 1 h in the 8:83700 5. Wt. of substance lossed (c–e). 2:00000 6:90700 1:93000 (cid:0) (cid:0) D D 1:93000 g 0:07000 g 6. Wt. of substance lossed in percentage. f 100 (cid:2) C 0:07000 2 (cid:2) D 100 3:5% D The substance lost are CO2 and steam. 12.2.3 EXPERIMENT NO. 3 Determination of Undissolved Residue Procedure: 1. 1 g of cement sample is put in a beaker of 150 ml and 25 ml of distilled water and 5 ml of concentrated HCl (d 1:185) are added. By shaking the content, 50 ml of distilled water added. Then this mixture was heated for 15 min by covering the beaker with watch glass on a heater. D 12.2. SAMPLE ANALYSIS AND THEIR REPORT 55 2. The mixture was ﬁltered on a white-band ﬁlter paper by using funnel. The precipitate was washed with cold water until chloride ions were removed (this was tested with AgNO3) and after that the content of the ﬁlter paper was transferred to the beaker by washing it with a 30 ml hot 10%Na2CO3 solution. 3. The content of the beaker was covered with watch glass and heated the necessary time for maximum moisture removal. 4. Then the mixture was ﬁltered on the ﬁlter paper and washed with hot distilled water. Then 10 drops of 10% HCl were added on the ﬁlter paper and it was washed until free from chloride ion with water (this was tested with AgNO3). 5. The ﬁlter paper with the residue was put inside a previously weighed crucible and ignited for 1 h at 1000(cid:14)C in furnace then cooled in desiccators for 20 min and weighed. Data obtained and calculation 1. Wt. of crucible 2. Wt. of crucible D C 6.90700 g. residue after ignition 6.92045 g. D 3. Wt. of residue (b–c) 4. Wt. of undissolved residue in percentage 6:92045 (cid:0) 6:90700 D 0:01345 g: C 100 wt. of sample D (cid:2) 0:01345 100 (cid:2) 1:00000 1:345%: D 12.2.4 EXPERIMENT NO. 4 Determination of Silicic Acid as SiF4.(SiO2:SO3) Procedure: 1. 0.4 g of cement sample is added into a 50 ml porcelain dish and to this 15 ml of distilled water and 10 ml HCl (d 1:185) added. D 2. The mixture was evaporated on sand both until all the HCL disappears. 3. Then the dry residue was treated with 10 ml of HCl (d 1:185) and evaporated again. D 4. The content of the porcelain dish was grained with the glass pestle and collected toward the center of the dish and moistened with a few drops of HCl. 56 12. TECHNICAL ANALYSIS OF CEMENT 5. 30 ml of hot distilled water was added to the content and the mixture was heated for 10 m, and ﬁltered on a red-band ﬁlter paper using funnel. Grains precipitate from the dish were transferred to the ﬁlter paper with the use of of additional ﬁlter paper. The ﬁltrate was saved for the next experiments. 6. The precipitate was washed with hot distilled water until all the chloride ions are removed (this was checked with AgNO3). 7. The ﬁlter paper with precipitate was placed in a reweighed porcelain crucible and dried in an oven at 110(cid:14)C for 30 min and ignited in the furnace for 3 h at 1000(cid:14)C. 8. Then it was cooled in desiccators for 20 min and weighed. 9. The content was ignited, cooled, and weighed again until constant weight obtained. * The weighed form was white in color. 10. The content of the crucible was moistened with 2 ml of distilled water and 2 ml of 40% HF was added and evaporated under the hood. 11. Then 1 ml of HCl was added and evaporated. Near the end of evaporation 2 ml of conc. 1:84) was added and heating was continued till white fumes of SO3 appear H2SO4 (d (this indicates that all the SiF4 and HF have evaporated). D 12. Heating was continued until the white fume (SO3) disappears. 13. Then, after cooling the crucible with residue it was weighed. Date obtained and calculation 1. Wt. of crucible 2. Wt. of crucible D C 16.78900 g. precipitate after ignition 16:88000 g. D 3. Wt. of precipitate (b–a) 16:88000 (cid:0) 16:78900 D 0:09100 g: 4. Wt. of the precipitate in percentage C 100 wt. of sample D (cid:2) 0:09100 0:4 (cid:2) 100 D 22:75%: 5. Wt. of precipitate 16:87000 g. C crucible after treating with 40% HF and then after igniting D 12.2. SAMPLE ANALYSIS AND THEIR REPORT 57 6. Wt. of the evaporate (b–e) 16:88000 (cid:0) 16:87000 D 0:00600 g: 7. Wt. of evaporate in percentage f 100 wt. of sample D (cid:2) 0:00600 0:4 (cid:2) 100 D 1:5% SO3: 8. Percentage of SiO2 (d–f ) 22:75 1:5 (cid:0) D 21:25: * The purpose of adding H2SO4 is to obtain SO3 by oxidation which shows the complete evaporation of SiF4 and HF by its appearance. 12.2.5 EXPERIMENT NO. 5 Determination of Iron and Alumina Oxides (R2O3) Procedure: 1. The ﬁltrate saved from determination of SiO2 was heated in about a 200 ml beaker to boil. 2. Then, 0.5 ml of conc. HNO3 (d was added. D 1:185) and 4 drops of 0.01% methyl orange solution 3. Finally, 10% NH4OH solution was added drop by drop unit the solution becomes slightly alkaline (orange in color). 4. Then the muddy solution was kept in hot place until the entire precipitates settle, and the liquid above the precipitate become transparent. 5. The precipitate was ﬁltered on red-band ﬁlter paper and washed with 35% NH4NO3 so- lution until all the chloride ions are removed. * The ﬁltrate was saved for the next experiment. 6. The ﬁlter paper with the precipitate was transferred to a porcelain crucible and dried until it starts charring (in drying oven) and then ignited in a furnace at 1000(cid:14)C for 1 h then cooled and weighed. Data obtained and calculation: 1. Wt. of crucible 2. Wt. of crucible D C 6:90900 g. R2O3 after ignition 6:94300 g. D 58 12. TECHNICAL ANALYSIS OF CEMENT 3. Wt. of R2O3 (b–a) 4. % of 6:94300 (cid:0) 6:90900 D 0:03400 g: R2O3 0:03400 0:4 (cid:2) D 100 D 8:5%: 9%. From this, 6.5% is Al2O3 and 2.5% is Fe2O3. The average (%) proportions of R2O3 Therefore, D 9—–6.5 8.5—–? 8:5 6:5 (cid:2) 9 D 6:138% Al2O3 6:138 9 (cid:0) D 2:362% Fe2O3 . 12.2.6 EXPERIMENT NO. 6 Determination of Calcium Ion Procedure: 1. The ﬁltrate which was saved from determination of R2O3 was acidiﬁed with few drops of HCl (pink color appears) and boiled. 2. 25 ml of hot saturated (NH4)2C2O4 solution was added, and 10% NH4OH was added drop by drop until the solution became orange. The precipitate (Ca2C2O4/ is formed. 3. The solution was boiled until the precipitate settles and the mixture stood for 1 h undis- turbed. 4. The precipitate was ﬁltered with white-band ﬁlter paper and washed with hot 0.1% (NH4)2C2O4 solution at ﬁrst until all the chloride ions are removed and then with hot water four times. * The ﬁltrate was saved for the next experiment. 5. The ﬁlter paper with the precipitate was carefully transferred to a 250 ml beaker, ﬂattens it on the wall of the beaker and was poured 150 ml of hot 5% H2SO4 solution, gradually moving the ﬁlter paper outwards using a glass rod. 6. Then the solution was heated to 70(cid:14)C and titrated with 0.0929 N KMnO4 solution. NB No indicator was used for the titration because KMnO4 has a pink color. One drop of KMnO4 solution changes the colorless solution to pink at the equivalent point. Data obtained and calculation 12.2. SAMPLE ANALYSIS AND THEIR REPORT 59 • CaC2O4 H2SO4 C (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! CaSO4 C H2C2O4. • Volume of solution (H2C2O4) 150 ml. D • Volume of KMnO4 used for titration 98:5 ml. D • Normality of KMnO4 0:0929 N. D • Normality of H2C2O4 ? D H2C2O4 KMnO4 V1N1 • Normality of V2 . (cid:3) (cid:2) H2C2O4 98:5 0:0929 (cid:2) 150 D D 0:06100 N • CaC2O4 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! CaO C CO2. • Gm. eq. of Ca 20.04 g. D • Wt. of CaO (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! 56 ? (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) Ca D 0:0610 (cid:2) 20:04 100 (cid:2) 150 D 0:183366 g Ca 40 g 0.183366 56 (cid:2) 0:183366 40 D 0:2567124 g 0.2567124 ? (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) 0.4 g 100 g %CaO 100 (cid:2) 0:2567124 0:4 D D 64:1781%: 12.2.7 EXPERIMENT NO. 7 Determination of Magnesium Ion Procedure: 1. The ﬁltrate after removal of CaCC ions was evaporated almost to dryness in a 250 ml beaker. 60 12. TECHNICAL ANALYSIS OF CEMENT 2. After cooling the beaker, the residue was moistened with 3 ml HCl (d of distilled water was added and heated. The solution is pink. 1:185) and 50 ml D 3. The solution was acidiﬁed with HCl (d 1:19) after adding 4 drops of methyl orange. The solution became light yellow in color. D 4. 30 ml of 5% Na2HPO4 and 10% NH4OH was added until the solution just turns alkaline (checked by litmus). 5. After cooling, the solution was diluted with 100 ml distilled water and 15 ml of 25% NH4OH solution was added. 6. The precipitate waited for 3 h and then ﬁltered through a white-band ﬁlter paper. 7. The precipitate was washed with 2.5% NH4OH until all the Cl(cid:0) ions are removed. 8. The ﬁlter paper with precipitate was dried in drying oven with a previously weighed porce- lain crucible and ignited in the furnace at 1000(cid:14)C until the constant weight obtained. Data obtained and calculation 1. Wt. of crucible 2. Wt. of crucible D C 6.90900 g. residue after ignition 6.91955 g. D 6:90900 3. Wt. of residue (MgO) 6:91955 (cid:0) D 4. % of MgO D C 100 wt. of sample D (cid:2) Other Calculations 1. The upper limit for CaO (lime) 0:01055 g. D 0:01055 0:4 (cid:2) 100 D 2:6375%: MgO Al2O3 D 3 CaO SiO2 C C 2:6375 6:138 D 66:8156 27:388 D 2:4396: 64:1781 21:25 C C 2. The lower limit for CaO (lime) SiO2 CaO MgO C .Al2O3 (cid:0) 64:1781 21:25 C 2:6375 8:5 C (cid:0) Fe2O3/ D not less than 3 66:8156 12:75 D D 5:2404: 3. The hydraulic modulus 12.2. SAMPLE ANALYSIS AND THEIR REPORT 61 Hm CaO D SiO2 C R2O3 D 1:8 22 (cid:0) 64:1781 64:1781 21:25 C 8:5 D 29:75 D 2:1572: 4. The silicate modulus Sm D 2:0 2:5 (cid:0) (cid:0) (cid:0) SiO2 R2O3 D 21:25 8:5 D 2:5: How do you grade this cement? Inferior, good, why? The cement is graded as good quality because of the following. 1. The main composition of mineral oxides are found according to their proportion range in 64:178% 21:25% SO3 15% D % CaO SiO2 D D D D D Al2O3 Fe2O3 6:138% 2:3620% MgO 2:6375% 2. From the value of upper limit of CaO, we can see that excess of lime was not present, there- fore, no possibility for expansion and cracking of mortar or concrete, and from the value of lower limit of CaO, we can see that there is no possibility of formation of undesirable 2CaO.Al2CaO.SiO2. 3. From the hydraulic value range we can see that the cement has hydraulic property. 4. When SiO2 is too high, (Al2O3 Fe2O3) is decreased and the temperature of burning is raised, the inﬂuence of high lime is also lost. Cement with high silicate modulus hardness slowly, that with low silicate modulus set rapidly. From the silicate modulus value we can see that, the value is in the required range. C 5. From the content of MgO value we can see that there will be no possibility for soundness (decrease in volume) of cement at the early setting slage. 6. From all the chemical composition values we can see that the amount of gypsum added to control the setting time was a required amount. 62 12. TECHNICAL ANALYSIS OF CEMENT 12.3 CONCLUSION From the theoretical expression, the cement production in any country must meet the good quality in order to carry out satisfactory construction work. As we can see from the sample analysis result, the cement which was produced in Ethiopia has good quality. Since Ethiopia is a developing country, the demand of cement increases from time to time in every construction ﬁeld. To fulﬁll this demand great work must be done in cement production and this must meet with modern technology and for this, skilled manpower is also very important. References 63 [1] Bye, G. C. Portland Cement: Composition, Production and Properties, Thomas Telford Pub- lishing, London, 1999. 47 [2] Ghosh, S. N. Advances in Cement Technology. Cement Institute of Research of India, New Delhi, India, 1983. DOI: 10.1016/0008-8846(83)90070-4. 29 [3] Mukhlyenov, I., Kuznestov, D., Furmer, L., Tumarkina, E., and Averbukn. A Chemical Engineering. The Higher School Publishing (part two), Hous, Moscow. 1 [4] Peray, K. E. Cement Manufacturer’s Handbook. Chemical Pub. Co-Technology & Engi- neering, U.C.D Library, 1979. 39 [5] Singh, S. Engineering Materials, 2nd ed. Technical Education, Delhi Administration, 1979. 11 Author’s Biography 65 TADELE ASSEFA ARAGAW Tadele Assefa Aragaw is a lecturer in Chemistry and Environmental Engineering, a Researcher, and a Facility Manager in the Chemical and Food Engineering at the Bahir Dar Institute of Technology. Since 2017 he has been involved in a research project in the area of Ethiopian kaolin characterization for diﬀerent industrial applications as well as an indigenous microalgae investigation from wastewater for biodiesel production. In 2012, Tadele received his B.S. in Chemistry from the University of Gondar. In 2014, he started studying for his master’s degree in Environmental Engineering while also teaching an Analytical Chemistry and Environmental Engineering course for Chemical Engineering students. He received his M.Sc. in Environmental Engineering in 2016 from the Bahir Dar Institute of Technology, Bahir Dar University. Tadele has published articles in the ﬁeld of his profession, Environmental Engineering.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=7833474.pdf&bkn=7833473&pdfType=book	Series ISSN 1939-5221 The Human Side of Engineering John Heywood, Trinity College Dublin-University of Dublin While in many university courses attention is given to the human side, as opposed to the technical side of engineering, it is by and large an afterthought. Engineering is, however, a technical, social, and personal activity. Several studies show that engineering is a community activity of professionals in which communication is central to the engineering task. Increasingly, technology impacts everyone in society. Acting as a professional community, engineers have an awesome power to influence society but they can only act for the common good if they understand the nature of our society. To achieve such understanding they have to understand themselves. This book is about understanding ourselves in order to understand others, and understanding others in order to understand ourselves in the context of engineering and the society it serves. To achieve this understanding this book takes the reader on 12 intellectual journeys that frame the big questions confronting the engineering professions. J O H N H E Y W O O D T H E H U M A N S I D E O F E N G N E E R I I N G ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Synthesis Lectures provide concise Library of Engineering and Computer Science. original presentations of topics, published information, visit our website: quickly http://store.morganclaypool.com in digital and print formats. For more important research and development store.morganclaypool.com The Human Side of Engineering John Heywood e Human Side of Engineering Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. e Human Side of Engineering John Heywood 2016 Engineering Principles in Everyday Life for Non-Engineers Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 e Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: e Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 iv e Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 e Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering ermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape ermal Optimization Using Bejan’s Constructal eory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 v Survive and rive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: e DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2017 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. e Human Side of Engineering John Heywood www.morganclaypool.com ISBN: 9781627056649 ISBN: 9781627056656 paperback ebook DOI 10.2200/S00748ED1V01Y201612ENG028 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Series ISSN Print 1939-5221 Electronic 1939-523X e Human Side of Engineering John Heywood Trinity College Dublin-University of Dublin Foreword by Mani Mina Iowa State University SYNTHESIS LECTURES ON ENGINEERING #28 CM&cLaypoolMorganpublishers&ABSTRACT While in many university courses attention is given to the human side, as opposed to the technical side of engineering, it is by and large an afterthought. Engineering is, however, a technical, social, and personal activity. Several studies show that engineering is a community activity of profession- als in which communication is central to the engineering task. Increasingly, technology impacts everyone in society. Acting as a professional community, engineers have an awesome power to inﬂuence society but they can only act for the common good if they understand the nature of our society. To achieve such understanding they have to understand themselves. is book is about understanding ourselves in order to understand others, and understanding others in order to understand ourselves in the context of engineering and the society it serves. To achieve this understanding this book takes the reader on 12 intellectual journeys that frame the big questions confronting the engineering professions. KEYWORDS agency, assumptions, change, common good, communication, community, contrac- tualism, constructivism, consequentialism, curriculum, duty, development, engineer- ing, engineering education, enterprise, epistemology, ethics, engineering ethics, fear, higher education, judgement, knowledge, language, learning, learning organization, life-long learning, management, mobility, morality, open-system, closed system, organization, the person, perception, philosophy, philosophy of engineering, pro- fessional, realism, reﬂection, responsibilities, rights, schema, self-management, so- cial system, transfer of learning, team-work, technological literacy, truth, university, virtues, ways of thinking, work, workforce Contents ix Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Preface and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv 1 “It all Depends on What You Mean by...” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 inking about inking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 ings are not Always What ey Seem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 5 6 Meaning—True or False: Real or Imagined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 From Perception to Self-Perception and a Little Management En-route . . . . . . 37 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Sharing Problems: Living in Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 7 inking about Making a Good Engineer Possible . . . . . . . . . . . . . . . . . . . . . . . 59 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 8 9 Aspiration in Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Preparing for the Future: Individuals and Organizations . . . . . . . . . . . . . . . . . . 81 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 x 10 Changing Us: Changing Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 11 Journey’s End: A New Beginning? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 12 Questioning our Assumptions: Adaptability and Change . . . . . . . . . . . . . . . . . 119 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Foreword xi THE BIG PICTURE is book is a series of essays that were originally created by John Heywood for a seminar at Iowa State University—Electrical Engineering EE510M—that I created during the Fall 2013. Faculty and students from diﬀerent perspectives, disciplines, and departments attended and contributed to the seminar class. is version of “the Journeys,” as his explorations in the seminars were called, is a result of interactive participation, discussion, and feedback from the followers of the seminar, and ﬁnally the discussions between John and I. e journeys are explorations into the multidi- mensional and connected world of engineering, technology, and society. ey invite the reader to explore the same territories and ﬁnd their own answers, not those of a text book. I thought it would be of value to provide the story of how these journeys started, what were the goals, objectives, and hopes that we I had when we embarked on this project. Hopefully, this will help you, the reader, to examine your perspectives and belief structures, and reﬂect on your ﬁelds of interest as it helped us and our friends, associates, and colleagues examine ours. We hope that readers will be encouraged to participate in more constructive dialogues and reﬂective activities about engineering and its purposes and, in consequence, engineering education. As John says at the end of the ﬁrst journey “We […] are taking a series of journeys so we may better reﬂect on who and what we are as individuals and engineers within a society that is becoming increasingly complex.” THE SEMINAR CLASS e idea for the seminar was the result of a very successful session that we did in the Spring of 2013 in the ﬁrst class of electrical engineering [Electrical Engineering (EE185)] in our department. Because I had for some time used student reﬂections to monitor their experience and provide them with a method of self-evaluation I thought their development would be enhanced if they were enabled to engage in dialogue with an outside scholar so I asked John if he would meet with the class via Skype. A week before the meetings, I introduced John and his ideas and writings to the class. For that week in EE185 we discussed who John is and students read about him by reading his memories of 50 years of being in IEEE (on the IEEE History website). e students then created a set of questions for him to answer. e questions were sent to John a few days before the meeting. On the day of the Skype meeting, he answered these and in dialogue with the students other questions put to him by them. e students not only liked the session but also kept asking to have xii FOREWORD more sessions like that. In particular, they wanted to have more sessions with John. is session was so successful and students loved it to so much that I thought it would be even better if we could engage higher-level students, so we decided to do a seminar class with a new audience and create more in-depth discussions. THE BEGINNING Later that year, at ASEE’s annual meeting (Atlanta, Georgia, 2013) we reviewed what had hap- pened and considered how we could have a seminar class on the subject of engineering pedagogy and philosophy, promote discussion and debate within in them, and record the participants’ re- ﬂections on them. John had the vision that we could bring the self, the person as an agent into the discussions and help the participants realize how to create their own journey in critical think- ing, personal philosophy, and pedagogy. Eventually, he decided to create a few essays to trigger discussion that would help a selected group of faculty and senior students to debate, think, dis- cuss, and appreciate the role of the humanities and social sciences in engineering and engineering education as a means of reﬂective practice. When I returned from the conference the ﬁrst thing I did was to visit the undergraduate oﬃce at Iowa State University Department of Electrical and Computer Engineering. I asked the Director Vicky orland-Oster the following: “I would like to make a class for Fall 2013 on Critical Reﬂections on Engineering, Engineering pedagogy, and philosophy, can you help me with that?” Vicky paused, looked at me, and said that the idea is great but we cannot create a class unless the curriculum committee approves it. is was not possible since the committee did not have meetings during the summer of 2013. But I had to make it happen! is was so special to us that we had to get it done. We just had to…. To make the seminar happen within the constraints of university bureaucracy, I decided to go through the regular academic system and create a special topic class. Since I am a member of the Faculty of Electrical Engineering in the Electromagnetic area, I used a special topic class for the Fall 2013 semester called EE510M. e class was oﬃcially (according to the Iowa State University catalog) a special topic class with the following title “EE510M: Special topics on Elec- tromagnetism.” John mentioned that since 50 or more years ago he had worked on ionospheric research in industry, this may ﬁt! While this was a real stretch, it was the only way that we could have a class in the time that we had. After the class was created I began to invite people to par- ticipate. In order to be more descriptive about the seminar class we decided to adapt the title to “Critical Reﬂections on Engineering and Engineering Pedagogy”. e Journeys would focus on how we develop and ﬁnd our own belief structures as individuals and educators in the context of engineering and technology. CREATING A PLATFORM FOR THE DISCUSSIONS: THE JOURNEYS John Heywood started to write his personal reﬂections in a set of essays called “the Journeys.” In this development he led with his ideas and reﬂections on engineering, pedagogy, and develop- FOREWORD xiii ment of personal philosophy. John and I have been active members of the American Society for Engineering Education (ASEE) and in particular in its Technological and Engineering Literacy and Philosophy of Engineering (TELPhE) division. As a part of that group we believed that in order to enrich our eﬀorts in engineering education and pedagogy we need to question our epistemology of what is engineering, our roles as educators, our value systems as engineers and engineering educators, and more especially as individuals. As we engage in these activities and discussions we end up developing a philosophy of engineering and engineering education driven by our personal philosophy. John started to write the Journeys for the class to review and discuss them with him at weekly session. John Pritchard, graduate student, researcher, and good friend, would record via Skype, direct the sessions, and put them into the ﬁnal form that would be posted on the website he created for this seminar series. Copies of the scripts, and the accompanying notes too which John attached great importance to, would also be made available so a participant could choose to view the Skype recording or read the script or use both. In so far as was possible, the Skype would take place on Mondays and a Skype seminar would follow on Fridays. THE SEMINARS e seminars were advertised during the middle to end of August 2013. en they began on the ﬁrst week of September 2013. We met every Friday afternoon from 2–3 pm (8–9 pm in Dublin), the essay and the readings having been posted earlier in the week. ose who wanted to attend would be in the class during the live Skype session with John. e sessions would start with questions and comments by the participants. Some of the questions were created and sent to John via email; the others were asked and discussed during the sessions. Based on the discussions, suggestions, interactions, and feedback from the participants, John modiﬁed the Journeys, added items, clariﬁed points, and included some of the participant’s points of view in the revision of the text. e Journeys that are published in this book are the modiﬁed and ﬁnalized ones. We believe the modiﬁcations that came about through dialogue have improved and enriched the original Journeys since the ﬁnal forms do reﬂect the interactions and discussion by the participants. THE PARTICIPANTS AND SOME OBSERVATIONS e class was divided into three groups: 1. those who attended the live sessions from undergraduate and graduate students (from the U.S. and other countries) from electrical and computer engineering. In addition, we had faculty of engineering, English, rhetoric, and physics attending the seminar class; 2. those who followed the reading and activities within the campus of Iowa State University. is group included some administrative staﬀ from the Department and the oﬃce of Dean of engineering including Associate Deans. In addition, there were a number of faculty and xiv FOREWORD graduate students in engineering, sciences, English, philosophy who were following our activities via our website; and 3. ﬁnally, interested national and international colleagues and friends including some of mem- bers of Technological and Engineering Literacy and philosophy of Engineering Division of ASEE and others also followed some of the activities also via our website. We received reﬂections, critiques, and ideas from many of our caring and kind colleagues and participants. ey patiently helped us think and rethink the activities and discussions. e Journeys reﬂect the feedback from the attendees and patrons who were kind enough to commu- nicate with us during the progress of the project and after the completion of the Journeys as a part of ongoing critique and discussions. In particular, we are very thankful to our special colleagues and friends in ASEE Technological and Engineering Literacy and Philosophy of Engineering Division including Professors Alan Cheville at Bucknell University and John Krupczak at Hope College. e class was very successful, and I have received requests to organize more seminar series of this kind. e engagement of the participants and continuations of support, and requests for more of this kind of activity, showed that our eﬀorts were needed and that they should be continued in many forms. When I reﬂect back on the class, I realized that in particular the class became an eﬀective vehicle for all to reﬂect and think more deeply about their beliefs and perspectives in their ﬁeld and their relationship to education. Finally, it helped all participants to advance their eﬀorts to develop their own “philosophy”. We began the class with the title of “Critical Reﬂections on Engineering and Engineering pedagogy,” and somewhere during the ﬁrst half of the seminar it became “Critical Reﬂections on Engineering, Engineering Pedagogy, and Philosophy.” One of the more interesting observations was the reaction of the engineering participants and followers of the Journeys. ey were fundamentally diﬀerent to those the other groups. Here are some of the more interesting questions put to us by the engineering group. • “ese are wonderful words: How do they help me be better educator?” • “Knowing all of this is ﬁne: How could it help me do better as an engineer?” • “If engineering is taking action, doing and designing things, how does philosophy help me do it better?” • “is is of great value and importance. We do not have anything like that in our curriculum, and it has worked well.” • “Do we really need to change anything in our education system? It seems to work.” • “e engineering curriculum is based on skills, math, physics, and all of engineering con- cepts and practice. If we engage in pedagogical and philosophical discussions, reﬂections, and debates, it could reduce the students’ engineering knowledge base. We would then de- velop weak students.” FOREWORD xv • “What would industry think? Would they still hire our graduates?” e following question summarizes the overall engineering participant’s questions and con- cerns: “ese are nice words, and great perspectives, but how can I apply it to engineering and engineering education?” In a way, the engineering team is looking for a summary and action items to help them with possible implementation. To our surprise, the physics, math, and English participants did not have such questions. ey tried to absorb, participate, and contribute. One may think physics and engineering are close, but physics members did not really ask the same types of questions and did not show the same concerns as those reﬂected in the above list. Generally, the physics members were much more accepting and integrated the ideas and discussions; they were not looking for action items. Why? We need to remember that physics is usually placed in the college of sciences and liberal studies, and that this ﬁeld of study was historically called natural philosophy. It only changed to physics about the second half of 19th century. us, physics is likely to be closer to a philo- sophical perspective than engineering; the true essence of this issue and observation needs more exploration, however. All in our team claimed that they had to read some of the journeys and parts of the Journeys more than once to really see the point and connection to their intentions. We recommend that the reader, having read the Foreword and the Preface, to ﬁrst read the journeys in order to become comfortable with the style, and the way the notes are used to support the argument on the one hand, and on the other hand provide a bridge for further exploration. e Journeys are meant to make the reader think, wander, enjoy, question, and argue with the writer as did the participants in the exercise. A NEED; A SPECTER OF SOMETHING MORE Upon review and discussion John, I, and many of our colleagues believe that the experiences and insights gained by participants point toward a fundamental void in the engineering community and in particular the engineering education community. ere seems to be a lack of dialogue, creative discussion, and philosophical examination of what engineering is. For example, “Why do we teach what we teach? What is needed? What should all engineers know?” ese are questions of the utmost importance for the ﬁeld and its educators. Currently, there are few forums for such discussions in the arena of engineering education. However, there seems to be a need of national and international venues for creating meaningful and visible dialogue and discussions on engineering, engineering pedagogy, and philosophy of engineering and engineering education. Mani Mina Departments of Industrial Design and Electrical and Computer Engineering Iowa State University August 2016 Preface and Introduction xvii e title of this book, e Human Side of Engineering is both borrowed from and inspired by one of the outstanding books on management, Douglas McGregor’s e Human Side of Enterprise published in 1960. It’s theories X and Y continue to help us understand the behavior of indi- viduals at work and the impact that organizations have on them (see Journey 5). While in many courses some attention is given to the human side of work, it is by and large an afterthought, for engineering is thought to be a technical and personal activity. Journey 1 uses a model of a three-legged stool to oﬀer an explanation of how engineering produces a technology. Engineering is seen to be a process and technology the product of that process. e base of the stool is where the process begins: it represents the mind of the engineer and the beliefs, attitudes, and values that it generates. From this mind, informed by the values of the society in which it exists, come the product designs intended to solve the problems with which it is presented. In an engineering company that information is conveyed by those concerned with marketing about products that can be changed or new products that seem to be required. e resulting design is fed to manufacturing, or the problem is sent to R & D and subsequently back to manufacturing resulting in a technology that impacts on the economy and society. All this is done in an organization which links together all the components in order to produce the tech- nology. at organization comprises roles, humans, and technical and the task of management is to coordinate and integrate them [1]. Resulting from studies of engineers at work the Aus- tralian engineering educator James Trevelyan concluded that four major competences required by expert engineers are technical coordination, project management, negotiation, and teaching [2], none of which have anything to do with skill in engineering science and engineering design, but everything to do with working with human beings. Much of what Trevelyan found Michael Youngman, Bob Oxtoby, Denis Monk, and I found in a study of engineers at work during the nineteen seventies [3]. Whereas we reported only on our research, Trevelyan provides a substantive guide to what students need to know to become expert engineers. Had it been published before these journeys I would certainly have referenced it on several occasions. But there is a great deal in common between the ﬁndings of Trevelyan’s research and ours. Primarily, as my diagram in the ﬁrst journey shows engineering is far more than a bench at things are designed, made and tested. We found that roles, however precisely deﬁned, depend on interpersonal relationships for their eﬀective functioning. is means that engineers have to have high level interpersonal skills, skills that engineers are not known to possess to any great degree, so it is assumed. One of the major complaints of industrialists in the UK and U.S. is that universities do not produce graduates who can communicate or work in groups [4]. eir technical abilities are not questioned. xviii PREFACE AND INTRODUCTION In his search to understand engineering epistemology in the aircraft manufacturing indus- try, Walter Vincenti’s reported that engineering is a community activity in “What Engineers Know and How they Know It” [5]. is community activity is largely informal. All the elements that Trevelyan highlight are present in the few short paragraphs that Vincenti devotes to explaining the way knowledge is exchanged, structured, and built upon. Technology impacts on everyone from the richest to the poorest. Acting as a community engineers have an awesome power to inﬂuence society. But this can only be done if engineers understand the nature of this community. To achieve that understanding we have to understand ourselves. is book is about understanding ourselves in order to understand others and under- standing others in order to understand ourselves. is is a problem that each one of us faces, engi- neer or not. At the same time it faces curriculum designers with a problem because the knowledge required to do this has to be drawn from a wide range of disciplines, as for example, sociology, psychology, literature, economics, philosophy, and theology, and that is by no means the end, especially if it is assumed that the way to obtain this knowledge is through study of these disci- plines. Yet that is what the present approaches to university education that focus on the study of subject disciplines would require. However, it is evident that in everyday living we obtain vast quantities of knowledge that we assemble and make judgements about or discard. It is equally evident that some of those judgements are not as informed as they should be. Consider voting behavior. I suggest that the view which has recently emerged, particularly in the UK, that those who are educated are better able to make political decisions than those who have had little education is without foundation. Be that as it may when we solve problems we generally bring knowledge from a variety of areas to bear on the problem much of it acquired haphazardly. If we are more systematic we explore many avenues before deciding to pursue a course of action or learning depth. at is what children do in their early years. ey explore everything. Albert North Whitehead the mathematician philosopher calls this a stage of “romance” in his theory of rhythm in education [6]. Romance is necessarily one of transdisciplinarity [7] because it is a stage of exploration, a stage of discovery. He writes, “e stage of ﬁrst apprehension (a stage of ferment). Education must essentially be a setting in order of a ferment already stirring in the mind: you cannot educate the mind in vacuo. In our conception of education we tend to conﬁne it to the second stage of the cycle, namely precision. In this stage knowledge is not dominated by systematic procedure. Romantic emotion is essentially the excitement consequent on the transition from bare facts to ﬁrst realisations of the import of their unexplored relationships.” So too is the ﬁnal stage of generalization (synthesis) which is, “A return to romanticism with the added advantage of classiﬁed ideas and relevant technique.” Between these stages is one of precision (grammar) in which, “width of relationship is subordinated to exactness of formulation. It is the stage of grammar, the grammar of language and the grammar of science. It proceeds by forcing on the students’ acceptance a given way of analysing the facts, bit by bit. New facts are added but they are the facts which ﬁt into the analysis.” PREFACE AND INTRODUCTION xix It is here that the language, which is the “style” of a particular subject, is learnt, and the interest found in the stage of romance turned into a search for expertise. Whitehead does not expect the stage of romance to be one that is simply a collection of “scraps of information.” In a lecture on the aims of education to mathematics teachers he said, “Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God’s earth. What we should aim at producing” are [is] persons [men] who possess both culture and expert knowledge in some special direction. eir expert knowledge will give them ground to start from, and their culture will lead them as deep as philosophy and as high as art [6, p. 1]. Education is then, “the acquisition of the art of utilisation of knowledge” [6, p. 6], and one of the functions of the stage of romance is to help the student ﬁnd that “special direction.” Looked at from the perspective of Whitehead’s formal philosophy engineering and technology are creative activities. e stage of “romance” is not only one of discovery but of creative exploration [8]. It is a view that ﬁts well with what an engineer seeks to do. e intention of these journeys is that they should be a stage of romance. ey are intended to create a debate as well as to inform. e extensive notes are designed as guides to further study and result from the debates that the journeys caused when they were delivered. ey are a bridge between romance and precision and grammar. e goals of the stage of “romance” relate to • the motivation of students; • how we know and learn. How our learning styles inﬂuence the way we learn; • the exploration of our personal value systems; • personal development; and • practical experience with what is learned. ese journeys are explorations (Mani who organized them would prefer “reﬂections”) of ourselves and organizations that have the purpose of helping you and I establish who and what we are as individuals, engineers and educators in a society that is becoming increasingly complex. e roads that I took were not always familiar and eventually they led to consideration of the “common good,” and to the view that the basis of all professional study is a liberal education which I explore in the last but one and ﬁnal journeys. My answer to those who asked Mani “how will it help me to do better as an engineer?”—is that good engineering is a community activity that depends on wisdom and skill in practical reasoning as it is often called. ese journeys are essays in practical reason [9]. Notwithstanding the diﬃculty of summarizing short essays, I will engage in the task in the hope that it will be helpful. Journey 1 is about meaning and language. rough a brief analysis of the engineering processes involved in the making of a technology product we learn that engineers xx PREFACE AND INTRODUCTION have to speak many languages. At the end of this journey you are invited to participate in an activity that is a preparation for Journey 2 which is about perception, or about the meaning that reality has for you and I. At the same time, it shows the relevance of a philosophy of engineering that seeks to answer such questions as—“how and why do engineers diﬀer from scientists and business people?” e road widens and broadens our understanding of perception. Both Journeys 2 and 3 show that the boundaries between philosophy and psychology are often blurred. Journey 3 takes us past some of the best known illusions to the importance of personal relationships, and from there to how we handle the mass of information with which we are faced each day, and how the inﬂuence of past experience aﬀects the way we solve problems, particularly engineering problems. Journey 4 brings us to another blurred boundary, that between philosophy and sociology and their respective theories of knowledge. Our understanding of “how we know” and “how we learn” impact on our everyday behavior, and inﬂuence our attitudes, opinions, and values. ey impact on how we learn, how we teach, how we manage, and how we are managed, and in consequence the way we organized or are organized. e boundaries between philosophy, psychology, and sociology become almost merged when in Journey 5 we consider what it means to live in a plurality of social systems, and the de- mands they make on us. e focus of the journey changes to managing ourselves and others since in the future it is more likely we will have to manage ourselves. e questions self-management presents to us are philosophical in nature, starting with “who am I?” at question cannot be answered without reference to other persons, and in the diﬀerent systems that make up the communities we inhabit. Engineering knowledge is typically a com- munity activity that is committed to “doing.” e Journey 6 explores our interdependence, what it means for rights and responsibilities, and how the ideal organization be it a university or a ﬁrm is a learning community. Communities that persist have a common ethic. e “good” in the title of Journey 7 is ambiguous. It could mean engineering a product that is good, a person who does this regularly being a “good” engineer. Or, it could mean being a good person, that is, one whose behavior is driven by moral principles. is journey explores the relationship between the two. When we think about making the good engineer possible, “What are our aspirations?” Journey 8 ﬁnds an answer to the question “What are our aspirations?” In Bowne’s aspira- tional ethic for engineers that is grounded in Martin Buber’s view of the relationship between individuals (I/ou) and McIntyre’s virtue ethics. All engineers need to take an active role in con- sidering the ethical implications of their work, and these cannot be divorced from their personal lives. Journey 9 brings us face-to-face with technology and the impact that it is having on the structure of the workforce. Current models of the workforce seem no longer to apply. At the same time, the banking collapse of 2008 has raised questions about existing economic models and the nature of the ﬁrm—“What constitutes a company?” more profoundly “what constitutes PREFACE AND INTRODUCTION xxi the common good?” Engineering students need to experience what it is to be in a community. How within all the constraints imposed on educational institutions can a collegiate climate be introduced and extended to the ﬁrm so as to enable permanent learning (continuous professional development)? Journeys 10 and 11 seek an answer to this question. e Journey 10 begins by doubting if universities can claim to be learning systems when so few of their faculty know anything about learning or development. eory X and Y are applied to teaching in engineering education but the central focus is on the design of the curriculum for development—cognitive and personal, and with engineering curricular that have been designed for that purpose. As the structure of higher education changes and embraces life-long learning, the ﬁndings of research on adult learning will have increasing relevance. e ﬁnal paragraphs argue that teaching in engineering is a professional activity that is a discipline that has its own knowledge base. Journey 12 is both a summary and an argument that engineering education is at a crossroads and that at the present time there are opportunities for major change. It is three years since these journeys were given and much has happened since then. In discussions with Mani Mina and Joel Claypool, the publisher, we decided that the integrity of the seminars should be retained for which reason they have not be altered. Where it was thought new material would be valuable it has been added in a postscript to the journey, or in the notes, or both, and an additional journey has been added at the end. John Heywood December 2016 NOTES [1] Whoever the individual, whatever his or her personality, they will adapt their behavior to the situation in which they ﬁnd themselves. us, just as human organizations can be conceived of as systems, so they may also be conceived of as conglomerates of role players, for in any social system the basic unit is the role. A role is, therefore, a pattern of behavior associated with a particular position. “It carries out activities that, if the system is to achieve its goals, have to be coordinated. One activity of management is, therefore, the coordina- tion and integration of roles. e role does not have to be a human: it could be a machine […]. Problems arise for management because a variety of individuals, each with their own value system and idiosyncracies, occupy roles in the organization. Very often personnel come into conﬂict with each other simply because of personality diﬀerences. Sometimes conﬂict is created because of the perception that individuals haven have of their role. Even in a bureaucracy it is not possible to deﬁne a role so exactly that there are no diﬀerences xxii PREFACE AND INTRODUCTION in perception about how it should be performed. A major problem for employers, indeed ourselves, is the fact that at one and the same time our goals create for us a plurality of social systems. ere is not merely one role system that connects the job to other jobs in the organization for work purposes, but the career system, the peer-group system and, not least the family system. All of these systems make demands on our energies and there is no way of escape. e ways we use to reduce these tensions and sometimes conﬂicts inﬂu- ence our performance at work for better or for the worse […]. Conﬂict and tensions are normal consequences of living systems […]. Whenever we anticipate a role, we generate expectations of what will be expected of us in that role and very often we will have to ad- just those expectations […]. e need to deﬁne roles will be evident, ambiguities in roles can cause role conﬂict and individuals much stress.” Extracts from Heywood, J. (1989). Learning, Adaptability and Change; the Challenge for Education and Industry, London, Paul Chapman/Sage, pp. 39–47. In recent organizational research much attention is paid to networks, the structure and management of teams, etc. xvii [2] Trevelyan, J. (2014). e Making of an Expert Engineer. London. CRC Press/Taylor and Francis. xvii [3] Youngman, M. B., Oxtoboy, R., Monk, J. D., and J. Heywood (1978). Analysing Jobs. Aldershot, UK, Gower Press. xvii [4] Heywood, J. (2016). Assessment of Learning in Engineering Education. Hoboken, NJ, IEEE/Wiley. xvii [5] Vincenti, W. G. (1993). What Engineers Know and How they Know It. Analytical Studies from Aeronautical History. Baltimore, e Johns Hopkins University. xviii [6] Whitehead, A. N. (1950). e Aims of Education. 2nd ed. London, Benn. xviii, xix [7] Transdisciplinary derives from the need to respond to a single complex, concrete problem that requires the assistance of several disciplines that give a variety of viewpoints to the solution of the problem which is not resolvable by a single discipline but requires the syn- thesis of a number of solutions. is deﬁnition has its origins in a 1973 OECD document which is summarised in (a) Heywood, J. (2005). Engineering Education. A Review of Re- search and Development in Curriculum and Instruction. Hoboken, NJ, Wiley/IEEEE. For a discussion of various models of interdisciplinarity see (b) Fogarty, R. (1993). Integrating the Curriculum. Pallatine, IL, IRI/Sky Publ. xviii [8] I have translated Whitehead’s major concept of creativity to ﬁt this argument but I think he would have agreed. For Whitehead every concrete entity an individualization of the universal creative force that is his ultimate. See p. 268 of Lowe, V. (1990). Alfred North Whitehead. e Man and his Work, Vol. II. Baltimore, e Johns Hopkins University Press. xix PREFACE AND INTRODUCTION xxiii [9] Kallenberg writes “practical reasoning is the stuﬀ of relationships both at the personal level as well as city wide (according to Aristotle) one needed to do practical reasoning well in order to live successfully each day.” Kallenberg argues that “morality is identical to practical reasoning. Any act that derives from practical reasoning-whether it is telling a joke or con- structing a road-is inherently moral.” Kallenberg, B. J. (2013). By Design: Ethics, eology, and the Practice of Engineering. Cambridge UK, James Clarke publishers. See also Book 6 of Aristotle. e Nicomachean Ethics (1996). Introduction by S. Watt. Wordsworth Clas- sics. Ware Herts, Wordsworth editions. xix Sternberg found among diﬀerent groups of academics that their implicit theories of wis- dom varied but could contribute to our understanding of wisdom. In his work on intelli- gence he had distinguished between academic and practical intelligence. In his balanced theory of wisdom he considers that wisdom is a special case of practical intelligence that requires the balancing of multiple and often competing interests. He said, “wisdom is de- ﬁned as the application of tacit as well as explicit knowledge mediated by values towards the achievement of a common good through a balance among (a) intrapersonal, (b) inter- personal, and (c) extrapersonal interests, over the (a) short and (b) long terms, to achieve a balance among (a) adaptation to exiting environments, and (c) selection of new envi- ronments.” Sternberg, R. J. (2001). Why schools should teach for wisdom. e balance theory of wisdom in educational settings Educational Psychologist 36, pp. 227–245. is note is based on Bassett, C. L. (2006). Laughing at gilded butterﬂies: Integrating wis- dom, development, and learning in Hoare, C. (Ed.), Handbook of Adult Development and Learning. Oxford, Oxford University Press. Acknowledgments xxv John and I are very thankful for John Pritchard’s great and gracious technical help in patiently taping, editing, and creating the sessions. In addition, John Pritchard created and managed the website. is activity would not have been possible without the participants to whom we express our thanks and appreciation for their active participation. Professors John Hauptman (Physics), Gregory Wilson (Rhetoric and English), Jennifer Lowey (English), and John Basart (Electrical and Computer Engineering) doubted, questioned, challenged, and made many suggestions. We are also grateful for the generous participation of doctoral students Robert Bouda, John Prichard, David Lastine, Mohamaduo A. Diallo, and Mirzad Mohandespour. ere were a number of our friends, associates, and colleagues who were unable to attend the live sessions due to time conﬂicts and scheduling. We would like to thank them for following our work and encouraging us as we went on. Finally, we would like to thank Vicky orland-Oster for helping us to create this class, Broke Ascher for his kind suggestions, editing and encourage- ments, the Engineering and Liberal art On-line (ELO) team for their great support, and Anthony Moore for his encouragement and support in all aspects of this project. Mani Mina December 2016 As Dr. Mina has explained these journeys were undertaken in dialogue with a group of educators and doctoral students. e journeys were modiﬁed in places and the notes considerably extended as a result of these dialogues. e ﬁrst of the dialogues began when Dr. Mina and John Pritchard recorded the journeys. During the course I was able to discuss what I thought was happening and where I was going with Dr. Alan Cheville of Bucknell University with whom I was already in conversation about such matters. I am very grateful to them, to Mani in particular, and the course participants for making these journeys so meaningful. John Heywood December 2016 J O U R N E Y 1 1 “It all Depends on What You Mean by...” During the 1940s and 50s, the “BEEB” (as the British Broadcasting Corporation is aﬀectionately known in Britain), broadcast a radio show known as “e Brains Trust.” During each of the 84 broadcasts that were made, a panel of four erudite personalities attempted to answer questions that were put to them. ree of them anchored the program and the fourth place was occupied by some well-known intellectual. Some of them regularly occupied this space. One of the three respondents who anchored the program began his response to any question by stating that “it all depends on what you mean by.......” a particular word or phrase. He was C. E. M. Joad, a philosopher and psychologist who had written an excellent introduction to philosophy. His phrase became part of everyday language usage in the British Isles: even teenagers would be heard using it. With a laugh of course! Many years later during an interview for a senior academic post I used the same phrase in response to an interviewer who was asking me to comment on the philosophy of R. S. Peters. Professor Peters was responsible for making the study of educational philosophy something that had to be done in university departments responsible for the education of teachers. He had said that “education was the initiation of worthwhile activity” or words to that eﬀect [1]. Forty ﬁve or more years on it would be foolish to suggest that I can remember how the question was put, but I do know that I knew little or nothing of Peters work and that my response was to say “it all depends upon what you mean by education,” etc. Of course I did not get the job! Nowadays, I appreciate that the phrase merits some discussion. For example, it revolves around what you mean by “worthwhile activity.” I suspect that in any group of a dozen or so people while some would give similar answers others would give diﬀerent answers as to what they perceived worthwhile activities to be. ere would have to be some clariﬁcation, and the development of the ability to clarify is something that the activity of philosophy can encourage. But let us stay with the issue for a minute. Suppose we ﬁnd that the focus of some of the answers is on worthwhile activities in the classroom while other responses refer to a range of activities from such things as gardening to going to a pop- concert, we might argue, as an observer, that only the former are educational. But who are we to say that no learning takes place in the latter? So if we change the meaning of education to learning, and if we take it that more or less everything we have to do is worthwhile, by deﬁnition we arrive at something we know to be universally true, that is, that learning takes place all the 2 1. “IT ALL DEPENDS ON WHAT YOU MEAN BY...” time, contingent though it may be. Take another step and we begin to recognize that the system of formal education is a social artifact. Finally, we ﬁnd that someone else is prepared to take all these arguments apart. at is what philosophers do. ey take each other’s arguments/systems apart, and that is how philosophy moves on but never escapes from the arguments of the past. Joad or “Professor Joad” as he was known was being a philosopher. He showed us that many statements require clariﬁcation if their meaning is to be understood. Read the Wikipedia biography of Joad, or any other biography that you can call up, and you will ﬁnd it was Joad who popularized philosophy, that he was a socialist, that he liked the ladies, that he liked mixing with the grandees, that he wrote proliﬁcally, that near his death bed he returned to Christianity but, you will ﬁnd little or nothing about his philosophical beliefs. However, among the long list of his publications you will ﬁnd “Critique of Logical Positivism.” is suggests that he allowed for metaphysics in his thinking which logical-positivism does not. One of those who joined him as the fourth panellist in the Brains Trust was the philosopher who introduced the British public to “dogmatic logical-positivism” A. J. “Freddie” Ayer. He did this through a book called Language, Truth and Logic which was published in 1936 [3]. Ayer was then professor of philosophy at University College London. Like Joad, he had socialist leanings although he was not a paciﬁst. He, too, liked the ladies to the extent that he was married four times. However, his philosophy was quite clear. Only scientiﬁc statements can be proved to be either true or false and this implies a limitation on science, and therefore philosophy, since science has to be restricted to observable aspects of nature. Metaphysical and theological statements have no meaning, and the activities of philosophy become focused on how to replace ordinary language with more precise and standardized equivalents. is is the reason for mentioning it here although as a philosophy logical positivism is no longer in the vogue that it was. Here, it is with the view that ordinary language is imprecise that we are concerned, and that is something about which most reasonable people would say of much that is spoken and written. Wittgenstein, an engineer by education, is regarded by many as the greatest philosopher of the 20th century. In his ﬁrst major study (“e Tractatus”) he took a similar position to Ayer [4]. However, in later years that position was modiﬁed [5]. Nevertheless, the logical-positivists drew much support from Wittgenstein’s thesis that only propositions in the natural sciences are true, moreover, it is impossible to say anything meaningful about ethics, aesthetics, and metaphysics. us, the clariﬁcation of meaning, which is what Wittgenstein considered to be the role of phi- losophy, is conﬁned to natural science. Although the average member of the public, and for the most part that is you and I would not want to engage in the abstract conversations of philosophers on language, some things have trickled down into the public arena. For example, we have become increasingly aware of the need to clarify meaning: we know that if the questions we set in a public examination are unclear there is the possibility that we will be taken to court. More pertinently, we know that if an instruction we give to a technician is misunderstood and leads to an accident that we are ultimately responsible for what happened. So we need to check that our instructions are understood and not misunderstood. 3 Nowhere does the problem of meaning raise its ugly head than in the interpretation of statistics, particularly those to be found in newspapers. Since the year 2000 engineering educators in the U.S. have been required by ABET to ensure that the programs they teach will achieve certain speciﬁed outcomes. Before they were introduced in the year 2000 engineering educators were able to attend meetings that clariﬁed the meaning of these outcomes. Two engineering educators, Yokomoto and Bostwick, argued among other things that “secondary meanings of some words are sometimes used, such as using the term “criteria” to describe the level of performance that students must achieve and “outcomes” to describe the learning behaviors students must demonstrate” [6]. A more common deﬁnition of “outcome’ is “result” or “consequence,” and anyone attaching that meaning to the word will surely become confused in any discussion about writing measurable outcomes. Yokomoto and Bostwick said that the aims listed by ABET (Exhibit 1.1) were considered to be too broad to be assessed directly and in the tradition of e Taxonomy of Educational Objectives [7] they recommended that those aims should be broken down into smaller more measurable units. e essence of their argu- ment was that accrediting agencies should explain the terms used, and use them consistently, and to this end they made a distinction between course outcomes and course instructional objectives. Again such distinctions are debatable. Exhibit 1.1: e list of program outcomes in Section II of Engineering Criteria 2000. e Accredi- tation Board for Engineering and Technology (ABET). It is easy to fall into the trap of making ambiguous statements. For example, recently I wrote in a chapter of a book a modiﬁcation of a statement that I had written in a paper in 1986 [8]. Engineering programs must demonstrate that their graduates have:(a) an ability to apply knowledge of mathematics, science, and engineering;(b) an ability to design and conduct experiment, as well as to analyze and interpret data;(c) an ability to design a system, component, or process to meet desired needs;(d) an ability function in multi-disciplinary teams;(e) an ability to identify, formulate, and solve engineering problems;(f) an understanding of professional and ethical responsibility;(g) an ability to communicate effectively;(h) the broad education necessary to understand the impact of engineering solutions in a global/social context;(i) a recognition of the need for and an ability to engage in life-long learning;(j) a knowledge of contemporary issues; and(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineer-ing practice.4 1. “IT ALL DEPENDS ON WHAT YOU MEAN BY...” It was a deﬁnition of technology in which I now substituted “engineering” for “technology.” e revised statement which related to the model shown in Exhibit 1.2 reads, “Engineering is the art and science of making things that meet the needs of self and society. It is both an activity and a system that serves both individuals and society that creates new problems for both. erefore, engineering literacy is necessarily interdisci- plinary and a liberal study. Engineering literacy is about the process of engineering whereas as technological literacy is about the products of engineering and their impact on society.” It was the phrase in italics that bothered the reviewer. He or she wrote- “Meaning engineering creates new problems for both? Or the fact that it serves both individuals and society creates problems?” [9] e ambiguity is immediately apparent. I was intending the former but isn’t the second point valid? In the original statement the word technology was used because those of us who wanted to include some engineering science in the middle and high school curriculum in England failed to get our idea established. Governments had begun to replace the industrial arts (woodwork and metalwork) with an approach that was based on design and make projects, and a syllabus based on a black box systems approach. Since then as members of the Technological Literacy Division of the American Society for Engineering Education have pointed out I have allowed the two literacies to become interchangeable when there are discernible diﬀerences. Some argued that I was confusing the issue so it became evident that there was a need for clariﬁcation and deﬁnition. At the same time the Division also questioned the meaning of the term technology in its title in relation to its aims. A group led by John Krupczak gave separate and diﬀerent deﬁnitions of engineering and technological literacy which has caused the division to change its name so as to embrace both engineering and technological literacy. is is why summaries of their deﬁnitions are incorporated in the last sentence of the statement that has been considered [10]. Both statements were written as an introduction to the diagram which shows a model of the interrelationships between the areas of knowledge and the achievement of a technological artefact for society and the economy. First, both engineering and technology have to function within the constraints legal and otherwise, imposed by society and the environment. e base of the model represents the person. e mind that supports the whole activity is the source of our values, beliefs and technical understanding: it is the source of our attitudes and opinions in the diﬀerent social systems in which we ﬁnd ourselves: it is the driver of our actions. at is how this dimension of the model has been presented on several occasions but it is also the source of our ideas and creativity. Understanding how our beliefs and values (moral and otherwise) are formed is important to our conduct as engineers and individuals but it belongs primarily to the domains of philosophy and theology which are diﬀerent languages. e three legs of the stool represent the technological aspects of engineering: research and development; data acquisition; information technology; design; manufacturing data and produc- tion; marketing data and sales. e ﬁrst two legs are the domains of engineering science, de- sign, and manufacturing. e third leg is the knowledge domain of business, legal, and economic 5 Exhibit 1.2: A model of the engineering processes engaged in the production of a technology (tech- nological product [8]). understanding. Supporting the legs are the trusses that represent individuals and the way the organization is structured. ese are the domains of organizational behavior and behavior in or- ganizations. e seat represents the economy and society within which the product is placed. My purpose in introducing this limited discussion of the model is to show all the diﬀer- ent languages that an engineer or a manager, indeed each participant has to learn if they are to understand the “meanings” that each person brings to the activity of engineering [12]. Joad’s rhetoric was not idle. I make no apology for greatly simplifying the philosophical debate about logical positivism and more generally the analytic tradition in Britain because it caused the public to understand that much care should be taken to ensure that the “meanings” they Product(s)/TechnologyThe MindValuesValuesThe Economy/SocietyManufacturing Data Information TechnologyProductionResearch Development Data Infomation Technology DesignMarketing Data Information Technology SalesIndividualsOrganizationsIndividualsOrganizations6 1. “IT ALL DEPENDS ON WHAT YOU MEAN BY...” wished to convey are understood in the way they wished them to be understood [12]. Wittgenstein did not consider there was any such thing as “pure” thought. It is the language we possess that enables us to think. It is a way of life. All language is shared but that is part of another journey. is short journey into the meaning of meaning has been taken to illustrate the kind of problem that philosophers tackle. It was inspired by a popular British philosopher’s persistence in a series of radio broadcasts to query the meaning of words and statements. En-route brief excursions were made into the British analytic movement and logical positivism. No attempt was made to deﬁne philosophy. e reader was allowed to determine that philosophers consider profound questions and sometimes these lead to “isms” like American pragmatism [13]. Indeed, one way to learn philosophy is to consider its “isms.” Since these “isms” are often associated with particular philosophers another way to learn philosophy is to learn about the great philosophers in historical sequence. We, in contrast, are taking a series of journeys so that we may better reﬂect on who and what we are as individuals and engineers within a society that is becoming increasingly complex. Our next journey is into the world of reality where we continually cross over the boundary between philosophy and psychology. NOTES [1] Peters, R. S. (1964). Education as Initiation. London, Evans. 1 [2] Joad, C. E. M. (1960). Critique of Logical Posivitism. London, Gollancz. [3] Ayer, A. J. (1936 rep 2001). Language, Truth and Logic. Harmondsworth, Penguin. 2 [4] Wittngenstein, L. (1922). Tractatus-Logico-Philosophicus. Trans. G. K. Ogden. London. Routledge and Kegan Paul. 2 [5] Wittgenstein, L. (1953). Philosophical Investigations. Trans. G. E. M. Anscombe. Oxford, Blackwell. 2 [6] Yokomoto, C. F. and W. D. Bostwick. (1999). Modeling the process of writing measur- able outcomes for Ec 2000. Proceedings Frontiers in Education Conference 2, 11b1, 18–22. Piscatawy, NJ, IEEE. 3 [7] Bloom, B. (Ed.). (1956). e Taxonomy of Educational Objectives. Handbook 1 Cognitive Domain. New York, David McKay. 3 e Taxonomy is the most widely referenced educational text of all time. Many engineer- ing educators have used it, and it is claimed to have had a signiﬁcant inﬂuence on education worldwide. It provides a hierarchical framework for categorizing educational objectives for use in test and curriculum design. e hierarchy is made up of six domains and in the text these are accompanied by sub-categories. ese are expressed in terms of the behaviors a student would demonstrate if they possessed the skill required. us, a student has the 7 “ability to produce a unique communication” is one of the categories of the domain of syn- thesis. e six domains are Knowledge, Comprehension, Application, Analysis, Synthesis, and Evaluation. It was open to much criticism (see Chapter 2 of Heywood, J. (2005). Engi- neering Education. Research and Development in Curriculum and Instruction. Hoboken, NJ, Wiley/IEEE). e authors of the Taxonomy made it clear that their descriptors were of the “outcomes” of education. e inﬂuence of this approach can be seen in the ABET 2000 Ec list of outcomes, and the outcomes for the diﬀerent levels of the Bologna agreement. But those authorities did not use the Taxonomy and they preferred as have very many other educa- tional authorities to use the term “outcome” rather than objective. e taxonomy was revised in 2001. e Knowledge Domain was sub-divided into four— Factual knowledge, Conceptual knowledge, Procedural knowledge and Meta-cognitive knowledge. Six cognitive process dimensions were included- Remember, Understand, Ap- ply, Analyze, Evaluate, and Create. Anderson, L. W. et al. (Eds.) (2001). A Taxonomy for Learning Teaching and Assessing. A Revision of Bloom’s Taxonomy of Educational Objectives. New York, Addison Wesley Long- man. [8] Heywood, J. (1986). Toward technological literacy in Ireland: An opportunity for an in- clusive approach in Heywood, J. and P. Matthews (Eds). Technology, Society and the School Curriculum: Practice and eory in Europe. Manchester, Roundthorn. 3, 5 [9] Personal communication, June 2013. 4 [10] Krupzcak, J. et al. (2012) Deﬁning engineering and technological literacy. Proceedings An- nual Conference of the American Society for Engineering Education. 4, 7 [11] Bucciarelli has made a detailed study of language usage in design teams. He points out that each person in the team lives in his/her own object world which has its own object world language. “An engineer’s will be rooted in a particular scientiﬁc paradigm which serves as a basis for conjecture, analysis, testing, and designing within that world” [10]. Among the examples that Bucciarelli gives are the diﬀerences between the languages of structural and electronics engineers. As the model indicates, a design team will have to cope with other world languages outside of those in engineering and Bucciarelli notes that at the beginning of a design the perceptions that each of the members of the team have of the design will diﬀer, and the ﬁnal design will be the result of much negotiation. In this respect Bucciarelli argue that design is a social enterprise “that at its core is a conversation spoken in a language of its own invention.” Design like language is a social process. Bucciarelli, L. L. (2003). Engineering Philosophy. Delft, Netherlands, Delft University Press. Chapter 2. 8 1. “IT ALL DEPENDS ON WHAT YOU MEAN BY...” For a detailed examination of Bucciarelli’s ideas in the context of engineering ethics, see Kallenburg, B. J. (2013). By Design. Ethics, eology and the Practice of Engineering, Cam- bridge, UK. James Clarke. [12] Magee, B. (2001). Writes a section in his book called Common Sense that “meanwhile (in the 1930’s) in Britain a near-contemporary and lifelong friend of [Bertrand] Russell’s called G. Moore had been pursuing the analysis of statements in ordinary language using neither science or technical logic as his yardstick but common sense [...] into a mode of philosophy that was eventually to displace Logical Positivism. It became known as “linguis- tic philosophy” or “linguistic analysis,” and its criterion was the ordinary use of language. e Logical Positivists had been mistaken said the linguistic analysts in trying to force the straight jacket of scientiﬁc standards on all forms of utterance. Umpteen diﬀerent sorts of spontaneous discourse go to make up human life, and each one has its own logic. Philo- sophical problems arise when a form of utterance appropriate to one mode of discourse is mistakenly used in the wrong context” [pp. 200–201]. Magee writes of Wittgenstein that in his later philosophy “linguistic analysis achieved its ultimate degree of reﬁnement” [p. 202]. 5, 6 Magee, B. (2001). e Story of Philosophy. London, Dorling Kindersley. [13] e term “pragmatic” is in common use. In that usage it is the judgment (justiﬁcation) “of any assertion of any assertion solely by its practical bearing on human interests” [Oxford Dictionary]. Alternatively as a philosophy it is the “theory that a proposition is true if holding it to be so is practically successful or advantageous” [Richard Rorty in the Penguin Dictionary Of Philosophy, 2nd ed., 2005]. 6 e principal American pragmatist philosophers are John Dewey, William James, and Charles Sanders Pierce. Biographies of Dewey and James will be found in the Penguin Dictionary of Philosophy (2005) 2nd ed., London, Penguin. A short biography of Pierce who was the ﬁrst of the pragmatists will be found in Collinson, D. (1987) Fifty Major Philosophers. A Reference Guide. London, Routledge. He focused on the clariﬁcation of meaning and his best known paper is called “How to make our ideas Clear” (Popular Sci- ence Monthly, pp. 286–302, January 1978). e relevance of pragmatism, in particular the thinking of Dewey to engineering can be found in Omidvar, I. and M. Mina (2012). Imag- ining an undergraduate curriculum based on the educational philosophy of John Dewey. Proceedings Frontiers in Education Conference, 256–257. Piscataway, NJ, IEEE. Dewey, following Pierce, argued that learning was accomplished by “doing” since knowledge is an activity. He believed that when we met a problem its solution was found by a mental pro- cess that we would recognize today in a variety of problem solving paradigms including the process of design. AN ACTIVITY BETWEEN JOURNEYS Before the next journey please look at a tap slowly dripping water into a bowl. Write a description of what you see as you watch the water coming out of the tap and joining the water in the bowl below. A kitchen tap dripping into a washing-up bowl is likely to be suitable, but you may choose any convenient tap and bowl or basin. e tap should be set to drip roughly once a second. You will probably want 300 words for your description. When you have written your description please answer the following questions. 9 1. I wrote my description (a) while I was observing the tap. (b) after watching the tap, staring to write about ........................... minutes/hours after ﬁnishing watching the tap. (c) from my recollections (without making special observations for the present exercise) (i) of taps in general. (ii) with one particular tap in mind. 2. e tap and basin which I described (a) are speciﬁed in the description which I have written. (b) I did not specify. ey were in fact .............................................................. . is exercise was devised by the late Dr. Ronald Stansﬁeld of City University London. J O U R N E Y 2 11 inking about inking One of the best kept secrets in education, let alone higher or engineering education, is how we learn. Very occasionally freshmen are exposed to courses in learning how to learn. By and large, however, it is assumed that we know how to learn by some kind of in-built intuition. A few tutors have argued that the more we reﬂect on our own learning, an act that they call meta-cognition, the more likely we will be to enhance the skill that is learning [1]. John Pritchard’s response to the dripping tap activity shows how it can cause reﬂective thinking (Exhibit 2.1). Ask yourself how easy would it be for you to write a completely diﬀerent response to that activity? You will ﬁnd among any group of individuals who have completed the exercise responses that range from accounts of the physics involved to essays of imagination, and perhaps, the occasional piece of poetry. is is not say that John Pritchard’s view is not imaginative. It clearly is. Neither does it consider all the physics that is possible. Each view only provides a limited picture of the dripping tap. If we are to obtain the “grand-view” we have to consider each of the views presented by a mix of participants in relation to one another. Let us stop contemplating the tap and join John Henry Newman, a 19th century British sage and Cardinal now a Beatus. In his renowned lectures on “e Idea of a University” he asks us to “contemplate man himself as our object of contemplation; then at once we shall ﬁnd we can view him in a variety of relations; and according to those relations are the sciences of which he is the subject-matter, and according to our acquaintance with them is our possession of true knowledge of him. We may view him in relation to the material elements of his body, or to his mental constitution, or to his household and family, or to the community in which he lives, or to the being who made him; and in consequence we treat him, respectively, as physiologists, or as moral philosophers, or as writers of economics, or of politics, or as theologians. When we think of him in all these relations together, or as the subject at once of all the sciences I have named, then we may be said to reach unto and rest in the idea of man as an object or external fact, similar to that which the eye takes from the outward form [...] And if there be one relation about which we know nothing at all except that it exists, then is our knowledge of him, confessedly and to our own consciousness, deﬁcient and partial [...]” [2, p. 47 ﬀ ]. Dwight Culler, an American commentator on Newman paraphrased his statement thus, “what is true of man in general would also be true of any portion of reality however minute. If we wished to know a single material object—for example [Canterbury Cathedral], (one of the great medieval Gothic cathedrals of England)—to know it thoroughly we should have to make it the focus of universal science. For the science of architecture would speak only of its artistic form, 12 2. THINKING ABOUT THINKING Exhibit 2.1: John Pritchard’s experience of the dripping tap exercise. engineering of its stresses and strains, geology of the nature of its stones, chemistry and physics of the ultimate constitution of its matter, history of its past, and literature of the meaning which it had in the culture of the people. What each one of these sciences would say would be perfectly true in its own idea, but it would not give us a true picture of [Canterbury Cathedral]. For that all the sciences would have to be recombined [...]” [3, p. 182]. Dripping WaterIn this exercise, I focused on the sound of dripping water for 5 min and reflected on the experience immediately after (taking notes). From a bird’s eye view of my thought process, I focused specifical-ly on the following thoughts, in chronological order:1. The literal visualization of the dripping system in sync with the sound I heard.2. A 2-D transformation of the sound.3. A 3-D transformation of the sound.In the first thought, I pictured, in time, the growing mass of water beginning to seep from the spout until its weight overcame the surface tension along the spout’s metallic rim. I then intended to match the imagined droplet’s impact on the water to the sound I heard. However, I skipped imagining the droplet itself in the process of free fall. Maybe the brief moment of silence caused this.After some time, I began to focus only on the sound. I first pictured the sound as a single trace, similar to the way a heartbeat signal would look. This is what I now call a 2-D transformation of the sound. I think the shape I imagined was a result of the secondary drip heard after the initial impact. I noticed an inconsistency of the sound type of the successive impacts. This confused me since we set up a more or less steady state system (predetermined flow and water level). I then realized that the droplets created ripples in the pool below, causing the droplet to impact the pool’s waves at different surface angles. This would lead to different sounds. I decided that this observation draws on life’s events. Meaning, it seems that no matter how perfect we plan, the unexpected always seems to find its way into our lives.My last thought attempted to expand the sound into what I now call a 3-D transformation of the sound. Hearing the secondary impact led me to visualize a small hardened ball ricocheting off of two transverse surfaces. Maybe this is similar to a coated Ping-Pong ball bouncing off of a table and hitting a paddle.After writing this, I observed that no matter where my thoughts about the droplets start, I always seem to transform them into a visualization of sorts and provide technical details about the process of transformation. This may be a result of my college education, or maybe the accumulation of my experiences in all realms of life. Nonetheless, this activity has allowed me to further explore how I think.13 Exhibit 2.2: Mani Mina’s response to the dripping tap exercise. John Henry Newman’s statement came from the third discourse that he gave when he founded the Catholic University of Ireland in 1851/2. Today it would doubtless be presented in gender neutral terms but it remains the epistemology that underpins liberal education, I hasten to add not general education. We may regard general education as a step toward liberal education in that, certainly as in the American scene, those who study the liberal arts do so in a variety I did not start the tap, I did not follow the directions of the assignment. I did not do what I was supposed to do, but…. The tap found me. It found me while intruding into the moments of confusion. I woke up, things were quiet and there was nothing to think about, except, all the things that I need to do, all the things that I have not done well, and all the problems that I need to address…..Things are so confusing when you are half-asleep and are sort of dreaming about issuesAnd right there, between the dark quite time-space continuum which was reality of that moment and was accented with confusing circular thoughts, the tap found me. It was pushing its existence in my continuum; I heard it and had to react. It was something beckoning me to let go of the unending thoughts and I had to address an immediate task.It could be a rodent, but the sound had a consistent periodic life to it. My searches and the sounds that I made did not change its persistence. It continued regardless of anything around it. It did not care about me, so why do I care about it?Someone’s action, for not torqueing the screw to stop the water has made an ongoing dripping tap. A wasteful existence that did not care about anyone, and time was of no value to it. I thought that I need to envy that I the circling thoughts, wrapped themselves around and put the tap in the center. Images changed but were much more direct, focused, and as usual wasteful.I thought about time lost, resources wasted, lessens that were not learned, and lives that kept going, while being ignored,….The drips helped me found memories that were lost, and helped me dream of a different future or possible futures. They, the dripped that did not care about anything, made the floods, the rivers, and the seas. Small items, particles, interaction that we take for granted do make difference and to most of us they are not interesting.Then I dreamed again, into the night, how do we know what is interesting what is important, and what will make the most difference to us, to the world, and to others….But life is meant to be experienced, meanings come out of our interactions, thoughts, leanings, playing, and getting confused. Mistakes are important part of our learning, wastefulness is and can relative.Here we are humans with our subtle emotional delicacy, mental toughness, and imaginations that are hoping to reach the farthest stars. I wondered how many did spend sleepless nights thinking about these, I know that I am not alone and the tap does not care about me.14 2. THINKING ABOUT THINKING of subjects. But it is only liberal when the relations between them are considered in relation to some overarching concept such as “man” or more appropriately the “person,” or perhaps better still “man and woman.” at is roughly what Newman meant by universal knowledge. It is the recombination of that knowledge which is the object of university education. rough it the student seeks a true and balanced picture of reality and so the mind is enlarged. Liberal education is distinguished from general education in that it is an activity of synthesis. Many commentators object that such an education is not possible in the complex society in which we live. ose who continue to support the idea of a liberal education argue that only through such an education can an individual learn to cope with the complexity of life. In the con- text of the diagram of the activities of engineering and technology presented in the last journey surely we should focus on what the engineer needs to know about man (woman)? Why answers to this question have signiﬁcance is illustrated by IBM’s approach to the recruitment for one of its research programs in 2006 that was reported in IEEE Spectrum (December 2006, p. 6 – Ex- hibit 2.3). e article draws attention to the fact that in the U.S. and Europe 83% of jobs are ﬁlled by barbers, teachers, doctors, lawyers, closet reorganizers, and their like but their productivity is below those working in agriculture and industry. IBM’s response was along with other manage- ment experts to devote more research eﬀort to “ﬁguring out how people think, work and think Exhibit 2.3: Extracts from the article in regular section Spectral Lines—IBM’S New Motto: ink… About how others think. IEEE Spectrum, December 2006, p. 6. Technology gave its first big boost to productivity on the farm, its next on the factory floor. Now comes the hard part: services in which it is rarely obvious how to rationalise our work […] How can we help a barber cut more hair?Barbers, teachers, doctors, lawyers, closet reorganizers and their like fill 83 per cent of all jobs in the United States, and nearly as many in Europe, so it matters that their productivity lags behind that of their brethren in industry and agriculture.Even engineers with their calculators and CAD/CAM programs, do not always outwork profes-sional forebears who had slide rules and drawing tables.Many management experts say we should devote more of our research efforts to figuring out how people think, work and think about their work. The biggest company betting on this approach is IBM ranked 10th in R& D spending in a list compiled for IEEE/Spectrum by Standard and Poor’s.Senior Editor Harry Goldstein and Ron Hira of the Rochester Institute of technology, in New York state, took a close look at Big Blue’s effort. They found that it now devotes a quarter of its R & D budget to services, up from zero three years ago. It is hiring anthropologists, and economists that it has created new, non-engineering titles for them, together with a new academic discipline called “services, science, management and engineering”. The company is trying to convince leading universities to offer courses in it.15 about their work.” Harry Goldstein and Ron Hira found that IBM now “devotes a quarter of its budget to services, up from practically zero three years ago. It is hiring so many anthropologists, sociologists and economists that it has created new non-engineering titles for them together with a new academic discipline called ‘services sciences, management and engineering.’ e company is trying to convince leading universities to oﬀer courses in it.” Clearly, IBM does not think much of the engineer’s ability to think him/herself into some else’s shoes. Yet historians have to think themselves into other people’s shoes in order for them to be able to comprehend a particular set of circumstances at some time in the past. Given that IBM has decided to make use of persons from other disciplines, why is it that engineers’ should understand the ways of thinking that persons have in other occupations? e most elementary and possibly the most important answer is that it enables communication but IBM seems to assume that it also helps design. But this article presupposes that engineers cannot ask the questions that will enable them to understand how other people think and work. Is that true? Could/should engineers undertake the task that the “outsiders” have been asked to do? Is it true that there are ways of thinking particular to a speciﬁc activity of work? Can we put ourselves inside the mind of another? What diﬀerentiates other jobs from engineering? [4]. Answers to these questions have a bearing on the education engineers receive. For example, the view that engineers should understand that there are diﬀerent modes of thinking requires some provision in the curriculum which is unlikely to be achieved without their participation in activities that require a mix of students from other disciplines. e dripping tap is an example where the perceptions of engineering students per se while yielding the possibility of reﬂective thought as happened in the case of the example in Exhibit 2.1 does not reveal the perceiving, thinking, and communication processes that exist in a community. at can only be achieved when students in disciplines “distant” from science and engineering show their thought processes to engineering students. To illustrate this point I have put a description of a course for freshman sudents of English. Students that had an intention of training students to cope with unstructured situations in Exhibit 2.4. (For other details of this course see note 5). I submit that not only would engineering students have beneﬁted from participation in this activity but the students of English would also have beneﬁted from the participation of the engineers. By itself such a project for a particular group of students contributes to their general not liberal education. It becomes a liberal education (as deﬁned by Newman) when a mix of students from diﬀerent disciplines are its participants. I acknowledge that there are some engi- neering courses in which students from the humanities and social sciences participate in activities (projects) with engineers that may achieve such goals. You may contend that the dripping tap activity would be suﬃcient to bring about the questions desired. In the foundation years of the University of Lancaster students taking a single honors degree in the arts and the humanities were required in their second year to pursue a courses in one of the sciences. It accounted for one-ninth of the honors degree program. e courses were devised by lecturers who had a speciﬁc interest in the subject. e Vice-Chancellor (President) and those 16 2. THINKING ABOUT THINKING Exhibit 2.4: Extract from Roller, D. R., Giardina, R., Herman, G. and G. Woditsch (1972). e ﬁrst year of the ﬁrst little college. Journal of Higher Education, 43(5), 337 [5]. who created the idea believed that as between one subject and another there were diﬀerent ways of thinking and that students in the arts and the humanities should be exposed to the ways of thinking in a science. is is no diﬀerent to what is being proposed here for engineers. e person in charge of the physics course Hugh Montagu Pollock asked me if I would evaluate the course and for this purpose I became a participant observer. We wanted to see if students came to an understanding of the diﬀerences between their major subject and physics. So in a compulsory essay we asked the following question: Distinguish between the terms “mistake,” “discrepancy,” “uncertainty,” “systematic error” and “random error” as applied to the experimental testing of a hypothesis. Com- pare the usefulness of the concept of error as used in physics with that of the errors occurring in the study of your major subject. About 1,000 words plus diagrams (i.e, study as used in the sense of knowledge rather than as study for an examination). If the course had been in engineering among the concepts that might have been included would be “failure’ and “risk.” is approach suggests that one way we can ﬁnd about the diﬀerent approaches to subjects is to see how the participants respond to such concepts as “uncertainty,” “risk” and “failure.” What, for example, constitutes evidence in engineering, law and say history. Exhibit 2.5 is an example of the handling of evidence by lawyers and engineers. It was suggested by a distinguished American engineering educator omas T. Woodson. To conclude with another interesting question raised by the IBM development: IBM has created a new academic discipline for these non-engineering personnel. ey call it “services sci- ences management and engineering.” Could this be Engineering and Technological Literacy in another guise? It is to answer questions such as these that a philosophy of engineering is nec- essary. So how, for example, do engineers diﬀer from scientists on the one hand and business The second course had the aim of focusing on what each student was now thinking, and on what they had learned in the last twenty-odd years about his(her) own perceiving, thinking and communication processes. This was achieved first by exposing the students to a range of experiences, and then analysing their processes of thinking about these experiences in relation to such questions as “can different or personal ways of perception be communicated? How do different cultural backgrounds and different group situations affect people’s perceptions? To what extent does the English language restrict our abilities to think, or even imagine other ways of seeing the world?” the students were then asked to devise exercises. Anything was allowed so long as it involved creative effort. Many students found the initiative and responsibility with which they had to cope more than they could handle. The project also broke up then group experience which, while not a panacea, is consonant with the broadest aims of liberal education in that it enables the student to gain comprehension and control over his present capabilities and some perspective on his present value.17 Exhibit 2.5: Example of evidence from engineering and legal viewpoints from Woodson, T. T. (1966) Introduction to Engineering Design. p. 46. New York, McGraw Hill. people (managers) on the other? at is our next problem but before that, however, we should take time to investigate how we learn. POSTSCRIPT Since the manuscript was submitted for printing I have tried to understand the forces at work in the election for a President of the United States. One of my friends referred me to a book that had just been published with the title Strangers in their Own Land with the sub-title “Anger and Mourning on the American Right.” e publisher had chosen to add on the dust jacket A Journey to the heart of Our Political Divide (New York, e New Press). Journey it is; taking some ﬁve years. It was undertaken by Arlie Russell Hochschild a social anthropologist from U.C. Berkeley. She was concerned that the nation was becoming politically divided and that the split was becoming Legal(Evidence that Mr. A contracted to perform X for Mr. BNature of the evidenceEngineering(Evidence that a motor design A has a 10,000-hr bearing life under given conditions)Th e original contract itselfProof inherentEngineer witnesses tests; exam-ines the parts (being familiar with motors)A photocopy of the contract (which is not immediately available)Proof availableEngineer reviews data of tests run by his employeeX is being and has been regu-larly performed by Mr. A for Mr. BProof circumstantialMotor design. A has been sold elsewhere for similar 10, 000-hr dutyExpert testifi ed that Mr A has accomplished X.Expert testimonyConsultant in motor fi eld states he knows motor design. A has passed 10,000-hr testsEyewitness Mr C testifi es see-ing Mr. A performEyewitness testimonyNon-expert, who observed the tests at a distance, reports the resultsMr. D testifi es he heard Mr. A performed XHearsayMan on next project heard that motor design A passed18 2. THINKING ABOUT THINKING increasingly hostile. While she thought she had some understanding of the liberal left camp she wanted to know what was happening on the right and, in particular, “how life feels to people on the right—that is in the emotion that underlies politics. To understand their emotions, I had to imagine myself into their shoes.” If an engineer is to understand how others think, as IBM seem to have wanted then to do, then it will not be suﬃcient to understand their cognitive processes for their “being” depends as much on their emotions as anything else. Engineers have to understand people, yet as Trevelyan says you will be lucky if you can ﬁnd the study of people as a core part of the engineering curricu- lum. “Strangers in their Own Land” is as good an entry point. ere are two points that relate to our journey. e ﬁrst is that it is not an easy to understand people beyond the micro culture in which we live. e second is the concept of the “empathy wall” which we have to overcome if we are to know people from the “inside.” “An empathy wall is an obstacle to the deep understand- ing of another person, one that can make us feel indiﬀerent to those who hold hostile beliefs, or whose childhood is rooted in diﬀerent circumstances” (p. 5). Hochschild found it quite diﬃcult to overcome the “empathy wall” between her and the people of Louisiana she wished to understand from the inside. Few people will not have come across such walls in their own lives. NOTES [1] is journey and Journey 3 are based on parts of Ch. 2 Perception and learning in Hey- wood, J. (1989) Learning Adaptability and Change. e Challenge for Education and Industry. London, Paul Chapman/Sage. In Managing and Leading Schools as Learning Organizations; Adaptability and Change (2009- Dublin, Original Writing for the National Association of Principals and Deputies) it was revised and extended to include a model of the process of perception. is took into many factors that limit perception including other person char- acteristics, organization, and personality characteristics. ese were also shown to relate to motivation. e ﬁve interdependent processes were considered under the following head- ings; the acquisition of information: learning, categorization, memory and the inﬂuence of personality. Searching and sampling: our limited capacity. Expectancy and expectations: expectancy and ﬁrst impressions: expectancy and cognitive dissonance. e acquisition of information: attribution, expectancy, and gossip. e acquisition of information: attention: receiving: trial and check. Consolidation: the problem of experience. 11 [2] Newman, J. H. (1852, 1923 Impression). e Idea of a University Deﬁned and Illustrated. London, Longmans, Green. 11 [3] Culler, A. D. (1955). e Imperial Intellect. A Study of Newman’s Educational Ideal. Newhaven, CT, Yale University Press. In the original text Culler used Westminster Abbey where the Kings and Queens of England are crowned. I used Canterbury Cathedral as it is better known to me being in the City where I went to school. 12 19 [4] Heywood, J. (2007). “ink...about how others think.” Liberal education and engineering. IEEE/ASEE Proceedings of the Frontiers in Education Conference, T3C, 2- t0 24. Piscat- away, NJ. 15 [5] Although written many years ago this example seems to remain pertinent. I cited it in a section on meeting the goals of perceptual learning in the curriculum in Assessment in Higher Education, (1989, 2nd ed., Chichester, Wiley). e text with which it is associ- ated read (pp. 184–185) “e authors of the Images course at Little College (Roller et al., 1972) believed, like us, that the capacities of freshmen were unused and that the freshman curriculum had a stiﬂing eﬀect. After seminars with the students they decided to initi- ate a course on the processes by which man conceptualized his universe and in turn both shapes his experiences and is himself shaped by his images or concepts. We decided to call the course ‘e Making and manipulation of Images’ a title inspired by one of Kenneth Boulding’s books on our list of core readings. Rather than organize our course around a topical division of materials or disciplines, we developed a generic model of the image- building process and adopted that as a broad outline for the course. In essence, the model and outline were a simpliﬁed version of the ‘scientiﬁc method’ intentionally stated in terms so as to be universally applicable viz.” 16 Roller, D. R., Giardina, R., Herman, G. and G. Woditsch (1972). e ﬁrst year of the ﬁrst little college. Journal of Higher Education, 45(5,) 337. (1) Encounter. Meeting with new and unexplained phenomena. (2) Articulation. e formulation of an explanation tentatively held until tested. (3) Conﬂict. Discovering the inadequacy of the image to explain the phenomena and/or discovering in the implications of newly validated image a conﬂict with a previously held image. (4) Internalization. Acceptance (whether by an individual or a society) of the new image, a conﬂict with previously held and validated images. (5) Rule and reign of images. Guiding thought and conﬂict to establish and elaborate image systems, sometimes even when some portion of the image system is in conﬂict with or fails to explain newly encountered phenomena. J O U R N E Y 3 21 ings are not Always What ey Seem Sitting in a MacDonald’s in Denver many years ago I was reminded of what I was going to do at the beginning of a management course that I had to give when I arrived home. MacDonald’s had given me a tray that had a sheet of paper on it. I imagine it was a substitute for a tray cloth. On it were printed a number of optical illusions. ey reminded me that on many occasions I had begun my management course with what Peter Hesseling called a “healthy choc des opinions” [1]. With managers who were very skeptical that academics knew anything about management at all, I would organize the room so that the tables formed a complete square with no entry to the middle. I would let the class assemble. Say nothing for a few minutes and wait until they got a bit restive. en I would throw some money in the form of notes and coins into the center of the square, and watch for their reactions. At the same time I would pick on some of them and suggest that they might be thinking “what’s this chap up to?” or “Oh my God we’ve got an awful lecturer here” and so on. It provided a nice introduction to the study of worker-manager relationships, as well as the idea that perhaps this crazy academic had something to oﬀer. Another opening that I have used with both mangers and student teachers is to set a psy- chological test. At least that is what I told them, and in no uncertain terms. “It is a psychological test!” It should be remembered that psychological tests are among other things, used for the selection of people as well as counseling in school, college, and work. ey are also associated with the measurement of IQ on this side of the Atlantic. Depending on the audience I would give a formula which described the reasons why I wanted them to take the test. For example, graduate student teachers were told that the purposes of the exercise were (1) to show the importance of standardization when setting tests, (2) to illustrate objective items, and (3) to illustrate a test that was culture-free. ey were also told I would not look at their scores. ey were required to give one answer to each of ﬁve questions, each set to test their un- derstanding of a certain aspect of a picture displayed on a screen. ey were told there was only one right answer to each question which was set in multiple-choice form. ey were also told that the pictures would be presented at speed since speed is related to intelligence. Several repetitions were made of the rule that there was only right answer. One of the pictures used was the Muller-Lyot illusion. It is surprising that so many people have not seen it and when faced with it on ﬁrst sight assume that line “b” is longer than line “a”. 22 3. THINGS ARE NOT ALWAYS WHAT THEY SEEM ose who have seen it before know that both lines are the same distance. Ask them which line is the longest and give them no choice and they will answer (a) or (b). Even given the option of “neither” many will be drawn into the trap of answering (a) or (b) (see Exhibit 1.1). e other pictures came from a book called the Anatomy of Judgement by Jane Abercrom- bie [2]. It was one of the ﬁrst books published in the ﬁeld of Higher Education in the UK and is a classic, well worth reading. It reports research on the judgments made by medical students. It contains probably, the ﬁrst reported use of the discussion group as a vehicle for obtaining data for research from students in higher education. One of the pictures shows three persons in a tunnel. Many people perceive them to be of diﬀerent height but, in fact they are all the same height. From somewhere else I got the old lady/young lady illusion. Is she old or young? Is she a blonde or brunette? [3, p. 19, Exhibit 2]. So why go to all this trouble to create an exercise that annoyed everyone when I told them that contrary to the information given that there was only one right answer to each question, there were no right answers to any of the questions! ey felt they had been brainwashed which to an extent they had. Once, after I had done this exercise with a 100 or more graduate student teachers, a nun shouted from the back of the class “you are immoral!” In so far as student teachers were concerned I wanted them to grasp that their students may not always perceive what the teacher is doing or saying in the same way that the teacher wishes them to do, and that this may be the cause of misunderstanding. e dripping tap exercise is a reminder to teachers that among their students there may be a variety of interpretations, and, therefore understandings of what the teacher is saying. For example, the way problems are set can aﬀect the understanding that individuals have of a problem. In the case of management it is a warning, particularly when faced with an unheralded problem, such as an angry member of the workforce, that the manager can easily misunderstand the situation. In such circumstances the manager has to slow things down so that his/her response is considered rather than re-acting quickly and living to regret his/her re-action. Within this context, when I was moderating engineering science projects at a school in the north of England, the teacher responsible for the course, Glyn Price, sent me the letter that is shown in Exhibit 3. is drew attention to a problem that has been noted by other teachers of engineering. Namely that student’s can solve an engineering science problem with the correct use of mathematics and yet not understand the physics. Teachers need to ensure that students have an understanding of the physics which is the primary purpose of classroom assessment. To summarize: 1. “things” in a classroom, staﬀ room or elsewhere in the work situation may not always be what they seem; 2. communication is a two-way aﬀair; and 3. communicators do not always perceive each other in the same way. 23 Lest we forget, when we communicate we establish relationships and it is these relationships that give us our being. e Scottish philosopher John Macmurray provides a philosophical insight into the signiﬁcance of relationship [4]. He argues that the “Self ” ﬁnds its being through the relationships it has with others. Macmurray asks us to consider the Self in relation to the world. “When I act I modify the world. Action is causally eﬀective, even if it fails to produce the particular eﬀect that is intended. is implies that the Self is part of the world in which it acts and in dynamicrelation with the rest of the world. On the other hand, as subject the Self stands “over against” the world which is its object. e Self as subject then is not part of the world it knows, but withdrawn from it, and so, in conception, outside it, or other than its object. But to be part of the world is to exist, while to be excluded from the world is to be not-existent” [4, p. 91]. We depend on the world for our identity. In these terms we choose to exist or not-exist as a person or a professional. If we choose the former then there is an obligation to understand the world beyond that of the technicalities of our chosen profession. Since the “Self is a person” and “persons only develop in relation to other persons we come to be who we are as personal individuals only in personal relationships” [4, p. 15]. Given this view of personal relationships it is incumbent on each individual to understand the others with whom we relate. Such understanding can be obtained by reﬂecting on our own behavior and how it aﬀects others. ere is no better beginning for such reﬂection than with perception. So how do our perceptions shape our learning? e ﬁrst thing we might have induced from the dripping tap exercise is a warning. at is, not to be governed by stereotypes or, things are not always what they seem. Many years ago I found an exercise in an American Journal that had the intention of il- lustrating this point (among other things) which I tried out on the engineering students I was teaching [5]. I asked them to spend an hour walking in pairs around the center of a large city (Liverpool). When they got back to the class I asked them to write down what they had seen. Since they had all been sent along the same route you would have expected all the main land- marks to be listed in their reports such as the railway terminus, a large hotel, the philharmonic hall (home of the Royal Liverpool Philharmonic Orchestra), and two cathedrals. Not so: as the American authors had predicted a variety of descriptions would emerge. Remember they walked in pairs: there was no instruction that they should not talk to each other. It is highly unlikely that they did not talk about the issues that were bothering them: and a quick skip through the reported scenarios suggested that they might have been inﬂuenced what they had seen. ere is an early 19th century building in the street opposite to where I had my oﬃce in Trinity College Dublin before I retired. My students would have passed it many times. It has a “cemented” freeze that goes round its wall which is twelve inches or so above eye level. At intervals are a number of carvings at the base of pillars that decorate the building. One is of mice playing billiards. When I ask my students what they have observed about this building when they had walked passed it, very few of them mentioned these carvings. What, then, governs our thinking when we are walking by ourselves or with friends when we walk around a city center? Why do 24 3. THINGS ARE NOT ALWAYS WHAT THEY SEEM we notice some things and not others? In my case I know that when I get oﬀ a bus near college I look up to see what the time is on a clock ﬁxed to a wall: this diverts my attention away from the book display immediately in front of me in the window of one of the few surviving bookshops in Dublin. So while these books may catch my eye for a brief second I don’t remember them. I do remember the time. e fact of the matter is that there is so much information available to us that our mind has to have a mechanism for selecting items from that information. For our purpose let us follow Jane Abercrombie’s explanation. Even though much research has been completed on perception since the 1960s her general explanation is consistent with the facts as we observe them for ourselves. First we store information. As long ago as 1932 the British Psychologist F. C. Bartlett had said we organize our past experience so that we can relate it to the present. Clearly, we have many such organizations and he called them schema. Philip Vernon another British psychologist called them schemata. He said they were “persistent deep-rooted and well organized classiﬁcations of ways of perceiving, thinking and behaving” [2, p. 28]. Other authorities such as the American G. W. Allport have called them categories which are, “frames of reference for fresh perceptual samples of immediate modes of behavior.” In my work I tended to use Allport’s term frames of reference. Abercrombie summed it up by saying that “schemata can be regarded as tools which help us to see, evaluate and respond.” I used the term “frames of reference” because they appeared to be rather large organizations of built up frameworks of concepts rather than the individual concepts themselves. ey had “meaning” and they help us to give “meaning” to the objects we see in our world. So, when we are walking along a street, we relate the objects that we see to these “frames of reference”and in consequence some objects have more meaning for us than others. ese deﬁnitions do not propose anything as simple as a “memory bite.” Nevertheless, it is easy to see how useful this concept can be in information processing models of problem solving and decision making. e nature of learning is immediately clear. It is that process by which expe- rience develops new and re-organizes old concepts. e concepts are the means we use to describe our schema. ese schema contain within them ﬁrst principles. Concepts are classes of stimuli that have common characteristics. Without them the world is meaningless and communication is im- possible. at is why we put things in categories and build up frames of reference. How they are learnt and how they are taught are problems of great signiﬁcance, but that is another issue [6]. When we walk round a street as a purposeful activity we approach that (and indeed any) situation with pre-conceptions to which our expectations are related. ere is a tendency for these preconceptions to organize our perceptions of the task(s) we propose to undertake. is applies as much to research, as it does to learning, as it does to beginning a new job, or dealing with a colleague of whom we have been given some knowledge but never met. To this extent we give meaning to the objects of knowledge, hence, the adage that no two persons see the same things alike. us, what we see, and more signiﬁcantly what is presented to us (as well as how it is presented-as for example this seminar) also control that knowledge. 25 is means that whether we like it or not we are “prejudiced” or “biased.” A person from a poor neighborhood will have very diﬀerent experiences to a person from a wealthy district. In eﬀect they will speak diﬀerent languages [7]. e former are likely to have fewer words and grammatical forms to call on. Much has been written about these diﬀerences. But the diﬀerent experiences to which individuals are exposed will lead to diﬀerent prejudices, attitudes, and values. Apart from family and school there are other inﬂuences on our perceptions not least the people with whom we work. Industrial and commercial organizations create their own culture and it has been shown that working to and within such cultures can breed successful organiza- tions. Such cultures can also be self-defeating. Firms develop their own systems of categories and language associated with those categories. As it passes on to individuals, because of the limita- tions of the jobs they do, this language and the schema with which it is associated also become limited. A perception that has been developed within a narrow range of activities is sometimes called “deformation professionelle” [7, p. 19]. It is a characteristic of specialism (specialist knowl- edge). Furthermore, it causes individuals to over rely on past experience. I found among a group of engineers who had been highly inventive in the past that when they were faced with a new problem they began to solve it by seeing if they had done anything like it in the past. ey did not, contrary to what might have been expected, necessarily hypothesize about the new problem and bring the “principles” that they had learned in their education to bear on the issue [7, p. 95]. In these circumstances experience becomes an impediment to innovation [8]. I would not wish to argue that adult motivation is tied to the past but the way in which we try to meet our needs may well be governed to some extent by this factor. It seems to me that there is an in-built tendency to rely on experience in preference to training. In one inquiry persons below the age of 40 valued training where as those over the age of 40 thought their experience was more important. Moreover, there was some indication that the training might have been valued less for its educational merit than for its contribution to future promotion. at research was a long time ago. Consider the present situation. ere is some evidence of unemployment among middle-aged engineers. Moreover, some employers prefer younger employees in the belief they are more innovative. But they too will be made redundant and possibly face unemployment as they age [9]. All of this has to have implications for the education system and the role of employers in that system. Clearly, students not only have to be educated to be adaptable and ﬂexible but to be prepared for continuing professional and personal development (CPPD). Management will no longer be able to devolve responsibility for CPPD to the education system. We have to view ourselves as learning systems that have to comprehend many worlds of experience. Understanding how we learn is therefore the ﬁrst skill in acquiring the abilities of adaptability and ﬂexibility. POSTSCRIPT After I had completed these seminars I was given a book on the philosophy of engineering [10] in which there was a chapter on “Roboethics and Telerobotic Weapons Systems” [11] which rein- 26 3. THINGS ARE NOT ALWAYS WHAT THEY SEEM forced my views about the importance of perception, more especially as it relates to the intelligent control of weapon systems, and therefore, the morality of their use [12]. Sullins writes, “the op- erators of telerobots” (we think of drones) “necessarily see the world a little diﬀerently when they look at it through the sensors and cameras mounted on the machine and this may impact their ability to make ethical decisions or at least inﬂuence the kinds of ethical decisions they choose while operating the machine. When one is experiencing the world through the sensors on a robot one is experiencing the world telepistemologically, meaning that the operators are building be- liefs about the situation that the robot is in even though the operator may be many (thousand) “miles away from the telrobot. is adds a new wrinkle to traditional epistemological questions. In short how does looking at the world color one’s beliefs about the world?” More signiﬁcantly how does it color one’s decision making when one has to distinguish between innocent people and an enemy? And this, as Sullins says is “a monumental problem” [13]. He argues that while telepistemological distancing has been one of the reasons that it is diﬃcult to exercise intelligent control over machines they have had the ability to reduce casualties. When he wrote his article he was not able to say whether the ethically positive outweighed the negative. He pointed out that if telerobotic warfare fostered hatred and caused the moral agency of an enemy to be disregarded then ethical conditions for a just war would not be reached [14]. Not only do these weapon systems illustrate the importance of perceptually driven behavior but they also show that epistemology is not a trivial subject [15]. NOTES [1] Choc des Opinions. Hesseling (p. 19) points out that “practice eﬀects perceptions by estab- lishing tentative frames of reference which increasingly articulate and structure our experi- ences.” It follows that these experiences become “reliable aspects of our experience” and so we come to value experience because of the perceived reliability of our experience. Hessel- ing then says that applied to specialism autistic tendencies are fostered “because one tends to deﬁne each situation as ﬁtting one’s own schemata” (p. 19). Now says Hesseling appoint a specialist to a general management position and he/she will have to take in schemata that do not yet ﬁt their own experience that is based on his/her prior specialism. Now he/she is faced with taking in information from a range of specialisms. Hesseling argues that the manager has to be shown how his “thinking” is based on his specialism and that he needs to restructure it to cope with his new cognitive environment. is can be done by giving the manager a frustrating experience to demonstrate the deﬁciency of their own schemata in other ﬁelds. “ey need to be confronted by specialists in other ﬁelds in order to get a healthy choc des opinions” (p. 19). 21 is shows the value of a liberal education in which a person lives in a mixed community. Nevertheless, the individual would still have to be shown what was being sought (i.e., aided to transfer perception). 27 Related to choc des opinions is déformation professionelle. e deformation represents “the usually highly eﬃcient categories when viewed in the context of one’s specialism.” Most people tend to persist in using these categories outside of their specialism. Hesseling, P. (1966). A Strategy for Evaluation Research. Aassen, Van Gorcum. [2] Abercrombie, J. (1960, 1989 reprint). e Anatomy of Judgement. London, Free Association Books. 22, 24 [3] Heywood, J. (1989). Learning Adaptability and Change: e Challenge for Education and Industry. London, Paul Chapman/Sage. 22 [4] Macmurray, J. (1957). e Self as Agent. London, Faber and Faber. 23 [5] Dinkelspeil, J. R. (1971). A teachable subject. Journal of Higher Education, 42(10), 42. 23 [6] See Ch. 4 – Concepts and Principles in Heywood, J. (2005). Engineering Education. Re- search and Development in Curriculum and Instruction. Hoboken, NJ, Wiley/IEEE. 24 [7] In 1961 the distinguished British sociologist Basil Bernstein drew attention to two types of language which he called “public” and “formal.” ese broadly related to language use in diﬀerent socio-economic groups. He subsequently redeﬁned the terns. A “restricted” code was used by those in lower socio-economic status groups and an “elaborated” was used by those in higher socio-economic status groups. e “restricted” code limits both the scope of expression and thought. It progressively orients the child to lower level conceptu- alization. It is through using the language of implicit meaning that it becomes diﬃcult to make explicit, and to elaborate verbally, subjective matter. e teacher who speaks with an elaborated code has, according to Bernstein, to make that code available without depriv- ing the pupils of the dignity of their own restricted codes. Common characteristics of the restricted code are: (1) short, grammatically simple, often unﬁnished sentences; (2) simple a repetitive use of conjunctions; (3) little or no use of subordinate clauses; (4) rigid and limited use of adjectives and adverbs; and (5) frequent use of statements where the reasons and conclusion are confounded to produce a categoric statement. 25 As between the subjects of the curriculum it is self evident that pupils from any social class may use a “restricted” code because of limitations in their understanding (e.g., second languages and science; see for example Champagne, A. B. Gunstone, R. F., and L. E. Klopfer (1983). Naïve knowledge and science learning. Research in Science and Technological Education 1, 173–184). A contrasting view to Bernstein’s was put by an American linguist W. Labov (1973) who studied African-Americans in New York. He argued that the “myth” of verbal deprivation is particularly dangerous because it diverts attention from real defects in our educational system to imaginary defects in the child. He distinguished between standard dialects used 28 3. THINGS ARE NOT ALWAYS WHAT THEY SEEM by middle classes and non-standard dialects used by the lower classes. He is critical of Bernstein whom he argues, sees middle class language as logical in every respect. In con- trast, Labov saw much middle class language as verbose with no inherent logic. e average middle class speaker is enmeshed in verbiage, the victim of socio-linguistic factors beyond his control. Non-standard dialects are highly structured systems. e above remarks are taken from a text published by this writer in 1984. But they do have a relevance in 2016 when in the UK those advocating exit from the European Union who it seems came mainly from the working classes were written oﬀ as unintelligent. ey were contrasted with graduates who tended to vote remain. e implication was that the graduates were more intelligent. Is wisdom the province of a particular social class or does everyone possess wisdom irrespective of dialect? Bernstein, B. (1966). Elaborated and restricted codes: their social origins and consequences in A. G. Smith (ed.) Communication and Culture. New York, Holt Rinehart and Winston. Labov, W. (1973). e logic of non-standard English in N. Keddie (ed.). Tinker, Tailor, e Myth of Cultural Deprivation. New York, Academic Press. Heywood, J. (1984). Considering the Curriculum during Student Teaching. London, Kogan Page. [8] Youngman, M. B., Oxtoby, R., Monk, J. D. and J. Heywood (1978). Analysing Jobs. Alder- shot, UK, Gower Press. 25 [9] Heywood, J. (2012) e response of higher and technological education to changing pat- terns of employment. Proceedings Annual Conference of the American Society for Engineering Education. Washington, DC. 25 [10] Michelfelder, D. P., McCarthy, M. and D. E. Goldberg (eds.) (2013). Philosophy and En- gineering: Reﬂections on Practice, Principles and Process. New York, Springer. 25 [11] Ibid. Chapter 18. Sullins, J. P. Roboethics and Terobotic Weapon Systems. 25 [12] Sullins writes (p. 229) “A technology is used ethically when it is intelligently controlled to further a moral good.” e philosopher Carl Mitcham explains that intelligent control of technology requires: “(1) Knowing what we should do with technology, the end or goal toward which technological activity ought to be directed; (2) knowing the consequences of technological actions before the actual performance of such actions; and (3) acting on the basis of or in accord with both types of knowledge-in other word, translating intelligence into active volition” (Mitcham, C. (1994). inking through Technology. e Path between Engineering and Philosophy. Chicago, Chicago University Press. 26 [13] Sullins writes (p. 231) “even just getting a robot to autonomously recognize a soda can in a lab environment is tough. One solution is to have a human agent help the machine make these determinations telerobotically by having the human operator analyze the data coming in from the machine to help it determine if an object is a soda can or some other object. If we move the robot out of the lab and onto a battleﬁeld, and task it to not just look for innocent soda cans but for enemy agents who are actively trying to deceive the machine, and then added to all this complexity we also have to distinguish the enemy and the neutral agents who are also present at the scene, then we must realize that this is obviously a monumental problem that will tax out telepistemological systems design to the limit.” 26 29 [14] Bowen, a distinguished engineer, writes points out from the earliest times there have been attempts to deﬁne a “just” war. Following Jones (1998) he lists ﬁve conditions for dealing with the decision to begin a war. ese are as follows. 26 “1. ere must be a just cause (such as to repel an aggressor). 2. ere must be just in- tent (such as to restore peace and justice). 3. War must be a last resort, every possibility of peaceful settlement having been exhausted. 4. e declaration of war must be by a legiti- mate authority. 5. ere must be a good prospect of success.” Just how diﬃcult it is to get agreement about these is well illustrated in the UK in the responses to the Chilcot Report on the Iraq War published in July 2016. In so far as the conduct of the war is concerned there are two requirements: “6. e innocent must not be directly attacked, but only the armed forces of the enemy. 7. e means must be propor- tionate to the end in view.” e latter is clearly open to much debate. It will be noticed that there are no requirements for the “peace.” In the case of the Iraq War, it is clear that the US or the UK had no sensible plan to deal with the aftermath of the war, and the consequences of that failure remain with us. Bowen, W. R. (2009. Engineering Ethics. An Aspirational Approach, London, Springer-Verlag. See also Jones, R. G. (1998). Peace, violence and war in B. Hoose (ed.). Christian Ethics. London, Continuum pp. 210–222. [15] Epistemology. “eory of knowledge, the branch of philosophy that inquires into the na- ture and the possibility of knowledge. It deals also with the scope and limits of human knowledge, and with how it is acquired and possessed. It also investigates related notions, such as perception, memory, proof, evidence, belief and certainty.” p. 194. e Penguin Dictionary of Philosophy. London, Penguin Books. (See Journey 4.) 26 J O U R N E Y 4 31 Meaning—True or False: Real or Imagined Our last Journey took us into the realm of psychology. Clearly, the questions posed by philoso- phers are sometimes posed by psychologists. e same is true of sociology where sociologists have developed a very substantial theory of knowledge, traditionally the province of philosophers. is journey brings us face to face with some of the fundamental questions of philosophy such as “What is knowledge?” and “What is truth?” It also brings us into the realm of the philosophy of science (education). A question that has to be resolved in these journeys is whether or not there is an area of knowledge that is the philosophy of engineering (education). I put education in brackets because some engineering educators with whom I work believe that you ﬁrst have to resolve the issue as to whether or not there is a philosophy of engineering that is separate from the philosophy of science before you can resolve the issue of whether or not there is the possibility of a philosophy of engineering education that is separate from a philosophy of science education. e starting point for this journey is the view expressed in Journey 3 that learning is the process by which experience develops new and reorganizes old concepts (schema). At issue is the mechanism that develops new and reorganizes old concepts. Some authors, such as John Mac- murray, call this process apperception. One answer lies in what I shall call psychological con- structivism. It arises from the well-known research on children’s learning by Jean Piaget. He said that concept development arises from the personal, individual, and intellectual construction that children make as a result of their activity in the world. Knowledge is not passively received from the environment, but is actively constructed by the child. It is an axiom that directly challenges the transmission model of learning. But beyond that is a much more controversial axiom which says that “coming to know is an adaptive process that organizes one’s experiential world: it does not discover an independent pre-existing world outside the mind of the knower” [1, p. 141]. To put it in another way, “facts are made by us and our way, of experiencing them” [2]. Seen in this light all knowledge is relative. Constructivists believe that their theory has implications for teaching, particularly that of children. Ruth Driver suggested that the constructivist teaching of children takes place in six steps. ese are elicitation (in which the students ﬁnd out where they are at); restructuring ideas (in which the students clarify meanings together); constructing new ideas in the light of these dis- cussions: evaluating these ideas by thinking them through or by experiment; applying these tasks to diﬀerent situations; and reviewing them, i.e., reﬂect on the on the outcomes. Ruth Driver and 32 4. MEANING—TRUE OR FALSE: REAL OR IMAGINED her colleagues liken this last stage to learning how-to-learn or meta-cognition as understanding how we learn is often called [3]. It is only a small jump to see the activity of design mirrored in this process for constructivists value non-directive teaching and discovery learning. Two well-known American engineering educators Ron Miller and Barbara Olds developed a unit operation laboratory in chemical engineering that was based on constructivist methodology. ey described the behavior of the tutors in these terms “rather than acting as acknowledged authorities transmitting objective knowledge to passive students, laboratory faculty use coaching and Socratic questioning techniques to help students understand complex technical phenomena by constructing mental models which perceive reality as perceived by acknowledged experts while minimizing models containing signiﬁcant misconceptions” [4]. ey go on to argue that “use of constructivist pedagogics creates an ideal context for assessing students’ abilities to complete authentic engineering tasks rather than relying on artiﬁcial examinations which emphasize non- contextual recall of facts and closed ended problem solving.” But as Michael Matthews, an Australian philosopher of science has pointed out the con- structivist approach to teaching is not unique [5]. I certainly did not discuss examinations and assessment in the way I have done from a constructivist position but rather from that of a moder- ate realist. Michael Matthews notes that constructivism is a particular development of empiricism and also points out that the debate in science between empiricism and realism can be traced back to at least Aristotle. e fundamental philosophical problem is that the two views represent two diﬀerent the- ories of knowledge and truth. Put simply, constructivist theory holds that our understandings and misperceptions are phenomena for we have no direct access to the real world. It leads to a “notional’ view of science. In contrast the realist view holds that there is an objective world that is independent of the learner. e world is learner independent and it is possible to seek truths about that world, as they are currently understood. ere is the possibility of universals. Realists hold a “correspondence” theory of truth. is says that a statement is true if it corresponds to what it is that it attempts to describe. A British philosopher Peter Vardy gives as an example— “an atom is the ultimate invisible element is true if, and only if the ultimate indivisible element is an atom” [6, p. 12] but it only remains true until it is proved otherwise. e same would be true of Newton’s principles which in spite of relativity remain true for a great number of situations. Realists take the view that while we may not necessarily know the truth or falsity of a particular statement there is a truth to be found. e opposite view is a “coherent” view of truth. Statements are true because they cohere with other statements. To cite Radford “my knowledge of the world hangs together in a coherent bundle of propositions representing beliefs and understandings. My inclination to believe in the truth of particular statements rests on the fact that they ﬁt with others” [7, p. 139]. Peter Vardy illustrates the diﬀerence between the two as follows: “e realist about music will maintain that there is some absolute standard of music against which two types of music can 33 be measured, while the anti-realist will say that within one culture Mozart’s music might be more highly rated than that of the Beatles, but there is no absolute standard and in another culture a contrary view might be held” [6, p. 14]. It is this theory that is in the ascendancy in modern society. Truth is relative; therefore there is not much point in searching for the truth [8]. Of course nothing is as simple as it seems and I have presented a rather stark comparison. ere are several realist positions and there is a group of constructivists (anti-realists) who re- ject the “notional” (nominalist) view of science. Hernstein Smith, in the wonderfully titled book Scandalous Knowledge. Science, Truth and the Human, gives a full-scale defense of the non-relativist constructivist position [9]. Whatever view a person takes it inﬂuences his/her values, opinions, and attitudes not only as a person but as an engineer. From an educational point of view there are things to be learned from constructivism just as there are from realism. Sociological phenomenology is a case in point. It has its origins in the work of Alfred Schutz which was made accessible when in 1966 two American Sociologists, Peter Berger and omas Luckmann, published a book called e Social Construction of Reality [10]. It is said to be one of the most widely read theory books of its time. eoretically, it is a study in phenomenological sociology. It is an attempt to construct a sociology of everyday life. By way of reinforcement of the previous comments on Piagetian constructivism the view taken by Berger and Luckmann is that reality is a social construct, and our construction of that reality depends on prior experience. at would seem to be no diﬀerent to what happens to us when we learn. As we have seen, experience dictates to a large extent what we learn, and that experience is of the family, school, college, work, and our more general social relationships. Sociological constructivism is not concerned so much with what individuals believe but with how the social structure (environment) of those individuals determines what they believe, and it is clear from Berger and Luckmann that social organizations created for the learning of science and engineering are no exception. One of the reasons why educators sometimes have diﬀering views to industrialists as to what should happen in engineering education is possibly due to the fact that they have diﬀerent constructions of what engineering actually is. Many engineering educators have come round to the view that there is a need to understand what it is that engineers actually do and why. e larger problem for engineering educators is that in theories of this kind knowledge is not absolute but relative. Consider the challenge to engineering educators as expressed by a student teacher. She said that the theory “is based on a phenomenological approach to the anal- ysis of reality. In this view consciousness is subjective: when we perceive something we bestow meaning on it, which will depend on our subjective consciousness, which has been determined by our past experience. us, knowledge is not something to be brought into the classroom in neat ﬁxed packages, but is something which is determined in the classroom by the perceptions of the individuals therein” [11, p. 192]. If this is true then why am I oﬀering a series of packages? I won’t claim they are neat, far from it: I will claim that they are designed to draw your attention to the 34 4. MEANING—TRUE OR FALSE: REAL OR IMAGINED questions we have to ask about ourselves and what it is to be an engineer, and more pertinently what it is to be human. If I pursue my student’s axiom then I am faced with the view that I ought to negotiate the curriculum with each of you so that each individual has his or her needs met. at might be okay in the liberal arts but is it okay in engineering? My answer lies ﬁrst in the view that a major goal of education is to develop a philosophical disposition to learning, a reﬂective habit which in the case of the curriculum asks questions like: “what do we know already?” “What do we want to know and need to ﬁnd out?” “How will we go about ﬁnding out?” “How will we know and show, that we’ve found out when we’ve ﬁnished?” Such questions would seem to be a normal part of thinking. ey certainly have to be asked when we invent or design a product. We are asked to become reﬂective practitioners. Let us take the argument a little further. An Australian educator Garth Boomer said that “there can never be an exact congruence between what a teacher or a textbook means and what a learner makes of that meaning” and that applies as much to mathematics as it does to any other subject. at is surely veriﬁed by the after-class conversations that students have with each other about statements in textbooks and what the teacher said. As Boomer goes on to say, “the dance between teacher and taught represents a continuing negotiation of meaning” [12]. It is a complex matter of continuous negotiation and in terms of complexity theory it is the activity from which student learning is “emergent” [13]. But in engineering it is a negotiation that takes place within a correspondence view of truth. But one step more. Universities are supposed to be diﬀerent places to schools yet so much of what is done in schools is replicated in universities, often badly. In universities students should be at a stage where they are able to accept responsibility for their learning. is places on the uni- versity an obligation to place them in environments where they can exercise that learning. Given that this is the case it is clear from the literature and common room discussion, that irrespective of the changes that universities have experienced over the centuries, the idea that they are, or rather should be communities of scholars seeking “emergent” meanings remains the key descriptor of what they should be, even if they aren’t. ey are unlikely to be committed to anyone form of learning, that is directive or non-directive but should be anchored to learning situations that are most likely to achieve the particular objectives that have to be achieved. Some of these are likely to be negotiated as for example the requirement that students should choose their own projects during certain stages of the program. Engineering like teaching should be a reﬂective practice. NOTES [1] Lerman (1989). Cited by Matthews, M. R. (1994). Science Teaching. e Role of the History and Philosophy of Science. London, Routledge, p. 141. 31 [2] Ibid. 31 35 [3] Driver, R. and V. Oldham. (1986). A constructivist approach to curriculum development in science. Studies in Science Education, 13, pp. 105–122. 32 [4] Miller, R. L. and B. M. Olds. (2001). Performance assessment of EC 2000 outcomes in the uit operations laboratory. Proceedings Annual Conference of the American Society for Engineering Education. Paper 3513. 32 [5] Matthews, M. (1994). Science Teaching. e Role of the History and Philosophy of Science. London, Routledge. 32 [6] Vardy, P. (1999). What is Truth? Sydney, University of New South Wales Press. 32, 33, 35 [7] Radford, M. (2008). Complexity and truth in educational research. In M. Mason (Ed). Complexity eory and the Philosophy of Education. Chichester, Wiley/Blackwell. 32 [8] Vardy [6, p. 10] lists ﬁve groups that take an anti-realist stance. Mainstream analytic phi- losophy which has given up the search for ﬁrm foundations of knowledge. ose in the philosophy of religion who hold that “religious truths are essentially internal to a ﬁctitious story.” In ethics, aesthetics are “culturally determined and have no reality independently of such settings.” Post-modernism rejects any single truth. 33 [9] Hernstein Smith, B. (2005). Scandalous Science. Science, Truth and the Human. Edinburgh. University of Edinburgh Press. Chapter 1 of this book gives a review of the history of con- structivism that takes in authorities other than Piaget. In this chapter she writes “in the Social Construction of What Ian Hacking observes that nominalism is a crucial conceptual commitment in the constructivist epistemology” [which as it happens, he calls, “social con- structionism”]. Hacking explains nominalism as the “denial” contra realism’s aﬃrmation, that Nature is inherently structured in certain ways. Contrary to his implication, how- ever constructivists do not characteristically “deny” metaphysically what realists evidently metaphysically maintain: “namely, ﬁrst that nature is structured in certain ways inherently (meaning independent of our perceptions, conceptions and descriptions) and, second that we properly assume (Hacking says “hope”) that those ways are in accord with our percep- tions, conceptions and descriptions of them. Rather, constructivists typically decline, in their historical, sociological, or psychological accounts of science and cognition, to pre- sume either any particular way the world inherently is or such an accord. is professional ontological agnosticism is not, as realists may see it, a perverse refusal of common sense but an eﬀort at due methodological modesty and theoretical economy.” 33 Hacking, I. (1999). e Social Construction of What? Cambridge, MA., Harvard University Press. [10] Berger, P. and T. Luckmann. (1966). e Social Construction of Reality. New York, Dou- bleday. 33 36 4. MEANING—TRUE OR FALSE: REAL OR IMAGINED [11] Heywood, J. (1982). Pitfalls and Planning in Student Teaching. London, Kogan Page. 33 [12] Boomer, G. (1992). Negotiating the curriculum. In G. Boomer et al. (Eds.), Negotiating the Curriculum. Education for the 21st Century. London, Falmer Press. 34 [13] Morrison, K. (2008). Educational philosophy and the challenge of complexity theory. In M. Mason (Ed.), Complexity eory and the Philosophy of Education. Chichester, Wi- ley/Blackwell. “In complexity theory, learning becomes a joint voyage of exploration, not simply a recycling of given knowledge. For learning to be promoted, rich and positive feedback between learners and teachers is essential. Cognition is dialogic and high qual- ity verbal interaction is essential. e teacher is vital, intervening judiciously to scaﬀold and create the conditions for learning through-self-organization and the child’s (students) emergent knowledge. Cognition is not simply the acquisition of new knowledge: it engages motivation, personalities, learning styles, dispositions and preferences, the whole-person. Teaching and learning take place at the intersection of the individual and society, and the outcomes are unpredictable. is is a diﬃcult model for those managers to entertain who seek certainty, control, predictability and narrow accountability. Learning is on-going, emergently choreographed dance, between partners and agents (co-evolution through re- lationships connections); the partners both create, and are in, their dance. All parties come together as co-evolving, co-adaptive and ﬂuid communities of practice” [p. 23]. 34 J O U R N E Y 5 37 From Perception to Self-Perception and a Little Management En-route Over ﬁfty years ago in the early 1960s Tom Burns, a Scottish sociologist with a particular interest in innovation in engineering, promoted the concept of a “plurality of social systems” [1]. By this he meant that during the average day we mix in several diﬀerent social systems. If we have a family then before we go to work we live in the family system: once we are at work we are in the working system. When we go home we are in the traﬃc system and. if when we return home we play some sort of sport we join the football system, or tennis system, or golf (system) club, or whatever. Life is a continual movement between social systems. Even at work we live in diﬀerent systems one of the most important of which is the career system, that is, if the organization is large enough. Many engineers work in large organizations where progress up the career ladder is important. An equally important system is the peer-group system, whether in industrial organizations, university faculty, or among students who learn as much from each other as they do in class. Each of these has a pull on our intentions and may impede the performance required of us to achieve the goals of the formal or informal organization that we currently inhabit. ere is no escape from the demands that these systems make on our everyday lives. Wit- ness a TV “soap” comedy about oﬃce work, or the many that portray life in hospitals. Doubtless there is certain amount of truth in them. We ﬁnd that doctors and surgeons are subject to the same highs and lows as we are, and may be there is some cause for alarm. How these diﬀerent systems aﬀect our everyday life is a function of our personal goals. Consider the young engineer whose ﬁrst job is in a large organization or the young teacher about to begin his/her career: if the work he or she is given to do is motivating then he/she may well want to work at it beyond what is actually required, or as we might say “beyond the call of duty.” ey may act like that on many occasions but when they marry and have children the situation changes. For many people the family becomes more important than the organization. One hurries home to be with the young- ster before he/she goes to bed, or to put them to bed. ere is a continuing conﬂict between the demands of the family and the demands of the organization that diﬀerent individuals resolve in diﬀerent ways. Much stress is generated. Most of us have to ﬁnd ways to reduce the tensions and sometimes conﬂicts that arise from having to function in a plurality of social systems if we are to maintain a satisfactory performance 38 5. FROM PERCEPTION TO SELF-PERCEPTION at work. It is not surprising that the perceptions that people have of us are a function of the behaviors we display. To the observer it may appear that we change personalities as we occupy diﬀerent roles. As pointed out in Journeys 2 and 3, diﬀerent observers may see what we see quite diﬀerently. Hesseling in the language of manufacturing of the nineteen sixties gave the example Exhibit 5.1. Exhibit 5.1: Hesseling’s example of diﬀering perceptions at work. As Robert Burns the Scottish poet more or less said “Oh that we had the gift of God to see ourselves as others see us.” Apart from the illustration that this provides of how diﬀerent people perceive the same situation as a function of their roles, it is also a reminder that while we may be fairly good at observing what is happening in a situation external to us, we are not so good at summing up our own position in terms of what others may perceive us to be. It is part of the task of management to reduce ambiguities such as these by ensuring that everyone understands what the role of the person is. It is also part of management’s task to recog- nize factors that aﬀect our performance adversely and to take steps to alleviate them if possible. Typically, in large organizations engineers work in teams. It takes very little to upset the ﬂow of teamwork. In some cases a manager may have to change a person’s role to make a team more eﬀective for the role is the basic unit of any social system. e problem is that although the nature of work undoubtedly inﬂuences our attitude to work, the orientations we bring to work will be inﬂuenced by the other systems with which we interact [3]. ese orientations to work (as well as the other systems in which we move) are also inﬂuenced by personality. Taken together they contribute the meaning that work has for us. us, one of the most powerful inﬂuences on role behavior is the expectations’ that we have of role keepers irrespective of the persons who occupy them. is is as true in the classroom situation as it is anywhere else. Teachers are managers of learning and their orientations are determined by the beliefs they have about how students learn and are motivated to learn. In the absence of any formal training they rely on their previous experience. In this situation, any group of teachers “A student had to make a work sampling study of charge-hands* in a fairly confined factory without a complete introduction. He started on a Monday morning. A new product was assembled and production was under time stress. Because he often spoke to charge-hands and was continually making notes, he appeared to most of the young assembly workers as controller of their bosses. His appearance near the assembly lines was welcomed with some satisfaction: they became bolder towards the charge-hands. They made jokes and nudged each other when he was approaching. To the chargehands he became a menace: they became uncertain and nervous and they concerned themselves more with the production process itself than with their group of workers. To the departmental manager he became a scapegoat: he blamed several production faults on this work sampling study and he walked about the factory more than usual”charge-hand=type of shop foreman39 is likely to divide into what in the latter half of the 20th century were commonly called eory X and eory Y. Douglas McGregor proposed these to describe two diﬀerent orientations to management. ey equally apply in teaching as Exhibit 5.2 shows. Column A is adapted from a description by Schein of eory X and eory Y is is clearly related to the potential for learning. A teacher who believes eory X explains student learning is much more likely to be committed to a monologue form of teaching than a teacher who thinks eory Y approximates to the truth. e key question that faculty have to answer, irrespective of their beliefs, is number 5. If the answer is “no’, what are they going to do about it? In reality human behavior is very complex as Exhibit 5.3 shows [4]. Exhibit 5.2: eory X vs. eory Y. Given that a role is a pattern of behavior associated with a particular position, it carries out activities that if the system is to achieve its goals, have to be co-ordinated. us, one of the tasks of management is the integration and co-ordination of roles. is is not an easy task for the way an organization works depends on the psycho-social dispositions of the people in the organization or team, and people can be very awkward as the list of behaviors in meetings given in Exhibit 5.4 shows [5]. ey are easily recognizable be they in a meeting of industrialists, or of university faculty as for example, a departmental meeting, or a meeting of a student society. Peter Drucker places the responsibility for eﬀective team work ﬁrmly on the members of the team who have to commit to the purpose of the team which is “to make the strengths of A. Theory X1. The student is primarily motivated by academic incentives and will do whatever gets him or her the greatest gain.2. Since academic incentives are under the control of the institution, the student is essential a passive agent to be manipulat-ed, motivated, and controlled by the organization.3. The student’s feelings are essentially irrational and must be prevented from interfering with his or her rational calculation of self-interest.4. Institutions and their organizational (curriculum) arrangements can and must be designed in such a way as to neutral-ize and control their feelings and therefore their unpredictable traits.B. Theory Y1. The expenditure of physical mental effort is as natural as play or rest. The ordinary person does not inherently dislike work: according to the conditions, it may be a source of satisfaction of punishment.2. External control is not the only means for obtaining effort. A person will exercise selfdirection and self-control in the service of objectives to which he is committed.3. The average human being learns, under proper conditions, not only to accept but to seek responsibility.4. Many more people are able to contribute creatively to the solution of organiza-tional problems than do so.5. At present, the potentialities of the average person are not fully being used.40 5. FROM PERCEPTION TO SELF-PERCEPTION Exhibit 5.3: e complex learner (adapted for the academic context from Schein [4]). each person eﬀective, and his or her weaknesses irrelevant.” [6]. Do we assess team projects for these qualities? Do we help students develop these qualities? “If the organization is to perform, it must be organized as a team” [7]. I am aware that many authorities will claim that they do such assessments but the issues are to what level of depth are such assessments made and are students, or for that matter most of us capable of the real reﬂective thought that answers to such questions require. I think we are but that we need to be put in situations like the face-to-face tutorial where we are forced to reﬂect on and come to an argued position on fundamental issues. A major problem is that the idea of reﬂective thinking is thrown at us very late in our educational careers when it ought to be part and parcel of our cognitive and emotional development from kindergarten onwards: part of a spiral curriculum. We should not be put in the position that Matthews found himself in when he tried to show his students that doing philosophy was natural. He hit “on the strategy of showing them that as children many of them had already done philosophy. It 1. The learner (worker, manager, or teacher) is complex: the individual is highly variable and at any time has many motives, some of which are more important than others. Since an individual’s motive patterns are complex, the individual’s response to incentives will also change with circumstances.2. The learner (worker, manager, or teacher) is capable of learning new motives that affects his behaviour through his/her curriculum, work and institutional experience. The psychological contract that that the individual makes with his or her peers, managers and teachers is the result of a complex interaction between perceived needs and learning (work) and institution-al experiences.3. The learner’s (worker’s, manager’s, or teacher’s) motives in different institutions or different sub-systems of the same institution may be different; the student (worker) who is alienated in the formal structure may find fulfilment of social and self-actualization needs in the student union (societies), trade union, or other parts of the extra-mural system, or outside the system altogether, as for example in a hobby or the family. If the curriculum work is complex, in respect of perceived needs or abilities, some parts of the curriculum (work) may engage some motives, while other parts engage other motives.4. The learner (worker, manager, or teacher) can become productively involved with the curricu-lum (work) and institution on the basis of many different kinds of motive. The individual’s ultimate satisfaction in the institution depends only in part on the nature of personal motivation. The nature of the task to be performed, the abilities and experience of the learner (worker), and the nature of the teachers, administrators and managers in the institu-tion, all interact to produce a certain pattern of work and feelings.5. The learner (worker, manager, or teacher) can respond to many different types of learning (work) strategy depending on his/her own motives and abilities and the nature of the task. There is no one correct learning (working) strategy that will work for all learners (workers) at all times.41 Exhibit 5.4: List of behaviours in meetings. occurred to me that my task as a college philosophy teacher was to reintroduce my students to an activity that they had once enjoyed and found natural, but that they had later been socialized to abandon” [8]. I think there are some techniques that can help us develop such skills. For example, in the Appendix I have shown a questionnaire designed by Bill Humble of the British Steel Corporation, Jim Freeman and myself for self-assessment by persons working together in groups in search of a policy. In this case, the intention was to video managers and trade union negotiators in session after which they would be asked to watch the video and then complete the questionnaire. I would argue that the more we know about the behavior of human behavior whether through some understanding of social psychology or extensive reading, as for example literature and biography, the more we will understand ourselves. R. M. Belbin, a British management research worker and consultant with an interest in training, found that eﬀective teams were composed of people who collectively employed the eight roles shown in Exhibit 5.5 [9]. Even though we may be irritated by some members of the team we need to recognize that each type is needed and has a valuable role to play. It is the task of each individual to extract that value ﬁrstly from him or herself, and secondly from the other members of the team. I (we) did not speciﬁcally look at team behavior during a study we undertook to ﬁnd out what engineers actually did. But I was impressed by the way in which individually, those in en- gineering functions not only “managed” but also had to “manage” their jobs irrespective of the Type BehaviorTh e aggressor A person who increases his or her status at the expense of others. S/he criticizes and is generally hostile.Th e blocker A person who disagrees with everything without good reason.Th e comedian A person who messes about, and may make negative jokes.Th e competitor A person who challenges others.Th e devil’s advocate A person who can be useful but may turn the group to his/her own way of thinking.Th e digressor A person who cannot stick to the point whose contributions can be long-winded.Th e dominator A person who makes loud and lengthy interventions.Th e side talker A person who continually talks to his/her next door neighbor.Th e under contributor A person who contributes little or nothing to the meeting.Th e withdrawer A person who might be expected to contribute to the meeting but doesn’t.42 5. FROM PERCEPTION TO SELF-PERCEPTION Exhibit 5.5: R. M. Belbin’s eight team roles. level of the job in the hierarchy. ey told me how by necessity they had to widen the scope of the initial brief through communication and cooperation with other people. e role deﬁnitions were often inadequate, but to my surprise, in some cases this seemed to have been an advantage. Often in order to get a job done, an individual would have to persuade another, over whom they had no authority, to do a job. For example, a person responsible for a contract that required the company to maintain a spare parts store at a military air base might have to organize the replace- ment of a single specialized component to replace one that had been used. e contracts engineer had to persuade those responsible for the manufacture (small batch and unit) of the company’s products to slip this job in with their other work. No formal system existed for this work, yet it had to be done or the contract would be broken. e contracts engineer had to develop his role to achieve this goal. In so doing he used management skills. Other similar situations came to light: it seemed that persons were appointed to roles that they had to change, so as to implement an action. To achieve that goal personal characteristics and skill in communication were essential. It was in such situations that feelings of responsibility were engendered and motivation enhanced, and I came to the view that the organization was not rigidly hierarchical but more a system of persons in relation [10]. In a sense it was communitarian. “A person is a psycho-social system. Within the boundaries of that system most individuals wish to be “organic” to use a term ﬁrst suggested by Burns and Stalker for this context [1]. ey wish to be able to take actions and decisions as well as mature. ey wish to have some responsi- bility. e boundaries of these psycho-social systems arise as a function of the needs of the job and Team RoleDescriptionChairmanTask to obtain the objectives. May be dominant but will not be assertive and try and use all the talents in the group.Th e ShaperA person who wants to bring everything together. A bundle of nervous energy.Th e PlantTh e person with imagination who will look for new ideas when the team is in diffi culty.Th e Monitor-Eval-uatorBrings dispassionate analysis to the problem.Th e Company WorkerPlenty of character that brings a disciplined approach to implementation.Resource InvestigatorLooks outside for ideas and brings them back to the group.Team WorkerA person who understands the emotional needs of the group.Th e FinisherA person who worries about detail and expects things to be done properly.43 the needs of the person. When these are matched for each person in the organization a hierarchic system becomes structured by individuals who are organic within their own system. e system itself becomes organic so that it can respond to the needs of individuals. Both systems have to be self-adjusting” [11] and that is true of any organizational structure. It seems that the some executives in the IT industry have established self-adjusting systems, and that such systems aided the development of Silicon Valley [12]. As long ago as 1960, Barnes of the Harvard Business School reported a study of two electronics organizations that showed the more communitarian (my word) they were the more successful they were likely to be [13]. He distinguished between open and closed systems [14]. e more open the system the more successful it was likely to be. It is a study that is still worth reading. Looking back it seems that what I was looking at was a community of some two hun- dred people called engineers. Perhaps we would get a better understanding of organizations if we understood them as imperfect communities where not everything goes smoothly. Communities depend for their success on interdependence and the commitment of the communitarians, for which reason when a community is failing and its members blame the leadership they are failing to look at themselves and their agency as a cause of whatever went wrong. Whichever way the data was analyzed, that is by ability groupings or by functional groups some sub-abilities that involved direction control were listed. Every person directed and controlled at a level necessary for the performance of their job. e Little Oxford Dictionary (1966) tells us that management is direction and control. Given that this is the case, then every person in that community was a manager to a greater or lesser degree, even if it was mainly of himself. Every day that is true of each and every one of us [15]. Everyone is a manager and from that we derive a whole lot of personal responsibility for what we do. Moreover, when we are not allowed to take responsibility some of us get very frustrated. Of course some of us take on too much responsibility to the frustration of others! Exactly the same argument can be made about leadership [16]. If that is the case then each individual is given considerable responsibility in whatever situation they ﬁnd themselves—the family, the tennis club, work etc. For the individual is the agent of his/her own actions and in that sense is both manager and leader of him or herself. Of course it is clear that some of us man- age ourselves and other people terribly badly. Some of us do not have the personality to engage with others and prefer to be managed in many diﬀerent situations. But there is a situation when allowing someone else to manage is an act of management. For example, democratic approaches to management in which everyone is allowed an input often fail to create action because either there is no consensus or there is no one able to lead the assembled out of the morass. Groups require leaders/managers who take the ultimate responsibility but in a democracy it is an act of leader- ship/management on the part of its participants to allow the leader/manager to lead/manage. But this, as Greenleaf wrote long ago, requires a new concept of leadership/management “the moral principle of which holds that the only authority deserving one’s allegiance is that which is freely and knowingly granted by the led to the leader in response to, and in proportion to, the clearly 44 5. FROM PERCEPTION TO SELF-PERCEPTION evident servant stature of the leader. ose who choose to follow this principle will not casually accept the authority of existing institutions. Rather, they will freely respond only to individuals who are chosen as leaders because they are proven and trusted servants. To the extent that this principle prevails in the future, the only truly viable institutions will be those that are student led” [17]. While I have completed the quotation for the sake of its integrity I do not wish to pursue the idea of the servant leader here, although I have done this elsewhere [18]. e Scottish philosopher John Macmurray asks us to consider the “self ” in relation to the world. “When I act I modify the world.” In my terms, management of the self is taken with a view to modifying my world. Macmurray goes on, “Action is causally eﬀective, even if it fails of the particular eﬀect that is unintended. is implies that the “self ” is part of the world in which it acts, and in dynamic relation with the rest of the world [...] to be part of the world is to exist, while to be excluded from the world is to be non-existent. It follows that the self exists as agent, but not as subject” [19]. In my submission an act of agency is an act of management but it is also an act of management to submit to direction and control as happens in two-way relationships. All relationships are two-way since as Macmurray argues the “self ” is a person and persons only develop as persons in relation to other persons, and a major relationship in that development in college is the tutor-student relationship. e basic motivation for managing and being managed is for the sake of “communion.” So a community depends on the purposeful management of individuals in the pursuit of the community’s aims. In higher education students and tutors have common purpose. ey necessarily carry with them responsibilities for managing themselves. It is a reminder of the need to match a person’s talents to what an organization (college or industry) has to oﬀer in order for that person to be fulﬁlled and better meet the needs of the organization (see Exhibit 5.6). is brings us to Drucker, America’s most famous management guru. He wrote that “more and more people in the workforce-and most knowledge workers-will have to manage themselves. ey will have to place themselves where they can make the greatest contribution; they will have to learn to develop themselves. ey will have to learn to stay young and mentally alive during a ﬁfty-year working life. ey will have to learn how and, when to change what they do, how they do it and when they do it” [20, p. 163]. “Knowledge workers, therefore, face drastically new demands: 1. ey have to ask: Who am I? What are my strengths? How do I work? 2. ey have to ask: Where do I belong? 3. ey have to ask: What is my contribution? 4. ey have to take relationship responsibility. 5. ey have to plan for the second half of their lives.” I consider the ﬁrst question to be the most important and all-embracing question of them all. It’s implication for the curriculum, not only that of engineering are profound for where better 45 Exhibit 5.6: pp. 33 & 34 of note 15. to begin the pursuit of these most philosophical of questions than in a university—if you can ﬁnd one that still philosophizes! APPENDIX A questionnaire designed for use in negotiating skills development training by W. Humble, J. Freeman, and J. Heywood and cited in Heywood, J. (1989). Learning, Adaptability and Change, London, Paul Chapman, pp. 48 and 49. Students and Individuals Bring to Their Work1. Knowledgea. Generalb. About his/her specialism or subjects of studyc. About business or college2. Physical Skillsa. Healthb. Related to psychomotor skills3. Cognitive and affective skillsa. Abilities to recognize and solve problems (creative skills)b. Ability to make judgmentsc. Ability to communicated. Ability in the development of satisfac-tory interpersonal relationships4. Personality and drivea. A certain activity level-normb. A certain level of risk-takingc. Aspiration and expectationsd. Acceptability5. Valuesa. Interestsb. A moral dispositionCollege or Organization Help People be Effective by the Following:1. Job or lecture analysisa. Providing a definition of the key results the job is required to produce, or the aims and objectives of a curriculum programb. A definition of the knowledge and skills required for the performance of the taskc. Details of information necessary for the completion of the job, or homework, or project or practical class2. College or organizationa. Provides a structure in which people can work or learnb. A management or teaching style that will motivate3. Recruitment, education, and traininga. Matching what an individual brings to the job, the needs of the job, or matching student abilities to the requirements of the programb. Background knowledge and experience of similar work or instructional situations likely to be of usec. Training or instruction in specific knowledge and skills for a defined function46 5. FROM PERCEPTION TO SELF-PERCEPTION . e r i a n n o i t s e u Q : 7 . 5 t i b i h x E Questionnaire for use in negotiating-skills development training SELF-APPRAISAL—BEHAVIOUR IN DISCUSSIONPlease study your performance from the video playback. This is a privateassessment, so be perfectly frank in answering the questions—otherwise youare only fooling yourself.In this discussion I tended to: Yes NoAsk specific questions about the topic under discussion Try to score debating pointsGet irritated with an opponentAsk for clarification/facts about a point made by the other sideContribute helpful suggestionsAdmit I was misinformed/wrongInterrupt before a speaker had finishedOpt out of answering an oppontnt’s question on the groundsthat I would appear to give wayCriticize when I had not really got a real point to makeClose the door to further argumentChange my mind when my assumptions were shown to be faultyKeep quiet when I had nothing constructive to sayOverrule the chairman/leaderPrepare my case before the meetingNot listen to an opponent’s argument because I disagreedwith his or her casePLACE THE SHEET INSIDE THE FOLDED SHEET 2 AND FOLD OVER THE RIGHT-HAND EDGE SO THAT THE ANSWERS SHOW IN CUT-OUTSNow compare your results and consider whether yourcontribution to the meeting was:Potentiallydestructive to your caseNow compare what you have written with youroriginal scoreNow attempt to define ways in which training couldhelp you improve your performance in discussionBecause I was:bloody-mindedCo-operativeBenignQuarrelsomeFlexibleRigidTolerantIntolerantOpen-mindedClosed-mindedSilentTalkative– Points+ PointsIndependentDependentWell-informedLacking ininformation/knowledgePotentiallyhelpfulto your caseCorrect answers (R)Incorrect answers (W)Questions unanswered (U)CORRECT ANSWERSNOW FOLD OVER THELEFT-HAND EDGEAND ANSWER THEQUESTIONS-3-2-1-1-2-30-3-2-1-1-2-30£ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ Score: R – W5 NOTES 47 [1] Burns, T. and G. Stalker. (1961). e Management of Innovation. London, Tavistock. 37, 42 [2] Hesseling, P. (1966). A Strategy for Evaluation Research. Assen, van Gorcum. [3] Orientation- disposition towards. For example Christian Bey and American sociologists distinguished between students who had academic, intellectual, and social orientations to- wards college. ose with a social disposition seek out the social life that the institution has to oﬀer. ey are not particularly concerned with academic performance as those with an academic orientation would be or the few with an intellectual orientation and concern for knowledge as its own end (Bey, C. (1961) A social theory of higher education. In N. San- ford (Ed.), e American College. New York, Wiley). ere are clearly a number of students in high school whose orientation is instrumental. ey arrange their work so as to make their dislike of schooling tolerable. Such attitudes derive from the meaning that life and school have for these young adolescents. If school performance is related to work success, and they perceive that they will be unemployed, they will undoubtedly develop an instru- mental attitude toward schoolwork, and why shouldn’t they? e problem for school is to provide a curriculum that has meaning for them, and this may mean a radical appraisal of what is taught but also how it is taught, with all the implications this has for small group work and individualized instruction. It is clearly a beneﬁt to society to ensure that every young person is both literate and numerate. I would argue that investment in the education of this group of people should be prioritised above all other sectors of education. 38 Clearly, the type of work we do gives rise to particular orientations. An assembly line job or work in housekeeping in a hotel to take but two examples may well lead to an instrumen- tal disposition where work is done solely for its remuneration, and some people may seek highly paid but routine jobs for the purpose of supporting their families. ey ﬁnd their satisfaction elsewhere. Others may ﬁnd satisfaction in the formal and informal groups they ﬁnd at work. ey obtain satisfaction from the group activities they involve themselves in, as for example a trade union. Other more lucky people—professionals seek rewards from the work they do, as for example the engineer- researcher, designer, and manufacturer. (based on Heywood, J. (1989). Learning, Adaptability and Change. e Challenge for Edu- cation and Industry. London, Paul Chapman/Sage.) (See also note 13). [4] From ch. 4 of Heywood, J. (1989). Learning, Adaptability and Change. e Challenge for Ed- ucation and Industry. London, Paul Chapman/Sage. e models of the student are adapted from Edgar Schein’s descriptions in Organizational Psychology (1965). Englewood Cliﬀs, NJ, Prentice Hall. Original in D. M. McGregor (1960). e Human Side of Enterprise. New York, McGraw Hill. 39, 40 48 5. FROM PERCEPTION TO SELF-PERCEPTION [5] Hodgson, P. and J. Hodgson. (1992). Eﬀective Meetings cited in Heywood, J. (2009). Man- aging and Leading Schools as Learning Organizations. Adaptability and Change. Dublin, Na- tional Association of Principals and Deputies/Original Writing. pp. 101–102. Trevelyan found that the key work that engineers do is technical coordination which demands a high level of liaison. Trevelyan, J. (2014). e Making of an Expert Engineer. London, CRC Press/Taylor and Francis. 39 [6] Drucker, P. (1993). Managing Non-Proﬁt making Organizations. London, Butterworth- Heinemann. 40 [7] Drucker, P. (2008). Classic Drucker. Essential Wisdom of Peter Drucker from the pages of the Harvard Business Review. Boston, Harvard Business School Publishing Corporation. p. 151. 40 [8] Matthews, G. (1980). Philosophy and the Young Child. Cambridge, MA, Harvard Univer- sity Press. 41 [9] Belbin, R. M. (1981). Management Teams. Why they Succeed or Fail, London, Heinemann. 41 [10] Youngman, M. B., Oxtoby, R., Monk, J. D., and J. Heywood (1978) Analysing Jobs. Alder- shot, Gower Press, p. 114–115. 42 [11] Ibid., p. 115. 43 [12] Lécuyer, C. (2007). Making Silicon Valley. Innovation and the Growth of High Tech, 1930– 1970. Cambridge. MA, MIT Press. 43 “Innovator-entrepreneurs in Silicon Valley also devised new ways of relating with employ- ees. ey were under the constant threat of unionization and they needed to secure the cooperation of a skilled workforce in order to build and control complex manufacturing processes. As a result, Silicon Valley ﬁrms developed a corporatist approach to manage- ment. ey gave substantial autonomy to their engineering staﬀs and often organized en- gineering work around teams. ey sought to involve their professional employees in the decision making process. In addition, they developed unusual ﬁnancial incentives for their work force: proﬁt-sharing programs, stock ownership, and stock option plans.” “Within the corporatist framework, one can distinguish three diﬀerent approaches. Eitel- McCullough, Litton Industries and microwave tube ﬁrms adopted a participatory and pa- ternalistic management style that emphasized proﬁt-sharing and generous employee ben- eﬁts. Varian Associates had a socialist streak, developing communal organizational and ownership structure. In contrast Fairchild Semiconductor and most semiconductor ﬁrms pioneered an entrepreneurial form of corporation organized around stock options.” [p. 299] [13] Barnes, L. B. (1960). Organizational Systems and Engineering Groups. Harvard Graduate School of Business Administration. 43 49 [14] An open system is one that is in exchange with its environment, whereas a closed system is one that has no exchange with its environment. A closed system will eventually die, whereas the open system maintains itself because it is able to export and import “material” from the environment. is description of biological and thermodynamic systems may be applied to organizations. An industrial and commercial organization is in exchange with its market. If it does not respond to the market it will die. Within the market it also has to choose how to compete with the same type of “good” companies over a range of products or only in technical areas where it has product advantage. Similarly, the case for free trade among nations is based on systems theory. 43 e way in which the senior management of an enterprise views the environment may also condition their attitudes within the organization, a point that is well illustrated by Barnes. He described the attitudes of management and a particular section of a particular company in the electronics industry. is company not only had to operate in a highly competitive way but also had to meet the goals of its parent organization. e pressures on the general manager were for low prices and high quality with the eﬀect that engineering management believed that productivity was much more important than quality. is meant that developmental work in the department investigated did not have high standing even though it seemed that development work was required. Barnes shows how the chief engineer and supervisor were placed in middle-man roles. Management and business values (practical engineering and productivity) were stressed to their colleagues, whereas to their seniors, in contrast, they emphasized the value of the scientiﬁc approach to their supervisors, thereby reﬂecting the views of their staﬀ. On the one hand the supervisor “stresses scientiﬁc principles and deplores production engineering’s ‘knob twisting approach.’ On the other hand he builds up subordinate resistance by asking them to turn out more ‘quickies’, to get out into the factory, and to be less scientiﬁcally rigorous.” (Shades of the Challenger story some 27 years later—See Davis, M. (1998). inking Like an Engineer, Oxford University Press). In contrast, Barnes described another company in the same business that was also highly competitive but making products in which it had a technical advantage. It is not surpris- ing to ﬁnd that in this company scientiﬁc and technical knowledge was valued, and that the attitudes throughout the organization were diﬀerent. e ﬁeld engineer who was the equivalent of the chief engineer in the other company did not present one face to his en- gineers and another to management. ere were no pressures on him for productivity and practicality. e pressure that came through, if it can be called pressure, was manage- ment’s encouragement of individual development. Oﬃcials at the top of the organization 50 5. FROM PERCEPTION TO SELF-PERCEPTION put down company success to the informality that spread across the organization (shades of Google!). So the ﬁeld engineer in responding to this dictate, arranged for his subordinates to have high autonomy while at the same time requiring that interaction between them and himself so that a system of mutual inﬂuence was created. As things stood the second company was more eﬃcient than the ﬁrst by Barnes measures. He put this down to the organizational structure of the company. e ﬁrst company’s was relatively closed, and within the section hierarchically organized with several small sub- sections. Barnes stresses the term “relatively” and argues that the second organization was relatively more “open.” e ﬁrst discouraged individual performance while the second en- couraged it. In the ﬁrst the engineers thought they should be doing engineering whereas the pressure was on them to worry about production. In the second there were no explicit pressures for productivity and practicality of the knob twisting kind. Of particular interest is the fact that the organization of the ﬁrst department seemed to highlight the diﬀerent value dispositions between the individuals and the groups. ose who were oriented toward the values of science (for example, truth and knowledge) tended towards relatively low non-work activities, low interaction, and low mutual friend- ships. ose who wanted to attain promotion, acceptance and prestige within the organi- zation tended towards relatively high interaction and mutual friendship. Barnes called the ﬁrst group “the professionals” and the latter group the “organizationals.” e third group he called the “socials” or those who wanted popularity and acceptance by the high-status groups. ey were characterized by high non-work activities, high interaction but low mu- tual friendships (see note 3). ere was little mixing between the grades. By contrast, in the second department there was much more mixing between the grades, and there was a higher level of participation in non-work activities. e two structures inﬂuenced the way in which individuals in the departments behaved and worked, and they in their turn were inﬂuenced and reinforced by the mode of work. Barnes concluded that the more open system was more eﬀective than the more closed system. (Adapted from pp. 77–79 of Heywood, J. (1989). Learning, Adaptability and Change. e Challenge for Education and Industry. London, Paul Chapman/Sage). [15] Heywood, J. (1989). Learning, Adaptability and Change. e Challenge for Education and Industry. London, Paul Chapman/Sage. See Chapter 4. 43 [16] Ibid. See Chapter 11. 43 [17] Greenleaf, R. K. (1973) e Servant as Leader. Peterborough, NH, e Windy Row Press. 44 [18] Ibid. Note 16. 44 [19] Macmurray, J. (1957). e Self as Agent. Faber and Faber, p. 91. 44 [20] Drucker, P. (1999). Management Challenges for the 21st Century. New York, Harper. 44 51 J O U R N E Y 6 53 Sharing Problems: Living in Communities To continue where I left oﬀ at the end of Journey 5, that is ﬁrst with the view put forward by Macmurray that the “self ” is a person and persons only develop as persons in relation to other persons: and second with the ﬁrst question that Drucker suggests knowledge workers have to ask themselves which is “Who am I?” But my purpose in asking this question is not utilitarian but humanitarian. Macmurray wrote that “a personal being is at once subject and object; but he is both because he is primarily agent. As subject he is “I,” as object he is “YOU,” since the “YOU is always “the other’, the unity of the personal is then to be sought in the community of the “YOU’ and “I’, and since persons are agent, this community is not merely a matter of fact, but also a matter of intention” [1, p. 27]. Ponder for a moment the last phrase which is to the eﬀect that a community is “a matter of intention.” Communities are intended for us, we, in our turn are intended for communities. Consider for a moment the reﬂective activities in which we are encouraged to engage. ey are acts of expression but they are pointless if they are not shared with somebody else [2, p. 187]. at is why those concerned with children and adults who are drug abusers try to create communities that care [3], or why people who have some problem or another ﬁnd it helpful to share their experiences with others. I have not tried to deﬁne community. Rather, I have allowed them to be what we com- munally observe. We ﬁnd that they can range from the community based on a church to the global community that can be created by scientists. Engineering students are made aware that engineering is a global activity. Presumably some communities are established that go beyond networks. Some persons are busily creating virtual communities the pioneers of which must have been the Ham radio enthusiasts. David P. Munns an American historian of science and tech- nology in the post-second war period including the cold war, has pointed out that scientists live in intellectual communities. He refers his readers to a ﬁlm called e Dish which is about the Parkes radio-telescope in Australia. It was this telescope that “ﬁlmed” Neil Armstrong making the ﬁrst human landing on the moon. Munns writes “Radio astronomers played a small part in that grand spectacle having built a world-wide network of radio telescopes. at such a network existed by 1969 is a testament to the radio astronomers’ international and interdisciplinary scien- 54 6. SHARING PROBLEMS: LIVING IN COMMUNITIES tiﬁc community” [4, p. 172]. In this respect the October 2013 issue of Astronomy and Geophysics (the house journal of the Royal Astronomical Society) gives a 3-page spread to the establishment by 12 British astronomers of the UK SETI (Search for Extra-terrestial Intelligence) network to promote academic SET in the UK, having as its patron the Astronomer Royal (Lord Martin Rees). Munns argues that the social world of the radio astronomers was shaped by their intel- lectual world. We saw in the last journey that this was in no small measure the case in the two electronics ﬁrms that Barnes compared. A corresponding story about engineering is to be found in Vincenti’s study of the establish- ment of the design requirements for aircraft in the period 1918 to 1943 [5]. He wrote “, [...] the generation of engineering knowledge is characteristically a community activity. While a number of people play visible roles, no individual or individuals dominate our account; the protagonist must be seen as the entire ﬂying-quality community. is community consisted however, of at least four sub-communities having to do individually with design, engineering research, instru- ment development, and test ﬂying. ese sub-communities overlapped intimately and the gener- ation of knowledge took place -indeed, had to take place-simultaneously and interactively in all of them” [6]. Elsewhere, Vincenti concludes that “engineering knowledge is thus the product of communities committed to “doing” and having a sense of collective identity fostered by complex interaction based in part on a shared problem” [7]. e failure to share problems can create other problems that may be of a more serious nature. All communities acquire their own mores in order that their members can live together. It is likely they will contain members whose experience and specialization is expressed in a way of thinking that diﬀers to other members of the group. It is important that any one individual recognizes this to be the case and is willing to learn that lesson. at seems to be the lesson of the IBM story that ended Journey 2. e questions that engineers have to ask are—What is their community and what are its boundaries? Current criticisms of engineering and engineering education suggest that its boundaries are limited and that it tends to be a closed rather than an open system. Michael Davis in what must rank as one of the seminal works in the philosophy of engi- neering incorporated information from the documentation of the Challenger disaster because not only did it highlight the problems of corporate decision making but “it will help us understand what engineers do, what can go wrong ethically, and what can be done to prevent ethical wrong doing” [8, p. 44]. It can help us begin to understand the concept of community within engineer- ing, and the diﬀerent ways of thinking that go with diﬀerent jobs undertaken by diﬀerent people in a community. Exhibit 6.1 is Davis’ summary of what happened. Davis begins his very considerable analysis by asking should Lund have thought like an engineer or a manager. Unfortunately, the term manager confuses things a little because quite clearly business considerations would have been behind the request to think like a manager. In this respect Davis’ analysis could have been strengthened. 55 Exhibit 6.1: From pp. 43–44, Davis, M. (1995). inking Like an Engineers. Studies in the Ethics of a Profession. New York, Oxford University Press. “Managers are trained to handle people. Engineers are trained to handle things” [p. 44]. Davis writes, “Lund was asked to concern himself primarily with how best to handle his boss, the Space Center, and his own engineers. He was to draw on his knowledge of engineering only as he might draw on his knowledge of a foreign language, for example to help him understand what his engineers were saying. He was to act as much as he would if he had never earned a degree in engineering” [p. 44]. Apart from this being an impressive example of role conﬂict it illustrates in the ﬁrst in- stance two diﬀerent orientations or ways of thinking created by the diﬀerent perceptions that the participants had at ﬁrst of their roles. e conﬂict is introduced when the key person in the “On the evening of January 27, 1986, Robert Lund, vice-president for engineering at Morton Thiokol, had a problem. The Space Center was counting down for a shuttle launch the next day. Earlier that day, Lund presided at a meeting of engineers who unanimously recommended against the launch. He concurred and informed his boss, Jerald Mason. Mason informed the Space Center; Lund expected the flight to be postponed. The Space Center had a good safety record. It had achieved it by not allowing a launch unless the technical people approved”.“Lund did not approve because the temperature at the launch site would be close to freezing at lift-off. The Space Center was worried about the ice already forming on the boosters, but Lund was worried about the O-Rings that sealed the boosters’ segments. They were a good idea, permitting Thiokol to build the huge rocket in Utah and ship it in pieces to the Space Center two thousand miles away. Building at Utah was so much more efficient than building on-site that Thiokol was able to underbid competition. The shuttle contract had earned Thiokol $150 million in profits. But the O-rings were not perfect. Data from previous flights indicated that the rings tended to erode in flight, with the worst erosion occurring on the coldest temperature preceding lift-off. Experimental evidence was sketchy but ominous. Erosion seemed to increase as the rings lost resiliency and resiliency decreased with temperature. Unfortunately almost no testing had been done below 40°F. The engineer had had to extrapolate. But with the lives of seven astronauts at stake, the decision seemed clear enough, safety first”.“Well, it had seemed clear earlier that day. Now Lund was not so sure. The Space Center was “surprised” and “appalled” by the evidence on which the no-launch recommendation was based. The Space Center’s senior managers wanted to launch, but they could not launch without Thiokol’s approval. They urged Mason to reconsider. He re-examined the evidence and decided the rings should hold at the expected temperature. Joseph Kilminster, Thiokol’s vice-president for shuttle programs, was ready to sign a launch approval, but only if Lund approved. Lund’s first response was to repeat his objections. But then Mason said something that made him think again. Mason asked him to think like a manager rather than an engineer. (The exact words seem to have been, “Take off your engineering hat and put on your management hat”) Lund did so and changed his mind. On the next day the Shuttle exploded during lift-off, killing all on board. An O-Ring had failed”.56 6. SHARING PROBLEMS: LIVING IN COMMUNITIES decision-making process is asked to change his role from a professional activity with a particular ethic to one that had a diﬀerent ethic. However, if a quite diﬀerent view is taken of what manage- ment is, that is the view I presented in the previous journey, then by deﬁnition every engineer is a manager. In that view managers have very considerable responsibilities to themselves as well as to others. ere can, therefore, be no diﬀerence between the ethical commitment of the company’s executives and those of the professional engineers. But such principles have to be legitimised, and a community provides such legitimisation. Its ethic, to cite Macmurray, should be that “we need one another to be ourselves. is complete and unlimited dependence of each of us upon the oth- ers is the central and crucial fact of personal existence [...] it is only in relation to others that we exist as persons; we are invested with signiﬁcance by others who have need of us; and borrow our reality from those who care for us. We live and move and have our being not in ourselves but in one another; what rights or powers of freedom we possess are ours by the grace and favor of our fellows” [1, p. 211]. But rights and powers bring with them responsibilities that extend in every direction within the community. As the story is told it does not suggest an extended community that reached from the senior executives to the engineering executive and his engineers that would invite a pause for reﬂection. At the same time it shows two communities, one of which was apparently not at ease with reﬂective activity. But as Davis points out disasters of this kind do not just have one cause. If we venture beyond the two diﬀerent modes of thinking the question would seem to be why was there not a common ethic throughout the ﬁrm that would have caused everyone to reﬂect on the engineers’ concern in the light of the common good. Davis concludes that one of the many lessons that can be learnt from the Challenger disaster is that “the ethics of engineers is as important to the success of engineering as good design or testing is” [p. 49]. e story is a tragic reminder of the need to and value of sharing problems and the need for each person to accept responsibility for every other person in the community in which they work. In this case, the astronauts were an integral part of that community. One ﬁnal thought: we understand quite easily that universities and colleges should be learn- ing communities. Whether they are or not is a diﬀerent matter. It is more diﬃcult to see that an organization is or should be a learning community. But they should be. ere is no better illustration of this principle than the Challenger disaster. Neither is there any better example of the need for communities to be driven by a common ethic. NOTES [1] Macmurray, J. (1962). Persons in Relation. London, Faber and Faber. 53, 56 [2] Macmurray, J. (1957). e Self as Agent. London, Faber and Faber. 53 [3] Hawkins, J. D., Catalano, R. F., and associates. (1992). Communities that Care. Action for Drug Abuse Prevention. San Fransisco, Jossey Bass. 53 57 [4] Munns, D. P. D. (2013). A Single Sky. How an International Community Forged the Science of Radio Astronomy. Cambridge, MA, MIT Press. 54 [5] Vincenti, W. G. (1990). What Engineers Know and How they Know It. Analytical Studies from Aeronautical History. Baltimore, e Johns Hopkins University Press. 54 [6] p. 52. Vincenti argues that the evidence that he presented supported the “community of technological practice” described by Edward Constant (1990) in e Origins of the Turbojet Revolution. Baltimore. 54 [7] Vincenti. p. 239. Here he is citing a William Rifkin. See p. 316. 54 [8] Davis, M. (1998). inking Like an Engineer. Studies in the Ethics of a Profession. New York, Oxford University Press. Challenger was a manned artiﬁcial earth satellite that exploded during lift –oﬀ killing all seven of its occupants. 54 J O U R N E Y 7 59 inking about Making a Good Engineer Possible “e ethics of engineers is as important to the success of engineering as good design or testing is,” so concluded Davis [1]: but so it is in everyday life. Consider some of the things that happened during the days that I wrote this text Private Bradley Manning was told that he was not guilty of helping the enemy but was guilty on other charges; e President of Ireland signed into law controversial legislation on abortion that clariﬁed the role of doctors in a country where abortion except in exceptional circumstances is forbidden. In the UK, police in Manchester arrested a 21- year-old on suspicion of the harassment on Twitter of a Ms. Criado-Perez who had campaigned successfully to have Charles Darwin replaced on an English bank note by Jane Austen. She had been threatened with rape among other things. is had caused the San Fransisco-based director of trust and safety at Twitter to seek a meeting with Ms. Criado-Perez to address her concerns. Yesterday the House of Lords (the second chamber of the UK Parliament) debated a ruling of the European Court for Human Rights that the denial of the vote to prisoners held in English jails infringed their human rights, a ruling that the press tell us is vigorously opposed by the British public. Today the Appeal Court in England has issued a judgment on whether or not it was permissible for a health professional to travel with a person who wished to travel to a clinic in Switzerland for assisted dying. In England where the health service is free, frequent cases are brought against it when it refuses to sanction a very expensive drug that may extend a patient’s life for a short time. Everyday there are cases that involve moral principles and require ethical judgments because we have to choose. For the most part we are not faced with making diﬃcult choices. Probably, for that reason most of us, it would seem, take very little notice of such dilemmas until we are faced with one, and for the most part we accept the judgments of the courts. Of course these are big decisions: yet, every day we have to make ethical decisions which inﬂuence our behavior and that of those around us. In family life how and when to discipline a child involves us in ethical decisions for one deﬁnition of ethics is that it “refers to the customary way to behave in society” [2]. But the Greek word ethikos from which ethics is derived relates to character and is used by the philosopher Aristotle in this way in e Nicomachean Ethics. Aristotle gave us the ﬁrst study in what is now called “virtue ethics.” Virtues are the qualities needed “to lead any sort of recognisably human life. For example, she needs to be able to live and work with others; she needs to be able to confront diﬃculties and threats; she needs to be able to control 60 7. THINKING ABOUT MAKING A GOOD ENGINEER POSSIBLE her desires, and so on” [3]. A person who has these qualities is virtuous so those who exhibit the behaviors that these qualities demonstrate are behaving ethically. e study of ethics is therefore a very practical matter. Most of us I would suggest, and I am one, confuse morality with ethics and vice versa. Unlike ethics morality is of Latin origin (moralis) and is to do with whether an action is right or wrong. We might be forgiven this confusion because encyclopedias often include the whole history of ethics when they deﬁne or write about the problems of moral philosophy [4]. However, it is agreed that the central problem is that of right or wrong and it is to this dimension that the decision to ﬂy the Challenger belonged and codes of ethics are related. Codes of ethics are guides to virtuous practice. us, in engineering education much atten- tion in ethics courses has been given to codes of conduct and whistle blowing such as that done by Private Bradley Manning. Recently, a former President of the National Academy of Engineering William A. Wulf asked us to distinguish between Herkert’s concepts of macro-ethics which are the ethical issues that are faced by a profession, and micro-ethics that are the issues faced by individual practition- ers [5]. Clearly, much attention has been paid to the latter in engineering courses but little to the former. He contends that it is on the former that our thinking should be focused. e examples given earlier are a mix of the two. He cites the problem of the allocation of resources in medicine, and while he thinks that is a matter for the profession he concedes that “perhaps society guided by the profession” [5] should be involved in the decision. But should it not be the profession guided by society? And isn’t the problem, in the case of decisions aﬀecting engineering that society does not know or care about the engineering profession? e answer lies in the axiom that an education is not truly liberal that does not involve engineering as is the present case. But I do not wish to travel along this route at this time. DIFFERENCES IN PHILOSOPHY Each day on Today the premier news radio program transmitted by the BEEB (by which the British Broadcasting Corporation is aﬀectionately known in Britain) there is a three minute slot when a person normally of a religious persuasion, but by no means always Christian oﬀers some reﬂections on something that is relevant in the news (ought for Today). is morning the rector of one of London’s most fashionable churches, e Rev. Lucy Winkett, oﬀered a reﬂection on conﬁdentiality that was triggered by Edward Snowden’s release of information about the interna- tional surveillance activities of the U.S. Edward Snowden was holed up in Moscow Airport for a month or so before being given political asylum by Russia. e Rector made the point that atti- tudes to the release of conﬁdential information of the kind made public by Manning and Snowden varied. She thought that some would take an idealistic view that would hold that in a democratic society everything should be transparent. Others, she said would take a realist position and allow that for the state to function in an imperfect world some things would necessarily have to remain conﬁdential. Her problem was that bureaucracies very often reinforce their own legitimacy by creating excessive levels of conﬁdentiality. is creates a problem for realists. e other problem is the power that accrues to agencies/institutions that collect information about each and every one of us. But these are also matters for discussion at another time. One point to be drawn from this illustration is that our opinions represent a philosophical disposition. In her case idealism was contrasted with realism she was trying to determine that disposition or rather enabling us to make such a determination. ere are many theories of ethics that try to account for the principles of our beliefs [6]. 61 ENGINEERS AS CONSEQUENTIALISTS OR CONTRACTUALISTS Bowen suggests that engineers have approached ethics from either a consequentialist, or a con- tractualist, or duty-based perspectives [7]. Consequentialism is a term due to the British Catholic philosopher Elizabeth Anscombe. It is a form of utilitarianism and is on the one hand a theory of responsibility, and on the other hand, a theory of right and wrong. From an engineering perspec- tive it is a reminder to designers of the importance of assessing the consequences of their designs, for they are not only responsible for the intended outcomes of a design but for its unintended but foreseen consequences. e O-Rings on the Challenger Rocket are a case in point. Bowen, a Fellow of the Royal Academy of Engineering using a deﬁnition due to J. Finnis (given in the box), suggests that it makes consequentialism attractive to engineers and notes the “similarity to the familiar and more limited exercise of cost-beneﬁt analysis” [8]. ey might ﬁnd Bentham’s hedonic calculus equally attractive [9]. ...postulate some good as the human good and then seek to identify the act that will maximize the good: that act is (by deﬁnition) the act of greatest utility and (by ethical stipulation) the right act. [Cited by Bowen 7, p. 31: 8, p. 81: 7]. Bowen points out that in engineering consequences are important but he asks why so much of the world’s resources are put into weapons development and the pursuit of war and so little put into the provision of drinking water and sanitation in the third world. His answer is to hope with Mill that a change in resource allocation will be “by the contagion of sympathy and the inﬂuences of education” [8, p. 33]. He is interested in what engineers can do about this state of aﬀairs (see Journey 8). MACMURRAY’S THREE MODES OF MORALITY John Macmurray distinguishes between three modes of morality, one of which he describes as positive and the others as negative. e communal mode is based on a positive apperception. It is heterocentric because when an agent seeks to act rightly, the agents center of reference is always the personal Other. “To act rightly is then to act for the sake of the Other and not oneself. e Other in this mode, always remains fully personal; consequently its objective must be the main- 62 7. THINKING ABOUT MAKING A GOOD ENGINEER POSSIBLE taining of positive personal relations between all agents as the bond of community” [10, p. 122]. It is characterized in the Judaeo-Christian tradition by the command to “love your neighbor as yourself,” and given that communities are inevitably a mix of people the command to “love your neighbor” is very challenging. Macmurray hesitates to call this Christian morality, even though that is what it is, because he thought that what was often identiﬁed as Christian morality was misconceived in the negative mode of contemplation, an ideal world that we can imagine. “e real world is the spiritual world, and the real life the spiritual life.” Both negative modes are egocentric. Our purpose here is to concentrate on the other nega- tive mode which, to confuse matters, he calls “pragmatic.” It is the opposite of the communal for it describes those who have as their intention that which they are determined to realize. Clearly, in these circumstances there is a need to keep the peace whether it is between individuals or na- tion states. e mechanism or as Macmurray calls it “technique” for maintaining harmony in any society is the law. “e pragmatic mode of morality will then be conceived as obedience to the law [...]. It will be a morality of self-control, power over the self, limiting its own freedom for the sake of the community. It will be expressed in terms of will, obligation and duty, as a set of rules or principles, which are the same for all, and which limit for each the use of his own power to do what he chooses” [10, p. 123]. Macmurray considers the greatest exponent of this moral philosophy, which has its origin in stoicism, to be Immanuel Kant. THE CONCEPT OF “DUTY “AND ENGINEERING ETHICS Duty is a concept that is well understood by the English. It is exempliﬁed by the Monarch Queen Elizabeth II. She carries out her obligations as a matter of duty whether or not she likes them, and this characteristic is to be found among English people. But there are those who act in accordance with duty because it satisﬁes them so to do and Kant holds that their motivation is no diﬀerent to those who commit immoral actions. Paul Hurley illustrates this in a way that is relevant to life today. “e person who gives to the poor because it gives him or her pleasure is motivated in exactly the same way as is the person who spends everything on him or herself. Each is motivated by the desire for pleasure. But just as the person who spends everything on him-or herself because it gives him or her pleasure deserves no moral credit, so the person who spends much of his or her money on others because it gives him or her pleasure deserves no moral credit. Each is simply doing whatever he or she happens to be naturally inclined to do” [11, p. 305]. In Kant’s view it is those who do the right thing because it is the right thing to do who are acting from duty and deserve moral praise. is seems to imply that there is no satisfaction to be gained from acting from duty. Yet there seems to be no reason why actions that stem from a respect for the moral law should not bring pleasure. All that is required by Kant is that reason should be the cause of our motivation although as Bowen points out Kant recognized this weakness and wrote about the need for “a feeling of pleasure or of delight” if the obligation of duty is to lead to action (cited in [6, p. 37]). Bowen’s criticism of Kant is that the categorical imperative does not allow a motivation based on personal compassion [12]. As Bowen points out, the concept of duty (obligation) has played a signiﬁcant role in the development of engineering ethics. 63 CONTRACTUALISM AND CODES OF CONDUCT When we make a contract we agree to abide by the conditions (rules) of the contract. Sometimes our elected representatives make contracts on our behalf. International treaties and conventions are examples. Sometimes they are nearer to home such as the “social-contracts” that have been entered into by some governments in Ireland and the UK in which the principal partners are the Unions and the Government of the Day [13]. Such agreements are very diﬃcult to keep even though they are supposed to be binding. An election in a democracy is the aﬃrmation of a contract (manifesto) with a particular political party that is binding for a limited number of years. In this contract individuals give up part of their natural liberty in order that civil society may accrue some advantages. According to Rawls who is one of the major 20th century exponents of social contract theory, a social contract is based on two principles. ese are the principle of liberty and the principle of diﬀerence. e former requires that we can do what we wish so long as we do not harm others either directly or indirectly. e latter arises from the fact that people diﬀer in many ways among themselves, so any contract has to allow for these diﬀerences [1, pp. 138–141]. Acceptance of these principles will inevitably lead to some inequality and Rawls would require the pattern of distribution to favor the less well oﬀ. One of the major problems that Rawls theory seeks to oﬀ-set is that of self-centerdness, and as we can all testify escaping from personal opinion is always very diﬃcult [14]. Codes of conduct are also contracts. ose for engineers diﬀer in that they are voluntary but as we have said we can feel obliged from a sense of duty to obey a code of conduct. When we join an organization like the IEEE we agree to abide by its code of conduct (Exhibit 7.1). Engineering educators whose courses are accredited by ABET agree to ABET’s code of conduct. In England the awarding authority for the status of Chartered Engineer, the Engineering Council requires each institution that it licences to develop a code of professional conduct (Exhibit 7.2) and the Council provides guidelines for the constitution of these codes. So when a person accepts the designation “Chartered Engineer” or becomes a member of the IEEE they enter into a contract to abide by the relevant code of conduct. e principle that governs contractualism is that rules of conduct derive their validity from actual agreements between the parties concerned. Note that the IEEE code begins with the statement—“We the members of the IEEE” [...]. Most people would assent to this when they join a society. If they seriously transgress the code then they will be asked to leave the society. is is not always the case especially if it is religion. Many Catholics continue to practice even when they break the rules, as for example in the case of the practice of contraception. One of the problems with these codes is that they are voluntary. You do not have to be a chartered engineer to obtain work as an engineer in industry. For them to be enforced there 64 7. THINKING ABOUT MAKING A GOOD ENGINEER POSSIBLE Exhibit 7.1: e IEEE Code of Ethics [15]. would have to be an industry-wide agreement. Another point that has been made is that most engineers are employees [17]. ey have to do what their employers require, hence the problem of whistle-blowing. While whistle blowing is encouraged by the authorities in the case of wrong doing it is by no means clear that what might be called a responsible whistle blower is protected. But what is responsible whistle blowing? e pertinence of this question is highlighted by the activities of Private Manning and Edward Snowden. In this respect Bowen draws our attention to the failure of international treaties and con- ventions to have eﬀect when they are needed [7, pp. 17–20]. Bowen took into account the work of John Rawls who believed that his account of justice was superior to that of utilitarianism, proposed that “contractualism provides more of a basis for securing the present arrangements, even of justifying ethical mediocrity, rather than promoting an opportunity for promoting an ethos of high ethical aspirations” [7, p. 9]. Elsewhere he writes “[...] reading something like these guidelines is as close as many engineers come to encouragement to make the most eﬀective use of their skills” [7, p. 36]. We, the members of the IEEE, in recognition of the importance of our technologies in affecting the quality of life throughout the world, and in accepting a personal obligation to our profession, its members and the communities we serve, do hereby commit ourselves to the highest ethical and professional conduct and agree:1. To accept responsibility in making decisions consistent with the safety, health, and welfare of the public, and to disclose promptly factors that might endanger the public or the environ-ment;2. To avoid real or perceived conflicts of interest whenever possible, and to disclose them to affected parties when they do exist;3. To be honest and realistic in stating claims or estimates based on available data;4. To reject bribery in all its forms;5. To improve the understanding of technology; its’ appropriate application, and potential consequences;6. To maintain and improve our technical competence and to undertake technological tasks for others only if qualified by training or experience, or after full disclosure of pertinent limita-tions;7. To seek, accept, and offer honest criticism of technical work, to acknowledge and correct errors, and to credit properly the contributions of others;8. To treat fairly all persons regardless of such factors as race, religion, gender, disability, age, or national origin;9. To avoid injuring others, their property, reputation, or employment by false or malicious action;10. To assist colleagues and co-workers in their professional development and to support them in following this code of ethics.65 Exhibit 7.2: From the Engineering Council’s Guidelines for Codes of Conduct [16]. Cited by Bowen [7, pp. 35–36]. “We do not” writes R. W. Lovin, “begin reﬂecting on the moral life by opening the textbook at page 1 and proceeding in order through the lessons. It is in the nature of ethics that we are always already living the subject when we start to think about it” [18, p. 124]. When we start to think about it we make the good engineer possible, but how do we escape the legalistic approach and what should our aspirations be? POSTSCRIPT I was not aware of Brad J. Kallenberg’s treatise on ethics, theology, and the practice of engineering when I wrote this journey for the very good reason it was also published in 2013 [19]. Had I been, it would probably have altered the structure of these journeys. at said he does oﬀer a solution as to how we might escape the legalistic approach by changing our aspirations, or rather how we think about ethical codes. e title of his chapter on codes of conduct makes one through stop and ponder: at least it did me. It reads, “Reading Professional Codes of Ethics Design.” Reading…. We have to read and then we have to interpret. We can argues Kallenberg read codes as a stipulation warrant or something else. Stipulations are clear-cut rules. “Deﬁnitions j Prevent avoidable danger to health or safety.Prevent avoidable adverse impact on the environment.Maintain their competence.Undertake only professional tasks for which they are competent.Disclose relevant limitations of competence.Accept appropriate responsibility for work carried out under their supervision. Treat all persons fairly, without bias, and with respect.Encourage others to advance their learning and competence.Avoid where possible real or perceived conflict of interest.Advise affected parties when such conflict arises.Observe the proper duties of confidentiality owed to appropriate parties.Reject bribery.Assess relevant risks and liability, and if appropriate hold professionalism indemnity insurance.Notify the Institution if convicted of a criminal offence or upon becoming bankrupt or disquali-fied as a company director.Notify the Institution of any significant violation of the Institution’s Code of Conduct by another member.1. 2. 3a. 3b. 3c. 4a. 4b. 4c. 5a. 5b. 6. 7. 8. 9. 10. 66 7. THINKING ABOUT MAKING A GOOD ENGINEER POSSIBLE are warrants that use descriptive moral vocabulary such as good, stipulations often use modal moral vocabulary, words like ought and should” [19, p. 66]. Kallenberg suggests that we should read codes of conduct heuristically. Chasing after a code of ethics for teachers of engineering Alan Cheville and I have shown that most codes of conduct are limited, imperfect if you prefer [20]. Kallenberg argues that even imperfect codes may be useful. e problem is that there is a tendency to read codes as stipulation warrants whereas they may be read as emblems, expert consensus, covenant, conversation-starters, and prescriptions. Kallenberg argues that most codes of conduct “fall short of their hoped for power” because they are read in the wrong way. As stipulations they are little more than decision theory. ey are “most helpful when read (1) as a kind of badge of honor (or emblem), (2) as thumbnail sketch of expert practice, (3) as a covenant formed among friends, (4) as a series of ice breakers that open up vast vistas of deep and signiﬁcant design conversation, and (5) as a kind of ‘athletic’ training regimen” [19, p. 97]. e “athletic” metaphor relates to his view that we should think of codes as prescriptive rather than proscriptive. Certainly in the UK the population is prescribed regular physical ex- ercise in order to reduce the potential for or obesity. “Prescription makes for a training regimen that is self-transforming,” and that is how we should view codes of conduct. He gives the example of the ASME Code which is prescriptive in outlook “Engineers shall continue their professional development throughout their career and shall provide opportunities for the professional develop- ment of those engineers under their supervision” [fundamental canon # 3 of the ASME code 19, p. 96]. All of which raises the question “What is a professional? [21]. But that is for another day. In the next journey Bowen’s “aspirational,” which might equally be called “transforming” ethic is discussed. NOTES [1] Davis, M. (1998). inking like an Engineer. Studies in the Ethics of a Profession. New York, Oxford University Press. 59, 63 [2] Vardy, P. and P. Grosch. (1999). e Puzzle of Ethics. 2nd ed. London, Harper-Collins (Font). p.4 59, 67, 68 [3] Watt, S. (1996). Introduction to: Aristotle. e Nicomachean Ethics. Ware, Herts. Wordsworth Classics. P. xiv. 60 [4] See for example Mautner, T. (Ed.) (2005). Dictionary of Philosophy. London, Penguin. p. 405. or Honderich, T. (Ed.) (2005). e Oxford Companion to Philosophy. Oxford Uni- versity Press, pp. 627–630. 60 [5] Wulf, W. W. (2004). Engineering ethics and society. Technology and Society. 24, pp. 385– 390. 60 67 See Herkert, J. R. (2004). Microethics, Macroethics, and Professional Engineering Soci- eties. Emerging Technologies and Ethical Issues in Engineering. Washington DC, National Academies Press. Cited by Donna Riley (2008). Engineering and Social Justice. San Rafael, CA, Morgan & Claypool Publishers, p. 110. [6] For example, McInerney, R. (1990). A First Glance at St. omas Aquinas. Notre Dame, IN, Notre Dame Press. 61, 62 [7] Bowen, W. R. (2009). Engineering Ethics. Outline of an Aspirational Approach. London, Springer Verlag. 61, 64, 65 [8] Finnis, J. (1983). Fundamentals of Ethics. Oxford, Clarendon Press. 61 [9] e principle of utility is that an action is approved if that action has an overall tendency to promote the greater amount of happiness. is leads to the idea that the amounts of pleasure and pain can be measured according to intensity; duration; certainty; extent; re- moteness; richness; and purity. Vardy and Grosch [2] give a lengthy example as to how it might work. ey point out that there are problems with measuring “pleasure” and deter- mining what pleasure is. Politicians in Europe have become interested in recent attempts to measure “happiness,” a fact that indicates the utilitarian nature of present day politics. 61 [10] Macmurray, J. (1961). Persons in Relation. London, Faber and Faber. 62 [11] Hurley, P. (1993) Kant’s moral philosophy in Scott-Kakures, D. et al. (Eds.), History of Philosophy. Harper Collins College Outline, New York, Harper Collins. See also Copleston (p. 316) who cites Kant’s own example. “Kant makes a distinction between actions which are in accordance with duty and acts which are done for the sake of duty. His own example serves to make clear the nature of this distinction. Let us suppose that a tradesman is always careful not to overcharge his customers. His behaviour is certainly in accordance with duty; but it does not necessarily follow that he behaves in this way for the sake of duty, that is, because it is his duty so to behave. For he may refrain from overcharging his customers simply from motives of prudence; for example, on the ground that honesty is the best policy. us the class of actions performed in accordance with duty is much wider than the class of actions performed for the sake of duty.” Copleston, F. (1994). A History of Philosophy. Vol. VI. New York, Image Books (Doubleday). 62 [12] Kant distinguishes between hypothetical and categorical imperatives. A hypothetical im- perative is of the form “If I stop smoking I will not get cancer” or “If I jog daily I will lengthen my life.” ey suggest we do things that are a means to some end, and are the result of what Kant calls pure reason. ey do not necessarily result in action. In contrast categorical imperatives result in action. ey are ends in themselves and not means to other ends. Moral duties are imperatives. ey are arrived at by practical reason and undertaken 68 7. THINKING ABOUT MAKING A GOOD ENGINEER POSSIBLE for the sake of duty and no other reason. (See 1, or alternatively 9). A code of conduct should, therefore, be a list of categorical imperatives. Vardy and Grosch note that Kant gives diﬀerent formulations of these terms and they cite a translation by H. J. Paton [14] that gives the three that Kant provides in his summary of e Groundwork of the Metaphysics of Morals. ese are:” (1) e Formula of the law of Nature: Act as if the maxim of your ac- tion was to become through your will a universal law of nature.” (2) e Formula of the End in Itself. Act in such a way that you always treat humanity, whether in your own person, or in the person of any other, never simply as a means, but always at the same time as an end.” (3) e Formula of the Kingdom of Ends. So act as if you were through your maxims a law-making member of the kingdom of ends” [slightly adapted from 1, pp. 57–60]. 63 e second principle might be interpreted as “do unto others as you would do unto your- self.” It is the principle of equity. e highest aspiration of a human being is according to Kant—good will. Kant’s theory is called “deontological” because it is based on duty. [13] Social contract theory has a long history. In the 20th century a major exponent of this the- ory has been the American philosopher John Rawls (1971, revised 1999) A eory of Justice. Boston, Belknap Press, Harvard University). Vardy and Grosch [2] give the example of a shipwreck that leaves people on a desert island who have to learn to live together. In order to develop a community they have to agree to certain rules—a social contract that is binding on everyone. Rawls assumes that people in this situation are self-interested, have an equal ability and freedom to make suggestions about the contract, are rational in their thinking, and have access to knowledge of human nature. He makes a ﬁfth assumption that is known as “the veil of ignorance.” at is if they know nothing about their particular futures (role and status) in the society they are building then Rawls believes that compassion is ensured because it prevents self-centredness. Curran points out that the Kantian categorical im- perative can have the same eﬀect. (Curran, C (1999). e Catholic Moral Tradition Today. Washington, DC, Georgetown University Press. p. 189). 63 [14] Paton, H. J. (1948). e Categorical Imperative. A Study in Kant’s Moral Philosophy. London, Hutchinson. 63, 68 [15] IEEE Code of Ethics. August 3, 2013. http://WWW.IEEE.Org. 64 [16] Bowen cites Engineering Council UK (2007). Guidelines for Institutions Codes of Conduct. London, Engineering Council UK. http://www.engc.org.uk/ecuk%20documents/i nterne%20Aug.%203rd%202013. 65 [17] One of the earliest reports on this aspect was by Moon, J. (1968). e ethical issues of char- tered mechanical engineers and their relationship to education. M. Litt. thesis, University of Lancaster UK. See also Davis, M. (1998). inking like an Engineer. Studies in the Ethics 69 of a Profession. Oxford UP. Davis [p. 170] takes the view that “To be a ‘true professional’ is to act as the employer orders insofar as the orders are consistent with the profession’s standards.” He argues that it is in an employer’s interests for engineers to be professional. 64 [18] Lovin, R. W. (2000). Christian Ethics. An Essential Guide. Nashville, TN, Abingdon Press. 65 [19] Kallenberg, B. J. (2013). By Design. Ethics, eology and the Practice of Engineering. Cam- bridge, James Clarke & Co. 65, 66 [20] Cheville, A. and J. Heywood (2015). Drafting a code of ethics for engineering education Proceedings Frontiers in Education Conference (IEEE), October. 66 [21] Heywood, J. and A. Cheville (2015). Is engineering education a professional activity?. Pro- ceedings Annual conference of the American Society for Engineering Education, Paper 12907. 66 J O U R N E Y 8 71 Aspiration in Engineering Whenever I ride on a bus or train, or pass through an airport or shop in a mall I can’t help but see numerous notices that tell you what not do. As far as I can see, the only notices that tell you what to do are those that show you where to go in the event of a ﬁre. I ﬁnd it all rather depressing because most of the things I am told not to do I would not do anyway. To put it in another way civilized people would not do such things. e fact that we are told that we should not do them suggests that those who authorised the instructions do not think we are very civilized. Perhaps we are not, and if that is the case, given what we believe to be our present sophistication compared with previous generations, how sad. Such notices bring out the negative in me and I think codes of conduct have the same eﬀect. ey do not inspire and as Professor Bowen says they do not make us want to aspire. Fortunately, rather than being put oﬀ by the codes for engineering Professor Bowen set out to establish an aspirational approach to engineering ethics [1]. To understand Bowen’s starting point think back a few years to the oil spill in the Mexican Gulf, one of the largest of man-made disasters. e Chief Executive Tony Hayward of BP, the ﬁrm with overall responsibility for the rig, came out pretty quickly to the Gulf to solve the problem. He saw that as his task and he made it pretty clear that that was what he had come to do. e result was that he gave BP and engineering a pretty bad image. Rightly or wrongly, he was perceived to have put technique before people (public relations). Long before that I had interviewed employers to ﬁnd out what they expected of graduates from Colleges of Advanced Technology in England and I had come away with the strong impression that they wanted them to work at the lab bench and not seek positions in management [2]. ey wanted them because of their skill with technique. I thought that really what they wanted were technicians. ey did not mind what they were called so long as they did the bench work. To a certain extent it seemed that those engineers were only too willing to oblige. People who become engineers, I use the term in the broadest sense, do so because they like playing with and designing gadgets. Professor Alan Cheville of Bucknell University takes a diﬀerent, and some would say more hopeful view. He believes that students want to become engineers to improve the world. But do they? Last year Dr. Mina gave 30 or so of his students a simple questionnaire about what the purposes of engineering were. e answers given did not go one way or the other. Some clearly showed they wanted to help the human race: others indicated a preference for playing with gadgets. Bowen looking at matters from the perspective of the UK curriculum wrote that “at its best engineering changes the world for the beneﬁt of humanity. However, there are at present signif- icant imbalances in the application of engineering knowledge” [1, p. 6]. By this he meant there 72 8. ASPIRATION IN ENGINEERING is a tendency in engineering education, “as presently taught and practised, to prioritize technical ingenuity over helping people” [1, p. 6]. He gives two examples of the failure to use technology to better the circumstances of humankind. e ﬁrst is water treatment. Water shortages aﬀect 2 billion people in 40 countries, and 25,000 people die every day from water-related hunger. His second example is the engineering used to develop inappropriate technologies such as cluster mu- nitions. Among the things that Princess Diana is remembered for by the British is her patronage of organizations that tried to clear the war ﬁelds of Africa of live munitions which killed people, especially children, long (years) after ﬁghting had ceased. Bowen believed that “engineers need to think creatively and become smarter in using engineering to avert war in non-military ways. An alternative to the use of engineering in preparation for military deterrence and pre-emptive war is to use the same basic skill resources in preparation for genuine peace” [1, p. 7]. John Forge goes so far as to argue that “engineers have a duty not to provide the means to harm, whatever other duties they may have” [3, p. 35]. However, he does not believe that there should be a total ban on weapons research and that some could be justiﬁed. He dismisses the idea that there can be purely defensive weapons. Given the exceptionally large number of engineers that are employed in military research every engineering student needs to be faced with these issues within the curriculum they have to study. It is not the task of academics to attempt to dictate such views but to enable students to clarify their values and opinions [4]. ey have to decide when a job creates conﬂict with their codes of ethics and this may not be as easy as it seems. Even codes of conduct can be ambiguous and that, as things stand, is a major reason why engineering students should have to study them; but, such study should take them into the realm of social justice as Bowen’s thesis implies [5]. He would, however, argue that traditional ethical views should be left to their own limitations, and that change will only be brought about if there is an aspirational engineering ethic. Bowen believes that “an aspirational ethos for engineering requires an antidote to the ten- dency of individuals to adopt lower ethical aspirations in professional contexts than in private contexts” [1, p. 12]. He argues that to change attitudes individuals have to perceive life to be a “whole” in which work ethics are not separated from a person’s private ethic. He uses the term “narrative unity” to describe this state of aﬀairs. e ethical aspirations of our work life then be- come the same as those for our personal life. I would hold that the personal should be the driver, which is why I advocate that engineering students should have some acquaintance with the great problems of philosophy and theology, apart from some practice in the philosophical method. Further, if change is to be brought about it has to be recognized that the emotions are involved because ethics is about relationships whether at a macro or micro-level. As we have seen in an earlier journey the Scottish philosopher John Macmurray points out that we only develop as persons in relation to other persons [7]. We come to be who we are as personal individuals only in personal relationships. Macmurray distinguished between positive and negative personal relations to avoid using the word love which in his view had become dis- torted: he variously described positive relations such as friendship, fellowship, communion, and 73 community. If this is so, and reﬂection suggests it is, then it gives a quite diﬀerent understanding of the ﬁrm as a community which is consistent with what I have argued in an earlier journey. Macmurray argues that “the building of positive relations requires that there be essentially one ethic for all human interaction-not one for private life (altruistic care for the Other), and a totally contradictory one for public life (cut throat competition). Public relationships are subject to the same ethical imperatives as the ethics of the individual or family relationships: they must aim for full community in freedom and equality, and be open to participation in that community by oth- ers. is was not (or is) “the dominant view of human beings at work in western society during the modern era” [8, p. 327]. Given that this is the case the development of an aspirational ethic depends as much on the organization (ﬁrm) as it does on the individual. Bowen does not draw on Macmurray but on the Jewish philosopher Martin Buber, one of Macmurray’s admirers. It is evident that their philosophies had many similarities [9]. For exam- ple, Buber argues that reality arises between agents as they transform each other through their dialogue. Reality for Buber is dialogical. As between people Buber distinguishes two primary re- lationships which he labels I-ou and I-It. e former is personal, the latter impersonal. I-ou corresponds with Macmurray’s personal relationship. It is the relationship that engenders care. e I-It relation is the world where a person, “works, negotiates, bears inﬂuence, undertakes, concurs, organizes, conducts business, oﬃciates” [10, p. 39, cited by Bowen]. Bowen argues that while engineers are familiar with this world they are not familiar with the I-ou. It is, he says, an analysis that is lacking in most modern engineering. Both Bowen and Macmurray see the I-It dimension as being at the root of individualism and the materializm with which it is as- sociated. Bowen argues that “Buber’s insight has the unique advantage of encompassing both person/person and person/natural world (environmental) relations and of recognizing the impor- tance of technological knowledge. It also vitally balances the priority presently given to rule and outcome approaches in engineering ethics. However, the nature of engineering requires an exten- sion of the I-ou interactions in terms of I-You interactions based on care but lacking personal proximity” [1, p. 11]. e point here is that individuals make demands on other individuals who in turn make demands on them. is is another way of understanding how even mechanistic or- ganisations inevitably have an organistic dimension to them, to use the terminology of Burns and Stalker [11]. Bowen found that that the European writer E. Levinas, whose works have been translated by the Duquesne University Press, makes “an even stronger statement of the priority of the de- mands that others make on us, which he designated by the strikingly visual notion of the face.” He describes an ethical act as, “a response to the being who in a face speaks to the subject and tolerates only a personal response” [[12, p. 219]: cited in [1, p. 11]]. Bowen writes, “in simple terms, and changing the metaphor, we need to hear the voice of others saying, ‘It’s me here, please help me!’ ” [1, p. 11]. e issue of personal proximity that Bowen points to is of present interest because Man- ning and Snowden who do not have personal proximity with the world community surely acted 74 8. ASPIRATION IN ENGINEERING with a moral intention based on their previous experience, and their judgment of things as they perceived them at the time. Whether or not they were prudent is another issue? “Moral discourse has the moral commonplaces of Natural Law at one end and singular judgements in ﬂeeting and unrepeatable circumstances at the other, and in between are general judgements which can guide us for the most part, but it is up to us to judge when and how and where and how much. ere are no rules for applying rules. For that we need prudence” [13, p. 169]. Prudence is one of the intellectual virtues listed by Aristotle in his Nicomachean Ethics [14]. It is to a present day exponent of “virtue theory” that Bowen turns for other key con- cepts in the development of his aspirational ethics for engineering. He is the Scottish/American philosopher Alasdair MacIntyre who came to public notice in 1981 with the publication of Af- ter Virtue [15]. Nicolas Dent considers that because MacIntyre’s approach to ethics [16] which relates changes in moral ideas to the many inﬂuences that form the individual and the society in which he lives, (e.g., historical, cultural, religious), is so broadly based, it makes it accessible to the “non professional” reader [17]. It is evident that the thesis presented in his various works is attractive to Bowen because MacIntyre objects to the view (philosophy) that the individual is the sovereign chooser of the values they wish to live by. is philosophy MacIntyre suggests has led to dislocations in society, a breakdown of social ties and given rise to activities that take away the dignity of human living. MacIntyre argues that without virtues, communities of whatever size, collapse. In many respects this view is similar to that of David Selbourne, a political philoso- pher who proposed the principle of duty as a guiding principle of the civic order. He wrote, “that the language of civic morality should seem to have become the language of a lost age is both the consequence and further cause of disaggregation and of the extensive dissolution of citizen feeling” [18]. MacIntyre argues that when we participate in the small communities that give life to the area in which we live such as a school’s parents association, or a handicapped group, or within societies like the local golf and tennis clubs we have the opportunity to develop and sustain the virtues. According to MacIntyre the learning and sustenance of the virtues occurs because we live our lives through a narrative structure. We practice the virtues with the support of institutions. e virtues in their turn support the institutions. “A rugby (football) club is sustained by players who see the worth of the game, and the worth of the game is both ensured and enhanced by traditions established by the club” to cite Vardy and Grosch [19, p. 105]. is example is of some interest because in the British Isles disputes over sporting activities, that is, those that are considered to be sportsmanlike as opposed to unsportsmanlike, often revolve around what commentators and the public consider to be virtuous. Vardy and Grosch quote MacIntyre thus, “e virtues therefore are to be understood as those dispositions which will not only sustain practices and enable us to achieve the goods internal to practices, but also sustain us in the relevant kind of quest for the good, by enabling us to overcome the harms, dangers, temptations and distractions we encounter” [15, p. 219]. 75 Bowen believes that MacIntyre’s theory of virtues can provide a starting point for a recog- nisable description of engineering that is acceptable to professionals. He suggests a number of virtues that are appropriate to engineering and draws attention to the principles of—accuracy and rigor; honesty and integrity; respect for life, law, and the public good; responsible leader- ship, listening and informing, which are in the Royal Academy of Engineering’s statement of ethics [20]. He goes on to argue that Macintyre’s terminology also provides a very appropriate description of the outcomes of engineering activity. “ese are internal goods, including standards of technical excellence and the satisfaction arising from personal accomplishment, and external goods, including engineered artefacts and wealth.” e description of engineered artifacts as goods allows such physical technological accomplishments to be distinguished from the end or goal of engineering activity, which may be described as the promotion of human ﬂourishing through con- tribution to material wellbeing. “Such an analysis leads to an important conclusion that the present imbalanced prioritization in engineering of technical ingenuity over helping people may be considered as arising from mistaking the external goods of the practice for the real end of the practice” [1, p. 12]. I want to suggest that the public make the same mistake and see technology as means of solving problems without considering the broader ends. For that reason both the public (politicians) and employers tend to view engineers as a “commodity,” to quote Alan Cheville. e practical outcomes of Bowen’s aspirational ethic would be: “e personal ethical responsibility of every engineer. All engineers need to take a more active role in considering the ethical implications of their work. Our aspiration should be summarized: “Here I am, how can I help you?” [1, p. 13]. “In education [...] give greater emphasis to the goal of beneﬁts in terms of the quality of life” and to the need to take “personal responsibility for professional activities” [1, p. 13]. “Industry and work practices [...] promote “the widespread adoption of aspirational codes of conduct” and provide “career development plans that bring employees into closer proximity with end –users at least for part of their working life” [1, p. 13]. “Engineering Institutions [...] progressively incorporate degrees of compassion and generos- ity” into their codes of practice and support “the development of an international engineering initiative to promote aspirational practice” [1, p. 13]. ese have been ordered diﬀerently to the one given by Bowen. Everything follows from the ﬁrst principle. Second, if these goals are to be achieved there have to be radical changes in at- titudes within education and industry and links have to be made between them that show clearly the importance of aspiration. I have omitted his outcome for positioning engineering in the public and intellectual mainstreams because I regard that as a sine-qua non. Similarly, he sees an aspira- tional role for engineering in international initiatives such as the United Nations Declaration and Programme of Action on a Culture of Peace. In this he is not alone among engineering professors as Aarne Vesilind of Bucknell University and his collaborators have shown [4]. It is likely that he will have his critics for he has not mentioned social justice. Yet thinking in this area, as illustrated by 76 8. ASPIRATION IN ENGINEERING the work of Donna Riley, not only supports and overlaps with his thinking but is complementary to it as well [21]. POSTSCRIPT While these journeys were being given we asked Donna Riley to write about how her work on social justice related to philosophy for a series of handbooks that were being prepared by the Tech- nological Literacy Division of the American Society for Engineering Education. e conclusion of her paper [22] provides a ﬁtting and challenging end to this journey. “By and large, one could say that engineering has reﬂected the values of mainstream society, of neoliberalism, of military and corporate interests. is is due in part to, and continually justiﬁed by engineers’ commitment to considering themselves as value-neutral or objective. But because there is no such thing as value neutrality, engineering has reﬂected some unjust biases embedded in our social structure to the point where they have become so mainstream as to be rendered invisible. is default set of values has been inculcated in engineering through the engineering education process. In all these areas of historical and traditional injustice, voices are emerging, asking, for whom and by whom is engineering done? How is engineering done, and who wins and who loses from engineering activity? ese are fundamental questions that need to be asked of programs of engineering and technological literacy, and we have an opportunity to transform the profession for the better.” NOTES [1] Bowen, W. R. (2009). Engineering Ethics. Outline of an Aspirational Approach. London, Springer-Verlag. 71, 72, 73, 75 [2] Heywood, J. (1969). An Evaluation of Certain Post-War Developments in Higher Tech- nological Education. esis. University of Lancaster, UK. (two volumes) 71 [3] Forge, J. (2005). e morality of weapons research. In P. Aarne Vesilind (Ed.), Peace Engineering. When Personal Values and Engineering Careers Converge. Woodsville, NH, Lakeshore Press. 72 [4] Vesilind, P. A. (2005). University life and Peace Engineering. In P. Aarne Vesilind (Ed.), Peace Engineering. When Personal Values and Engineering Careers Converge. Woodsville, NH, Lakeshore Press. 72, 75 Describes how clear thinking is the defence against indoctrination in the following [p. 139]. “Consider a session I recently taught in the professional ethics course. In this course we try hard to take issues apart and to discover what values drive decisions and how a diﬀerence in values can lead to signiﬁcant disagreements. e best examples come from unpredictable sources. For example, we recently received a campus wide notice to come to a rally in 77 support of our soldiers who had been ﬁghting overseas, and some of the students wanted to talk about it. We decided that when one goes to such a rally, perhaps carrying an American ﬂag, one is sending signals. What exactly is being supported?” “e students decided that there are three diﬀerent recipients of such show of support: 1. America as a nation as an idea. 2. e soldiers who are placed in harm’s way, and 3. e political leaders who place the soldiers in harm’s way.” “None of us had any problems with supporting the ﬁrst two, but we could not ﬁgure out how to show support for the ﬁrst two without also unwittingly showing support for the last one. I did not tell them to avoid the rally, and I would never oﬀer my own reason for not going, but the discussion allowed them to think through the problem.” I used to share this view but now I will give my views if asked, and will argue the point if invited. [5] For example, Professor Emeritus Aarne Vesilind writes, “Engineering, as a profession, states its purpose and objectives in a Code of Ethics, and at least in the United States, the code of ethics of almost every engineering discipline begins with the statement”: 72 e engineer in his professional practice, shall hold paramount the health, safety, and welfare of the public. “e two key words are “shall” and “paramount.” ere is no equivocating about this as the primary commitment of engineering, and the vast majority of engineers agree with this statement and practice their profession accordingly.” “ere is, however, a problem with this statement when it comes to engineers working for the military establishment and it centers on the word “public.” What exactly is the “public?” Suppose an engineer works for a company that designs and produces landmines. Is “public” the people who pay his or her salary? Has the “public” decided through a democratic process that the manufacture of landmines is necessary? Or is the “public” of record those people who will eventually have to walk over the ground in which these landmines have been planted and be killed and maimed by the explosions” [6, pp. 9–10]. [6] Vesilind, P. A. (2005). e evolution of Peace Engineering in P. Aarne Vesilind (Ed.), Peace Engineering. When Personal Values and Engineering Careers Converge. Woodsville, NH, Lakeshore Press. 77 [7] Macmurray, J. (1961). Persons in Relation. London, Faber and Faber. 72 [8] Costello, J. E. (2002). John Macmurray: A Biography. Edinburgh, Floris Books. [p. 321] I have given this quotation because Costello includes a very good summary of the Giﬀord lectures that produced Macmurray’s two great books—pages 324 to 330. 73, 78 78 8. ASPIRATION IN ENGINEERING [9] Both thought that the conceptualization of the form of the personal was the philosophical projects given to the twentieth century. “Martin Buber considered himself to be the poet of this project, and saw Macmurray as its metaphysician, and told him so” [8, p. 15 and p. 322]. 73 [10] Buber, M. (2004). I and ou. London, Continuum. (Originally published in German in 1923. Buber lived between 1878 and 1965). 73 [11] See Journey 5. Burns, T. and G. Stalker. (1961). e Management of Innovation. London, Tavistock. 73 [12] Levinas, E. (1969). Totality and Inﬁnity. Pittsburgh, Duquesne University Press. Fransis- can monks of my acquaintance ask their congregations to see the face of Christ in others— particularly in those who suﬀer. 73 [13] On the meaning of prudence see McInerney, R. (1990). A First Glance at St. omas Aquinas. Notre Dame, IN, University of Notre Dame Press, p. 169. See also Gilson, E. (1956). e Christian Philosophy of omas Aquinas, Notre Dame, IN, University of Notre Dame Press, p. 287 ﬀ. 74 Prudence or practical wisdom (phronesis): the virtue that helps us balance our interests with those of others. Vardy and Grosch argue that without this virtue the other intellectual virtues revert to being skills [19, p. 28]. For a detailed discussion of prudence in relation to engineering design see Kallenberg, B. J. (2013). By Design: Ethics,eology and the Prac- tice of Engineering, Cambridge, UK, James Clarke.” Practical wisdom is the art of doing practical reasoning well” [p. 249]. [14] Aristotle. e Nicomachean Ethics. Introduction by S. Watt. Ware, UK, Wordsworth Clas- sics of World Literature, 1996. Aristotle 384—322 BC. His moral theory is based on the virtues and is sometimes called virtue theory. Aquinas (1225—1274) developed virtue the- ory within the context of natural law and belief in a personal God (see 13, Gilson, p. 259 ﬀ ), also Vardy, P. and P. Grosch. (1999). e Puzzle of Ethics. London, Fount/Harper Collins which has separate chapters on Aristotle, Aquinas, and virtue theory which in particular summarises the views of two British philosophers-Elizabeth Anscombe and Philippa Foot. 74 Aristotle distinguishes between moral and intellectual virtues. e moral virtues are courage, temperance, liberality, magniﬁcence, magnanimity, proper ambition, patience, truthfulness, wittiness, friendliness, modesty, and righteous indignation. e intellectual virtues are art or technical skill (techne), scientiﬁc knowledge (episteme), prudence or prac- tical wisdom (phronesis) as distinct from wisdom, and intelligence or intuition (nous). [15] MacIntyre, A. (1981). After Virtue. A Study in Moral eory. Revised in 1984. London, Duckworth. 74 79 [16] MacIntyre, A. (1966). A Short History of Ethics. London, Macmillan. 74 [17] Dent, N. J. H. (2005). MacIntyre, Alasdair in Honderich, T (Ed) e Oxford Companion to Philosophy. Oxford. UP, p. 549. 74 [18] Selbourne, D. (1994). e Principle of Duty. An Essay on the Foundations of Civic Order. London, Sinclair-Stevenson, p. 4. 74 [19] Vardy, P. and P. Grosch. (1999). e Puzzle of Ethics. London, Fount/Harper Collins. 74, 78 [20] Royal Academy of Engineering (2007). Statement of Ethical Principles. London, Royal Academy of Engineering. 75 [21] Riley, D. (2008). Engineering and Social Justice. San Rafael, CA, Morgan & Claypool Pub- lishers. 76 [22] Riley, D. (2014). Social Justice framings for conversations on engineering and philoso- phy in J. Heywood and A. Cheville (Eds.) Philosophical Perspectives on Engineering and Technological Literacy. Washington. DC, Technological Literacy Division of the American Society for Engineering Education. 76 J O U R N E Y 9 81 Preparing for the Future: Individuals and Organizations Many of us hoped that the ﬁnancial crisis of 2007–2008 would bring some changes to the capitalist system which had proved like most other systems that there was a point at which it stopped functioning. We hoped that politicians and those responsible for ﬁnancial systems would stop chasing money for the sake of money and use it to invest wisely in the future. One hoped there would be an end to short termism and that good CEOs would be encouraged to stay with and grow their organizations. We hoped that the gap between rich and poor would narrow. We hoped that the minimum wage would become a fair wage. Five years down the line not much seems to have happened. Few have been held responsible for their irresponsibility and the gap between rich and poor seems to have widened, and economists talk to themselves. At the same time during those ﬁve years there has been massive social change brought about primarily by technology. e good and the bad consequences of social networks have been exposed but there has been relatively little response to the structural change that is evidently underway. An article in e Times (of London) newspaper with the sub-title “with their jobs vanishing and incomes squeezed, the middle classes may never see things getting better” drew no comment in the letter columns of that newspaper. Commenting on the rich poor gap the author Jenni Russell had much the same thing to say as the distinguished American economist and politician Robert Reich. She wrote that “the root cause of the crash, as the IMF (International Monetary Fund) conceded two years ago, was that across the developed world the rich were taking too great a share of the world’s growth leaving workers to maintain their lifestyles by taking on mass unmanageable debt. No economy can run like that for long” [1, p. 17]. No one will lend anyone anything in the British Isles and small businesses in particular are being starved of cash. Worse, the labor model that said new jobs will be created with each new technological innovation appears to no longer hold. e failure of workforce models to take into account the eﬀects of technological change on jobs has been highlighted by Erik Brynjolfson and Andrew MacAfee of MIT. e sub-title of their book reads “How the Digital revolution is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy” [2]. Jobs are being destroyed and new skills are required in the workforce. It is striking that their recommendations for providing these new skills focus on the school curriculum, not the university. Like Jim Clifton whose report 82 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS will be discussed later they see a pressing need for entrepreneurs who can successfully place some innovations in the market. But what is the relevance of all this to engineering. Engineers many of whom belong to the middle class are making life diﬃcult for the same middle class for the technologies they develop not only put other people out of work but themselves too. In 2011 I suggested there was suﬃcient evidence available to support the view that there was not a shortage of highly qualiﬁed manpower and that a con trick had been worked on politicians [3]. Since then there has been a ﬂow of papers in support of the view that there was a shortage of students for STEM courses [4, 5]. But this view has been seriously challenged in the U.S. where three academics have pointed out the irony of employing large numbers of guest workers in IT industries while at the same time U.S. colleges graduate 200,000 more scientists and engineers than ﬁnd employment in these ﬁelds [8]. ey point out that the IT ﬁrms by employing guest-workers to ﬁll two thirds of the positions available have been able to keep wages at the same level for the last ten years. Is this, they ask, a question of market failure? One telling statistic came from e US Bureau of Labor Statistics who recorded for the decade ending 2010 that techno-scientiﬁc employment fell by 19%, in Silicon Valley and that average wages fell by 14% [9]. But the most worrying information related to data that suggested there is unemployment among middle aged and older engineers [10]. Other commentators sug- gested that immediately (today) the demand is for technicians. Salzman, Lowell, and Kuehn pointed out that the guest workers who enter IT are being employed in what they call “commod- ity like” production jobs such as programers and systems analysts. An unusually long article in the September 2013 issue of IEEE Spectrum reviewed the STEM debate and came down gently on the side of those who think that there is not a STEM shortage [10]. Charette cites Teitelbaum who said that “the problem with proclaiming a STEM shortage when one does not exist is that such claims can actually create a shortage down the road. When previous STEM cycles hit their “bust” phase, up-and-coming students took note and steered clear of those ﬁelds as happened in computer science after the dot-com bubble burst in 2001” [p. 52]. e problem that the engi- neering profession has is the possibility that the products of universities will come to be treated as commodities for those jobs where the only interest is in engineering techniques. ere was an all too brief conversation in ASEE Prism where it was reported that middle- aged and older engineers were being asked to take a cut in salary, or in the software industry be replaced by cheaper graduate entry personnel in the belief they had more up to date skills [11]. Professor Plotkin in a comment questioned whether or not anyone would want to work in an industry that treats its workers in the ways described by Wadwha. Nevertheless, it seemed there was a serious unemployment problem among middle aged and older engineers in some sectors of the U.S. Wadwha’s response was to cite the metaphor of a roller coaster and suggest that the universities need to prepare students for that ride so that when the need arises they are able and interested to change jobs. It does seem as though the futurists will at last be proved correct. e majority of the working population will be faced on at least one occasion, and possibly more, in 83 their working lives with having to ﬁnd a job outside the perceived range of their abilities. Hence, the need to take the concept of life-long learning more seriously and to design courses of contin- uing professional development that support engineers on that roller-coaster. Such programs are likely to be as much about personal development as they are about speciﬁc topics in engineering. One thing that is certain from the available data is that changing technology will change society. It is equally clear that the 2008 crash has not created an international debate about the future of society yet the future of the international ﬁnance system is intimately linked to that future because of its links with technology. e other thing that is certain is that there will be a jobs war. is is Jim Clifton’s view, and being CEO of Gallup he has a great deal of worldwide data [12]. Although he is concerned with the problem as it aﬀects America the general principles apply to any country. He writes [A country] “goes broke when its GDP falls and jobs can’t be found. A country goes broke one company at a time and then one citizen at a time. It grinds down. And it’s happening now because the U.S. is going broke. All this is happening because jobs and GDP live together, and are the cause and eﬀect of one another. ey are the chicken and egg. So without signiﬁcant sudden GDP growth, America will not experience signiﬁcant job growth. America will not experience meaningful job growth” [12, p. 18–19]. He thought that cities should encourage entrepreneurs to bring innovation to the market, a view as we have seen that is held by Brynjolfson and McAfee. at was written in 2011. Among Clifton’s points that resonated on this side of the Atlantic, certainly in Britain and Ireland, is the fact that while in 2011 Gallup put American unemployment at 10% it placed underemployment at around 20%. Against this Gallup found that across the world what people wanted was a “good job.” Hence, the title of Clifton’s book e Coming Jobs War. “e biggest problem facing the world is an inadequate supply of good jobs. [...]e great global dream is now focused on having a good job [...] Job creation is the new currency of all world leaders. e most important social value in the world is my job” [12, p. 186]. e trouble is that no one seems to know how to create them. A problem for engineering education is that too little is known about what engineers ac- tually do and who they are in the small and medium sized ﬁrms where most jobs are created [12, p. 29:13]. Many of them do not pursue a career in engineering. What do they do and what is the value of engineering education to them? ese are pressing issues. Irrespective of Clifton’s solutions, it is important to note, that he is a ﬁrm supporter of free enterprise and capitalism. at is my view too, but I think that in its extremes capitalism can function against the “common good.” I also believe that the utilitarian model on which modern capitalism is based has not in the long run been a servant of the “common good.” Money chasing money so that bankers make more money does not contribute to wealth creation, and not therefore to the “common-good.” Some would consider this to be amoral. Some might consider that short term investment where investors want quick returns comes within this category since it causes CEO’s to change the organization so that it is easily saleable. e stories of many mergers cast doubt on the view that they always create stronger organizations. It is diﬃcult to believe that 84 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS CEOs who come to an organization with a view to remaining for two or three years can create an eﬀective organization. e argument to be oﬀered here is that all organizations, irrespective of whether they are part of the free enterprise system or the State system, are obliged to serve the common good by the production of useful goods and services. By common good is meant, “e sum total of social conditions which allow people, either as groups or individuals, to reach their fulﬁlment more fully and more easily” [14]. Apart from the fact that the state should intend to achieve the common good, it follows from this principle which is welded into the Judaeo-Christian tradition [15] that all organizations have a social function by creating opportunities for meeting, cooperating, and the enhancement of the abilities of the people involved. It is argued here that businesses have neglected their social function particularly in regard to education, training and career development and that in the future this will have to be reversed. Another way of looking at the problem is to follow Loughlin Hickey’s advice and conduct a public (open) examination of the relationship between purpose, performance and proﬁts [16]. is view has implications for the structure of organizations as will be evident in the discussion that follows. If it is assumed that as technology changes many persons will have to change their jobs at regular and relatively short intervals then individuals may be called on to change their jobs as many as 6 times in a 40–50-year work-span. e U.S. diﬀers from Europe in that there are no age limits placed upon the age when a person can retire. Until recently, retirement has been ﬁxed at 65 in the UK and the state pension has been paid from that age. In the future the age will be set at 67. It is likely that as the average life span increases that that age will be further increased. Very many people make provision for private pensions more often than not through their employer. During the ﬁrst decade of this century most ﬁnal salary schemes have come to an end (except in the public service) because pension funds in the private sector have had large black holes. Notwithstanding the problems of the sector it is the pension funds that have by far the largest money resource available for investment. e pension funds have been criticized for not taking a pro-active role in the management of companies particularly in respect of salaries paid to Boards of Directors. Not only is there a problem of getting funds to be proactive but there is a question of how to ﬁnd members who can exercise some inﬂuence over the fund even though they have no votes in the fund. Similar problems exist in Ireland. Apart from family-owned businesses and the occasional employee owned business the ma- jority of companies are limited (incorporated) liabilities. In law they are owned by their share- holders. e public have the picture that they are pretty ineﬀective at holding their CEO’s and directors to account. John Macmurray’s philosophy would produce a diﬀerent picture of the com- pany because it asks the question “What constitutes the company?” His answer, I suggest, would be the relationships within its boundaries. ose boundaries extend from the shareholders to the consumers via the workers. Everyone has an investment in the organization. e sharehold- ers depend on their being a market (consumers), and workers who can create and produce for that market. Without workers and consumers shareholding is pointless, perhaps we should say 85 valueless. Within such an organization there are proximate and close relationships some more in- terdependent than others but all interdependent in determining the success of the organization. Seen as a community they have a social function within society. e point to be made here is that all persons in the community are equally important. Legally that is not the case for a ﬁrm and it is for this reason that in the UK some interest has focused on the John Lewis Partnership. It is the third largest private company in the UK, and comprises a number of department stores like Macy’s, and a supermarket chain called Waitrose. It is what is sometimes called a “mutual’ because it is owned and managed by its employees. e annual proﬁts are divided between the employees. Last year the turnover was £9.4 billion and each employee was rewarded with the equivalent of two additional month’s salary. It would be too much to suppose that there would be trends to create organizations of this kind but there is no reason not to develop this idea of a ﬁrm, or for that matter any organization structured on the basis of a community, of persons in relations where all take responsibility for the development of the organization. Clearly, some structures are more favorable to the development of a community. But the success of a community depends more on the attitudes and beliefs of the members than it does on structure. Within a community work has to be regarded as a good for every one; it is not for the personal interests of any particular individual. It does demand moral behavior, and we should demand of its actions that they should not be so much as right or wrong but good or bad in so far as it serves the agreed goals of the community. Since, as Macmurray argues, the moral rightness of an action has its ground in the relation of persons, each individual in a community contributes to the personal development of the Other. e principle of community requires that those responsible for the community (management) have to ensure that each person in the community is able to achieve the limits of their own excellence. “Minimally, the principle of community rules out selﬁsh or exploitative goals, even when they require a high level of individual excellence. A person does not live a good life by developing skills of manipulation and persuasion that allow one to prosper at the expense of others, and a community does not encourage excellence by arranging matters so that some people develop their skills as a result of keeping others in subordinate positions with limited possibilities. Put more positively, the principle of community suggests that we should choose those goals that enrich the lives of other people and enable them to live good lives of their own. is requires thoughtful attention to the needs of others, but it also requires a careful assessment of our own needs so that we develop the skills and capacities that will contribute most fully to the good of others. People who have the stamina, coordination, and intellect to be surgeons, or the patience and communicative skills to be teachers have possibilities to help many other people live good lives, but they will also have to seek support from many other people in order to achieve excellence in those endeavours” [17, p. 31]. A community will be made up of diverse capabilities and personalities, some of which will be diﬃcult to manage but the advantages of diversity are considerable. If you ﬁnd the concept of community diﬃcult be reminded that there is such a thing as the engineering community. One 86 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS reason we do not discuss the engineering community is, as the Chinese social scientist Lee Bocong reminds us, because most attention has been given to the study of the scientiﬁc community [18]. It is community that creates goods for the material world and unlike science which has its goal the understanding of nature engineering’s goal should be the common good. But communities are not closed systems. Because technological developments create in- stability in the labor force, organizations have an obligation to society to ensure that persons no longer suitable for the tasks required in that organization are prepared to undertake tasks in an- other organization. ese tasks may be at a distance from the tasks they have been doing (that is, the abilities they have been using). ey may be in a diﬀerent part of the labour arena [19]. is is how an organization partly meets the objectives of the “common good.” Organizations cannot escape responsibility for professional development for the future. It is not a question of handing this responsibility to the state but of sharing it with the education system. To a large extent this is what happens in the German dual system of education of training. Industry takes joint responsi- bility with the education system for training. Britain, despite legislation, in 1964 has never been able to obtain such commitment. Germany also runs a tripartite system of school education with the gymnasium the place for academic study [20]. But unlike Britain of the 1970s there seems to be no concern for status as between demand for the diﬀerent types of school. e Germans also give status to company workers through representation on the management boards responsible for the direction the ﬁrm takes. Given that Germany has probably been the most continuously successful of the industrialized nations since the end of the second-world war there is much to be said for taking notice of its approaches to industrial development. e changes that are taking place in society as a result of the impact of technology will undoubtedly have a profound eﬀect on the system of higher education. Clearly, it has to be a “real” preparation for life. It will have to be a base for continuing professional development (CPD) or permanent education as lifelong learning was once known. But what should those who are responsible for engineering be considering in the immediate term. It is clear that engineers require a much wider range of understanding than that provided by the application of science. In the U.S. a review of what goes for liberal education would seem to be required. Let me make one submission. All education systems are bound by severe structural constraints. One of these is the way the time table is constructed, to enable students to meet speciﬁed credits. Combined with the timetable the credit system allows for little innovation. It would, for example, be extremely diﬃ- cult to introduce short intensive courses. e other is the way subjects have become so large that teaching is done in subject enclaves. I won’t go so far as to call them ghettoes but you get the gist. Engineering students need to experience what it is to be in a true community. ey need to be able share their learning and learn with a diverse community. In this respect it is worth looking at the studies done by Alexander Astin [21]. Now 20 or more years’ old, but in my submission still relevant even though they were undertaken with liberal-arts students, they lead to the view that the best social support that students could receive is a collegiate climate. is recommenda- tion was made both in respect of student well-being and learning. How within all the constraints educational institutions have to face can a collegiate climate be introduced and extended to the ﬁrm so as to enable permanent learning? I will examine this question and the problem of change in the ﬁnal journeys. 87 POSTSCRIPT Recent research reinforces the views put forward in this chapter in regard to the workforce and its structure.. First, Teitelbaum (2014) has now clariﬁed his thinking in a substantial treatise [22]. He summarizes his ﬁndings as follows. • “First that the alarms about widespread shortages or shortfalls in the number of US Scien- tists and engineers are quite inconsistent with the available evidence. • Second that the similar claims of the past were politically successful but resulted in a series of booms and busts that did harm to US science and engineering and made careers in these ﬁelds increasingly unattractive: and • ird that the clear signs of malaise in the US science and engineering workforce are struc- tural in origin and cannot be cured by simply providing additional funding. To the contrary recent eﬀorts of this kind have proved to be destabilizing, and advocates should be careful what they wish for” [22, p. 3]. It seems fairly clear that worldwide changing technology, in particular AI, will have an impact on the structure of the workforce. Globalization may kill jobs. As this journey suggests, the models that are currently in use are open to challenge, and it is not surprising that there should be a number of diﬀerent views about the future. e optimistic view is that the current model is correct: changes in technology will continue to bring about other avenues of employment is a the position of Brynjolfsson and McAfee. A middle view put forward by two English scholars, father and son, Richard and Daniel Susskind, who argue that “capable machines will transform the work of professionals giving new ways of sharing practical expertise in society,” the eﬀect of which will in the short run be some unemployment but in the long run new jobs will emerge [23]. e Susskinds study is of professional work. With many illustrations they argue the “the traditional professions will be dismantled, leaving most (but not all) professionals to be replaced by less expert people and high performing systems.” Technicians rather than technologists. ey expect new roles will arise, but we are unsure how long they will last, because these too, in due course, may be taken on by machines” [23, p. 303]. ey say that they are not determinist because how technology is used is very much in the hands of the professions. “We can shape our own future; more than this, we believe that we ought to, from a moral point of view” [23, p. 304]. Given that engineers play a major role in developing these technologies they should also be presenting to the public their views on how they would shape the future. ey cannot do this without a personal philosophy. 88 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS e pessimistic view is put forward by myself that there will be permanent and increasing loss of jobs. Whichever view is taken it has implications for the structure and content of higher educa- tion. It is also clear that whatever position is taken a basic element of the curriculum throughout schooling and higher education has to be technological literacy and that has to extend beyond the art and science of making things to IT/AI but more expressly to the moral dimensions of technology, one of which is who will own and control practical expertise [23, p. 304–307]. NOTES [1] Russell, J. (2013). Recovery will only widen the rich-poor divide. e Times, August 2. 81 Reich, R. B. (2015). Saving Capitalism: For the Many not the Few. New York, Alfred A. Knopf. “For three decades after World War II the average hourly compensation of Amer- ican workers rose in lockstep with productivity gains […] beginning in the late 1970s the virtuous circle came to a halt. While productivity gains continued much as before and the economy continued to grow, wages began to ﬂatten. Starting in the early 1980s, the me- dian household’s income stopped growing altogether, when adjusted for inﬂation.” e standard explanation is that American workers priced themselves out of the market. “If they want jobs, they have to settle for lower wages and less security. If they want better jobs, they need better skills. So hath the market decreed.” A familiar story not only in the U.S. but the UK as well, but Reich while agreeing that this explanation is relevant argues that it is far from the whole story. He argues that the “underlying problem, then, is not that average working Americans are worth “less” in the market than they have been, or that they are living beyond their means. e problem is that they have steadily lost the bargaining power needed to receive as large a portion of the economy’s gains commanded in the ﬁrst three decades after World War II, and their means have not kept up with what the economy could otherwise provide them. To attribute this to impersonal workings of the “free market” is to ignore how the market has been reorganized since the 1980’s and by whom […] “it is to overlook the marked decline of countervailing power in our political economic system.” (extracts from chapter 13). [2] Brynjolfsson, E. and A. McAfee (2011) Race Against the Machine. Lexington MA. Digital Frontier Press. 81 [3] Heywood, J. (2011). e Response of Higher and Technological Education to Changing Patterns of Employment. Proceedings Annual Conference of the American Society for Engi- neering Education. 82 “To a large extent policy has been governed by the regularly reported predictions that there is and will be a shortage of engineers and scientists, and that the pool of students available to pursue these occupations is too small and declining in quality. In both the UK and the 89 U.S. this perception is taken to be correct and it is held that this will be detrimental to future economic prospects. Much attention has been paid to remedying this shortage particularly by focusing on the supply side of the equation. Michael S. Teitelbaum a Program Director at the Alfred P. Sloan Foundation said at a conference on the U.S. Scientiﬁc and Technical Workforce “the supposed causes are weaknesses in elementary, secondary, or higher ed- ucation, inadequate ﬁnancing of the ﬁelds, declining interests in science and engineering among American students, or some combination of these. us it is said that the United States must import students, scientists, and engineers from abroad to ﬁll universities and work in the private sector-though even this talent pool may dry up eventually as more foreign nationals ﬁnd attractive opportunities elsewhere”[4]a. But Teitelbaum went on to argue that such data that was available was weak and often misinterpreted [4]b. ere was no evidence for a shortage of qualiﬁed personnel and in a submission to a sub-committee of the House of Representatives he said that, “despite lawmakers being told by corporate lob- byists that R & D is being globalized in part due to shortages of scientists in the US no one who has studied the matter with an open mind has been able to ﬁnd any objective data of such general shortages.” He concluded with the controversial view that, “Federal policy encourages an over production of science professionals” [5]. It has created its own system of vested interests. If the continuing attention to the shortage of students for STEM education is anything to go by this system is alive and well [6]. Of course it may not be true of other countries [7]. [4] (a) Teitelbaum, M. S. (2003). Do we need more scientists? e Public Interest No 153. Washington DC, National Fairs Inc. He presented his paper at a 2007 conference on e US Scientiﬁc and Technical Workforce. Improving Data for Decision Making. Organized by Rand Science and Technology. e proceedings were edited by Kelly, T. K., Butz, W. P., Carroll, S., Adamson, N. M., and G. Bloom, pp. 11–31. It is interesting to note that forty three years ago John Jewkes in the UK asked a similar question, How much science? In his Presidential address to the economics section of the British Association at the 1960 meeting of the Association (Advancement of Science, 67, 1960). 82, 89 (b) Lowell, B. L. and H. Salzman. (2007). Into the Eye of the Storm: Assessing the Evi- dence on Science and Engineering Education, Quality, and Workforce Demand. Urban Insti- tute. 48 pages. It also considers that there is no shortage of scientists and engineers and examines in detail the perceptions that have led to the opposite view. [5] Cited in First Bell. Today’s Engineering and Technology News under the heading, Labor re- searchers tell Congress U.S. not lacking in scientists, engineers. Washington, DC, ASEE. See also (a) First Bell 07:06:2011 Some experts say STEM crisis is overblown and con- trast with 21:10:2011, Demand for STEM skills increasing, study ﬁnds. (b) Patel, P. (up dated 2010). Where the engineering jobs are... the news is good but not great for engineers looking for work in 2010. IEEE Spectrum, downloaded 03:01:2012. 82, 89 90 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS [6] For example, (a) First Bell reports on 28:10:2009, High-achievers defect from STEM ﬁelds of Study ﬁnds: 23:05:2011, experts voice concern over high STEM dropout rate:16:06:2011, training programs oﬀer pointers on incorporating STEM into lessons: 03:02: Technology, engineering overlooked when STEM education discussed, teacher writes (in London e Times 01:03: 2012 in an article on the importance of science to Britain’s recovery, no mention is made of engineering): 08:02:2012, Obama to request $80 Million for education funding for training math, science teachers: 13:02:2012, Labor Department oﬃcial discusses Importance of STEM at the University of Dayton. 89 (b) Ellis, R. A. (2007). Eﬀects of recent revisions in Federal Standard Occupational Classiﬁ- cation (SOC) Categories of the Employment of STEM Professionals. New York, Commission on Professionals in Science and Technology. (c) Future of STEM Curricula and Instructional Design. A Blue Sky Workshop. December 1–3, 2009. Center for the Study of the Mathematics Curriculum. [7] Blau, J. (updated 19:08:2011). Germany faces shortage of engineers. IEEE Prism Down- loaded 03:01:2012. Also, Schneiderman (2010) Economy and shortages aﬀect European job outlook. e bigger high-tech companies in Europe are recruiting EE’s. Talent is in short supply, especially to smaller ﬁrms looking for very speciﬁc skills. IEEE Spectrum, March. 89 [8] Widely publicized. Salzman, B., Lowell, L., and Kuehn, D. (2013) Guest workers in the high skill U.S. Labor market: An analysis of supply, employment and wage trends. 82 [9] Cited by Zachary, G. P. (2011). Jobless Innovation? IEEE Spectrum, April, p. 8. 82 [10] Charette, R. N. (2013). e STEM Crisis is a Myth. IEEE Spectrum, September pp. 40– 43, 50–52. Charette interviewed Teitelbaum who said that anxiety about manpower in the US dates from World War II (the same is true of the UK-my comment). Ever since then it has tended to run in cycles deﬁned by “alarm, boom and bust. e cycle usually starts when someone or some group sounds the alarm that there is a critical crisis of insuﬃcient numbers of scientists, engineers, and mathematicians” and as a result the country “is in jeopardy of either a national security risk or of falling behind economically” [...] e gov- ernment responds either with money (for research), or more recently with visas to increase the number of STEM workers. is continues for a number of years until the claims of a shortage turn out not to be true and a bust ensues. Students who graduate during the bust are shocked to discover they can’t ﬁnd jobs, or they ﬁnd jobs but not stable ones.” No one mentions the point that it is in the interests of engineering educators to have a shortage of engineers! 82 [11] Wadhwa, V. (2011). Leading edge: over the hill at 40. ASEE Prism, p. 32. 82 91 [12] Clifton, J. (2011). e Coming Jobs War. New York, Gallup Press. 83 [13] A step in this direction has been taken by the authors recently published Engineering Prac- tice in a Global Context: Understanding theTechnical and the Social. (2013). Edited by B. Williams, J. Figueiredo, and J. Trevelyan. London, CRC Press (Taylor and Francis). Since this journey was written, J. Trevelyan has published a major work on e Making of the Expert Engineers (CRC Press, Taylor and Francis, 2014) which is based on studies of en- gineers at work and the skills (comopetencies) they use. [14] Author. (1966). Gaudium et Spes, 26, AAS 58. Second Vatican Ecunemical Council. Cited in Compendium of the Social Doctrine of the Church (2005). Dublin, Veritas, p. 79. 84 [15] For a Jewish perspective on the common good, see Sacks, J. (2007) e Home We Build Together: Recreating Society. London, Continuum. 84 [16] Hickey, L. (2013). Change from within. e Tablet, September 25. 84 [17] Lovin, R. (2000). Christian Ethics. An Essential Guide. Nashville, TN, Abingdon Press. 85 [18] Bocong, L. (2010). e rise of philosophy of engineering in the East and West. In I. Van de Poel and D. E. Goldberg (Eds.), Philosophy and Engineering. Dordrecht, Springer. 86 [19] See Youngman, M. B., Oxtoby, R., Monk. J. D. and J. Heywood (1978 Analysing Jobs. Aldershot, Gower Publishing, p. 106)—“e development of a more ﬂexible approach to employment, and thus to training requires substantial changes in attitude on the part of employers, managers and workers’ organisations. It is bound to aﬀect the structure and content of aprenticeships as well as the institutions of tertiary education and work. e current high levels of unemployment reinforce the view since they relate to whole regions of industry. In other words the chances of an individual being able to ﬁnd exactly similar work are small. e role that our technique of job analysis can play in such circumstances is best illustrated by omas and Madigan’s study of redundancy. ey found that the response to redundancy among a group of workers was best understood ‘in terms’ of the groupings formed on the basis of the technological/organization system operating in a particular ﬁrm and more generally, in a particular industry. ese groupings act as a useful means of indicating the structures of perceptions held by our sample, in terms of which they evaluated the redundancy and planned their action to achieve their ends.” omas and Madigan suggested that a theory of labour arenas which reﬂects the ‘political’ nature of job choice might provide a more adequate basis for the analysis of job search and job change. 86 Our concept of a labour arena, that is a group of skills which is already possessed or which may be readily acquired, crosses the divide of job perceptions derived from job titles. It is relatively easy for employer and employee to check whether or not they can cope with 92 9. PREPARING FOR THE FUTURE: INDIVIDUALS AND ORGANIZATIONS the operations in jobs as described by the components of nucleus operations necessary to performance which are derived from analyses, as opposed to relying on assumptions about the roles implicit in a job (p. 106). omas, B. and C. Madigan. (1974). Strategy and job choice after redundancy: a case study in the aircraft industry. Sociological Review, 22, 83–102. [20] Author: Vocational Training in the Dual System in the Federal Republic of Germany. Bonn, Federal Ministry for Education and Science. “In the dual system the larger part of learn- ing takes place not in the school, but in the production facilities or service enterprises in industry and commerce. e student is a trainee in a company or practice in one of the liberal professions, or in the Civil Service. He or she is released for the purposes of attend- ing training school, i.e., is also a student at a vocational school at the same time. In the dual system, training is divided between the two establishments responsible for providing training: the company and the vocational school. In the Federal Republic of Germany, these are subject to diﬀerent authorities. Federal law applies to the training received in a company. e school element is the responsibility of the Länder” [p. 6]. 86 [21] Astin, A. (1994). What Matters in College? Four Critical Years Revisited. San Fransisco, Jossey-Bass. 86 See also Chambliss, D. F. and C. G. Takacs (2014). How College Works. Cambridge, MA, Harvard University Press. “[r]elationships to be central to a successful college experience. ey are the “necessary precondition, the daily motivator, and the most valuable outcome” [p. 155]. “[s]peciﬁc human beings matter. A student must have friends, needs good teachers, and beneﬁts from mentors. A student must have friends, or she will drop out physically or withdraw mentally. When good teachers are encountered early, they legitimize academic involvement, while poor teachers destroy the reputation of departments and even institutions…relationships are important because they raise or suppress the motivation to learn; a good college fosters the relationships that lead to motivation.” [22] Teitlebaum, M. S. (2014). Falling Behind: Boom, Bust and the Global race for Scientiﬁc Talent. Princeton, NJ, Princeton University Press. 87 [23] Susskind, R. and D. Susskind (2015). e Future of the Professions. How Technology will Transform the Work of Human Experts. Oxford. Oxford University Press. 87, 88 J O U R N E Y 10 93 Changing Us: Changing Society While we may understand that universities and colleges should be learning communities it is complacent to suggest that they are, at least, purposefully so. ere is one quite simple test of this proposition and that is to ask a large sample of university teachers, teachers of engineering in particular, if they have any understanding of what learning is, and in particular, adult learn- ing. It is doubtful if many teachers would claim to have an understanding of what learning or for that matter development is: that is, in terms of how they are presented by writers who specialize in learning in higher education, except perhaps those in the education and psychology commu- nities. Some will have heard of Piaget but may or may not have understood his theory. is is not surprising for very many teachers in higher education have received little or no training in instruction and curriculum. But like everyone else they have been to school and college and like everyone else they think they know more about teaching than the teachers in whose care they leave their children. As parents they want their children to experience an environment that will enable those children to develop to their potential. But there are often contradictions in their position. ey may place their child in an environment that will ensure that child passes the entrance test for universities like Harvard and Yale, and Oxford and Cambridge which are not necessarily en- vironments that ensure the child will develop to its full potential (whatever that might imply). Decisions made by politicians often lead to management and curriculum operations in schools that function against this goal. For example, it is quite clear that while we want students to be “rounded,” to cite a well worn but almost meaningless term, yet we pay far less attention (if any) to the aﬀective domain of development than we do to the cognitive and ignore the fact that the aﬀec- tive is important to development in the cognitive domain [1]. We do not attend to the “rounded” development of the person at all. Similarly, we worry about the status of subjects. “Hard” subjects like mathematics have higher status than “soft” subjects like “social studies” with the eﬀect that teachers of the so-called “soft” subjects try to turn them into science subjects. Students cotton on to these attitudes and in engineering many of them do liberal studies because they have to, and not for personal development. Often they feel their engineering teachers have little regard for liberal studies. Happily you will ﬁnd engineers who valued such studies when they were students. In sum the fact is that educational decisions by tutors and students often have little to do with learning outcomes and personal development either at the institutional or political level. One reason for this is the models we have of teaching, learning and development. I venture to suggest that teachers divide along a similar continuum to that of managers. At one end of 94 10. CHANGING US: CHANGING SOCIETY the spectrum teachers will have a theory X view of learning while at the other end will be found those who advocate a theory Y approach. e model that we have grown up with tends to be theory X. It is of a nineteenth century assembly line, highly controlled in which the irrational feelings of students are overcome by a drill approach to education. It has a long history going back to those Greek philosophers who thought the mind is a “slate” on which things are written. It is assumed that the slate interprets what is written in the same way that the lecturer or writer intended. ose who do not get the right interpretation fail. It encourages a passive approach to learning. is is an extreme view of what John Eggleston called a “received” curriculum [2]. Such a curriculum is based on the view that there is a ﬁxed body of knowledge that has to be handed down (transmitted) from generation to generation. It is structured by disciplines often called subjects that have to be “covered” willy-nilly. e engineering curriculum belongs in this category. ere is received body of knowledge that has to be handed down. But the “received” curriculum does change with time. In response to changes in technology new subjects are drafted in, and there are modiﬁcations to some of the traditional subjects, but as Dr. Mina reminds me “electricity and magnetism” to use the title of my youth remains largely unchanged except for the units in which it is taught. I remember the change from cgs to mks units in the 1950’s. In engineering new technologies cause new courses but the tendency is to allow them to add to programs that are already pretty full. While there have been papers written that criticize the overloaded curriculum in engineering they seem to have had very little impact [3]. ere seems to be little or no attempt to ask what is essential in terms of the key concepts that should be grasped. So we complain that while we want our students to be creative our lecture and test regimes have to be completed at the expense of creativity: and, the technical-system in which we operate—50-min sessions, credit hours, regular tests, and so forth—supports the assembly line approach to instruction. Little or no account is taken of the way students learn and develop. In the “received” model of the curriculum engineering students are oppressed and teachers are the oppressors, to use Alan Cheville’s extrapolation of Paulo Freire’s philosophy of the op- pressed (personal communication). is is counter to what a university should be about but it is often supported by the system of testing and examining (and the system of accreditation) that is used. It is a matter of fact that the tests we set reinforce the teaching we give. Most complaints about tests whether of their validity or reliability tend to assume that nothing can be done about their design. is prevents a debate about how tests can be designed to have a positive eﬀect on learning and cognitive development. Any system of testing that beneﬁts learning and achieves the goals we wish to achieve will inevitably be multiple-strategy in its approach. A good exam- ple of that approach is the “Advanced” level examination in Engineering Science set by the Joint Matriculation Board in the 1970s and 1980s in England [4]. A multiple-strategy approach to assessment inevitably necessitates a multiple-strategy ap- proach to instruction, learning and development. ere is no doubt that the ways in which stu- dents are assessed and taught contribute to what John Henry Newman called the genius loci or spirit of the place. 95 When Newman founded the Catholic University of Ireland he was much concerned with the genius loci of the institution and in one of his discourses on e Idea of a University he con- trasted a residential university with one that relied mainly on examinations (at the time the Uni- versity of London). He said, “when a multitude of young men, keen, open-hearted, sympathetic and observant, as young men are, come together and freely mix with each other, they are sure to learn one from another, even if there be no one to teach them; the conversation of all is a series of lectures to each, and they gain for themselves new ideas and views, fresh matter of thought and distinct principles for judging and acting, day by day. An infant has to learn the meaning of information which its senses convey to it, and this seems to be its employment. It fancies all that the eye presents to it to be close to it, till it actually learns to the contrary and thus by practice does it ascertain the relations and uses of those ﬁrst elements of knowledge which are necessary for its animal existence. A parallel teaching is necessary for our social being, and it is secured by a large school or college; and this eﬀect may fairly be called in its own department an enlargement of mind. It is seeing the world on a small ﬁeld with little trouble; for the pupils or students come from very diﬀerent places, and with widely diﬀerent notions, and there is much to generalize, much to adjust, much to eliminate, there are interrelations to be deﬁned, and conventional rules to be established, by which the whole assemblage is moulded together, and gains one tone and one character” [5]. Newman believed that a university’s generation of the genius loci depended as much on the students as it did on anyone else. e importance of learning from peers could not be underestimated hence the signiﬁcance he attached to small halls of residence. We in academia tend not to appreciate the role of peer group learning in helping students to understand our subjects. It is through such learning that students begin to understand themselves as agents and how they are interdependent. It is here they learn the value of community and the problems and practice of living in a community. One thing is clear the tutor can no longer be the oppressor. Tutors have to be agents that guide; mentors that co-learn for this is what a learning community is. And, what does research tell us in the second decade of the 21st century? It says, “[for] intellectual development (including critical thinking), the breadth of student involvement in the intellectual and social experiences of college, rather than any particular type of involvement mat- ters most”[...] “e student—peer contacts that matter most appear to be those that expose the student to diverse racial, cultural, social, value and intellectual perspectives. at is, students de- rive the greatest developmental beneﬁts from engagement in peer networks that expose them to individuals diﬀerent from themselves...interactions with diverse peers have modest but consis- tently positive impacts on knowledge acquisition, dimensions of cognitive development such as critical thinking and complexity of thought, principles moral reasoning, and self-rated job skills after college.” So wrote Pascarella and Terenzini in volume 2 of their masterful study of the aﬀects that college has on American students [6, p. 615]. is same research tells us that college education does have an impact on students. ank- fully students do develop in higher education and beyond: at the same time it is diﬃcult to deny 96 10. CHANGING US: CHANGING SOCIETY that universities take very little notice of student development in planning courses. is is not to say that it cannot be done. Back in the early 1980s the Colorado School of Mines (CSM) de- signed an engineering program to meet the requirements of a theory of student development put forward by William Perry based on his studies of students whom he counseled at Harvard. It was taken up by Dick Culver of CSM who with J. T. Hackos showed in Engineering Education [7] how its application led to a complete rethinking of the engineering curriculum. Instead of discrete units that were not necessarily brought together in the students mind it required a curriculum that might be best described as being more holistic (my term). It was a tree with branches rather than a set of discrete courses. Up to that time much thinking about pupil/student development had been conditioned by Piaget’s idea of developmental stages. Put simplistically, part of Piaget’s argument was that children move through orderly stages of development [8]. e ﬁrst stage is from birth to about one-and-a-half years. is is the development of sensorimotor intelligence. e second major stage is called the period of representative intelligence and concrete operations which takes the child up to 11 or 12 years. Finally, the child moves into a stage of formal operations. It is this stage that is of interest to those working in higher education for the child is now able to undertake abstract thinking, to hypothesize, deduct, experiment and theorize. ese are, of course, the skills necessary for study in higher education. us, there was some concern when some studies reported that many students who were in higher education were not at the level of formal operations. Be that as it may, and not withstanding substantial criticisms of Piaget’s theories, the idea of development is grounded in the literature and there are a number of equally interesting theories of development such as those of Jerome Bruner [9]. e point to be made here is that the stage of formal operations seems to imply that it is the end of development. Perry’s post-Piagetian theory of intellectual development challenges that view. William Perry argued that the organization of the curriculum and teaching discourages students from developing the higher level thinking skills that are expected of them [10]. In en- gineering we might express the goal as being able to deal with fuzzy problems rather than single solutions. One reason for this is that we collude in training students to solve problems that have single right answers and while we may be able to set fuzzy or wicked problems we ﬁnd them diﬃ- cult to score because there may not be a right answer. “Challenger” set management and engineers a fuzzy problem. Perry presented a post-Piagetian theory of development of nine stages (Exhibit 10.1). He held that the attitudes we hold and the concepts and values with which they are associated de- pend on the stage of cognitive and ethical development we are at. ey relate to curriculum and instruction in so far as together they either reinforce the stage we are at or help us move forward to another stage. Perry argued that much teaching tends to reinforce the earlier stages and inhibit such development. Perry argues that in these ﬁrst stages students come to university with the ex- pectation that they will be told the truth; that is, what is right and what is wrong. Subject-based knowledge is right or wrong, or true or false. us, in stage 1 all problems are seen to have right 97 Exhibit 10.1: e Perry Positions or Stages after Culver, Woods, and Fitch (1990) [12]. answers and authority must be followed. At this stage those who are rated the best teachers will be those who administer a received curriculum. By stage 3, however, it is apparent that the au- thorities are “seeking the right answers” and only in the future will we know the right answer. Perry calls these ﬁrst three stages “dualism.” From “dualism” the student moves into the phase of “scepticism” for now it is clear that not only does authority not have the right answers but everyone including the student has the right to hold his or her own opinions, and some of these can be supported by evidence. us, by stage 5 some answers are to be found that are better than others, and knowledge has to be considered in context. It is a stage of relativism. Among those who have tried to design engineering courses to meet the requirements of this theory are Marra and Palmer. ey suggested that the transition from stage 4 to 5 is the most signiﬁcant transition because the students “now accept knowledge is for the most part transient and contextual [...]. Students now accept themselves as one among many legitimate sources of knowledge and often forego their former view of instructors as absolute authorities” [11]. e student begins to see that good choices are possible and that commitments have to be entered into. ere are valid criticisms of this theory one of which is that those who use it as a basis for their teaching are as equally dogmatic as are those who teach by drill and encourage students to remain in the initial stages of development [13]. at criticism would not hold for those courses, like cooperative courses, which require a student to have some industrial experience before they Positions 1 and 2: DualismAll knowledge is known, and it is a collection of information. Right and wrong answers exist for everything. Teachers are responsible for giving information; students are responsible for reproduc-ing it.Position 3: Early multiplicityKnowledge includes methods for solving problems. There may be more than one right answer. Teachers help students learn how to learn. Students are responsible for understanding and apply-ing knowledge.Position 4: Late multiplicityUncertainty with respect to knowledge and diversity of opinion become legitimate. Teacher requires evidence to support opinions and design choices. Students learn how to think and analyze.Position 5: RelativismAll knowledge must be viewed in context. Teachers are consultants; students can synthesize and evaluate perspectives from different contexts.Positions 6–9: Commitment within relativismFor life to have meaning commitments must be made, taking into account that the world is a changing, relativistic place.98 10. CHANGING US: CHANGING SOCIETY undertake academic study. It was commonly said after the second-world war that students re- turning from the armed forces were more disciplined and motivated to study. In England many students are encouraged to obtain some kind of work or voluntary experience before they embark on third-level study. ey call it a “gap” year. ere are other developmental theories. Personally, I think that King and Kitchener’s the- ory of reﬂective judgement is to be preferred to Perry’s model [14]. But what seems to me to be inescapable is that we continue to develop while we are in college, and research in adult learning would suggest that we continue to develop with age. By 1990, Alexander and Langer had pub- lished Higher Stages in Human Development; Perspectives on Adult Growth [15], and in 2006 Ca- role Hoare was able to produce a substantial Handbook of Adult Development and Learning [16]. e chapters in both books support the view that development is a life-long process. Clearly, there is a need to bring the research on learning in higher education into this frame if we are to understand how to redesign the system of higher education to support the life-long learning that social-technical changes in our society are demanding, and, particularly if we are to understand how interrelated work and study can contribute to the evolution of professional competence. Garrett McAuliﬀe who has reviewed research in this area writes of Torbett’s strategist frame of professional development “for those who would be highly competent experts and leaders, learn- ing should lead them toward strategist thinking with its emphasis on dialogue, experience and self-reﬂection. Instead, however, current educational and in-service training programs teach to the technician worldview, with its ideological tunnel vision and disinterest in stepping outside of professional standards. us, such professionals remain embedded in the usual practices of their own ﬁelds and are less attuned to the situational contextual dynamics that professionals must ac- count for in good portion” [17]. He argues that expertise depends as much on the ability of “how to know” as it does on “what to know.” So a key question for educators who want their students to develop expertise is to what extent do they help their students acquire the skill of “learning -how-to-learn?” When I was completing my 2005 book, Don Evans of Arizona State University who pio- neered the use of Concept Inventories in engineering education asked me why it was that there was so much resistance in engineering education to the use of educational strategies that were aﬃrmed by considerable research? Dr. Mani Mina assures me ten years later that the situation has not changed. We have, for example, known about the relationship between learning-how- to-learn (reﬂective capability) and expertise for years, but has much been done about it? At the time the one answer that I did not give Dr. Evans was “fear of the unknown.” But this is surely the heart of the matter! Very little training is given to engineering educators or, for that matter, educators in higher education more generally, neither is engineering education seen as a matter for professional development. In these circumstances no one is prepared for the “unknown.” Perhaps if we grasped, as Trevelyan has pointed out, that many of the professional skills can be learned through developing skill in teaching. He argues that students should be given the opportunity to teach which suggests that engineering educators ought also to learn how to 99 teach [18]. To be fair there are many teaching and learning centers for higher education through- out the world [19] but especially in the U.S., and Utschig, Schaefer, and Visco recently proposed a competency based program for teaching and learning [20]. When she was at Harvard, K. Patricia Cross argued that the way forward was to encour- age educators to realize that their classrooms were laboratories for research [21].ey could do in the classroom what they did when engaged in their engineering research. Others, like myself, who had responsibility for the training of teachers argued that the way to professionalize teach- ing was to train teachers to be researchers of their own instruction. Such evaluation renders the professional accountable; such evaluation induces another dimension to the motivation to teach. At the level of professional development I used the same idea to promote the idea of instruc- tional leadership [22]. I have described what is meant by this in engineering education in detail in the extended introduction to my 2005 book. Brieﬂy, departments (schools) would provide an instructional leader from among their number who would be available to oﬀer advice, update and encourage faculty to take a live interest in educational developments. Overall, there is no substi- tute for the development of mind that accepts that education is a professional activity just as much as engineering is, so that steps are taken to acquire the knowledge that identiﬁes that profession. at knowledge has to encompass the curriculum, how and what should be taught, in particular the role of ethics and other liberal arts subjects in that curriculum; and, how it should be assessed and credentialed, how it should be learnt, and the role of instruction. NOTES [1] For example, the importance of the aﬀective domain in the learning and practice of math- ematics by engineers has been demonstrated by Goold, E. and F. Devitt. (2013). Mathe- matics in engineering practice: tacit trumps the tangible inWilliams, B., Figueiredo, J. and J. Trevelyan (Eds.) Engineering in Practice in a Global Context. Understanding the Technical and Social. London, CRC Press/Taylor and Francis. 93 [2] Eggleston, J. (1977). e Sociology of the School Curriculum. London, Routledge. Suggests three perspectives on the curriculum, the received, the reﬂexive and the restructuring. e received perspective arises from the belief that there is a ﬁxed body of knowledge which has to be handed down from generation. It is structured by disciplines which we call subjects. In certain societies some subjects acquire more prestige than others. In Britain and Ireland, profoundly inﬂuenced by the liberal education movement of the nineteenth century, the “pure” is preferred to the “applied,” “theoretical” to “practical” and “university” to “tech- nical college.” Support for a disciplines approach to education is to be found in the work of Paul Hirst. (1975—Knowledge and the Curriculum, London, Routledge). e reﬂexive perspective is in contrast to the received perspective and ﬁnds it s base in the sociology of knowledge presented by such theorists as P. Berger and T. Luckman (1966—e Social Construction of Reality. London, Allen Lane). Knowledge is socially constructed and de- 100 10. CHANGING US: CHANGING SOCIETY pends on our experience and environment. In this situation teachers and students should deﬁne a curriculum which is real to them in their social context. In this sense the cur- riculum should be negotiated and worked out to meet the individual needs of students. Eggleston suggested a restructuring perspective that brings together these two paradigms as two related modes of understanding both the realities of knowledge in the curriculum and the possibilities of change therein. His model shows how in the received curriculum the dominance of the teacher perceptions and the way in which these perceptions can be inﬂuenced by the students to restructure the curriculum. It brings together the components of knowledge acquisition and knowledge making. 94 [3] See Ch. 7, Curriculum change and changing the curriculum, in Heywood, J. (2005). Engi- neering Education. Research and Development in Curriculum and Instruction. Hoboken, NJ. IEEE/Wiley. 94 [4] Heywood, J., Carter, G., and D. T. Kelly. (2007). Engineering Science A Level in the UK. A Case Study in the balanced assessment of student learning. Educational policies and edu- cational scholarship. Proc. Frontiers in Education Conference. S4F, pp. 9–12, (ASEE/IEEE) (See Exhibit 10.2). 94, 101 [5] Newman, J. H. (1852/1923). e Idea of a University: Deﬁned and Illustrated. London, Longmans p. 164. 95 [6] Pascarella, E. T and P. T. Terenzini. (2005). How College Aﬀects Students Vol. 2. A ird Decade of Research. Hoboken, NJ, John Wiley. 95 [7] Culver, R. S. and J. T. Hackos, (1982). Perry’s model of intellectual development. Engi- neering Education, 73(2), pp. 221–226. 96 [8] Piaget’s theory argues that children move through orderly stages of development. e ﬁrst stage is from birth to about one-and-a-half years. is is the development of sensorimotor intelligence. Within this stage, there are six sub-stages. Each of these is a problem solving activity involving its own logic. us, after about 18 months the child is able to solve a detour problem by going round a barrier even if this means departing from the original goal for a short time. e child can infer causes from the observation of eﬀects and begins to predict eﬀects from observing causes; the child also begins to invent applications of something previously learned. 96 e second major stage of development is called the period of representative intelligence and concrete operations. is takes the child up to 11 or 12 years. e ﬁrst part of this period is between two and seven and is called the preoperational stage. e second phase is that of concrete operations. It is in this stage that the child learns conservation. For example, the size-weight illusion is resolved. Children take this problem in relation to matter, weight, and volume. Piaget claims that the order of such learning is invariable. 101 Exhibit 10.2: Table illustrates the multiple strategy approach to assessment adopted for the assessment of engineering science [4]. Learning by doing is the essence of concrete operations. In this period children learn to seriate, classify, and establish correspondence. e ﬁnal period when the child moves from the middle childhood to adolescence is that of formal operations. Now the child is able to undertake abstract thinking, to hypothesize and deduct experiment and theorize. It is the stage of in-built maturity. is summary does less than justice to Piaget’s work. I have not related it to the more general theory of development or how the change from one stage to another is made (see below). e theory has been criticized and of importance to this text are the criticisms of Sub Test/AssessmentObjective and Technique of Assessment and Duration of Tests% of Total Score on which Re-ported Grade is BasedWriten Paper IKnowledge and short-chain problem solving (1 hour, 40 ob-jective items)13.5Written Paper IIAComprehension exercise. Can-didates read article in a journal and answer questions on it ( 1 hour)13.5Written Paper IIBProject planning and design ex-ercise (1 hour)13.5Written Paper IIIAApplications of engineering sci-ence (application and analysis) (1½ hours. 6 out of 9 questions)20.0Written Paper IIIBApplications of Engineering Science (1½ hours. 3 out of 6 questions)20.0Coursework 1Two Experimental Investiga-tions (written report)Coursework 2Individual project (50 hours laboratory time written report)20.0** Coursework assessed by the student’s teacher and moderated by the examiners. 20% of the final score was given for all coursework combined.102 10. CHANGING US: CHANGING SOCIETY those who argue that young children can deal with the fundamental problems of philoso- phy in their own language (e.g., Matthews, G. B. (1980). Philosophy and the Young Child, Cambridge, Harvard University Press. A feature of Piaget’s theory is the attempt to relate it to the epistemological processes which go on in the child’s mind as he or she learns by solving problems. Piaget’s often quoted example is of the way a child uses clay. From experimenting with clay rolled into a sausage shape, the child learns the following. 1. ere is less clay in a thin sausage and more in a long sausage. 2. A sausage can be long and thin. 3. If a sausage can become longer, it can become shorter. 4. Length and thickness can compensate for each other. e transition between 2 (conﬁguration) and 3 (transformation is an example of equilibra- tion; the children learn by their actions on the environment. Level 4 is called conservation by Piaget because a transformation does not change the quality of the matter. [9] In Bruner’s theory of cognitive development three modes of representation follow in se- quence. e ﬁrst is called enactive. Bruner notes that conditioning and stimulus-response learning are appropriate to this mode of learning: it is learning through action without words. e second stage, which is one of mental representation, is called iconic. In this stage the child uses concrete visual imagery. e ﬁnal stage of representation is symbolic. Because children are able to translate experience into language and think with language, they are able to develop abstract images. It is arguable that mature learners go through such stages when solving problems. 96 Bruner holds the belief that children can be helped to learn at the level of the most kind of thinking in which they engage. at is a teacher can help a child to undertake more sophisticated kinds of thought process. us, Bruner would argue that we should teach readiness and not have to wait for it as in Piaget’s theory. It is this theory that leads some to say that a child can be taught anything in a language appropriate to him/her at the time and encourages books about “relativity” for children. [10] Perry, W. B. (1970). Forms of Intellectual and Ethical Development in the College Years. New York, Holt, Reinhardt and Winston. 96 [11] Marra, R and B. Palmer (1999). Encouraging intellectual growth: senior engineering pro- ﬁles. Proc. Frontiers in Education Conference (IEEE), 2, 12C1 pp. 1–6. 97 [12] Culver, R. S., Woods, D. and P. Fitch (1990) Gaining professional expertise through design activities. Engineering Education. 80(5), pp. 533–536. 97 [13] loc. cit. note 3, Ch. 6, p. 154. 97 103 [14] King, P. M. and K. S. Kitchener. (1994). Developing Reﬂective Judgement. San Fransisco, Jossey Bass. 98 e diﬀerences between King and Kitchener’s model and Perry’s model are seen immedi- ately by comparing the stages of each model as shown in Exhibits 10.1 and 10.3. Clearly, the earlier stages owe much to Perry. Some critics think that the ﬁrst three stages are the same as Perry’s. e idea of “reﬂective judgement” was inﬂuenced by Dewey. “We now think of reﬂective judgements as beginning with an awareness of uncertainty. Such judgements involve integration and evaluating data, relating those data to theory and well-informed opinions, and ultimately creating a solution to the problem that can be defended as reasonable and plausible.” Exhibit 10.3: Stages of the King and Kitchener reﬂective judgment model (adapted). King and Kitchener noted that their investigations were related to what other researchers were doing in the areas of critical thinking and intelligence, and they found that while some aspects of the deﬁnitions overlapped, other aspects were quite distinct. Like Perry, the model assumes that as individuals develop, so they become more able to evaluate the claims of knowledge, and both models advocate and support their points of view about controversial issues. “e ability to make reﬂective judgements is the ultimate out- come of this progression.” To arrive at this destination the learner passes through seven stages, each of which has its own assumptions and logic. e stages develop from the relatively simple to the relatively complex, each with a diﬀerent strategy for solving ill-structured StageDescriptionStage 1Knowing is limited to single concrete observations. What a person observes is true.Stage 2Two categories for knowing: right answers and wrong answers. Good authorities have knowledge; bad authorities lack knowledge.Stage 3In some areas, knowledge is certain and authorities that have that knowledge. In other areas, knowledge is temporarily uncertain. Only personal beliefs can be known.Stage 4Concept that knowledge is unknown in several specifi c cases leads to the abstract general-ization that knowledge is uncertain.Stage 5Knowledge is uncertain and must be understood within a context; thus justifi cation is context specifi c.Stage 6Knowledge is uncertain but constructed by comparing evidence and opinion of diff erent sides of an issue or across contexts.Stage 7Knowledge is the outcome of a process of reasonable inquiry. Th is view is equivalent to a general principle that is consistent across domains.104 10. CHANGING US: CHANGING SOCIETY problems. us each stage has its own view of knowledge and concept justiﬁcation. Re- ﬂective thinking takes place in stages 6 and 7. “True reﬂective thinking pre-supposes that individuals hold epistemic assumptions that allow them to understand and accept real uncer- tainty.” It is only when they engage in ill-structured or novel problems that they engage in reﬂective thinking as deﬁned by King and Kitchener. ey found that their model complemented another model due to Fischer. He argued that individuals will only operate at their optimal levels when they practice skills in familiar domains and receive environmental support for high level performance. ere will be lots of “Eureka” moments en-route. Unlike stage theory, which holds that all children pass through the same stages of development Fischer’s skill theory argues that the steps which individuals take to attain a skill vary considerably as between one individual and the next, as a function of the environment and the individual. Because of these variations it will be diﬃcult to ﬁnd any two children who spontaneously follow the same steps in any domain. At the same time the theory states that irrespective of the path taken all skills pass through the same developmental levels. All skill acquisitions involve the same group of transfor- mation rules. e position taken by Fischer and his colleagues is similar to that taken by information-processing theorists namely that the “same fundamental acquisition processes occur in development, learning and problem solving at all ages.” Instruction and assessment should, therefore, be designed to take account of these diﬀerent needs. is theory has considerable implications for the design of modular (credit-unit) curriculum systems and the pacing of assessment and learning within them. In the Reﬂective Judgment model a spurt marks the emergence of a new stage. e skill levels in the Fischer model correspond directly to the stages of the Reﬂective Judgment Model. King and Kitchener argued that the decisions students make when they are in relativistic frames of reference should reﬂect a level of cognitive development beyond rel- ativism. In the Perry model, the student remains within the relativistic frame and has to make an act of faith in reaching a commitment. e purpose of the Reﬂective Judgment model is to deal with the form and nature of judgements made in the relativistic frame- work. Individuals, it is held, hold epistemological positions beyond relativism. Whatever else one may say such a position would seem to be more satisfying than Perry’s. King and Kitchener had much to say about teaching in higher education and they take a broad of view of who may be a teacher and what teaching is. According to the Reﬂective Judgment Interview, ﬁrst-year students in the United States lie in the range stage 3 to stage 4. Seniors were found to be around stage 5. ey argue that many seniors are at a loss when they are asked to defend their answers to ill-structured problems. erefore, if reﬂective thinking is to be developed, teachers should do the following. • Show respect for students regardless of the developmental levels they may exhibit. 105 • Understand that students diﬀer in the assumptions they make about knowledge. • Familiarize students with ill-structured problems within the teacher’s area of exper- tise. • Create multiple opportunities for students to examine diﬀerent points of view. • Informally assess (i.e., from student journals, assignments etc.) assumptions about knowledge and how beliefs may be justiﬁed. • Acknowledge that students work within a developmental range of stages and set ex- pectations accordingly; challenge students to engage in new ways of thinking while providing them with support; and recognize that students diﬀer both in their per- ceptions of ill-structured problems and their responses to particular learning environ- ments. • Share with one another what they do and what they expect to achieve. King and Kitchener do not, however, believe there is one best way of teaching reﬂective thinking. e diﬀerences between stage 3 and stage 6 from a teaching perspective are shown in Exhibit 10.4. It will be appreciated that since these descriptions could apply at any level of education they would have to be developed to describe the requirements of a particular level (e.g., year on course, course level). It is clear that if students in schools are to develop critical thinking they will have to tackle ill-structured problems, and this has implications for assessment. King and Kitchener designed an instrument called e Reﬂective Judgment Interview (RJI to detect the stage at which a student is. e interview is structured with standard probe questions, each with a speciﬁc purpose. us, two questions, that will clearly elicit a level of development that are of direct relevance to today’s media governed society are: (1) How is it possible that experts in the ﬁeld have such diﬀerent views about the subject? and (2) How is it possible that experts in the ﬁeld should disagree about the subject? While it is not the intention to examine the psychometric properties of this instrument it is of some interest since the questions may help with the design of assessment. ere is also one important comment from one of the analysts to the eﬀect that diﬀerences between the samples were more pronounced at lower levels of educational attainment than at the higher levels. Wood who undertook this analysis thought that this was consistent with the view that performance on the RJI is dependent on verbal ability (which is a necessary, but not suﬃcient condition for high scores). Once again the need for a high level of verbal ability to think critically or reﬂectively is highlighted. In an earlier paper Kitchener had pointed out that no single instructional or curricular experience over a limited period is likely to have an impact on development that a carefully 106 10. CHANGING US: CHANGING SOCIETY Exhibit 10.4: Promoting reﬂective thinking in the King and Kitchener model—stages 3 and 6. Rea- soning. (Adapted from King and Kitchener, 1994. In their description (pp. 250–254) they also give for each stage a list of diﬃcult tasks from the perspective of the particular stage, a sample of developmental assignments, and suggestions for developmental support for instructional goals). constructed set of cumulative experiences over a long period of time is likely to have. e implication for teachers is that in planning the curriculum they have to work as a team and share with one another what they do and what they expect to achieve. ere is unlikely to be one best way of teaching reﬂective thinking. But there is a more profound implication for the system. If reﬂective thinking is to be developed and pupils are to be prepared for life and work in which higher education is included then the cumulative experiences should extend from primary through post-primary to third level. What better than a program of the type developed by Lipman (Philosophy for Young Children program). Stage 3Characteristic assumptions of stage 3: ReasoningKnowledge is absolutely certain in some areas and temporarily uncertain in other areas.Beliefs are justified according to the word of an authority in areas of certainty and according to what “feels right” in areas of uncertainty.Evidence can neither be evaluated nor used to reason to conclusions.Opinions and beliefs cannot be distinguished from factual evidence.Instructional goals for studentsLearn to use evidence in reasoning to a point of view.Learn to view their own experience as one potential source of information but not as the only valid source of information.Stage 6Promoting reflective thinking.Characteristic assumptions of Stage 6: ReasoningKnowledge is uncertain and must be understood in relationship to context and evidence.Some points of view may be tentatively judged as better than others.Evidence on different points of view can be compared and evaluated as a basis for justification.Instructional goals for studentsLearn to construct one’s own point of view and to see that point of view as open to re-evaluation and revision in the light of new evidence.Learn that though knowledge must be constructed, strong conclusions are epistemologically justified.107 is statement is copied from Heywood, J. (2009). Instructional and Curriculum Leader- ship. Towards Inquiry Oriented Schools. National Association of Principals and Deputies/ Original Writing, Dublin, pp. 358–352. [15] Alexander, C. N. and E. J. Langer (Eds.) (1991). Higher Stages of Human Development. New York, Oxford University Press. 98 [16] Hoare, C. (2006). (Ed.) Handbook of Adult Development and Learning. New York, Oxford University Press. 98 [17] McAuliﬀe, G. (2006). e evolution of professional competence. Ch. 21 in C. Hoare, (Ed.), Handbook of Adult Development and Learning. New York, Oxford University Press. McAuliﬀe summarises research on the linkage between professional competence and adult development including summaries of work by Donald Schön (1993—e Reﬂective Prac- titioner. San Fransico Jossey Bass.) and its origins in Argyris, C. and D. S. Schön (1978). Organizational Learning. Reading, MA, Addison Wesley; Kegan’s Fourth and Fifth orders of consciousness and professional competence (Keegan, R. (1994—In Over Our heads. e Mental Demands of Modern Life, Cambridge, MA, Harvard University Press), and Torbert’s frames of professional development (Torbert, W. R. (1994) Cultivating post-formal adult development: Higher Stages and contrasting interventions. In M. Miller and S. Cook- Greuter (Eds.), Transcendence and Mature ought in Adulthood: the Further Reaches of Adult Development (pp. 181–203. Lanham, MD, Rowman and Littleﬁeld). 98 e reference in the main text is to Torbert’s taxonomy of developmental positions for pro- fessionals especially managers which comprises six frames. ere is a similarity with the Perry model in that they move from stages of concreteness and conformity to capability in abstraction and a willingness to tolerate ambiguity. Torbert’s ﬁrst frame is called “oppor- tunistic.” To simplify, the current way of knowing of the opportunistic is the only way to view the world to McAuliﬀe (p. 487) “ey experience others without empathy, as objects to be manipulated” and “tend to use force and deception to reach short-term ends.” One positive aspect is that their self interest can force them to become entrepreneurs (my inter- pretation). e second frame is called “Diplomatic.” To simplify, professionals operating in this frame ﬁt into Belbin’s roles (see Journey 5) quite nicely. ey are “company men” who have loyalty to the rules of the organization but they ﬁnd it diﬃcult to make diﬃcult decisions. e third frame is called “technician” and is the mode referred to in the text. To cite McAuliﬀe “Technician professionals are narrowly focused on eﬃcient methods and the internal logic of objective standards. In the process technicians fail to see the larger systems of which they are part, for they are enamoured of the consequence of their own doctrines. To them, there is no room for alternate explanations. eir logic is the only logic. Fisher and Torbert propose that the technician’s embrace of “standards” can be inspiring for co-workers. is position is especially important in explaining professional behaviour, as it is the largest single group of professionals” (p. 489). 108 10. CHANGING US: CHANGING SOCIETY e other frames are “Achiever” which is held to be a wider frame that of the “techni- cian.” ey are guided by the goals of the ﬁeld beyond their own career expectations and can provide leadership. McAuliﬀe does not mention McClelland’s achievement motiva- tion in his discussion of this frame but it clearly has a bearing. He points to the negative dimension that achievers are likely to pursue their agenda to the exclusion of other goals and alternatives although being open to feedback. ey can be open to learning. e next frame is the “strategist.” McAuliﬀe uses a comment by a manager in one of Torbert’s pa- pers to describing this frame as moving from “having very explicit goals and timetables [and] a structured organization to...the collaborative process [which] focuses on inquiry, constructing shared meanings from experience and building consensus through responsible interaction” (p. 401). [18] Trevelyan, J. (2010). Engineering students need to learn to teach. Proc. Frontiers in Edu- cation Conference, F3H-1 to 6. 99 [19] For example with reference to Israel see Muller, O. and V. Dangur. (2012). Integrating a college of engineering teaching and learning center into a leading position in the institu- tion. Proc. Frontiers in Education Conference, pp. 429–430. 99 [20] Utschig, T. T. and D. Schaefer. (2012). A proposed teaching and learning curriculum for COMPLEETE based on current national trends. Proc. Frontiers in Education Conference, pp. 423–428, (ASEE/IEEE). 99 [21] Cross, K. P. (1986). A proposal to improve teaching. (AAHE), American Association for Higher Education Bulletin), Bulletin, September, pp. 9–15. 99 [22] Heywood, J. (2009). Instructional and Curriculum Leadership. Towards Inquiry Oriented Schools. Dublin, National Association of Principals and Deputies/Original Writing. 99 J O U R N E Y 11 109 Journey’s End: A New Beginning? RECOLLECTION When Dr. Mina invited me to undertake these journeys he asked me to bring you on a series of journeys that would help you and I reﬂect on who, and what, we are as engineers and educators within a society that is being increasingly complex. We were inviting you to philosophize with us and this we did as is evident from how the discussions inﬂuenced the ﬁnal text and structure of the journeys. ese discussions were undertaken within the framework of a model of the engineering processes engaged in the production of a technology (or technological product). Presented in the ﬁrst journey in the form of a three-legged stool it showed quite clearly that engineering decisions are based on value decisions and as such have a philosophical dimension. e outcomes of these decisions, as illustrated by the seat of the stool, produce artifacts and ideas that can have a profound inﬂuence on society whether deliberately or unforeseen. It is incumbent, therefore, that engineers have some idea of how society and technology interact and are able to make predictions about the possible impact of the artefacts and ideas they design. Commonly, we call this the study of “society and technology.” ose who engage in it often do so in interdisciplinary teams. Although we did not dwell in any great detail on the nature of inter-disciplinarity within the engineering curriculum, it is ever present in these discussions because engineering problems are often very complex and rely on the contributions of more than one discipline. e process of producing a product is complex and as we saw in Journey 5 the way engineers are organized in groups contributes to the success or failure of the organization. Competence in understanding people and organizations and how they interact with each other and in organizations is a key skill that should be possessed by engineers. Our early journeys explored the characteristics of that skill. It was argued that the study of ethics had to be much more than the study of codes of practice for we all have moral purpose and this purpose is a source of motivation. Bowen’s as- pirational ethics for engineers was taken as an example of how the subject might be developed. But it was also argued that such developments should take place in a more general framework where individuals (students) reﬂect on their own philosophies and the impact that they have on their philosophy of engineering. Finally, the present problems of society were examined and it was argued that the nature of the ﬁrm required it to be re-examined in the light of the common- good. Views about stake-holding need to be changed; at the same time, organizations have to be 110 11. JOURNEY’S END: A NEW BEGINNING? allowed to achieve. e common good has to come before proﬁt which is to be used in the service of the common good. ese thoughts were provoked by substantial changes in the workforce not least the redundancy being experienced by many middle aged engineers, and the view that fact has replaced the platitude that many people in the workforce may have as many as three or four dif- ferent careers in the much longer lifetimes they will live. is has profound consequences for the system of education and training, not least of which is the provision of a culture in which persons can move across labour arenas. It is with these consequences that this ﬁnal journey is concerned. HIGHER EDUCATION—THE NEXT “BUBBLE?” e time is opportune for such discussion because there is a strong support for the thesis that higher education may become the next bubble. In any case it would seem to be in crisis! I take up the argument where I left it in Journey 10. at Journey was devoted to a discussion of the impor- tance of how the structure of the peer-group might inﬂuence learning and personal development. It was illustrated by Newman’s famous assertion that he would prefer that type of education that simply brought people together in a hall (college) to that where a student simply sat an exami- nation. It is a view that to a certain extent I share. Where I diﬀer, and I imagine I am not alone, is with the view that what emerges from such discussion is necessarily rational and reasonable. It is quite clear that it would be possible for some groups to create a terrorist cell. After all, it is only 50 or so years since we discovered that a Soviet spy ring had been created at the University of Cambridge. Five undergraduates and one tutor, all of Trinity College, were recruited by the Soviet Spy Agency and worked at the same time for the British security agency MI5 [1]. In the U.S. Alexander Astin’s longitudinal studies of students in general education programs in the U.S. showed the signiﬁcance of the peer group and that students were likely to take on the views of the dominant members of the group [2]. at said it is clear that Newman felt that the university had a signiﬁcant role to play which was to inform student thinking and that students would bring the range of that thinking to their private discussions, a position that is entirely consistent with his epistemology. Otherwise, why did he bother with the rest of his discourses? A university’s task is to throw out a series of challenges to students in order to help them think and this means that it must promote a view of knowledge that is universal. But that is precisely what the modern university does not do. I shall argue that the failure to promote a truly liberal education at the expense of specialization is a disservice to students and more generally to society at large for many students, although not all may ﬁnd their career mobility restricted. HIGHER EDUCATION, THE ECONOMY, AND MOBILITY In the British Isles Newman’s view and that of the Oxford dons of the university curriculum was rejected in favor of a utilitarian specialist education the idea of which had been promoted in Scotland. Students come to university to study a speciﬁc discipline be it English literature, history, physics, or engineering. As it has developed so governments in collusion with the univer- 111 sities have taken the view that the purpose of higher education is utilitarian or economic growth. Consequently, support has been much greater for scientiﬁc and technological subjects than it has for subjects in the arts (humanities). In parallel with the UK government’s belief in the eco- nomic value of higher education it has considerably expanded the number of full-time students in university education and accompanied it by a large increase in the number of institutions given university status. ere is a corresponding search each year by new graduates for jobs thought to be worthy of a university education. Newspaper reports suggest that many are unlucky. At the same time the UK government has found that the costs of higher education are not inconsiderable for which reason it has followed the American practice of charging fees for attendance at universities in England, Northern Ireland, and Wales while at the same time it encourages students to take out loans. British newspaper reports have suggested that a student will end his/her university study owing £45,000 as compared with an American student who will owe about £15,000. Given that earnings among the middle classes have ﬂat-lined in recent years this can place an enormous burden on students and their families. Could it be that the next bubble will be higher education? And what eﬀect would that have on social mobility? If a bubble occurs in higher education it is likely that students and parents will begin to question the value of higher education? If they do, and numbers begin to fall, where will that leave some institutions of higher education that do not have the reserves to maintain themselves? Second, in the UK a report was published (October 17, 2013) of a study sponsored by the govern- ment and undertaken by a former minister Alan Milburn (Labour) indicated a total lack of social mobility. e newspapers made much of the fact that many children being born to the middle classes would not be as well-oﬀ as their parents. is ﬁts in well with American data especially that of Clifton which suggests the most important crisis facing nations will be shortage of good jobs [3]. Clearly, higher education can only prosper if there is growth and with that growth an increase in the wealth of the middle classes. Every culture diﬀers in how the social eﬀects of educational policy are played out. For example, there is a paradox in Britain which suggests that on the one hand there is a problem of up-skilling the working classes but on the other hand if this is done it can restrict social mobility. More generally, it may be argued that specialization generally operates in that direction. It creates rigidities rather than ﬂexibilities. T. H. Marshall, a distinguished British sociologist many years ago argued that foundation of many occupational groups that claim professional status is the specialized technique, and “it is the multiplication of these techniques that makes possible the spread of these organizations.” He wrote: “It is important to notice the eﬀects of these changes on social mobility; an organized profession admits recruits by means of an impartial test of their knowledge and ability. In theory they are selected on merit, but it is merit of a particular kind [...] A narrow road leads into the profession through certain educational institutions. How far this favors social mobility depends on whether these institutions are open to the masses, so that merit can win recognition in all classes.” Presumably thinking of the British system of education he continued: “But the chance 112 11. JOURNEY’S END: A NEW BEGINNING? to move comes early, during school days. Once it has been missed and a career has been started at a non-professional level the whole system of formal qualiﬁcations makes movement at a later- stage well-nigh impossible.” And later [...] “But many of these new semi-professions are really subordinate grades placed in the middle of the hierarchy of the modern business organization. e educational ladder leads into them but there is no ladder leading out” [4]. In these circumstances it would seem that a general education through high school and into university is the best preparation for the career paths that individuals are likely to have to pursue in the future. Specialization should be postponed for as long as possible. But then industry, it would seem, is looking for the person with a specialized technique which in a few years will become redundant. Where does that person go then? Translate this to other non-middle class groups who have diﬃculty with general education and are encouraged to study for a trade, for some, especially the more able, the educational sub-system could not be more perverse [5]. e complexity of the issues raised here should not be underestimated or the diﬃculties of ﬁnding a solution under-emphasized. But this search needs to be tempered with the understanding that a higher education undertaken for an economic purpose alone does not serve the common good. Its overall aim has to be the preparation of individuals for life, and that is a multi dimensional task that begins with an eﬀective liberal education which seems to contradict the view that some people are better suited to an academic education and others to a vocational education. GENERAL VS. LIBERAL VS. VOCATIONAL EDUCATION e intention of schooling is to provide a good general education. By this is meant that students should study a range of subjects that include disciplines from the sciences to, humanities and languages. Technical subjects have not for the most part been considered key to this education in spite of the contribution they can make to certain mental and psycho-motor abilities [6]. While students acquire the basic “grammar” (to use Whitehead’s term) of subjects in high school (say from twelve years onwards) their study does not constitute a liberal education neither should it [7]. A general education is a condition for liberal education. e purpose of a liberal education diﬀers from that of general education in that it brings to our attention how the diﬀerent disciplines help us to understand who we are as persons and our place in the universe (nature). For this we have to have the breadth of knowledge that a general education gives, that is, we have to be literate in the sciences, technologies, arts and languages. But our object is to be able to see the relationships between subjects, one with another, in order to recombine that knowledge in a new synthesis. As we saw in Journey 2, Newman held that it is this recombination of knowledge that is the object of university education. If we are to understand the person it requires a breadth of knowledge that includes philosophy and theology. But it also includes technology which is an inherently vocational study. You cannot have a liberal education without the inclusion of the vocational. In the second journey I gave Newman’s illustration of how the diﬀerent subjects contribute to this search for understanding. Now in Exhibit 11.1 I 113 Exhibit 11.1: p. 175 MacIntyre, A. (2009). God, Philosophy, Universities. A History of the Catholic Tradition. London, Continuum. give MacIntyre’s modern illustration of the task and ask this question, what do we gain, from an understanding of engineering, and what do we gain from an understanding of medicine? Newman also gave a description of what the product of a liberal education would be able to do. It is shown in Exhibit 11.2. When I examined his famous description of the attributes derived from a university education I came to the conclusion that these were exactly what in- dustry sought. ese complaints did not relate to the knowledge obtained in courses but to the ability to work with others in a constrained situation in pursuit of the objectives of the ﬁrm. ey were what in the nineteen-nineties in the UK were called personal transferable skills. ey were commonly grouped into the four categories of Management and Organizing, Communication, Teamwork and Problem Solving (creativity) [8]. e UK Employment Department sponsored ﬁve year projects in most universities that had as their objectives the development of these skills, called “the skills of enterprise learning” within each department (school) of the participating uni- versity. No subject was singled out for special treatment; it was thought that all potential graduates would beneﬁt from such training. A working group of the department drew up a statement of four broad areas of learning that they thought would equip students for their working lives. Inspection of these areas (Exhibit 11.3) suggests that the persons described by Newman would be similarly equipped which suggests that there is no real conﬂict between the aims of a liberal education and those purported to emanate with employers. I wondered if employers would be able to cope with employees educated in this way! I also wondered how many engineering departments could say they achieved the goals implicit in this list with validity and justiﬁcation. Exhibit 11.4 might be judged by some to be the least liberal of the three statements. It is a group of recommendations made in 1989 that MIT should adopt. It is clear that it seeks a broadening of engineering ed- ucation and that the attitudes and skills that accompany a liberal education will be required if the graduates are to obtain senior positions in management. ere is an emphasis on practical “From the standpoint of physics human beings are composed of fundamental particles interacting in accordance with the probabilistic generalizations of quantum mechanics. From that of chemis-try we are the sites of chemical interactions, assemblages of elements and compounds. From that of biology we are multicellular organisms belonging to species each of which has its own evolu-tionary past. From that of historians we are intelligible only as emerging from long histories of social and economic transformations. From that of economists we are rational profit-maximizing makers of decisions. From that of psychology and sociology we shape and are shaped by our perceptions, and emotions, our social roles and institutions. And from that of students of the literature and the arts it is in the exercise of our various imaginative powers that we exhibit much that is distinctive about human beings. But how do all these relate to each other? In what does the unity of the human being consist? And how should the findings of each of these disciplines contribute to our understanding of ourselves and our place in nature?”114 11. JOURNEY’S END: A NEW BEGINNING? Exhibit 11.2: Cardinal Newman’s 1852 statement of the Aims of University Education. e Idea of a University. Deﬁned and Illustrated. pp. 177–178. 1923 impression. London, Longmans. problem solving that is not to be found in the REAL statement (Exhibit 11.3), and there is more emphasis on the “technical” as opposed to the “whole” person where as the direction of this text is that it is the attitudes and beliefs of the “whole” person that informs his “other” persons. Since then, during the last four or ﬁve years, Louis Bucciarelli—A Professor of Engineering and Tech- nology Studies at MIT has promoted, with considerable detail, the idea of a Bachelor of Arts In Engineering. A quite remarkable coincidence between the generic categories established by the Sheﬃeld study is to be found in a comparison of the skills that experts in intelligence and lay people con- sider to be the parameters of intelligent behavior (Exhibit 11.5). e similarities with Newman’s statement will be evident. Of them, all Newman’s statement best conveys the role of the emotions in a person’s behavior. Sternberg who derived these parameters deﬁned intelligence “as a mental activity directed toward purposive adaptation to, and selection and shaping of, real world environments relevant to one’s life.” If it is correct that individual’s will in the future have to make career choices that take them out of their career comfort frame then a major goal of university education should be the But a university is the great ordinary means to a great but ordinary end: it aims at raising the intellectual tone of society, at cultivating the public mind, at purifying the national taste, at supplying true principles to popular enthusiasm and fixed aims to popular aspiration, and giving enlargement and sobriety to the ideas of the age, at facilitating the exercise of political power, and refining the intercourse of private life. It is the education which gives a man a clear conscious view of his own opinions and judgements, a truth in developing them. It teaches him to see things as they are, to go right to the point, to disentangle a skein of thought, to detect what is sophisticated and what to discard what is irrelevant. It prepares him to fill any post with credit and to master any subject with facility. It shows him how to accommodate himself to others, how to throw himself into their state of mind, how to bring before them his own, how to influence them, how to come to an understanding with them, how to bear with them. He is at home in any society, he has common ground with every class, he knows when to speak and when to be silent: he is able to converse, he is able to listen: he can ask a question pertinently and gain a lesson seasonably, when he has nothing to impart himself; he is ever ready, yet never in the way: he is a pleasant companion and a comrade you can depend on; he knows when to be serious with effect. He has the repose of mind which lives in itself, which lives in the world and which has resources for its happiness at home when it cannot go abroad. He has a gift which serves him in public and supports him in retirement, without which with good fortune is but vulgar and which failure and disappointment have a charm. The art which tends to make a man all this, is the object which it pursues as useful as the art of wealth or the art of health, though it is less susceptible of method and less tangible, less certain, lees complete in its result.115 Exhibit 11.3: e four broad areas of learning together with the elements they comprise that are important for equipping students for their working lives, as deﬁned by the REAL working group of the UK Employment Department—1991 [4]. Exhibit 11.4: Recommendations for MIT in Ch. 12. How universities should change. In Made in America: Regaining the Productive Edge by M. Dertouzos, R. K. Lester, and R. M. Solow and the MIT Commission on Industrial Productivity. (1989) Cambridge, MA, MIT Press. Cognitive knowledge and skills1. Knowledge: Key concepts of enterprise learning (accounting, economics, organizational behaviour, inter and intra personal behaviour).2. Skills: The ability to handle information, evaluate evidence, think critically, think systemati-cally (in terms of systems), solve problems, argue rationally, and think creatively.Social skills: as for example the ability to communicate, and to work with others in a variety of roles both as leader and team leader.Managing one’s self: as for example, to be able to take initiative, to act independently, to take reasoned risks, to want to achieve, to be willing to change, to be able to adapt, to know one’s self and one’s values, and to able to assess one’s actions.Learning to learn: to understand how one learns and solves problems in different contexts and to be able apply the styles learnt appropriately to the solution of problems.MIT should broaden its educational approach in the sciences, in technology and in the humanities and should educate students to be more sensitive to productivity, to practical problems, to team-work, and to the cultures, institutions and business practices of other countries.Create a new cadre of students and faculty characterised by (1) interest in, and knowledge of real problems and their societal, economic and political context; (2) an ability to function effectively as members of a team creating new products, processes and systems; (3) an ability to operate effec-tively beyond the confines of a single discipline; and (4) an integration of a deep understanding of science and technology with practical knowledge, a hands-on orientation and experimental skills and insight.Where possible, revise subjects to include team projects, practical problems, and exposure to international cultures.Encourage student- teaching to instil a stronger appreciation of life-long learning and the teaching of others. Reinstitute a foreign-language requirement in the undergraduate admissions process.116 11. JOURNEY’S END: A NEW BEGINNING? Exhibit 11.5: Abilities which contribute to intelligence. Obtained from questions about the nature of intelligence, academic intelligence, and unintelligence put to experts in research on intelligence and lay persons by R. H. Sternberg and his colleagues. Among the ﬁndings was the fact that research workers considered motivation to be an important function of motivation whereas lay persons stressed interpersonal competence in a social context. In R. H. Sternberg (1985) Beyond IQ. A Triarchic View of Intelligence. Cambridge, New York, Cambridge University Press. development of intelligent behavior. It is in that context that the objective in the MIT statement that students should be able to think outside their own discipline makes sense, but I argue that the epistemology of liberal education as outlined by Newman makes better sense in the context of life-long education to which the MIT statement also draws attention. DISCUSSION I have argued that university education has to be conceived as something more than a preparation for economic activity. It has to about life and living. It is about more than a career in the workforce. For this to be achieved it is necessary to return to the concepts of a liberal education. I have argued that a liberal education necessarily embraces the vocational. Elsewhere I have also argued that my representation of the engineering (technological) process requires that the engineer (technologist) see’s the relationships between many subjects. Taught in this way engineering is a mini-liberal curriculum and as such a preparation for the broader curriculum. Ultimately, the aim has to be the common good which embraces the person qua person the one hand and on the other hand society. As I have tried to demonstrate a close inspection of the views of industrialists about university education suggests that they too want graduates who have received a liberal education, 1. Practical problem solving ability: Reasons logically and well, identifies connections among ideas, sees all aspects of a problem, keeps an open mind, responds to other’s ideas, sizes up situations well, gets to the heart of the problem, interprets information accurately, makes good decisions, goes to original sources of basic information, poses problems in an optimal way, is a good source of ideas, perceives implied assumptions and conclusions, listens to all sides of an argument, and deals with problems resourcefully.2. Verbal ability: Speaks clearly and articulately, is verbally fluent, converses well, is knowledge-able about a particular field, studies hard, reads with high comprehension, reads widely, deals effectively with people, writes without difficulty, sets times aside for reading, displays a good vocabulary, accepts norms, and tries new things.3. Social competence: Accepts others for what they are, admits mistakes, displays interest in the world at large, is on time for appointments, has social conscience, thinks before speaking and doing, displays curiosity, does not make snap judgements, assesses well the relevance of information to a problem at hand, is sensitive to other people’s needs and desires, is frank and honest with self and others, and displays interest in the immediate environment.117 but I wonder if they would know how to handle the products of such an education. If they deny that that is their view then they have to give an alternative explanation as to what is wrong. In any case perhaps you can only be oriented to the work place in the work place. If that is the case, and I think it is then employers have some responsibility for an individual’s development. Whatever is the case, properly conceived a liberal education should provide for the development of skills that help and individual to be adaptable and ﬂexible in order to cope with the exigencies of tomorrow’s world. I have not tried to establish what might be called a “continuous” curriculum although it is clear that the aims of higher education cannot be declared without attention to the school curriculum on the one hand and the post university curriculum on the other. I share Charette’s view that instead of “spending our scarce resources on ending a mythical STEM shortage, we should ﬁgure out how to make all children literate in the sciences, technology, and the arts to give them the best foundation to pursue a career and then transition in tot new ones” although I ﬁnd it rather to damming of the schools system. It has to be a joint enterprise and of course engineers are helping schools to teach engineering. e issue is whether such courses produce engineering literate individuals which is a problem that bothers the Technological and Engineering Literacy Division of the American Society for Engineering Education. Very many students may not need a lengthy initial course in higher education institutions but need to build on the knowledge received in them as their work life progresses, and I believe that this has to be done in partnership with their employers. It is not merely an orientation when they arrive in a new employment that is required. e common good demands that employers contribute to the workers development. is may be in how a worker is employed, or it may be in encouraging the worker to do a course in philosophy as happened to me when I worked in industry! Finally, I do believe that higher education, and in consequence engineering education, is at a crossroads. I believe it is an opportunity for major change and as I have tried to show elsewhere philosophers like Alfred North Whitehead provide us with frameworks to engineer that change. NOTES [1] e tutor was Sir Anthony Blunt, an art historian subsequently stripped of his knighthood. 110 [2] Astin, A. (1997). What Matters in College. Four Critical Years Revisited. San Francisco, Jossey Bass. 110 “the students peer group is the single most potent source of inﬂuence on growth and de- velopment in the undergraduate years, and in so far as the aﬀective development of stu- dents are concerned students’ values, and aspirations tend to change in the direction of the dominant values, beliefs and aspirations of the peer group.” Astin concluded that the institutional structure is not the institution as such, rather it is the kinds of peer groups and 118 11. JOURNEY’S END: A NEW BEGINNING? faculty environments that tend to emerge under these diﬀerent environments. He found of examples of large institutions in the U.S. that were trying to develop communities. It seems self-evident that cooperative learning groups can be nascent communities. But this draws attention to another major contradiction in the life of engineering educators for it is very clear from research in the U.S. that while cooperative learning groups lead in many circumstances to the better achievement of learning outcomes than traditional methods associated with the lecture there remains much resistance to their use. [3] Clifton, J. (2011). e Coming Jobs War. New York, Gallup Press. 111 [4] Marshall, T. H. (1963). Professionalism in relation to social structure and policy reprinted in Marshall, T. H. Sociology at the Crossroads and other Essays. London, Heinemann. 112, 115 [5] e Times (October 15 2013) reports that a new network of technical colleges is being established for entry at fourteen years of age. ey will be taught to become chefs, health technicians and carers but will continue to study math, English, and science. Given that the education system fails very many students by the age of 14 this cannot be a bad thing. However given the British class structure those who are very bright may not be able to change career easily once they become established in the jobs for which they are trained. us the acquisition of personal transferable skills appropriate to their capabilities is as important for this group as it is for university students. 112 [6] In pre neuro-psychological science terms practical subjects such as woodwork and metal work may enhance the development of spatial ability. As long ago as 1964 MacFarlane Smith argued that one of the reasons there was a shortage of engineers in Britain was the failure of the academic curriculum to incorporate subjects that developed spatial ability. (MacFarlane Smith, I. (1964) Spatial Ability. London, University of London Press.) 112 [7] Whitehead, A. N. (1932) .e Aims of Education and Other Essays. London, Benn. 112 [8] e model was developed by the Personal Skills Unit based at the University of Sheﬃeld. A full description of the model and a summary of its implications for teaching are given in Heywood, J. (2005). Engineering Education. Research and Development in Curriculum and Instruction. Hoboken, NJ, IEEE/John Wiley, pp. 39–45. e model was derived by Suzan Green who analysed 10,000 job advertisements in the quality newspapers published in Britain during a ﬁxed period. 59% percent of the advertisements for graduates explicitly contained reference to required personal characteristics. Of the remainder, a further 15% could be inferred to require such characteristics. Of the 32 signiﬁcant characteristics that were isolated, 20 were considered to be genuine transferable skills, and these collated into the 4 generic categories. 113 J O U R N E Y 12 119 Questioning our Assumptions: Adaptability and Change When Michael Youngman, Bob Oxtoby, Denis Monk, and I were analyzing the jobs that engi- neers did in an organization in the aircraft industry [1] I was led to a brief study of the history which had been published by John Gledhill [2]. is led me to believe that the ﬁrm could be understood as a learning system in the sense that innovations and organizations go through the same phases as we do when we are problem solving and decision making. ere was no diﬀerence in the process. Both were goal seeking endeavours. If learning is the process by which experience develops new responses and reorganizes old ones, the process of bringing a product into regular manufacture may be regarded as a process by which the organization proceeds from relatively disorganized state of knowledge to a relatively organized one. So in report to our sponsors (the Department of Employment) I sketched the diagram that subsequently appeared in our book (Exhibit 12.1). e way in which individuals worked together in the organization would safely be called a learning community today [3]. It was evident to me that these curves related to the structure of the workforce which was reinforced by Jack Blears who showed that diﬀerent kinds of personnel were required for the diﬀerent activities [4]. It is self-evident today that research personnel are diﬀerent to production personnel. Blears was concerned with the process of innovation to product, and pointed out that once the product was up and running it required personnel whose essential task was care and maintenance. ey required quite diﬀerent skills to the innovator. Today we have also recognized that products require entrepreneurs if they are to be sold; they too require a diﬀerent skill set. Richard Foster of McKinsey’s showed how such curves could be used in business forecasting [5]. e focus here, is with learning. At the time George Carter, Deryk, Kelly, and myself could also see the same process at work among the students who were pursuing projects in engineering science [6]. Moreover, we could relate the skills used to cybernetic models of problem solving that were appearing in the educational literature of the time. e problem had to be formulated, data gathered, solutions proposed, evaluated, one developed, produced and evaluated the results being fed back into the system, leading to the further development of the product. Of course problem solving and decision making are not a linear activities, but the models highlight certain key skills necessary for the best solution (however best is deﬁned). ey also enable diagnostic and summative rubrics of assessment. 120 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE Exhibit 12.1: (a) Shows the pattern of innovation in the ﬁrm showing process from problem iden- tiﬁcation to problem solved, feedback and the next curve in the process of development and so on; (b) illustrates the rate of change in demand for speciﬁc types of workforce as a function of the learn- ing/innovation curve. Application of new techniques to previous technologyEffect of new materialFirm sponsors design studyInspiration (collected experience turned into applicationAward of design study contract196019641968Levels of knownledge as products or sub-systems FEDCBA19401953(a)(b)DemandTime, YearsEffects of new technologies and market on the demand for manpower121 We found that some students had diﬃculty in formulating problems, sometimes they had diﬃculty in generating alternative solutions, and in evaluation or as it was called “critical review” they were sometimes less than critical. ey were helped if they could see examples of what was wanted. A particular skill that these bright students sometimes found diﬃcult was to recognize the assumptions they were making and the inﬂuence they had on both their practical work and evaluations. At the heart of changing peoples is the attitudes and assumptions that people make. Just consider how important the assumptions we make in everyday life are to political dia- logue. Today is July 18, 2016. e following are a few of the things we have had to think about in the last week in America and Europe. First, during last week Britain got a new Prime Minister. Its second woman in that position. A conservative, she upset some industrialists by promising to legislate for worker representatives on companies governing boards while demanding a cap on the pay of executives. On ursday, in France, a large lorry (truck) drove a-mock for a mile along the Promenade des Anglais among thousands of people celebrating France’s Bastille day (the equivalent of the American day of In- dependence), and killing nearly 100 men women and children at the last count. On Friday, came news of a military coup in Turkey only to fail on Saturday. Last night, we heard that three police oﬃcers had been shot in Baton Rouge, and today the British broadcasters are telling us about the Republican Convention in Cleveland. e media people interview so-called experts on why these things happened; we jump to our own conclusions. ey are “assumptions” and sometimes they turn out to be completely untrue. At the same time, as Journeys 2 and 3 show, they may arise from deeply held prejudices. As for politics and voting, most of us if we are really forced to sit back and reﬂect, will agree that often our views are not well supported by facts let alone argument. I venture to suggest that that is somewhat of an understatement. UNDERSTANDING THE ASSUMPTIONS WE MAKE e importance of understanding the signiﬁcance of assumptions is to be found in the recent debate that the British have had about whether or not to leave the European Union. I should state that I was one of those who thought we should leave, in spite of the fact that I am living in another country in the European Union and may well be faced with diﬃculties. One of my views was that it might restore achievement motivation which seemed to me to be needed. My American friends were agog when the vote went in favor of exit, and it surprised Europe, big time. e No’s are called Brexiteers and those who wanted to remain—“remainers.” It was a bitterly contested ﬁght which went on for a number of months and was characterized by fear. e Brexiteers were characterized as creating fear about the number of immigrants being admitted into the country through false claims about the numbers likely to come in the future. On the other side the remainers argued that the economy would collapse. ey cited numerous experts 122 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE and President Obama was persuaded to come and tell the British that if they left Europe they would go to the end of the queue of those seeking to negotiate trade deals with the U.S. It was very diﬃcult to determine what was true and what was false. Certainly the public were not educated in asking questions about the economic forecasts that were bandied about. Toward the end of the campaign I came across a little advertised critique of forecasts made by the Treasury (Ministry/Department of Finance) by a Professor David Blake of the Cass Busi- ness School of the City University London [7] which put an entirely diﬀerent gloss on matters. It was a technical report which would have delighted engineers. e Treasury use a gravity model. Blake models it as a solar system in which the EU is the sun and the diﬀerent European countries are planets orbiting the sun. e countries with largest GDP’s and population become the biggest planets. Planet size can compensate for distance. ose countries closest to the EU gain the most economic beneﬁts. e Eurozone (the countries with the common euro currency) are nearest to the sun. e rest of the world is farthest away. e model shows that if the UK is moved further away from the sun it will be worse oﬀ. It would be better oﬀ, as would all the countries in the world if they joined the Eurozone. Professor Blake points out that had the gravity model been used in 2000–2002 when the Eurozone was created the UK would have been better oﬀ, a proposition that has been shown to be false. ere are well-known problems with long-distance forecasting. e treasury model predicts that by 2030 the GDP per household will be lower than by £4300 (say $5000). But the Treasury assumes that the UK will not be able to negotiate a more favorable deal than currently exists with the EU or the rest of the world. e Brexiteers argued that it is highly unlikely that 5th largest economy in the world would not be able to negotiate a better deal. ey support this argument with the fact that between the UK and Europe there is a net imbalance that favors Europe. In extremis were there to be high tariﬀ levels imposed German automobile manufacturers, and French farmers would be seriously aﬀected. Professor Blake notes that a similar model predicts that if Scotland were to leave the UK its trade with the rest of the UK would fall by 80%. Face validity suggests that this could not be the case. Blake’s critique will be tested pretty quickly because the Treasury uses another model to predict short term eﬀects. is model suggests that the “leave” vote will cause an economic shock equivalent to 50% of the 2007–2008 global ﬁnancial crisis, and that this shock will last for two years. According to Blake it is assumed that there will be no policy response to the shock whereas the response to the 2008 crisis was to inject £375 billion into the economy. e evidence so far is that the Government and the Bank of England, especially the Bank of England, are prepared to take the necessary steps. One other factor that was not seriously debated is the potential instability of the EU. All sorts of shocks may hit it in the next few years. e main campaign assumes that it is a highly stable system. We shall soon know how accurate the short-term predictions are. e assumptions of both camps are that the UK will be better oﬀ. Primarily, that means “more wealthy.” But better oﬀ means other things. Remainers say that continuing peace in Eu- rope is more likely if the UK remains in the EU which is a large assumption. An equally large assumption of the leavers is that the restoration of full sovereignty will provide better fortunes. In all of this it is not clear that the leave vote is not made up of some voters who are grumbling about politicians in general. It does seem that in many parts of the world there is discontent and a corresponding disconnect between the voters and the political classes, and that this is due to increasing inequalities in wealth. 123 DIALOGUE When it comes to educational change, M. M. Cohn and R. B. Kottcamp, who carried out a major study of teachers in Florida in the 1980s, argued that if learning is to be made more mean- ingful then the assumptions and structure of the prevailing educational system will have to be changed [8]. at view is not diﬀerent to the view of those who believe that engineering educa- tion ought also to be changed. ey cite Schaefer who in 1967 wrote “we can no longer aﬀord to conceive of schools simply as distribution centers for dispensing cultural orientations, infor- mation and knowledge developed by other social units. e complexities of teaching in formal classrooms have become so formidable and the intellectual demands on the system so enormous that the school must be much more than a place of instruction. It must be a center of inquiry-a producer as well as a transmitter of knowledge. One basic fact is our ignorance of teaching. We simply do not know how to master the abstract knowledge and analytical skills modern society demands. It seems necessary to transform at least some schools into centers for the production of knowledge about how to carry out the job.” at was written a long time ago but it still applies especially to universities. ere is a great deal of knowledge in the system but it is not conveyed to the average teacher and the dialogue between the researchers and the practitioners is not great which is why Cohn and Kottkamp recommend assumptional dialogues. ey are “opportunities to raise awareness and examine largely unrecognized assumptions that currently underlie educational structures and practices (in a school, university, institution or system) to generate alternatives to them” [9]. ey are something that we are not terribly good at doing for fear of the unknown. K. Patricia Cross, also a long time ago argued that things will not improve until teachers see their classrooms as laboratories for research into instruction [10], a proposition that she explained in great detail with Tom Angelo and Mimi Steadman [11]. THE TRANSFER OF LEARNING ere was also evidence that some students had diﬃculty with within in-subject transfer of skill (knowledge). is is a key skill that is essential for independent learning, and therefore, for con- tinuous professional development. Even of more importance is the ability of horizontal trans- fer which Kallenberg calls cross-domain transfer [12]. Sometimes its exercise is the result of 124 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE what Bernard Londergan calls “insight” [13]. Lonergan repeats the well-known story thus; “of Archimedes rushing naked from the baths of Syracuse with the cryptic cry, Eureka!” King Hi- ero, it seems, had had a votive crown fashioned by a smith of rare skill and doubtful honesty. He wished to know whether or not baser metals had been added to the gold. Archimedes was set the problem and in the bath had hit upon the solution. Weigh the crown in water. Implicit in this directive were the principles of displacement and of speciﬁc gravity [12, p. 3]. Kallenberg describes a problem that Cambridge students were trying to solve by geometry which seemed, and would seem too many of us to be the correct approach. ey had to make a perfects square quilt by sewing together 10 squares each with its own unique size. It was only when the students dropped that approach, and looked at it from the perspective of electric circuits (Kirchoﬀ ’s Law), that they obtained a solution. Kallenberg gives several other examples in order to make the point that practical reasoning may be helped by cross-domain transfer whether it is in design or ethics. e point to be made here is that cross-domain transfer is at the heart of the stage of romance. It necessarily happens but the skill is lost. If this approach to the “Human Side of Engineering” is to be successful then irrespective of insight individuals have to be prepared to dive into other areas of knowledge. We cannot aﬀord to be afraid, yet fear so often governs our behavior, particularly it seems, in elections. FEAR e British are getting used to referenda. e recent one ( June 23rd) was the second in a couple of years. e latter gave the Scots the opportunity to say whether or not they wanted to leave the UK. e commentariat seem to believe that fear played a large part in causing voters to say they would remain in the UK although the margin in their favor was not great. It seemed that fear was behind the two campaigns in the recent referendum. Fear of increasing immigration contrasted with fear of economic collapse, often expressed as collapse of the markets, coupled with fear of the unknown. During the referendum the remainers continually made the point that the markets would fall and fall and do the economy irreparable damage. If a voter is going to make a reasoned judge- ment they are going to have to obtain a working knowledge of how markets work. Fortunately, the 2007–2008 crisis has forced numerous analyses of what went wrong and spawned a num- ber of readable texts on both sides of the Atlantic. Economists seem to agree with the French economist omas Piketty’s,view that ﬁnancialization ensures “the rich to get richer and the poor get poorer.” Foroohar, an American ﬁnancial journalist, who cited Piketty argues that one of the reasons for the slower growth exhibited by the American economy is due to ﬁnancialization, and moreover, the regulators have helped to bring this about [14, pp. 15–20]. Reich, a distinguished American civil servant and academic, asks us to understand that there is no such thing as a “free market.” He writes, “Few ideas have more profoundly poisoned the minds of more people than the notion of a “free market” existing somewhere in the universe, into which government “intrudes.” In this view, whatever inequality or insecurity the market 125 generates is assumed to be the natural and inevitable consequence of impersonal “market forces.” What you’re paid is simply a measure of what you’re worth in the market. If you aren’t paid enough to live on, so be it. If others rake in millions, they must be worth it. If millions are unemployed or their pay checks are shrinking or they have to work two or three jobs and have no idea what they’ll be earning next month or even next week, that’s unfortunate but it’s the outcome of “market forces.” [15, p. 3]. e market can do no wrong is the belief of many of those on the very right wing of the political spectrum. Interventions which many on the left will reduce inequality will so the right wing believe distort the market. Reich argues that the left/right views or government intervention vs. non-intervention mis- understand the problem for without government there can be no market. e market is inher- ently linked to the concept of civilization, and civilization does not allow ruthless Darwinian competition. Civilization “is deﬁned by rules: rules create markets and governments generate the rules” [15, p. 4]. Reich is of the view that the rules that govern the functioning of the free market are of more importance than the size of government. He, and writers like Foroohar, believe that the rules, (or lack of rules-deregulation that is) have changed in favor of “Wall Street.” ey have aided the ﬁnancialization that has brought about a situation where the prime purpose of ﬁnancial institutions was to invest in the real economy became one in which the system of ﬁnance has become an end in itself. Its growth is supported by increasing debt. e problem is that “the more debt is likely to be created in excessive quantities. And it means that the more debt there is in an economy, beyond some level, the less stable that economy will inevitably be” [16]. From an industrial perspective, ﬁnancialization led to short termism because of the need to ever increase the returns to shareholders who were in the Friedman doctrine held to be paramount. In order to satisfy their investors large ﬁrms have begun to behave like shadow banks. Foroohar suggests that one of useful things that could be done is to re-visit the whole notion of the company and who companies are for, a discussion that is occasionally held in the UK. Reich wants to ﬁnd some way of restoring the countervailing power that was lost during the last two or three decades [17]. His most radical suggestion is that everyone should be given a minimum income “that enables them to be economically independent and self suﬃcient.” He cites support from the conservative economist F. A. Hayek. It would eliminate the need for government welfare payments and other transfers to the poor and reduce people’s dependence on private employers and so restore some countervailing power. ere are, of course, many other suggestions to be found in the literature that is now emerging. But the Queen’s question remains. THE QUEEN’S QUESTION In 2009 on a visit to the economics department of the renowned London School of Economics, Her Majesty the Queen on a fact ﬁnding mission asked the question “why did no one see it coming?” She had to wait for a letter to get an answer. Six years later we learn in one of several analyses of the crash that macroeconomics held that understanding the monetary workings of the economy could be understood without reference to the banking system [16, pp. 31,170,245]. 126 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE is had the eﬀect that the models could not show that the ﬁnancial system could be a cause of instability. e kind of mistakes that can be made in engineering were apparent, as for example two of the assumptions that were made. First, it was assumed that the behavior of people is rational and can, therefore, be predicted. Unfortunately, they did not have the beneﬁt of Khaneman’s research which did not make the headlines until 2013 [18]. Second, it was assumed that ﬁnancial markets are eﬃcient in terms of the textbook. A positivist view prevailed in which mathematical precision was taken to provide the correct answers. Professor Buiter of Oxford University, cited by Adair Turner, said that, “Complete markets macroeconomics theories not only did not allow the key questions about insolvency and illiquidity to be answered. ey did not allow such questions to be asked” [16, p. 241]. ere is some simi- larity here with Robert Lund who in eﬀect was asked to ask and answer questions like a manager than an engineer when agreeing to the launch of the Challenger. Turner argues that “underlying these speciﬁc failings was also a methodological and philo- sophical bias—a preference for mathematical precision and elegance at the expense of realism […]” [16, p. 243]. Is this not similar to the complaints that industrialists make about the engi- neering curriculum? Both are accused of theoretical reasoning at the expense of practical reason- ing. Tomas Sedlacek [19], a historian of economics writes, “e more important elements of a culture or ﬁeld of inquiry such as economics are found in fundamental assumptions that adherents of all the various systems within the epoch unconsciously presuppose.” Such assumptions appear so obvious that people do not know what they are assuming, because no other way of putting things has ever occurred to them, as the philosopher Alfred Whitehead notes in Adventures of Ideas [20]. is is true of any subject and engineering is no exception. is is no better illustrated than by the questions Sedlacek asks of economics, “What are we doing? And why? Can we do (ethically) all that we can do (technically)? And what is the point of economics? What is all the eﬀort for?” (Questions that I have had to try and answer in respect of teacher education). “And what do we really believe and where do our (often unknown) beliefs come from?” If science is “a system of beliefs to which we are committed, what beliefs are they?” It is fundamental questions such as these that criticism of ABET invokes or the criticisms of industry that colleges do not prepare their students adequately for work in industry. But they have to be asked in the context of higher education more generally and the purposes which it serves. Are we commodities or persons? POSTSCRIPT While the page proofs of this book were being prepared Donald Trump was elected to be the next President of the United States, and yesterday the Italian Prime Minister lost a referendum on the constitution. Simultaneously, a vast number of tracts were published that tried to account for these developments that were seen as a challenge the neo-liberal consensus. In the literature I have read 127 there have been very few references to the future and our rapidly changing society, which is rather surprising given the circumstances. e Wall Street Journal on October 13, 2016 suggested that dashed employment promises of the 1990s fuelled Donald Trump’s political rise, but the fact that technology is on track to further reduce jobs, a point made in a letter in the UKs Guardian on November 17 was not considered in any of debates. Whether or not you believe that all will turn out well, or believe that unemployment will take over the middle classes as it has the working classes there is little doubt that technology is changing the culture in which we live. For this we have to thank engineers and engineering. is raises questions about the responsibilities engineers have for the impact of their designs. ese questions are primarily philosophical but relate to the fundamental issue of who is controlling whose mind. Do they escape these responsibilities because, for the most part, they are employees, or do they have a moral obligation to lead debates in what is currently called “Technological Literacy?” It was a positive answer to the latter that led to these journeys. NOTES [1] Youngman, M. B., Oxtoby, R., Monk, J. D., and Heywood, J. (1978). Analysing Jobs. Aldershot, UK, Gower. 119, 128 [2] Gledhill, J. (1966). Recent developments in electric power generating equipment for air- craft. e English Electric Journal, 21(6), p. 35. 119 [3] It was clear that the eﬀectiveness of the organization was dependent on the interdepen- dence of its workforce. Because roles were not deﬁned with precision we found that even at the lower levels individuals needed to widen the scope of their initial brief through skills of communication and liaison in order to take some action. It appeared that communication was a complex skill, the nature of which varied with the activities undertaken. It seemed that persons were appointed to roles which they had to change in order to communicate. e organization was more a system of persons-in-relation than a strictly hierarchy. 119 It is in such structures that feelings of responsibility are acquired. We often allow ourselves to confuse status and responsibility: I am as guilty of that as anyone else. To put it in another way, we often have to seek status in order to be responsible and that may be the reason why many persons seek to take on managerial roles. e feeling of responsibility accompanies or generates a feeling that the person is doing something worthwhile. In this organization almost everyone was directing and controlling, to a greater or lesser degree, and for some it was mainly a function of themselves. Job satisfaction is, to some extent, a measure of the degree to which an individual’s needs for direction and control are satisﬁed. In our study we showed that this was as much a function of personality as it was of history, ability and interest. What is an acceptable goal to one person will not be to another: some wanted to be stretched others wanted a strict routine. No two persons in a section will be exactly alike. 128 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE It may contain both aggressive people and timid people who can work together in a way that enhances of inhibits learning. Some who are taken outside their sphere of controlling may have to be supported. “A person is a psycho-social system. Within the boundaries of that system most individuals wish to be ‘organic,’ to modify a term used by Burns and Stalker (1961). ey wish to be able to take actions and decisions as well as mature. e boundaries of these psycho-social systems arise as a function of the needs of the job and the needs of the person. When these are matched for each person in the organization a hierarchic system becomes structured by individuals who are organic within their own system, and grow in it in such a way that the organizations goals are achieved when it also becomes organic. Both systems have to be self-adjusting and when they are doing that the organization is learning.” (ese paragraphs are based on pages 114 and 115 of Youngman et al. [1]. e third para- graph is verbatim) Burns, T. and G. Stalker (1961). e Management of Innovation. London, Tavistock. [4] Jack Blears, Director of the Division of Industrial Studies, Faculty of Engineering Science, the University of Liverpool. 119 Youngman et al. [1] write, “when knowledge is relatively organized and the products are in manufacture and subject to minor improvement then there will be little demand for manpower. However, during the innovatory stage or period when knowledge is relatively disorganized, there will be a demand for the kind of manpower which can structure knowl- edge in new ways. Further analysis of the innovatory process suggests that when develop- ments in applied technologies are applied to existing products, they may lead to a decrease in demand for manpower” […] (p. 103). [5] See Chapter 3 of Heywood, J. (2016). e Assessment of Learning in Engineering Education. Policy and Practice. Hoboken, NJ, IEEE/Wiley. 119 [6] Foster, R. (1986). Innovation. e Attacker’s Advantage. London, MacMillan. 119 e S curve is a learning curve that describes the eﬀort put into improving a product or a process, and the results the company obtains from that investment. In my diagram (Ex- hibit 12.1) each new adaptation represents an additional cost. [7] Blake, D. (2016), Measurement without eory: On the extraordinary abuse of economic models in the EU Referendum debate. London. Cass Business School, City University London. http://www.pensions-institute.org/BlakeReviewsTreasuryModels.p df. 122 [8] Cohn, M. M. and R. B. Kottcamp (1993). Teachers. e Missing Voice in Education. Albany, NY, State University of New York Press. 123 129 [9] Ibid. p. 267. 123 [10] Cross, K. P. (1986). A proposal to improve teaching or what taking teaching seriously should mean. AAHE Bulletin, 9, p. 14. 123 [11] Angelo, T. and K. P. Cross (1993). Classroom Assessment Techniques. San Fransisco, Jossey Bass. 123 Cross, K. P. and M. Steadman (1996). Classroom Research: Implementing the Scholarship of Teaching. San Fransisco. Jossey Bass. [12] Kallenberg, B. J. (2013). By Design: Ethics, eology, and the Practice of Engineering. Cam- bridge, UK, James Clarke. 123, 124 [13] Lonergan, B. J. F. (1957). Insight. A Study of Human Understanding. London, Darton, Longman and Todd. 124 [14] Foroohar, R. (2016). Makers and Takers: e Rise of Finance and the Fall of American Busi- ness. New York, Crown (Random House/Penguin). 124 [15] Reich, R. B. (2015) Saving Capitalism. For the Many not the Few. New York, Alfred Knopf/Random House Penguin. 125 [16] Turner, A. (2016). Between Debt and the Devil: Money, Credit, and Fixing Global Finance. Princeton, NJ, Princeton University Press. 125, 126 One of the drivers of the 2007–2008 collapse was increasing inequality. “Richer people tend to spend a lower proportion of their income than do middle income and poorer people. Increasing inequality will therefore depress demand and economic growth unless the in- creased savings of the rich are oﬀ-set by increased borrowing among middle or low income earners. In an increasingly unequal society, rising credit and leverage become necessary to maintain economic growth but lead inevitably to eventual crisis.” One of the many contradictions in Conservative party policy in the UK is that following its belief that people need to make their own choices it continues to allow increases in university fees which in a period of ﬂat lining of incomes simply causes people to borrow more or opt out which does not help social mobility at all. [17] As for example, common to the UK and the U.S. is the loss of trade union power. Reich writes “What is the appropriate balance between stimulating new inventions and invest- ments that could possibly improve the quality of life for millions of people and not concen- trating too much wealth in the hands of the few, thereby impoverishing almost everyone else? ere is no correct answer. But with adequate countervailing power we could have more conﬁdence in the ability of our political economic system to decide. We could better 130 12. QUESTIONING OUR ASSUMPTIONS: ADAPTABILITY AND CHANGE trust that the resulting distribution of income and wealth represents a trade-oﬀ society is willing to make” [p. 212]. 125 [18] Kahneman, D. (2013). inking, Fast and Slow. New York, Farrar, Strauss and Giroux. 126 [19] Sedlacek, T. (2011). Economics of Good and Evil. e Quest for Economic Meaning from Gilgamesh to Wall Street. Oxford, Oxford University Press. 126 [20] Whitehead, A. N. (1985 ed.). Adventures of Ideas. New York, Free Press. 126 Author’s Biography 131 JOHN HEYWOOD John Heywood is a Professorial Fellow Emeritus of Trinity College Dublin-University of Dublin. He was given the best research publication award of the Division for the Professions of the Amer- ican Educational Research Association for Engineering Education: Research and Development in the Curriculum and Instruction in 2006. Recently, he published e Assessment of Learning in Engi- neering Education: Practice and Policy. Previous studies among his 150 publications have included Learning, Adaptability and Change; e Challenge for Education and Industry, and co-authored Analysing Jobs, a study of engineers at work. He is a Fellow of the American Society for En- gineering Education, a Fellow of the Institute of Electrical and Electronic Engineers, and an Honorary Fellow of the Institute of Engineers of Ireland. In 2016 he received the Pro Ecclesia et Pontiﬁce award from the Pope for his services to education. Author Index 133 Abercrombie, M. L. J., 22 Adamson, N. M., 89 Alexander, C. N., 98, 102 Allport, G. W., 24 Anderson, L. W., 7 Angelo, T., 123, 129 Anscombe, E., 61 Aquinas, T., 78 Argyris, C., 107 Aristotle, xxiii, 32, 59, 72, 78 Armstrong, N., 53 Astin, A., 86, 9, 117 Austen, J., 59 Ayer, A. J., 2 Barnes, L. B., 43, 47, 48, 49, 52 Bartlett, F. C., 24 Bassett, C. L., xxiii Belbin, R. M., 41, 48, 107 Berger, P., 33, 35, 99 Bernstein, B., 27 Bey, C., 47 Blake, D., 122, 128 Blau, J., 90 Blears, J., 119, 128 Bloom, B., 6 Bloom, G., 89 Blunt, A., 117 Bocong, Lee, 86, 91 Boomer, G., 34, 36 Bostwick, W. D., 3 Bowen, W. R., 14, 61, 62, 63, 71, 72, 73, 74, 75, 76, 109 Bruner, J., 96, 102 Brynjolfson, E., 81, 87, 88 Buber, M., 73, 78 Bucciarell, L. L., 6, 7, 8, 114 Buiter, 123 Burns, Robert, 38 Burns, T., 37, 42, 47, 73, 78, 128 Buts, W. P., 89 Carroll, S., 89 Carter, G., 100, 119 Catalano, R. F., 56 Chambless, D. F., 92 Champagne, A. B., 27 Charette, R. N., 82, 90, 117 Cheville, A., 66, 69, 71, 75, 79, 94 Clifton, J., 81, 83, 89, 111, 118 Cohn, M. M., 123, 128 Collinson, D., 8 Cook-Greuter, S., 107 Copleston, F., 67 Costello, J. E., 78 Criado-Perez, Ms, 59 Cross, K. P., 108, 123, 129 Culler, A. D., 11, 18 Culver, R. S., 96, 97, 100, 102 Dangur, V., 108 Darwin, C., 59 134 AUTHOR INDEX Davis, M., 49, 53, 55, 56, 57, 59, 61, 62 Dent, N., 74 Dent, N. J. H., 79 Dertouzos. M., 117 Devitt, F., 99 Dewey, J., 8 Diana, Princess, 72 Dinklespiel, J. R., 27 Driver, R., 31, 34 Drucker, P., 39, 44, 48, 49 Eggleston, J., 94, 99 Ellis, R. A., 90 Evans, D., 98 Figueiredo, J., 91, 99 Finnis, J., 65 Fische, K. W., 104 Fitch, P., 957, 102 Forge, J., 72, 76 Foroohar, R., , 125, 129 Foster, R., 117, 128 Freeman, J., 41, 45 Freire, P., 94 Giardina, R., 16, 18 Gilson, E., 78 Gledhill, J., 127 Goldberg, D. E., 28 Goldstein, H., 14, 15 Goold, E., 99 Gosch, P., 74, 78, 79 Greenleaf, R. K., 43, 50 Grosch, P., 66, 68 Gunstone, R. F., 27 Hackos, J. T., 96, 100 Hawkins, J. D., 56 Hayek. F. A., 125 Hayward, T., 71 Her Majesty the Queen, 125 Herkert, J. R., 60, 66 Herman, G., 16, 18 Hernstein-Smith, B., 33, 35 Hesseling, P., 2, 38, 47 Heywood, J., xii, 7, 17, 18, 26, 28, 35, 47, 48, 50, 69, 76, 79, 88, 100, 106, 108, 118, 127, 128 Hickey, L., 84, 91 Hira, R., 14, 15 Hirst, P., 99 Hoare, C., 107 Hodgson, J., 48 Hodgson, P., 48 Honderich T., 66 Hoose, B., 29 Humble, B., 41, 45 Hurley, P., 62, 65 James. W., 8 Jewkes, J., 89 Joad, C. E. M., 2, 5 Jones, R. G., 29 Kallenberg, B. J., xxiii, 65, 66, 59, 78, 123, 124, 129 Kant, I., 62, 67 Keegan, R., 107 Kelly, D. T., , 89, 100, 119 Khaneman, D., 126, 130 Kilminster, J., 55 King, P. M., 102, 103, 104, 105 Kirchoﬀ, 124 Kitchener, K. S., 102, 103, 104, 105 Klopfer, L. E., 27 Kottkamp, R. B., 123, 128 Krupczak, J., 4, 7 Kuhen, D., 82, 90 Labov, W., 27 Langer, E. J., 98, 107 Lécouyer, C., 48 Lerman, 34 Lester, R. K., 117 Levinas, E., 73, 78 Lindsay, B., 82, 89 Lipmann, 106 Lonergan, B., 124, 129 Lovin, R., 91 Lovin, R. W., 65, 69 Lowell, B., 82, 89 Luckmann, T., 33, 35, 99 Lund, R., 54, 55, 126 MacAfee, A., 81, 87, 88 MacFralane Smith, I., 118 MacIntyre, A., 74, 75, 78, 79, 113 Macmurray, J., 23, 26, 44, 49, 53, 56, 61, 62, 72, 73, 77, 84, 85 Madigan, C., 91, 92 Magee, B., 7, 8 Manning, B., 59, 64 Marra, R., 102 Marshall, T. H., 111, 118 Mason, J., 55 Mason, M., 36 Matthews, G., 40, 48 Matthews, G. B., 101, 102 Matthews, M., 32, 35 Maunter, T., 66 McAuliﬀe, G., 98, 107 McCarthy, N., 28 McGregor, D., 39, 46 McInerney, R., 67, 78 Michelfelder, D. P., 28 Milburn, A., 111 Mill, J. S., 61 Miller, M., 107 Miller, R., 32, 35 AUTHOR INDEX 135 Mina, M., 8, 13, 71, 94, 98, 109 Mitcham, C., 28 Monk, J. D., 119, 127 Monk, J. D., 21, 48, 91 Moon, J., 68 Moore, G., 7 Morrison, K., 36 Mozart, 33 Muller, O., 108 Munns, D. P., 53, 54, 57 Newman, J. H., 11, 13, 18, 94, 95, 99, 110, 112, 113, 114 Obama, President, 121 Oldham, V., 35 Olds, B., 32, 35 Omidvar, I., 8 Oxtoby, R., 28, 48, 91, 119, 127 Palmer, B., 107 Pascarella, E. T., 95, 100 Paton, H. J., 68 Perry, W., 96, 97, 98, 102, 103, 104 Peters, R. S., 1 Piaget, J., 31, 96, 100, 101 Pierce, C. S., 8 Piketty, T., 124 Pollock, H. Montagu, 16 Pritchard, J., 11, 12 Queen Elizabeth II, 62 Rawls, J., 63, 64, 68 Rees, M. (Lord), 52 Reich, R., 88, 124, 125, 129 Riley, D., 76, 79 Roller, D. R., 16, 18 Rorty, R., 8 Russell, B., 7 136 AUTHOR INDEX Russell, J., 81, 88 Salzman, H., 82, 89 Sanford, N., 47 Schaefe, Dr., 99, 108 Schein, E., 47 Schôn, D., 107 Sedlacek, T., 126, 130 Selbourne, D., 74 Snowden, E., 60, 64 Solow, R. M., 117 Stalker, G., 42, 47, 73, 78, 128 Stansﬁeld, R., 9 Steadman, M., 123, 129 Sternberg, R. H., xxiii, 114, 116 Sullins, J. P., 26, 28, 29 Susskind, D., 87, 92 Susskind, R., 87, 92 Takacs, C, G., 92 Teitelbaum, M. S., 82, 87, 89, 92 Terenzini, P. T., 95, 100 omas, B., 91, 92 Torbert, W. R., 107 Trevelyan, J., xxii, 46, 91, 98, 99, 107 Trump, D., 126 Turner, A., 126, 129 Utschig, T. T., 98, 107 Vardy, P., 32, 35, 66, 68, 74, 78, 79 Vernon, P., 24 Vesilind, A., 75, 76, 77 Vincenti, W. G., xxii, 54, 57 Wadwha, V., 82, 90 Whitehead, A. N., xxii, 111, 117, 118, 126, 130 Williams, B„ 91, 99 Winkett, L., 60 Wittengenstein, L., 2, 6, 7 Woditsch, G., 16, 18 Wood, P. K., 104 Woods, D., 97, 102 Woodson, T. T., 16 Wulf, W. A., 60, 66 Yokomoto, C., 3 Youngman, M. B., 28, 48, 91, 119, 127, 128 Zachary, G. P., 90 Subject Index 137 ABET, 3, 7 Abortion, 59 Adult learning, 93 Aﬀective domain, 93, 99 Aircraft design, 54 Ambiguity, 38 Analytic philosophy, 35 Apperception, 31 ASME, 66 Aspirational ethic, 71ﬀ Assumptional dialogues, 123 Assumptions, 121, 122, 123ﬀ Bologna Agreement, 7 Bowen’s aspirational ethic, 75 British Broadcasting Corporation, 60 Bruner’s theory of cognitive development, 102 Bureaucracy, 60 Canterbury cathedral, 18 Capitalist system, 81 Challenger, 54, 55, 56 Chilcot report, 29 Choc des opinions, 21, 26 Codes of conduct, 60ﬀ, 66, 72 College (impact of ), 92 Colleges of Advanced Technology, 71 Colorado School of Mines, 96 Common good, 84, 110 Communication, 15, 22, 23 Community (ies), 15, 26, 43, 53, 54, 56, 85, 86 Company (concept of ), 84, 85 Complex learner, 40 Complexity theory, 36 Concepts, 16, 24 Conﬁdentiality, 60 Consequentialism, 61 Constructivism, 31, 32, 33, 35 Continuing Professional; and Personal development (CPPD), 25 Contractualism, 61, 63, 66 Creativity, xxii, 66 Culture (organizational), 25 Curriculum (models of ), 94, 99, 100 Curriculum (negotiated), 34 Deformation professionelle, 27 Dependence, 56 Design (social process), 7 Development (student), 93, 96ﬀ Dialect, 27, 28 Dripping water exercise, 11, 13 Duty, 62, 67 Education system(s), 86 Empathy Wall, 18 Engineering, 4, 71, 72, 80, 126 Engineering, 126 Engineering Council, 65 Engineering curriculum, 94 138 SUBJECT INDEX Engineering education, 83 Engineering literacy, 4, 16, 117 Engineering science exam, 94, 101 Engineers, 83 Enterprise learning (skills of ), 113, 115 Episteme (scientiﬁc knowledge), 79 Epistemology, 13, 29 Ethics, 2, 8, 29, 55, 59, 62, 64, 71, 109, 124 Ethics (of engineering), 56 Ethics-aspiration, 64 Expectancy, 18 Experts (expertise), 121 Fear, 124 Financialization, 124, 125 Frames of reference, 24 General education, 112, 113, 114 Genius loci, 94, 95 German dual system, 92 Goods, 75 Higher education, 86, 93, 110, 111 IBM, 13, 14, 15, 16, 1, 54 IEEE, 64, 68 Illusion(s), 21, 22 Images course, 16, 19 Imperatives, 67 Inequality (ies), 123, 125 Insight, 124 Intelligence, 113 Intelligence (Academic), xxiii Intelligence (Nous), 79 Intelligence (practical), xxiii I-ou interactions, 73 Just war, 29 King and Kitchener’s theory of development, 98, 103, 104, 105 Knowledge, 128 Labour arena, 91 Language (public and formal), 27 Language (s), 1, 2, 5, 7 Leadership, 43, 44 Learning, 24, 31 Learning organizations, 56, 119, 208, 125 Liberal education, 26, 60, 112, 113, 114 Little College, 16 Logical positivism, 2, 5, 8 MacDonald’s, 21 Man (views of ), 11 Manage,r/Management, 43, 47, 48 Manager, 55 Market, 48, 124, 125, 126 Meaning, 1, 2, 3 Meetings, 41 Misperception(s), 22 MIT, 113, 115 Mobility, 111, 112 Moral principles, 59 Morality, xxiii, 61, 62 National Academy of Engineering, 60 Natural law, 74 Organization (types of ), 48 Organizational structure & performance, 43 Orientations (to learning and work), 47, 50 Outcome{(s), 3 Peace engineering, 77 Peer group, 8, 117, 118 Perceiving, 15 Perception, 17, 18, 22, 23, 24, 25 Perception (Exercise in), 9 Perry’s theory of development, 97, 103 Person (personal), 53, 128 Personal development, 86 Personal relations, 72, 73 Personal transferable skills, 113, 118 Philosophy, 1, 40 Philosophy (for young children), 41, 100, 104 Philosophy of engineering, 31 Piaget’s theory, 100, 101, 102 Practical problem solving ability, 116 Pragmatism (Pragmatic), 8 Preconceptions, 24 Prejudice (bias), 25 Problem formulation, 121 Problem(s), 22 Professional 56., 66, 69, 77 Professional development, 86, 98, 99 Professional development (Torbert’s frames), 96, 105, 106 Prudence (Practical Wisdom), 74, 78 -Psychological, 31, 32, 33 Psycho-social system, 128 Public relations, 73 Qualities, 39, 40 Radio Telescopes, 53 Realism, 32, 33 Reality (perception of ), 33 Reason (practical), 67 Reason (pure), 67 Reasoning (practical), xxiii Reﬂection (reﬂective thinking), 23, 40, 98, 103, ﬀ Reﬂective judgment Interview, 105 Relationships, 44 Relationships (personal), 23 Research (engineering education), 98 Roboethics, 25, 26, 27, 28 Role(s), xxi, xxii, 39, 42, 49, 85, 88 Royal Academy of Engineering, 75 Royal Astronomical Society, 54 Schema (Schemata), 24, 26 SUBJECT INDEX 139 Self, 23, 31, 44 Shareholders, 84 Short-termism, 125 Social change, 81, 83, 86 Social competence, 116 Social justice, 76 Social System, xxii, 37 Society, 109 Society and technology, 109 -sociological, 33, 35 Socratic questioning, 32 Spatial ability, 118 STEM, 80, 86, 87, 88, 117 Systems, 43, 47, 48, 49 Tacit knowledge, xxiii Taxonomy of educational objectives, 6 Teams (team behaviour), 41, 42 Technical coordination, 47 Technicians, 71 Technological literacy, 4, 16 Technology, 4, 81, 86, 109 Telepistemology, 26 Telerobotic warfare, 26, 28, 29 e Queen’s question, 125, 126 eory X, 39 eory X, 94 inking, 11, 13, 15, 18 inking, 76, 77 Torbert’s frames of professional development, 107, 108 Trade Union power, 129 Transdisciplinary course, xxii Transfer of learning, 131, 126 Truth, 32, 122 Truth (true), 122 United Nations, 75 Universities, 34 140 SUBJECT INDEX University (Idea of ), 95 University education, 116, 117 University technical colleges (U.K.), 118 Utility, 67 Values, 4, 25, 49, 50, 76 Verbal ability, 116 Verbal deprivation, 27 Virtue(s), 59, 74, 75, 78 Vocational education, 112, 113, 114 Weapons research, 72 Whistleblowing, 64 Wisdom, xxiii, 79 Wisdom (practical), 79 Work, 38 Workforce (jobs), 81ﬀ, 84ﬀ, 119
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813709.pdf&bkn=6813708&pdfType=book	Series ISSN: 1939-5221 Series ISSN: 1939-5221 SYNTHESIS LECTURES oN ENGINEERING SYNTHESIS LECTURES oN ENGINEERING A little Book on Teaching A little Book on Teaching A Beginner’s Guide for Educators of A Beginner’s Guide for Educators of Engineering and Applied Science Engineering and Applied Science Steven F. Barrett, University of Wyoming Steven F. Barrett, University of Wyoming illustrated by J. Barrett, Closer to the Sun International, Inc. illustrated by J. Barrett, Closer to the Sun International, Inc. It is often a challenging and overwhelming transition to go from being a It is often a challenging and overwhelming transition to go from being a student to being a teacher. Many new faculty members of engineering and student to being a teacher. Many new faculty members of engineering and science have to make this dramatic transition in a very short time. In the science have to make this dramatic transition in a very short time. In the same closing months of your Ph.D. program you are trying to complete same closing months of your Ph.D. program you are trying to complete your research, ﬁnish and defend your dissertation, ﬁnd a job, move to a your research, ﬁnish and defend your dissertation, ﬁnd a job, move to a new location, and start a new job as a faculty member. If you are lucky, new location, and start a new job as a faculty member. If you are lucky, you’ve had the opportunity to serve as a teaching assistant and possibly you’ve had the opportunity to serve as a teaching assistant and possibly have taught a university-level course. If you have served as a research as- have taught a university-level course. If you have served as a research as- sistant, your teaching opportunities may have been limited. Somehow, in sistant, your teaching opportunities may have been limited. Somehow, in this quick transition from student to teacher, one is supposed to become a this quick transition from student to teacher, one is supposed to become a good teacher and be ready for the ﬁrst day of school. good teacher and be ready for the ﬁrst day of school. This book is intended as a basic primer on college-level teaching and This book is intended as a basic primer on college-level teaching and learning for a new faculty member of engineering and applied science. learning for a new faculty member of engineering and applied science. New faculty members in other disciplines will ﬁnd much of the informa- New faculty members in other disciplines will ﬁnd much of the informa- tion applicable to their area of expertise as well. First and foremost, this tion applicable to their area of expertise as well. First and foremost, this book is about learning and teaching. However, it also provides helpful in- book is about learning and teaching. However, it also provides helpful in- formation on related topics such as mentorship, student challenges, gradu- formation on related topics such as mentorship, student challenges, gradu- ate students, tenure, and promotion and accreditation. This book is also ate students, tenure, and promotion and accreditation. This book is also intended as a reference for seasoned professionals. It is a good reference intended as a reference for seasoned professionals. It is a good reference for those mentoring the next generation of college educators. for those mentoring the next generation of college educators. ISBN: 978-1-60845-868-4 ISBN: 978-1-60845-868-4 90000 90000 9 781608 458684 9 781608 458684 B A B B R A A R R R R E R T E E T T T T T A A A l i l l T i i T T T l T T E l l E E B o B B o o o o o k k k o o o n n n T E T T A E E c A A c h c h h i n i i n g n g g M M M o o r o r g g r a g a n n a n & & & C C l l C a a l y y a p p y o o p o o o l o l l A Little Book on Teaching A Beginner’s Guide for Educators of Engineering and Applied Science Synthesis Lectures on Engineering A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 iii Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2012 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett www.morganclaypool.com ISBN: 9781608458684 paperback ISBN: 9781608458681 ebook DOI 10.2200/S00406ED1V01Y201203ENG017 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #17 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X A Little Book on Teaching A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett University of Wyoming illustrated by J. Barrett Closer to the Sun International, Inc. SYNTHESIS LECTURES ON ENGINEERING #17 CM& Morgan & cLaypool publishers ABSTRACT It is often a challenging and overwhelming transition to go from being a student to being a teacher. Many new faculty members of engineering and science have to make this dramatic transition in a very short time. In the same closing months of your Ph.D. program you are trying to complete your research, ﬁnish and defend your dissertation, ﬁnd a job, move to a new location, and start a new job as a faculty member. If you are lucky, you’ve had the opportunity to serve as a teaching assistant and possibly have taught a university-level course. If you have served as a research assistant, your teaching opportunities may have been limited. Somehow, in this quick transition from student to teacher, one is supposed to become a good teacher and be ready for the ﬁrst day of school. This book is intended as a basic primer on college-level teaching and learning for a new faculty member of engineering and applied science. New faculty members in other disciplines will ﬁnd much of the information applicable to their area of expertise as well. First and foremost, this book is about learning and teaching. However, it also provides helpful information on related topics such as mentorship, student challenges, graduate students, tenure, and promotion and accreditation. This book is also intended as a reference for seasoned professionals. It is a good reference for those mentoring the next generation of college educators. KEYWORDS teaching, engineering education, learning, new faculty, college-level teaching, instruc- tion, mentorship, tenure and promotion Contents vii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii 1 What makes a Great Teacher? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 What makes a great teacher? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3.1 The Atlantic, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3.2 What Great Teachers Do Differently . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.3 U.S. Professors of the Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.4 What Makes a Great Teacher? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.5 Top Five Character Traits of Superior Teachers . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.6 What makes a great teacher —take two! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Pulling it all together: a synthesized model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Great teachers as role models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 2 A little learning theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 The physiological basis of learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Levels of learning — Bloom’s Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Personality Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Jung, Myers and Briggs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Felder and Silverman: Bridging the gap between learning and teaching styles . . . 21 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.8 viii 3 4 5 Preparation for the ﬁrst day of classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 The student as a customer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 3.3 What did you want from a teacher when you were a student? . . . . . . . . . . . . . . . . . 27 Course development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4 3.4.1 Accreditation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.2 Syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4.3 Textbook selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.4 Lesson plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 Other items to consider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Establishing good student relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Conducting the lecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.7 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.8 Available resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.10 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.11 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Assessment of your students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Assessment of you . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3 Self assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 Assessment of your course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.7 Beyond the ﬁrst day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1 Mentoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.1 Traits of a good mentor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.2 Finding a good mentor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.3 Being a good mentor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Teaching Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2 5.3 Finding Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4 Where to go from here? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.5 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 ix A Sample syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 B Personal Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Preface xi It is often a challenging and overwhelming transition to go from being a student to being a teacher. Many new faculty members of engineering and science have to make this dramatic transition in a very short time. In the same closing months of your Ph.D. program you are trying to complete your research, ﬁnish and defend your dissertation, ﬁnd a job, move to a new location, and start a new job as a faculty member. If you are lucky, you’ve had the opportunity to serve as a teaching assistant and possibly have taught a university-level course. If you have served as a research assistant, your teaching opportunities may have been limited. Somehow, in this quick transition from student to teacher, one is supposed to become a good teacher and be ready for the ﬁrst day of school. What is this book about? This book is intended as a basic primer on college-level teaching and learning for a new faculty member of engineering or applied science. New faculty members in other disciplines will ﬁnd much of the information applicable to their area of expertise as well. First and foremost, this book is about learning and teaching. However, it also provides helpful information on related topics such as mentorship, student challenges, graduate students, tenure, and promotion and accreditation. This book is also intended as a reference for seasoned professionals. It is a good reference for those mentoring the next generation of college educators. Chapter 1 investigates teaching, characteristics of great teachers, and reviews some of the great teachers of the past and present. The chapter also provides some self-exploration exercises to answer such questions as what characteristics of teachers in your past made them memorable and effective and what kind of teacher do you want to be? Chapter 2 reviews some of the key theories of teaching and learning from the literature. As one begins their teaching career, it is important to be aware of the theoretical underpinnings of the teaching profession. By necessity, only several theories are discussed.The theories are used to develop a series of practical techniques that can be used in the classroom to enhance student learning. Chapter 3 provides practical pointers for preparing for the ﬁrst day of class including syllabus preparation, selection of textbooks, preparing lesson plans and teaching materials, and establishing a good classroom dynamic. Chapters 4 discusses the critical areas of assessment of students and students’ assessment of teachers. It also provides suggestions on how to assess your course and evaluate how effective it is in supporting student outcomes. Chapter 5 looks beyond the ﬁrst day of class and delves into the areas of effective mentoring, the rewards of teaching and some practical guidelines of balancing all the demands placed upon the new educator. The chapter concludes with suggestions on how to continue to be a good and effective educator. xii PREFACE A little bit about the author. I do not pretend to be an expert educator. I have taught for many years and in various venues, however, I consider myself a lifetime student and practitioner of the teaching profession. My teaching career began rather inauspiciously. While still an undergraduate student at the University of Nebraska at Omaha, my home church was having a difﬁcult time ﬁnding a teacher for a large class of active sixth graders. I volunteered to teach this class and quickly discovered I was in over my head! I wanted to teach the students about spiritual matters by carefully studying lesson materials. This was not a good approach for active-minded, spirited sixth graders. After several frustrating weeks of feeling like I was making little progress, I changed my approach. I planned a lot of varied activities to engage the students in lively and applied discussions of spiritual topics. I challenged them to determine methods to apply these techniques to their daily lives. The students and I became a close knit group and we covered a lot of spiritual ground that year. I enjoyed the experience so much I continued to teach the class for several more years. That was over 30 years ago. I have continued to teach challenging classes ever since. After completing my undergraduate studies in 1979, I was commissioned in the United States Air Force. I was initially assigned to a missile base in northern Montana. I had a knack for describing complex missile tasks to my fellow crewmembers. You see, teaching rambunctious sixth graders is not much different than teaching rambunctious young Air Force (AF) ofﬁcers. Both groups demand a high level of energy and creative teaching techniques. After being on missile crew for about a year, I was assigned to the missile instructor shop where I was to write the monthly training package for the crew force. After doing this for about a year, I was promoted to the Senior Instructor Crew. In this role, my crew partner and I were responsible for the monthly training requirements of all instructors and all crew members—approximately 150 talented, young ofﬁcers. Following this assignment, I served at the 4315 Combat Crew Training Squadron in Cali- fornia. In this position, I taught new AF ofﬁcers the intricacies of missile operations and also the awesome responsibility with which they were entrusted. After serving there for two years the AF transferred my family back to Omaha, Nebraska in a non-teaching assignment. I could not bear to be away from the classroom, so I volunteered to teach a Conﬁrmation class for 6-8th graders at my home church. I also completed my Master’s degree which allowed me to serve as an adjunct professor at my alma mater, the University of Nebraska at Omaha. My teaching dreams came true in 1988 when I was selected to teach at the United States Air Force Academy in Colorado Springs, Colorado. This undergraduate institution is charged with transforming high school graduates into dedicated, disciplined Air Force ofﬁcers. I served at the Academy from 1988 until my retirement from active duty Air Force service in 1999. While at the Academy I served in a number of positions of increasing responsibility and academic rank in the Department of Electrical and Computer Engineering. I also taught part time at night at a local university primarily intended for adult students. I retired from the Air Force and the Academy in 1999 as a full professor and the deputy department head. PREFACE xiii I was very excited about the prospect of starting a second academic career as an assistant professor. I was thrilled to be offered a tenure-track position at the University of Wyoming in 1999. Since arriving at UW, I have taught at all levels: from middle school and high school recruiting courses; a freshman orientation course; a sophomore circuits course; and a wide variety of senior and graduate-level design courses. I was promoted to associate professor and received tenure in 2005 and was promoted to full professor in 2011. I now serve as Associate Dean for Academic Programs in the College of Engineering and Applied Science. However, by choice, I maintain a full teaching load (and then some). I provide this background to establish credibility as a seasoned (but not an expert) educator. As I mentioned before, I am a lifetime student of good teaching practices. My approach to teaching has not changed much in 30+ years. My goal is to keep students actively engaged and committed to their own education. I believe that students learn best when they are actively engaged in exciting activities. This book contains information on effective teaching practices, from the literature along with lessons I have learned along the way. I’ve also been blessed to have outstanding teachers throughout my education and have also worked with a number of gifted educators. I have tried to capture what I learned from them in these pages as well. What this book is not. In the book I have purposely avoided involved discussions of learning and teaching theory. I consider this body of work to be of the upmost importance and hold it in the highest regard. Key theoretical concepts are discussed in Chapter 2. This brief chapter does not do justice to the many decades of outstanding research in learning and teaching theory. However, this book is about providing the fundamental tenets to help an aspiring educator quickly and successfully come up to speed on basic teaching concepts. No disrespect is intended toward the theoretical underpinnings that provide the foundation on which all teaching concepts are grounded. Workshop. If you are interested in the author conducting a workshop for beginning instructors at your institution, please contact him at [email protected]. If you are interested in conducting your own workshop, workshop materials are available from the author. Feel free to visit the book website at www.alittlebookonteaching.com. Also, if there are topics and concepts that should be included in future book editions, please contact the author through the website. Steven F. Barrett Laramie, WY March 2012 Acknowledgments xv I dedicate this book to the outstanding teachers and mentors I’ve had throughout my life. I also thank Joel Claypool of Morgan and Claypool Publishers who encouraged me to pursue this project. I also dedicate this book to my family who is my constant source of inspiration. I am the product of a family of gifted educators. My father, although not a formally trained educator, taught and inﬂuenced many young men and women by his example of a well-lived life of service to others. My mother was a registered nurse and served many years educating the next generation of nurses. She also served for many years as a teacher of challenged children. My wife serves as an aide for elementary school students who need extra help. My daughter is a gifted and dedicated elementary school teacher in Colorado. I also offer a special thank you to my oldest son Jonathan Barrett for providing book illustrations and web development. For additional informational please contact him at Closer to the Sun International, Inc. at www.CloserToTheSunInternational.com. Also, I offer a special thank you to Graham Barrett my youngest son for his careful edits of the ﬁnal manuscript and his thoughtful suggestions on how to improve the book. He too has served as an educator as a graduate teaching assistant and also working with summer high school enrichment programs. My goal is to one day be a great teacher. I hope to continue teaching for another 30 years (really!). I have learned a great deal about teaching while writing this book. I’ve put a lot of the material to practice already in the classroom. For the students! Steven F. Barrett March 2012 List of Figures xvii 1.1 What makes a great teacher? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Tenets of a great teacher: a synthesized model [2, 4, 6]. . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Measuring the volume of a radar sphere atop a tower. . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 “How do I get started? [ J. Barrett, Closer to the Sun International, Inc.]” . . . . . . 14 2.1 Model of memory storage [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Bloom’s taxonomy of cognitive learning [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Myers and Briggs personality types [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 “How do I reach them? [ J. Barrett, Closer to the Sun International, Inc.]” . . . . . . 24 3.1 How does your course support program accreditation [2]? . . . . . . . . . . . . . . . . . . . 31 3.2 “This is going to be a challenging course. The syllabus has a table of contents! [ J. Barrett, Closer to the Sun International, Inc.]” . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Textbook selection matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1 “A 57% average. What went wrong? [ J. Barrett, Closer to the Sun International, Inc.]” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Continuous improvement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.1 Serving as an educator is a lifelong profession based on continual improvement and growth [ J. Barrett, Closer to the Sun International, Inc.] . . . . . 56 C H A P T E R 1 1 What makes a Great Teacher? 1.1 OVERVIEW This chapter provides an introduction to the challenging and rewarding career of university-level teaching. The chapter begins with a review of what the literature has to say about what makes a great teacher. We review a variety of sources and ﬁnd amazing consistency in the tenets of good teaching. A synthesized list of tenets of great teachers is then developed. A series of case studies of good teachers, including an award-winning middle school science teacher and a world-renowned high school teacher, follows. You will then be asked to take a trip down memory lane and remember the great teachers you’ve had and list the tenets of what made them special and such an effective teacher. You then complete an exercise to determine what kind of teacher you want to be. Our goal for the chapter is for you to discover the tenets, activities, and attitudes of great teachers and include them in your own professional repertoire. 1.2 WELCOME Welcome to the noble profession of university-level teaching. You will ﬁnd this vocation to be challenging, rewarding, exciting, and doable. As a new faculty member you probably feel a bit over- whelmed with all that you have to do in a short amount of time. This book provides practical information and techniques to become an effective university-level educator. We also discuss tech- niques to balance the demands of research, service and teaching. We begin by investigating what the literature has to say about the tenets of effective teaching. 1.3 WHAT MAKES A GREAT TEACHER? This section reviews the tenets of effective teaching from a wide variety of sources from the literature. In each case we brieﬂy review the main tenets of the article. It is highly recommended that you add each of these sources to your professional reading list. Full citations for each source are provided at the end of the chapter. We summarize the traits of effective teachers in Figure 1.1. At the end of this section we pull together a synthesized list of traits discussed in the articles. 1.3.1 THE ATLANTIC, 2010 An article in the January/February 2010 issue of The Atlantic magazine posed the question: “What makes a great teacher?” The author, Amanda Ripley, investigated how teachers in similar grade school classroom environments can have dramatically different results in student progress. Using 2 1. WHAT MAKES A GREAT TEACHER? data gathered from the “Teach for America,” program similar traits of great teaching emerged. Here is what they found. Great teachers [1]: (cid:129) set big goals for their students. (cid:129) always look for ways to be more effective. (cid:129) involve family members in the educational process. (cid:129) have students work with their peers to help with understanding. (cid:129) matter. Effective teaching has a greater impact on student success than other factors such as a speciﬁc school or well the school is funded. (cid:129) frequently check to make sure students understand material using fun, non-threatening feed- back techniques during classroom activities. (cid:129) are well-prepared. Based on intended outcomes and objectives, they work back from intended outcomes to develop thorough and well-developed educational programs and lesson plans. They then stay on track and focused on lesson delivery. (cid:129) care about the success and well-being of their students. As an example, the article shadowed Mr. William Taylor, a ﬁfth grade teacher at Kimball Elementary School in Washington D.C. During the school year, Mr. Taylor moved his class from 40% performing at math grade level to over 90% at or above grade level by then end of the year. Mr. Taylor used a variety of effective teaching skills including having a deep commitment to his students. As an example, Mr.Taylor cooks his students a hot breakfast on the days when they take standardized tests. The The Atlantic article further reported that “Teach for America” leadership has spent con- siderable time poring over data in an attempt to predict future teaching success. Interestingly, those who have demonstrated perseverance, a grit, in dealing with life challenges tend to become good classroom teachers. Also, success in the last several years of college correlated with good classroom teaching performance [1]. 1.3.2 WHAT GREAT TEACHERS DO DIFFERENTLY Todd Whitaker is a seasoned, expert educator. He has served as a middle school and high school educator, a middle school and high school principal, and as a middle school coordinator. He now is a Professor at Indiana State University in the College of Education. Professor Whitaker has written a series of books about being an effective teacher and principal. In “What Great Teachers Do Differently — 14 Things That Matter Most,” Professor Whitaker provides 14 traits of effective teachers. In his book, Professor Whitaker devotes a chapter to illustrate each of these 14 traits of great teachers. These traits of effective teachers are brieﬂy summarized below [2]. 1.3. 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WHAT MAKES A GREAT TEACHER? (cid:129) People skills are extremely important for effective teaching and determining the quality of a school. (cid:129) Clear expectations must be set early and then followed throughout the academic year. Setting clear expectations sets a consistent tone for students for the entire year. (cid:129) An effective teacher appropriately responds to misbehavior to prevent it from happening again. They employ a variety of techniques to effectively and in a professional manner manage the situation. Throughout the encounter the teacher treats the student and parents with respect. Their focus is changing the student’s response and behavior in the future. In contrast, an ineffective teacher seeks revenge against misbehaving students. (cid:129) High expectations are extremely important. Most teachers set high expectations for their students. Great teachers set high expectations for themselves and hold themselves accountable. They focus on their own performance and how it relates to their student’s success. (cid:129) Effective teachers realize they are the most important variable in the classroom over which they have control. They constantly hold themselves accountable, take responsibility for classroom success, and consistently try to improve their performance. (cid:129) Great teachers create a positive atmosphere in their classroom based on respect, dignity and care for each and every student. These teachers effectively use genuine compliments and praise to positively inﬂuence their students and also their colleagues. They model appropriate behavior. (cid:129) Effective teachers set the tone for all interactions with positive professionalism. Students will respond in kind.To set a positive tone, teachers ﬁlter out negative inﬂuences such as complaints, demonstrate a positive attitude and enthusiasm toward their job, and do not let their private lives and concerns invade the classroom. (cid:129) Effective teachers place great importance in maintaining a positive relationship with students, parents and colleagues. They strive to treat everyone with respect and dignity. They also work to repair damaged relationships. (cid:129) Great teachers are aware of what goes on within their classroom. However, they carefully choose when to correct an offending student. In other words, they exercise great self control and wisely choose when to correct offenses. They rationally respond to inappropriate behavior without escalating the situation. Furthermore, they do not ignore the high achievers but provide them needed recognition to allow them to continue moving forward. (cid:129) Effective teachers construct plans for learning activities and reﬂect on the success of their efforts. If things do not go according to plan they proactively adjust their approach to achieve intended goals. 1.3. WHAT MAKES A GREAT TEACHER? 5 (cid:129) Great teachers carefully consider the impact on others before making changes. In particular, they make decisions to insure they meet their intended purpose and consider the thoughts of their best students. (cid:129) Great teachers carefully consider the feelings of others regarding decisions that have been made. They insure the good students are comfortable with the change while those that are uncomfortable will change in a positive direction. (cid:129) Good teachers keep standardized testing in perspective. They realize that good test scores are important but also value other measures of student achievement. (cid:129) Great teachers care about their students by establishing a positive approach, treating everyone with dignity and respect and modeling to their students how to treat others. It must be emphasized this list of outstanding teacher traits are based on the expertise in teaching provided by Todd Whitaker [2]. This book is a must read for the dedicated teacher. We next examine traits of excellent teaching provided by the U.S. Professors of the Year award program. 1.3.3 U.S. PROFESSORS OF THE YEAR The U.S. Professors of the Year awards program annually recognizes outstanding undergraduate teaching at the state and national levels. The awards program is sponsored by the Council for Ad- vancement and Support of Education (CASE) and the Carnegie Foundation for the Advancement of Teaching. A review of CASE award criteria provides further insight into tenets of great teaching. The CASE criteria include [3]: (cid:129) excellence in the impact on and involvement with undergraduate students; (cid:129) a demonstrated scholarly approach to teaching and learning; (cid:129) contributions in undergraduate education to the nominee’s institution, community and pro- fession; and (cid:129) the support of colleagues and former undergraduate students. In an effort to gain a wider perspective on what constitutes great teaching, several websites devoted to sharing characteristics of useful techniques for outstanding classroom instruction were visited. A brief summary of each is provided below. 1.3.4 WHAT MAKES A GREAT TEACHER? GreatSchoolsT M (www.greatschools.org) provides a sharing forum for users to obtain informa- tion on school performance.The purpose of the site is to “help parents to be more effectively involved in their children’s education [4].” The senior management and board of directors for GreatSchools are experts in the educational world. The GreatSchools staff compiled the characteristics of great teachers. They indicate that great teachers [4]: 6 1. WHAT MAKES A GREAT TEACHER? (cid:129) Set high expectations for all their students and do not give up on underachievers. (cid:129) Have clear, written objectives, lesson plans and learning goals for each assignment. Further- more, assignments are graded consistently and in a timely manner. (cid:129) Are prepared and organized and ready to teach. They present lesson material in a clear, orderly and structured manner. (cid:129) Engage students and have them look at issues in a variety of ways. They effectively engage all students in the class by asking questions to make sure students are following the lesson and vary their delivery approach. (cid:129) Care about their students, form strong relationships with them and are engaged in student and school activities. (cid:129) Are enthusiastic and thoroughly know their subject matter and work to stay current. (cid:129) Communicate on a regular basis with parents about student progress. Later is this section we develop a synthesized model of tenets of effective college teachers. We shall see that many of the tenets listed here are also applicable in the college classroom while others are not. As an example, the Family Educational Rights and Privacy Act (FERPA) provides strict guidance on what information may be shared with the parents of college students. 1.3.5 TOP FIVE CHARACTER TRAITS OF SUPERIOR TEACHERS “So You Want to Teach” is a website forum that allow practicing educators to share techniques on effective teaching. A poll of the top ﬁve character traits of superior teachers was provided. The top ﬁve traits were inspirational, compassionate, demanding, sense of humor, and subject matter knowledge [5]. A clear trend is starting to develop on the tenets, traits, and practices of good teachers. We are not quite ready to construct a synthesized model. We ﬁrst visit one more site to pick up a few more tenets that have not been mentioned yet. 1.3.6 WHAT MAKES A GREAT TEACHER —TAKE TWO! “Practical Theory” is another website forum that allows educators to share techniques on effective teaching. An article entitled “What makes a great teacher?” provided a list from a seasoned educator on what sets great teachers apart. Some of the tenets provided will now be quite familiar to you, others are new. The article indicates a great teacher [6]: (cid:129) Loves their students. (cid:129) Has a passion for teaching. (cid:129) Loves their subject material. 1.4. PULLING IT ALL TOGETHER: A SYNTHESIZED MODEL 7 (cid:129) Is constantly trying to improve. (cid:129) Is organized and has structure in their class. (cid:129) Is willing to change based on interaction with students. (cid:129) Is humble and realizes it is about and for the students. (cid:129) Has a strong ego to survive the days when things do not go so well. (cid:129) Is willing to work collaboratively within the school community to make it better. (cid:129) Is willing to reﬂect on what worked and what did not and make changes accordingly. (cid:129) Has a strong work ethic. Teaching takes considerable time and commitment outside the classroom. (cid:129) Understands the bigger picture of their role in student’s lives. Great teachers know that some of the best teaching moments occur outside the classroom. 1.4 PULLING IT ALL TOGETHER: A SYNTHESIZED MODEL As you read over the last several sections you probably noticed many similarities between the views of what constitutes a great teacher. In Figure 1.2, we have synthesized the different views into a single model. Note how the tenets conveniently ﬁt into three categories: attitude, preparation, and classroom. Two of these categories are completely within your control while many aspects of the classroom control category are also within your control. We have also removed two pieces from the model: communicating frequently with parents and standardized testing. The Family Educational Rights and Privacy Act (FERPA) provides very strict guidelines concerning a student’s right to privacy. In a nutshell, student records belong to the student. The protected information includes grades, ﬁnances, and discipline records. Parents are not allowed access to student records or information on progress without the written permission of the student [7]. Concerning standardized testing, many engineering schools require their students to complete the Fundamentals of Engineering (FE) examination as a graduation requirement. It is one of the steps to becoming a licensed professional engineer. FE examination results also provide valuable program assessment data helpful for ongoing continuous improvement and accreditation efforts [8]. Although the results of the FE examination are quite important, the exam results do not drive curricular content. Let’s take a closer look at the categories of teaching tenets within the synthesized model. Attitude. I was blessed with an outstanding mother and father. Both worked a variety of challenging, difﬁcult jobs in service to others. One of my father’s favorite maxims is “Attitude is everything!” He believes and demonstrates that any job or task approached with the proper attitude and gusto will be 8 1. WHAT MAKES A GREAT TEACHER? 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So it is with teaching. Much of our success in teaching depends on having a positive and resilient attitude. As shown in Figure 1.2, many of the tenets of a great teacher pertain to attitude. These tenets include: good relationship repair; being inspirational, humble, compassionate, and considerate; carefully considering decisions; a demonstrated strong work ethic; and a demonstrated passion for teaching. Preparation. I am a product of the military. My father served 26 years in the Air Force and my mother was a Naval Flight Nurse. I served in the Air Force for 20 years. Throughout my military career I frequently heard the adage “Proper prior planning prevents poor performance.” (There are other similar, more colorful versions.) Often referred to as the “6 Ps,” this adage packs considerable wisdom. Simply stated, careful preparation goes a long way toward success. As an educator, much of your success depends on preparation for the classroom. The tenets of a great teacher included in the 1.5. GREAT TEACHERS AS ROLE MODELS 9 area of preparation include establishing clear, written objectives; being well-prepared and organized; and establishing high expectations for your students and yourself. In the classroom. The two remaining tenets of great teachers pertain to classroom manage- ment. A great teacher proactively deals with behavioral challenges, ignores trivial disturbances and works to redirect student action such that misbehavior is not repeated. In the next section we study several outstanding teachers to see how these tenets are put into action. 1.5 GREAT TEACHERS AS ROLE MODELS In this section we showcase two outstanding teachers: a middle school teacher and a high school teacher. Paul Crips. Paul Crips is a seventh grade science teacher serving at Carey Junior High School in Cheyenne, Wyoming. For 34 years, he has taught industrial technology and science to 7th–12th graders. He is also certiﬁed to teach mathematics. I have worked with Paul on a number of projects and was honored to interview him for this book. Although Paul is the son of a elementary school educator, his motivation for entering the teaching profession came from his very caring and dedicated high school welding and wood fabri- cation teacher, Mr. Don Freshette. Paul was really bothered by the treatment he had received from several junior high mathematics teachers he had. He did not enjoy school. As he put it, “nobody lit my ﬁre.” In fact, he remembered that the teachers were quite negative and talked down to the students. Some teachers were openly cruel to students. This all changed when he took a class from Mr. Freshette in high school. Mr. Freshette openly demonstrated care and concern for his students. He listened to them and allowed them to work within the shop on various projects; however, he had high performance expectations for those in his classes. Paul felt a connection to Mr. Freshette and knew that he cared. In retrospect, Paul is amazed at how much inﬂuence, either positive or negative, that a single teacher can have on your life. Following a two and half year stint in the Navy, Paul enrolled at the University of Wyoming and completed a Bachelor of Science degree in Industrial Arts from the College of Education in 1978. Paul accepted his ﬁrst job in Cheyenne at an alternative high school for at-risk students. He taught vocational education courses there for three years before being hired away to Carey Junior High School. He taught all areas of industrial arts for 16 years before becoming a science teacher in 1996. Since then, he has taught Physics, Chemistry, Biology, and Earth and Space Science. Paul describes the tenets of a great teacher as one who cares deeply for the well being and success of their students. To really care you need to establish a trusting rapport with your students by showing, via actions, that you really care and will not give up on them regardless of how they perform or behave. He added that it is easy to become angry at the misbehavior of a student but he quickly added you must separate the action from the student. Regardless of the challenge, you need to overcome and work with each student toward success. He acknowledged that this is difﬁcult 10 1. WHAT MAKES A GREAT TEACHER? to do with a large classroom of many students with a wide variety of background, preparation, and capability. To provide opportunities to work individually with each student, Paul has enlisted the aid of students in higher grades to serve as mentors for the younger grades. He further added that you can not ignore the gifted students. They need to be challenged so that they too can realize their needs and dreams. Paul indicated another tenet of a good teacher is to engage their students. To engage students from the ﬁrst day of school, Paul greets each one as they enter the classroom. He works hard to be personal, humble, and human. His goal is to demonstrate that he is approachable and can be trusted. He also uses his sense of humor to keep students engaged. Paul’s efforts to establish rapport with his students does not mean he ignores or condones misbehavior. He is adamant that punishment does not accomplish anything. Instead, it reinforces poor behavior. When a student misbehaves Paul takes them aside and talks to them about their actions. His goal is to proactively engage and redirect their energy in a positive manner and move on. A related goal is not to allow students to leave his classroom angry. He also does not tolerate cheating. When a cheating incident occurs, he uses the situation to have the student identify their incorrect behavior and helps them understand that the consequences of cheating later in life will be much more severe. To further engage students Paul indicated it is important to interview students to ﬁnd out where their interest lies and tie curricular content to their interests. Paul is a self-proclaimed “gear head.” He spends considerable time rebuilding cars. He has found his students also have a mutual interest in this area which has provided a bridge to curricular content. To engage students in a variety of topics, Paul has mentored a number of after-school programs in robotics, short wave radio, and astronomy. Currently, he mentors an after-school program where students learn the basics of programming using small robots controlled by a Texas Instruments TI-84 calculator. In the classroom, Paul keeps students engaged with curricular content with carefully chosen, problem-based activities. For example, to teach a variety of math concepts, Paul takes students on a short hike to a nearby radar sphere mounted atop a high tower. He then wonders out loud, “How might we measure the volume of the radar sphere?” He allows students to brainstorm on possible solutions. He then reminds them of helpful curricular concepts previously discussed in class such as the equation for the volume of a sphere and right triangle relationships (sine, cosine, and tangents). He then allows the students to brainstorm on how they might use these concepts to measure the volume of the radar sphere atop the tower. Students typically realize that if there was some method to measure the height of the top and bottom of the sphere, they would be able to calculate the sphere volume. Paul then produces a tape measure and an inclinometer and asks the students how these tools might be used to gather the required data. See Figure 1.3. Paul’s teaching is guided by a number of principles. We have already discussed establishing student rapport and keeping them engaged. Paul notes that students are not all wired the same. Many need pictures and diagrams to understand concepts. He indicated that the illustrations take 1.5. GREAT TEACHERS AS ROLE MODELS 11 ,(cid:10)-(cid:10)./0(cid:10)π(cid:10)(cid:9)0 β α + Figure 1.3: Measuring the volume of a radar sphere atop a tower. away much of the anxiety that many have toward mathematics and allows them to visualize solutions to posed problems. To a new educator Paul offers the following advice. Be kind to yourself and be patient. You have a lot to learn and things will not always go how you have planned. Most importantly, never give up. If you won’t give up, neither will your students. In closing, he indicated in the teaching profession you are free to become who you want to be as an educator. It is very important to reﬂect on the good and not so good teachers you’ve had in your past. Model and become the best of those from your past. It is not surprising that Paul has earned a number of teaching awards for his dedication to students. In 1994, he was the Wyoming recipient of the Christa McAuliffe Fellowship. It is also no surprise that he used the fellowship money to purchase telescopes for his students to use. In 1996, he was named Wyoming’s U.S. West Teacher of the Year.This was followed in 1999 by being named one of 39 teachers nationwide named as a recipient of the Walt Disney Corporation American Teachers Award. Also that year he was Wyoming’s Milken Foundation Teacher of the Year. In 2004, he was one of four teachers chosen statewide for the Arch Coal Teacher of the Year Award. Paul takes all of the awards in stride and is not comfortable talking about the recognition and accolades he has received. Instead, he simply reminds all of us “it’s all about the students.” Jamie Escalante. You may already be familiar with the work of Jaime Escalante. His dedicated, lifetime work as an educator of students was showcased in the Warner Brothers movie “Stand and Deliver.” It would have been an honor to interview him for this book; however, Mr. Escalante died 12 1. WHAT MAKES A GREAT TEACHER? in 2010. Jay Mathews wrote an excellent book on Mr. Escalante, “Escalante – The Best Teacher in America.” This book is a must read for the dedicated teacher. Mr. Mathews did an excellent job catching the infectious spirit of Mr. Escalante’s commitment to teaching excellence and most importantly his students.The information for the following vignette was obtained from Mr. Mathews book [9]. Mr. Escalante taught mathematics at James A. Garﬁeld High School in East Los Angeles. In December 1982 the Los Angeles Times reported that 14 of 18 Garﬁeld High School students taking the Calculus Advanced Placement (AP) examination had been accused of cheating. The students were eventually cleared of any misdoing. Mr. Mathew’s book does an outstanding job describing the incident and its resolution [Mathews]. However, the real story is how Mr. Escalante and other dedicated faculty and staff at Garﬁeld High School prepared students against difﬁcult challenges and odds to prepare for this examination. I pored over Mathew’s book to unlock Mr. Escalante’s secrets of good teaching. Mathew’s indicated his motivation for writing about Mr. Escalante’s was “to describe in detail how Escalante taught and how Garﬁeld had come so far, other teachers and schools with similar challenges might see something they could use. If I could honestly portray the setbacks, misunderstandings, and personal tensions that accompanied Garﬁeld’s achievement, perhaps others would not become disheartened when they found the path to learning particularly rough [9].” We thank Mr. Mathew’s for his carefully researched and documented biography of Mr. Escalante. Mr. Escalante was born and raised in La Paz, Bolivia into a family of teachers. The family placed a great emphasis on education. He attended a demanding Jesuit High School. He taught at several schools in Bolivia before immigrating to the United States in 1963 when he was 33 years old. Unfortunately, his Bolivian teaching credentials were not accepted in the U.S. Therefore, he worked a variety of jobs and received a National Science Foundation Scholarship to achieve his teaching degree in order to obtain a teaching license [9]. Mr. Escalante passionately worked daily to be an outstanding teacher. Early on he set high standards and expectations for his students and appealed to their pride to meet them. He also had his students assume responsibility for their own actions. However, it was clear that he cared deeply for his students. In fact, “Escalante and his students became part of the same team, ﬁghting a common foe, rather than adversaries in a war in which the teacher always had the upper hand and the students often contemplated revolt or desertion [9].” Mr. Escalante employed a variety of techniques to always keep his students interested and engaged. He kept careful notes that contained his lesson plans, math short cuts, and insights honed over many years studying and teaching mathematics. He worked to bridge complex mathematical concepts to real world things that students knew and understood. He was convinced that students learned by doing and kept them engaged with in class demonstrations and problem drills. He was particularly skillful at linking math concepts to examples in sports and small business. Furthermore, he would not miss the chance to illustrate a concept with a fun, enjoyable illustration. For example, to illustrate the concept of fractions he would don a chef ’s hat (from a previous job) and slice apples to illustrate fundamental concepts. As follow up, students could count on multiple homework problems to hone their understanding of new concepts. The common theme throughout Mr. Escalante’s approach was he cared deeply for his students’ progress and well being and worked daily to make difﬁcult mathematical concepts accessible [9]. 1.6. SUMMARY 13 1.6 SUMMARY In this chapter we identiﬁed the tenets of great teaching from a variety of sources. These sources were then combined into a synthesized model that includes attitude, preparation, and classroom skills. It is important to realize most of these tenets of great teaching are under your direct control. In an upcoming chapter we develop concrete techniques to apply these tenets in the classroom. The tenets of great teaching was then explored through a series of vignettes. Our goal throughout the chapter is for you to develop a personal teaching philosophy that incorporates these tenets. REFERENCES AND FURTHER READING [1] Ripley, Amanda “What makes a great teacher?” The Atlantic. Online. Internet. Jan- uary/February 2010. www.theatlantic.com Cited on page(s) 2 [2] Whitaker,Todd. What Great Teachers Do Differently — 14 Things That Matter Most. Larchmont: Eye On Education, Inc, 2004. Cited on page(s) xvii, 2, 5, 8 [3] “U.S. Professors of the Year Award Program.” Online. Internet. www.uspprofessorsoftheyear.org Cited on page(s) 5 [4] “What Makes A Great Teacher?” 3 pp. Online. Internet. www.greatschools.org Cited on page(s) xvii, 5, 8 [5] “Top 5 (Plus 14) Character Traits of Superior Teachers.” 6 pp. Online. Internet. www. soyouwanttobeateacher.com Cited on page(s) 6 [6] “What Makes A Great Teacher?” 2 pp. Online. Internet. www.practicaltheory.org Cited on page(s) xvii, 6, 8 [7] “Family Educational Rights and Privacy Act (FERPA).” Online. Internet. www2.ed.gov Cited on page(s) 7 [8] “NCEES—Advancing Licensure for Engineers and Surveyors.” Online. Internet. www.ncees. org Cited on page(s) 7 [9] Mathews, Jay. Escalante—The Best Teacher in America. New York: Henry Holt and Company, 1988. Cited on page(s) 12, 13 14 REFERENCES AND FURTHER READING Figure 1.4: “How do I get started? [ J. Barrett, Closer to the Sun International, Inc.]” 1.7 CHAPTER ACTIVITIES 1. Develop your personal list of tenets of great teaching that you will follow. 1.7. CHAPTER ACTIVITIES 15 2. Spend some time reﬂecting on teachers both good and bad from your past. Develop a list of both good and bad tenets from your personal reﬂections. 3. Develop a personal teaching mission statement based on the tenets of great teaching from the area of attitude. 4. Select a course you are currently teaching or will teach in the near future. Develop objectives for that course. How do the course objectives support student outcomes? 5. For the course discussed in the previous question, develop lesson-by-lesson objectives for the course. 6. Develop a list of concrete methods to use in the classroom to apply the tenets of great teaching summarized in the synthesized model. 7. In the Paul Crips vignette, what tenets of great teaching were exhibited? 8. In the Jaime Escalante vignette, what tenets of great teaching were exhibited? 9. Identify a teacher you greatly admire; interview them, identify the tenets of great teaching they exhibit, and write a teaching vignette about them. 10. Write your own personal teaching vignette. C H A P T E R 2 17 A little learning theory 2.1 OVERVIEW This chapter is devoted to the concept of learning and related teaching theories. To be a good teacher one needs to be familiar with some of the theoretical underpinnings behind sound instruc- tion techniques and how they are related to learning. These theoretical concepts will help you better understand the learning process and provide concrete methods on how to best reach your students. Kupfermann succinctly links the important concepts of this chapter: learning, knowledge, and mem- ory. He describes learning as “the acquisition of knowledge about the world” and “memory is the retention or storage about that knowledge [1].” This chapter begins with a brief review of the physiological basis of learning with an emphasis on the difference between short term and long term memory and the conversion or consolidation of short term memory to long term memory. We then investigate the different levels of cognitive learning, as described by Benjamin Bloom, followed with a brief introduction to the work of Myers and Briggs in identifying 16 different personality types based on the work of C.G. Jung. A teacher needs to be aware of their own personality type and those of their students so they can best develop teaching strategies to reach them. The work of Felder and Silverman, who bridged a variety of learning styles to teaching styles, is then reviewed. It should be no surprise that a teacher maximizes their effectiveness by employing a variety of teaching styles to meet the needs of a variety of student with different learning styles. 2.2 THE PHYSIOLOGICAL BASIS OF LEARNING To understand the process of learning we need to brieﬂy review some physiological fundamentals related to memory. Memory consists of two distinct types: short-term or primary memory and long-term or secondary memory. Short-term memory is the ability to retain speciﬁc bits or pieces of information for a brief amount of time.These tidbits of information may be retrieved instantaneously. Long-term memory, on the other hand, may be retained for a much longer period of time; however, recall of this information may take longer [2, 3, 5]. Figure 2.1 provides a model of the relationship between short-term and long-term memory. The goal of learning is to take knowledge of the world and retain it in long-term memory. The process begins as an input to short-term memory. Short-term memory is converted to long-term memory through a process called memory consolidation [1]. 18 2. A LITTLE LEARNING THEORY (cid:5)(cid:7)(cid:2)(cid:18)(cid:11) (cid:4)(cid:14)(cid:6)(cid:9)(cid:11)(cid:10)(cid:11)(cid:12)(cid:9)(cid:28) (cid:28)(cid:12)(cid:28)(cid:6)(cid:9)(cid:29) (cid:28)(cid:12)(cid:28)(cid:6)(cid:9)(cid:29) (cid:13)(cid:6)(cid:7)(cid:4)(cid:6)(cid:16)(cid:5)(cid:19)(cid:3)(cid:11)(cid:5)(cid:6)(cid:7) (cid:16)(cid:6)(cid:7)(cid:15)(cid:10)(cid:11)(cid:12)(cid:9)(cid:28) (cid:28)(cid:12)(cid:28)(cid:6)(cid:9)(cid:29) (cid:4)(cid:12)(cid:3)(cid:9)(cid:13)(cid:14)(cid:10)(cid:3)(cid:7)(cid:19)(cid:10)(cid:9)(cid:12)(cid:3)(cid:19)(cid:10)(cid:6)(cid:18)(cid:11) (cid:6)(cid:18)(cid:11)(cid:2)(cid:18)(cid:11) Figure 2.1: Model of memory storage [1]. Memory consolidation converts short- to long-term memory through a variety of anatomical and physiological changes that occur at the cellular level within the brain. It is important to note that this process takes time [1, 2, 3]. There are several techniques to accelerate the process. (cid:129) Rehearsal or repeating the information accelerates and potentiates (enhances) the consolida- tion (conversion) of short term to long term memory [3]. This is called habituation [4]. (cid:129) Very strong, repeated, and strongly pleasant (or unpleasant) input has an excellent chance of being converted from short term to long term memory [2]. This is called sensitization [4]. (cid:129) Information that is codiﬁed (categorized) has a good chance of being converted from short term to long term memory. That is, if new information is compared to similar existing long term memory items, it has a better chance of becoming long term memory [3], With a fundamental understanding of the physiological process of learning in place, let’s investigate the different levels of cognitive learning as described by Benjamin Bloom. 2.3 LEVELS OF LEARNING — BLOOM’S TAXONOMY Learning may be divided into three different areas: cognitive, affective, and psychomotor. Cognitive learning involves the development of intellectual skills. Affective learning involves the development of emotions including feelings, values, and attitudes. Psychomotor learning involves the development of physical movement, coordination and the development of motor skills. As educators we are primarily concerned with the development of cognitive learning. Benjamin Bloom developed a taxonomy or hierarchy of cognitive learning skills to allow “educators to evaluate learning of students systematically [6].” Bloom’s taxonomy of cognitive learning is illustrated in Figure 2.2. The taxonomy consists of advancing cognitive skills from the knowledge level up through the evaluation level. To develop higher-level cognitive skills one must ﬁrst develop a base in the lower levels [7]. 2.3. LEVELS OF LEARNING — BLOOM’S TAXONOMY 19 (cid:4) (cid:12) (cid:4) (cid:4) (cid:12) (cid:13) (cid:6) (cid:9) (cid:2) (cid:10) (cid:11) (cid:14) (cid:15) (cid:18) (cid:6) (cid:14) (cid:11) (cid:10) (cid:9) (cid:12) (cid:14) (cid:15) (cid:14) (cid:5) (cid:18)(cid:19)(cid:11)(cid:15)(cid:5)(cid:11)(cid:3)(cid:4)(cid:12)(cid:13) 1(cid:19)(cid:12)(cid:11)(cid:12)(cid:9)(cid:28)(cid:5)(cid:7)(cid:12)$ (cid:4)(cid:12)(cid:16)(cid:12)(cid:13)(cid:11)$(cid:10)(cid:13)(cid:9)(cid:5)(cid:11)(cid:5)%(cid:18)(cid:12)2 (cid:20)(cid:21)(cid:13)(cid:3)(cid:22)(cid:7)(cid:16)(cid:4)(cid:16) 1(cid:8)(cid:6)(cid:9)(cid:28)(cid:18)(cid:16)(cid:3)(cid:11)(cid:12)$ (cid:28)(cid:3)(cid:24)(cid:12)(cid:18)(cid:2)$(cid:10)(cid:19)(cid:12)(cid:4)(cid:5)(cid:15)(cid:7)2 (cid:2)(cid:13)(cid:11)(cid:15)(cid:21)(cid:16)(cid:4)(cid:16) 1(cid:19)(cid:12)(cid:9)(cid:5)(cid:17)(cid:12)$(cid:10)(cid:12)#(cid:2)(cid:16)(cid:3)(cid:5)(cid:7)2 (cid:2)(cid:10)(cid:10)(cid:15)(cid:4)(cid:23)(cid:11)(cid:3)(cid:4)(cid:12)(cid:13) 1(cid:13)(cid:3)(cid:16)(cid:13)(cid:18)(cid:16)(cid:3)(cid:11)(cid:12)$(cid:10)(cid:4)(cid:6)(cid:16)(cid:17)(cid:12)2 (cid:14)(cid:12)(cid:17)(cid:10)(cid:9)(cid:7)(cid:22)(cid:7)(cid:13)(cid:16)(cid:4)(cid:12)(cid:13) 1(cid:12)#(cid:2)(cid:16)(cid:3)(cid:5)(cid:7)$(cid:10)(cid:5)(cid:7)(cid:11)(cid:12)(cid:9)(cid:2)(cid:9)(cid:12)(cid:11)2 (cid:24)(cid:13)(cid:12)(cid:25)(cid:15)(cid:7)(cid:6)(cid:26)(cid:7) 1(cid:16)(cid:5)(cid:4)(cid:11)$(cid:10)(cid:4)(cid:11)(cid:3)(cid:11)(cid:12)2 Figure 2.2: Bloom’s taxonomy of cognitive learning [6]. Bloom divided the taxonomy into six different levels of learning, as illustrated in Figure 2.2. Provided with each level are action verbs associated with the speciﬁc level.1 In ascending order, from the lowest to the highest cognitive level, is [6]: (cid:129) Knowledge: recalling or repeating facts verbatim. Action verbs include list or state [6]. (cid:129) Comprehension: demonstrating understanding of terms and concepts. Action verbs include explain (in your own words) and interpret [6]. (cid:129) Application: applying learned information to solve a problem. Action verbs include calculate and solve [6]. (cid:129) Analysis: breaking concepts into their primary elements, forming theoretical, logical or math- ematical models to explain observed phenomena. Action verbs include derive and explain [6]. (cid:129) Synthesis: creating something, combining elements in a new way. Action verbs include for- mulate or design [6]. 1Goel et al. [8] compiled an extended list of action verbs from the literature associated with Bloom’s Taxonomy in Goel and Sharda. 20 2. A LITTLE LEARNING THEORY (cid:129) Evaluation: making and justifying value judgments or selecting from a number of alternatives. Action verbs include determine, select or critique [6]. As educators of engineering and applied science, it is important to understand the fundamental concepts of Bloom’s Taxonomy. These concepts may be employed in a number of different areas. (cid:129) When initially developing a course, you should carefully consider at what level cognitive skills will be developed. This should be kept in mind when developing speciﬁc course objectives. We discuss the development of objectives in the next chapter. (cid:129) If your course will develop higher level cognitive skills, you need to ascertain where the lower- level skills will be developed. For example, will they be developed in a pre-requisite course? Another alternative would be to develop the lower-level skills early in the course followed by higher-level skills later in the course. (cid:129) In an upcoming chapter we discuss student assessment. When assessing students via quizzes and examinations, they should be assessed at the same cognitive level at which they have been taught. (cid:129) If our goal is to develop some of the highest level cognitive skills such as design (synthesis), then students should be provided practice exercises at this cognitive level during the course. Goel et al. report the top levels of Bloom’s Taxonomy “represent higher-level cognitive activities that require and develop mental faculties of creativity, critical thinking and innovative problem solving [8].” Aside from having a ﬁrm understanding of the different levels of cognitive learning, the effective teacher must be self aware of their own personality type. Furthermore, the effective teacher must be aware of the wide variety of different personality types. To reach students, we must tailor our teaching approach to a learning style compatible with their personality type. In the next section we discuss the work of Myer and Briggs in identifying different personality types ﬁrst elucidated by Carl Jung. 2.4 PERSONALITY TYPES In the next several sections we brieﬂy review Carl Jung’s seminal, fascinating work in personality theories. We also examine the work of Katherine Briggs and Isabel Briggs Myers in codifying Jung’s personality traits into a test of approximately 125 questions to determine one’s personality type. This test is commonly known as Myers-Briggs TypeR Indicator or MBTIR and places an individual in one of 16 different personality types. Certain personality traits are more in tune to speciﬁc learning styles than others. Furthermore, due to our own personality type, we as educators are more comfortable with speciﬁc types of teaching styles. To effectively reach our students we need to bridge their learning style with our teaching style. We close with the ground-breaking work of Felder and Silverman in bridging this gap with concrete teaching techniques to address all learning styles. 2.5. JUNG, MYERS AND BRIGGS 21 2.5 JUNG, MYERS AND BRIGGS Carl Jung developed a theory of personality traits. It is based on the fundamental difference between introversion and extroversion. Introverts are more comfortable with their internal thoughts and feelings while extroverts prefer things, people and related activities. As we deal with the world around us, as introverts or extroverts, there are four basic functions we employ: sensing the world by looking or listening, thinking by evaluating information, intuiting by integrating a large amount of information, and feeling by evaluating information using our emotional response. The proportion of each of these functions places us in a speciﬁc personality type [9]. Myers and Briggs developed a test tool, designated Myers-Briggs Type IndicatorR or MBTIR, to identify an examinee’s personality type via a series of 125 questions. The questions illuminate an examinee’s preferences in dealing with the world in four different preference areas as described by Jung [9, 10]: (cid:129) What is your favorite world, extroversion (E) or introversion (I) [10]? (cid:129) How do you process information, sense basic information (S) or interpret and add meaning (N) [10]? (cid:129) How do you make decisions, do you apply logic and thinking (T) or do assess people and related circumstances (F) [10]? (cid:129) In dealing with the world, do you prefer to decide things (judging ( J)) or do you keep your options open (perceiving (P)). The four preferences and resulting 16 personality types are illustrated in Figure 2.3. A per- sonality type is identiﬁed by a four-letter designator such as (ISTP, ENTJ, etc.). A brief explanation of each personality type is provided at [10]. Also, if you are interested in determining your own personality type via the MBTI instrument, please see [10]. 2.6 FELDER AND SILVERMAN: BRIDGING THE GAP BETWEEN LEARNING AND TEACHING STYLES As previously mentioned, based on one’s personality type, we have a preferred method of learning new material. Also, as educator’s we have a preferred teaching style linked to our personality type. Richard Felder and Linda Silverman published a paper in 1988, “Learning and Teaching Styles in Engineering Education” to assist engineering educators in bridging the gap between the diverse learning styles of their students and their own teaching styles [11]. They proposed a ﬁve axis preferred student learning style based on perception, input, organi- zation, processing and understanding. Correspondingly, they proposed a ﬁve axis teaching style based on content, presentation, organization, student participation, and perspective. Their hypothesis was that engineering educators who adapt their teaching style to include the extremes of each axis of 22 2. A LITTLE LEARNING THEORY (cid:31)(cid:20)(cid:28)(cid:8) 2 (cid:18)(cid:20)(cid:28)(cid:8) 5 (cid:5) 1 (cid:10) (cid:15) (cid:7) (cid:4) (cid:7) (cid:12) (cid:4) (cid:31)(cid:20)(cid:30)(cid:8) (cid:5)(cid:7)(cid:11)(cid:9)(cid:3)(cid:17)(cid:12)(cid:9)(cid:11)(cid:10)142 (cid:8)(cid:3)(cid:17)(cid:6)(cid:9)(cid:5)(cid:11)(cid:12)(cid:10)(cid:23)(cid:6)(cid:9)(cid:16)(cid:19)(cid:10) (cid:11)(cid:14)(cid:5)(cid:7)(cid:24)(cid:5)(cid:7)(cid:15)(cid:10)1!2 (cid:18)(cid:20)(cid:30)(cid:8) (cid:19)(cid:12)(cid:13)(cid:5)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4) (cid:8)(cid:3)(cid:17)(cid:6)(cid:9)(cid:5)(cid:11)(cid:12)(cid:10)(cid:23)(cid:6)(cid:9)(cid:16)(cid:19)(cid:10) (cid:12)#(cid:11)(cid:9)(cid:3)(cid:17)(cid:12)(cid:9)(cid:11)(cid:10)132 (cid:7) (cid:6) (cid:5) (cid:11) (cid:3) (cid:28) (cid:9) (cid:6) (cid:8) (cid:7) (cid:5) (cid:19)(cid:12)(cid:13)(cid:5)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4) (cid:31)(cid:27)(cid:28)(cid:8) (cid:8)(cid:12)(cid:12)(cid:16)(cid:5)(cid:7)(cid:15)(cid:10)172 2 6 1 (cid:10) (cid:7) (cid:6) (cid:5) (cid:11) (cid:5) (cid:18) (cid:11) (cid:7) (cid:5) (cid:18)(cid:27)(cid:28)(cid:8) (cid:2)(cid:12)(cid:9)(cid:13)(cid:12)(cid:5)(cid:17)(cid:5)(cid:7)(cid:15)192 (cid:4)(cid:11)(cid:9)(cid:18)(cid:13)(cid:11)(cid:18)(cid:9)(cid:12) (cid:18)(cid:27)(cid:30)(cid:8) (cid:18)(cid:20)(cid:28)(cid:29) (cid:31)(cid:27)(cid:30)(cid:8) (cid:31)(cid:20)(cid:28)(cid:29) 2 5 (cid:5) 1 (cid:10) (cid:15) (cid:7) (cid:4) (cid:7) (cid:12) (cid:4) (cid:31)(cid:20)(cid:30)(cid:29) (cid:11)(cid:14)(cid:5)(cid:7)(cid:24)(cid:5)(cid:7)(cid:15)(cid:10)1!2 (cid:7) (cid:6) (cid:5) (cid:11) (cid:3) (cid:28) (cid:9) (cid:6) (cid:8) (cid:7) (cid:5) (cid:19)(cid:12)(cid:13)(cid:5)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4) (cid:5)(cid:7)(cid:11)(cid:9)(cid:3)(cid:17)(cid:12)(cid:9)(cid:11)(cid:10)142 (cid:8)(cid:3)(cid:17)(cid:6)(cid:9)(cid:5)(cid:11)(cid:12)(cid:10)(cid:23)(cid:6)(cid:9)(cid:16)(cid:19)(cid:10) (cid:8)(cid:3)(cid:17)(cid:6)(cid:9)(cid:5)(cid:11)(cid:12)(cid:10)(cid:23)(cid:6)(cid:9)(cid:16)(cid:19)(cid:10) (cid:12)#(cid:11)(cid:9)(cid:3)(cid:17)(cid:12)(cid:9)(cid:11)(cid:10)132 (cid:19)(cid:12)(cid:13)(cid:5)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4) (cid:31)(cid:27)(cid:28)(cid:29) (cid:7) (cid:6) (cid:5) (cid:11) (cid:3) (cid:28) (cid:9) (cid:6) (cid:8) (cid:7) (cid:5) (cid:8)(cid:12)(cid:12)(cid:16)(cid:5)(cid:7)(cid:15)(cid:10)172 (cid:18)(cid:27)(cid:28)(cid:29) 2 6 1 (cid:10) (cid:7) (cid:6) (cid:5) (cid:11) (cid:5) (cid:18) (cid:11) (cid:7) (cid:5) (cid:31)(cid:27)(cid:30)(cid:29) (cid:21)(cid:18)(cid:19)(cid:15)(cid:5)(cid:7)(cid:15)182 (cid:18)(cid:27)(cid:30)(cid:29) Figure 2.3: Myers and Briggs personality types [10]. 2.6. FELDER AND SILVERMAN 23 student learning styles are apt to provide “an optimal environment for most (if not all) students in the class [11].” It might appear to be an insurmountable task to link a diverse group of student preferred learning styles with an educator’s teaching style; however, Felder and Silverman indicated usual methods of engineering education adequately address many categories. Furthermore, they indicated the addition of a small number of additional teaching techniques accommodates the learning style of every student in the class [11]. As you may have already gathered, the article by Felder and Silverman is a “must read” in its entirety. Felder and Silverman concluded the article with a list of teaching techniques to address all learning styles. I highly encourage you to obtain a copy of this article and keep the list of teaching techniques available for ready and regular reference. Here is an abbreviated version of their list [11]: (cid:129) Relate new material to what has already been presented and to student’s prior experience. For example, when teaching new material, relate it to concepts presented in pre-requisite courses. I also ﬁnd it helpful to present the course framework during the ﬁrst session of the course. I refer to it frequently throughout the course to show how new material relates to the overall class [11]. (cid:129) Provide balance between concrete and abstract information. This may be accomplished by supplementing theoretical concepts with practical real world examples. I believe students grasp new concepts quicker if they can see how they might use the material on the job or how to solve a speciﬁc engineering challenge. Felder and Silverman suggest using the scientiﬁc method to link theoretical material with concrete examples [11]. (cid:129) Use a wide variety of visual material and computer-assisted instruction to enhance learn- ing [11]. When I served on the faculty at the United States Air Force Academy, I had the opportunity to audit a microcontrollers course taught by Dr. Pamela (Pam) Neal. She effec- tively used a series of visual worksheets and executing computer code projected on classroom screen to illustrate the link between assembly language programming and its effect on computer registers. (cid:129) Felder and Silverman strongly recommended not ﬁlling classroom time with only lecturing and writing on the board. Instead, they recommend short, periodic breaks for student reﬂection. They also recommend active, small-group brainstorming activities during classroom sessions to involve students in active learning [11]. (cid:129) Felder and Silverman also recommended assigning a reasonable number of homework exercises to practice and apply the material taught in class. The exercises should align with the intended Bloom’s Taxonomy level of the course objectives. Furthermore, they recommended allowing students to work together on homework assignments [11]. 24 2. A LITTLE LEARNING THEORY Figure 2.4: “How do I reach them? [ J. Barrett, Closer to the Sun International, Inc.]” 2.7 SUMMARY This chapter was devoted to the concept of learning and related teaching theories. To be a good teacher we need to be familiar with some of the theoretical underpinnings behind sound instruction techniques and how they are related to learning. These theoretical concepts will help us better understand the learning process and provide concrete methods on how to best reach our students. The chapter began with a brief review of the physiological basis of learning with an emphasis on the difference between short-term and long-term memory and the conversion or consolidation of short- term memory to long-term memory. We then investigated the different levels of cognitive learning as described by Benjamin Bloom followed with a brief introduction to the work of Myers and Briggs in identifying 16 different personality types based on the work of C.G. Jung. A teacher needs to be aware of their own personality type and those of their students so they can best develop teaching strategies to reach them. The work of Felder and Silverman who bridged a variety of learning styles to teaching styles and provided concrete advice on how to reach all of the students in our classroom was then reviewed. REFERENCES AND FURTHER READING 25 REFERENCES AND FURTHER READING [1] Kupfermann, Irving. “Learning.” Principles of Neuroscience. Ed. Eric Kandel and James Schwartz. 2nd edition. New York: Elsevier, 1985. Cited on page(s) xvii, 17, 18 [2] Martini, Frederic and Edwin Bartholomew. Essentials of Anatomy and Physiology. 2nd edition. Upper Saddle River: Prentice Hall, 2000. Cited on page(s) 17, 18 [3] Guyton, Arthur.Textbook of Medical Physiology. 7th edition. Philadelphia: W.B. Saunders, 1986. Cited on page(s) 17, 18 [4] Ganong, William. Review of Medical Physiology — 1989. 14th edition. Norwalk: Appleton and Lange, 1989. Cited on page(s) 18 [5] Kandel, Eric and James Schwartz. Principles of Neuroscience. 2nd edition. New York: Elsevier, 1985. Cited on page(s) 17 [6] Bloom, Benjamin. Taxonomy of Educational Objectives, The Classiﬁcation of Educational Goals, Handbook 1 Cognitive Domain. New York: David McKay Company, Inc, 1956. Cited on page(s) xvii, 18, 19, 20 [7] Eisner, Elliott. “Proﬁles of Famous Educators, Benjamin Bloom, 1913-99,” Prospects 30(3) (September 2000): 387-395. Cited on page(s) 18 [8] Goel, Sanjay and Nalin Sharda “What do engineers want? Examining engineering education through Bloom’s taxonomy.” 15th Annual Conference for the Australian Association for Engi- neering Education, AaeE 2004. September 27-29, 2004, Toowoomba, Queensland, Australia, 2004. Cited on page(s) 19, 20 [9] Boeree, C. George“Personality Theories—Carl Jung, 1875-1961.” 13 pp. Online. Internet. Webspace.ship.edu/cgboer/jung.html Cited on page(s) 21 [10] “The Myers and Briggs Foundation.” Online. Internet. www.myersbriggs.org Cited on page(s) xvii, 21, 22 [11] Felder, Richard and Linda Silverman “Learning and Teaching Styles in Engineering Educa- tion,” Engineering Education 78(7) (1988): 674-681. Cited on page(s) 21, 23 26 REFERENCES AND FURTHER READING 2.8 CHAPTER ACTIVITIES 1. In your own words, describe the physiological basis of learning. 2. Describe processes to accelerate memory consolidation. 3. Provide a sketch of Bloom’s Taxonomy. Provide a list of action verbs associated with each cognitive level. 4. How does the work of Myers and Briggs relate to the personality theories of Carl Jung? 5. Determine your personality type using the MBTIR test instrument. 6. What is the difference between learning and teaching styles? 7. How did the work of Felder and Silverman bridge the gap between learning and teaching styles? 8. Based on the work of Felder and Silverman, develop your own personal list of techniques to bridge your teaching style to the learning styles of your students. C H A P T E R 3 27 Preparation for the ﬁrst day of classes 3.1 OVERVIEW This chapter provides practical suggestions on getting ready for the ﬁrst day of classes. The chapter begins by reiterating the theme that we have used throughout the book: our students are our cus- tomers. As faculty members we owe our students our very best preparation. A trip is then taken down memory lane to reﬂect on what we expected from teachers when we were students. The developed list of desired attributes will become what to work towards as faculty members. A brief introduction to ABET accreditation requirements is then provided to include a review of basic terms and most importantly see how our individual courses contribute to program accreditation. The development of a course syllabus, textbook selection, and the development of course material followed by a dis- cussion on proactive methods to establish a good relationship with our students is then discussed. The chapter concludes with a forthright discussion of challenges facing faculty members. 3.2 THE STUDENT AS A CUSTOMER I believe all of us became faculty members because we enjoy working with students. If this is not true, perhaps we should consider a different line of work. At the most fundamental level, our jobs as faculty members would not exist if it were not for the students. A common thread throughout this book, and also my personal inspiration as a faculty member, is a student-ﬁrst attitude. That is, our guiding principle in what we do on a day-to-day basis is guided by what is best for the student collectively and individually.This principle should not be misinterpreted as being academically “easy” on students. It is quite the contrary. We as dedicated educators set high expectations for our students and then work with them to help them achieve the goals we have set. 3.3 WHAT DID YOU WANT FROM A TEACHER WHEN YOU WERE A STUDENT? In this section we take a trip down memory lane to remember what we wanted from teachers when we were students. This is only a partial list; you are encouraged to add to the list. As a student this is what I wanted from my teachers. 28 3. PREPARATION FOR THE FIRST DAY OF CLASSES (cid:129) A well-deﬁned course syllabus. As a student, it was important to know what the course was about, a detailed schedule of what would be covered during each lesson, when examinations would occur, and a detailed list of homework assignments. During my undergraduate years, I was carrying a very full academic load and was also working 20-30 hours per week. I was also newly married. My time was precious and it was important to know when key events in each course were scheduled. I considered a vague, general syllabus virtually useless. It communicated to me (and maybe unfairly so) that the instructor did not know where the course was going. (cid:129) Big picture of course. I found it very helpful if the instructor provided a detailed overview, a framework, of the course during the ﬁrst meeting. The overview helped me to connect the course with prior coursework I had completed. Also, an overall framework provided a scaffold where I could connect new course concepts. I also found it very helpful when the instructor would review the big picture periodically throughout the course. This was an effective tool to keep on track and also provide structure for all course concepts and material. As we discovered in Chapter 1, providing this structure helps to provide the same structure within our own memory and aids in the recall and application of course material. (cid:129) Objectives. As a student, clear course objectives were important to me. I wanted to know what I would be learning in the course and to what level I would be held accountable for the material. (cid:129) Expectations. I, as a student, like many students, was motivated to excel in my coursework. It was important to me to know exactly what was expected of me to achieve a speciﬁc grade in each course. Furthermore, I was challenged by high instructor expectations. (cid:129) Well-prepared, understandable lectures. As a student I thought that a faculty member’s primary responsibility was to translate complex course material into a well-prepared, compre- hendible lectures. Now that I am a faculty member, I still feel the same way. We owe it to our students to provide nothing less than our best efforts in classroom preparation and delivery. (cid:129) Real world examples. As a student I always wanted to know how I would use the concepts and information presented in class to solve real world problems. If I could make the connection to a real world application, I found the material easier to understand, comprehend, learn and apply. Material we learned in Chapter 2 backs this up as a sound teaching style [1]. (cid:129) Knowledgeable, available, approachable, and helpful. Like many, many students, I worked very hard to do well in school. When I got stuck on a homework assignment, I appreciated helpful suggestions and insight from my teachers. It was important to know that I could ﬁnd my teachers during scheduled ofﬁce hours. I found it frustrating to seek out an instructor for help and either had a difﬁcult time ﬁnding them or if they were available they often seem disgruntled to provide help. We owe it to our students to provide regular, advertised ofﬁce hours and be available and willing to help. 3.4. COURSE DEVELOPMENT 29 (cid:129) Laboratory exercises that worked. As a student of many engineering and science courses, I completed many, many laboratory assignments. The laboratory is an essential component of many courses. I found it very frustrating as a student to work on poorly constructed or unworkable laboratory exercises. Fortunately, this did not occur very often. (cid:129) Fair examinations. As a student examinations brought closure. I enjoyed studying hard to prepare for a well-written, fair examination. I deﬁned a fair examination as one that thoroughly covered the presented material at the same depth and level at which the material was taught. (cid:129) Fair, timely, and transparent grading. Students work very hard to excel in class and earn their grades. It is important that faculty provide fair, consistent, timely and transparent grading on course assignments and examinations. For example, a written rubric is useful to grade written assignments. In like manner, grading examinations against a prepared solution with established partial credit clearly delineated is very helpful. As a student I felt treated fairly if a faculty member could clearly describe why I missed points on assignments and examinations. Also, timely feedback on examinations and homework is important. I found it very difﬁcult as a student to apply myself and concentrate on new material if I did not know how I performed on previous work. With this list of what students want (and deserve) from faculty members, the remainder of this chapter provides practical, useful advice to accomplish these expectations. 3.4 COURSE DEVELOPMENT In this section, we discuss techniques to develop a course. We begin with a brief discussion of ABET, Incorporated followed by syllabus development and textbook selection. We then discuss the development of teaching materials including lesson plans and other courseware such as laboratory exercises. 3.4.1 ACCREDITATION ABET, Incorporated provides accreditation services for programs in engineering, engineering tech- nology and computer science throughout the United States and several countries throughout the world. Other disciplines have similar accreditation agencies. As a faculty member, it is essential that you are familiar with some of the basic ABET concepts or those of your discipline’s accrediting body. In this section we provide a basic overview of ABET accreditation, review key terms, and most importantly, describe how your course(s) support your program’s accreditation process. It is important to realize that ABET does not accredit universities, colleges, or departments. They accredit programs within a department. For example, a department of electrical and com- puter engineering may have several accredited programs in electrical engineering and computer engineering. 30 3. PREPARATION FOR THE FIRST DAY OF CLASSES The key concept of a strong, viable, current program is continuous improvement. The purpose of continuous improvement is to regularly assess the health of a program via a number of measurable attributes. If issues or challenges are found within a program, they are proactively corrected before becoming major stumbling blocks for the program. This is achieved by performing a regular, deﬁned assessment process. Associated with this continuous improvement process is a series of related concepts. These are quoted verbatim from a key ABET source document: “Criteria for Accrediting Engineering Programs [2].” (cid:129) Program Educational Objectives: “Program educational objectives are broad statements that describe what graduates are expected to attain within a few years of graduation. Program educational objectives are based on the needs of the program’s constituencies [2].” Constituents are those who your program serves. (cid:129) Student Outcomes: “Student outcomes describe what students are expected to know and be able to do by the time of graduation. These relate to the skills, knowledge, and behaviors that students acquire as they progress through the program [2].” “The ABET Criterion 3 (a) through (k) student outcomes for engineering programs are [2]: (a) an ability to apply knowledge of mathematics, science, and engineering (b) an ability to design and conduct experiments, as well as to analyze and interpret data (c) an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability (d) an ability to function on multidisciplinary teams (e) an ability to identify, formulate, and solve engineering problems (f ) an understanding of professional and ethical responsibility (g) an ability to communicate effectively (h) the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context (i) a recognition of the need for, and an ability to engage in life-long learning (j) a knowledge of contemporary issues (k) an ability to use the techniques, skills, and modern engineering tools necessary for engi- neering practice [2].” So how does your course support ABET accreditation efforts for your department programs? Figure 3.1 demonstrates the accountability trail from the university mission, to the college and department missions, to different department programs, to program objectives, to student outcomes, and to your speciﬁc course objectives. It is important to know which student outcomes your course 3.4. COURSE DEVELOPMENT 31 :(cid:7)(cid:5)(cid:17)(cid:12)(cid:9)(cid:4)(cid:5)(cid:11)(cid:29)(cid:10);(cid:5)(cid:4)(cid:4)(cid:5)(cid:6)(cid:7) <(cid:6)(cid:16)(cid:16)(cid:12)(cid:15)(cid:12)(cid:10);(cid:5)(cid:4)(cid:4)(cid:5)(cid:6)(cid:7) ’(cid:12)(cid:2)(cid:3)(cid:9)(cid:11)(cid:28)(cid:12)(cid:7)(cid:11)(cid:10);(cid:5)(cid:4)(cid:4)(cid:5)(cid:6)(cid:7) ’(cid:12)(cid:2)(cid:3)(cid:9)(cid:11)(cid:28)(cid:12)(cid:7)(cid:11)(cid:10)9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28)(cid:4) 9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28) 9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28) 9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) 9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) 5(cid:11)(cid:18)(cid:19)(cid:12)(cid:7)(cid:11)(cid:10)=(cid:18)(cid:11)(cid:13)(cid:6)(cid:28)(cid:12)(cid:4) 5(cid:11)(cid:18)(cid:19)(cid:12)(cid:7)(cid:11)(cid:10)=(cid:18)(cid:11)(cid:13)(cid:6)(cid:28)(cid:12)(cid:4) <(cid:6)(cid:18)(cid:9)(cid:4)(cid:12)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) <(cid:6)(cid:18)(cid:9)(cid:4)(cid:12)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) Figure 3.1: How does your course support program accreditation [2]? 32 3. PREPARATION FOR THE FIRST DAY OF CLASSES supports. As you develop your course, it is essential that your course objectives support these student outcomes. Course objectives help develop the content of the course. They describe what the student will learn by the completion of the course. They also help the student understand the content of the course and the level to which they will be held accountable. A course objective describes. (cid:129) What each student will be able to do by the end of the course. (cid:129) The required cognitive level of learning for the objective. The required level of learning is speciﬁed using one of Bloom’s Taxonomy action verbs discussed in Chapter 2. (cid:129) The ABET student outcome (3(a)–3(k)) the objective supports. Example. Here are some example course objectives from a senior level, design intensive course in Verilog Hardware Descriptive Language. Students shall: 1. (ABET: 3(c), 3(e), 3(k)) Design a Verilog Hardware Description Language module to imple- ment a State Machine diagram. 2. (ABET: 3(b), 3(k)) Create test benches to validate correct operation of HDL implemented design. 3. (ABET: 3(b), 3(c), 3(e), 3(k)) Design a Verilog HDL based system to meet established re- quirements. Verify system design using Verilog test benches. 4. (ABET: 3(f )) Relate the concepts of ethical practice to the proper testing of a new design. 5. (ABET: 3(g)) Construct a written and oral report on your Verilog HDL based system em- ploying provided guidelines. Present a 15 minute oral presentation on your design. In the next section, we discuss development of a course syllabus. The objectives for your course are included in the syllabus. 3.4.2 SYLLABUS For several years a close friend and I would take our adult sons and their mutual friends on a ﬁshing trip to Lac Laronge in Northern Saskatchewan, Canada. We met in Cheyenne, Wyoming and then caravaned through eastern Wyoming and Montana into the beautiful province of Saskatchewan. It is about a 2,000 mile round trip. Could you imagine making this trip without prior planning and without a map? Teaching a course without a detailed syllabus would be a similar challenge. Some universities (including mine) specify the minimum essential parts contents for a syllabus. These include (quoted from UW Regulation 6-809 [3]): (cid:129) A description of the course, including its purpose, content, and goals, (cid:129) Meeting times and/or schedule of the course, (cid:129) The general requirements and expectations for the course, (cid:129) The instructor’s contact information and ofﬁce hours, (cid:129) Academic dishonesty policies, with a statement or a reference to the appropriate university 3.4. COURSE DEVELOPMENT 33 regulation, (cid:129) Grading and attendance policies, (cid:129) A list of required materials, including texts, etc, (cid:129) A statement or a reference to the University Disability Support Services website. (cid:129) If a University Studies Program (General Studies) course, include what requirement(s) it fulﬁlls. In addition to these minimum speciﬁed requirements, I would like to add the following: (cid:129) A detailed lesson-by-lesson schedule of topics, reading assignments and homework assign- ments. (cid:129) A listing of course objectives and the ABET student outcomes supported by the course. (cid:129) A description of where course material can be found. For example, if the course has an associated website, provide the location in the syllabus. (cid:129) A list of class expectations (attendance, cell phones, participation, etc.) A sample syllabus is provided in the Appendix. 3.4.3 TEXTBOOK SELECTION It is important to select a good textbook that supports your course objectives. Potential textbooks in a speciﬁc topic area may be obtained from textbook publisher representatives or may be requested from publisher websites. It is also very helpful to review textbooks at engineering educators’ conventions such as the annual American Society for Engineering Education (ASEE) Annual Conference and Exposition [6]. I try to choose textbooks from both the students’ and educators’ point of view. From the students’ point of view, I try to ﬁnd textbooks that are readable, have multiple worked examples, and ample illustrations. From the educators’ point of view, I look for the same thing as from the students’ point of view but also look for included teaching materials such as lecture slides, supplemental materials, and sample code. To choose the best textbook for a course, it is helpful to construct a textbook selection matrix as shown in Figure 3.3. Course concepts are listed in the ﬁrst column. Potential textbooks are listed along the top row. If desired, you may assign a weight to the importance of each concept. Each textbook is then scored in each of the course concept areas. The best textbook for the course is readily identiﬁed via this process. 34 3. PREPARATION FOR THE FIRST DAY OF CLASSES Figure 3.2: “This is going to be a challenging course. The syllabus has a table of contents! [ J. Barrett, Closer to the Sun International, Inc.]” 3.4.4 LESSON PLANS Much like a syllabus guides the ﬂow and conduct of a course, a lesson plan guides the ﬂow and conduct for each lesson. A lesson plan contains. (cid:129) Lesson objectives. While attending Academic Instructor School (AIS) many years ago at Maxwell Air Force Base, Alabama; I was taught the format for lesson objectives with the acronym “tootlifest.” This acronym stands for “The objective of this lesson is for each student to (insert level of learning)(insert concept) [4].” The construction of lesson objectives helps you to focus on the speciﬁc content of the lesson. The level of learning will be one of the Bloom’s Taxonomy action verbs discussed in Chapter 2. An objective is required for each major concept to be taught during the lesson. (cid:129) A listing of assigned reading material. (cid:129) A listing of assigned homework exercises. 3.4. COURSE DEVELOPMENT 35 2 " A > 1 (cid:10) (cid:11) (cid:14) (cid:15) (cid:12) (cid:30) (cid:5) 2 C > A C 1 (cid:10) (cid:15) (cid:7) (cid:5) (cid:11) (cid:3) B > (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! ? (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! 0 (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! . (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! " (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! @ (cid:10) (cid:24) (cid:6) (cid:6) (cid:20) (cid:11) # (cid:12) ! <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10)> <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10)? <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10)0 <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10). <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10)" <(cid:6)(cid:7)(cid:13)(cid:12)(cid:2)(cid:11)(cid:10)@ !(cid:6)(cid:11)(cid:3)(cid:16) Figure 3.3: Textbook selection matrix. (cid:129) An outline of the material to be discussed. This section is the heart of the lesson plan. Some faculty members will provide great detail in this area while other only provide a listing of topics. Personally, I write very detailed lesson plans and insure I understand the details of the material I will teach. I have found that concepts that are vague to me while preparing lesson plans will be a complete blank when lecturing in front of a room of sharp students. Detailed lesson plans prevent this from happening. 36 3. PREPARATION FOR THE FIRST DAY OF CLASSES (cid:129) Examples to be used during the course of the lecture. (cid:129) A record copy of student handouts used to support the lecture. (cid:129) Related support materials such as power point slides. (cid:129) A record copy of student in class exercises. (cid:129) As you prepare the lesson plan, remember from Chapter 2 that you are serving a wide variety of learning styles. (cid:129) A core theme when developing lessons is to remember we are preparing students for a pro- fession. It is important to weave in practical illustrations of real world examples involving integrity, ethics and doing the right thing. The public good depends on engineers and sci- entists performing their duties with the utmost integrity. For example, in a design-intensive course, it is important to emphasize that a design is as only as good as the test plan that supports it. You can emphasize the ethical considerations of properly and exhaustively testing a new design or product before it goes into production. The ﬁrst time I teach a course, I spend considerable time developing good lesson plans. I will then reuse the lesson plans and update them each time the course is taught. Also, I readily share my lesson plans with other faculty members. It takes quite a bit of time to develop good lesson plans. However, once they are complete, they are a real treasure. I would highly encourage you to seek out others who have taught courses you have been assigned to teach. Rather than starting lesson plans from scratch, you can use their lesson plans and most importantly their wisdom as a starting point for developing your own plans. 3.5 OTHER ITEMS TO CONSIDER There are a number of important concepts to cover in the professional development of an engineer or scientist. Many of these concepts are required by accreditation bodies. Often these concepts are not covered by a speciﬁc course but instead our spread throughput the curriculum. These concepts include but are not limited to [2]: (cid:129) Design. (cid:129) Economic concepts. (cid:129) Environmental considerations. (cid:129) Societal impacts. (cid:129) Political aspects. (cid:129) Ethical considerations. 3.6. ESTABLISHING GOOD STUDENT RELATIONSHIPS. 37 (cid:129) Health and safety. (cid:129) Manufacturability. (cid:129) Sustainability. (cid:129) Multidisciplinary teamwork. (cid:129) Global considerations. (cid:129) Contemporary issues. (cid:129) Leadership. (cid:129) Management. (cid:129) Professional licensure. 3.6 ESTABLISHING GOOD STUDENT RELATIONSHIPS. It is essential to establish good student relationships. As a student it was important to me for my teachers to be available, friendly, and approachable. Here are a few pointers to help get this started. (cid:129) Be warm, friendly, approachable, and respectful. Park your ego.There is no room for arrogance, pride, disrespect, or a condescending attitude when trying to establish a positive and productive relationship with your students. (cid:129) Be available. Provide publicized ofﬁce hours and keep them. When students come by for help be warm, friendly, and approachable. (cid:129) Keep an open-door policy. During non-ofﬁce hours be available to help students that come by for assistance. This is easily accomplished by keeping your door open any time you are in your ofﬁce. (cid:129) Learn students’ names. There are several methods to do this. As you hand back graded quizzes and examinations, work to associate the student’s names with their faces. Some of my colleagues take pictures of their students early in the semester to help them learn student’s names. This only requires a few minutes of class time but goes along way to making students feel welcome. (cid:129) Tell students that you care about their success and then show it. (cid:129) Encourage students to ask questions when they arise. It is important they understand concepts occurring earlier in the lecture to avoid confusion on more complex, related concepts that may come up later in the lecture. (cid:129) Always, always, always treat students with respect. 38 3. PREPARATION FOR THE FIRST DAY OF CLASSES 3.7 CONDUCTING THE LECTURE As a student I thought that a faculty member’s primary responsibility was to translate complex course material into a well-prepared, comprehendible lectures. I still believe this. So, with a good lesson plan in hand, how do we deliver a good lesson? Here are a few basic guidelines. (cid:129) Start the lesson on time. (cid:129) Start with an overview of lesson plan contents and related course announcements. (cid:129) Brieﬂy review key concepts from the previous lesson. (cid:129) Brieﬂy describe how new lesson concepts link to those previously covered. (cid:129) Present the lesson content detailed in your lesson plan. During lesson plan development, carefully consider how the material is best presented and how available board space will be used and then follow your plan. (cid:129) During the lesson presentation, speak clearly and with suitable volume. (cid:129) Encourage questions from students to clarify course concepts. (cid:129) Observe students during the lecture for feedback queues. Are they following the lecture? Are they bored? I always look at student eyes for queues on how the lesson is progressing. (cid:129) Encourage active student participation with in class demonstrations and student exercises. (cid:129) Conclude the lecture with a brief summary of lesson concepts. (cid:129) Conclude the lecture on time. 3.8 CHALLENGES As faculty members we sometimes must deal with complicated and challenging situations. In this section we brieﬂy discuss professional conduct, academic dishonesty, and challenging parents. Professional conduct. As faculty members it is important that we conduct ourselves in a competent, professional manner–always. We must model professional conduct for our students. Our actions, conduct and speech must be beyond reproach. In a similar manner, we should be very careful not to place ourselves into difﬁcult situations. I always keep my door open when meeting with students. If a sensitive matter must be discussed behind closed doors, I will always ask another faculty or staff member to sit in on the discussion as an impartial observer. We must also insure that all members of our classroom feel welcome and comfortable. In- appropriate remarks concerning a student’s sex, race, national origin, or sexual orientation will not be tolerated. In all contacts with students, we should be professional, warm, friendly, approachable, 3.8. CHALLENGES 39 and respectful. There is no room for arrogance, pride, disrespect, or a condescending attitude when trying to establish a positive and productive relationship with your students. Academic Dishonesty. One of the greatest challenges facing faculty members is establishing a charge of academic dishonesty against a student. It is a very stressful situation for all involved; however, an academic dishonesty situation must be dealt with appropriately. Your institution has published regulations and guidelines concerning academic dishonesty.You should familiarize yourself with their contents to insure you comply with directives when a situation occurs. As mentioned above, it is highly recommended that another faculty or staff member be present when you discuss the situation with the student. Furthermore, you should carefully document all that transpires in relation to the academic dishonesty situation. Well-meaning parents and FERPA. Occasionally you may be contacted by concerned par- ents. As a parent of three college graduates, I was frequently concerned about how they were doing in their coursework, their college life, and their overall well-being. Sometimes you may be contacted by parents who demand that you provide them information on their child. Under no circumstances may you share information with the parent without the student’s written permission. The Family Educational Rights and Privacy Act (FERPA) provides very strict guidelines concerning a student’s right to privacy. In a nutshell student records belong to the student. The protected information includes grades, ﬁnances and discipline records. Parents are not allowed access to student records or information on progress without the written permission of the student [5]. In addition to not sharing student information with parents without written student permis- sion, there are other FERPA rules which must be adhered to [5]. (cid:129) Grades may not be posted with student names. A unique code known by the student and the teacher may be used to link a speciﬁc student and their grade for posting. Even if encoded, a grade list may not be posted in alphabetical order. In like manner, graded material may not be left unattended for students to pick up. The basic premise is that a student must not be in a position to view the grades or graded work of another student. (cid:129) Class rosters and grade sheets should always be protected. Social security numbers should not be disclosed. Also, under no circumstances will a list of students be provided to any third party for commercial purposes or otherwise. (cid:129) In like manner, a student schedule may not be shared with anyone without speciﬁc student permission. (cid:129) Potential employers or employers do not have the right to access student educational infor- mation. This includes letters of recommendation. You may not include information on grades, grade point average, or class standing without permission. (cid:129) Access to online student records is on a strict need to know basis. You must have a legitimate educational need to access a speciﬁc student’s record. 40 3. PREPARATION FOR THE FIRST DAY OF CLASSES 3.9 AVAILABLE RESOURCES There are a number of instructional resources available to the faculty member from online sources, your university library and professional societies. We discuss each in turn. (cid:129) Online resources. There are a number of online resources available to the instructor. For example, AcademicPub allows an instructor to develop a custom textbook from a variety of sources. This is especially helpful of your course contains a variety of concepts not contained within a single textbook. The company handles copyright permissions and releases. The ﬁnal assembled textbook is then available in print or digital copy www.academicpub.com. (cid:129) Library resources. Your best source of information may be your university library. You will ﬁnd a visit with your professional discipline’s librarian to be time well spent. I recently met with librarians at my university to discuss education and discipline speciﬁc resources available to the new instructor. Here is a sample of what they shared [7]: – A wide variety of educational resources are available from ERIC, the Education Resources Information Center. ERIC is a U.S. Department of Education sponsored online digital library of education research and information. ERIC provides access to education based literature to support educational research, improve practice in learning and teaching, and educational decision-making www.eric.ed.gov. – Professional disciplines have national level databases to support the discipline. For ex- ample, engineering programs are supported by Engineering Village. Engineering Village describes itself as an “information discovery platform of choice for the engineering com- munity www.ei.org.” – The library stacks are a rich resource on how students learn. Resources available on higher education may be found in the “LB” section of the stacks. – Subscriptions. Your library subscribes to a large number of journal and possibly textbook resources. For example, Morgan & Claypool Publishers (the publisher of this book) pro- vide a series of Synthesis digital libraries. If your library subscribes to this service; faculty, staff, and students at your university may download digital books from the series www. morganclaypool.com. (cid:129) Professional societies. Your discipline’s professional society (e.g., ASCE, IEEE, ASME, etc.) provides considerable teaching resources on disciple concepts of interest. Also, the national engineering and computer science professional practice societies (e.g., NSPE, ACM, etc.) have information on ethical practice and a code of ethics for use in lesson development. Also, the NCEES has considerable information available on professional licensure. 3.10. SUMMARY 41 3.10 SUMMARY This chapter provided practical suggestions on getting ready for the ﬁrst day of classes. It began by reiterating the mindset that we have used throughout the book—our students are our customers. A trip down memory lane was then taken to reﬂect on what we expected from teachers when we were students. A brief introduction to ABET accreditation requirements to see how our individual courses contribute to our program accreditation was then provided followed by a discussion on the development of a course syllabus, textbook selection and the development of course material. We then discussed proactive methods to establish a good classroom dynamic with our students. The chapter concluded with a forthright discussion of challenges facing faculty members. REFERENCES AND FURTHER READING [1] Felder, Richard and Linda Silverman “Learning and Teaching Styles in Engineering Educa- tion,” Engineering Education 78(7) (1988): 674-681. Cited on page(s) 28 [2] “ABET—Assuring Quality in Technical Education.” Online. Internet. www.abet.org Cited on page(s) xvii, 30, 31, 36, 48 [3] “Course Syllabus Requirement.” UW Regulation 6-809. September 12, 2008. Cited on page(s) 32 [4] “Academic Instructor School” Online. Internet. www.au.af.mil Cited on page(s) 34 [5] “Family Educational Rights and Privacy Act (FERPA).” Online. Internet. www2.ed.gov Cited on page(s) 39 [6] “American Society for Engineering Education (ASEE).” Online. Internet. www.asee.org Cited on page(s) 33 [7] Melissa Bowles-Terry and Lawrence Schmidt. Personal interview. January 30, 2012. Cited on page(s) 40 42 REFERENCES AND FURTHER READING 3.11 CHAPTER ACTIVITIES 1. Develop a list of attributes that you expected from a teacher when you were a student. Which ones will you follow as a teacher? 2. What is your department mission? 3. What is the difference between program objectives and student outcomes? 4. What are your program’s objectives? 5. What are your program’s student outcomes? 6. What student outcomes does your course(s) support? 7. Develop objectives for your course(s). 8. Develop a syllabus for your course(s). 9. Develop a textbook selection matrix for your course(s). 10. What are the differences between course objectives and lesson objectives? 11. Develop lesson objectives for each lesson within your course. 12. What are the key elements of a lesson plan? 13. Deliver a lesson plan and capture the delivery for later review. Review the captured lesson. What did you learn about your delivery? In what areas can you improve? 14. What techniques will you employ to establish good student relationships. 15. Locate and read in detail the academic dishonesty policies for your university. 16. What is FERPA? What are your responsibilities under FERPA? C H A P T E R 4 Assessment 43 4.1 OVERVIEW As a faculty member it is imperative that we regularly assess the academic health of our students, ourselves, and our courses. This chapter is divided into three separate sections covering each of these topics. The chapter begins by discussing techniques to regularly assess student performance. This is followed by a discussion on the assessment of our performance as teachers including a discussion on assessing our course(s). In this section we see how our course-level assessment and the related activity of evaluation is an integral part of our department’s continuous improvement program. The term assessment is used throughout this chapter to include the gathering, interpretation, and evaluation of data to render improvements in our students, our performance as instructors and in our course content. 4.2 ASSESSMENT OF YOUR STUDENTS As educators we want our students to succeed and be successful in our courses. The student also has a shared responsibility to keep up with and complete course requirements. In this section we provide proactive methods to assess students’ progress in our lectures and during the course of our class. Our goal is the early detection of student issues so we can proactively make corrections for student success. Assessing ongoing lectures. When giving a lecture it is important to periodically assess students’ understanding during the course of the lecture. There is no reason to move on to more advanced concepts if the majority of students do not understand the concepts already covered. There are several methods to quickly assess student understanding and progress during a lecture. As mentioned earlier, watching student eyes for attentiveness and understanding during the course of the lecture is a good barometer of lecture progress. If students appear to be attentive and following the lecture, it might be safe to proceed to other lecture concepts. On the other hand, if students appear confused, corrective action may be required. When this occurs, it is helpful to remind students of how the concepts being covered are related to previous covered concepts. Also, it is helpful to “hit the rewind button.” That is, brieﬂy highlight the main points of the concepts just covered. Most importantly, ask the students if they have any questions on the material before moving on. Another technique to engage students and assess their progress during a lecture is to conduct a “secret poll.” In this technique, ask the students to close their eyes for a few moments. They are then asked to put their thumb up in the air pointing up if they comfortable with the current concept being 44 4. ASSESSMENT covered, point their thumb sideways if they grasp the concept but would like additional information or examples, or point their thumb down if they are lost or confused. The students seem to enjoy this exercise and it readily provides their view on how the lecture is going. It provides you the chance to quickly assess how the lecture is going and to make adjustments to your lecture as necessary for student comprehension. This technique was originally learned from William “Bill” Parker who served with and taught for many years with the National Weather Service. I frequently use this technique to assess the health of ongoing lectures. Quizzes. A quiz is an effective tool to periodically take the pulse of your course. It also provides students an opportunity to gauge how they are progressing in your course. It also provides them a glimpse of how you write examination questions. To carefully craft a quiz question, determine the concept to be covered and the Bloom’s Taxonomy level at which it will be assessed. The quiz question may now be written. If a one-hour examination typically consists of ﬁve questions, allow students ten minutes in class to complete a quiz. The goal is to help students prepare for the rigor of an examination by providing quiz questions of similar rigor under similar time constraints. If possible, quizzes should be graded and handed back at the beginning of the next lecture. It is difﬁcult for students to concentrate on new lecture material if they (and you) do not know how they performed on previous concepts. A technique a colleague of mine, Dr. David “Dave” Whitman, has used with great success is for the students to grade their own quiz. After students have completed the quiz, Dave reviews the quiz and has students correct their own quiz during the review. The students are instructed to make corrections in a different color of ink than that used while taking the quiz. This is an effective method of emphasizing quiz concepts and providing timely feedback on the quiz. Dave then collects the quizzes and assigns appropriate grades later and returns them to students at the beginning of the next lecture. Examinations. An examination is prepared in much the same way as a quiz. As a starting point, draw up a list of concepts to be covered by the examination. For each concept, determine the Bloom’s Taxonomy level at which it will be assessed. It is also helpful to determine if the examination questions are testing established course objectives. Each examination question may now be written. It is also helpful to include a cover sheet for the examination which provides a location for the student’s printed name and signature. The cover sheet also provides a summary of points assessed for each examination problem and a point total and grade. When you have ﬁnished writing the examination, it is important to “test drive” the exami- nation. Ideally, the examination should be completed by a colleague familiar with the examination concepts. The colleague can provide feedback on examination concepts and time allotted for the ex- amination. If this is not possible, you should work the examination to insure questions are complete and accurate. An answer key with partial credit deﬁned for each portion of the examination should be completed before the examination is administered. It is essential to provide fair, timely, and transparent grading on the examination. As mentioned with quizzes, every attempt should be made to return graded examinations the next time the course 4.3. ASSESSMENT OF YOU 45 meets. Often, this will require considerable work and dedication on your part to make this happen.To insure fair assignment of partial credit, grade all examinations a single question at a time against the answer key. Also, it is important to provide written comments on how to successfully solve incorrect problems. Also, while grading examinations, it is important to maintain student anonymity. Your grading and assignment of partial credit is based only on the prepared key. When examinations are returned at the beginning of the next class, hand them back individ- ually. This helps associate names with faces and also preserves students’ privacy. The examination is then brieﬂy reviewed. I inform the students that I will not quibble over partial credit since it was established before the examination was given. However, if a mistake in examination grading has occurred, students are encouraged to make a note of it on the examination cover sheet and return the examination for further review. It is also helpful to pass around a grade sheet showing student progress after a major event (such as an examination) in a course. Students naturally want to know how they are performing in class. Insure the grade sheet does not provide any identifying information on the student in accordance with FERPA rules discussed elsewhere in the book. 4.3 ASSESSMENT OF YOU It is essential for you to regularly assess your progress as an instructor and implement required changes to improve your performance and that of your students. This will require a great deal of honesty and self assessment on your part. There are a number of sources of available data to evaluate your progress as an instructor. We discuss several. Student performance on quizzes and examinations. Quiz and test results may be used as a barometer of your performance as an instructor. On average, if students are performing on par in course assignments, quizzes, and examinations; no adjustments may be required. On the other hand, if on average, you are disappointed with student’s performance, perhaps adjustments on your part are required. When a quiz or examination average is not where you would like it to be, ask yourself the following questions. (cid:129) Is there a particular concept that students are struggling with? If so, how can I reinforce this concept in class? (cid:129) Have I examined students on a concept at a higher level of Bloom’s Taxonomy then where I taught them? If so, is this fair? (cid:129) Was the quiz or examination too long for the allotted time? (cid:129) Were examination questions and instructions written clearly? (cid:129) Did the examination require information or concepts that were not covered in the course? Midterm course critiques. Another method of obtaining data to evaluate how your course is progressing is to use midterm course critiques. Your institution may mandate a midterm course 46 4. ASSESSMENT Figure 4.1: “A 57% average. What went wrong? [ J. Barrett, Closer to the Sun International, Inc.]” 4.4. SELF ASSESSMENT 47 assessment. If so, midterm critiques provide valuable insight into how the course is progressing. Study critique results carefully to determine if midcourse corrections are required. If so, make them. You owe this to your students. Many institutions do not require midterm critiques. Instead, you may employ an informal method of obtaining student feedback. A lesson or two after handing back the ﬁrst examination pass out a 3 by 5 inch card to each student. Ask them to anonymously give you a grade from “A” to “F” and ask them to tell you what they like about the course and how you might immediately modify it to improve their performance in the course. Typically, students are more than willing to provide honest feedback on the course and instructor performance. Leave the room while the students are completing the card and ask them to place the cards face down on a desk at the front of the room when they are complete. Then review the cards in your ofﬁce and see if there are areas of improvement to be made. Then decide on what improvements should be made and then shred the students cards. Most importantly, report back to the students during the next lecture on what they said and improvements you will make in response to their comments. Then implement the changes required. End-of-course critiques. Most institutions mandate some form of formal end-of-course critiques. Encourage students to complete the course critiques. Emphasize the results are used to improve the course and to improve your teaching. When course critiques are received, it is important to carefully review the critique results to determine possible corrective action for your course or your delivery of course content. You may receive critiques that appear to be unfair or unfounded. One suggestion is to read over the critiques and then let them lie for a week. Revisit the critiques after you’ve had time to get past your emotional response to them.Then review the critiques dispassionately to determine if corrections in your teaching methods are required. 4.4 SELF ASSESSMENT In previous chapters we developed a list of tenets of good instructors and also what you expected from instructors when you were a student.These tenets establish a benchmark against which to assess your performance. Your personal assessment will require complete honesty and deep soul searching on your part. To perform a self assessment, list the tenets of good instructing that you have committed to professionally live by. Based on your end-of-course critiques, assign yourself a grade from for each of the tenets “A” to “F.” Where there is room for improvement, provide concrete changes that you will make to improve your performance. In the next chapter we discuss the role of a mentor. It is a good idea to share the results of your self assessment with a trusted mentor and advisor. Your mentor will be able to provide additional feedback on how best to improve your performance. 48 4. ASSESSMENT 4.5 ASSESSMENT OF YOUR COURSE In Chapter 3 we discussed the connection between your course and meeting ABET program ob- jectives and student outcomes [1]. ABET also provides deﬁnitions associated with continuous im- provement. Some of these deﬁnitions are quoted verbatim from a key ABET source document: “Criteria for Accrediting Engineering Programs [2].” Computer Science and Technology programs have similar criteria documents. (cid:129) Assessment: “Assessment is one or more processes that identify, collect, and prepare data to evaluate the attainment of student outcomes and program educational objectives. Effective assessment uses relevant direct, indirect, quantitative and qualitative measures as appropriate to the objective or outcome being measured. Appropriate sampling methods may be used as part of an assessment process [2].” (cid:129) Evaluation: “Evaluation is one or more processes for interpreting the data and evidence accumulated through assessment processes. Evaluation determines the extent to which student outcomes and program educational objectives are being attained. Evaluation results in decisions and actions regarding program improvement [2].” (cid:129) Continuous Improvement: Continuous improvement uses the results of evaluation processes for the program educational objectives and the student outcomes and any other available information as input to make program improvements [2]. Before continuing with this chapter, it would be helpful if you familiarized yourself with your program’s educational objectives and student outcomes. Provided in Figure 4.2 is a sample continuous improvement model.This diagram picks up from Figure 3.1. Recall from Figure 3.1 that course objectives directly ABET support student outcomes 3(a) through 3(k).We also discussed deriving lesson objectives and content from the course objectives. Periodically we need to assess and evaluate how well our course is achieving speciﬁc course and lesson objectives. This is accomplished using the two step assessment and evaluation process. In the assessment step we gather data on the course. This would include student course performance, data gathered from course critiques, and also other sources of information. In the evaluation step the data is interpreted to determine if course and lesson objectives have been achieved. An important part of the evaluation process is to determine what improvements will be made. The short-term improvement cycle may occur at the completion of the course. In your eval- uation you may decide to modify course objectives, lesson objectives, or lesson content to meet established goals. Your program has established procedures in place to complete the long-term (12– 18 month) improvement cycle. The long-term cycle provides feedback on how well and to what level program objectives and student outcomes have been achieved. The bottom line is your course is not stagnant. It is alive and constantly evolving. It is imperative that we strive to continually improve the content and delivery of our courses. Our students deserve nothing less. 4.5. ASSESSMENT OF YOUR COURSE 49 9(cid:9)(cid:6)(cid:15)(cid:9)(cid:3)(cid:28)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) 5(cid:11)(cid:18)(cid:19)(cid:12)(cid:7)(cid:11)(cid:10)=(cid:18)(cid:11)(cid:13)(cid:6)(cid:28)(cid:12)(cid:4) <(cid:6)(cid:18)(cid:9)(cid:4)(cid:12)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) +(cid:12)(cid:4)(cid:4)(cid:6)(cid:7)(cid:10)=(cid:20)(cid:21)(cid:12)(cid:13)(cid:11)(cid:5)(cid:17)(cid:12)(cid:4) +(cid:12)(cid:4)(cid:4)(cid:6)(cid:7)(cid:10)<(cid:6)(cid:7)(cid:11)(cid:12)(cid:7)(cid:11) D(cid:4)(cid:4)(cid:12)(cid:4)(cid:4)(cid:28)(cid:12)(cid:7)(cid:11) A(cid:10)5(cid:11)(cid:18)(cid:19)(cid:12)(cid:7)(cid:11)(cid:10)(cid:2)(cid:12)(cid:9)(cid:8)(cid:6)(cid:9)(cid:28)(cid:3)(cid:7)(cid:13)(cid:12) A(cid:10)<(cid:6)(cid:18)(cid:9)(cid:4)(cid:12)(cid:10)(cid:13)(cid:9)(cid:5)(cid:11)(cid:5)%(cid:18)(cid:12)(cid:4) A(cid:10)73(cid:10)3#(cid:3)(cid:28)(cid:5)(cid:7)(cid:3)(cid:11)(cid:5)(cid:6)(cid:7)(cid:10)(cid:9)(cid:12)(cid:4)(cid:18)(cid:16)(cid:11)(cid:4) 3(cid:17)(cid:3)(cid:16)(cid:18)(cid:3)(cid:11)(cid:5)(cid:6)(cid:7) A(cid:10)4(cid:7)(cid:11)(cid:12)(cid:9)(cid:2)(cid:9)(cid:12)(cid:11)(cid:10)(cid:19)(cid:3)(cid:11)(cid:3) A(cid:10)D(cid:13)(cid:14)(cid:5)(cid:12)(cid:17)(cid:12)(cid:19)(cid:10)(cid:29)(cid:6)(cid:18)(cid:9)(cid:10)(cid:15)(cid:6)(cid:3)(cid:16)(cid:4)(cid:31) A(cid:10)E(cid:6)(cid:23)(cid:10)(cid:23)(cid:5)(cid:16)(cid:16)(cid:10)4(cid:10)(cid:5)(cid:28)(cid:2)(cid:9)(cid:6)(cid:17)(cid:12)(cid:31) (cid:16) (cid:6) (cid:7) (cid:15) (cid:10) (cid:11) (cid:12) (cid:9) (cid:28) (cid:10) (cid:5) (cid:28) (cid:2) (cid:9) (cid:6) (cid:17) (cid:12) (cid:28) (cid:12) (cid:7) (cid:11) (cid:4) (cid:4) (cid:11) (cid:7) (cid:12) (cid:28) (cid:12) (cid:17) (cid:6) (cid:9) (cid:2) (cid:28) (cid:5) (cid:10) (cid:28) (cid:9) (cid:12) (cid:11) (cid:10) (cid:11) (cid:9) (cid:6) (cid:14) (cid:4) Figure 4.2: Continuous improvement. 50 REFERENCES AND FURTHER READING It is often difﬁcult to obtain external, unbiased data on your course. One source of data is the Fundamentals of Engineering (FE) examination.The FE examination is administered twice per year typically in late April and late October by the National Council of Examiners for Engineering and Surveying (NCEES).The examination consists of a common four hour morning portion of 120 ques- tions covering the following topics: engineering economics, electricity and magnetism, chemistry, ethics, engineering statistics, ﬂuid mechanics, strength of materials, thermodynamics, mathematics, statics and dynamics, computers, and material properties. The afternoon session is also 4 hours long and consists of 60 discipline speciﬁc questions. Examinees may select from one of the following disciplines: civil, electrical, industrial, mechanical, environmental, or general engineering [2, 3]. If students from your institution take the FE examination, NCEES provides results of ex- amination pass rates and also topic speciﬁc assessment data. For example, if you teach a course in thermodynamics you can obtain data on how well the FE examinees from your institution performed in this area relative to all examinees nationwide. This is valuable, unbiased data for use in assessing your course [2, 3]. 4.6 SUMMARY As a faculty member it is imperative that we regularly assess the academic health of our students, ourselves, and our courses. This chapter was divided into three separate sections covering each of these topics. The chapter began by discussing techniques to regularly assess student performance. This was followed by a discussion on the assessment of our performance as teachers. We concluded with a discussion on assessing our course(s). In this section, we saw how our course-level assessment and the related activity of evaluation is an integral part of our department’s continuous improvement program. REFERENCES AND FURTHER READING [1] “ABET—Assuring Quality in Technical Education.” Online. Internet. www.abet.org Cited on page(s) 48 [2] “National Council of Examiners for Engineering and Surveying (NCEES).” Online. Internet. www.ncees.org Cited on page(s) 50 [3] S.F. Barrett, W. LeFevre, J.W. Steadman, J.S. Tietjen, K.R. White and D.L. Whitman, “Us- ing the Fundamentals of Engineering (FE) Examination as an Outcomes Assessment Tool.” Online. Internet. www.ncees.org Cited on page(s) 50 4.7 CHAPTER ACTIVITIES 1. Why is assessment and evaluation important? 2. What is the difference between assessment and evaluation? 4.7. CHAPTER ACTIVITIES 51 3. Describe methods of obtaining feedback on lecture progress during the course of the lecture. 4. Describe basic guidelines in writing a quiz. 5. Describe basic guidelines in assembling and writing an examination. 6. Describe basic guidelines in conducting a self assessment. 7. Conduct a self assessment of your teaching progress. 8. Conduct an assessment of your course. Are you achieving course objectives? What proactive changes can you make to improve the course? 9. How may the Fundamentals of Engineering Examination be employed in your course assess- ment and evaluation? C H A P T E R 5 Beyond the ﬁrst day 53 This chapter looks beyond the ﬁrst day of class and delves into the areas of effective mentoring, the rewards of teaching, and some practical guidelines of balancing all the demands placed upon the new educator. The chapter concludes with suggestions on how to continue to be a good and effective educator. 5.1 MENTORING Everyone needs someone to talk to, consult with, bounce ideas off of, obtain professional advice from, or commiserate with when things are not going well. That is where a good mentor can help. In this chapter we discuss the traits of a good mentor, how to ﬁnd one, and how to be one. This chapter is based on a column on mentorship that was originally published in the IEEE Computers and Science Engineering Magazine. This chapter is dedicated to the great mentors I’ve had in my professional development. 5.1.1 TRAITS OF A GOOD MENTOR Please take a moment to answer the four following questions [1]: (cid:129) Why did you become a engineer or scientist [1]? (cid:129) At what point in your life did you decide to pursue a career in science or engineering career [1]? (cid:129) Were there people in your life who helped you see the excitement to be found in a technical career [1]? (cid:129) Were there people in your life who encouraged you when things were not going so well [1]? The answers to these questions illuminate the importance of mentors in career develop- ment [1]. I recently participated in a university committee on mentoring. One of our tasks was to identify traits of a good faculty mentor. We identiﬁed many traits including: good mentors are committed members of the community of scholars; enthusiastic; always learning, interested in new ideas; selﬂess; friendly; caring; warm; engaged; hard-working; and inspiring. 5.1.2 FINDING A GOOD MENTOR As a new faculty member it is important to ﬁnd a good mentor. Your job responsibilities will typically fall into three overlapping categories of teaching, research, and service. Ideally, it would be helpful 54 5. BEYOND THE FIRST DAY to ﬁnd a mentor who will be helpful in all three areas but that is not always possible. A different mentor for each category of your job is perfectly acceptable. I did not have to seek out a mentor. They came to me. The ﬁrst day on the job at the University of Wyoming, Dr. Raymond (Ray) Jacquot, Ph.D., P.E. and Dr. Jerry Cupal, Ph.D. came by my ofﬁce and welcomed me to Wyoming and the University. They made it clear they were available to help in any way possible. I never forgot their hospitality and helpful spirit. I took them up on their offer for advice and assistance many times. To ﬁnd a mentor, I would recommend ﬁnding a kindred spirit, someone that you feel com- fortable talking to and sharing your greatest concerns. For teaching assistance, I recommend seeking out the help of those faculty members who teach similar courses in your area of expertise. They may be a source of lesson material and advice on how to best present the material. For research mentoring, seek out the assistance of those who work in a similar or related area. They may be a source of collaboration. It is also helpful to have a sounding board when pursuing new research ideas. 5.1.3 BEING A GOOD MENTOR I was blessed with an outstanding graduate advisor, Dr. Ashley J. (A.J.) Welch of the University of Texas at Austin (UT). Dr. Welch was always readily available, approachable, and held me to a high level of accountability. Upon my arrival at UT, Dr. Welch told me what my graduate research project would be. He then gave me the time and latitude to develop a research plan to reach the research goal. We reviewed the plan in detail and iteratively developed a strong plan with key milestones well deﬁned. I knew exactly what I was supposed to do and had an achievable, workable plan to get there. We met weekly over the next three years. At each meeting, Dr. Welch and I would go over what I had worked on the previous week and then discuss goals for the coming week. It should be mentioned that Dr. Welch used this approach with all of the multiple masters and Ph.D. students he was advising. When I step back from my speciﬁc situation and try to determine what made Dr. Welch such a successful graduate advisor, I see a common pattern appear. Dr. Welch worked very hard to be accessible to his students and develop a strong relationship based on trust. He also set high expectations for each of his students and then helped us to achieve them. This was accomplished through setting a clear research goal early in each student’s program and then meeting with them on a regular basis to review progress and provide assistance as needed. Along the way, Dr. Welch’s students became strong, independent researchers and I suspect good research mentors. Your time will be very precious as you begin your career. If you elect to serve as a mentor to develop the next generation of engineers and scientists, here are some suggestions on how to get involved: visit local junior and senior highs to describe science and engineering careers; get involved with freshmen orientation and retention programs; volunteer to give information sessions to prospec- tive students; and help teach summer outreach programs to junior and senior high students [1]. 5.2. TEACHING REWARDS 55 5.2 TEACHING REWARDS Teaching is a very fulﬁlling profession. You will ﬁnd it challenging and exciting with no two days the same. There will be good days when you feel that you have made a difference in students’ lives. On the other hand, you will have days when you will wonder if you were really meant to be a teacher. Fortunately, these days are few and far between. Often, the challenging days are where we learn the most toward becoming better educators. There are obvious tangible beneﬁts and rewards of serving as an educator. These tangible beneﬁts include promotion and tenure. As a new educator it is essential that you know exactly what is expected of you to achieve these milestones. Your job description will provide performance expectations in the areas of teaching, research and service. Sometimes these expectations are provided as a percentage of your workload. For example, a new faculty member may have a job distribution of 50% teaching, 40% research and 10% service. It is important that you know what the expectations are for your performance and how it will be assessed. A seasoned mentor help you successfully navigate the tenure and promotion process. Also, a regular meeting to discuss your performance with your department head is highly recommended. There are many intangible beneﬁts of serving as an educator. You will not ﬁnd a more fulﬁlling profession. You will go home from work every night (typically exhausted) knowing that you have made a positive difference in a number of students’ lives. You will celebrate with them when they graduate but you will also be there to encourage them when they have failed an examination or a class. The high points of your career will come when a student unexpectedly drops by some years after their graduation and tell you what an impact you had on their professional development and their success. There is no greater reward. 5.3 FINDING BALANCE The education profession is not a sprint, it is a marathon. You will need to ﬁnd balance between your professional and personal life to remain healthy and invigorated for the long haul. In the early years of your appointment it will be important to pursue with vigor the requirements of tenure and promotion. However, your personal life is equally (or more) important. Constantly strive to ﬁnd the balance between the two. Also, you will be asked to participate in a number of committees and projects. When asked to participate in these worthwhile activities, carefully consider the impact on your time and career progression. Learn to graciously say “no.” 5.4 WHERE TO GO FROM HERE? This book was intended as a basic primer on college-level teaching and learning for a new faculty member of engineering or applied science. First and foremost, this book was about learning and teaching. However, it also provided helpful information on related topics such as mentorship, student challenges, graduate students, tenure and promotion, and accreditation. I hope you have found this book useful in preparing for service as a faculty member. However, it is only a beginning. Serving 56 5. BEYOND THE FIRST DAY Figure 5.1: Serving as an educator is a lifelong profession based on continual improvement and growth [ J. Barrett, Closer to the Sun International, Inc.] as an educator is a lifelong profession based on continual improvement and growth. You need to constantly work toward self improvement as a teacher and in your course delivery and content. So where to from here? I would recommend the following. (cid:129) Track down and read each of the references in this book. You will ﬁnd them to be a wealth of information and inspiration and a springboard to related material. (cid:129) Your institution most likely has a center for teaching excellence. Become a regular attendee (and contributor) to their professional development seminars. (cid:129) Find a mentor and meet regularly with them. (cid:129) Commit to becoming the best educator possible. If does not take a lot of time. You owe your students nothing less. (cid:129) Read the book “Survive and Thrive: A Guide for Untenured Faculty,” authored by Wendy Crone [2]. (cid:129) Become a member of the American Society for Engineering Education (ASEE) (www.asse.org). They host an annual symposium which highlights the best practices in engi- neering education through the presentation of papers, workshops and vendor displays. Also, a number of resources for the teacher are available from their website including access to published ASEE papers. For the students! 5.5. SUMMARY 57 5.5 SUMMARY This chapter looked beyond the ﬁrst day of class and delved into the areas of effective mentoring, the rewards of teaching and some practical guidelines of balancing all the demands placed upon the new educator. The chapter concluded with suggestions on how to continue to be a good and effective educator. REFERENCES AND FURTHER READING [1] S. F. Barrett. “Mentoring and Making a Difference: What Can One Person Do?” Computing in Science and Engineering, 13(1): 70-73, 2011. Cited on page(s) 53, 54 [2] W. C. Crone. “Survive and Thrive: A Guide for Untenured Faculty,” Morgan & Claypool Publishers, 2010. Cited on page(s) 56 58 REFERENCES AND FURTHER READING 5.6 CHAPTER ACTIVITIES 1. Who were the mentors in your life? Were there character traits they shared? 2. What are the traits of a good mentor? 3. Find mentors for the teaching, research, and service aspects of your job. 4. What are the expectations for your job performance? Develop a plan on how you will meet these expectations. 5. Develop a plan on how you will continue to grow as an educator. 6. Develop a personal mission statement to be the best educator possible. 59 A P P E N D I X A Sample syllabus EE4490 Hardware Descriptive Language (HDL) Digital Design, Fall 2011 Course Information and Policies Instructor: Steve Barrett, Ph.D., P.E., EN2076, Phone: 766-6181, e-mail: [email protected] Class time: M, W, F, 1:10-2:00 PM, CR103 Ofﬁce hours: M, W 2:00-5:00 PM, EN2076 Texts: (cid:129) “Verilog HDL: A Guide to Digital Design and Synthesis,” Samir Palnitkar (SP), Sun Mi- crosystems Press – A Prentice Hall Title, 2003, second edition, ISBN: 0-13-044911-3 (cid:129) “Logic and Computer Design Fundamentals,” Mano and Kime (M&K), Pearson- Prentice Hall, 2008, 4th edition, ISBN: 0-13-600158-0. This textbook is required. (cid:129) “EE4490 HDL Digital Design” course notes – available from bookstore Grading: Grades will be awarded at the standard 90%, 80%, 70%, and 60% break points. Prerequisites: It is expected that the student has had a class in digital circuit design (EE2390 or equivalent). Course description: Hardware Descriptive Language (HDL) Digital Design. 3. Hardware De- scriptive Language design of digital systems. Industrial CAD tools are used to produce a functional description of hardware that is both simulated and then synthesized into hardware. Methods to describe both combinational logic and synchronous devices are given. Devices such as CPLDs and FPGAs are targeted in this design process. Emphasizes design techniques. Prerequisite: EE2390. 60 SAMPLE SYLLABUS Course objectives: Students shall: 1. (ABET: 3(c), 3(e), 3(k)) Design a Verilog Hardware Description Language module to imple- ment a State Machine diagram. 2. (ABET: 3(b), 3(k)) Create test benches to validate correct operation of HDL implemented design. 3. (ABET: 3(b), 3(c), 3(e), 3(k)) Design a Verilog HDL based system to meet established re- quirements. Verify system design using Verilog test benches. 4. (ABET: 3(f )) Relate the concepts of ethical practice to the proper testing of a new design. 5. (ABET: 3(g)) Construct a written and oral report on your Verilog HDL based system em- ploying provided guidelines. Present a 15 minute oral presentation on your design. Topics covered: (cid:129) Economic/time to market incentives behind an HDL (cid:129) The design ﬂow process with an HDL (cid:129) Target hardware from an HDL (cid:129) Fundamentals of the Verilog HDL (cid:129) Application of Verilog to combinational logic, synchronous logic, and ﬁnite state machines (cid:129) Use of behavioral and structure state machine diagrams for Verilog HDL development and documentation (cid:129) Importance of testing the designs for correctness and reliability (cid:129) Appropriate use of the Xilinx Verilog HDL simulation and synthesis tools (cid:129) Design, implementation, and documentation techniques (cid:129) Real world design issues Requirements: The course consists of 3 one-hour lectures per week for a total of 15 weeks. A heavy emphasis is placed on practical, regular homework assignments. All students are expected to satisfactorily complete the assignments. If code is used from another source, you must reference the source in your program. Two exams will be given throughout the semester and a comprehensive ﬁnal examination. You will also be required to complete a team-based ﬁnal design project to demonstrate your capability to solve a challenging digital design project using Verilog HDL as the target solution. SAMPLE SYLLABUS 61 Homework: Homework sets will be periodically given with prescribed due dates. Assignments must be handed in at the beginning of class time on the speciﬁed due date. No credit will be given for late assignments. Assignments must be worked neatly, properly documented, and tested. You will work on a two-person team for each homework assignment. The student team is responsible for developing a test bench to thoroughly document the operation of their homework solution. A single assignment solution will be turned in for each two-person student team. However, each student will be held individually accountable for all material covered in the homework via quizzes, examinations, and ﬁnal examinations. Attendance: Attendance at every scheduled class session is highly encouraged. Students who are habitually absent will be at a disadvantage. Students are responsible for all material presented in class. Attendance is required for scheduled examination times. Students who miss an examination must obtain an excuse in accordance with the UW bulletin. For absences not covered by these rules, students must contact the instructor immediately to avoid a grade of zero for missed examinations. Suggestions: This course covers considerable material. Some recommendations for success include: (cid:129) Attend every class – new material is covered each lecture. (cid:129) Read assigned material in advance as detailed in the syllabus. (cid:129) Start homework assignments early. Seek instructor help as needed early. (cid:129) Do not ignore homework. It comprises 20% of your grade. It is the best preparation for examinations. (cid:129) Ask questions in class, during discussions, and during ofﬁce hours. Class project: The purpose of the ﬁnal class project is to demonstrate your ability to design, test, and document a challenging digital design project using Verilog HDL design techniques. (cid:129) Two-person teams (cid:129) Potential projects – Data encryption/decryption – Asynchronous Communications – Synchronous Communications 62 SAMPLE SYLLABUS – Priority Encoder – Rate Multiplier – Johnson Counter – Cyclic Redundancy Check Generator – Pulse Width Modulator Signal Generator – Stepper Motor Controller – 4 channel – Linear Feedback Shift Registers – Autonomous Robot Controller – Simple Pipeline Processor (cid:129) Project must be approved in advance by instructor via proposal (cid:129) Single page proposal due Wednesday, Oct 5, 2011 (cid:129) Proposal consists of title, abstract, keywords, and requirements (cid:129) Deliverables: – 25 minute presentation – 5 page written report – Design solution with test bench demonstrating proper project operation – Written Report - I will grade your written report for: ∗ Organization - following the prescribed format (10%) ∗ Title ∗ Abstract ∗ Keywords ∗ Background ∗ Requirements ∗ Design ∗ Testing ∗ Results ∗ Conclusions ∗ Appendices · Verilog Project · Test bench – Grammar, technical completeness, and readability (10%) – Sufﬁcient background information – depth as well as breadth of material (20%) – Literature search - you must use at minimum three separate references (10%) – Your design – did it meet requirements? Did you prove that it worked via testing proce- dures (50%) SAMPLE SYLLABUS 63 (cid:129) Oral Report: Your fellow students will anonymously score your oral presentation from 0 to 100. The students’ scores will be averaged and serve as your score for the oral presentation. You will also be graded on the number of student presentations you attend. On the ﬁnal examination you will be responsible for information presented during the student presentations. Disability assistance: If you have a physical, learning, or psychological disability and require accom- modations, please let the instructor know as soon as possible. You must register with, and provide documentation of your disability to University Disability Support Services (UDSS) in SEO, room 330 Knight Hall. Appropriate protocols will be developed after that time. Academic Honesty: The University of Wyoming is built upon a strong foundation of integrity, respect, and trust. All members of the university community have a responsibility to be honest and the right to expect honesty from others. Any form of academic dishonesty is unacceptable to our community and will not be tolerated. Teachers and students should report suspected violations of standards of academic honesty to the instructor, department head, or dean [University Regulation 6-802]. 64 SAMPLE SYLLABUS k r o w e m o H t n e m n g i s s A 1 S W H n o i t p i r c s e D t c e j o r P s s a l C , w e i v r e v O e s r u o C 2 2 g u A M , - i b m o c : w e i v e R n g i s e D l a t i g i D l a i t n e u q e s , n g i s e d t i u c r i c l a n o i t a n s t n e n o p m o c , I S M n g i s e d t i u c r i c 4 2 g u A W , 6 2 g u A F , g n i d a e R s c i p o T e t a D n o i s s e S 1 S W H : e u D , 2 S W H ) P S ( 1 p h C w e i v r e v O 9 2 g u A M , 2 S W H : e u D 9 p e S , F 3 S W H ) P S ( 3 p h C - r e p O d n a , s e p y T a t a D , s e v i t i m i r P 7 p e S W , s r o t a ) P S ( 2 p h C s t p e c n o C g n i l e d o M l a c i h c r a r e i H 1 3 g u A W , - x E s e s s a l C y a d i l o H y a D r o b a L 5 p e S M , d e s u c 2 p e S , F n o i t a t n e s - e r p e r l a c i r e m u n t n i o p g n i t a o l F 2 1 p e S M , 0 1 1 2 3 4 5 6 7 8 9 SAMPLE SYLLABUS 65 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 , W O c t 1 2 , M O c t 1 0 , F O c t 7 , W O c t 5 , M O c t 3 F , S e p 3 0 , W S e p 2 8 B e h a v i o r a l M o d e l i n g C h p 7 ( S P ) P r o p o s a l d u e H W S 5 H W S 6 , D u e : N o c l a s s – i n s t r u c t o r t r a v e l P r o j e c t P l a n n i n g , M S e p 1 9 , M S e p 2 6 D a t a F l o w M o d e l i n g C h p 6 ( S P ) i l o g M o d e l s , W S e p 2 1 i S m u l a t i n g H a r d w a r e w i t h V e r - H W S 5 F , S e p 2 3 E t h i c s a n d s y s t e m t e s t i n g D u e : H W S 4 , W S e p 1 4 M o d u l e s a n d P o r t s C h p 4 ( S P ) H W S 4 G a t e L e v e l M o d e l i n g F , S e p 1 6 M o d e l i n g S t r u c t u r e w i t h V e r i l o g , C h p 5 ( S P ) D u e : H W S 3 S e s s i o n D a t e T o p i c s R e a d i n g A s s i g n m e n t H o m e w o r k 66 SAMPLE SYLLABUS : e u D , 9 / 8 / 7 S W H 6 S W H k r o w e m o H t n e m n g i s s A s e n i h c a M e t a t S e t i n i F g n i l e d o M h t i w s r e l l o r t n o C h t a p a t a D d n a g o l i r e V 4 1 t c O F , 7 1 t c O M , m e t s y S n o i t a g i r r I : e l p m a x E 9 1 t c O W , 1 2 t c O F , g n i d a e R s c i p o T e t a D n o i s s e S : e u D 1 1 , 0 1 S W H ) K & M ( 7 r e t p a h C s r e f s n a r T r e t s i g e R d n a s r e t s i g e R 4 2 t c O M , g n i n n a l P t c e j o r P 9 / 8 / 7 S W H , 5 0 1 3 N E M P 8 - 6 , 1 m a x E 6 2 t c O W , 8 2 t c O F , 1 3 t c O M , 1 1 / 0 1 S W H : e u D 2 1 S W H ) K & M ( 9 r e t p a h C s c i s a B n g i s e D r e t u p m o C 7 v o N M , ) K & M ( 8 r e t p a h C s c i s a B y r o m e M 2 v o N W , 4 v o N F , 4 2 5 2 6 2 7 2 8 2 9 2 0 3 1 3 2 3 3 3 4 3 F i n a l E x a m M o n , D e c 5 , 1 : 1 5 - 3 : 1 5 P M C R 1 0 3 , SAMPLE SYLLABUS 67 4 3 4 2 4 1 4 0 3 9 3 8 3 7 3 6 3 5 , F D e c 2 P r o j e c t p r e s e n t a t i o n s ( 3 ) , W N o v 3 0 P r o j e c t p r e s e n t a t i o n s ( 3 ) , M N o v 2 8 P r o j e c t p r e s e n t a t i o n s ( 3 ) , F N o v 2 5 T h a n k s g i v i n g B r e a k , W N o v 2 3 T h a n k s g i v i n g B r e a k N o c l a s s N o c l a s s , M N o v 2 1 E x a m 2 i n g U n i t s , F N o v 1 8 R I S C a n d C I S C C e n t r a l P r o c e s s - C h a p t e r 1 1 ( M & K ) , W N o v 9 , F N o v 1 1 I n s t r u c t i o n S e t A r c h i t e c t u r e C h a p t e r 1 0 ( M & K ) , M N o v 1 4 , W N o v 1 6 N o c l a s s – i n s t r u c t o r t r a v e l i n g m e n t i T m e P r o j e c t D e v e l o p - 1 2 P r o j e c t D u e : H W S S e s s i o n D a t e T o p i c s R e a d i n g A s s i g n m e n t H o m e w o r k 69 A P P E N D I X B Personal Worksheet Personal Worksheet (cid:129) Develop your personal list of tenets of great teaching that you will follow. (cid:129) Spend some time reﬂecting on teachers, both good and bad, from your past. Develop a list of both good and bad tenets from your personal reﬂections. 70 B. PERSONAL WORKSHEET (cid:129) Develop a personal teaching mission statement based on the tenets of great teaching from the area of attitude. (cid:129) Select a course you are currently teaching or will teach in the near future. Develop objectives for that course. How do the course objectives support student outcomes? (cid:129) Develop a list of concrete methods to use in the classroom to apply the tenets of great teaching summarized in the synthesized model. 71 72 B. PERSONAL WORKSHEET (cid:129) In the Paul Crips vignette, what tenets of great teaching were exhibited? (cid:129) In the Jaime Escalante vignette, what tenets of great teaching were exhibited? 73 (cid:129) Identify a teacher you greatly admire; interview them, identify the tenets of great teaching they exhibit, and write a teaching vignette about them. 74 B. PERSONAL WORKSHEET (cid:129) Write your own personal teaching vignette. (cid:129) Based on the work of Felder and Silverman, develop your own personal list of techniques to bridge your teaching style to the learning styles of your students. 75 76 B. PERSONAL WORKSHEET (cid:129) Develop a list of attributes that you expected from a teacher when you were a student. Which ones will you follow as a teacher? (cid:129) What techniques will you employ to establish good student relationships? 77 78 B. PERSONAL WORKSHEET (cid:129) Conduct a self assessment of your teaching progress. (cid:129) Conduct an assessment of your course. Are you achieving course objectives? What proactive changes can you make to improve the course? 79 80 B. PERSONAL WORKSHEET (cid:129) Who were the mentors in your life? Do they share any character traits? (cid:129) What are the traits of a good mentor? 81 82 B. PERSONAL WORKSHEET (cid:129) What are the expectations for your job performance? Develop a plan on how you will meet these expectations. (cid:129) Develop a plan on how you will continue to grow as an educator. 83 84 B. PERSONAL WORKSHEET (cid:129) Develop a personal mission statement to be the best educator possible. Author’s Biography 85 STEVEN F. BARRETT Steven F. Barrett, Ph.D., P.E., received a BS in Electronic Engineering Technology from the University of Nebraska at Omaha in 1979, a M.E.E.E. from the University of Idaho at Moscow in 1986, and a Ph.D. from The University of Texas at Austin in 1993. He was formally an active duty faculty member at the United States Air Force Academy, Colorado and is now the Associate Dean of Academic Programs at the University of Wyoming. He is a member of IEEE (senior) and Tau Beta Pi (chief faculty advisor). His research interests include digital and analog image processing, computer-assisted laser surgery, and embedded controller systems. He is a registered Professional Engineer in Wyoming and Colorado. He, along with co-author Dr. Daniel Pack, wrote six textbooks on microcontrollers and embedded systems. In 2004, Barrett was named “Wyoming Professor of the Year” by the Carnegie Foundation for the Advancement of Teaching and in 2008 was the recipient of the National Society of Professional Engineers (NSPE) Professional Engineers in Higher Education, Engineering Education Excellence Award. 87 Index “Stand and Deliver”, 11 6 Ps, 8 ABET accreditation, 29 academic dishonesty, 39 assessment, 43, 48 attitude, 7 Bloom’s Taxonomy, 18 Bloom, Benjamin, 18 Carnegie Foundation, 5 CASE, 5 challenges, 38 codiﬁed, 18 consolidation, 18 continuous improvement, 48 conversion, 18 course assessment, 48 course critiques, 47 course objectives, 32 Crips, Paul, 9 Escalante, Jaime, 11 evaluation, 48 examinations, 44 FE examination, 7, 50 Felder and Silverman, 21 FERPA, 7, 39 Garﬁeld High School, 12 GreatSchools, 5 Jung, Carl, 20 Kupfermann, 17 lecture, 38 lecture assessment, 43 lesson objectives, 34 lesson plans, 34 long term improvement, 48 Mathews, Jay, 12 MBTIR, 20 memory consolidation, 17 memory model, 17 mentoring, 53 midterm critiques, 45 Myers-Briggs, 20 NCEES, 7 parents, well-meaning, 39 personal assessment, 45 preparation, 8 professional conduct, 38 program educational objectives, 30 quizzes, 44 rewards, 55 self assessment, 47 sensitization, 18 short term improvement, 48 88 INDEX student outcomes, 30 student relationships, 37 syllabus, 32 synthesized model, 7 textbook selection, 33 tootlifest, 34 U.S. Professors of the Year, 5 Whitaker, Todd, 2
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https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813309.pdf&bkn=6813308&pdfType=book	SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING Series ISSN: 1939-5221 Series ISSN: 1939-5221 Series ISSN: 1939-5221 Engineering Thermodynamics and Engineering Thermodynamics and Engineering Thermodynamics and 21st Century Energy Problems 21st Century Energy Problems 21st Century Energy Problems A Textbook Companion for Student Engagement A Textbook Companion for Student Engagement A Textbook Companion for Student Engagement Donna Riley, Smith College Donna Riley, Smith College Donna Riley, Smith College Energy is a basic human need; technologies for energy conversion and use are fundamental to human Energy is a basic human need; technologies for energy conversion and use are fundamental to human Energy is a basic human need; technologies for energy conversion and use are fundamental to human survival. As energy technology evolves to meet demands for development and ecological sustainability survival. As energy technology evolves to meet demands for development and ecological sustainability survival. As energy technology evolves to meet demands for development and ecological sustainability in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges posed by current and future energy problems. Further, engineers need to cultivate a commitment to and posed by current and future energy problems. Further, engineers need to cultivate a commitment to and posed by current and future energy problems. Further, engineers need to cultivate a commitment to and passion for lifelong learning which will enable us to actively engage new developments in the ﬁeld. This passion for lifelong learning which will enable us to actively engage new developments in the ﬁeld. This passion for lifelong learning which will enable us to actively engage new developments in the ﬁeld. This undergraduate textbook companion seeks to develop these capacities in tomorrow’s engineers in order undergraduate textbook companion seeks to develop these capacities in tomorrow’s engineers in order undergraduate textbook companion seeks to develop these capacities in tomorrow’s engineers in order to provide for future energy needs around the world. to provide for future energy needs around the world. to provide for future energy needs around the world. This book is designed to complement traditional texts in engineering thermodynamics, and thus is This book is designed to complement traditional texts in engineering thermodynamics, and thus is This book is designed to complement traditional texts in engineering thermodynamics, and thus is organized to accompany explorations of the First and Second Laws, fundamental property relations, and organized to accompany explorations of the First and Second Laws, fundamental property relations, and organized to accompany explorations of the First and Second Laws, fundamental property relations, and various applications across engineering disciplines. It contains twenty modules targeted toward meeting various applications across engineering disciplines. It contains twenty modules targeted toward meeting various applications across engineering disciplines. It contains twenty modules targeted toward meeting ﬁve often-neglected ABET outcomes: ethics, communication, lifelong learning, social context, and ﬁve often-neglected ABET outcomes: ethics, communication, lifelong learning, social context, and ﬁve often-neglected ABET outcomes: ethics, communication, lifelong learning, social context, and contemporary issues. The modules are based on pedagogies of liberation, used for decades in the humanities contemporary issues. The modules are based on pedagogies of liberation, used for decades in the humanities contemporary issues. The modules are based on pedagogies of liberation, used for decades in the humanities and social sciences for instilling critical thinking and reflective action in students by bringing attention and social sciences for instilling critical thinking and reflective action in students by bringing attention and social sciences for instilling critical thinking and reflective action in students by bringing attention to power relations in the classroom and in the world. to power relations in the classroom and in the world. to power relations in the classroom and in the world. This book is intended to produce a conversation and creative exploration around how to teach and This book is intended to produce a conversation and creative exploration around how to teach and This book is intended to produce a conversation and creative exploration around how to teach and learn thermodynamics differently. Because liberative pedagogies are at their heart relational, it is important learn thermodynamics differently. Because liberative pedagogies are at their heart relational, it is important learn thermodynamics differently. Because liberative pedagogies are at their heart relational, it is important to maintain spaces for discussing classroom practices with these modules, and for sharing ideas for to maintain spaces for discussing classroom practices with these modules, and for sharing ideas for to maintain spaces for discussing classroom practices with these modules, and for sharing ideas for implementing critical pedagogies in engineering contexts. The reader is therefore encouraged to visit the implementing critical pedagogies in engineering contexts. The reader is therefore encouraged to visit the implementing critical pedagogies in engineering contexts. The reader is therefore encouraged to visit the book’s blog at http://smiththermo.wordpress.com. book’s blog at http://smiththermo.wordpress.com. book’s blog at http://smiththermo.wordpress.com. About SYNTHESIs About SYNTHESIs About SYNTHESIs This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development provide concise, original presentations of important research and development provide concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com visit www.morganclaypool.com visit www.morganclaypool.com Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers Mor gan Cl aypool Publishers & & & ISBN: 978-1-60845-363-4 ISBN: 978-1-60845-363-4 ISBN: 978-1-60845-363-4 90000 90000 90000 w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m 9 781608 453634 9 781608 453634 9 781608 453634 R R R I I I L L L E E E Y Y Y E E E N N N G G G I I I N N N E E E E E E R R R I I I N N N G G G T T T H H H E E E R R R M M M O O O D D D Y Y Y N N N A A A M M M I I I C C C S S S A A A N N N D D D 2 2 2 1 1 1 S S S T T T C C C E E E N N N T T T U U U R R R Y Y Y E E E N N N E E E R R R G G G Y Y Y P P P R R R O O O B B B L L L E E E M M M S S S M M M o o o r r r g g g a a a n n n & & & C C C l l l a a a y y y p p p o o o o o o l l l & & & CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers CM& Mor gan Cl aypool Publishers Engineering Thermodynamics and Engineering Thermodynamics and Engineering Thermodynamics and 21st Century Energy Problems 21st Century Energy Problems 21st Century Energy Problems A Textbook Companion for Student Engagement A Textbook Companion for Student Engagement A Textbook Companion for Student Engagement Donna Riley Donna Riley Donna Riley SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING Engineering Thermodynamics and 21st Century Energy Problems A textbook companion for student engagement Synthesis Lectures on Engineering Engineering Thermodynamics and 21st Century Energy Problems: A textbook companion for student engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey, Jeffrey W. Holmes 2008 iii Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam, Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam, Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard, Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2012 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Engineering Thermodynamics and 21st Century Energy Problems: A textbook companion for student engagement Donna Riley www.morganclaypool.com ISBN: 9781608453634 paperback ISBN: 9781608453641 ebook DOI 10.2200/S00387ED1V01Y201110ENG016 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #16 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X Engineering Thermodynamics and 21st Century Energy Problems A textbook companion for student engagement Donna Riley Smith College SYNTHESIS LECTURES ON ENGINEERING #16 CM& Morgan & cLaypool publishers ABSTRACT Energy is a basic human need; technologies for energy conversion and use are fundamental to human survival. As energy technology evolves to meet demands for development and ecological sustainability in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges posed by current and future energy problems. Further, engineers need to cultivate a commitment to and passion for lifelong learning which will enable us to actively engage new developments in the ﬁeld. This undergraduate textbook companion seeks to develop these capacities in tomorrow’s engineers in order to provide for future energy needs around the world. This book is designed to complement traditional texts in engineering thermodynamics, and thus is organized to accompany explorations of the First and Second Laws, fundamental property relations, and various applications across engineering disciplines. It contains twenty modules targeted toward meeting ﬁve often-neglected ABET outcomes: ethics, communication, lifelong learning, social context, and contemporary issues. The modules are based on pedagogies of liberation, used for decades in the humanities and social sciences for instilling critical thinking and reﬂective action in students by bringing attention to power relations in the classroom and in the world. This book is intended to produce a conversation and creative exploration around how to teach and learn thermodynamics differently. Because liberative pedagogies are at their heart relational, it is important to maintain spaces for discussing classroom practices with these modules, and for sharing ideas for implementing critical pedagogies in engineering contexts. The reader is therefore encouraged to visit the book’s blog at http://smiththermo.wordpress.com. KEYWORDS energy, thermodynamics, entropy, liberative pedagogies, critical pedagogy, feminist ped- agogy, engineering education, climate change, engineering ethics, communication, life- long learning, social context, contemporary issues, development, service learning Contents vii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Why College? Why Thermodynamics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Why this Book? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A Textbook Companion: A Book of Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 An Open Discussion for Students and Teachers: Learning Objectives . . . . . . . . . . 4 Learning Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Evaluating Student Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 What and Why? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Module 1.1. Thermodynamics is About Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.1 Exploration: What is Energy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Module 1.2. Pedagogy: How to Learn Using this Book . . . . . . . . . . . . . . . . . . . . . . 12 1.2.1 Exploration 1: Principles of Critical Pedagogies . . . . . . . . . . . . . . . . . . . . . . 14 1.2.2 Exploration 2: Models of Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Module 1.3. US and World Energy Needs and Uses . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.1 Exploration 1: Energy Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.2 Exploration 2: Women, Poverty, and Energy . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.3.3 Exploration 3: 1 kW per capita? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4 Module 1.4. US and World Energy Policies: What are the Issues? . . . . . . . . . . . . 24 1.4.1 Exploration 1: Copenhagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4.2 Exploration 2: The Cost of Energy [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5 Module 1.5. Getting Education Right for a Sustainable Energy Future . . . . . . . . 28 1.5.1 Exploration 1: Power/Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5.2 Exploration 2: What do Current Engineering Students Need to Learn to be Able to Work on Energy Issues? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 viii 2 3 4 The First Law: Making Theory Relevant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1 Module 2.1. Learning from History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1.1 Exploration 1: First Law in Western Europe . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.1.2 Exploration 2: De-Centering Western Thermo . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Module 2.2. Energy Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.1 Exploration 1: “Foreign” Oil Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.2 Exploration 2: Energy Independence Reconceived . . . . . . . . . . . . . . . . . . . . 39 2.3 Module 2.3. Evaporative Coolers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Module 2.4. Hunger, Poverty, and Obesity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5 Module 2.5. Thermo to Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 The Second Law and Property Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1 Module 3.1. The Limits of Efﬁciency: Heat Engines vs. Other Energy Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 Module 3.2. Perpetual Motion Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Module 3.3. Entropy as a Social Construct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Exploration 1: Origins of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.2 Exploration 2: Entropy’s Philosophical Implications . . . . . . . . . . . . . . . . . . 56 3.4 Module 3.4. Evaluating Entropy Analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.5 Module 3.5. Making Math Relevant: Thermodynamic Relations in Context . . . . 59 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Thinking Big Picture about Energy and Sustainability . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Module 4.1. Climate Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Module 4.2. Selection Criteria for Energy Technologies . . . . . . . . . . . . . . . . . . . . . 66 4.2.1 Exploration 1: Developing Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.2 Exploration 2: Evaluating and Selecting Power Generation Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.3 Exploration 3: Evaluating and Selecting Transportation Technologies . . . 69 4.3 Module 4.3. Is it Green? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3.1 Exploration 1: Nuclear Power as a Green Alternative? . . . . . . . . . . . . . . . . . 71 4.3.2 Exploration 2: Ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.3 Exploration 3: Coal Train [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.4 Module 4.4. Home Energy Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.4.1 Exploration 1: Solar Cooker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.4.2 Exploration 2: Refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.4.3 Exploration 3: Dean Kamen’s Stirling Engine . . . . . . . . . . . . . . . . . . . . . . . . 78 4.5 Module 4.5. Ethics of Energy Disasters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 ix Acknowledgments Many of the innovations in this book came from my own students in thermodynamics, and from friends and colleagues kind enough to help me think through the course and my pedagogy. In the early years it was Stefan Brueck and Sylvia Thorson-Smith who introduced me to bell hooks’s work and the critical pedagogy tradition. Colleagues at Smith including Lisa Armstrong, Alex Keller, Ginetta Candelario, Jennifer Guglielmo, and Marguerite Harrison have helped me think further about my teaching. In more formal settings colleagues participating in the Kahn Institute on Disorder and the Sherred Center Teaching Circles on Diversity and on the Gulf Spill have further helped me develop ideas in this book. I thank Kamyar Haghighi and the Purdue Engineering Education faculty for hosting me on sabbatical while I worked on this book, and particularly thank Alice Pawley and Julia Thomson for discussing the book with me at some length. I thank the Engineering, Social Justice, and Peace community, particularly George Catalano and Caroline Baillie, for the opportunities they have extended to me to develop ideas for this book, especially George’s grant from Campus Compact that resulted in the development of the module on hunger, poverty, and obesity. Some of the material in this book is based upon work supported by the National Science Foundation under grants 0448240 and 1037655. Any opinions, ﬁndings, and conclusions or recom- mendations expressed in this material are those of the author and do not necessarily reﬂect the views of the NSF. All along my students in the thermodynamics course have been great sports – whether they came along enthusiastically or reluctantly, I thank them for all they did to improve learning in my course over the years. Student researchers Lindsay Holle and Ally Gorin worked on this project with Smith College funding, and students from the Liberative Pedagogies Project and later the e-book Dissemination Project also contributed to this book. I particularly thank Nora Paul Schultz and Ida Ngambeki for their contributions to the development of modules in thermo, and Haley Dell’Orso and Amanda Nadeau for reviewing drafts of this book. I thank Lionel Claris and Eleanor Jaffee, my colleagues on the Liberative Pedagogies Project, for their immeasurable contributions to this project. In the early years of the project Lionel in particular helped shape many of the curricular innovations found in these pages. It was a joy and a delight to engage in this creative work with them both. Thanks to the faculty collaborators in the NSF E-book dissemination project who reviewed and tested out many of the modules in this book, and continue to help improve them in many ways. I could not have done this without the support of friends and family. Susannah Howe and Borjana Mikic, friends and colleagues in the Picker Engineering Program, were sounding boards for ideas in their infancy. Running partners Lisa, Daphne, Marybeth, Kim and Pam (and Susannah and xii ACKNOWLEDGMENTS Borjana) provided support and a much needed stress release. The Tribe (you know who you are) was there to listen and support me, and provide me with hilarity, excellent food and friendship along the way. My familiars Willow and Raven were constant companions through the writing of the book. I thank my family for offering me support and encouragement. Finally, to Phil, for being a fellow scientist who “gets it,” for cheering me on, for believing in me as I dream the impossible, for being at the center of the fullness of my life outside work, my deepest love and gratitude. Donna Riley October 2011 Introduction 1 Energy is a basic human need; technologies for energy conversion and use are fundamental to human survival. As energy technology evolves to meet demands for development and ecological sustainability in the 21st century, engineers need to have up-to-date skills and knowledge to meet the creative challenges posed by current and future energy problems. Further, engineers need to cultivate a commitment to and passion for lifelong learning which will enable us to actively engage new developments in the ﬁeld. This undergraduate textbook companion seeks to develop these capacities in tomorrow’s engineers in order to provide for future energy needs around the world. WHY COLLEGE? WHY THERMODYNAMICS? I usually start my thermodynamics class off by asking students why they are in college. Typically, my students are taken aback by the question; most haven’t thought about it, at least not recently. They describe college as a “logical next step,” as something expected of them, by parents who went to college as well as by those who did not. Some describe college as necessary to be credentialed for particular kinds of jobs that they view as desirable. I work with them to challenge their assumptions, to help them see college as a choice they have made, to take ownership over that choice. Only once every few years does a student draw on liberal education ideals in her/his/hir answer: she/he/ze is in college to learn, to develop her/his/hir intellect and abilities in independent and critical thought. After we discuss why they are in college, I also ask my students why they are taking my course in thermodynamics. The vast majority respond that they are there because it is required for the engineering major. I want students, and I want you, the reader, to have other reasons for engaging with this book: intellectual curiosity, and a commitment to engage with energy issues as future professionals and/or as citizens of the planet. I don’t want you to read this because it is assigned, but because energy matters. Energy availability, production, and use have enormous political and economic implications. The First and Second Laws are central organizing principles for science and technology, for industry and commerce. Using theoretical principles like these as well as mathematics to describe physical phenomena and to model or design useful products and processes goes to the very heart of what engineering is all about. With applications in such a breadth of areas – transportation, electric power, refrigeration, heating, ventilation, and air conditioning (HVAC), nutrition and exercise, manufac- turing of pharmaceuticals, distillation of liquor and gasoline, analyzing behavior of contaminants in environmental media, and the list goes on – how can an engineering student not ﬁnd something relevant to their lives and livelihoods, something of interest personally or professionally? 2 ACKNOWLEDGMENTS WHY THIS BOOK? Current engineering thermodynamics textbooks seem to adhere to an unspoken canon, grounded in 19th century developments of the steam engine in Europe, and subsequent fossil fuel technologies. While several texts have added updates, sidebars, and problems on more recent technologies, they do not frame their texts around what engineers need to know to innovate and lead society into a sustainable energy future. Alfred Carlson, professor of chemical engineering at Rose-Hulman Institute of Technology, commented in ASEE Prism, “Most thermo books either have no new info or outdated or useless material.”[1] This book takes a fresh look at the engineering knowledge and skills required for current and emerging technologies, and organizes learning around acquiring them. It incorporates innova- tive engineering pedagogies that foster intentional and independent learning, preparing students to face new problems and approach new energy technologies with a spirit of inquiry and conﬁdence throughout their careers. Because our energy future is at least as much about political will as it is about technological know-how, it includes the fundamentals of energy policy analysis and assists en- gineering programs in meeting accreditation criteria related to the social implications of technology, communications skills, and professional ethics. The book’s distinguishing features include the following: (cid:2) Liberative pedagogies and intentional learning – This book embodies the principles of critical, feminist, anti-racist and post-colonial pedagogies, which seek to empower students as independent learners and thinkers. Liberative pedagogies engage students where they are, starting from what students already know from their life experience, and connecting with the things they ﬁnd relevant. Recognizing student authority builds conﬁdence and de-mystiﬁes es- oteric material. With an inductive approach that fosters critical thinking and the development and pursuit of important questions, readers are encouraged to collectively and independently explore topics of individual or collective interest. Critical engagement with the world in the form of reﬂective action is the ultimate goal of liberative pedagogies, and to this end, exercises in the book encourage reﬂection on one’s own learning, and on our collective energy future. Readers are further challenged to take action as involved citizens and professionals on energy issues locally, regionally, nationally, and globally. (cid:2) Sustainability – The ability to properly assess the ecological impacts of different energy technologies is increasingly important as sustainability becomes a basic design criterion for energy systems, in response to deepening concerns about environmental quality and global climate change. This book takes a critical approach to sustainability and seeks to examine deﬁnitions of sustainability in broader economic, political, and social context. (cid:2) Global Perspective – As industrially developing nations plan to meet energy needs for eco- nomic growth, they are poised to make crucial and far-reaching decisions for developing new energy infrastructures. This is an exciting time for engineers, offering a teaching moment for students to consider the impacts of technology and the importance of forward-thinking design. It is equally important that engineers learn to understand issues of power in the economic and political contexts of globalization, and this book encourages students to explore global issues in ways that take these dynamics into account. ACKNOWLEDGMENTS 3 (cid:2) Policy considerations – Politics drives our energy priorities, and our choices of energy tech- nologies can drive our foreign and domestic political priorities. Engineers must have a working knowledge of policy and politics as it relates to energy technology. (cid:2) Ethics and social responsibility – Energy poses ethical questions that must be confronted at multiple levels of analysis. Engineers face both individual and collective decisions as pro- fessionals with important ethical dimensions. Local, national, and international communities face ethical choices about energy systems and uses. Engineers need a set of analytical skills to understand the factors that inﬂuence their ethical decision making in all of these settings and roles. Presenting ethics and social responsibility provides realistic and signiﬁcant professional and social context for technical material in thermodynamics. (cid:2) A multidisciplinary approach – Today’s complex energy systems require a multidisciplinary approach that spans all engineering disciplines. Engineering Thermodynamics is typically taken as a required course (or multiple courses) by engineering undergraduates in speciﬁc disciplines. This book covers a range of applications across engineering disciplines; while applications are rarely speciﬁc to a particular discipline, the intent is to broaden the perspectives of engineers in every discipline. (cid:2) History – The historical development of thermodynamics is important for engineers to un- derstand. Historical presentations of information can provide insight and make the material approachable for some readers using the drama of discovery. Historical material is made rele- vant to students’ understanding of key concepts and to current issues in energy. A TEXTBOOK COMPANION: A BOOK OF IDEAS There are many thermodynamics textbooks available for engineering classes today. This book does not replicate this effort, but is designed as a companion to these. It does not cover fundamentals or provide the typical practice problems found in traditional texts. It is designed for the Morgan and Claypool Synthesis series, such that students at subscriber institutions might be able to use the book in electronic form at no additional cost. Each module in this book is an idea that can be implemented in courses and classrooms any number of ways. It is up to professors and students to adapt these ideas as appropriate for different circumstances and learning settings. I have intentionally avoided being prescriptive; instead, modules represent suggestions that can no doubt be improved upon implementation. 4 ACKNOWLEDGMENTS AN OPEN DISCUSSION FOR STUDENTS AND TEACHERS: LEARNING OBJECTIVES This book is written with both students and instructors in mind. It is a principle of critical pedagogies to blur these roles intentionally. And so I hope that students as well as instructors will read this section on accreditation criteria as they relate to course design and learning objectives. As ABET’s educational outcomes criteria (Figure 1) have been implemented within engineer- ing programs over the past decade, the need for textbooks that cover social context and professional ethics has grown. This book provides content to meet ABET criteria while co-existing with tried- and-true textbooks. The book is designed to help students develop knowledge and abilities primarily related to outcomes (f-j): ethics, communication, context, lifelong learning, and contemporary issues. (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) (k) ABET OUTCOMES CRITERIA an ability to apply knowledge of mathematics, science, and engineering an ability to design and conduct experiments, as well as to analyze and interpret data an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability an ability to function on multidisciplinary teams an ability to identify, formulate, and solve engineering problems an understanding of professional and ethical responsibility an ability to communicate effectively the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context a recognition of the need for, and an ability to engage in life- long learning a knowledge of contemporary issues an ability to use the techniques, skills, and modern engineer- ing tools necessary for engineering practice. Figure 1: ABET outcomes [2]. ACKNOWLEDGMENTS 5 While thermodynamics instructors will note that this book does not emphasize ABET out- comes (b) (experiments and data), (c) (design), (e) (problem solving), or (k) (modern tools), most traditional thermo courses already heavily emphasize (e), also (b) and (k) when taught with a lab- oratory, and (c) if a design project is incorporated into the course. The teamwork outcome (d) can be addressed if the modules are implemented in teams. It is up to the instructor and students to implement modules in ways that fulﬁll this outcome if desired. Throughout the book modules that address particular ABET outcomes are identiﬁed with the icons shown in Figure 2. a SEM knowledge c e f design problems ethics g communi- cation h context i j lifelong learning contemporary issues Figure 2: ABET outcomes icons. LEARNING PROCESS This book uses a modular format and employs a particular set of pedagogies to accomplish its learning objectives. All modules are laid out using a four-step process that draws on critical pedagogies (Figure 3). First, students engage a topic, usually through reading given material and/or searching for material on their own. Next, students analyze a process or situation related to the topic. Sometimes analysis is technical, sometimes social. Sometimes analysis is quantitative, sometimes qualitative. Then students reﬂect on a particular question or what they have learned from the analysis. Finally, students are challenged to initiate some change, either to their way of thinking or in the world at large as a result of what they have learned. This process is normally iterative, where the change may initiate another question to engage, and so on. This book will ask students to “do something,” to engage in learning and teaching in ways that might be unfamiliar and demand more responsibility than is familiar (more on this in Module 1.2). Some work may occur in the classroom as traditional assignments. Some of it, I hope, readers will choose to do independently out of a particular interest. The actions aren’t the same as most typical “hands on” work done in the lab or design shop. It might not be what most have thought of as “engineering” before. But this is part of the work we need to do if we want engineering and engineers to have something meaningful to say about the nation’s and world’s energy issues. Instructors and students should each understand the additional workloads that are required when exploring relevant material. There may be limits on what is realistically achievable, given available resources or institutional policies. Expanding these possibilities is part of the struggle for education. We need to acknowledge the power dynamics at work in our institutions, and become creative as we dismantle or work around constraints. This is a process that takes time. This book is 6 ACKNOWLEDGMENTS Figure 3: Learning process for modules. the result of 10 years of creative experiment and iteration. I recommend introducing modules from this book incrementally rather than all at once, and evaluating each effort, adapting the materials for particular students in particular settings. Some will argue that thermodynamics instructors already have too great a challenge before them in helping students understand the technical material. There is no time for these “extras,” which would be nice, but are not necessary. I believe skills in context, ethics, communication, and contemporary issues are absolutely essential, and underemphasized in engineering education today. So on one level, this may simply be a question of priorities and values. However, even if technical skills are considered of the utmost value, it has been my experience that teaching material in this book actually helps students with their technical understanding, by providing motivation and new perspectives on the material. Thinking in terms of synergy rather than zero-sum games reveals what these modules have to offer. It helps to remember that concerns about coverage can be counterpro- ductive if insistence on coverage impedes learning overall. The question should be the following: what is really important for students to learn now? It is possible to prioritize in order to incorporate some of these important topics in the thermodynamics classroom? We need to work toward learning those things that are going to serve students and society best in the long run. With additional work for students, and with innovative pedagogies introduced into a classroom that is very reliant on traditional modes of learning, students should expect to feel challenged and uncomfortable at times, and instructors should expect resistance from students. To the extent that REFERENCES 7 introducing these topics bucks institutional trends (department, institution, discipline…), expect resistance there as well. The best thing for both students and instructors to do is be transparent and intentional, always providing the motivation behind our decisions and actions. This does not remove the dynamic of resistance, but it moves the conversation forward. It is worth the extra effort if this book can contribute to the development of its readers as thinkers, leaders, ethical decision-makers and agents of social change.Ultimately, I hope each reader, instructor and student alike, will come away from this book having learned something new – about energy, or about learning itself. I hope the book leads us all to ask different kinds of questions, hard questions that change the world and change our own ways of thinking about the world. EVALUATING STUDENT WORK Faculty assigning some of the modules in this book, and students undertaking these asignments, will ﬁnd themselves outside their comfort zones – these are not problem sets. Even the modules that require quantitative analysis are open-ended and do not have a single right answer. Several modules are well suited to in-class discussions or other kinds of interactive activities. Some are suited to community-based learning projects. For instructors new to some of these teaching methods, it may be helpful to consult resources on techniques such as leading discussions. An excellent resource on this topic is the Canadian Society for Teaching and Learning in Higher Education (CSTLHE) Green Guide [3]. When it comes to assigning written work, I have found that the development and sharing of evaluation rubrics as part of the assignment prompt can help students perform better on these assignments, and remove some of the anxiety around what is perceived as more subjective evaluation of student work. Generally, I have used the ABET criteria on communication, context, contemporary issues, ethics, and lifelong learning as performance criteria on the rubric, specifying for each item what constitutes excellent, average, and poor work. Students sometimes need to iterate to learn the kind of depth of reﬂection and critical or original thinking required of lifelong learning, and here I have found that early feedback is particularly helpful. Many students need practice in developing and supporting effective arguments in written work, and writing in ethics often requires reminding students of the importance of using multiple, different ethical frameworks to build their arguments and explore the ethics of an issue in depth. REFERENCES [1] Sharp, J.E.M. (2005). High Tech Text Books. Prism 15(3) (November 2005). Accessed June 6, 2011 from http://www.prism-magazine.org/nov05/tt_01.cfm. Cited on page(s) 2 [2] ABET (2011). Criteria for Accrediting Engineering Programs. Accessed May 31, 2011 from http://www.abet.org/Linked%20Documents-UPDATE/Criteria%20and%20PP/ E001%2010-11%20EAC%20Criteria%201-27-10.pdf. Cited on page(s) 4 8 REFERENCES [3] Kustra, E.D.H. and Potter, M.K. (2008). Leading Effective Discussions. Green Guide, No. 9. London, Ontario: Society for Teaching and Learning in Higher Education. Ordering in- formation accessed September 19, 2011 from http://www.stlhe.ca/resources/green- guides/. Cited on page(s) 7 C H A P T E R 1 What and Why? 9 This book is organized as a textbook companion. It is meant to supplement and complement other more technically focused thermodynamics textbooks. It is organized into stand-alone modules that parallel the general development of most thermodynamics texts, so that students and instructors can engage this book as little or as much as time permits. This chapter provides an introduction to the book, to the study of thermodynamics, and to energy problems on a local, national, and global scale. It asks readers to think about what students need to learn as engineers and as citizens of the planet, to build a sustainable energy future. The ﬁrst module asks readers to develop their own deﬁnitions of energy and thermodynamics. The second module provides a hands-on, learn-by-doing introduction to the pedagogies used in this book. The third and fourth modules tackle big-picture questions: How much energy do we need? For what do we need energy? How do our energy needs relate to global problems such as climate change and war? The last module challenges readers to think about what’s in a thermodynamics textbook or syllabus, and whether that constitutes what engineers need to know about energy in the Twenty-First Century. Who decided what students should be learning, and what inﬂuenced that decision? What do you think students need to know? How will you pursue this knowledge? Module 1.1: Thermodynamics is About Energy. Module 1.2: Pedagogy: How to Learn Using this Book. Module 1.3: US and World Energy Needs and Uses. Module 1.4: US and World Energy Policy: What are the Issues? Module 1.5: Getting Education Right for a Sustainable Energy Future. 1.1 MODULE 1.1. THERMODYNAMICS IS ABOUT ENERGY Thermodynamics is, and ought to be, the study of energy. For some reason, the word thermodynamics is daunting, off-putting, and esoteric. Thermodynamics is something your professor knows about, or other kinds of experts with many degrees in physics or chemistry or engineering. You hope they will tell you about it in class, or you will read about it in your expensive textbook, and you will write it down and practice solving problems and hopefully absorb some of what they know. g i communi- cation lifelong learning 10 1. WHAT AND WHY? This book is built on the premise that traditional learning, as the saying goes, “from professor’s notes to students’ notes and through the minds of neither” is the wrong way to go about learning thermodynamics. In fact, thermodynamics is nothing more than – and nothing less than – the study of energy. Most of us have been studying energy our whole lives; we know a lot about it from hands- on experience. The trouble is most thermodynamics textbooks only focus on a small, outdated slice of what energy is and how it is used in socio-technical systems. This book starts with the recognition that you already know about energy, and that you can speak with some authority about it. This book is also realistic in acknowledging that there is an existing curriculum in thermodynamics that will continue to exist for some time, perpetuated by textbooks, accreditation criteria, industry demand, and other forces.The book is therefore organized to parallel the organization of many typical thermodynamics textbooks, using the concept mapping of Figure 1.1. Figure 1.1: A schematic of concepts in an Introductory Thermodynamics course. Typically, courses start by covering four building blocks in thermodynamics. Clearly, the First and Second Laws are fundamental ideas that take up the bulk of time in a ﬁrst thermodynamics course. The idea that energy is conserved and can be converted from one form to another is a central organizing principle for science and industry. Understanding how the Second Law limits achievable efﬁciencies in energy systems is crucial for realistic design. To put these two laws of thermodynamics to use, it is necessary to understand the properties of working ﬂuids and other substances on a conceptual level (what are entropy, enthalpy, and internal energy? What is the difference between heat and work?). It is also necessary to be able to look up, calculate, and/or estimate property data 1.1. MODULE 1.1. THERMODYNAMICS IS ABOUT ENERGY 11 using equations of state and either computerized or printed data tables. While property relations are not emphasized in every ﬁrst course on thermodynamics depending on mathematical preparation and other considerations, they play an essential role in developing an understanding of thermodynamic relationships and in making it possible to quantify properties that are difﬁcult to measure from those that are easier to measure. These four areas can be thought to form a basis that is common among different “ﬂavors” of thermodynamics in physics, chemistry, mechanical engineering, chemical engineering, etc. The pyramids one might build on top of this foundation are many and varied. The most common sets of applications might be engine cycles common in mechanical engineering (including automobile and jet engines, electric power generation, and refrigeration cycles) or solution theory and phase and chemical reaction equilibria in chemical engineering. All of this may have begun to seem esoteric, full of new technical vocabulary and presented in the abstract.The following exploration returns us to concrete and familiar considerations, developing a clear deﬁnition of energy. 1.1.1 EXPLORATION: WHAT IS ENERGY? engage Write down what you know or believe about energy, and why it Is necessary. change Can you develop your own definition of energy? Of thermodynamics? analyze Now look up several definitions of energy. You might want to check a few textbooks and Internet sources. reflect How do different definitions fit together? Do they address why energy is so necessary? What questions do you have about this? Figure 1.2: What is energy? Old Faithful, a geyser in Yellowstone National Park, Wyoming, USA, is a dramatic example of geothermal energy. Photo by Jon Sullivan, Public Domain. http://pdphoto. org/PictureDetail.php?mat=pdef&pg=5274. At this point, a traditional textbook would typically supply you with a deﬁnition of energy. Instead, this book asks you: what is energy? I think you already know. That doesn’t mean I think you 12 1. WHAT AND WHY? can repeat a formal deﬁnition that will be the same as one an expert would write. It means I think in your life experience you have come to know what energy is. 1. Engage. Write down what you know about what energy is. Some of it may be what you remember from other classes you’ve had. Some of it may be what you’ve learned by experiencing the world. It’s ok if what you write is not 100% correct in expert terms – this is what learning is all about. 2. Analyze. Use your information literacy skills to gather a few different deﬁnitions of energy. You might want to start with your course textbook, or some reliable sources in the library or on the Internet. Write these down, and keep track of the source and page numbers, or the permanent URL and date accessed for Web resources. 3. Reﬂect. Evaluate these deﬁnitions. Don’t try to select a single most valid deﬁnition, though you may want to consider the reliability of different sources you have selected. Think about what value you draw from each deﬁnition, and how they might be related. What questions do you have about how different deﬁnitions you’ve read ﬁt together? Do the deﬁnitions make clear why energy is such an important part of our world today? If not, how could they? 4. Change. Can you develop a deﬁnition of energy that brings together what you know, expert knowledge, and energy’s importance in life? Now move through steps 1-3 again to develop your own working deﬁnition of thermodynamics. Why do you think most engineering courses and textbooks are called engineering thermodynamics and not energy engineering? The previous module challenged you to develop your own deﬁnitions of energy and thermo- dynamics. It utilized a four-step process that included engagement, analysis, reﬂection, and some action for change. This process is somewhat different from the typical engineering design process, or engineering problem solving processes that would be commonly used in a thermodynamics course. What is the basis for this learning process, and why is it being employed here? The next module provides an opportunity to explore the development of the process and the educational theory behind it, contrasted with more familiar approaches to teaching and learning. Some of the learning activities in the next module involve theatre techniques that build an embodied knowledge of what it means to learn using different pedagogies. While it may be outside the experience of many students, and instructors may be apprehensive to incorporate acting into a course, creating opportunities to do the unexpected, even if it means leaving one’s comfort zone, can lead to breakthrough insights not achievable in routine and familiar settings. 1.2 MODULE 1.2. PEDAGOGY: HOW TO LEARN USING THIS BOOK i lifelong learning 1.2. MODULE 1.2. PEDAGOGY: HOW TO LEARN USING THIS BOOK 13 You may have noticed that this book is written for students, yet these modules read a bit like something that might be considered a lesson plan. This transparency is intentional. The book is based on a set of learning techniques that have come to be known by labels such as critical pedagogy, feminist pedagogy, or liberative pedagogy. [1] It is based on the following principles: The point is not only to understand the world, but also to change it. [2] The study of energy should begin with real-world problems, addressing what matters now.Theory is explored as it relates to these real needs of people.Then those ideas are put to work in communities, and the experiences of communities contribute to new theories, and so on in a continuing conversation. “No education is politically neutral.” [3] In engineering in particular we tend to think we are just learning the facts about science and technology, and we don’t often notice the ways in which what we learn has a political bent. We therefore need to ask “Who beneﬁts? Who loses? Who isn’t even at the table?” We not only ask this of the syllabus, of the text, of energy research agendas and energy company portfolios, but also we need to ask this of ourselves in the classroom. For example, thermodynamics textbooks focus centrally on the contributions of 19th century European males. A broader examination of history reveals important contributions to thermodynamics from every continent East to West, by men as well as women, of all races and ethnicities. In diverse classrooms, one can no longer assume a common base of knowledge acquired through a common cultural or social background, and one can no longer take a “one size ﬁts all” approach to education. Instead, offering diverse learning opportunities and multiple points of access can build a strong foundation for everyone to share their strengths and learn from each other. Power relations are everywhere and the classroom is a perfect place to learn how power relations work and how to resist unjust power relations. For example, we want to challenge the idea that the professor knows everything, the students know nothing, and the professor makes deposits in students’ brains, which are hopefully retained and regurgitated later [4]. We want to explore what the opposite of this might be. Disrupting classroom hierarchies is an aspiration; although many forces work to resist this, working toward this goal is itself meaningful. Student responsibility for learning. If we take this project seriously, and students have more power in the classroom, it means more responsibility, and more work for you the student. But the work is different from endless grueling late-night problem sets. It is, or should be, work that matters – to you, and to your community, however that is deﬁned in a given situation. A lot of things will be more open-ended than you are used to. There will not always be a single right answer, or a single right approach to a problem. You will wonder what it is you are expected to do. The way to approach such things is to try a little, see what happens, reﬂect on that in order to learn from it, and maybe try something else, and so on. One of the hardest things to put into a book form is the centrality of relationships to this kind of learning. This approach challenges the primacy of individualism – so you want to learn not 14 1. WHAT AND WHY? only independently, but also interdependently in a community of scholars. In my classes, this means I am accessible to students, and they work with each other a lot. It is up to you to ensure that this element is present in your learning. It is absolutely at the heart of these pedagogies. The phrase “pedagogies of liberation” has caused some critics to ask what students are supposed to be liberated from (or to), and to challenge masculinist assumptions in the language of liberation [5]. However, Bell Hooks [3] has suggested that liberatory language has resonance in particular for some women of color, and takes on the phrase “education as the practice of freedom” as a central goal of her pedagogy. My students are sometimes anxious about this shift in the classroom in terms of both content and pedagogy. Year after year I am convinced by the results – students with deep understanding and conﬁdence in their knowledge, and abilities that endure, as seniors return from their Fundamentals of Engineering exam and report that “I rocked the thermo part.” The following two explorations employ techniques of an approach closely related to liberative pedagogies known as Theatre of the Oppressed [6, 7]. Developed by Brazilian theatre practitioner and educator Augusto Boal in the 1960s, this set of practices explores relevant topics in an embodied way with “spect-actors” who participate in generating the performance, providing opportunities for individuals and groups to create, visualize, and live out scenarios for personal or social transformation. Using these methods, you will act out your understandings of traditional and critical pedagogies and explore what they might mean in engineering education. 1.2.1 EXPLORATION 1: PRINCIPLES OF CRITICAL PEDAGOGIES 1. Engage. Design a classroom experience in which learning is minimized. What does it look like? Act it out in a skit that illustrates your vision. 5 min. to brainstorm, 15 min. to plan, 10 min. for a couple of performances. 2. Analyze. Discuss the performances. What did you learn about effective pedagogies from viewing and/or acting out their opposite? 3. Reﬂect. What does it mean to learn? What is the goal of education? 4. Change. What would need to change about engineering education to fully apply the principles presented and that you’ve developed here? What are the primary obstacles to achieving these goals, and how might they be overcome? 1.2. MODULE 1.2. PEDAGOGY: HOW TO LEARN USING THIS BOOK 15 engage Design a classroom experience in which learning is minimized. What does it look like? Plan and perform a short skit illustrating your vision. change What would need to change about engineering education to fully apply the principles discussed? analyze Discuss the performances. What did you learn about effective pedagogy from viewing/acting out its opposite? reflect What does it mean to you to learn? What is the goal of education? Figure 1.3: Learning process. 1.2.2 EXPLORATION 2: MODELS OF LEARNING 1. Engage. Read the tableaus on the following pages. Assign one to each of three groups to act out for the others. engage Read the Tableaus that follow. Create a frieze illustrating each learning model. change What would you change about each scene to align it better with the principles you’ve developed so far? analyze Identify the similarities and differences among the three scenarios. reflect What questions does the comparison raise for you about learning? 16 1. WHAT AND WHY? Each group will create a frieze, or collection of actors “frozen” in the midst of a particular action or relationship, that illustrates each model of learning. Choose one person from each group who can narrate the scene and explain it to the others. 2. Analyze. What is similar about each of the three friezes? What are the differences among them? What does it mean to learn in each of these models? 3. Reﬂect. What questions arise for you in thinking about these different learning models? How does comparing the models change your own thinking about what learning means to you, or what learning might mean to society? 4. Change. What would you change about each scene to align it better with the principles of critical pedagogy as you understand them? What does this imply about what needs to change in engineering education? The modules in this book utilize the liberative learning processes explored here in order to help students explore some of the big questions about energy that have relevance to all of our lives. The rest of this chapter will explore world energy needs, uses, and policies, and then return to the question of what engineers need to know to work effectively in these contexts both now and in the future. 1.2. MODULE 1.2. PEDAGOGY: HOW TO LEARN USING THIS BOOK 17 i n t h e w o r l d d , w i t h t h e w o r l d d , a n d w i t h e a c c h o t h e r . t e a c h e r ’ s e e x i s t e n c e - - b u t u n l i k e t h e s l a v e e , t h e y n e v e r d i s c o v e r t h a t t h e e y e d u c a t e t h e e t e a c h e r . e x i s t e n c e . T T h e s t u d e n t s , a l l i e n a t e d l i k e t h e e s l a v e i n t h e H e g e l i i a n d a e c t t i c l , a c c e p t t h e i r i r g n o a n c e a s j i u s t i f y n g t h e l l k n o w e d g e e a b e u p o n t h o s s e w h o m t h e y c c o n s i d e r t o k n o o w n o t h n g i . j j P r o e c t i n g a n a b s o o u t e l i r g n o a n c e o n t o o t h e r s , a a r c h a a c t e r i s s t i c o f t h e i l d e o o g y o f r o p p e s s i o n , n e g a t e s e d d u c a l t i o n a n d k k n o w e d g e a s p p o c e s s e s o r f i n q u i r y . T h e t e a c h e r I i n t h e b a n k n g c o o n c e p t o f e d u c c a t i o n , l k n o w e d d g e i s a g i f t b e s s t o w e d b y t h o s s e w h o c o n s i d e r t h e m s e v e s l r p e s e n t s h m m s e i l f t o h i s s t u d d e n t s a s t h e i r n e e c e s s a r y o p p o s s i t e ; b y c o n s i d e r i n g t h e i r i r g n o a a n c e a b s o u t e l , h e j u s t i f i e s h i s o o w n o n y l r t h o u g g h i n v e n t i o n a n d d r e - i n v e n t i o n , r t h o u g h t h e r e s s t l e s s , i m p a t i e n t t c o n t i n u n g i , h o o p e f u l i n q u i r y h u u m a n b e n g s p u r s u e i m i i s g u d e d s y s t e m . F o r a p a a r t f r o m i n q u i r y , , a p a r t f r o m t h e e p a x i s , r i i i n d v d u u a l s c a n n o t l b e t r u y h u m a n . l K n o w e d g e e m e e g e s r l t h e p e o p e e t h e m s e v e s l w h h o a e r f i l e d a w a a y r t h o u g h t h e l a c k o f r c e a t i v i i t y , t r a n s f o m a r t i i o n , a n d k n o w e e d g e l i n t h i s ( a t b e s t ) i w h c h t h e s s c o p e o f a c t i o n n a l l o w e d t o t h e e s t u d e n t s e x t e n d s o n y a s l f a r a s r i e c e v n g i , f i l i n g , a n d s t o r i n g g t h e d e p o s i t s . T T h e y d o , i t i s t r u e e , h a v e t h e o p p p o r t u n i t y t o b e c c o m e c o l l e c t o r s s o r l t c a a o g u e r r s o f t h e t h n g s i t t h e y s t o e r . B u t i n t h e l a s t a n a y y s i s , l i t i s i w h c h t h e s t u d d e n t s p a t i e n t l y r e c e v e i , m e m o o r i z e , a n d r e p e a a t . T h i s i s t h e ` b a n k n g i ' c o n c e p p t o f e d u c a t i o n n , i n a n d r e p e a t s t h e s e p h a s e s r w w i t h o u t i r p e c e v n g w h a i t f o u r t i m m e s f o u r r e a l l y m e a n s , o r r e a l i i z z n g t h e t r u e t e a c h e r i s t h e d e p o s i t o r . I n s t e e a d o f c o m m u n c a i t i n g , t h e t e e a c h e r i i s s u e s c o o m m u n q u é s a n n d m a k e s d e p o o s i t s a n d w h a r r t P a a m e a n s f o r B r a a z i l … . E d u c c a t i o n t h u s b e c c o m e s a n a c t o o f d e p o s i t i n g , i i n w h c h t h e s t u d d e n t s a e t h e d e e p o s i t o r r i e s a n d t h e s i g n i f i c a n c e o o f " c a p i t a l " i n t h e a f f i r m a t i o n " t h h e c a p i t a l o f P a a a r i s B e e m l , " t h h a t i s , w h a l t B e e e m m e a n s f o r P P a a r t r i r a n s f o m n g p p o w e r . " F o u r t i m m e s f o u r i s s i x t e e e n ; t h e c a p i t a l o o f P a a r i s B e e m m l . " T h e s t u d e n t r r e c o d s , r m e m o o r i z e s , T h e o o u t s t a n d n g c h a a c t e r i r i s t i c o f t t h i s n a r r a t i v e e d d u c a t h e s o n o r i t y o o f w o d s , r n o t t h h e i r T h e t e a c h e e r t l a k s a b o u t r e e a l i t y a s i f i t r r w e e m o t i o n e s s , l s t t a t i c , c o m p a r t m m e n t a l i z e d r e l s e h e [ s i c ] r c o n c e t e n e s s a n d b e c o m e a a h o l l o w , a l i e n a a t e d , a n d a l i e n a t h e t o t a l i t y t h a a t e n g e n d e e d d r t h e m a n d c o u u d g v e t h e m i l s i g n i f i c a n c e . r W o o d s a e e m p r t i e e d o f t h e i r s t u d e n t s w i t h t h e c o n t e n t s o f f h i s n a r r a t i o n - - - c o n t e n t s i r w h c h a e d e t a c h e d f r o m r e a l i t y , e x p o u n d s o n a i t o p c c o m p e e t e y a l l l i e n t o t h e e x i s t e n t i a l e x x p e r i e n c e o f t h e e s t u d e n t s . H i s t i s t o a a s k d d i s c o n n e c t e t d h e er o m " f i l l " f r , t i o n t i n g v e b t o h e s i t n y , . i s r [ 4 ] h t t . p p : / / w w w w e b s t t e r . e d u / ~ c o r b e e t r e / p h i l o s o p h y y / e d u c a t i E x c e r p t t f r o m P a u o F r e e i r e l , P e d a g o g y o f t h e O p p r e s s e d T a b l e e a u 1 : E d d u c a t i o n a s U s u u a l , r a n d d p e d c t o n / f r e i r e / f r e i r e - 2 . h t m O lO a b e . i l 18 1. WHAT AND WHY? n o i t a c c u d E d e e r e t n e C - - r e n r a e e L : 2 u a e e l b a T y n a m w o o H “ . ] 7 6 1 : 8 [ n r a e e L e p o e P w o H l , l i c n u o C h c r a e e s e R l a n o i t a N m m o r f t p r e c x E 7 6 1 = e g g a p & 3 5 8 9 = d _ d o c e r i . r ? p h p k o o o b n e p o / u d e p a a n w w w / / : p . . t t h ” ? ? r e h t e g o t l a . n o i t a a t u p m o c c i s a b b a f l o e p m a x e n a r o f t s e u q e r a a h t i w i s n g e b r e e h c a e t e h T e h t , l a a u s u s a d n A . s s p u o g r n i s r a j e h t f o k n h t i e e w f i , r e h t e g o t t l a r e a r e e h t s s e i l f r e t t u b y n a m m w o h t n u o c o t s u r o f r e i s a e e b l l i w t i , w o N . s e i l f r e t t u b r o f d n a t s l l i w m e h t t n i s r a t s e h T . s r r a j e h t r e a e e h h r , y a k O : r e h c a e T . s e i l f r e t t u b e h t t g n i t n u o c r o f r e e u d e c o p r . r e e h t e g o t l a s e i l f r e e t t u b y n a m t a h t d a h u o y w o n k k d u o Y ' : a c i s s e J ? s e i l f r e t t u b d d n a s r a j a t c c u r t s n o c d n a y y r o t s s ’ a c i s s e J e e t a r t s u l l i t x e n s t t n e d u t s d n a r e e h c a e t e h T e s o o h t t u o b a w o n k k I l d u o w t a h w , r e w s n a e h t d n u u o f d n a n o i t a c i i l p i t l u m s i h t d d i I f i d n A . t i n i s e i l f r e t t u b b 4 d a h h c a e d d n a , s r a j r 2 1 e e w w e e h T r ? 4 x 2 1 . . . . n o i t a c i l p i t l u m s i h t h t i w o g d u u o c t l a h t i y r o t s a e m e v g e n o y n n a n a C : r e h c a e T : r e h c a e T : a c i s s e J ] . s r a j 0 1 d n u o a p o o r l a w a a D r [ ? s i r s p u o g t t u o b a g n k n h t i i r o f r e b m u n e t i r o v a f s ' n a c i t i a m m e h t a m . 0 1 : y l l a S r u o f f o o s t e s 0 1 i g n p u u o g r f o n o i t a t n n e s e p e r r l a i r o t c c p i a t c u r t s n o c c s t n e d u t s d n a a r e h c a e t e h t s a s e s s e g o p r r n o s s e l e h T t r e p m a a L . 4 x 2 s u p l 4 x x O l s a f o t h g u o o h t e b n a c 4 x 2 1 t a h t i e z n g o o c e r y e h t ; p u o g g r e h t n i t o n s r a a j 2 i g n v a h d n a a s e i l f r e t t u b . s r a j 6 f o s p u o g g o w r t o t n i , l e p m m a x e r o f , s r a j e h t g n p u o g r i f o s s y a w r l l r e h t o e o p x e n e d r l i h c e h h t s a h n e h t 1.2. MODULE 1.2. PEDAGOGY: HOW TO LEARN USING THIS BOOK 19 c o n s i d e a r t i o n o f r e a l p o l i t i c a l r e a s o n s t h a t p e o p e l , i i l n c u d n g c h i l r d e n , i m g h t s t r i k e . r g a d e r s m o v e d f r o m a p e r s p e c t i v e o r i e n t e d t o w a d r t h e i r o w n d e s i r e f o r l p a y a n d p e a s u e r l t o a i w o u n d n g m a n y c h i l r d e n . i D a v d y e l l e d , " W h a t d o y o u m e a n , s t o p t h e w a r ? " s t r i k e t o s t o p t h e w a r i n f A g h a n i s t a n . ” T h a t t o o k m y r b e a t h a w a y . I n t h i s b r i e f i d a o g l , t h e s e f i r s t S t i l l l o o k n g i i n t e n t l y a t h i s c a c k e r r , A l l i a n s a d s o f t l y b u t c e a l r l y , i “ M a y b e k d s c o u d g o o n l " M a y b e w e c o u d d o l i t t o s t o p t h e w a r . " r t h o u g h o u t t h i s i a n m a t e d e x c h a n g e . V e r y i q u e t l y , w i t h h i s r c a c k e r n e a r h i s m o u t h , h e s a d i , A s h y , t h o u g h t f u l b o y n a m e d A l l a n h a d b e e n s i t t i n g i q u e t l y a t t h e e n d o f t h e t a b e l l p a y t i m e w a s n ' t s u c h a g e a r t r e a s o n t o s t r i k e . a n d n o t o i l e t , a n d w e g e t t o g o t o s c h o o l f o r f r e e . I ' d b e e m b a r r a s s e d t o t e l l t h e m w e d d i i t . " h a v e a n y . " A n o t h e r s t u d e n t r a g e e d , a n d D a v d i r e c o n s i d e e d r , s a y n g i t h a t m a y b e g e t t i n g m o e r J o h n a d d e d , " I i t h n k i k d s i f n A g h a n i s t a n r e a l l y w a n t t o g o t o s c h o o l t o o , a n d t h e y d o n ' t w o u d l i t h n k w e w e e r r c a z y . T h e y h a v e t o p a y m o n e y t o g o t o a s c h o o l w i t h r h a d y l a n y b o o k s C u r t i s l o o k e d o v e r a t a p o s t e r o f o u r p e n p a l s a t a r r u a l s c h o o l i n S o u t h A f r i c a . H e s a d i , " I i t h n k o u r p e n p a l s t h e l a n g u a g e o f t h e W h i t e m n o i r i t y t h a t r a n t h e i r c o u n t r y . T h e S o u t h A f r i c a n p o l i c e f i r e d w i t h o u t r w a n n g i , k i l l i n g a n d w h o w e n t o n s t r i k e i n 1 9 7 6 , h o w t h e y r e f u s e d t o a t t e n d l c a s s e s a n d d e m o n s t r a t e d t o r p o t e s t h a v n g i t o l r e a n A f r i k a a n s , s t r i k e ? " I s a d i t h a t w a s a g o o d q u e s t i o n , a n d t h o u g h t a b o u t i t . I t o d l t h e m a b o u t 1 5 , 0 0 0 S o u t h A f r i c a n s t u d e n t s i n S o w e t o t h e y i d e c d e d t o a s k m y a d v c e i . D a v d i , a n o u t s p o k e n b o y , a s k e d m e l o u d y . l " W o u d l t h a t w o r k , M s . C o w h e y ? C a n i k d s a m o n g t h e m , a b o u t w h e t h e r t h e y l s h o u d k e e p t h i s p o t l s e c e t r f r o m m e . r P e h a p s f i g u r i n g t h e i r c o v e r w a s a l r e a d y b o w n l , t h e m s e v e s l a b o u t t h e i d e a o f g o n g i o n s t r i k e t o d e m a n d m o e r r e c e s s a t s c h o o l . I d e t e c t e d a n o t e o f n e r v o u s n e s s i l n c a s s . " A s I o f t e n d o , I s a t d o w n a t a t a b e l o f s t u d e n t s t o h a v e m y s n a c k . T h e y w e e r e x c i t e d y l t l a k n g i a m o n g m a d e t h e t r a n s i t i o n t o s n a c k t i m e , I l t o d m y n e w s t u d e n t t e a c h e r , " Y o u h a v e t o b e c a e f u r l w h e n y o u r e a d a b o o k l i k e t h i s M y r f i r s t g a d e r s h a d a l i l v e y d i s c u s s i o n a b o u t d e m a n d s , s t r i k e s , a l l i e s , n e g o t i a t i o n s , a n d s o l i d a r i t y . A s t h e c h i l r d e n t h e s t r i k e , r e f u s i n g t o l a y e g g s u n t i l t h e y a n d t h e c o w s g e t e e c t r i l l c b a n k e t s . n o t e t e l l i n g t h e f r a m e r t h e y a e o n r s t r i k e u n t i l t h e y g e t t h e i r l e e c t r i l c b a n k e t s . W h e n t h e f r a m e r r e f u s e s , t h e i c h c k e n s j o n i t y p e a l e t t e r t o t h e f r a m e r , a s k n g i f o r l e e c t r i l c b a n k e t s b e c a u s e t h e b a n r i s c o d l . T h e f r a m e r r e f u s e s , s o t h e y w r i t e a n o t h e r c o w h e y & s o u r c e = b & o t s = V 3 W Y l l f I Q P d & s i g = s 7 f T P f b m k V - w A g # v = o n e p a g e & q = % 2 2 c l i l c k % 2 0 c a c k % 2 0 m o o % 2 2 % 2 0 m a r y % 2 0 c o w h e y & = a l s e f f f i l l C V 0 u u g u y 2 I 3 1 3 A & h = e n & e = X 1 M S T O b M A s W B A e d g s n X B w & s a = X & o = b o o k _ r e s u l t l i & c t = r e s u l t & r e s n u m = 3 & v e d = 0 C C E Q 6 A E I n t h e s t o r y , s o m e c o w s f i n d a n l o d m a n u a l t y p e w r i t e r i n t h e i r b a n r a n d t e a c h t h e m s e v e s l h o w t o t y p e . T h e y 8 2 , 8 4 . ] h t t i i l . p : / / b o o k s . g o o g e c o m / b o o k s ? d = E j x M O Q D F 1 U C & p g = P A 2 4 3 & p g = P A 2 4 3 & d q = % 2 2 c l l i l c k + c a c k + m o o % 2 2 + m a r y + 8 2 , 8 4 ] i T h n k n g C i r i t i c a l l y a n d T e a c h n g D i i f f e r e n t l y i n t h e P r i m a r r y G a d e s . P o r t l a n d , M E : S t e n h o u s e P u b l i s h e r s , 2 0 0 6 . P p . d e s c r i b e s t h e r e s u l t s o f t e a c h n g w i i t h l i b e r a t i v e p e d a g o g e s i i n t h i s e x c e r p t f r o m h e r b o o k , l B a c k A n t s a n d B u d d h i s t s [ 9 : [ I n J a n u a r y 2 0 0 2 M a r y C o w h e y r e a d C l i c k , l C a c k , M o o : C o w s T h a t T y p e b y D e b a C r o n n t r i o h e r f i r s t r g a d e c a s s . l S h e T a b l e a u 3 : L i b e r a t i v e L e a r n n g i 20 1. WHAT AND WHY? 1.3 MODULE 1.3. US AND WORLD ENERGY NEEDS AND USES Most engineering thermodynamics books do not include much information about the overall US and World energy landscape. a SEM knowledge e problems g communi- cation h context j contemporary issues There are entire books and courses on this topic [10], but undergraduate engineers rarely encounter this material. Knowing that information changes rapidly, this module presents some basics about where things stand now and, most important, where you might go for updated information. We might begin by asking how much energy people need. Basic uses might include cooking, heating and space conditioning, lighting, and food storage. Providing clean water and sanitation systems consumes energy. Transportation of goods and people requires energy. Energy powers in- dustrial and agricultural processes, including the production of building materials for shelter. Energy is further required for communication and commerce. The energy used for these activities can come from a number of different sources, and the amount of energy consumed varies widely. Energy analyst Amulya Reddy argues that rather than focusing on the sources and quantifying energy supply, we should think in terms of characterizing the demand for particular services that energy provides [11], and on meeting consumer requirements that energy be accessible, affordable, reliable, safe, of high quality, and ecological. The three explorations that follow address the issue of energy needs from different angles. First, we consider current energy use in different nations around the world, and consider why the United States is a disproportionate consumer, even among highly industrialized nations. Next, we take up the relationships among energy, poverty and gender inequality, critically questioning the conventional wisdom about the role of energy in development. Finally, we turn to the question of how much energy people need with a personal challenge to students in industrialized nations to live on one kilowatt per capita. 1.3.1 EXPLORATION 1: ENERGY USE 1. Engage. Find reliable sources of information on energy use in the United States and Worldwide. Places to start include the International Energy Agency [12], (http:// www.iea.org/textbase/nppdf/free/2009/key_stats_2009.pdf), the World Re- sources Institute [13], (http://earthtrends.wri.org/searchable_db/index.php? theme=6), and the BP Statistical Review of World Energy [14] (http://www.bp.com/ statisticalreview). 1.3. MODULE 1.3. US AND WORLD ENERGY NEEDS AND USES 21 engage Find reliable sources of information on energy use in the US and worldwide. analyze Find or create useful representation of energy use. change What are three best ways for the US to reduce energy use? Quantify your recommendations. Try to reduce to levels in Europe or Japan. reflect What story do your data tell? Why is US energy use so much higher even than other industrialized nations? 2. Analyze. Find or create useful representations of energy use (for example, pie charts on uses in different countries; bar chart of energy use per capita in different countries). Think about the units presented in the reports and reconcile them for your best presentation; do different sources of data suggest very different usages? Think about why that might be, and dig for more information about their assumptions and exactly what they are measuring or estimating. 3. Reﬂect. What is the story that your data tell? Have you formatted your presentation to tell the story best? Compare US energy use to that of other nations, including industrialized and developing nations. Why is US energy use so much higher, even when compared with industrialized nations like Japan or Germany? Is this justifable? Why or why not? What responsibilities or duties fall to engineers to address this imbalance? 4. Change. What are the best opportunities the US has for reducing energy consumption? Find research that makes recommendations on this topic, and synthesize the ﬁndings of several authors to arrive at your own recommendations. To start you off, try Lester Lave’s article [15] here: http://www.nae.edu/File.aspx?id=14867. 1.3.2 EXPLORATION 2: WOMEN, POVERTY, AND ENERGY 1. Engage. Can we critically examine the connections between women, poverty, and energy? Read Reddy’s [11] chapter on women, poverty and energy: http://manowar.ma.ohost. de/UNWEa/chapter2.pdf. How does he connect poverty and energy in developing nations? How does gender play a role? How is the story the same or different in industrialized countries? Reddy argues that energy needs to be given serious consideration in development plans. What roles can energy play in development, according to Reddy? 22 1. WHAT AND WHY? engage change What relationship does Reddy lay out among gender, energy, and poverty in the developing world and in industrialized nations? How will you gain knowledge about poverty and incorporate it into your professional practice? analyze Critique the argument that energy development plays a critical role in both poverty eradication and achieving gender equality. reflect Consider the energy- poverty nexus in the Chicago Heat Wave of 1995. What do engineers need to know about poverty for ethical practice? Figure 1.4: Woman with improved cookstove. Accessed June 2 from http://commons. wikimedia.org/wiki/File:Cameroon_2005_-_cooking_woman.jpg. Creative commons license 2.0 TreesForTheFuture, originally posted to Flickr as Cameroon2005. 2. Analyze. Engineers may jump to the conclusion that energy development will end poverty and beneﬁt women – a win-win and a moral imperative that calls for immediate involvement. But the realities of the situation are far more complex. First, can energy development actually end poverty or improve the status of women, as Reddy argues? It may be helpful to com- pare Reddy’s argument with writing on gender and development such as NailaKabeer’s paper on gender and poverty eradication: http://www.unescap.org/esid/gad/Publication/ DiscussionPapers/13/Paper13.pdf. [16] What are the problems with reducing complex issues such as poverty or gender inequality to a single technical issue such as energy? What is the signiﬁcance of Reddy’s discussion of productivity and women’s involvement in producing energy, as compared with a more traditional development model in which energy is provided for consumption by a community from outside? What do you make of the image presented here of a woman with a cookstove, from this perspective? Is she/he/ze producing or consuming energy? What opportunities does this use present for development or for poverty eradication? 3. Reﬂect. Consider the energy-poverty nexus in the case study of the Chicago Heat Wave of 1995: http://www.slate.com/id/2125572/. [17] What is the role of engineers in preventing such disasters? The author makes a connection to Hurricane Katrina, in which engineers also played a signiﬁcant role. What do engineers need to know about poverty? How should they consider poverty in responsible professional practice? 1.3. MODULE 1.3. US AND WORLD ENERGY NEEDS AND USES 23 4. Change. What will you do to acquire knowledge about poverty and other critical social is- sues that surround your areas of expertise as an engineer? How will you incorporate these considerations in your professional practice? 1.3.3 EXPLORATION 3: 1 KW PER CAPITA? In the 1980s, a group of development energy experts proposed that the world could meet basic needs and in fact reach the standard of living of 1970s Europe on 1 kW per capita – provided optimal use of available efﬁcient technologies [18] (http://www.jstor.org/pss/4313148). Rather than focusing on developing nations’ energy development goals, these experts present a daunting challenge to residents of developed countries and particularly energy-intensive nations like the United States, which uses on the order of 10 kW per capita [12, 13]. The thought experiment that follows is aspirational and hopefully will also prove inspirational. What would it take for you to live on 1 kW? engage Track your energy consumption for a week and try to live on 1kW. change How can you reduce your energy use to come closer to 1kW? How does this relate to your goals as an engineer? analyze Tracking your energy requires understanding where your energy comes from and efficiencies in its production. reflect What would you have to change about your lifestyle to live on 1kW? What things do you consider basic needs? Figure 1.5: José Goldemberg, Brazilian physicist and educator, put forward the 1 kW per capita con- cept in 1985. Accessed June 2 from http://www.sect.am.gov.br/arquivos/imagens/noticias/ 20110117150231josegoldemberg.jpg. 1. Engage. Keep a journal or blog for a week or more. Can you live on 1 kW? (Hint: begin by thinking through the units here and be sure you understand where time comes into this picture.) 2. Analyze. Structure your analysis – think about energy services including transportation, light- ing, refrigeration, computing, cooking, heating, and food manufacturing, preparation and con- sumption. How do one-time large energy expenditures, such as jet travel, impact your analysis? 24 1. WHAT AND WHY? How do you estimate energy inputs for items you consume such as books, food packaging, clothing, etc.? 3. Reﬂect. What would you have to change about your lifestyle or about the infrastructure of society to live on 1 kW? What things do you consider basic needs? How would you evaluate the 1 kW proposal in terms of ethics or justice? 4. Change. Develop a plan to reduce your energy use. How close can you realistically come to 1 kW now? What structural changes can you work for in the future to help you get even closer? How does this relate to your goals as an engineer? Having explored energy needs and uses and their relationship to development, we next take up questions of national and international policy. Given these contexts of energy needs, and energy use and over-use, how do governments and multilateral institutions make decisions about energy? 1.4 MODULE 1.4. US AND WORLD ENERGY POLICIES: WHAT ARE THE ISSUES? To comprehensively study a nation’s energy policy, or international energy policies, would require another volume, and another course. f h ethics context j contemporary issues But engineers need to understand the national and global contexts in which we work in order to design technology in an informed way. Speciﬁc global and US energy policy questions are visited throughout this book in an attempt to connect critical policy issues with the existing curriculum in engineering thermodynamics. Here we explore the big picture brieﬂy to motivate continued discussion of energy policy issues in a thermodynamics course. Governments must decide how best to build, maintain, and retool energy infrastructures for economic development (in both developing and developed nations). Energy cannot be considered in isolation because of its relationship to basic human needs, the economy, as well as to peace and security, generation of pollution, and global climate change. Traditionally, engineers respond to national priorities set by others. What role could engineers play nationally and internationally to inform the setting of these priorities? Is this desirable? Would engineers’ involvement in such questions represent a conﬂict of interest? Would engineers tend to support the status quo in order to maintain job security? As industrially developing nations are currently planning to meet energy needs for economic growth, they are poised to make critical and far-reaching decisions for developing new energy infrastructures. This is an exciting time for engineers, offering a teaching moment for students to consider the impacts of technology, global economic inequality, and the importance of forward- thinking design. 1.4. MODULE 1.4. US AND WORLD ENERGY POLICIES: WHAT ARE THE ISSUES? 25 While some of the modules found later in this book tackle questions of energy technology selection and development of renewable energy sources, government decision making is often not as straightforward as choosing and pursuing particular technologies. The two case studies that follow illustrate the complex contexts in which governments approach energy issues. In the ﬁrst case, countries in the global South look to wealthier nations for commitments on carbon reduction and renewable energy development, which are largely resisted in the North. In the second case, the United States secures energy resources through costly military conﬂict. 1.4.1 EXPLORATION 1: COPENHAGEN engage Read about the 2009 Copenhagen summit here and in other sources you can find. analyze Were the actions taken by the nations at the Copenhagen summit ethical? Examine this from a number of ethical and stakeholder perspectives. change What can you do to achieve greenhouse gas emission reductions on your campus, in your community, and at the state and federal levels? reflect Why was the United States particularly reluctant to agree to greenhouse gas emission reductions? Figure 1.6: Global Day of Action for Climate, mass demonstration and march at the Copenhagen COP15 Climate Summit, December 12, 2009. Photo from Greenpeace Finland/Lauri Myllyvirta. Used under Creative Commons 2.0 license. Accessed June 2, 2011 from http://commons.wikimedia.org/ wiki/File:Global_day_of_action.jpg. 1. Engage. Read the following information about the Copenhagen Climate Summit [19], and seek out other sources on this meeting and subsequent and prior international climate meetings. Climate scientists have created models that predict numerous changes in climate caused by increased atmospheric concentrations of greenhouse gases, including carbon dioxide. While these changes are expected to be widespread across the planet, some changes will be more damaging than others, and some places will be hit harder than others. Many scenarios predict signiﬁcant damage in the global South, where many people and their governments lack the resources needed to adapt to climate change. In 2009, at the Copenhagen climate summit, 26 1. WHAT AND WHY? Lumumba Di-Apping, chair of the G77 group of developing nations, declared a 2 degree rise in global temperature a “suicide pact” for Africa. At Copenhagen as at both previous and subsequent international meetings on climate change, the South sought leadership from the global North in curbing emissions and in offering economic development funds for building renewable energy infrastructure. Wealthy nations committed to less than half the emissions cuts needed, and declined to offer development funds for renewable energy infrastructure. Europe offered to cut 20% by 2020, and the US 4% by 2020. 60% reductions are required in order to avoid a 2 degree temperature rise. Economics is a primary rationale for lack of action on climate change. The conventional perspective in the US and global North is that cheap energy derived from fossil fuels forms the basis for economic activity worldwide and must be maintained in order to compete with emerging economies such as China and India. Many governments in the global South view energy as essential to development, and want to have the chance northern countries did to use cheap energy to develop their economies. They argue this is necessary to lift people out of poverty, meet basic human needs, and to overcome the long history of colonialism that led to today’s global economic inequalities. 2. Analyze the ethics of the Copenhagen agreement (or lack thereof ) from a variety of philo- sophical standpoints and stakeholder perspectives. What duties or responsibilities do nations have to one another and to the planet, or the global North to the global South and vice versa? What would the principle of justice require of nations at this summit? What rights apply to nations in this context, and how are these balanced against responsibilities to the international community? As India, China and other nations develop energy infrastructure, they are draw- ing on their strengths, using resources available in country where possible – ought they do otherwise? Who should decide? 3. Reﬂect. Why is the United States particularly reluctant to cooperate with climate agreements, more so than other wealthy nations? Why are the US reductions so small compared to Europe, especially when Europe’s energy consumption and climate emissions are already so much lower on a per capita basis? 4. Change. What level of greenhouse gas reductions would you like to see your country achieve? Has your campus complied with this level of reduction? Has your local community? Where might a city begin to take action that would lead a signiﬁcant reduction in greenhouse gas emissions? How does this scale up to larger groups of people? Take some action to expand the scope of reductions on a state, national, or international level. 1.4.2 EXPLORATION 2: THE COST OF ENERGY [20] 1. Engage. At the time of writing, the National Priorities Projectestimates the cost of in Iraq and Afghanistan since 2001 at $1.26 trillion and total Defense and war 1.4. MODULE 1.4. US AND WORLD ENERGY POLICIES: WHAT ARE THE ISSUES? 27 engage Gather data on the cost of war to secure oil resources, the volume and cost of oil imports, and gasoline use in the United States. change Propose some ways to reduce the price we pay for energy. Estimate their impact. analyze If monetary costs of war were paid for through a gas tax at the pump, how much more would we pay per gallon? reflect What about the non- monetary costs of war? How else have we paid for oil that isn’t reflected in dollars per gallon? Figure 1.7: Rumaylah Oil Fields, Iraq (April 2, 2003) – A US Army soldier stands guard duty near a burning oil well in the Rumaylah Oil Fields. US Navy photo by Photographer’s Mate 1st Class Arlo K. Abrahamson. Public Domain. http://upload.wikimedia.org/wikipedia/commons/9/99/ US_Navy_030402-N-5362A-010_A_US_Army_soldier_stands_guard_duty_near_a_burning_ oil_well_in_the_Rumaylah_Oil_Fields.jpg. Homeland Security spending at $7.6 trillion [21]. According to the US Energy In- formation Agency, the US imported about 9 million barrels of crude oil per day in 2010 [22]. (http://www.eia.gov/pub/oil_gas/petroleum/data_publications/ company_level_imports/current/import.html) about $78/barrel [23]. (http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET& s=WTOTWORLD&f=W). The trade group NACS estimates that the US consumes about 9 million barrels/day of gasoline and diesel fuel for highway use [24]. (A little more than half of a barrel of crude oil is processed into gasoline.) (http://www.nacsonline.com/NACS/Resources/ campaigns/GasPrices_2011/Documents/GasPriceKit2011.pdf) Can you conﬁrm and/or update this information? an average price of at 2. Analyze. If the war costs were paid for by a gasoline tax instead of income tax, how much more would we pay per gallon of gas for “securing” oil in the Middle East? If our total Defense and Homeland Security budget were paid for with a gasoline tax, how much more would be pay per gallon? One might rightly observe that not all of the Homeland Security and Defense 28 1. WHAT AND WHY? budget is related to middle east conﬂict. Using resource [21] and other sources, estimate what percentage is related, and calculate the cost per gallon of gas. 3. Reﬂect. The monetary costs of war do not begin to account for the total costs. What are the costs of war beyond dollars and cents? How else have American taxpayers paid for this access to oil in the region? What have been the non-monetary costs of US Homeland Security efforts? 4. Change. If each of the 200 million cars and light trucks in the US were traded in for replacement vehicles that saved 10 mpg, by what fraction would this reduce US oil imports? Each vehicle drives 12000 miles per year, on average. What other proposals can you make that would reduce US dependence on oil and military involvement to secure these resources in other parts of the world? The brief exploration of energy needs and energy policy in this chapter may feel unsettled or unsettling. How do we decide what we believe the relationships are between national security and energy? How do we know how much energy would meet basic human needs, or how best to achieve that? Many engineers retreat from these kinds of uncertainties into seemingly politically neutral equations and facts. Some feel that technology is a refuge where at least you can calculate things and know them for certain. Some even think that once you understand the technology, it will point you toward a correct policy solution. However, these approaches leave out – or worse, dismiss as unimportant – political and social realities that inﬂuence and are inﬂuenced by technology in countless ways. We will see throughout this book as we explore the history of thermodynamics and its contemporary applications that what we believe about energy, and what we believe is important to know or ask about energy, is inﬂuenced by social factors in much the same way as larger global questions about energy. The following module explores the question of what is important for engineers to know about energy and how answers to this question are themselves shaped by forces of power in the profession and in society. 1.5 MODULE 1.5. GETTING EDUCATION RIGHT FOR A SUSTAINABLE ENERGY FUTURE Twentieth century social theorist Michel Foucault wrote about how, even in science, there is a dual relationship between power and knowledge. h context i lifelong learning What becomes considered to be valid knowledge is laden with the decidedly political process of who gets to decide what is true or untrue. In turn, knowledge is used in the interest of power and powerful institutions. This is to be distinguished from the conventional Baconian belief that “knowledge is 1.5. MODULE 1.5. GETTING EDUCATION RIGHT FOR A SUSTAINABLE ENERGY FUTURE 29 power,” i.e., that coming into knowledge makes one powerful. Instead, Foucault posits that yes, knowledge is power, but power is also knowledge. He explains the ways in which institutions – Figure 1.8: Michel Foucault. http://www.msa.ac.uk/mac/Assets/Embedded%20Websites/ Panopticon/Images/Michel_Foucault_Par23100007_130145833_std.jpg. science, universities, government – play a role in validating knowledge. The following exploration is intended to stimulate your critical thinking about your own learning, course and curriculum content, and engineering in society. It lays the groundwork for connections made later to thermodynamic theory, especially the Second Law. 1.5.1 EXPLORATION 1: POWER/KNOWLEDGE 1. Engage. First, excerpt read this from Foucault on Truth and Power in sci- ence [25]: http://www.scribd.com/doc/10262971/Foucault-Truth-and-Power- in-Power-Knowledge (pp. 131–133). It’s important to acknowledge for those of you who have not encountered Foucault before that his work may seem abstract at ﬁrst, but is in fact highly relevant when grounded in context. His writing is not linear or direct, and this is some- what intentional. Derrida, Foucault’s contemporary, wrote about how language can impose constraints upon what we are able to say, reﬂecting and perpetuating a certain kind of power relations. Foucault consciously sought to challenge the power embedded in language. A wise colleague in ﬁlm studies once told me that reading Foucault is a bit like surﬁng – you ride the wave for a while when you are in tune with his thoughts, but you do not have the same mind, so you necessarily slip off the board – and that is the point. But it was a great ride, and you can always get back on the board and go again [26]. 30 1. WHAT AND WHY? engage Read Foucault’s excerpt from “Truth and Power” analyze What is Foucault’s regime of truth? How does science wield power in the construction of knowledge? change How can you determine what you believe, given the institutional power structures that influence what is presented as truth? reflect How have you seen power/knowledge dynamics operating in the world? 2. Analyze. Answer the following four questions: a. What does Foucault mean by “a regime of truth” and how does this ﬁt with his deﬁnition of truth on p. 133? b. Foucault is often characterized assaying that truth is relative, but he is saying rather that truth is political. How are these two concepts different? c. Foucault focuses on science as an important institution appointed as the arbiter of truth in present day society. How does the institution of science wield power in the construction of truth? d. Foucault’s conception of power, which he writes on extensively elsewhere, is that power is NOT one-way or top-down, but rather one of power relations in which power neces- sarily produces resistance. How does this conception of power play out in the notion of power/knowledge? 3. Reﬂect.Think of a concrete example from your experience that illustrates the dual relationship between power and knowledge that Foucault discusses. Make sure the example shows not just knowledge supporting power, but also ways in which power constructs knowledge. How might power/knowledge manifest itself in a thermodynamics course, or in the engineering curriculum? For example, who controls what you learn in thermodynamics, or what courses you take in order to receive an engineering degree? 4. Change. How can you determine what you believe, given the institutional power structures that inﬂuence what is presented as truth? 1.5. MODULE 1.5. GETTING EDUCATION RIGHT FOR A SUSTAINABLE ENERGY FUTURE 31 Given these power relations in engineering where accreditation and academic processes resist changes to the accepted body of knowledge in the ﬁeld, this book explicitly seeks to challenge the engineering canon as it relates to thermodynamics and energy. It also seeks to encourage students to engage your power of resistance by taking responsibility for your own learning in a system that usually seems to remove a lot of student choice in order to adhere to a standard set knowledge. In the next exploration, you will identify what you think engineering students need to learn to be able to work on energy issues, and compare that curriculum to your current education. It may be tempting to resist the new ideas here and reinscribe traditional ideas about what belongs in a thermodynamics class; try to keep an open mind as you deliberate on these questions. 1.5.2 EXPLORATION 2: WHAT DO CURRENT ENGINEERING STUDENTS NEED TO LEARN TO BE ABLE TO WORK ON ENERGY ISSUES? 1. Engage. Make a list of what you think engineering students need to learn as undergraduates in order to prepare to work on energy problems. Think about what kinds of technical skills, professional skills, values or ethics, and ways of thinking will be essential in this work. 2. Analyze. Compare your list with what’s emphasized in your textbook, your course syllabus, your engineering curriculum overall, and ABET’s accreditation criteria (see Introduction, Figure 1). Reﬁne your list if you come across items you’d like to add or take away. engage Make a list of what you think engineering students need to learn today to work on tomorrow’s energy issues. change What else do you need to learn, and where will you find it? Develop a strategy to learn what you need to work on today’s energy problems. analyze How does this list match or not match with ABET criteria, your textbook’s contents, and your engineering curriculum? reflect How does the content of your thermo text (curriculum, ABET criteria) reinforce certain energy choices? 3. Reﬂect. How does the content of your thermodynamics textbook (or course syllabus, or ac- creditation criteria, etc.) reinforce certain energy choices? What material is not found in thermodynamics? Is it found in other engineering courses, or courses outside of engineering but required for the major, or is it not part of your curriculum at all? 32 REFERENCES 4. Change. What else do you need to learn, and where will you ﬁnd it? Develop a strategy to learn what you need to know to work effectively on energy problems today and in the future. What can you learn on your own, and where do you need to seek assistance and guidance from a mentor? REFERENCES [1] Darder, A., Maltodano, M. P., and Torres, R.D. (2008). Critical Pedagogy Reader, 3rd ed. New York: Routledge. Cited on page(s) 13 [2] Marx, K. [1845] (1976) Theses on Feuerbach. In K. Marx and F. Engels (Eds.), Collected Works of Karl Marx and Friedrich Engels, 1845–47, Vol. 5: Theses on Feuerbach, The German Ideology and Related Manuscripts. New York: International Publishers, p. 8. Cited on page(s) 13 [3] Hooks, B. (1994) Teaching to Transgress. New York: Routledge, p. 37. Cited on page(s) 13, 14 [4] Freire, P. (1970) Pedagogy of the Oppressed. Translated by Myra Bergman Ramos. New York: Seabury Press. Cited on page(s) 13 [5] Luke, C. and Gore, J. (1992). Feminisms and Critical Pedagogy. New York: Routledge. Cited on page(s) 14 [6] Boal, A. (1985). Theatre of the Oppressed. Translated by Charles A. and Maria-Odilia Leal McBride. New York: Theatre Communications Group. Cited on page(s) 14 [7] Boal, A. (1992). Games for Actors and Non-Actors. Translated by Adrian Jackson. New York: Routledge. Cited on page(s) 14 [8] National Research Council (2000). How People Learn: Brain, Mind, Experience and School. Washington, DC: National Academy Press. Accessed June 10, 2011 from http://www.nap. edu/openbook.php?record_id=9853. Cited on page(s) [9] Cowhey, M. (2006). Black Ants and Buddhists: Thinking Critically and Teaching Differently in the Primary Grades. Portland, ME: Stenhouse Publishers. Cited on page(s) [10] See, e.g., Shepherd, W. and Shepherd, D.W. (2003). Energy Studies, 2nd ed. London: Imperial College Press. Cited on page(s) 20 [11] Reddy, A.K.N. (2000).Energy and Social Issues. In World Energy Assessment: Energy and the Challenge of Sustainability. New York: United Nations Development Program. Accessed June 10, 2011 from http://manowar.ma.ohost.de/UNWEa/chapter2.pdf. Cited on page(s) 20, 21 REFERENCES 33 [12] International Energy Agency (2009). Key World Energy Statistics. Paris: IEA. Accessed June 10, 2011 from http://www.iea.org/textbase/nppdf/free/2009/key_stats_2009. pdf. Cited on page(s) 20, 23 [13] World Resources Institute (2011). EarthTrends Energy and Resources Database. Washington, DC: WRI. Accessed June 10, 2011 from http://earthtrends.wri.org/searchable_ db/index.php?theme=6. Cited on page(s) 20, 23 [14] British Petroleum (2011).Statistical Review of World Energy. London: British Petroleum. Accessed June 10, 2011 from http://www.bp.com/statisticalreview. Cited on page(s) 20 [15] Lave, L. (2009). The Potential of Energy Efﬁciency: An Overview. The Bridge, 39(2): 5– 14. Accessed June 10, 2011 from http://www.nae.edu/File.aspx?id=14867. Cited on page(s) 21 [16] Kabeer, N. (2003).Gender Equality, Poverty Eradication and the Millennium Development Goals: Promoting Women’s Capabilities and Participation. Gender & Development Discussion Paper Series No. 13, United Nations Economic and Social Commission for Asia and the Paciﬁc. Accessed September 17, 2011 from http://www.unescap.org/esid/gad/Publication/ DiscussionPapers/13/Paper13.pdf. Cited on page(s) 22 [17] Klinenberg, E. (2005). When Chicago Baked: Unheeded lessons from another great urban catastrophe. Slate, September 2, 2005. Accessed September 17, 2011 from http://www. slate.com/id/2125572/. Cited on page(s) 22 [18] Goldemberg, J., Johansson, T.B., Reddy, A.K.N., and Williams, R.H. (1985). Basic Needs and Much More with One Kilowatt per Capita. Ambio, 14(4/5): 190–200. Accessed June 10, 2011 from http://www.jstor.org/pss/4313148. Cited on page(s) 23 [19] Livingstone, K. Copenhagen talks show south-north divide is alive, well, and ever-more polluting. Progressive London, Dec. 16, 2009. Accessed June 6, 2011 from http:// www.progressivelondon.org.uk/blog/copenhagen-talks-show-north-south- divide-is-alive-well-and-ever-more-polluting.html. Cited on page(s) 25 [20] Adapted from an assignment Frank von Hippel gave to Princeton University students in his course on Science, Technology, and Policy in the 1990s. DOI: 10.1038/sj.ijo.0801938 Cited on page(s) vii, 26 [21] National Priorities Project. (2011). US Security Spending since 9/11. May 26, 2011. Ac- cessed June 7, 2011 from http://nationalpriorities.org/en/publications/2011/ us-security-spending-since-911/. Cited on page(s) 27, 28 34 REFERENCES [22] US Energy Information Administration (2011). Crude Oil and Total Petroleum Imports. March 2011 Import Highlights. Accessed June 10, 2011 from http://www.eia.gov/ pub/oil_gas/petroleum/data_publications/company_level_imports/current/ import.html. DOI: 10.1001/jama.292.10.1232 Cited on page(s) 27 [23] US Energy Information Administration (2011). Petroleum and Other Liquids. Accessed June 10, 2011 from http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s= WTOTWORLD&f=W. Cited on page(s) 27 [24] NACS (2011). Fueling America: Key Facts and Figures. Accessed June 10, 2011 from http://www.nacsonline.com/NACS/Resources/campaigns/GasPrices_2011/ Documents/GasPriceKit2011.pdf Cited on page(s) 27 [25] Foucault, M. (1980) Truth and Power. In: C. Gordon (Ed.) Power/Knowledge: Selected Inter- viewsand Other Writings 1972–1977. New York: Pantheon, 131–133. Cited on page(s) 29 [26] Keller, A. (2005) Comments at Liberative Pedagogies workshop, used with permission. Cited on page(s) 29 C H A P T E R 2 35 The First Law: Making Theory Relevant The First Law of Thermodynamics, the idea that energy cannot be created nor destroyed, but is converted from one form to another, is familiar to many of us from our experience of the world. While the formal study of energy can quickly become abstract, the modules in this chapter are designed to keep our explorations rooted in topics that resonate with our lives. The ﬁrst module explores the First Law in its historical context. This can make the material more accessible because its presentation follows the arc of scientiﬁc discovery. The histories raise many questions about the practice of science: Who gets to do science? Why are the Western European discoveries the ones that became enshrined in our textbooks? What are some alternatives? What does it mean for us doing science today that individuals who “had the science wrong” in that they subscribed to now-debunked ideas like the caloric theory or the animal theory of heat nevertheless made bold contributions to science? In the following three modules we consider applications driven by particular needs to provide real-world context for exploring the First Law in an open-ended way. Notably, each of these questions or needs is occurring (more or less) outside of a for-proﬁt context and outside of military applications, which are the more common focuses in engineering. These modules raise the question of what is considered to be within our outside the bounds of the engineering discipline, and why. A ﬁfth and ﬁnal application allows you to choose your own setting for application of the First Law, perhaps something that is interesting and relevant to your life, or something you are curious about. Module 2.1: The First Law in Historical Context. Module 2.2.: Technology Selection for Energy Independence. Module 2.3: Evaporative Cooling. Module 2.4: Hunger, Poverty, and Obesity. Module 2.5: Thermo to Life. 2.1 MODULE 2.1. LEARNING FROM HISTORY g communi- cation h context i lifelong learning 36 2. THE FIRST LAW: MAKING THEORY RELEVANT While your engineering thermodynamics textbook may present thermodynamic theories as abstract principles and laws of nature, the particular ways in which these laws were discovered and articulated in history are rich and fascinating stories that can deepen our understanding and appreciation for thermodynamics. Different expressions of the laws of thermodynamics are grounded in particular historical times and places. Speciﬁcally, thermodynamics texts tend to rely on discoveries in Germany, England, and France in the 18th and 19th centuries. These stories (and the fact that these are the stories) tell us much about the process of science and the development of scientiﬁc knowledge, but the histories of thermodynamics from other times and places also deserve our attention. Therefore, the ﬁrst exploration below considers the development of the First Law in Europe, while the second poses an opportunity to uncover other histories of thermodynamic discovery in other times and places. 2.1.1 EXPLORATION 1: FIRST LAW IN WESTERN EUROPE engage Uncover histories of the development of the First Law in Western Europe. change Where do we identify social privilege in the practice of science today, and how can we work for change? analyze Write a biography that places the contributions of those who developed the First and Second Laws in the context of their lives and times. reflect What does this analysis tell us about the political process of the production of scientific knowledge? Figure 2.1: Sadi Carnot. Retrieved June 3, 2011 from http://upload.wikimedia.org/wikipedia/ commons/8/80/Sadi_Carnot.jpeg, Public domain. 1. Engage. Locate histories of the development of the First Law of thermodynamics in Western Europe. A good source is Hans Christian Von Baeyer’s book, Warmth Disperses and Time Passes: A history of heat. [1] He states that there were 12 different individuals who contributed to the discovery of the First Law, and discusses in detail the lives and work of Julius Mayer, Count Rumford, and James Joule, among others. 2.1. MODULE 2.1. LEARNING FROM HISTORY 37 2. Analyze. Choose one or more individuals to proﬁle. Read their publications if available. For example, you can ﬁnd Joule’s “On the Mechanical Equivalent of Heat”[2] at http:// www.chemteam.info/Chem-History/Joule-Heat-1845.html and Rumford’s “Heat is a Form of Motion”[3] at http://www.chemteam.info/Chem-History/Rumford-1798. html. Learn what you can about their lives. Write a short biography that provides context for their discoveries and explains their contributions. What enabled them to do the work they did? What did they know? What gaps in knowledge were they able to close, and what gaps remained? 3. Reﬂect. What does it mean that the laws of thermodynamics are not attributable to a single person, as Newton’s or Maxwell’s laws are? What was accepted as “truth” by the scientiﬁc establishment, and why were so many of the ideas surrounding the First and Second Laws initially rejected? What does it mean to be able to hold some ideas that have since been proven wrong, but still make a valid contribution to science? How did social privilege (gender, class, race) inﬂuence who was able to do science, and/or whose contributions are recognized today? What did people need to do science then? What is needed now? 4. Change. What do you take away from this for your own life doing science? How does social privilege persist in what you need today to engage in science? What can you do to address this problem? 2.1.2 EXPLORATION 2: DE-CENTERING WESTERN THERMO 1. Engage. Locate histories of the First Law (or thermodynamics more generally) outside of Western Europe. Think broadly as you select keywords for your search; histories of technology may be especially fruitful [4]–[8]. How did technologies make use of energy conservation and conversion, and how were these principles understood and discussed? 2. Analyze. Write a narrative about one or more contributions and explain the context of its development. Who are the main actors? What enabled them to do the work they did? What did they know? What gaps in knowledge were they able to close, and what gaps remained? 3. Reﬂect. How did you identify non-Western contributions to thermo? What does this tell us about what counts (and what ought to count) as science, or as scientiﬁc theory? 4. Change. How can non-Western contributions be made more visible in thermodynamics? Where else can you identify similar biases in your education, or your life? What can you do about them? While the histories of thermodynamic discovery are indeed dynamic and revealing, contem- porary conversations may also capture readers’ imaginations. The next module therefore takes up contemporary conversations around energy independence in order to explore further the usefulness and relevance of the First Law. 38 2. THE FIRST LAW: MAKING THEORY RELEVANT engage Uncover non-Western conceptions of/contributions to thermodynamics. analyze Write a narrative about one contribution that explains its context and development. change How can non- Western contributions be made more visible in thermo? In other areas of your education or your life? reflect How did you identify non-Western thermo? What does this tell us about what counts (and what should count) as science or scientific theory? Figure 2.2: Maria the Jewess, considered to be the ﬁrst alchemist and inventor of the still, lived in Alexandria in the ﬁrst or second century CE. From Michael Maier, Symbola aurea mensae duodecim nationum, 1617. Accessed June 3, 2011 from http://www.alchemywebsite.com/images/amcl111. jpg. 2.2 MODULE 2.2. ENERGY INDEPENDENCE Contemporary conversations in the United States around energy independence have strong political resonance. h context j contemporary issues This module critically examines claims made in the public arena about the goal of energy inde- pendence, and then entertains a reinterpretation of the concept of energy independence in local communities. 2.2.1 EXPLORATION 1: “FOREIGN” OIL INDEPENDENCE 1. Engage. US leaders have made much of the concept of energy independence on a national level. This phrase typically is used to mean independence from foreign oil sources. Watch a segment of the Rachel Maddow Show [9] (http://www.msnbc.msn.com/id/26315908/# 37769319) that argues that “energy independence” as conventionally conceived in US politics is a myth. 2. Analyze. Why does Maddow argue that energy independence is a myth? Would it be possible to achieve independence from foreign oil? If so, how? Try to think of multiple ways to achieve this goal. 2.2. MODULE 2.2. ENERGY INDEPENDENCE 39 3. Reﬂect. How dependent are you on oil? How would your life change if that oil were entirely produced in your country? Think both in terms of the practical aspects of your life and your experience of national or international politics. 4. Change. Maddow’s vision is for the US to become oil independent altogether. How can engineers help make this happen? What would need to change structurally to make this a possibility? engage Watch Rachel Maddow’s analysis of Energy Independence in US politics. change Maddow’s vision is for the US to become oil independent altogether. How can engineers help make this happen? analyze Would it be possible to achieve independence from foreign oil? If so, how? Try to think of multiple ways to achieve this goal. reflect How dependent are you on oil? How would your life change if that oil were entirely domestically produced? 2.2.2 EXPLORATION 2: ENERGY INDEPENDENCE RECONCEIVED A different kind of energy independence is occurring in local cities in the US and elsewhere: in- dependent, public ownership of utilities. With this model, local communities can create low-cost, sustainable energy alternatives. For example, in the state of Massachusetts, there are 41 cities that own their own municipal utilities (these mostly date back to the early 20th century). A recent state report found that these utilities offered signiﬁcantly cheaper rates than industrially owned facilities, from 14% cheaper in 2004 to 30% cheaper in 2006. At the same time, municipal utilities were as reliable or more reliable than their industrial counterparts, with more local control to respond rapidly to outages [10]. Many towns support changes in state law that would lift barriers to municipalization, so that new municipally owned facilities can be added [11]. 1. Engage. Select a site near you that could be electriﬁed using a new local energy resource. 40 2. THE FIRST LAW: MAKING THEORY RELEVANT engage Pick a site near you that could be sourced by a new local energy resource. change What is needed beyond these constructs of “first law” and “efficiency” to help us select an appropriate energy technology? analyze Use first law analysis to compare solar, geothermal, wind, hydro, and local biomass as potential sources. Calculate efficiencies for each. reflect How do the forms of the energy equation change, and what does efficiency mean for each? Can you use this analysis to select one best? Figure 2.3: Holyoke Dam, a municipally owned power generation facility in Holyoke, MA. Photo from US Fish and Wildlife Service, Public domain. Accessed June 3, 2011 from http://www.fws.gov/ r5crc/images/Fish/holyokedam.jpg. 2. Analyze. Use a First Law analysis (energy balance) to compare solar, geothermal, wind, hydro, and local biomass options for your plant. Calculate efﬁciencies for each. 3. Reﬂect. How do the forms of the energy equation change for each technology, and what does efﬁciency mean in each case? Can you use this analysis to select a single best technology? 4. Change. What is needed beyond the constructs of efﬁciency and energy balances to determine the best energy technology for municipal application? Where in your education can you learn these other pieces? What will you do to learn them? If municipalization represents a form of energy independence in the United States, what might energy independence look like in the global South? To explore one angle of this, consider that in development contexts, the notion of technology transfer can be controversial when wealthy nations in the North simply export their technologies to settings in the South without consideration for geographic or cultural differences, and often with economic strings attached. This traditional model of technology transfer can create dependence in a variety of forms, from reliance on imported parts and materials to foreign technical knowledge required to maintain continued operation. In the next module we consider examples of technologies emerging from the global South, utilizing the principle of evaporative cooling for refrigeration and space conditioning. 2.3 MODULE 2.3. EVAPORATIVE COOLERS Evaporative cooling makes use of the First Law of thermodynamics.The process of water evaporation requires heat as water changes phase from liquid to gas. 2.3. MODULE 2.3. EVAPORATIVE COOLERS 41 c e h design problems context i lifelong learning Several technologies make use of this principle by drawing heat from an area one is trying to cool – a warm room, for example, or vegetables one is trying to preserve – cooling the area of interest while evaporating water from the system. This module explores applications of this principle in technologies originating in countries in the global South. engage Read about one of several evaporative cooler designs presented. How do they work? change How could these technologies be used in your life to replace reliance on refrigeration or air conditioning? analyze Use first law analysis to estimate the cooling process for a typical scenario. How much water is used? How much cooling is produced? reflect What did you learn about these technologies? About the process of estimation and open- ended problem solving? Figure 2.4: Zeer pot. Accessed June 3, 2011 from http://practicalaction.org/images/zeer6- fresh.jpg. 1. Engage. Consider one of the many designs of evaporative cooling used in locales where electricity or electric refrigerators are unavailable. Although numerous clay pot designs have utilized evaporative cooling for centuries in many locations around the world, Nigerian Mo- hammad Bah Abba patented his design of a pot-in-pot refrigerator, generating international interest [12, 13]. There are also a number of designs for evaporative room coolers; for example, Myra Wong offers two versions [14] and Eric Rusten several more [15]. 2. Analyze. Use a First Law analysis to estimate the cooling process for a typical scenario. For the pot-in-pot case, assume typical outdoor temperatures on location, a typical pot size, and 42 2. THE FIRST LAW: MAKING THEORY RELEVANT estimate how much water would be used to cool what mass of vegetables. For the room coolers, assume typical room sizes, and outdoor temperatures/humidity on location, and the speciﬁcations described to determine how much water would cool how much room air. Your thermodynamics textbook will have data that can help you with these calculations. Can you make this connection? 3. Reﬂect. What did you learn about these technologies? About the process of estimation and open-ended problem-solving? About the First Law and how to apply it in engineering design? 4. Change. What improvements if any would you suggest for the design you reviewed? How could these kinds of technologies be used in your own life context? Under what conditions if any could they, for example, replace refrigeration or air conditioning? We’ve seen how the First Law can be used in engineering design applications. The next module illustrates its usefulness in a very different applied context: hunger and nutrition. 2.4 MODULE 2.4. HUNGER, POVERTY, AND OBESITY Betty Ann, of Nacogdoches, TX, posted the following comment to an online CNN article on food stamps: a SEM knowledge f ethics i j lifelong learning contemporary issues Granted, $3.00 a day is not very much for food and of course those who are hungry should receive more, however; in a country where over-weight and obese thrive, lets make sure these people are really needing the food… I can not tell you how many times I have been in line at the grocery behind an obese person who used food stamps to pay. Should people have to “weigh in” to receive the food assistance?.... There needs to be more control over the food stamps. The ones who are truly starving should be the recipients [16]. Betty Ann has hit upon a common misperception about hunger in the United States. Being hungry means not being able to supply sufﬁcient food for one’s self and family. Sufﬁcient food is not deﬁned in terms of a person’s size, and being a certain weight does not give us any information about that person’s access to adequate nutrition. In the United States, where processed foods abound, even in so-called “food deserts” where fresh produce is scarce, often the cheapest foods that are readily available are also the most Calorie-dense. This creates a situation where getting a large number of Calories (note that Calories in nutrional contexts is spelled with a capital C and denotes kilocalories in thermodynamic terms, so 1 Calorie = 1000 calories) does not necessarily result in sufﬁcient mass or volume of food to ﬁll one’s belly, or in sufﬁcient nutrition to support good health. Can we use the First Law of thermodynamics to link hunger, poverty and obesity in order to challenge popular misconceptions about what hunger looks like? 2.4. MODULE 2.4. HUNGER, POVERTY, AND OBESITY 43 What is Obesity? Is it a problem? Public health studies tell us that obesity rates in the United States have been rising. In 1995, less than 20 percent of the population in each of the 50 states was obese. By 2005, only four states had populations in which less than 20 percent were obese, and three states had more than 30% obese people (Louisiana, Mississippi, and West Virginia) [17]. It is not a coincidence that in 2005 those states ranking 1st, 2nd, and 3rd in obesity ranked 50th, 49th, and 47th in personal income per capita [18]. The highest rates of obesity in the United States are found among those with the lowest incomes [19]. At ﬁrst this may seem counterintuitive; worldwide, as countries develop economically, the population gains weight [20]. Why is it that in the United States, the highest rates of obesity are in low income groups? This is an important question, but it cannot be answered simply, as the relationship between the two is complex, and correlations do not imply causation. The link between obesity and health is also complicated and subject to a lot of misinterpreta- tion. The Centers for Disease Control deﬁnes obesity as “having a very high amount of body fat in relation to lean body mass,” or a Body Mass Index (BMI) of 30 or higher. The BMI is a measure of weight that accounts for different heights of individuals; to calculate the BMI, an adult’s weight (kg) is divided by the square of his/her height. A BMI ranging from 18.5-25 is considered healthy, while a BMI of 30 or more is considered obese [21]. Though a lot of evidence ﬁnds a correlation between high BMI and negative health outcomes including diabetes and cardiovascular disease, other public health researchers point out that direct measures of physical ﬁtness are better predictors of health outcomes, and that physically ﬁt obese people have better health outcomes than inactive people who are not overweight [22]. Feminists and others are quick to point out the dangers of a size-focused anti-obesity movement that heaps more stigma on a group already targeted for bullying and ridicule. [23] We have already seen in Betty Ann’s comment the way that fat stigma and classism combine in a vicious size-based judgment of a person’s worthiness to receive food stamps. So how do we make sense of the links among health, poverty, and obesity? Slate’s Daniel Engber [24] explores this question, concluding that health, poverty and obesity “are spun together in a dense web of reciprocal causality.” That is, being obese can make one poor as sure as being poor can make one obese, and both increase the likelihood of getting sick, and so on. Engber notes, importantly, that being poor is a stronger predictor of negative health outcomes than being obese. What is Hunger? In 2006, the US government stopped using the word “hunger” to describe the condition of not knowing where one’s next meal is coming from [25]. The current term is food insecurity. In 2005, the USDA reported that 12.6 million households (about 35 million people, or 12% of Americans) were food insecure, meaning that at some point during the year they were unable to afford sufﬁcient food for their family [26]. While the average US household spends about $40 per person per week on food, a typical food insecure household spends about $30 [25]. Adam Drewnowski and associates study the energy density and energy cost of food [19, 26]. Energy density is deﬁned as the ratio of energy provided by food (kcal) to its mass (g). Energy cost of food is the ratio of the amount paid ($) to the energy provided (kcal). Drewnowski and Darmon [26] considered the relationship between energy density and energy cost, and found that 44 2. THE FIRST LAW: MAKING THEORY RELEVANT the cost per Calorie of “healthy” foods such as fresh produce was several thousand percent higher than “unhealthy” foods such as fats and sweets. Furthermore, they showed using linear programming models that when food expenditures are restricted, diets become more energy dense, with fewer vegetables and more fats. Results from a USDA study corroborate this ﬁnding. When asked what foods they would buy if they had more money, low-income respondents indicated they would buy more meats, eggs, cereals, and bakery products. People only increased the amount spent on fruits, vegetables, and dairy products when the income level rose above 30 percent over the poverty level [27]. Anecdotal experiences of hungry Americans also support this idea. Consider the following account from the wife of a Marine: My husband knew he was going to be in the ﬁeld for three weeks. He also knew that I would be here by myself with very little money and no dishes or pots and pans. So he went down to McDonald’s on Sunday when hamburgers were thirty-nine cents and bought twenty-one of them. I’ve been eating one hamburger every day for the last twenty days [28]. engage Explore a local grocery store. Gather data on cost and energy content of foods. analyze Plan a day’s menu for yourself using three alternative budgets, while still meeting basic nutritional guidelines. change How would you critique thermo textbooks’ discussion of “biological systems,” based on what you have learned in this exercise? Reflect Compare Pollan and Drewnowski’s takes on causes of (and ways to address) hunger. What do you think should be done? Why? Figure 2.5: Smith Engineering students in the Fall 2010 Thermodynamics class created a graph similar to Drewnowski’s [16] based on data they collected from three food outlets in Springﬁeld, MA. The graph relates the energy density of selected foods (MJ/kg) with energy costs ($/MJ). As with Drewnowski’s ﬁndings, the energy cost difference between processed foods high in sugar and fat compared with fresh vegetables is striking (note the log scale). 1. Engage. Explore a local grocery store. 2.4. MODULE 2.4. HUNGER, POVERTY, AND OBESITY 45 a. Search for the cheapest item in each of the pyramid groups (grains, fruits, vegetables, milk/cheese/yogurt, meats/beans) you can ﬁnd and write down each one’s nutritional data from the USRDA label and cost. What is the energy cost ($/100kcal)? What is the energy density (kcal/kg)? b. Now ﬁnd the most nutritious item you can ﬁnd in each category in the store and write down their nutritional values and costs. What are their energy costs ($/100kcal) and energy densities (kcal/kg)? (Nutritious is a highly subjective term; use http://www. mypyramid.gov for some guidelines). c. Tip: make sure you write down information that can help you estimate the mass of food per serving. Don’t just copy what’s on the label, but think about what the real mass or volume of a serving will be, and whether the recommended serving on the label is realistic. 2. Analyze. Plan a day’s menu for yourself using each of three alternative budgets: a. $5 (maximum individual daily allotment for a food stamp recipient). b. $10 (low budget/student). c. Maximize nutrition regardless of cost. For each menu you must meet the national nutrition guidelines for a 21 year old female exercising less than 30 minutes per day, or 2000 Calories (kcal) [29] which including the following: 6 oz. grains, half of which are whole grains 2.5 c. vegetables, varied among dark green, orange, pea/bean, starchy, and others 2 c. fruits or fruit juices 3 c. milk, yogurt, cheese, or other calcium-rich food 5.5 oz. meat and beans Visit USDA’s website http://www.mypyramid.gov for more information. One question that will arise is whether one can buy bulk items, or any items with multiple servings. Can one assume that certain staples have already been purchased? You will need to make a reasonable judgment here. It is neither realistic to assume all costs are borne up front for a single serving, nor is it realistic to assume that costs can be inﬁnitely prorated – people on a tight budget don’t have the luxury of affording the “family size” item of everything in order to save money in the long run. 3. Reﬂect. Read Michael Pollan’s New York Times article on the Farm Bill (http://www. michaelpollan.com/article.php?id=88) [30]. Why, in his view, are carrots more ex- pensive than twinkies? Now consider Drewnowski and Darmon’s [27] supposition “that the rising obesity rates reﬂect an increasingly unequal distribution of incomes and wealth.” How might each analysis lead to different approaches to addressing hunger, poverty and/or obesity? What do you think should be done? Why? Provide at least two substantively different ethical arguments for your position. What speciﬁc action will you take as a result? 46 2. THE FIRST LAW: MAKING THEORY RELEVANT 4. Change. Many thermodynamics textbooks engage students with a discussion of “thermody- namic aspects of biological systems” and a series of related homework problems [31]. How would you critique this part of the textbook, based on what you have learned in this exercise? Can you think of a way to move the conversation forward about health effects of hunger, poverty and nutrition in the US without adding to social stigma around size or weight? Having explored the First Law in the contexts of developing strategies for national and local energy independence, designing evaporative cooling technologies, and understanding links among hunger, poverty, and obesity in the US, we now turn to a “free choice” module where you can explore the First Law in any application that strikes your interest and curiosity. 2.5 MODULE 2.5. THERMO TO LIFE a SEM knowledge e h problems context i lifelong learning engage Explore and describe the thermodynamic aspects of an everyday life interest; pose a question to explore further. change What might we change to improve the system, or our understanding? analyze Define a system and conduct an energy balance or other analysis employing thermodynamic principles that might address the question. reflect What does this analysis tell us about the phenomenon described? What did we learn? What new questions emerged as a result? Figure 2.6: Inveneo’s Bicycle Powered Generator, 2005. Photo by Ho John Lee, used under the Creative Commons Attribution 2.0 Generic license. Accessed June 8, 2011 from http://commons. wikimedia.org/wiki/File:Inveneo_bicycle_powered_generator.jpg. This module employs the idea of praxis, in which theory and practice are interdependent and inform one another, grounded in community and directed toward social change [32]. You will explore a question that arises from a social need related to energy, conduct an engineering analysis of that phenomenon, and take socially transformative action in response to what you have learned. The goal is to pick a topic that you ﬁnd relevant and interesting, and explore how the theory and analytical tools you are learning apply to your topic. 2.5. MODULE 2.5. THERMO TO LIFE 47 1. Engage. Choose a question that you have heard emerge from the community (you deﬁne com- munity here – it could be the campus community, your home community, a local community, or any other group that has posed a relevant question). Example questions might include the following: What would it take for my community to be compliant with the Kyoto Protocol, or other proposed climate change policies? Is it feasible to be carbon neutral? What would that entail? What is the potential for using more human-powered machines in my community? What would be involved in, say, developing a human-powered television? How do igloos work, and what would it take to construct a working igloo in my com- munity? What is the energy and nutritional content of local elementary school lunches? Some energy usage might be considered a basic human need, such as home heating in cold climates. How much energy goes to basic human needs locally, and how could we address the impact of rising energy costs, or the impact of policies such as a carbon tax, on the poor? What does it take to retroﬁt a car for biodiesel, or to reﬁne biodiesel fuel in my community? Conduct an energy audit on a local building to identify opportunities for energy and cost savings. You want to be sure your question will also meet the other requirements of the assignment (can it be subjected to analysis, and ultimately result in transformative action?). Present a background description and a qualitative write-up that explains the thermodynamics in layperson’s terms and illustrates the potential transformative value of the work you will do. 2. Analyze. Perform some quantitative analysis on your selection – this will most likely be an energy balance, but you could also perform other calculations that illustrate how it works thermodynamically – for example, an engine cycle analysis, or chemical reaction equilibrium analysis, depending on your chosen system. Some of the topics may not have been covered yet in your course, but you should feel free to explore topics as they are relevant and learn what you can about them, driven by your interest. Thoroughly explain the thermodynamics behind how it works. Make reasonable assumptions where necessary. Be as realistic as possible, but make simpliﬁcations if needed. 3. Reﬂect. Think (do not write or type, just think) for 15 minutes about what have you learned from your engagement and analysis so far. What questions emerge for you? Write a short 48 REFERENCES reﬂection on what you learned, and what you would like to explore further. Identify possible avenues of change or further exploration. 4. Change. Take some action that changes the situation. If your topic is policy-relevant, it may mean contacting your representatives and communicating with them about what you have learned. If your topic is local, it may mean communicating with the local community through pubic media or through private contacts. Perhaps you have an opportunity to suggest a design improvement and show either through calculations or some course of experimental action how your idea improves the artifact or situation. Be creative. Reﬂect on the potential or realized impact of your action. What else might you do in the future? REFERENCES [1] Von Baeyer, H.C. (1999). Warmth Disperses and Time Passes: a history of heat. New York: Modern Library. Cited on page(s) 36 [2] Joule, J.P. (1845). On the Existence of an Equivalent Relation between Heat and the ordi- nary Forms of Mechanical Power. Philosophical Magazine. Series 3, Vol. xxvii, p. 205. Ac- cessed June 12, 2011 from http://www.chemteam.info/Chem-History/Joule-Heat- 1845.html. Cited on page(s) 37 [3] Thompson, B. (Count Rumford) (1798). Heat is a Form of Motion: An experiment in bor- ing cannon. Philosophical Transactions (vol. 88). Accessed June 12, 2011 from http://www. chemteam.info/Chem-History/Rumford-1798.html. Cited on page(s) 37 [4] Al-Hassan, A.Y. and Hill, D.R. (1986). Islamic Technology: an illustrated history. Cambridge: Cambridge University Press. Cited on page(s) 37 [5] James, P. and Thorpe, N. (1994). Ancient Inventions. New York: Ballantine Books. Cited on page(s) [6] Macdonald, A. (1992). Feminine Ingenuity: Women and Invention in America. New York: Bal- lantine Books. Cited on page(s) [7] Stanley, A. (1993). Mothers and Daughters of Invention: Notes for a Revised History of Technology. New Brunswick, NJ: Rutgers University Press. Cited on page(s) [8] Andah, B.W. (1992). Nigeria’s Indigenous Technology. Ibadan: Ibadan University Press. Cited on page(s) 37 [9] Maddow, R. (2010). Oil Independence is a Myth. In B. Wolff (Producer), The Rachel Maddow Show, New York: MSNBC. June 17, 2010. Accessed June 12, 2011 from http://www.msnbc. msn.com/id/26315908/#37769319. Cited on page(s) 38 REFERENCES 49 [10] Massachusetts Department of Energy Resources. (2010). Municipal Utility Study. Technical Report. January 28, 2010. Accessed June 7, 2011 from http://www.mass.gov/Eoeea/docs/ doer/publications/doer-municipal-utility-rpt.pdf Cited on page(s) 39 [11] Massachusetts Alliance for Municipal Electric Choice. (2011). Website. Accessed June 7, 2011 from http://www.massmunichoice.org/. Cited on page(s) 39 [12] Practical Action (2011). How a Zeer Pot Fridge Makes Food Last Longer. Accessed June 7, 2011 from http://practicalaction.org/?id=zeerpots. Cited on page(s) 41 [13] Elkheir, M. (2004).The Zeer Pot: A Nigerian invention keeps food fresh without electricity. Sci- ence in Africa, September 2004. Accessed June 7, 2011 from http://www.scienceinafrica. co.za/2004/september/refrigeration.htm. Cited on page(s) 41 [14] Wong, M. (2003). An Evaporative Cooler. In Field Guide to Appropriate Technology, B. Hazel- tine and C. Bull eds. New York: Elsevier Science. pp. 257–258. Accessed July 7, 2011 from http://books.google.com/books?id=kEAOTpIYFBcC&pg=PA257&lpg=PA257&dq= %22myra+wong%22+%22evaporative+cooler%22&source=bl&ots=Pe6C0Ic9jM&sig= TBe12l8tYxtUZogMvv6Nn69ySb4&hl=en&ei=riYhTO_jNMH98AaE-c2ZAQ&sa=X&oi= book_result&ct=result&resnum=1&ved=0CB4Q6AEwAA#v=onepage&q=%22myra %20wong%22%20%22evaporative%20cooler%22&f=false. Cited on page(s) 41 [15] Rusten, E. (1985). Understanding Evaporative Cooling. VITA Technical Paper #35. Volunteers in Technical Assistance. Accessed June 7, 2011 from http://www.cd3wd.com/cd3wd_40/ vita/evapcool/en/evapcool.htm Cited on page(s) 41 [16] Anderson Cooper 360 Blog. Accessed June 15, 2007 from: http://www.cnn.com/ CNN/Programs/anderson.cooper.360/blog/2007/04/oregon-governor-tries- living-on-food.html. Cited on page(s) 42, 44 [17] Centers for Disease Control Obesity Trends. Accessed June 15, 2007: http://www.cdc.gov/ nccdphp/dnpa/obesity/trend/maps/ . Cited on page(s) 43 [18] US Department of Commerce, Bureau of Economic Analysis, Survey of Current Business. Web: www.bea.doc.gov/bea/regional/spi/. Cited on page(s) 43 [19] Drewnowski, A. and Specter, S.E. (2004). Poverty and obesity: the role of energy density and energy costs. American Journal of Clinical Nutrition, 79:6–16. Cited on page(s) 43 [20] Kumanyika, S., Jeffery, R.W., Morabia, A., Ritenbaugh, C. and Antipatis, V.J. (2002). Obesity prevention: the case for action, International Journal of Obesity, 26 (3):425–436. Cited on page(s) 43 [21] Centers for Disease Control Obesity Trends. Accessed June 15, 2007: http://www.cdc.gov/ nccdphp/dnpa/obesity/trend/maps/ Cited on page(s) 43 50 REFERENCES [22] Blair, S.N. and Church,T.S. (2004).The ﬁtness, obesity, and health equation: is physical activity the common denominator? JAMA 292 (10):1232–1234. Cited on page(s) 43 [23] Harding, K. and Kirby, M. (2009). Lessons from the Fat-o-Sphere: Stop dieting and declare a truce with your body. New York: Perigree Trade. Cited on page(s) 43 [24] Engber, D. (2009). Give me your poor, your tired, your big fat asses: Does poverty make people obese, or is it the other way around? Slate, Sept. 28, 2009. Accessed June 7, 2011 from http:// www.slate.com/id/2229523/. Cited on page(s) 43 [25] Williamson, E. (2006). Some Americans Lack Food, but USDA Won’t Call Them Hun- gry, Washington Post November 16, 2006. Accessed June 7, 2011 from http://www. washingtonpost.com/wp-dyn/content/article/2006/11/15/AR2006111501621. html. Cited on page(s) 43 [26] Nord, M., Andrews, M., and Carlson, S. (2006). Food Security in the United States, 2005, Economic Research Report No. (ERR-29) 68 pp, United States Department of Agriculture, November 2006. Cited on page(s) 43 [27] Drewnowski, A. and Darmen, N. (2005). The economics of obesity: dietary energy density and energy cost. American Journal of Clinical Nutrition, 82(suppl): 265S-273S. Cited on page(s) 44, 45 [28] Blisard, N. and Stewart, H. (2006). How Low-Income Households Allocate Their Food Budget Relative to the Cost of the Thrifty Food Plan Economic Research Report No. (ERR-20), United States Department of Agriculture, August 2006. Cited on page(s) 44 [29] USDA. MyPyramid Plan. Accessed August 23, 2007 from http://www.mypyramid.gov/ mypyramid/index.aspx. Cited on page(s) 45 [30] Pollan, M. (2007). You Are What You Grow. New York Times Magazine, April 22, 2007. Accessed August 23, 2007 from http://www.michaelpollan.com/article.php?id=88. Cited on page(s) 45 [31] Çengel and Boles. (2008). Thermodynamics: An engineering approach. 6th ed. New York: McGraw-Hill, pp. 193–200, 210–211. (Other texts have similar sections or sidebars.) Cited on page(s) 46 [32] Marx, K. [1845] (1976). Theses on Feuerbach. In K. Marx and F. Engels (Eds.), Collected Works of Karl Marx and Friedrich Engels, 1845–1847, Vol. 5: Theses on Feuerbach, The German Ideology and Related Manuscripts. New York: International Publishers, p. 8. Cited on page(s) 46 C H A P T E R 3 51 The Second Law and Property Relations This chapter explores the Second Law of thermodynamics and the related concept of entropy in practical, historical, and philosophical terms, and grounds the fundamental property relations of thermodynamics in relevant contexts. The best you can do is break even. Heat flows naturally from hot to cold. The Second Law and the related concept of entropy are often challenging for students to grasp initially; students often see multiple statements of the Second Law that have been developed his- torically as well as colloquial statements intended to assist student understanding, although it often leads to confusion as students struggle to reconcile disparate statements and long for a single, concise, and correct one. No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature. No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work This chapter is designed to help you with these new ideas by demonstrating their relevance in personal, professional, and philosophical terms. Using historical and social analysis to view the Sec- ond Law from multiple perspectives, you will gain insight into the concepts and their development, as well as into the scientiﬁc enterprise. The entropy of an isolated system (or the entropy of a system plus its surroundings) always increases (except for reversible processes where it remains constant). 52 3. THE SECOND LAW AND PROPERTY RELATIONS The ﬁrst module explores how we deﬁne efﬁciencies and what efﬁciency has to do with the Second Law.What do the limits of achievable efﬁciency mean in real terms for heat engines compared with other energy technologies? The second module considers the history of pursuit of perpetual motion in the United States and asks why so many are seduced by the idea even in contradiction of reason. The third module provides historical background on the development of entropy as a thermodynamic property and explores its philosophical implications. The fourth module tests the accuracy and helpfulness of entropy analogies used to help students with the concept of entropy. The ﬁfth module demonstrates the relevance of the mathematical “guts” of thermo, the fundamental property relations, by challenging you to apply them in a context of your choosing. Module 3.1: The Limits of Efﬁciency – Heat Engines vs. Other Technologies. Module 3.2: Perpetual Motion. Module 3.3: Entropy: Origins and Implications. Module 3.4: Entropy Analogies in Textbooks… Module 3.5: Making Math Relevant: Thermodynamic Relations in Context. 3.1 MODULE 3.1. THE LIMITS OF EFFICIENCY: HEAT ENGINES VS. OTHER ENERGY TECHNOLOGIES Efﬁciency is a central principle in thermodynamics; you may have been calculating the efﬁciencies of different systems as part of your problem solving in your thermo course. a SEM knowledge h context You may also have noticed popular discussions of energy efﬁciency as part of energy conservation strategies. What do each of these discussions of efﬁciency have to do with the Second Law? This module guides your work to answer this question by comparing deﬁnitions of efﬁciency, as well as comparing the limits of efﬁciency, for different types of systems. 1. Engage. What does efﬁciency mean? What is the difference between thermal efﬁciency and mechanical efﬁciency? Which kinds of efﬁciency apply to which energy technologies? Seek out some deﬁnitions of efﬁciency from textbooks and other sources. What is your deﬁnition? Pay attention to qualifying terms such as thermal or mechanical efﬁciencies. What is being measured, relative to what? 2. Analyze. Find or develop speciﬁc deﬁnitions of efﬁciency for solar, geothermal, wind, hydro, and coal ﬁred power plants. What is similar among them, and how do they differ? What is the difference in consequence (economic, environmental, social) of low (or high) efﬁciencies in each case? Can you conclude one technology is better than another based on efﬁciency ﬁgures? Why or why not? What is the maximum possible efﬁciency of each type? When does 3.2. MODULE 3.2. PERPETUAL MOTION MACHINES 53 engage Write some definitions of efficiency as you understand it and as it is described in your textbook or other sources. analyze Refine your definitions for specific energy systems. Characterize the impacts of low or high efficiency in each case. Can you compare systems? change What are some other ways of presenting essential performance information that help us think about sustainable energy? reflect How is efficiency properly used in engineering design? In public conversations about energy? Figure 3.1: Hoover Dam, Windmills in Lubbock, TX. What does efﬁciency mean? http:// www.windmill.com/images/Cluster_at_Sunset.jpg http://www.visitingdc.com/images/ hoover-dam-directions.jpg. Carnot Efﬁciency come in to play, and when is it irrelevant? Does the Second Law still apply to systems that are not heat engines? If so, how? 3. Reﬂect. Based on this exploration, how do you think efﬁciency is properly used in the context of engineering design? How is it properly used in public conversations or political debates about energy? 4. Change. What are some other ways of presenting information about an energy system’s per- formance, particularly with regard to sustainability? Can any of these new methods help us compare different kinds of technologies better? Having explored achievable efﬁciencies, the limits of what’s possible, we now turn to the seductive pursuit of the impossible: perpetual motion machines. 3.2 MODULE 3.2. PERPETUAL MOTION MACHINES For centuries, people have pursued machines that produce inﬁnite energy. g communi- cation h context i lifelong learning 54 3. THE SECOND LAW AND PROPERTY RELATIONS Why have such pursuits garnered so much attention, even well after science’s widespread acceptance of the Second Law? engage change How can science help? Learn about and retell an incident of perpetual motion machines in history. Choose from examples below or find your own. analyze reflect How did the technology violate either the first or second law? Why were people fooled for a time? Why are perpetual motion machines so seductive? Why do people readily distrust science in this and other areas? Figure 3.2: An ironic t-shirt referencing the debate over teaching evolution in public schools urges us to “teach the controversy” of perpetual motion. http://controversy.wearscience.com/img190/ perpetual.gif. Used with permission. 1. Engage. Learn about an incident in history where perpetual motion or “free energy” was pursued. Retell the story in your own words. Choose from the following examples detailed by Bob Park [1], in which the United States Congress gave time and attention to these ideas, despite their lack of scientiﬁc merit: The 1989 Cold Fusion experiments of Fleischmann and Pons. The Newman Energy Machine. The Giragossian Energy Machine. 2. Analyze. How did the technology violate either the First or Second Law of thermodynam- ics? Why were people fooled for a time? How was the idea debunked? Both Newman and Fleischmann/Pons continue to have defenders to this day. Why do you think that is? 3. Reﬂect. Why are perpetual motion machines so seductive? What would be the social and economic consequences if we could operate perpetual motion machines? Think about other present-day cases where science is distrusted or discounted – for example, in approaching evolution or climate change. What social and economic consequences might be at stake, driving a discounting or distrust of science? 3.3. MODULE 3.3. ENTROPY AS A SOCIAL CONSTRUCT 55 4. Change. The notion of critical thinking or skepticism is held up by both sides in these debates. Supporters of Newman and others claim that the scientiﬁc establishment is closed to new ideas, and evolution proponents argue for “teaching the controversy” – allowing religious accounts to be taught alongside scientiﬁc accounts in biology classrooms.Why are such positions ultimately uncritical? Here we’ve applied some social analysis to understand why and how some well-proven scien- tiﬁc concepts go unaccepted and not understood by people at large. In the next module we take up the more challenging task of applying social analysis to the development and acceptance of concepts by the scientiﬁc establishment itself, examining how entropy came to be, and its implications for other ﬁelds of knowledge. 3.3 MODULE 3.3. ENTROPY AS A SOCIAL CONSTRUCT Having encountered in the last module the persistence of challenges to the Second Law, it may be particularly provocative to title this section “entropy as a social construct.” g communi- cation h context i lifelong learning Let me be clear that I do not doubt entropy any more than I doubt gravity, but both concepts take on certain forms of expression that are shaped by the social and historical contexts in which they were developed, and are subsequently interpreted in new times and places. In this module we ﬁrst consider the social forces inﬂuencing the historical development of the concept of entropy, then explore the implications of entropy as interpreted in contexts far aﬁeld of heat engines. 3.3.1 EXPLORATION 1: ORIGINS OF ENTROPY 1. Engage. Read historical accounts of the conceptual development of entropy by Rudolf Clau- sius; Von Baeyer’s is particularly readable [2]. Clausius’s key papers can be found at http:// www.humanthermodynamics.com/Clausius.html. Von Baeyer argues that the history of entropy illustrates some central points about the “thematic content of science”[3] – that science has certain preferences in expressing theoretical content for both universal theory and for par- simony (mathematical simplicity that can be expressed on a t-shirt like Maxwell’s Equations or Einstein’s E=mc2). These preferences and biases drove Rudolf Clausius’s attempts to express the Second Law of thermodynamics in ways that were both elegant and parallel, as well as his attempts to create entropy as a mathematical quantity to put into an equation, which ends up an inequality that doesn’t “balance. 2. Analyze. Reviewing your textbook and other sources, gather as many expressions of entropy and the Second Law as you can. Write a short essay reviewing how the thematic content of science plays out in these forms of expression. What does it mean that there are so many ways 56 3. THE SECOND LAW AND PROPERTY RELATIONS engage How did the concept of entropy come to be? How did the preferences of scientific institutions shape this process? change What can you do to understand entropy better? Choose one thing and try it out. analyze How does the thematic content of science play out in multiple expressions of the Second Law? reflect What have you struggled with most in coming to understand the second law or the concept of entropy? Figure 3.3: Parsimony: Reducing Entropy to a symbol on a button http://rlv.zcache.com/ entropy_button-p145655327883250137t5sj_400.jpg. of expressing the same concept? What does it mean to acknowledge that entropy is socially and historically constructed? 3. Reﬂect. Why do you think students ﬁnd entropy difﬁcult to grasp on a ﬁrst encounter? How do the difﬁculties relate to the thematic content of science and our expectations to learn engineering concepts in certain forms? What have you struggled with most in coming to understand the Second Law, or entropy? 4. Change. What can you do to understand entropy better? Choose one action you can take and try it out. While entropy may be challenging to grasp at ﬁrst, it is rewarding in its profundity. Consider for example, entropy’s ability to answer why it is that we experience time as moving ever forward, never backward. 3.3.2 EXPLORATION 2: ENTROPY’S PHILOSOPHICAL IMPLICATIONS 1. Engage. Read some descriptions of the arrow of time [6]. In the quotes above, both Einstein and Vonnegut reference Minkowski’s concept of space-time, in which forward and backward in time would be matters of convention… in theory. But the Second Law gives time a direction – how? A good place to start is Von Baeyer’s summary [2] of the work of several physicists 3.4. MODULE 3.4. EVALUATING ENTROPY ANALOGIES 57 engage How does one get from the expressions of the Second Law in thermo to concepts like the arrow of time? analyze Explain how the Second Law shows that time moves ever forward… or at least almost ever. change What can you do to find or make deeper meanings in your work? reflect How did the practical considerations of Carnot, Kelvin, Planck, and others lead to profound philosophical insights? For those of us who believe in physics, this separation between past, present, and future is only an illusion, albeit a stubborn one. -Albert Einstein[4] It is just an illusion we have here on Earth that one moment follows another one, like beads on a string, and that once a moment is gone, it is gone forever…. So it goes. -Kurt Vonnegut [5] Figure 3.4: Albert Einstein (top) and Kurt Vonnegut (bottom) http://www.glsc.org/einstein/ images/einstein_3.jpg http://adreampuppet.files.wordpress.com/2007/04/vonnegut. jpg. and mathematicians instrumental in developing a probabilistic and microscopic approach to the Second Law, including Maxwell and Boltzmann. 2. Analyze. How did Maxwell and Boltzmann come to characterize the Second Law in terms of probability, and at the molecular level? How did entropy come to be characterized as disorder? How do the work of Ehrenfest, Ruelle, and Boltzmann come together to show that the proof of the Second Law is not absolute but statistical in nature (albeit with an astronomically high probability of holding true)? How do these ﬁndings give time a direction? 3. Reﬂect. How did we get from Carnot’s, Kelvin’s, and Planck’s very practical investigation of steam engines to philosophical conclusions about the direction of time? What follows directly, and what is indirect, unrelated, or even metaphorical? 4. Change. Engineers aren’t known for producing deep philosophical insights, and yet these grand ideas can certainly be traced back to engineers. Can we cultivate an appreciation for the insights, and the questions around these deeper meanings, in engineering? What can you do to ﬁnd or make deeper meanings in your work as an engineering student? Entropy is indeed an abstract concept, with implications waxing philosophical. It is not sur- prising then, that engineers in particular would seek to return the concept to concrete and practical considerations. We will see in the next module how some instructors and authors of thermo textbooks seek to make entropy more relevant through various analogies to common life experiences. 58 3. THE SECOND LAW AND PROPERTY RELATIONS 3.4 MODULE 3.4. EVALUATING ENTROPY ANALOGIES 1. Engage. Thermodynamics textbooks and other sources seeking to make thermodynamics relevant to everyday life will often use analogies to illustrate entropy. Some of these analogies are metaphorical, not literally true, while others have been developed as “entropy” in their own right, applied in other ﬁelds. For example, Çengel and Boles [7] discuss four different analogies: entropy in learning, in libraries, in rooms, and in armies. The concept of entropy is used in military science [8] and in information theory, the Shannon entropy represents missing information [9]. Neither of these is literally the same as thermodynamic entropy, and is instead an analogous concept, though there are strong theoretical connections between thermodynamic and information entropy that continue to be pursued [10]. 2. Analyze. Provide a critical discussion (as in critical thinking; you may defend or refute any part) of an entropy analogy from your textbook or another source. Include both thermodynamic and social considerations, discussing the following: Where do the analogies for entropy hold (thermodynamically and socially), and where do they fail? What are the (thermodynamic and social) implications of applying entropy in these ways, and of using these examples? What is a g SEM knowledge communi- cation i lifelong learning engage Find entropy analogies used in your textbook or another source. change How else might you make entropy concrete for students? analyze Provide a critical discussion of the analogy. Where does it hold? Where does it fail, in both thermodynamic and social terms? reflect Are these analogies helpful for your learning? Why or why not? Figure 3.5: Messy rooms are a misleading metaphor for students learning about entropy. http://www. roommatesusa.com/wp-content/wpuploads/2010/12/messy-room.jpg. 3.5. MODULE 3.5. MAKING MATH RELEVANT:THERMODYNAMIC RELATIONS IN CONTEXT 59 the bias of the source; do they seem to have a position on entropy as good or bad, desirable or undesirable? Can you challenge their assumptions? 3. Reﬂect. How do these analogies help you learn? How might they get in the way of learning? 4. Change. How else could you make entropy more concrete for students learning thermody- namics? Supply either a new analogy that you think holds better, or devise a new way to help students relate entropy to everyday life. Entropy is not the only abstract entity thermodynamics students come across. Indeed, making entropy useful in many engineering applications requires an understanding of the fundamental property relations, mathematical relationships that help us derive expressions for thermodynamic properties of interest in terms of quantities that are known or readily measured. Thus, the next module revisits the “Thermo to Life” approach used in Module 2.5 ﬁnding relevant applications of the thermodynamic relations. 3.5 MODULE 3.5. MAKING MATH RELEVANT: THERMODYNAMIC RELATIONS IN CONTEXT This module seeks to demonstrate the usefulness of the thermodynamic relations.The goal is to pick a topic that you ﬁnd relevant and interesting, where the thermodynamic relations can be applied. This is somewhat more difﬁcult than in the Thermo to Life exercise in Module 2.5 because of the narrower applicability of the material considered here. a SEM knowledge e problems i j lifelong learning contemporary issues 1. Engage. Find and describe an application of the thermodynamic relations in everyday life. You may ﬁnd your own or choose one of these: a. Calculating Entropy in terms of measurable quantities using Maxwell Relations. b. Predicting partitioning behavior of pollutants in soil, air, and water using Gibbs Energy and Fugacity [11]. c. How the Gibbs Energy is used to characterize Fuel Cell function [12]. d. Using the Gibbs Energy to describe fuel distillation or other separations processes (vapor- liquid equilibrium). e. Using Gibbs energy and chemical reaction equilibrium to understand fuel combustion. f. Using Gibbs energy and chemical reaction equilibrium to understand environmental controls on power plants. g. Using Helmholtz energy to predict behavior of volcanic eruptions or other explosions. 60 REFERENCES engage Find and describe an application of the thermodynamic relations in everyday life; choose from the list below or find your own. analyze Show how thermodynamic property relations are used to analyze this system. change What might we change to improve the system, or our understanding? reflect What does this analysis tell us about the system? What did we learn? What new questions emerged as a result? 3.6: Biodiesel processing equipment http://www.extremebiodiesel.com/photos/ Figure articles/full-Processor.jpg. 2. Analyze. How is thermodynamic theory used to characterize your system? Which thermo- dynamic properties are relevant? On which measurable properties do these depend? Find or create an illustrative example that demonstrates the usefulness of the thermodynamic prop- erties in characterizing your system. Thoroughly explain the thermodynamics behind how it works. Make reasonable assumptions where necessary. Be as realistic as possible, but make simpliﬁcations if needed. 3. Reﬂect. Think (do not write or type, just think) for 15 minutes about what have you learned from your engagement and analysis so far. What questions emerge for you? Write a short reﬂection on what you learned, and what you would like to explore further. Identify possible avenues of change or further exploration. 4. Change. Did your example provide a satisfactory case study explaining how thermodynamic theory can be useful in everyday life? If not, what would you explore further to establish a better link? REFERENCES [1] Park, R. (2000). Voodoo Science: The Road from Foolishness to Fraud. New York: Oxford University Press. Cited on page(s) 54 [2] Von Baeyer, H.C. (1999). Warmth Disperses and Time Passes: The History of Heat. New York: Modern Library. Cited on page(s) 55, 56, 61 REFERENCES 61 [3] The idea of the “thematic content of science” is attributed to Horton, G. (1973). Thematic Origins of Scientiﬁc Thought. Cambridge, MA: Harvard University Press, p. 47. Cited in [2, p. 56]. Cited on page(s) 55 [4] Einstein, A. (1972). Letter to Michele Angelo Besso’s son after his father’s death, 1955. In P. Speziali, ed., Albert Einstein–Michele Besso Correspondence. Paris: Hermann, p. 538–9. Cited on page(s) [5] Vonnegut, K. [1969] (1991). Slaughterhouse-ﬁve, or, The children’s crusade, a duty-dance with death. New York: Dell, p. 27. Cited on page(s) [6] Eddington, A. (1929). The Nature of the Physical World. New York: MacMillan, p. 68ff. Cited on page(s) 56 [7] Çengel and Boles. (2008). Thermodynamics: An engineering approach. 6th ed. New York: McGraw-Hill. Cited on page(s) 58 [8] Herman, M. (1998–9) Entropy-Based Warfare: Modeling the Revolution in Military Affairs. Joint Force Quarterly (JFQ) No. 20: 85–90. Accessed June 8, 2011 from http://www.au.af. mil/au/awc/awcgate/jfq/1620.pdf. Cited on page(s) 58 [9] Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Jour- nal, 27:379–423, 623–656. DOI: 10.1145/584091.584093 Cited on page(s) 58 [10] Von Baeyer [2] covers these connections. See also Maroney, O. (2009). Information Process- ing and Thermodynamic Entropy. Stanford Encyclopedia of Philosophy, E.N. Zalta, ed. Stan- ford, CA: Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University. Accessed June 8, 2011 from http://plato.stanford.edu/entries/ information-entropy/. Cited on page(s) 58 [11] Mackay, D. (1979) Finding Fugacity Feasible. Environmental Science and Technology, 13(10): 1218–1223. DOI: 10.1021/es60158a003. See also Mackay, D. (2004). Finding Fugacity Feasible, Fruitful, and Fun. Environmental Toxicology and Chemistry, 23(10): 2282–2289. DOI: 10.1897/03–465. DOI: 10.1021/es60158a003 Cited on page(s) 59 [12] Smith, J.M., Van Ness, H.C., and Abbott, M.M. (2001) Introduction to Chemical Engineering Thermodynamics. 6th ed. New York: McGraw Hill. Cited on page(s) 59 C H A P T E R 4 63 Thinking Big Picture about Energy and Sustainability The goal of the modules in this chapter is to create opportunities to think about complex, real- world issues in energy and sustainability. While the list of topics explored here is by no means comprehensive, each module is designed to help you learn how to consider technical and social contexts, engineering ethics, community needs, and public policy simultaneously. What should the United States do to curb its greenhouse gas emissions in order to mitigate climate change? Module 4.1 challenges you to develop and test out a concrete plan to achieve meaningful reductions. How does one choose a technology for a particular community or application in power generation or transportation? In Module 4.1 you will ﬁrst deﬁne and reﬁne selection criteria, then apply these to cases in the power generation and transportation sectors. Module 4.3 examines sustainability criteria, asking you to evaluate the “green-ness” of three scenarios: nuclear power generation, corn-based ethanol as a transportation fuel for the United States, and the transportation of western, low-sulfur coal to eastern power plants in the US. Module 4.4 takes up how consumers use energy in their homes, for cooking, refrigeration, and water puriﬁcation. Finally, Module 4.5 asks how we understand large-scale disasters that have come to be common occurrences in our quest for energy, and work for their prevention. All of these questions require keeping the big picture in mind, even as detailed analyses are brought to bear on these topics. Module 4.1: Climate Action. Module 4.2: Selection Criteria for Energy Technologies. Module 4.3: Is it Green? Module 4.4: Home Energy Uses. Module 4.5: Ethics of Energy Disasters. 4.1 MODULE 4.1. CLIMATE ACTION This module challenges you to move between a “big picture” contextual perspective and the focused, sometimes narrow world of engineering thought. e f problems ethics j contemporary issues 64 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY engage Identify a set of significant actions that can be taken to reduce US Greenhouse Gas Emissions by 1000Tg CO2 eq / year. change Take some action toward making these reductions happen. Document and reflect on the impact of your action. analyze Justify your reductions strategy in quantitative, qualitative, and ethical/moral terms. reflect What are the limits of individual behavior strategies such as green consumerism on GHG reductions? Figure 4.1: From Derrick Jensen and Stephanie MacMillan’s graphic novel As the World Burns: 50 Simple Things You Can Do to Stay in Denial [1]. Used with permission. Learning to move between these frames is essential in forming sound engineering judgment. This assignment also challenges you to move between theory and action, between your life as a student and your life as a citizen of the planet. Integrating theory and action is the essence of engineering; engagement reminds us it is a false distinction we sometimes make between “College” and “The Real World,” between an academic subject like “thermo” and what we more generally refer to as our “life.” 1. Engage. Identify a set of signiﬁcant actions that can be taken to reduce US greenhouse gas emissions [2]. Signiﬁcant in this case means it must have the potential to reduce greenhouse gas emissions to 1990 levels, when the atmospheric global carbon dioxide concentration was 354 ppm. This is a signiﬁcant reduction, but is also far from sufﬁcient when one considers that global increases in CO2 emissions from fossil fuel combustion between 1990 and 2008 have been much higher, around 40%, compared to the US’s 15% [3]. Despite these emissions increases abroad, the US remains a grossly disproportionate emitter of CO2, putting out 19% of global CO2 emissions from human activity (excluding deforestation) while comprising only 4.6% of the world population [3]. On this basis one could argue that US reductions need to be much deeper in order to be equitable and to allow developing economies to grow. 4.1. MODULE 4.1. CLIMATE ACTION 65 2. Analyze. Justify your choice by explaining what impact you expect your actions to have and put them in perspective. You must do this quantitatively, qualitatively, and in terms of ethical or moral argument. Quantitatively, estimate the total CO2 equivalent reductions your actions would bring about on an annual basis (see [2] for a deﬁnition of CO2 equivalents). The goal is to eliminate enough Tg of CO2 equivalent emissions per year to return the US to 1990 emissions levels. Keep track of uncertainty in your assumptions and present your estimated reductions with a sensitivity analysis (carry through +/- values that extend from a critical assessment of your own assumptions used in your estimates). Your sensitivity analysis should capture the range of emissions reductions that can reasonably be expected, given the uncertainty in your assumptions. Qualitatively, you need to describe why your proposed action is feasible in the time allotted, and why you expect it to be effective in the long-term toward bringing about the reductions targeted. Make an ethics-based argument for why your proposed action is necessary or justiﬁed, referencing multiple ethical frameworks (e.g., utilitarian, deontological, social justice, morally deep world, etc. – see [4]–[7] for more on ethics frameworks and how to apply them). 3. Reﬂect. How much can individual personal actions, such as using energy efﬁcient light bulbs impact climate change? How likely are individuals to comply with behavioral strategies? What adjustments would you make to your calculations to make sure they are realistic? What kinds of collective actions that target structural and infrastructural issues might be more likely to bring about signiﬁcant change? What are the barriers to individuals acting collectively for change? 4. Change. Take some action that demonstrates the effectiveness of your proposed reduction strategy or that works toward actually making these reductions happen. For example, you might implement one strategy on a small scale, which, if implemented widely, would result in the reductions claimed. Or you may work to bring about larger structural change through collective action – for example, working to pass national legislation. Document your actions and their short-term effects on yourself, your local community, and larger society. 5. Reﬂect. What are your accomplishments so far? Describe results quantitatively, qualitatively and in ethical or moral terms. What impact have your actions had globally, locally, and within yourself? What feedback have you received, and what new knowledge have you acquired as a result of your actions? How will you adjust your actions going forward, as a result of what 66 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY you learned? What opportunities for transformation lie ahead? What do you wish you had done differently? What future actions do you recommend or commit to do next? How did this exercise change you? What have you learned? How did this project connect to your learning thermodynamics? How will you use what you’ve learned in your future as a student? As a professional? As a citizen of the world? All climate strategies must take up the question of which energy technologies ought to be implemented to best support greenhouse gas reduction plans.The answers will be different depending on intended applications in speciﬁc communities. In the next module you will generate a set of criteria for energy technology selection, considering not only greenhouse gas emissions, but also other environmental, economic, social, and political considerations, and apply the criteria to uses in transportation and power generation. 4.2 MODULE 4.2. SELECTION CRITERIA FOR ENERGY TECHNOLOGIES How does one determine the appropriate energy technology for a given application? Here you will generate a set of criteria to use in approaching this problem, and apply the criteria in transportation and power generation. 4.2.1 EXPLORATION 1: DEVELOPING SELECTION CRITERIA 1. Engage. Brainstorm a set of criteria you think society should use in making choices about an energy technology. Some possible criteria are presented in Table 4.1, and details on how different energy sources address some of these criteria can be found in energy studies texts, e.g. [8]. Are there any criteria you would add or take away? How is each criterion deﬁned? Conduct background research to develop a working knowledge and critical understanding of what each criterion means in an energy context. Are terms different for different technologies, such that you can’t compare them directly? For example, efﬁciency means different things for different energy sources (see Module 3.1). Should it be included, and if so, how can it be used as a basis of comparison? A category like sustainability might have multiple criteria within it – air toxics, water pollution, greenhouse gas emissions – that cannot be compared directly. How sustainability is deﬁned may itself be contested. What human impacts deserve consideration? Job loss or gain, displacement of people, quality of life, environmental racism or classism in citing of energy resource extraction, production, or waste facilities? How do energy systems require certain types of control and certain social structures to maintain them? See Langdon Winne’s classic article “Do Artifacts have Politics?”[9] http://zaphod.mindlab. umd.edu/docSeminar/pdfs/Winner.pdf. 2. Analyze. Devise a strategy for determining whether a given criterion has been met. Is the goal to meet a set standard (if so, what is the standard?), or to maximize or minimize that quality? Is 4.2. MODULE 4.2. SELECTION CRITERIA FOR ENERGY TECHNOLOGIES 67 e f h problems ethics context j contemporary issues engage Brainstorm the considerations involved in choosing an energy technology. change Based on what you learned in your reflection, revise your decision-making plan to address ethical considerations. analyze How is each criterion defined and met? Devise a system for decision-making and test it with a few example energy technologies. reflect What difference does it make how the criteria are framed and evaluated against each other? What are the ethical considerations? Figure 4.2: Generators at Hoover Dam, Jon Sullivan, PDphoto.org. Public Domain. http://commons. wikimedia.org/wiki/File:Hoover_Dam%27s_generators2.jpg. anything a go/no-go criterion where something must be met at a given level or the technology should be rejected? Which if any criteria can be traded off against another? Develop a process for deciding about a technology – be careful of tools such as weighted objectives trees [10] or cost-beneﬁt analysis [11] that might not capture all considerations. Do a test run comparing several energy technologies – what comes out on top and why? 3. Reﬂect. How do different methods of decision-making, or different deﬁnitions of criteria, affect the choice that ends up on top? What ethical considerations come into play in setting up the rules of decisions? How do we currently make decisions about energy technologies? How should we? Who should devise criteria or decision-making plans, and who should apply them? 4. Change. Based on what you learned in your reﬂection, revise your decision-making plan to be more responsive to the ethical considerations you discussed. 4.2.2 EXPLORATION 2: EVALUATING AND SELECTING POWER GENERATION TECHNOLOGIES 1. Engage. Select an energy technology to evaluate (this could be a real technology in use or an ideal cycle you are studying – see Table 4.2 for ideas). You may want to have each person in 68 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY Table 4.1: Some Suggested Criteria for Energy Choices. Cost Efﬁciency Scale Sustainability Reliability Safety Rate Human impacts Social structures required engage Select an energy technology to evaluate and gather basic information about it. change What would you change about your course or textbook, given what you learned? analyze Evaluate the technology according to specified criteria. reflect What was difficult about the evaluations? What was surprising? What did you learn? Figure 4.3: The Brazos Wind Farm, also known as the Green Mountain Energy Wind Farm, near Fluvanna, Texas. Public domain. http://upload.wikimedia.org/wikipedia/commons/8/ 8b/GreenMountainWindFarm_Fluvanna_2004.jpg. the class choose a different one and compare results. For some technologies such as coal-ﬁred power plants, there are many different designs with different characteristics – so you will need to be speciﬁc about the type of plant, and in some cases, the type of fuel as well. If you are doing the assignment individually, you might choose more than one technology or plant designs, so you can compare those. Research how the technology works and other information relevant for your evaluation and write a brief description. 4.2. MODULE 4.2. SELECTION CRITERIA FOR ENERGY TECHNOLOGIES 69 2. Analyze. Evaluate each technology using the criteria you developed. Try to take uncertainty into account by working with reasonable ranges of values where appropriate. 3. Reﬂect. What was most difﬁcult about conducting the evaluations? What was most surpris- ing? How do the social and technical merge, interrelate and overlap in these considerations, becoming the socio-technical? What did you learn? 4. Change. What would you change about your course or textbook to incorporate this material? Where does it ﬁt? How would you teach it? Table 4.2: Possible Technologies to Consider for Evaluation and Selection. 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Engage. Select a transportation technology to evaluate. Use Table 4.3; though not exhaustive by any means, it provides a place to start. Begin with choosing an intended application (pas- senger or freight, start and end points?). Then mix and match choices of vehicle types, power source, and thermodynamic cycle as appropriate. There are many choices and conﬁgurations; be speciﬁc, and be careful, as some choices aren’t appropriate for all combinations. Research how the technology works and other information relevant for your evaluation and write a brief description. 2. Analyze. Evaluate each technology using the criteria you developed. Try to take uncertainty into account by working with reasonable ranges of values where appropriate. 70 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY engage Select a transportation technology to evaluate and gather basic information about it. change What would you change about transportation infrastructure or standards? analyze Evaluate the technology according to specified criteria. reflect What was difficult about the evaluations? What was surprising? What did you learn? Figure 4.4: Trafﬁc congestion, Brasilia, Brazil. Photo by Mario Roberto Duran Ortiz (Mariordo). Used with GNU Free documentation license http://upload.wikimedia.org/wikipedia/commons/e/ ec/Traffic_Congestion_Brasilia.jpg. 3. Reﬂect.What was most difﬁcult about conducting the evaluations? What was most surprising? What was different about these considerations compared with power generation? How do you feel being put in the position of decision-maker here? Who should decide? Government? Technocrats? Consumers? Citizens? 4. Change.What would you change about transportation infrastructure or standards (e.g., CAFE standards or limitations on shipping emissions) based on what you learned? Engage in public advocacy of your position by connecting with a group that represents your interests, writing a public ofﬁcial or media outlet. The explorations in this module have made clear some of the complexities involved in evalu- ating and selecting particular technologies for speciﬁc settings. The next module considers in greater depth how one evaluates the environmental performance, or “green-ness” of three different energy technologies. Table 4.3: A Wide Array of Options for Transportation Technologies. Choose a Mode of Travel and Vehicle Type, Fuel, and Cycle. 4.3. MODULE 4.3. IS IT GREEN? 71 Cycles Carnot Otto Diesel Brayton Stirling Rankine 2-or 4-stroke? Mode Vehicle type Fuel/Power type Road Cars Diesel (incl. 5-100% biodiesel) Tractor-trailers Buses Bicycles Water Rowboats Motorboats Cargo ships Sailboats Cruise ships Passenger planes Cargo planes Passenger trains Freight trains Air Rail Gasoline (incl. reformulations, oxygenates, up to 100% ethanol) Jet Fuel (conventional, biofuel) Electric (multiple sources) Electric Hybrid Steam (multiple sources) Hydrogen Fuel Cell (multiple sources) Wind Solar Human Power Natural Gas (fossil fuel or biodigested?) Biomass (wood, dung, grass, etc.) 4.3 MODULE 4.3. IS IT GREEN? e problems g communi- cation h context i lifelong learning j contemporary issues This module explores three instances where energy activities are labeled green, but upon closer examination, their claim to sustainability is perhaps more limited than previously assumed. Is nuclear power a green alternative to carbon-based power generation? Under what circumstances can ethanol be considered a sustainable fuel choice? When eastern power plants seek out low-sulfur coal from the western United States to control air pollution and acid rain, what environmental costs are introduced in transportation? In each case you are challenged to think more deeply about what sustainability might mean. 4.3.1 EXPLORATION 1: NUCLEAR POWER AS A GREEN ALTERNATIVE? 1. Engage. Patrick Moore [12] made waves when he published a “green” argument for nuclear power in 2006: http://www.washingtonpost.com/wp-dyn/content/article/2006/ 04/14/AR2006041401209.html. 72 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY engage Read widely on the debate over nuclear power as a green alternative. What are the arguments? change Advocate for your position in the public sphere. Join an action group, attend a rally, or write a public official. analyze reflect Evaluate the best arguments on both sides and make an evaluative judgment whether nuclear power is green. How did you make your decision? What criteria did you use in evaluating sources and their content? Figure 4.5: Have a nice day. Is nuclear as green as it looks? http://www.ecosprinter.eu/wp- content/uploads/2010/10/nuclear.jpg. Greenpeace [13] disputed Moore’s claims of afﬁliation with their organization and pointed out his ties to the nuclear industry: http://www.greenpeace.org/usa/en/campaigns/ nuclear/patric-moore-background-inform/. While some environmentalists see nu- clear power as an important part of addressing climate change, other environmentalists [14] take issue with the substance of Moor’s argument, pointing out the ways in which nuclear power is not green at all: http://www.counterpunch.org/montague11032008.html. Read these articles and search for additional material on the debate over whether nuclear energy is green. 2. Analyze. Evaluate the best arguments on both sides and make an evaluative judgment about whether nuclear power is green. In what ways is it green and in what ways is it not green? Be sure to include a range of conceptions of sustainability. Think holistically about the entire process from mining to waste disposal, and consider the environmental impacts of nuclear accidents. How do other “green” technologies such as wind, solar, and conservation/efﬁciency improvements compare? 3. Reﬂect. How did you make your decision? What criteria did you use in evaluating sources and their content? Are there considerations beyond the “green” aspect of nuclear power that affect its desirability? What are they? For example, does the fact that nuclear fuel presents a potential security risk raise issues of sustainability? Does the scale of a technology, or the amount of social control required to implement it, affect sustainability? Does its impact on marginalized communities, such as uranium mining on indigenous lands [15], affect sustainability? 4. Change. Advocate for your position in the public sphere. Join an action group, attend a rally or other event, or write a public ofﬁcial to express your views. 4.3. MODULE 4.3. IS IT GREEN? 73 4.3.2 EXPLORATION 2: ETHANOL engage Read debates on ethanol in Science. What are the key issues? change How will you take your independent learning strategies forward? analyze Write a dialogue among the paper authors to illustrate the key issues and authors’ main points. reflect What did you learn about reading the scientific literature to understand current topics in energy? Figure 4.6: Corn is the primary source of ethanol in the US. But is it a green choice? http://blogs. princeton.edu/chm333/f2006/biomass/ethanol%20corn%20gas.jpg. Is ethanol a green fuel? This is a surprisingly complex question to answer. It depends on what biosource is used to produce it, how it is produced, and perhaps most important, what is taken into account in the analysis, reﬂecting different deﬁnitions of what “green” means. In some cases, ethanol can provide a net beneﬁt, and in other cases, a net loss for the environment. How can you, as a student, or as a technically educated person who may not be an expert in this particular area, sort through literally hundreds of studies on this topic and come to an informed conclusion? This exercise guides you through one approach. 1. Engage. One useful place to go to learn about a topic with this level of policy relevance is the journal Science, which includes sections with readable introductions to technical issues in their public policy context. While the development of these debates over many years is itself quite interesting, here we will consider only a few of the most recent discussions of this issue in the journal. Read the following three articles: 74 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY Scharlemann and Laurance, How Green are Biofuels? [16] DOI: 10.1126/sci- ence.1153103. Robertson et al., Sustainable Biofuels Redux [17] DOI: 10.1126/science.1161525. Tilman et al., Beneﬁcial Biofuels: The Food, Energy, and Environment Trilemma [18] DOI: 10.1126/science.1177970. (Note: Some DOI links may be publicly available on the Internet, or you may need to authen- ticate through your campus libraries to access Science online.) 2. Analyze. Write a script that creates a dialogue (tri-alogue?) among the three articles to summa- rize their key positions and reﬂect the issues in the ethanol debate. Under what circumstances, if any, can ethanol be considered a sustainable fuel choice, and why? 3. Reﬂect. What did you learn from this exercise about using peer-reviewed articles to help you understand a current topic in energy? 4. Change. How can you take this independent learning strategy forward in other areas that spark your curiosity? 4.3.3 EXPLORATION 3: COAL TRAIN [19] 1. Engage. Read the essay “Coal Train” in John McPhee’s book Uncommon Carriers [20]. Why did the Clean Air Act of 1970 reinvigorate the railroading industry? Why don’t all eastern power plants use higher-Btu coal from nearby West Virginia and Pennsylvania as opposed to Wyoming? 2. Analyze. Perform a back-of-the-envelope calculation based on information in McPhee’s chap- ter. If a coal train weighs 3000 tons empty, and 19,000 tons when loaded with low-sulfur coal from Powder River Basin, and travels 1800 miles from Wyoming to Georgia: a. How much energy does it take to haul the coal this distance? Make simplifying assump- tions for an initial estimate. b. How much energy is in the coal being hauled? 3. Reﬂect. Under what conditions is it the “right” thing to do to move coal across the country? What criteria are you using to determine whether it is “right” or not? What other criteria that you haven’t considered might change the outcome of your evaluation? 4. Change. How does what you’ve learned here change your views on energy, if at all? How (if at all) does it change your consumption of energy? 4.4. MODULE 4.4. HOME ENERGY USES 75 engage Read John McPhee’s chapter on the Coal Train in Uncommon Carriers [20]. change How does this change your views on energy, if at all? How does it change your consumption? analyze Estimate the energy required to move a trainful of coal from Wyoming to Georgia, and how much energy that coal provides. reflect Under what conditions it is “right” to move coal across the country? What criteria influence this evaluation? Figure 4.7: Union Paciﬁc coal train with two locomotives (at the end) in Converse County close to Douglas, Wyoming USA. July 20, 2010. Photo by Wusel007. Used with permission under GNU Free Documentation License version 1.2 from http://commons.wikimedia.org/wiki/File:Union_ Pacific_Coal_Train_Douglas_WY.JPG. 4.4 MODULE 4.4. HOME ENERGY USES So far in this chapter we have primarily considered industrial and commercial uses of energy in electric power generation and transportation. c h design context This module turns our focus to applications in the home. It is interesting to note that engineering has traditionally focused on large-scale industrial and commercial applications, preferring these settings over the home environment. Historically, areas traditionally considered “women’s sphere” such as the home, or “women’s work” such as cooking or cleaning, were excluded from the engineering ﬁeld altogether, categorized instead as “home economics”[21]. Alice Pawley [22] has pointed out that the ﬁeld of engineering therefore looks something like Swiss cheese – certain areas that ought to be considered engineering are excluded, leaving holes. This module takes up to three explorations related to home energy uses: solar energy in cooking, three alternatives for refrigeration, and a Stirling-powered electrical generator combined with water ﬁltration. All three explorations have some potential and some limitations for sustainability, as well as applications in developed and developing nation settings. 76 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY 4.4.1 EXPLORATION 1: SOLAR COOKER engage Learn about designs of solar cookers. How do they work? What are the different types of designs available? change What would you change to improve your solar cooker for next time? analyze Design and build a solar cooker from scavenged objects. reflect Demonstrate your design. What worked well? What do you wish worked better? How does it fit or not fit with your culture’s cuisine and lifestyle? Figure 4.8: Solar cooker or solar barbecue Alsol 1.4 made in Spain: more information on http:// www.solarcookingatlas.com. Public domain. http://upload.wikimedia.org/wikipedia/ commons/e/ed/ALSOL.jpg. 1. Engage. Learn about designs of solar cookers. How do they work? What are the different types of designs available? What principles of heat transfer apply to their functioning? ◦ 2. Analyze. Design and build a solar cooker from scavenged or borrowed objects and tools ◦ that can bake a cookie (recommended temperature: 350 C; minimum temperature: 100 C). Make sure the cooker is of adequate size, easy to use and convenient, with low startup and cooking times. It should be durable and stable during operation. It should be aesthetically pleasing and achieve the highest quality construction possible, subject to the design constraints. Consider the ability of the cooker to collect sunlight at different times of day. You will need a method or device to help you determine whether the oven is aimed directly at the sun (do not look directly at the sun!) F, 160 ◦ 3. Reﬂect. Demonstrate your design. What worked well? What do you wish worked better? How does it ﬁt or not ﬁt with your culture’s cuisine? With your physical setting? With your lifestyle? (Or you could choose an application setting different from your own for this same evaluation.) Compare solar cookers to biomass stoves, natural gas stoves, or electric stoves, considering criteria from Module 4.2. 4. Change. What would you change to improve the design of your cooker in terms of its technical performance and/or its suitability for use in your culture? 4.4.2 EXPLORATION 2: REFRIGERATION 4.4. MODULE 4.4. HOME ENERGY USES 77 engage Learn about evaporative coolers, vapor-compression refrigeration, and absorption refrigeration. change What else do you need to know to complete a refrigeration design for a particular application? analyze Estimate design requirements for a single family using each refrigeration technology. reflect Should the analysis you did be considered engineering? How did your systems compare? Why does the US have mostly vapor-compression? Figure 4.9: Old Refrigerator, Restaurant, Mandeville, LA. Photo by Ingfrogmation of New Orleans. (Multi-license with GFDL and Creative Commons CC-BY 3.0) http://commons.wikimedia.org/ wiki/File:Mandeville_Maxens_refrigerator.JPG. 1. Engage. Learn about evaporative coolers (see Module 2.3), vapor-compression refrigerators, and absorption refrigerators. How does each work? What are they used for, and why are these uses important? What materials and energy are required for each? What are their typical operating temperatures? 2. Analyze. Select an application for each type of refrigeration in different home settings. Provide a back-of-the envelope estimate of the design requirements for a single family application in each setting. Give dimensions of the refrigerated space, amount of food that can be cooled, approximate temperature of the food, and energy requirements. Make reasonable and justiﬁed assumptions. 3. Reﬂect. Should the analysis you just did be considered engineering? Why or why not? How did the energy requirements compare for your different systems? Why do you think we have mostly vapor-compression systems in the United States and not other technologies? (See Ruth Schwartz Cowa’s history [23] at http://epl.scu.edu/∼stsvalues/readings/cowan2. pdf for an answer.) What recommendations would you make for home refrigeration in different settings? 78 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY 4. Change. What (else) would you need to know in order to complete a full design for a particular application 4.4.3 EXPLORATION 3: DEAN KAMEN’S STIRLING ENGINE engage Learn about Dean Kamen’s Stirling Engine that simultaneously creates household electricity and purifies water. analyze Evaluate the inventor’s claim about the performance of the engine. change How would you change the project? How has the project changed since the article was written? reflect Is Kamen’s technical claim reasonable? What other factors are important for implementation in the developing world? Figure 4.10: Dean Kamen’s Stirling Engine produces both electricity and heat to purify water in the Slingshot water ﬁlter. http://www.geekologie.com/2008/04/22/water-cleaner.jpg. 1. Engage. Consider the following excerpt from a recent article in the Manchester, NH Union Leader [24] http://forums.segwaychat.com/archive/index.php/t-286.html. NH inventor Kamen eyes Stirling Engine. By KATHARINE McQUAID, Union Leader Staff. Inventor Dean Kamen is inching closer to the creation of a Stirling Cycle Engine that can create enough electricity to run a few household appliances, while at the same time making contaminated water drinkable.... Kamen said he imagines the device will give people in remote villages of India and other third world countries a constant source of clean, safe, drinking water, as well as a central source of electricity. ‘‘It could be used to make a central place where people go to charge batteries for computers or cell phones, where people 4.5. MODULE 4.5. ETHICS OF ENERGY DISASTERS 79 could get access to electricity so that they could have light at night and, all the while, it could be turning 10 gallons of just about anything into potable water,’’ Kamen told Rather. The version unveiled by Kamen on last night’s program creates about 300 continuous watts of electrical power, according to Rather. 2. Analyze. Evaluate this claim by considering an ideal Stirling engine with helium as the working ﬂuid (Kamen’s patent states that helium could be used). Suppose it operates at one cycle per second, between temperature limits of 300 K and 1500 K, and pressure limits of 150 kPa and 1.5 MPa. Assuming the mass of the helium used in the cycle is 0.1 kg, determine the thermal efﬁciency of the cycle, the amount of heat transfer in the regenerator, and the work output per cycle. Assume that water puriﬁcation is achieved by boiling off all the water once, and that no heat is recovered through condensation. 3. Reﬂect. Is Kamen’s claim reasonable? Why or why not? What other considerations are nec- essary to determine whether this technology is suited to the proposed application? What else would you need to know? 4. Change. How would you change the project, either the device or implementation plan? How has the project changed since this article was written? Having explored the engineering involved in home uses of energy, the next module connects consumer energy choices with large scale energy disasters such as oil spills and nuclear accidents. 4.5 MODULE 4.5. ETHICS OF ENERGY DISASTERS This module examines connections between the ethics of two energy disasters: The BP Oil Spill following the explosion of the Deepwater Horizon rig in April 2010, and the meltdowns at the Fukushima Daiichi nuclear power plant following the earthquake and tsunami in Japan in March 2011. f ethics j contemporary issues Each disaster has parallels with past disasters that exclude it from being considered an “isolated incident.” As with mining accidents for energy resources such as coal and uranium, these disasters form patterns that repeat, in this case it seems every few decades. Social scientists who have studied engineering ethics cases such as the Ford Pinto case [25] or the space shuttle Challenger disaster [26] have pointed out the ways in which the cases don’t boil down to individual decisions of professional engineers, but have at their heart institutional and organizational norms (and beyond these, political and economic forces acting on organizations) that produce these outcomes as a matter of course. 80 4. THINKING BIG PICTURE ABOUT ENERGY AND SUSTAINABILITY engage Learn about the BP oil spill and Fukushima meltdowns. In what ways could they have been predicted 30 years ago? change Develop an effective concrete strategy to prevent future energy disasters, focusing on the collective nature of the disasters. analyze What are the structural forces that shaped the engineering of each facility? Were events preventable or inevitable? reflect Given that we can anticipate that things we can’t anticipate will occur, what kinds of preventive design strategies should engineers employ? Figure 4.11: Deepwater Horizon Offshore Drilling Unit on Fire, April 21, 2010. US Coast Guard photo, Public domain. http://cgvi.uscg.mil/media/main.php?g2_view=core.DownloadItem&g2_ itemId=836364&g2_serialNumber=5. 1. Engage.Watch the Rachel Maddow Show segment “That was then, this is then”[27] (http:// www.msnbc.msn.com/id/26315908/) from May 26, 2010. What are the similarities be- tween the BP Spill and the Ixtoc 1 Spill in 1979? Read the March 15, 2011 New York Times ar- ticle [28] on the Mark I containment system used at the Fukushima Daiichi reactors: http:// www.nytimes.com/2011/03/16/world/asia/16contain.html. What were the prob- lems identiﬁed in the early 1970s with the Mark I containment system? 2. Analyze. Watch a January 11, 2011 Maddow segment [29] in which a government report labels the BP disaster foreseeable and preventable with regulatory oversight. http://www. msnbc.msn.com/id/26315908/#41026520.Then watch this March 25, 2011 segment [30] that exposes regulators issuing new deep water drilling permits with the same blowout preven- ter device found to have a ﬂawed design: http://www.msnbc.msn.com/id/26315908/# 42278768. In what sense are these events preventable? In what sense are they predictable, or even inevitable? Watch “A is for Atom” a BBC documentary on nuclear power’s history [31]: http://www. bbc.co.uk/blogs/adamcurtis/2011/03/a_is_for_atom.html. While the entire doc- umentary is of interest, key segments are at minutes 20-29 and 36-42. What structural forces shaped the scale and safety system designs of nuclear plants in the United States? REFERENCES 81 3. Reﬂect. Sarah Pfatteiche’s book on the ethics of engineering and the 9/11 collapse of the World Trade Center asks a number of questions in the wake of that tragedy that can be translated for these and other energy disasters [32]. To what extent are energy disasters “business as usual?” Should they be prevented? Can they be prevented? Who is responsible to prevent them? It can be argued that in both cases considered here, energy companies believed they were taking sufﬁcient care and protecting people and the environment “to the extent possible.” What makes such measures possible or impossible? Are economics and a company’s desire for proﬁt-making legitimate constraints on the health, safety, and welfare of the public? Why or why not? Do engineers have a duty to design for the unanticipatable? That is, if we know things will go wrong that we can’t predict speciﬁcally (and thus design for), can we design out some of the problems – for example, by working at a smaller scale in the case of nuclear power, or not as deep in the case of ocean oil drilling? Can better regulation prevent disasters, or are other changes required? What are the responsibilities of individual engineers? Of their management? Of energy companies? Of government? Of consumers/citizens? 4. Change. Develop a strategy for change – among energy consumers, corporate culture at an energy company, or governmental regulations and oversight – that would best prevent future energy disasters. REFERENCES [1] Jensen, D. and MacMillan, S. (2007). As the World Burns: 50 Simple Things You Can Do to Stay in Denial. New York: Seven Stories Press. Cited on page(s) 64 [2] Environmental Protection Agency. Inventory Report. Accessed June 8, 2011 from http://www.epa.gov/climatechange/emissions/ usinventoryreport.html. Cited on page(s) 64, 65 (2011). US Greenhouse Gas [3] International Energy Agency. (2010). CO2 Emissions from Fuel Combustion High- lights. 2010 Edition. Accessed June 8, 2011 from http://www.iea.org/co2highlights/ CO2highlights.pdf. Cited on page(s) 64, 65 [4] Catalano, G.D. (2006). Engineering Ethics: Peace, Justice and the Earth. San Rafael, CA: Morgan and Claypool. Cited on page(s) 65 [5] Harris, C.E., Pritchard, M.S. and Rabins, M.J. (2005). Engineering Ethics: Concepts and Cases. 3rd ed. Stamford, CT: Thomson Wadsworth. Cited on page(s) [6] Martin, M.W. and Schinzinger, R. (1996). Ethics in Engineering. 3rd ed. New York: McGraw- Hill. Cited on page(s) [7] Whitbeck, C. (1998). Ethics in Engineering Practice and Research. New York: Cambridge Uni- versity Press. Cited on page(s) 65 82 REFERENCES [8] Shepherd, W. and Shepherd, D.W. (2003). Energy Studies. 2nd ed. London: Imperial College Press. Cited on page(s) 66 [9] Winner, L. (1986). Do Artifacts have Politics? In The Whale and the Reactor: A Search for limits in an age of high technology. Chicago: University of Chicago Press, 19–39. Accessed June 9, 2011 from http://zaphod.mindlab.umd.edu/docSeminar/pdfs/Winner.pdf Cited on page(s) 66 [10] Dym, C.L., Little, P., and Orwin, E.J. (2009). Engineering Design: A Project-Based Introduction. New York: Wiley. Cited on page(s) 67 [11] Fischhoff, B. (1977). Cost Beneﬁt Analysis and the Art of Motorcycle Maintenance. Policy Sciences, 8: 177–202. Accessed June 9, 2011 from http://sds.hss.cmu.edu/media/pdfs/ fischhoff/CostBenefitAnalysisMotorcyc.pdf. DOI: 10.1007/BF01712294 Cited on page(s) 67 [12] Moore, P. (2006). Going Nuclear: A Green Makes the Case. Washington Post, April 16, 2006. Accessed June 9, 2011 from http://www.washingtonpost.com/wp-dyn/content/ article/2006/04/14/AR2006041401209.html Cited on page(s) 71 [13] Greenpeace USA. Patrick Moore Background Information. Accessed June 9, 2011 from http://www.greenpeace.org/usa/en/campaigns/nuclear/patric-moore- background-inform/ Cited on page(s) 72 [14] Montague, P. (2008). Is Nuclear Power Green? Counterpunch, November 3, 2008. Accessed June 9, 2011 from http://www.counterpunch.org/montague11032008.html Cited on page(s) 72 [15] Brugge, D., deLemos, J.L., Bui, C. (2007). The Sequoyah Corporation Fuels Re- lease and the Church Rock Spill: Unpublicized Nuclear Releases in American In- dian Communities. American Journal of Public Health, 97(9): 1595–1600. Accessed June 12, 2011 from http://www.sric.org/Churchrock/SFCChurchRockAJPH2007.pdf DOI: 10.2105/AJPH.2006.103044 Cited on page(s) 72 [16] Scharlemann, J.P.W. and Laurance, W.F. (2008). How Green are Biofuels? Science 319(5859): 43–44. DOI: 10.1126/science.1153103 DOI: 10.1126/science.1153103 Cited on page(s) 74 [17] Robertson, G.P., Dale, V.H., Doering, O.C., et al. (2008). Sustainable Biofuels Redux. Science, 322 (5898): 49–50. DOI: 10.1126/science.1161525 Cited on page(s) 74 [18] Tilman, D., Socolow, R., Foley, J.A., Hill, J., Larson, E., Lynd, L., Pacala, S., Reilly, J., Searchinger, T., Somerville, C., and Williams, R. Beneﬁcial Biofuels—The Food, Energy, and Environment Trilemma. Science, 325 (5938): 270–271. DOI: 10.1126/science.1177970 Cited on page(s) 74 REFERENCES 83 [19] Michael Greenﬁeld, Chemical Engineering, University of Rhode Island had the idea for this exploration. Cited on page(s) viii, 74 [20] McPhee, J. (2006). Uncommon Carriers. New York: Farrar, Strauss, and Giroux, pp. 185–236. Originally published in two parts (Coal Train I: Disassembling the Planet for Powder River Coal and Coal Train II: Going into Thunder) in The New Yorker, October 32005, p. 72, and October 10, 2005, p. 62. Cited on page(s) 74 [21] Bix, A. (2002). Equipped for life: Gendered technical training and consumerism in home economics, 1920–1980. Technology and Culture, 43: 728–54. DOI:10.1353/tech.2002.0152. DOI: 10.1353/tech.2002.0152 Cited on page(s) 75 [22] Pawley, A. (2012). What Counts as “Engineering:” Towards a Redeﬁnition. In Engineering and Social Justice: In the University and Beyond. C. Baillie, A. Pawley, and D. Riley, eds. West Lafayette, IN: Purdue University Press. Cited on page(s) 75 [23] Cowan, R. S. (1985). How the Refrigerator Got Its Hum. In D. MacKenzie & J. Wajcman, (Eds.),The Social Shaping Of Technology. Philadelphia: Open University Press, pp. 202–218. Ac- cessed May 18, 2011 from http://epl.scu.edu/˜stsvalues/readings/cowan2.pdf. Cited on page(s) 77 [24] McQuaid, K. (2002). NH inventor Kamen eyes Stirling Engine. Union Leader (Manchester, NH) November 14, 2002, P. A1. Available June 8, 2011 at http://forums.segwaychat. com/archive/index.php/t-286.html Cited on page(s) 78 [25] Lee, M.T. and Ermann, M.D. (1999). Pinto “Madness” as a Flawed Landmark Narrative: An Organizational and Network Analysis. Social Problems 46(1): 30–47. Accessed March 30, 2011 from http://www.jstor.org/pss/3097160 DOI: 10.1525/sp.1999.46.1.03x0240f Cited on page(s) 79 [26] Vaughan, D. (1996). The Challenger Launch Decision: Risky Technology, Culture, and Deviance at NASA, Chicago: University of Chicago Press. Cited on page(s) 79 [27] Maddow, R. (2010). That was then, this is then. In B. Wolff (Producer), The Rachel Maddow Show, New York: MSNBC. May 26, 2010. Accessed June 9, 2011 from http://www.msnbc. msn.com/id/26315908/ Cited on page(s) 80 [28] Zeller, Jr., T. (2011). Experts had long criticized potential weakness in design of stricken reactor.New York Times, March 15, 2011. Accessed June 9, 2011 from http://www.nytimes. com/2011/03/16/world/asia/16contain.html. Cited on page(s) 80 [29] Maddow, R. (2011). Gulf Spill Report Shows String of Failures. In B. Wolff (Producer), The Rachel Maddow Show, New York: MSNBC. January 11, 2011. Accessed June 9, 2011 from http://www.msnbc.msn.com/id/26315908/#41026520. Cited on page(s) 80 84 REFERENCES [30] Maddow, R. (2011). Dubious Assurances on Deepwater Drilling Safety. In B.Wolff (Producer), The Rachel Maddow Show, New York: MSNBC. March 25, 2011. Accessed June 9, 2011 from http://www.msnbc.msn.com/id/26315908/#42278768. Cited on page(s) 80 [31] Curtis, A. (Writer and Producer) (1992). A is for Atom [documentary] London: BBC. Ac- cessed June 9, 2011 from http://www.bbc.co.uk/blogs/adamcurtis/2011/03/a_is_ for_atom.html Cited on page(s) 80 [32] Pfatteicher, S.K.A. (2010). Lessons Amid the Rubble: An Introduction to Post-Disaster Engineer- ing. Baltimore, MD: Johns Hopkins University Press. Cited on page(s) 81 Author’s Biography 85 DONNA RILEY Donna Riley is a founding faculty member and Associate Profes- sor in the Picker Engineering Program at Smith College, where she has been teaching thermodynamics for over 10 years. She received her B.S.E. in Chemical Engineering from Princeton University and a Ph.D. in Engineering and Public Policy from Carnegie Mellon University. Her technical research combines methods in engineering and the social sciences to characterize and communicate chemical risk. She seeks to integrate quantita- tive modeling of chemical risks (from sources to exposure end- points) with an understanding of the ways in which human beliefs and behavior inﬂuence risk. Past projects have involved charac- terizing the risks of mercury use as part of religious and folk traditions in Latino and Caribbean communities, and developing improved consumer-product warnings. She is currently collaborating with chemists at Smith and the University of Massachusetts on developing a community-oriented air quality research lab. In 2005 Riley received a CAREER award from the National Science Foundation for imple- menting pedagogies of liberation, based on the work of Paulo Freire, bell hooks, and others, into engineering education. Aspects of critical pedagogies that are operationalized in Riley’s classrooms include connecting course material to student experience, emphasizing students as authorities in the classroom, integrating ethics and policy considerations in the context of social justice, problematiz- ing science as objectivity, and incorporating contributions from women, people of color, and people living in the global South. This is Riley’s second book with Morgan and Claypool, having published Engineering and Social Justice in 2008.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=7224644.pdf&bkn=7224643&pdfType=book	Series ISSN: 1932-3166 A, B, See… in 3D A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu, PhD, P.E., Professor, San Antonio College The workbook provides over 100 3D visualization exercises challenging the student to create three dimensions from two. It is a powerful and effective way to help engi- neering and architecture educators teach spatial visualization. Most of the 3-D visual- ization exercises currently being used by students in Design and Graphics classes pres- ent the objects in isometric views already in 3-D, asking the viewer to create multiple views, fold patterns, manipulate, reflect, or rotate them. The exercises presenting the objects in incomplete multiview projections asking the students to add missing lines use mostly real 3D objects that are more easily recognizable to help the student cor- relate 2D with 3D. This workbook uses a different approach. Each view of the solid represents a letter of the alphabet. The letters are by definition 2D representations and when they are com- bined to create a 3D object, visualizing it becomes quite a challenge. This workbook is intended for Engineering, Architecture, and Art students and faculty that want to increase their 3-D visualization skills w w w . m o r g a n c l a y p o o l . c o m 9 781627 058186 ISBN: 978-1-62705-818-6 9 0 0 0 0 I I D M T R U I A , B , S E E … I N 3 D M O R G A N & C L A Y P O O L A, B, See… in 3D A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu, PhD, P.E. A,B,See… in 3D A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu, PhD, P.E. San Antonio College Copyright © 2015 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. A,B, See.... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu www.morganclaypool.com ISBN-13: 9781627058186 paperback ISBN-13: 9781627058193 ebook First Edition 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America Contents Table of Content .............................................................................................................. 1 Abstract ........................................................................................................................... 2 Introduction .................................................................................................................... 3 Methodology ..................................................................................................................... List of Problems by Difficulty ......................................................................................... 10 Alphabetical Listing by Letter Combinations ................................................................. 11 Chapter 1 - Combination of Cubes (C) ............................................................................ 12 Level of difficulty: Easy Chapter 2 - First Level (F) .............................................................................................. 25 Level of difficulty: Low Chapter 3 - Second Level (S) .......................................................................................... 52 Level of difficulty: Medium Chapter 4 - Third Level (T) ............................................................................................. 84 Level of difficulty: Difficult List of Problem Solutions by Chapter .............................................................................106 Chapter 1 (C) - Solutions ............................................................................................. 107 Chapter 2 (F) - Solutions ............................................................................................. 111 Chapter 3 (S) - Solutions ............................................................................................. 124 Chapter 4 (T) - Solutions ............................................................................................. 137 Author Info ..................................................................................................................144 1 ABSTrACT The workbook provides over 100 3D visualization exercises challenging the student to create three dimen- sions from two. It is a powerful and effective way to help engineering and architecture educators teach spatial visualization. Most of the 3-D visualization exercises currently being used by students in Design and Graphics classes present the objects in isometric views already in 3-D, asking the viewer to create multiple views, fold patterns, manipulate, reflect, or rotate them. The exercises presenting the objects in incomplete multiview projections asking the students to add missing lines use mostly real 3D objects that are more eas- ily recognizable to help the student correlate 2D with 3D. This workbook uses a different approach. Each view of the solid represents a letter of the alphabet. The letters are by definition 2D representations and when they are combined to create a 3D object, visualizing it becomes quite a challenge. This workbook is intended for Engineering, Architecture, and Art students and faculty that want to increase their 3-D visualization skills. 2 Introduction There is ample evidence that instruction in spatial visualization skills is effective in improving outcomes for engineering students. Research conducted since the early 1990’s has proven that spatial visualization practice and training leads to better grades in engineering graphics and engineering coursework, and in the retention of underrepresented groups in the field. In 1993 Dr. Sheryl Sorby (1998, 2006, 2009) of Michigan Technological University began work under and NSF grant to figure out why first-year women engineering students were more than three times as likely to fail the Purdue Spatial Visualization Test: Rotations (PSVT:R) as men, and what could be done about it. Sorby’s analysis of the results of the test and a background questionnaire she administered to test-takers showed that previous experience in design-related courses such as drafting, mechanical drawing, and art, as well as play as children with construction toys such as Legos, Lincoln Logs, and Erector Sets, predicted good performance on the PSVT:R. She and her colleagues then developed a three-credit hour spatial- visualization course and administered it to students who had failed the PSVT:R. The course covered topics such as cross sections of solids, sketching multiview drawings of simple objects, and paper folding to illus- trate 2-D to 3-D transformations. In the lab, students used solid-modeling computer-aided design (CAD) Software. Student’s tests scores on the PSVT:R improved from an average of 52% to an average of 82%. Work by Hsi, et al (1997) supported the effect of spatial strategies instruction on erasing gender differences and improving grades for engineering students. Additional spatial visualization training was also discovered to positively affect retention in engineer- ing for women. Sorby found that among the women who initially failed the PSVT:R and took the spatial- visualization course between 1993 and 1998, 77% were retained in Engineering Design, compared to 48% of the women who didn’t take the course (Female n=251). In additional studies Sorby also found that middle school girls who took a spatial-visualization course took more advanced-level math and science courses in high school than did girls who did not take the course, and that the materials were shown to be effective in improving spatial skills for undergraduate students outside of engineering, and for students in high school. After offering the three-hour spatial visualization course for six years (yielding improvements of 20 to 32 percentage points on the PSVT:R), Sorby condensed the course to a one-hour course and tested it be- tween 2000 and 2002, seeing average improvement on the PSVT:R of 26%. In 2003 Sorby, Beverly Baart- mans and Anne Wysocki, published a multimedia software-workbook package which contained content similar to the course Introduction to 3D Spatial Visualization, now used for engineering graphics education throughout the nation. At Penn State Erie, Dr. Kathy Holliday-Darr and Dr. Dawn Blasko (2009) conducted a one-credit- hour intervention with mechanical engineering technology and plastic engineering technology students who performed below criteria on the PSVT, the Mental Rotation Test (MRT, and paper-folding and water- level tasks. They used the Sorby and Wysocki multimedia package and found significant improvement compared to an untreated control group. The improvement was correlated with grades in other courses and scores on spatial tasks correlated with overall GPA and key courses taken in the following semester and year. 3 At Virginia State University, a Historically Black College or University (HBCU), retention of minori- ties in STEM-related majors tended to be lower than their non-minority peers, and students enrolled in introductory engineering graphics courses had significantly lower-than-average test scores on the PSVT. Dr. Nancy Study piloted changes to engineering graphics courses, including the use of sketching, blocks and multimedia, that resulted in improvement of students’ visualization abilities. Significantly higher GPAs were earned by students taking the enhanced pilot engineering graphics course, compared to a control group that did not take the enhanced course, and a higher percentage of students in the test group were retained both in an engineering or technology major and at the university even if they did change their major. Uttal, Meadow and Newcombe, (2010) conducted a meta-analysis of 200 studies on improvement of spatial skills and found that the average effect size of improvement for students who receive extensive prac- tice on spatially-relevant skills, such as mentally rotating figures or disembodying, was .53 (equivalent to an intervention improving SAT scores by more than 50 points or IQ scores by more than 7.5 points). They also found that the effects of training endured over time, after practice interventions were completed. Although the materials currently being used nationally are now assisting the new generations of en- gineering students to succeed, they do not challenge the student to create three dimensions from two. On today’s market there are some valuable tools with which engineering and architecture educators teach spatial visualization. Most of the 3-D visualization exercises currently being used for students in Design and Graphics classes present objects in isometric views already in 3-D, asking the viewer to create multiple views, fold patterns, manipulate, reflect, or rotate them. The materials presented in this workbook take a universally accepted 2-D flat pattern (a letter) and ask the viewer to mold it as part of a 3-D solid, in com- bination with two other flat-pattern letters from adjacent views. This workbook is intended for Engineering, Architecture, and Art students and faculty that want to increase their 3-D visualization skills. 4 Methodology The exercises use alphabet letters represented in standard multiview projections (front, top, right, left, or bottom side views). The 3-D object made up of the three letters, one in each view, has to be mentally as- sembled in 3-D, with no assistance from an isometric representation of the solution figure. The problems ask the solver to break out of the 2-D image of the letter and visualize the third dimension, the depth, or “Z axis”, and combine with the other two letters from the other views of the 3-D object. The exercises are presented with increasing degrees of difficulty to help students improve their 3-D visualization skills. No other universally-recognized flat patterns are currently being used to enhance students’ ability to spatially visualize 3-D objects. “A, B, See...” presents over 100 three-letter combinations many of them with multiple solutions and a brief instructional text on how to solve these exercises. The problems will build on the body of knowledge already developed in early stages of graphics core concepts such as: • Alphabet of lines (visible, hidden, and center lines) • Multiview Orthographic Projections • Surface and Edge Classifications (Normal, Inclined, Oblique, and Curved) The graphical problems are presented in order of increasing difficulty and they are designed to gradu- ally break students out of their 2-D preconceptions about 3-D space. The student must learn how to represent a variety of surfaces normal, inclined, oblique and cylindrical in multiple positions, visible and invisible, in edge view, true size and shape, or foreshortened in order to complete these assignments. No other universally-recognized flat patterns are currently being used to enhance students’ ability to spatially visualize 3-D objects. 5 Figure 1 Solution: 9 cubes Figure 2 Solution: 13 cubes How many cubes make the solid shown here in three views? _____ cubes Figure 3 6 Solution Figure 4 Figure 5 See solutions for Figures 4 and 5 on page 9. 7 Because letters are universally known, they are images that can be kept in mind by the student as they are mentally manipulated, rather than forcing the student to compare shapes on a page. Their universality also allows students to draw them from memory and manipulate them mentally. They can work on the assignments everywhere, at home, at lunch, or when they go for a walk in the park. For this reason, the solutions for these exercises are also easy to compare with other students’ solutions and argue about. In addition, within the alphabet soup is a progression of easy-to-difficult that gives students a sense of accomplishment as they advance through spatial skills levels. All letters of the alphabet are present in this workbook and while just as challenging as isometric workbook exercises, the letter-based problems appear more like puzzles, and therefore more like fun. Procedure The table of content has two configurations. The exercises are organized following the letter combinations and by the level of difficulty. There are five letter combinations and four categories of difficulty listed under four chapters. The first group of problems show straight letters that can be made completely out of cubes and, with one exception, have only normal edges and surfaces. The challenge is to determine the exact number of cubes needed to make the object despite the fact that a cube might appear in more than one view. The last three problems have more than one solution and the instructions ask for the minimum number of cubes required. The second chapter “First Level” takes the cube problems and by eliminating the cubes presents them as solids with straight faces without the cube partitions. Ten more combinations of letters are defining new solids in this chapter. Beginning with this chapter, the problems ask the solver to place the missing lines standing for visible and hidden edges and surfaces within the confines of the contours to complete the views. It is suggested that each exercise should be limited initially to the following cross sectional shapes: The following chapters “Second Level” and “Third Level” are increasingly challenging, as the solvers have to visualize letter parts that are not where they are appear to be from the 2D image. Almost all the problems have multiple solutions as the letter parts can be visualized from rectangular prisms, to triangular ones, or even cylindrical shapes as indicated above. At these advanced stages 8 students can experiment with other shapes as well such as a hexagon or a rhombus. The challenge is to have the correct representation with visible, hidden, and centerlines in each view. The advantage of all these exercises is that the solution can be easily verified for correctness by building a 3D model in any 3D modeling package. The standard front, top, and side view projections of the model should reveal all the necessary lines for verification. Many times the students propose new solutions or start to look for new combination of letters which is a challenge in itself because not all combinations of three letters can form a solid. That is another way to improve the visualization abilities. Imagination is the only limit! Solutions for Figures 4 and 5: Solution 1 Solution 2 Solution 3 Solution 1 9 List of Problems by Difficulty Chapter 1 - Combination of Cubes Level of difficulty: Easy Chapter 2 - First Level Level of difficulty: Low Chapter 3 - Second Level Level of difficulty: Medium Chapter 4 - Third Level Level of difficulty: Difficult Page # 12 25 52 84 10 Alphabetical listing by Letter Combinations Letters Made Out of Cubes EFT C 09 HHH C 10 C 08 HLE C 05 HLL C11 HTT C 03 IIH C 02 IIL C 01 IIT C 04 LLL C 12 LUF C 06 TTT UHL C 07 Three Identical Letters DDD F 21 S 22 EEE FFF S23 HHH F 11 F 06 LLL OOO F19 F 10 TTT T 21 XXX Two Identical + One Different EEN S 13 F 04 IIA F 03 IIH IIL F 02 IIM F 05 F 01 IIT F 09 LLA LLD F 08 LLQ S 03 TTH F 15 One Different + Two Identical ATT F 14 HLL F 07 MOO T 10 OHH F 16 XAA T 15 XTT F 13 XVV T 16 ZEE T 07 ZHH F 17 ZOO T 09 All Three Different Letters AUL DEL EDU EFD EFT ELM FEZ FJT GOP HEB HLE HMT HUT HUV 1 HUV 2 HZT KLE LCX LED LOT LUF MHE MHF MLU MOE MUD MUE MUG MUL MUZ NHB NUE NUL OLE OUA PET PFT PLE POT RET SET TAP UAL UHL VLT WMX WTF YTF ZEF ZXN F 26 F 20 S 12 S 14 F 12 S 15 T 01 T 02 T 03 T 18 F 18 S 01 S 16 S 17a S 17b S 24 S 05 T 04 S 02 S 04 F 24 T 05 T 06 S 18 S 19 S 20 S 21 S 22 S 23 S 30 T 17 S 26 S 25 S 27 T 11 S 06 S 08 S 09 S 10 S 07 S 11 T 19 S 28 F 25 S 29 T 20 T 12 T 13 T 08 T 14 11 Chapter 1 Problems - Combination of Cubes (C) Level of difficulty: Easy Problem Letters Page # C 01 C 02 C 03 C 04 C 05 C 06 C 07 C 08 C 09 C 10 C 11 C 12 IIT IIL IIH LLL HLL TTT UHL HLE EFT HHH HTT LUF 13 14 15 16 17 18 19 20 21 22 23 24 12 131415161718192021222324Chapter 2 - First Level (F) Level of difficulty: Low Problem Letters Page # F 01 F 02 F 03 F 04 F 05 F 06 F 07 F 08 F 09 F 10 F 11 F 12 F 13 F 14 F 15 F 16 F 17 F 18 F 19 F 20 F 21 F 22 F 23 F 24 F 25 F 26 IIT IIL IIH IIA IIM LLL HLL LLD LLA TTT HHH EFT XTT ATT TTH OHH ZHH HLE OOO DEL DDD EEE FFF LUF UHL AUL 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 25 2627282930313233343536373839404142434445464748495051Chapter 3 - Second Level (S) Level of difficulty: Medium Problem Letters Page # 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 S 01 S 02 S 03 S 04 S 05 S 06 S 07 S 08 S 09 S 10 S 11 S 12 S 13 S 14 S 15 S 16 S 17a S 17b S 18 S 19 S 20 S 21 S 22 S 23 S 24 S 25 S 26 S 27 S 28 S 29 S 30 HMT LED LLQ LOT KLE PET RET PFT PLE POT SET EDU EEN EFD ELM HUT HUV 1 HUV 2 MLU MOE MUD MUE MUG MUL HZT NUL NUE OLE UAL VLT MUZ 52 53545556575859606162636465666768697071727374757677787980818283Chapter 4 - Third Level (T) Level of difficulty: Difficult Problem Letters Page # T 01 T 02 T 03 T 04 T 05 T 06 T 07 T 08 T 09 T 10 T 11 T 12 T 13 T 14 T 15 T 16 T 17 T 18 T 19 T 20 T 21 FEZ FJT GOP LCX MHE MHF ZEE ZEF ZOO MOO OUA WTF YTF ZXN XAA XVV NHB HEB TAP WMX XXX 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 84 858687888990919293949596979899100101102103104105List of Problem Solutions by Chapter Chapter Chapter 1 (C) - Solutions Chapter 2 (F) - Solutions Chapter 3 (S) - Solutions Chapter 4 (T) - Solutions Page # 107 111 124 137 106 Chapter 1 (C) - Solutions Problem Letters Page # C 01 C 02 C 03 C 04 C 05 C 06 C 07 C 08 C 09 C 10 C 11 C 12 IIT IIL IIH LLL HLL TTT UHL HLE EFT HHH HTT LUF Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution 108 108 108 108 109 109 109 109 110 110 110 110 107 108 109 110 Chapter 2 (F) - Solutions # Letters Page # # Letters Page # F 01 IIT F 01 IIT F 01 IIT F 01 IIT F 02 IIL F 02 IIL F 02 IIL F 03 IIH F 03 IIH F 03 IIH F 04 IIA F 04 IIA F 04 IIA F 05 IIM F 05 IIM F 06 LLL F 06 LLL F 07 HLL F 07 HLL F 08 LLD F 08 LLD F 09 LLA F 09 LLA F 10 TTT Solution 1 Solution 2 Solution 3 Solution 4 Solution 1 Solution 2 Solution 3 Solution 1 Solution 2 Solution 3 Solution 1 Solution 2 Solution 3 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 112 112 112 112 113 113 113 113 114 114 114 114 115 115 115 115 116 116 116 116 117 117 117 117 F 10 TTT F 11 HHH F 11 HHH F 12 EFT F 12 EFT F 13 XTT F 13 XTT F 14 ATT F 14 ATT F 14 ATT F 15 TTH F 15 TTH F 16 OHH F 17 ZHH F 18 HLE F 19 OOO F 20 DEL F 21 DDD F 21 DDD F 22 EEE F 23 FFF F 24 LUF F 25 UHL F 26 AUL Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 3 Solution 1 Solution 2 Solution Solution Solution Solution Solution Solution 1 Solution 2 Solution Solution Solution Solution Solution 118 118 118 118 119 119 119 119 120 120 120 120 121 121 121 121 122 122 122 122 123 123 123 123 111 112 113 114 115 116 117 118 119 120 121 122 123 Chapter 3 (S) - Solutions # Letters Page # # Letters Page # S 01 HMT LED S 02 LLQ S 03 LOT S 04 LOT S 04 KLE S 05 KLE S 05 PET S 06 PET S 06 RET S 07 RET S 07 PFT S 08 PFT S 08 PLE S 09 POT S 10 SET S 11 EDU S 12 EDU S 12 EEN S 13 EEN S 13 EFD S 14 ELM S 15 S 15 ELM S 16 HUT Solution Solution Solution Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution Solution Solution Solution 1 Solution 2 Solution 1 Solution 2 Solution Solution 1 Solution 2 Solution 1 125 125 125 125 126 126 126 126 127 127 127 127 128 128 128 128 129 129 129 129 130 130 130 130 S 16 HUT S 17a HUV S 17b HUV S 18 MLU S 18 MLU S 19 MOE S 19 MOE S 20 MUD S 20 MUD S 21 MUE S 21 MUE S 22 MUG S 22 MUG S 23 MUL S 23 MUL S 24 HZT S 24 HZT S 25 NUL S 25 NUL S 26 NUE S 27 OLE S 28 UAL S 29 VLT S 30 MUZ Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution 1 Solution 2 Solution Solution Solution Solution Solution 131 131 131 131 132 132 132 132 133 133 133 133 134 134 134 134 135 135 135 135 136 136 136 136 124 125 126 127 128 129 130 131 132 133 134 135 136 Chapter 4 (T) - Solutions Problem Letters Page # T 01 T 01 T 02 T 03 T 04 T 05 T 06 T 07 T 08 T 09 T 10 T 11 T 12 T 13 T 14 T 15 T 15 T 16 T 16 T 17 T 18 T 19 T 20 T 21 FEZ FEZ FJT GOP LCX MHE MHF ZEE ZEF ZOO MOO OUA WTF YTF ZXN XAA XAA XVV XVV NHB HEB TAP WMX XXX Solution 1 Solution 2 Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution Solution 1 Solution 2 Solution 1 Solution 2 Solution Solution Solution Solution Solution 138 138 138 138 139 139 139 139 140 140 140 140 141 141 141 141 142 142 142 142 143 143 143 143 137 138 139 140 141 142 143 Author Info Dan D. Dimitriu, PhD, P.E., is a tenured professor in SAC’s Phys- ics, Engineering, and Architecture Department and has been the En- gineering Program Coordinator at San Antonio College since 2001. He has 21 years of teaching experience in post-secondary education, five years in academic research, and 23 years in private practice as a professional engineer. He has worked on research projects at North Dakota State University and holds also an MBA in International Economic Relations. He has managed several NSF and Department of Education MSEIP grants for SAC, and has been a co-PI for a NASA CIPAIR grant with the University of Texas at San Antonio and for an NSF CCLI grant with Wright University. He was elected Vice Chair of the Two Year College Division of ASEE in 2005 and was the recipient of 2006 NISOD Excellence in Teaching Award. He was also named “San Antonio’s Top Professor” by Scene in SA Monthly in 2006. In 2005 he was the only community college committee member and presenter for the “Enhancing Community College Pathways into Engineering Careers,” a collaborative effort by the National Academy of Engineering’s Committee on Engineering Education and the National Research Council Board on Higher Education and Workforce . Their final report described the evolving roles of community colleges in engineering education, identified exemplary programs at community colleges and model partnerships between two- and four-year engineering schools, and made recommendations for future research in this area. He has also made numerous presentations at the American Society for Engineer- ing Educators Annual Conferences. Dr. Dimitriu is also coordinator for the Alamo Community College District’s participation in NASA’s Aerospace Scholars program and concurrently serves as the director for SAC’s MESA Center. This workbook is a resultant of his leadership and expertise in developing curricula, coordinating engi- neering educational programs, years of teaching, and years of professional practice. 144 Series ISSN: 1932-3166 A, B, See… in 3D A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu, PhD, P.E., Professor, San Antonio College The workbook provides over 100 3D visualization exercises challenging the student to create three dimensions from two. It is a powerful and effective way to help engi- neering and architecture educators teach spatial visualization. Most of the 3-D visual- ization exercises currently being used by students in Design and Graphics classes pres- ent the objects in isometric views already in 3-D, asking the viewer to create multiple views, fold patterns, manipulate, reflect, or rotate them. The exercises presenting the objects in incomplete multiview projections asking the students to add missing lines use mostly real 3D objects that are more easily recognizable to help the student cor- relate 2D with 3D. This workbook uses a different approach. Each view of the solid represents a letter of the alphabet. The letters are by definition 2D representations and when they are com- bined to create a 3D object, visualizing it becomes quite a challenge. This workbook is intended for Engineering, Architecture, and Art students and faculty that want to increase their 3-D visualization skills w w w . m o r g a n c l a y p o o l . c o m
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8940927.pdf&bkn=8940926&pdfType=book	Series ISSN 1939-5221 Relativistic Classical Mechanics and Electrodynamics Martin Land, Hadassah College, Jerusalem Lawrence P. Horwitz, Tel Aviv University, Bar Ilan University, and Ariel University This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter τ to play the role of Newton’s universal and monotonically advancing time. Fundamental physics is described by the τ-evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five τ-dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as τ advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at τ to an infinitesimally close 4D block universe defined at τ+dτ. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com Synthesis Lectures provide concise original presentations of important store.morganclaypool.com Relativistic Classical Mechanics and Electrodynamics Martin Land Lawrence P. Horwitz L A N D • H O R W I T Z R E L A T I V I S T I C C L A S S I C A L M E C H A N I C S A N D E L E C T R O D Y N A M I C S M O R G A N & C L A Y P O O L Relativistic Classical Mechanics and Electrodynamics Synthesis Lectures on Engineering, Science, and Technology Relativistic Classical Mechanics and Electrodynamics Martin Land and Lawrence P. Horwitz 2019 Copyright © 2020 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Relativistic Classical Mechanics and Electrodynamics Martin Land and Lawrence P. Horwitz www.morganclaypool.com ISBN: 9781681737065 ISBN: 9781681737072 ISBN: 9781681737089 paperback ebook hardcover DOI 10.2200/S00970ED1V01Y201912EST001 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY Lecture #1 Series ISSN ISSN pending. Relativistic Classical Mechanics and Electrodynamics Martin Land Hadassah College, Jerusalem Lawrence P. Horwitz Tel Aviv University, Bar Ilan University, and Ariel University SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY #1 CM&cLaypoolMorganpublishers&ABSTRACT This book presents classical relativistic mechanics and electrodynamics in the Feynman- Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covari- ance with manifest Lorentz covariance and introducing a coordinate-independent parameter (cid:28) to play the role of Newton’s universal and monotonically advancing time. Fundamental physics is described by the (cid:28)-evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invari- ance leads to an electrodynamics derived from ﬁve (cid:28)-dependent potentials described by 5D pre-Maxwell ﬁeld equations. Events trace out worldlines as (cid:28) advances monotonically, inducing pre-Maxwell ﬁelds by their motions, and moving under the inﬂuence of these ﬁelds. The dy- namics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block d (cid:28). This elec- universe deﬁned at (cid:28) to an inﬁnitesimally close 4D block universe deﬁned at (cid:28) trodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classi- cal Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak ﬁeld gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory. C KEYWORDS spacetime, relativistic mechanics, classical electrodynamics, electrostatics, quantum ﬁeld theory Contents vii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 2 3 PART I Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Conceptual Approaches to Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Point Mechanics in 4D Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Two Aspects of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 The “Proper Time” Formalism in QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 The Stueckelberg–Horwitz–Piron (SHP) Framework . . . . . . . . . . . . . . . . . . . . 9 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 PART II Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Canonical Relativistic Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Lagrangian and Hamiltonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The Free Relativistic Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 The Relativistic Particle in a Scalar Potential . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Two-Body Problem with Scalar Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Many-Body Problem and Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 Classical Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 Classical Gauge Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Lorentz Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Field Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Ensemble of Event Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4 viii 4 5 3.5 The 5D Wave Equation and its Green’s Functions . . . . . . . . . . . . . . . . . . . . . . 33 3.6 The Mass-Energy-Momentum Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.7 Worldline Concatenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 PCT in Classical SHP Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.9 PART III Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Problems in Electrostatics and Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 The Coulomb Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1.1 Contribution to Potential from GMaxwell . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.2 Contribution to Potential from GCorrelation . . . . . . . . . . . . . . . . . . . . . . 50 Liénard–Wiechart Potential and Field Strength . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.3 Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4 4.5 Radiation from a Line Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.6 Classical Pair Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Particle Mass Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.7 Self-Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.7.1 4.7.2 Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Speeds of Light and the Maxwell Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.8 4.9 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Electrodynamics from Commutation Relations . . . . . . . . . . . . . . . . . . . . . . . . 97 5.1 5.2 Classical Non-Abelian Gauge Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3 Evolution of the Local Metric in Curved Spacetime . . . . . . . . . . . . . . . . . . . 110 Zeeman and Stark Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4 5.5 Classical Mechanics and Quantum Field Theory . . . . . . . . . . . . . . . . . . . . . . 116 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.6 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Preface ix This book presents classical relativistic mechanics and describes the classical electrodynamics of relativistic particles following the approach of Stueckelberg, Horwitz, and Piron (SHP). This framework, pioneered by E. C. G. Stueckelberg in 1941 and employed by Schwinger and Feyn- man in the development of QED, generalizes classical analytical mechanics to relativistic form by replacing Galilean covariance with Lorentz covariance, and introducing a new coordinate- independent evolution parameter (cid:28) to play the role of Newton’s postulated universal and mono- tonically advancing time. Fundamental physics is described by the (cid:28)-evolution of a system point through an unconstrained phase space, in which each event is represented by its covariant space- time coordinates and velocities or momenta. The full apparatus of analytical mechanics is thus made available in a manifestly covariant form, from Lagrangian and symplectic Hamiltonian methods to Noether’s theorem. This approach to relativistic classical mechanics makes SHP a convenient framework for analyzing the “paradoxes” of special relativity, and in particular pro- vides a clear resolution to the grandfather paradox. Making the free particle Lagrangian invariant under classical gauge transformations of the ﬁrst and second kind leads to an electrodynamics derived from ﬁve (cid:28)-dependent potentials, described by 5D pre-Maxwell ﬁeld equations. Individual events trace out worldline trajectories as (cid:28) advances monotonically, inducing pre-Maxwell ﬁelds by their motions, and moving under the inﬂuence of these ﬁelds. The resulting theory is thus integrable and well posed, governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe deﬁned at (cid:28) to an inﬁnitesimally close 4D block universe deﬁned at (cid:28) d (cid:28). This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is the most general interaction pos- sible in an unconstrained 8D phase space. We present examples that include classical Coulomb scattering, electrostatics, plane wave solutions, and radiation from a simple antenna. Standard Maxwell theory emerges from SHP as an equilibrium limit, reached by slowing the (cid:28)-evolution to zero, or equivalently, by summing the contributions over (cid:28) at each spacetime point. C A feature of SHP not present in standard Maxwell theory is that under certain condi- tions, particles and ﬁelds may exchange mass dynamically, under conservation of total mass, energy, and momentum. As a result, pair processes such as electron-positron creation and anni- hilation are permitted in classical electrodynamics, implementing Stueckelberg’s original goal. Two processes that tend to restore a particle’s mass to its standard value are described, one a self-interaction along the event trajectory and the other a general result in statistical mechanics. Mass restoration of this type has been found in mathematical simulations of event trajectories. Beyond its usefulness as an approach to electrodynamics, the theory presented in this book provides the basis for a systematic, step-by-step progression from relativistic classical mechanics x PREFACE to relativistic quantum mechanics, many-body theory, and quantum ﬁeld theory. As an example, we discuss the correspondence of the ﬁfth classical gauge potential to the Lorentz scalar potential used in quantum mechanical two-body problems to obtain manifestly covariant solutions for the bound state, scattering experiments, and relativistic entanglement in time. Similarly, we discuss the implications of the classical relativistic mechanics for quantum ﬁeld theory. This classical framework will thus be of interest to workers in quantum theory, as well as those interested in its foundations. Martin Land and Lawrence P. Horwitz December 2019 Symbols xi µ, ν, λ, ρ = 0, 1, 2, 34D spacetime indicesα, β, γ, δ = 0, 1, 2, 3, 55D formal indices (skipping 4)ηµν = diag(–1, 1, 1, 1)4D ﬂ at Minkowski metricηαβ = diag(–1, 1, 1, 1, η55)Formal 5D ﬂ at Minkowski metriccSpeed of light associated with x0 = ctc5Speed associated with x5 = c5t{F, G} = ∂F ∂G – ∂F ∂G ∂xµ ∂pµ ∂pµ ∂xµPoisson bracket[F, G] = F G – G F Commutator bracketDẋ µ = dẋ µ + Γ𝜈µ ρẋ 𝜈 ẋ ρ Dτ dτ Absolute derivative∇αXβ = ∂Xβ + XγΓβγα ∂x∂Covariant derivativeΓσµ λ = ½gµv (∂σg𝜈λ + ∂λg𝜈σ – ∂𝜈gλσ)Christoﬀ el symbolΦ(τ) = δ(τ) – (ξ λ)2 δ(τ)Interaction kernel for electromagnetic ﬁ eldλParameter with dimensions of timeξ = ½ 1 + c52Numerical factorφ(τ) = λ Φ–1 (τ)Inverse function for kernel c PART I Background C H A P T E R 1 3 Conceptual Approaches to Spacetime 1.1 POINT MECHANICS IN 4D SPACETIME By one measure of success, Newtonian analytical mechanics continues to outshine the mod- ern physics that has replaced it: the impact of its underlying physical picture on conventional notions of “reality” in the wider culture. Beyond science per se, this picture was absorbed into the foundations of Enlightenment philosophy, expanding into the modern humanities and so- cial sciences, lending it an appearance of self-evident ordinariness. Thus, in his inﬂuential text- book Classical Mechanics, Herbert Goldstein introduces the physical framework—space, time, simultaneity, and mass—by writing [1, p. 1] that “these concepts will not be analyzed criti- cally here; rather, they will be assumed as undeﬁned terms whose meanings are familiar to the reader.” This familiarity is understood to ﬂow from everyday experience with Newtonian objects qn 1; D f 1; of inﬁnite extent, whose conﬁguration develops through their functional dependence on the universal time t ﬂowing forward uniformly. Indeed, the Newtonian picture is so central to conventional understandings of the “everyday” that more than one hundred years after Einstein’s annus mirabilis, it is the relativistic character of the Global Positioning System (GPS) found in billions of smartphones that feels distinctly unfamiliar, and “weirdness” still seems an apt term for quantum phenomena. Moreover, it is easy to forget that much of the Newtonian worldview seemed similarly “weird” to many in Newton’s day, especially the uniform linearity of time, a no- tion seemingly at odds with certain varieties of human experience outside the laboratory, more readily described in the language of nonuniform and cyclical ﬂows of time. deﬁned as positions in an abstract Cartesian space n D ; N g qi n.t/ j (cid:1) (cid:1) (cid:1) ; 3; n ; N (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) D 1; g f i j As early as 1908, Minkowski [2, p. 34] declared that: “space and time as such must fade away into shadow, and only a kind of union of the two will maintain its reality.” Although ini- tially resistant to Minkowski’s tensor formulation, Einstein’s 1912 exposition of special relativ- ity [2, p. 128] elaborates the advantages of taking the event in 4D spacetime as the fundamental object. Then, in formulating general relativity, the deconstruction of the Newtonian view of space was a crucial step, as emphasized by Einstein in his 1921 lecture at Princeton [3, pp. 2–3]. Arguing that direct experience must be the basis for physical concepts, he declared that, “the earth’s crust plays such a dominant role in our daily life in judging the relative position of bod- ies that it has led to an abstract conception of space which certainly cannot be defended.” That contemporary textbooks on relativity must still repeat Einstein’s identiﬁcation of the spacetime 4 1. CONCEPTUAL APPROACHES TO SPACETIME event as actual experience—superseding antique notions of inﬁnite Euclidean space he deemed illusory—indicates not only the conceptual complexity of relativity, but also a continuing cultural disparity between modern physics and other realms of human knowledge. In 1937, Fock [4] generalized the Newtonian picture to relativistic form by writing events in 4D Minkowski spacetime as x(cid:22) n .(cid:28)/ f (cid:22) 0; ; 3; n 1; ; N ; g n.(cid:28)/ D where x0 ctn.(cid:28)/ represents the time registered for the event on the laboratory clock. These events describe a conﬁguration that evolves as the scalar parameter (cid:28), identiﬁed by Fock with the proper time, advances monotonically. Writing (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) D D j x(cid:22) .(cid:28)/ P D dx(cid:22) d (cid:28) he showed that by minimizing the action Z d (cid:28) (cid:18) 1 2 m x2 P C e x(cid:22)A(cid:22)(cid:19) c P S D (1.1) for a point event in an electromagnetic potential A(cid:22).x/, one obtains the classical relativistic equations of motion. Here and in the rest of the book we take the ﬂat metric in 4D spacetime to be Fock observed that the elimination of (cid:28) in favor of t in these equations is generally diﬃcult, but is easily accomplished for the free event satisfying 0 as x(cid:22) R D (cid:17)(cid:22)(cid:23) diag . 1; 1; 1; 1/ : D (cid:0) x.(cid:28)/ P D x0.(cid:28)/; (cid:0) P x.(cid:28)/(cid:1) P D (cid:0)u0; u(cid:1) H) d x dt D d x=d (cid:28) dt=d (cid:28) D u u0=c D for constant u (cid:0)u0; u(cid:1). Still, Fock’s generalization was not yet complete. In the Newtonian picture, a point particle whose position is described by the 3-vector trajectory x.t/ may follow any continuous curve. In 1941, Stueckelberg [5, 6] observed that the relativistic generalization described by Fock cannot represent all possible spacetime curves be- cause the evolution parameter is identiﬁed with the proper time of the motion. In particular, any worldline whose time evolution reverses direction must cross the spacelike region that separates future-oriented trajectories from past-oriented trajectories. Therefore, in curves of this type the sign of x2.(cid:28)/ will change twice and the computed proper time interval P ds.(cid:28)/ 1 c D q (cid:0) (cid:17)(cid:22)(cid:23)dx(cid:22)dx(cid:23) 1 c D p x2.(cid:28)/ d (cid:28) (cid:0) P fails as a parameterization. Recognizing a physical meaning in curves of this type, Stueckelberg argued for their inclusion in relativistic mechanics, requiring the introduction of an indepen- dent evolution parameter (cid:28), analogous to the time t in the Newtonian picture, and related to the proper time s through the dynamical relation c2ds2.(cid:28)/ x2.(cid:28)/d (cid:28) 2. In this, he followed Einstein’s approach, by deprecating an historical abstraction he saw as an obstruction to clear physical understanding of observed phenomena. D (cid:0) P 1.1. POINT MECHANICS IN 4D SPACETIME 5 Stueckelberg’s interest in general 4D curves can be understood from Figure 1.1 on page 5 (adapted from [5]). In his model, pair annihilation is observed in curve B when the worldline reverses its time direction, because laboratory apparatus registers two events (two points on the worldline) appearing at coordinate time t t2. The event ﬁrst propagates x0 < 0), continuing to forward in t (with P x0 < 0 piece of the earlier times while advancing in space. Stueckelberg’s identiﬁcation of the P trajectory with an antiparticle observed in the laboratory will be discussed in detail in Chapter 2. D x0 > 0) and then propagates backward in t (with P t1 but none at t D Figure 1.1: Three types of worldline identiﬁed by Stueckelberg. In a similar way, curve C represents pair creation as two events are observed at t t2 but none at t t1. These curves may thus be seen as the smooth classical equivalent of a Feynman spacetime diagram, and the physical picture they present is known as the Feynman–Stueckelberg interpretation of antiparticles [7, 8]. D D x0=ctxτ=−∞τ=−∞τ=−∞τ=∞τ=∞τ=∞t= 0t=t2t=t1ABC6 1. CONCEPTUAL APPROACHES TO SPACETIME Stueckelberg recognized that the standard Maxwell ﬁeld F (cid:22)(cid:23).x/ alone would not permit c2ds2.(cid:28)/ x2d (cid:28) 2 to change sign and proposed a modiﬁed Lorentz force D (cid:0) P x(cid:22) D P D(cid:28) D with local metric g(cid:22)(cid:23) and compatible connection (cid:128) (cid:22) that is required to overcome conservation of x(cid:22) d P d (cid:28) C x(cid:23) (cid:23)(cid:26) P x(cid:26) P (cid:128) (cid:22) D F (cid:22)(cid:23).x/g(cid:23)(cid:26) x(cid:26) P C G(cid:22).x/ (1.2) (cid:23)(cid:26). He also included a new vector ﬁeld G(cid:22).x/ x2, as seen through P D x2 D(cid:28) P x(cid:22) D P D(cid:28) D x(cid:22)G(cid:22).x/ P In the absence of G(cid:22), spacetime curves are single-valued in x0 and may, in principle, be repa- rameterized by the proper time of the motion. (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! ! x(cid:22) P G(cid:22) D 0: 2 2 0 As a simple example we consider a particle in ﬂat space in a constant electric ﬁeld E and take G(cid:22) D with solution 0. Writing the velocity c t R D F 0i xi P D .c t; 0; 0; P x P E D z P D z/, the equations of motion reduce to P z R F 30 x0 P cE D D t P E z O t.(cid:28)/ 1 E D sinh E(cid:28) z.(cid:28)/ c E D .cosh E(cid:28) 1/ (cid:0) C z.0/ which can be reparameterized by t as z.t/ D z.0/ c E C (cid:16)p1 .Et/2 1(cid:17) : (cid:0) C The velocities are t.(cid:28)/ P cosh E(cid:28) D conﬁrming that the mass is conserved with c2 c2 t 2 P z2 (cid:0) P D D 2 " (cid:19) c2 (cid:18) dt d (cid:28) 1 (cid:0) x(cid:22) x(cid:22) P P (cid:18) dz dt D (cid:0) 2# (cid:19) c sinh E(cid:28) z.(cid:28)/ P D c2 and so (cid:20)1 v2 c2 (cid:0) t P D 1 2 (cid:21)(cid:0) ; (cid:0)! G z and take E O D 0 D where v dz=dt. D Now, by contrast, we consider the particle in a constant ﬁeld G(cid:22) so that the equations of motion are with solution c t R D 0 G z R D t.(cid:28)/ (cid:28) D 1 2 z D G(cid:28) 2 1 2 D Gt 2: In this case the mass decreases with (cid:28) as and the motion may become spacelike (superluminal). x(cid:22) (cid:0) P x(cid:22) P D c2 (cid:0) G2(cid:28) 2 1.2 THE TWO ASPECTS OF TIME 1.2. THE TWO ASPECTS OF TIME 7 As seen in the previous section, curves B and C in Figure 1.1 cannot be parameterized by the co- ordinate time because they are double-valued in x0, and cannot be parameterized by the proper time of the motion s because s2 becomes negative in the region of the time reversal point. Realization of the classical Feynman–Stueckelberg picture thus requires the introduction of a parameter (cid:28) entirely independent of the spacetime coordinates—an irreducible chronological (historical) time, similar in its role to the external time t in nonrelativistic Newtonian mechan- ics. The simplicity of this picture in accounting for the observed phenomena of pair processes strongly supports the conclusion [9] that time must be understood as two distinct physical phe- nomena, chronology (cid:28) and coordinate x0. A laboratory clock registers the coordinate time of an event occurrence much as a 3D array of detectors (meter sticks) registers the event’s coordinate position. The chronological time determines the order of occurrence of multiple events, with natural implications for relations of causality. Thus, when laboratory equipment reparameterizes the observed events along curve B in Figure 1.1 by x0, two events approaching one another will be observed at t 0. But the underlying physics will be determined by ﬁeld interactions at the locations of four distinct, ordered events, governed by a microscopic dynamics such as (1.2) and registered sequentially at t t1 and again at t 0, and later at t 0, again at t t1, t t1. D D D D D D In this sense, there are no closed timelike curves in this picture. The so-called grandfather paradoxes, by which one may return to an earlier time to interfere with the circumstances that brought about ones own physical presence and agency, are thus resolved. We notice that the return trip to a past coordinate time x0 must take place while the chronological time (cid:28) con- tinues to increase. Since the occurrence of event x(cid:22).(cid:28)1/ at (cid:28)1 is understood to be an irreversible process that cannot be changed by a subsequent event occurring at the same spacetime location, x(cid:22).(cid:28)2/ x(cid:22).(cid:28)1/ when (cid:28)2 > (cid:28)1, the return trip cannot erase the earlier trajectory. This restriction is analogous to the conceptually simpler observation in nonrelativistic physics that a process may produce new events at any given moment, but cannot delete from the historical record events that occurred at an earlier moment. D A more complex problem is the twin scenario, in which a traveler initially at rest in an inertial frame makes a trip of total distance d at speed v, so that the round trip time measured d=v. The coordinates assigned to the traveler in the rest frame by a clock in this frame is (cid:129)t evolve as D .ct; x/ x D D 8 < : .c(cid:13)(cid:28); x0 .c(cid:13)(cid:28); x0 C C u(cid:28)/ u(cid:129)(cid:28) (cid:0) ; 0 (cid:28) (cid:20) u(cid:28)/ ; (cid:129)(cid:28)=2 (cid:129)(cid:28)=2 (cid:129)(cid:28) (cid:28) (cid:20) (cid:20) (cid:20) ; where d x d (cid:28) D d x dt dt d (cid:28) D u D (cid:13)v (cid:129)t D dt d (cid:28) (cid:129)(cid:28) D (cid:13)(cid:129)(cid:28) 8 1. CONCEPTUAL APPROACHES TO SPACETIME so that d as D u(cid:129)(cid:28) D v(cid:129)t. The coordinates assigned to the traveler in a co-moving frame evolve and so the elapsed time registered on the traveler’s clock is (cid:129)(cid:28) with the usual presentation of the twin scenario. D (cid:129)t=(cid:13). This result is consistent x0 D (cid:0)ct 0; x0(cid:1) D .c(cid:28); 0/ 1.3 THE “PROPER TIME” FORMALISM IN QED Although this book focuses on relativistic classical mechanics, we make a brief digression into the application of spacetime parameterization methods by Schwinger and Feynman in devel- oping quantum electrodynamics. In his 1951 calculation of vacuum polarization in an external electromagnetic ﬁeld, Schwinger [10] represented the Green’s function for the Dirac ﬁeld as a parametric integral and formally transformed the Dirac problem into a dynamical theory in which the integration variable acts as an independent time. Applying his method to the Klein– Gordon equation, we express the Green’s function as G D .p (cid:0) 1 eA=c/2 m2 i(cid:15) (cid:0) C so that writing the function satisﬁes G.x; x0/ G x j j x0 D h i D i Z 1 0 i.m2 dse(cid:0) i(cid:15)/s (cid:0) i.p (cid:0) e(cid:0) x h j eA=c/2s x0 j i (1.3) G.x; x0 s/ I x.s/ j D h x0.0/ x i.p e(cid:0) (cid:0) eA=c/2s j x0 j i ih i @ @s h x.s/ x0.0/ i D j (cid:16)p 2 A(cid:17) e c (cid:0) x.s/ x0.0/ i j h (1.4) with the boundary condition x.s/ lim 0h s ! j x0.0/ i D (cid:14)4.x x0/: (cid:0) Schwinger regarded x(cid:22).s/ and (cid:25) (cid:22).s/ that satisfy canonical relations D p(cid:22).s/ (cid:0) e c A(cid:22).s/ as operators in a Heisenberg picture (cid:140)x(cid:22); (cid:25) (cid:23)(cid:141) D i(cid:140)x(cid:22); K(cid:141) D (cid:0) i(cid:17)(cid:22)(cid:23) dx(cid:22) ds (cid:140)(cid:25) (cid:22); (cid:25) (cid:23)(cid:141) i(cid:140)(cid:25) (cid:22); K(cid:141) ie c D F (cid:22)(cid:23) d (cid:25) (cid:22) ds ; D (cid:0) (1.5) (1.6) 1.4. THE STUECKELBERG–HORWITZ–PIRON (SHP) FRAMEWORK 9 where K .p (cid:0) D eA=c/2. Using (1.5) and (1.6) we ﬁnd x(cid:22).s/ P D (cid:0) i(cid:140)x(cid:22); K(cid:141) D (cid:0) i (cid:20)x(cid:22); (cid:16)p 2(cid:21) A(cid:17) e c (cid:0) D 2 (cid:16)p(cid:22) e c (cid:0) A(cid:22)(cid:17) (1.7) and so may perform the Legendre transformation Z ds L Z ds (cid:0) x(cid:22)p(cid:22) P (cid:0) K(cid:1) D D Z ds (cid:18) 1 x2 4 P C e x c P (cid:1) A(cid:19) whose classical limit takes the form of the Fock action (1.1). Although Schwinger found this x(cid:22), representation useful because the scalar parameter s is necessarily independent of x(cid:22) and P and so respects Lorentz and gauge invariance, it is known [8] as the Fock-Schwinger “proper time method.” DeWitt [11] regarded (1.4) as deﬁning the Green’s function for a Schrodinger equation i @ @s s.x/ D K s.x/ (cid:16)p 2 A(cid:17) e c (cid:0) D s.x/ (1.8) which he used for quantum mechanical calculations in curved spacetime. Similarly, Feyn- man [12] used (1.8) in his derivation of the path integral for the Klein–Gordon equation. He im2s as the require- regarded the integration (1.3) of the Green’s function with the weight e(cid:0) ment that asymptotic solutions of the Schrödinger equation be stationary eigenstates of the mass operator i@(cid:28) . To pick the mass eigenvalue one extends the lower limit of integration in (1.3) from 0 to 0 for s < 0. Feynman noted that this requirement, equivalent to imposing retarded causality in chronological time s, leads to the Feynman propagator (cid:129)F .x x0/ whose causality properties in t are rather more complex. (cid:0) Related issues of causality arise in classical relativistic ﬁeld theory. , and adds the requirement that G.x; x0I (cid:0)1 D s/ 1.4 THE STUECKELBERG–HORWITZ–PIRON (SHP) FRAMEWORK In 1973, Horwitz and Piron set out to systematically construct a manifestly covariant relativistic mechanics with interactions. They observed that the principal diﬃculties in previous eﬀorts arose when attempting to deﬁne observables that respect a priori constraints associated with the presumed dynamics. For example, although it may seem natural to choose the proper time of the motion as the worldline parameterization, Stueckelberg showed that this choice prohibits a classical account of observed pair phenomena. Worse still, in the Fock–Schwinger formalism identiﬁcation of s with the proper time clashes with the formulation of quantum observables, since p x2 ds does not commute with x(cid:22), rendering the relations (1.5) and (1.6) D diﬃcult to interpret rigorously. dx2 (cid:0) P p (cid:0) A closely related question is reparameterization invariance. Although one might regard f .(cid:28)/ the parameter (cid:28) as arbitrary, the Fock action (1.1) is clearly not invariant under (cid:28) (cid:28) 0 D ! 10 1. CONCEPTUAL APPROACHES TO SPACETIME because the Lagrangian is not homogeneous of ﬁrst degree in the velocities. Invariance is often restored by replacing the quadratic term in the action with a ﬁrst-order form such as S D Z d (cid:28) (cid:16)mcp x2 (cid:0) P e x(cid:22)A(cid:22)(cid:17) c P C which leads to ﬁxed particle masses p(cid:22) D @L x(cid:22) D @ P mc x(cid:22) P p x2 C e c A(cid:22) (cid:16)p 2 A(cid:17) e c (cid:0) m2c2 D (cid:0) (cid:0)! (cid:0) P and restricts the system dynamics to the timelike region by imposing x2 < 0. P Although the Fock action permits mass exchange, the mass of individual particles is ﬁxed for interactions governed by Stueckelberg’s force law (1.2) when G(cid:22) 0. Similarly, in the Fock– 4K and thus corresponds to a classical constant Schwinger formalism (1.7) shows that of the motion. Thus, ﬁxed mass is demoted from the status of a priori constraint to that of a posteriori conservation law for appropriate interactions. x2 P D D Rejecting such a priori restrictions, Horwitz and Piron postulate that classical particles and quantum states can be described in an unconstrained 8D phase space .ct; x/ x D (cid:18) E c p D ; p(cid:19) with canonical equations x(cid:22) P D dx(cid:22) d (cid:28) D @K @p(cid:22) p(cid:22) P D dp(cid:22) d (cid:28) D (cid:0) @K @x(cid:22) ; where K is a scalar function that determines the system dynamics and its conservation laws. This framework is seen to include Newtonian mechanics by imposing the restrictions which leads to t (cid:28) D K D H.x; p/ E (cid:0) dxi dt D @H @pi dpi dt D (cid:0) @H @xi dE dt D @H @t ; where i 1; 2; 3. D To describe a free relativistic particle one may write so that dt=d (cid:28) D K p2 2M E=Mc2 and d x=dt D (cid:0)! x(cid:22) P D p(cid:22) M and p(cid:22) P D 0 pc2=E. In particular, for a timelike particle, D p2 M 2 D (cid:0) x2 P D m2c2 M 2 D constant; where the dynamical quantity m2.(cid:28)/ is conserved because @K=@(cid:28) 0. Similarly, a relativistic e particle in a four-potential A(cid:22).x/ is characterized by K c A/2=2M with results compa- rable to the classical limit of the Fock–Schwinger system. Moreover, Horwitz and Piron con- sidered a two-body problem with a scalar interaction characterized by the Hamiltonian .p D D (cid:0) 1.5. BIBLIOGRAPHY 11 p2 1 2M1 C p2 2 2M2 C K D V . x1 j x2 / ; j (cid:0) where V . j x1 x2 (cid:0) j V .(cid:26)/ / D D p.x1 x2/2 .t1 (cid:0) (cid:0) t2/2 (cid:0) generalizes action at a distance to action at a spacelike interval. As in nonrelativistic mechanics, the center of mass and relative motion may be separated as P (cid:22)P(cid:22) 2M C p(cid:22)p(cid:22) 2m C K D V .(cid:26)/; where P (cid:22) D (cid:0)M2p(cid:22) p(cid:22) 1 C p(cid:22) 2 M1p(cid:22) 2 (cid:1) =M 1 (cid:0) p(cid:22) M D M1 C M2 m M1M2=M: D D P (cid:22) The center of mass motion is thus free, satisfying P 0. For the relative motion, one has p(cid:22) P D (cid:0) @K @x(cid:22) D (cid:0) D @V @x(cid:22) (1.9) (cid:0) @V =@x(cid:22) with G(cid:22) in (1.2) so that individual particle masses in which case we may identify are no longer necessarily ﬁxed. In this framework, Horwitz and Arshansky found relativistic generalizations for the standard central force problems, including scattering [13, 14] and bound states [15, 16]. This formulation of the relativistic two-body problem can be extended to many bodies in the context of classical gauge theory, providing the basis for the SHP approach to classical relativistic mechanics. BIBLIOGRAPHY 1.5 [1] Goldstein, H. 1965. Classical Mechanics, Addison-Wesley, Reading, MA. 3 [2] Einstein, A. 1996. Specielle Relativitätstheorie, George Braziller, New York, English and German on facing pages. 3 [3] Einstein, A. 1956. The Meaning of Relativity, Princeton University Press, Princeton, NJ. DOI: 10.4324/9780203449530. 3 [4] Fock, V. 1937. Physikalische Zeitschrift der Sowjetunion, 12:404–425. http://www.neo-cl assical-physics.info/uploads/3/4/3/6/34363841/fock_-_wkb_and_dirac.pdf 4 12 1. CONCEPTUAL APPROACHES TO SPACETIME [5] Stueckelberg, E. 1941. Helvetica Physica Acta, 14:321–322 (in French). 4, 5 [6] Stueckelberg, E. 1941. Helvetica Physica Acta, 14:588–594 (in French). 4 [7] Halzen, F. and Martin, A. D. 1984. Quarks and Leptons: An Introductory Course in Modern Particle Physics, John Wiley & Sons, New York. DOI: 10.1119/1.14146. 5 [8] Itzykson, C. and Zuber, J. B. 1980. Quantum Field Theory, McGraw-Hill, New York. DOI: 10.1063/1.2916419. 5, 9 [9] Horwitz, L., Arshansky, R., and Elitzur, A. 1988. Foundations of Physics, 18:1159. 7 [10] Schwinger, J. 1951. Physical Review, 82(5):664–679. https://link.aps.org/doi/10. 1103/PhysRev.82.664 8 [11] DeWitt, B. 1965. Dynamical Theory of Groups and Fields, Gordon and Breach, New York. DOI: 10.1119/1.1953053. 9 [12] Feynman, R. 1950. Physical Review, 80:440–457. 9 [13] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:213. 11 [14] Arshansky, R. and Horwitz, L. 1988. Physics Letter A, 131:222–226. 11 [15] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:66. 11 [16] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:380. 11 PART II Theory C H A P T E R 2 15 Canonical Relativistic Mechanics LAGRANGIAN AND HAMILTONIAN MECHANICS 2.1 In many ways, the picture underlying classical relativistic mechanics is a generalization of its Newtonian predecessor, with the replacements 3D space chronological time t Galilean covariance 9 >>= >>; (cid:0)! 8 (cid:136)(cid:136)< (cid:136)(cid:136): 4D spacetime chronological time (cid:28) Lorentz covariance made in an analogous canonical structure. A spacetime event x(cid:22) refers to the 4-tuple .ct; x/ of coordinate observables that can, in principle, be measured by a clock and an array of spatially arranged detectors in a laboratory.1 Each event occurs at a chronological time (cid:28) such that for (cid:28)2 > (cid:28)1 the event x(cid:22).(cid:28)2/ is said to occur after the event x(cid:22).(cid:28)1/. Event occurrence is an irre- versible process—a given event cannot be inﬂuenced by a subsequent event, although laboratory equipment may present the history of events in the order of their recorded values of x0 ct. Following Fock and Stueckelberg, we consider a relativistic particle to be a continuous sequence of events traced out by the evolution of a function x(cid:22).(cid:28)/ as (cid:28) proceeds monotonically . The chronological time (cid:28) is taken to be an external universal parameter, playing from a role similar to that of t in Newtonian physics. (cid:0)1 1 to D In Stueckelberg–Horwitz–Piron (SHP) theory, event dynamics are deﬁned on an uncon- strained 8D phase space .x(cid:22); p(cid:22)/ by the canonical equations x(cid:22) P D dx(cid:22) d (cid:28) D @K @p(cid:22) p(cid:22) P D dp(cid:22) d (cid:28) D (cid:0) @K @x(cid:22) ; (2.1) where K.x; p; (cid:28)/ is a Lorentz invariant Hamiltonian. This framework thus inherits the canon- ical structure of Newtonian analytical mechanics, with the additional complexity of Lorentz covariance. Deﬁning Poisson brackets as F; G f g D @F @x(cid:22) @G @p(cid:22) (cid:0) @F @p(cid:22) @G @x(cid:22) 1Although this description oversimpliﬁes the measurement process, it will be suﬃcient here. 16 2. CANONICAL RELATIVISTIC MECHANICS we have for any function on phase space, dF d (cid:28) D @F @x(cid:22) dx(cid:22) d (cid:28) C @F @p(cid:22) dp(cid:22) d (cid:28) C @F @(cid:28) D @F @x(cid:22) @K @p(cid:22) (cid:0) @F @p(cid:22) @K @x(cid:22) C @F @(cid:28) D f F; K g C @F @(cid:28) 0, the Hamiltonian is a generalizing the result in nonrelativistic mechanics. Since constant of the motion unless K depends explicitly on (cid:28). Because of its unconstrained canonical structure, the conditions for the Liouville–Arnold theorem apply: the 4D system is integrable— solvable by quadratures—if it possesses 8 independent conserved quantities Fi ; i ; 8 sat- isfying f Performing the Legendre transformation from the Hamiltonian to the Lagrangian Fi ; Fj f 0 and K; Fi K; K g (cid:17) g D g D (cid:1) (cid:1) (cid:1) D 0. 1; f variation of the action D leads to the Euler–Lagrange equations (cid:14)S L x(cid:22)p(cid:22) D P K; (cid:0) (cid:14) Z d (cid:28) L .x; x; (cid:28) / P D 0 @L x(cid:22) (cid:0) @ P in familiar form. Under transformations x ! Noether theorem follows in the usual manner, so that for inﬁnitesimal variation (cid:14)x we ﬁnd @L @x(cid:22) D x0 D f .x/ that leave the action invariant, the d d (cid:28) 0 d d (cid:28) (cid:18) @L @ x(cid:22) (cid:14)x(cid:22)(cid:19) P 0 D leading to the conserved quantity .@L=@ Lorentz transformations (cid:131) with antisymmetric generators M(cid:22)(cid:23) x(cid:22)/ (cid:14)x(cid:22). In particular, since L is a scalar invariant under P x0 D (cid:131)x (cid:0)! (cid:14)x x0 x (cid:0) D ’ (cid:14)!(cid:22)(cid:23)M(cid:22)(cid:23) x the quantity l(cid:22)(cid:23) D (cid:16)@L=@ (cid:21)(cid:27) x(cid:21)(cid:17) (cid:0)M(cid:22)(cid:23)(cid:1) P x(cid:27) D x(cid:22)p(cid:23) (cid:0) x(cid:23)p(cid:22) is conserved, and the Poisson bracket relations C express the Lie algebra of the Lorentz group. The components of l(cid:22)(cid:23) can be split into C D C (cid:8)l(cid:22)(cid:23); l(cid:26)(cid:27) (cid:9) g(cid:23)(cid:26)l(cid:27)(cid:22) g(cid:22)(cid:26)l(cid:23)(cid:27) g(cid:23)(cid:27) l(cid:22)(cid:26) g(cid:22)(cid:27) l(cid:26)(cid:23) so that (cid:15)ij kxj pk Li D Ai D x0pi (cid:0) xi p0 l 2 D 2 (cid:0)L2 (cid:0) A2(cid:1) (2.2) (2.3) generalizes the conserved nonrelativistic total angular momentum in central force problems. We write the velocity of a general event as 2.2. THE FREE RELATIVISTIC PARTICLE 17 D with no restrictions on its orientation— case, an observer can boost to a co-moving frame in which D x.(cid:28)/ P (cid:0)c t; P x(cid:1) P (cid:0)u0.(cid:28)/; u.(cid:28)/(cid:1) x may be timelike, lightlike, or spacelike. In the timelike P and so by Lorentz invariance, D (cid:0) be a dynamical result in the rest frame, it is not an a priori constraint. in any instantaneous frame. Still, while (cid:0)c x2 P 2 t (cid:1) P 1 may t P D x.(cid:28)/ P D (cid:0)c t; 0(cid:1) P 2.2 THE FREE RELATIVISTIC PARTICLE As in the earlier work of Fock and Schwinger, the free particle Hamiltonian is taken to be p2 2M K D generalizing the nonrelativistic form. Applying the canonical equations (2.1), the equations of motion are x(cid:22) P D with solution @K @p(cid:22) D p(cid:22) M p(cid:22) P D (cid:0) @K @x(cid:22) D 0 x(cid:22) x(cid:22) 0 C D u(cid:22)(cid:28) x(cid:22) 0 C p(cid:22) M (cid:28) D x(cid:22), a Legendre transformation leads to the free P as seen previously in Section 1.4. From p(cid:22) particle Lagrangian M D and so naturally, L x(cid:22)p(cid:22) D P K (cid:0) D 1 2 M x2 P D Given the absence of constraints, the sign of p2 depends on its spacetime orientation. D D L 1 2 M x2 P K p2 2M D constant: Introducing the mass m2 p2=c2 for a timelike event, we have m2c2=M 2 and D (cid:0) 1 in the rest frame. For this case, x2 P we generally take m D M so that m=M c2 (cid:0) x2 D P (cid:0) 2 x0(cid:1) (cid:0) P D (cid:0) c2 D (cid:0) t P D t 2 " 1 P D (cid:18) d x dt (cid:19) 2# (cid:0) (cid:0)! t P D (cid:6) p1 1 (cid:0) (cid:13); (cid:12)2 D (cid:6) where (cid:12) v=c, v D D d x=dt, and (cid:13) is the usual relativistic dilation factor. 18 2. CANONICAL RELATIVISTIC MECHANICS For a timelike free event evolving forward in coordinate time ( and recover the standard representation of relativistic velocity: t P (cid:21) 1), we choose t P (cid:13) D C (cid:0)u0; u(cid:1) x P D D (cid:13) .c; v/ (cid:18) E Mc ; p M (cid:19) ; D where E > 0. Choosing t P D (cid:0) free event evolving backward in coordinate time ( (cid:13) produces a solution of particular interest to Stueckelberg, the timelike 1), t P (cid:18) (cid:20) (cid:0) E j j Mc (cid:0) (cid:19) ; p M (cid:13) .c; v/ (cid:0) D D (cid:0) describing a negative energy event tracing out a trajectory that when reordered by the laboratory clock describes an antiparticle. x(cid:22) The general solution P p(cid:22)=M for a free particle can also accommodate tachyon (p2 > D 0) and lightlike (p2 0) worldlines with no loss of generality. D 2.3 THE RELATIVISTIC PARTICLE IN A SCALAR POTENTIAL Adding a scalar potential V .x/ to the Hamiltonian p2 2M C K D V .x/ leads to the equations of motion x(cid:22) P D @K @p(cid:22) D p(cid:22) M p(cid:22) P D (cid:0) @K @x(cid:22) D (cid:0) @V @x(cid:22) : Equivalently, the Lagrangian formulation is L D 1 2 M x2 P (cid:0) V .x/ d d (cid:28) @L x(cid:22) (cid:0) @ P @L @x(cid:22) D 0 M x(cid:22) R D (cid:0) @V @x(cid:22) : (cid:0)! As seen in (1.9), this problem may describe the reduced interaction of a two-body problem in relative coordinates. As a simpliﬁed but suggestive model, we consider the scalar potential V .x/ Ma x; (cid:1) D where a is a constant timelike vector. We choose a frame in which 2.3. THE RELATIVISTIC PARTICLE IN A SCALAR POTENTIAL 19 a .cg; 0; 0; 0/ V .x/ Mcgx0 (cid:0)! providing an analogy in the time direction to the approximate nonrelativistic gravitational ﬁeld close to earth. The equations of motion are D (cid:0) D M x(cid:22) R D (cid:0) @V @x(cid:22) D (cid:0) Ma(cid:22) becoming in this frame with solution M x0 R D (cid:0) Mcg M x R D 0 t .(cid:28) / t0 t0(cid:28) C P (cid:0) D 1 2 g(cid:28) 2 x .(cid:28)/ x0 C D u0(cid:28); where g, t0 and t0 are taken as positive constants. We recognize this parabolic trajectory as P describing the pair annihilation process shown in curve B of Figure 1.1. For simplicity, we now take t0 0. Thus, the event velocity is 0 and x0 D D t .(cid:28) / P t0 D P (cid:0) g(cid:28) x .(cid:28)/ P D u0 D constant and the trajectory reverses t-direction at t t 2 0 =2g when (cid:28) (cid:3) D P (cid:3) D P t0=g. From p(cid:22) D @L x(cid:22) D @ P M x(cid:22) P p0 E c D D Mc t P (cid:0)! (cid:0)! E Mc2 t P D we see that the event propagates forward in t with E > 0 for (cid:28) < (cid:28) 0 for (cid:28) > (cid:28) of an antiparticle. The velocity remains timelike except near (cid:28)0 in the interval and backward in t with E < portion of the trajectory corresponds to Stueckelberg’s interpretation . The (cid:28) > (cid:28) (cid:3) (cid:3) (cid:3) c2 (cid:0)P t0 (cid:0) 2 g(cid:28) (cid:1) (cid:0) u2 0 < 0 (cid:0)! u0 j cg j (cid:28) (cid:3) (cid:0) < (cid:28) < (cid:28) u0 j cg j ; (cid:3) C where it becomes spacelike (tachyonic). The event trajectory recorded in the laboratory may be reordered according to t. Thus, at 0 coordinate time t and a subsequent a negative energy event at (cid:28) . From this perspective, the two pieces of D the worldline appear as a pair of events approaching one another and mutually annihilating at t 0, two events will be recorded, a positive energy event that occurred at (cid:28) 2(cid:28) (cid:3) D D D t (cid:3) , with no events recorded with t > t In a similar way, taking . (cid:3) t0 and g to be negative constants, this solution describes a pair cre- P ation process. Although this account of pair processes is not physically realistic, we will present a more accurate description in Section 4.6 using the full apparatus of classical SHP electrody- namics. 20 2. CANONICAL RELATIVISTIC MECHANICS 2.4 TWO-BODY PROBLEM WITH SCALAR POTENTIAL As we showed in Section 1.4, the two-body problem with scalar interaction can be written as an equivalent one-body problem p2 1 2M1 C p2 2 2M2 C K D V .x1 x2/ (cid:0) D P (cid:22)P(cid:22) 2M C p(cid:22)p(cid:22) 2m C V .x/; (2.4) P (cid:22) 0. Arshansky [1] studied classical problems of where the center of mass motion satisﬁes P D this type (for the extension to quantum mechanics, see [2]), generalizing the standard nonrela- tivistic central force problems by taking V .x/ D V (cid:16)px2(cid:17) (cid:0)! V .x/ D V (cid:16)px2 c2t 2(cid:17) (cid:0) for spacelike separations, x2 > 0. Restriction to the spacelike region can be accomplished through a representation in hyperspherical coordinates of the type (cid:26) (cid:20) sinh (cid:12) cosh (cid:12) x D (cid:21) r O 2 r O D 4 sin (cid:18) cos (cid:30) sin (cid:18) sin (cid:30) cos (cid:18) 3 5 r2 O D 1: But it was found that reasonable solutions lie in a subspace of the full spacelike region, found by choosing a spacelike unit vector n(cid:22) and solving the equations of motion in the O(2,1)-invariant restricted space x (cid:8)x (cid:140)x j (cid:0) .x (cid:1) 2 n/n(cid:141)2 0(cid:9) (cid:21) for which the component of x orthogonal to n is itself spacelike. Arshansky has described this as a classical case of spontaneous symmetry breaking leading to a lowering of the energy spectrum. Taking n .0; 0; 0; 1/ this region has the representation D (cid:26) (cid:20) sin (cid:18) q O cos (cid:18) (cid:21) x D 2 q O D 4 sinh (cid:12) cosh (cid:12) cos (cid:30) cosh (cid:12) sin (cid:30) 3 5 q2 O D 1: (2.5) In addition to the O(3,1) invariant l 2 deﬁned in (2.3), the O(2,1) invariant 3 (cid:0) with components deﬁned in (2.2) is also conserved and plays a role in characterizing the solu- tions. In these coordinates, the ﬁrst integrals 1 (cid:0) D N 2 L2 A2 A2 2 p2 2M C K D V .x/ 1 2 M (cid:26)2 P D l 2 C 2M(cid:26)2 C V .(cid:26)/ (cid:20) D which is cyclic in (cid:12) and (cid:30), and 2.5. MANY-BODY PROBLEM AND STATISTICAL MECHANICS 21 l 2 D M 2(cid:26)4 P(cid:18) 2 C N 2 sin2 (cid:18) provide a separation of variables. As in nonrelativistic mechanics, but with an additional degree of freedom, solutions can be found from the four ﬁrst-order equations P(cid:12) (cid:30) P (cid:26) P P(cid:18) D D D D 0 0 s 2 M (cid:18)(cid:20) (cid:0) V .(cid:26)/ l 2 2M(cid:26)2 (cid:19) (cid:0) (cid:0)! Z (cid:28) D d(cid:26) r 2 M (cid:16)(cid:20) V .(cid:26)/ (cid:0) (cid:0) l 2 2M(cid:26)2 (cid:17) 1 M(cid:26)2.(cid:28)/ s l 2 N 2 sin2 (cid:18) (cid:0) Z d (cid:28) Z M(cid:26)2.(cid:28) / D (cid:0)! d(cid:18) ql 2 N 2 sin2 (cid:18) (cid:0) providing an example of Liouville integrability. In the quantum case, Horwitz and Arshansky [2–4] solved the bound state problem, lead- ing to a mass spectrum coinciding with the non-relativistic Schrodinger energy spectrum. For small excitations, the corresponding energy spectrum is that of the non-relativistic Schrodinger theory with relativistic corrections. 2.5 MANY-BODY PROBLEM AND STATISTICAL MECHANICS The many body problem and classical and quantum statistical mechanics, along with applica- tions to bound states, scattering, and relativistic statistical mechanics, are covered extensively in [5]. Here we provide a brief introduction to the subject as preparation for discussion of mass stabilization in Section 4.7.2. The generalization of (2.4) to N -bodies is K D N X 1 i D pi (cid:22)pi (cid:22) 2Mi C V .x1; x2; : : : ; xN / for which case one may deﬁne center of mass coordinates M Mi D X i X (cid:22) D Pi Mi x(cid:22) M i P (cid:22) p(cid:22) i D X i and relative coordinates p(cid:22) i D O p(cid:22) i (cid:0) .Mi =M / P (cid:22) x(cid:22) i D O x(cid:22) i (cid:0) X (cid:22) 22 2. CANONICAL RELATIVISTIC MECHANICS satisfying p(cid:22) i D O 0 X i Mi x(cid:22) i D O 0 X i for the phase space. The Poisson brackets are (cid:17)(cid:22)(cid:23) X (cid:22); P (cid:23) f x(cid:22) i ; (cid:8) O and although the relative coordinates do not satisfy canonical Poisson bracket relations, these relations become canonical in the thermodynamic limit N 0. The invariant Hamiltonian takes the form for which Mj =M (cid:17)(cid:22)(cid:23) (cid:0)(cid:14)ij Mj =M (cid:1) p(cid:23) j (cid:9) O ! 1 g D ! D (cid:0) P (cid:22)P(cid:22) 2M C K D p(cid:22) p(cid:22)i i O O 2Mi C X i V .x1; x2; : : : ; xN / so that for relative forces, V .x1; x2; : : : ; xN / decouples from the interacting system. The equations of motion x2; : : : ; O x1; O V . D xN / and the center of mass motion O P (cid:22) M D X (cid:22) P P (cid:22) M x(cid:22) PO i D P (cid:22) P 0 D p(cid:22) PO i D @K x(cid:22)i D (cid:0) @ O @V x(cid:22)i @ O are canonical in form. In statistical mechanics, one regards the N events as elements in a relativistic Gibbs en- semble. As a generalization of the nonrelativistic formalism, we set a mass shell condition K (cid:20), however this is not a suﬃcient restriction because integration over the hyperbolic 4D phase space may run to inﬁnity for ﬁnite p(cid:22)p(cid:22). We must therefore also set an energy shell condition Pi Ei 1 in this section). Fixing the energy shell is equiva- lent to choosing a Lorentz frame for the system relative to the measurement apparatus, without which we could not give meaning to the idea of temperature. The microcanonical ensemble of events at ﬁxed energy is then deﬁned as i (we take c E, where Ei p0 D D D D where (cid:128).(cid:20); E/ D Z d (cid:127)(cid:14).K (cid:20)/(cid:14).(cid:134)Ei E/; (cid:0) (cid:0) d (cid:127) D Y i d 4pi d 4xi D d 4N p d 4N x is the inﬁnitesimal volume element in the phase space of the many-body system. The entropy and temperature are given by S.(cid:20); E/ D ln (cid:128).(cid:20); E/ 1 T (cid:0) @S.(cid:20); E/ @E ; D where we take the Boltzmann constant kB D We may construct a canonical ensemble by extracting a small subensemble (cid:128)s from its en- vironment (cid:128)b (the bath), and summing over all possible partitions of energy and mass parameter between the subensemble and the bath, 1. 2.6. BIBLIOGRAPHY 23 (cid:128).(cid:20); E/ D Z d (cid:20)0dE 0 (cid:128)b (cid:0)(cid:20) (cid:20)0; E (cid:0) (cid:0) E0(cid:1) (cid:128)s (cid:0)(cid:20)0; E 0(cid:1) ; where both mass and energy may be exchanged. Similarly, a grand canonical ensemble may be constructed by summing over all possible exchanges of event number and volume between the subensemble and the bath. We return to the relativistic statistical mechanics in Section 4.7.2 to show that a particle represented as an ensemble of events possesses a mass that tends toward a stable equilibrium, even under perturbations. 2.6 BIBLIOGRAPHY [1] Arshansky, R. 1986. The classical relativistic two-body problem and symptotic mass con- servation. Tel Aviv University preprint TAUP 1479-86. 20 [2] Horwitz, L. P. 2015. Relativistic Quantum Mechanics, Springer, Dordrecht, Netherlands. DOI: 10.1007/978-94-017-7261-7. 20, 21 [3] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:66. [4] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:380. 21 [5] Horwitz, L. P. and Arshansky, R. I. 2018. Relativistic Many-Body Theory and Statistical Me- chanics, 2053–2571, Morgan & Claypool Publishers. http://dx.doi.org/10.1088/978- 1-6817-4948-8 DOI: 10.1088/978-1-6817-4948-8. 21 C H A P T E R 3 25 Classical Electrodynamics 3.1 CLASSICAL GAUGE TRANSFORMATIONS Historically, classical electrodynamics proceeded from experiment to theory. The Maxwell equa- tions (1860s) were initially posed as a summary of discoveries in the laboratory, including the Cavendish experiments in electrostatics (1770s), Coulomb’s studies of electric and mag- netic forces (1780s), and Faraday’s work on time-varying ﬁelds (1830s). But the importance of Maxwell’s mathematical theory was not fully recognized [1, p. xxv] until its prediction of electro- magnetic waves traveling at the speed of light was veriﬁed by Hertz in 1888. It was the successful incorporation of optics into electrodynamics that provoked Einstein to study the spacetime sym- metries underlying Maxwell theory in 1906 and led Fock to associate potential theory with gauge symmetry in 1929 [2]. Building on the success of such considerations, the Standard Model of fundamental interactions was developed by requiring invariance under more complex symmetry groups, as were the many candidates for a successor theory. As discussed in Chapter 1, Stueckelberg recognized that the perception of a worldline as a sequence of events following dynamical laws could lead to pair annihilation processes in classical mechanics. Such worldlines moving in the positive or negative direction of the Einstein time t should be parameterized by an invariant (cid:28), progressing monotonically in the positive direc- tion. Horwitz and Piron generalized this notion to make the parameter (cid:28) universal, and in this way were able to study the relativistic classical dynamics of many body systems. In this chapter, we approach classical electrodynamics in a similar manner. Instead of restricting the formal- ism to the known features of Maxwell theory, we begin with the Lorentz invariant Lagrangian description of a free event and introduce the maximal U(1) gauge invariance applicable to the action, leading to a generalization of the Stueckelberg force law (1.2). We construct an action for the ﬁeld strengths, again applying general principles of Lorentz and gauge invariance, and obtain (cid:28)-dependent Maxwell-like equations. The resulting framework can be understood as a microscopic theory of interacting events that reduces to Maxwell electrodynamics in a certain equilibrium limit. Thus, as we explore SHP theory, our points of comparison will be with the Maxwell theory we hope to generalize. The action for a free event Z d (cid:28) L S D Z d (cid:28) D 1 2 Mg(cid:22)(cid:23) x(cid:22) P x(cid:23) P 26 3. CLASSICAL ELECTRODYNAMICS with g(cid:22)(cid:23).x/ a local metric, is invariant under the addition of a total (cid:28)-derivative L (cid:0)! d d (cid:28) L C (cid:131) .x; (cid:28) / L D x(cid:22) @ @x(cid:22) (cid:131) .x; (cid:28) / C P @ @(cid:28) C (cid:131) .x; (cid:28) / (3.1) on condition that (cid:131) .x; (cid:28) / vanishes at the endpoints of the action integral. In analogy to x0 it is convenient to introduce the notation ct, D x5 c5(cid:28) D x5 P D c5 @5 D 1 c5 @ @(cid:28) and adopt the convention (cid:11); (cid:12); (cid:13); (cid:14); (cid:15) 0; 1; 2; 3; 5 D (cid:21); (cid:22); (cid:23); (cid:26); (cid:27) 0; 1; 2; 3; D where we skip (cid:11) be written in the compact form D 4 to avoid confusion with older notations for ct. In this notation (3.1) can L L (cid:0)! x(cid:11)@(cid:11)(cid:131) .x; (cid:28) / C P (cid:12) x(cid:12) . But we insist that in the presence suggesting a ﬁve dimensional symmetry acting as x0 of matter, x(cid:22) and (cid:28) belong to vector and scalar representations of O(3,1). Still, free ﬁelds may enjoy a 5D symmetry, such as L(cid:11) D (cid:11) O(4,1) for metric O(3,2) for metric L L 2 2 (cid:17)(cid:11)(cid:12) (cid:17)(cid:11)(cid:12) diag. (cid:0) 1; 1; 1; 1; diag. 1; 1; 1; 1; (cid:0) 1/ C 1/ (cid:0) D D which contain O(3,1) as a subgroup. Nevertheless, the higher symmetry does play a role in wave equations, much as nonrelativistic pressure waves satisfy (cid:18) 2 r (cid:0) 1 v2 @2 @t 2 (cid:19) p .x; t / 0 D speed of sound v D suggesting a 4D symmetry not physically present in the theory of acoustics. In light of (3.1), we introduce the ﬁve potentials a(cid:11).x; (cid:28)/ into the Lagrangian and note that the action Z d (cid:28) (cid:18) 1 2 S D M x(cid:22) P x(cid:22) P C (cid:19) e x(cid:11)a(cid:11) c P D Z d (cid:28) (cid:20) 1 2 M x(cid:22) P x(cid:22) P C e c (cid:0) x(cid:22)a(cid:22) P C (cid:21) c5a5(cid:1) is invariant under the 5D local gauge transformation (cid:0)! As a brief quantum aside, we may write the canonical momentum D C a(cid:11) .x; (cid:28) / a0(cid:11) .x; (cid:28) / a(cid:11) .x; (cid:28) / @(cid:11)(cid:131) .x; (cid:28) / : (3.2) p(cid:22) D @L x(cid:22) D @ P M x(cid:22) P C e c a(cid:22) x(cid:22) (cid:0)! P D 1 M (cid:16)p(cid:22) e c (cid:0) a(cid:22)(cid:17) 3.2. LORENTZ FORCE 27 to ﬁnd the Hamiltonian K p(cid:22) x(cid:22) P (cid:0) L D D 1 2M (cid:16)p(cid:22) e c (cid:0) a(cid:22)(cid:17) (cid:16)p(cid:22) e c (cid:0) a(cid:22)(cid:17) ec5 c a5 (cid:0) showing that under (3.2) the Stueckelberg–Schrodinger equation @(cid:28) .x; (cid:28)/ i (cid:132) D K .x; (cid:28)/ (cid:16)i @(cid:28) (cid:132) C (cid:0)! ec5 c a5(cid:17) .x; (cid:28) / 1 2M (cid:16)p 2 a(cid:17) e c (cid:0) D .x; (cid:28)/ enjoys the symmetry [3] .x; (cid:28)/ ! exp (cid:20) ie c (cid:132) (cid:131).x; (cid:28)/(cid:21) .x; (cid:28)/ expressing the local U(1) gauge transformation in the familiar form introduced by Fock. LORENTZ FORCE 3.2 To study the interaction of an event with the gauge potentials a(cid:11).x; (cid:28)/, we write the Lagrangian as C with local metric g(cid:22)(cid:23).x/. Applying the Euler–Lagrange derivative to the kinetic term we obtain C D L Mg(cid:22)(cid:23) 1 2 x(cid:22) P x(cid:23) P e c g(cid:22)(cid:23) x(cid:22)a(cid:23) P ec5 c a5 (3.3) g(cid:26)(cid:27) (cid:18) d d (cid:28) @ @ x(cid:27) (cid:0) P @ @x(cid:27) (cid:19) 1 2 Mg(cid:22)(cid:23) x(cid:22) P x(cid:23) P M x(cid:26) R D C M (cid:18)g(cid:26)(cid:27) @g(cid:27)(cid:22) @x(cid:23) (cid:0) 1 2 g(cid:26)(cid:27) @g(cid:22)(cid:23) @x(cid:27) (cid:19) x(cid:22) P x(cid:23): P Using the symmetry of the ﬁrst term in parentheses under (cid:22) g(cid:26)(cid:27) @g(cid:27)(cid:22) @x(cid:23) P x(cid:22) x(cid:23) P D 1 2 (cid:18)g(cid:26)(cid:27) @g(cid:27)(cid:22) @x(cid:23) C (cid:23) $ g(cid:26)(cid:27) @g(cid:27)(cid:23) @x(cid:22) (cid:19) x(cid:22) P x(cid:23) P we ﬁnd where g(cid:26)(cid:27) (cid:18) d d (cid:28) @ x(cid:27) (cid:0) @ P @ @x(cid:27) (cid:19) 1 2 Mg(cid:22)(cid:23) x(cid:22) P x(cid:23) P M x(cid:26) R D C M (cid:128) (cid:26) x(cid:22) (cid:22)(cid:23) P x(cid:23) P D M x(cid:22) D P D(cid:28) ; (cid:128) (cid:26) (cid:22)(cid:23) D 1 2 g(cid:26)(cid:27) (cid:18) @g(cid:27)(cid:22) @x(cid:23) C @g(cid:27)(cid:23) @x(cid:22) (cid:0) @g(cid:22)(cid:23) @x(cid:27) (cid:19) x(cid:22)=D(cid:28) is the absolute derivative of P x(cid:22) along a geodesic. P is the standard Christoﬀel symbol and D For the interaction term @ x(cid:27) (cid:0) P (cid:18) d d (cid:28) x(cid:22)a(cid:23) P @ @x(cid:27) (cid:0)g(cid:22)(cid:23) C (cid:19) @ c5a5(cid:1) (cid:18)g(cid:22)(cid:23) d d (cid:28) da(cid:27) d (cid:28) (cid:0) P x(cid:22) (cid:0)@(cid:22)a(cid:27) x(cid:22) (cid:0)@(cid:22)a(cid:27) D D D P D P x(cid:22) @ x(cid:27) a(cid:23)(cid:19) P @ P x(cid:22)@(cid:27) a(cid:22) (cid:0) @(cid:27) a(cid:22)(cid:1) @(cid:27) a(cid:22)(cid:1) (cid:0) (cid:0) @ @x(cid:27) (cid:0)g(cid:22)(cid:23) x(cid:22)a(cid:23) P C (cid:0) c5a5(cid:1) c5@(cid:27) a5 @(cid:28) a(cid:27) (cid:0) x5 .@5a(cid:27) C C P c5@(cid:27) a5 @(cid:27) a5/ (cid:0) 28 3. CLASSICAL ELECTRODYNAMICS so that the Lorentz force is M x(cid:26) R C M (cid:128) (cid:26) x(cid:22) (cid:22)(cid:23) P x(cid:23) P D (cid:0) e c D e c g(cid:26)(cid:27) (cid:0) x(cid:22) (cid:0)@(cid:22)a(cid:27) P (cid:0) @(cid:27) a(cid:22)(cid:1) x5 .@5a(cid:27) C P @(cid:27) a5/(cid:1) (cid:0) g(cid:26)(cid:27) (cid:0)f(cid:27)(cid:22) x(cid:22) P C f(cid:27)5 x5(cid:1) ; P where we have introduced f(cid:11)(cid:12) .x; (cid:28) / D @(cid:11)a(cid:12) .x; (cid:28) / (cid:0) @(cid:12) a(cid:11) .x; (cid:28) / (3.4) (3.5) as the gauge invariant ﬁeld strength tensor. We note that (3.4) reduces to the Stueckelberg force (1.2) if we put f(cid:22)(cid:23) .x; (cid:28) / F(cid:22)(cid:23) .x/ ! f(cid:22)5 .x; (cid:28) / G(cid:22) .x/ ! and so may be said to generalize the Stueckelberg ansatz, for which it provides a foundational justiﬁcation in gauge theory. In analogy to Maxwell theory, we may take a(cid:22) 0 in (3.3) and approximate D .ec5=c/a5.x; (cid:28)/ (cid:0) .e=c/(cid:30).x/ V .x/ D ’ (cid:0) to identify the ﬁfth potential with the scalar potential V .x/ used in Section 2.3. We put the Lorentz force into a more compact form as x(cid:26) D P D(cid:28) D M x(cid:26) R C M (cid:128) (cid:26) x(cid:22) (cid:22)(cid:23) P x(cid:23) P D e c g(cid:26)(cid:27) f(cid:27)(cid:11) x(cid:11) P (3.6) and notice that the index (cid:26) runs to 3, while the index (cid:11) runs to 5. The ﬁfth equation is found by evaluating D D(cid:28) (cid:18) (cid:0) 1 2 M x2(cid:19) P x(cid:26)M D (cid:0) P x(cid:26) P D x(cid:26) D(cid:28) D (cid:0) P e c g(cid:26)(cid:27) (cid:0)f(cid:27)(cid:22) x(cid:22) P C f(cid:27)5 x5(cid:1) P D c5 c ef5(cid:22) x(cid:22); P (3.7) (cid:17) 0. This expression shows that the f5(cid:22) ﬁeld, expressing the action of a5.x; (cid:28) / where we used f55 x2 and must play a role and the (cid:28)-dependence of a(cid:22).x; (cid:28)/, permits the non-conservation of P is classical pair processes. We will see in Section 3.6 that this non-conservation represents an exchange of mass between particles and ﬁelds, where total mass-energy-momentum of particles and ﬁelds is conserved. Notice that the mass exchange is scaled by the factor c5=c. As we shall see in Section 4.8, this factor is a continuous measure of the deviation of SHP electrodynamics from Maxwell theory, which is recovered in the limit c5=c 0. We will generally take this factor to be small but ﬁnite. ! 3.3. FIELD DYNAMICS 29 3.3 FIELD DYNAMICS To construct a dynamical action for the ﬁelds we ﬁrst rewrite the interaction term as x(cid:11)a(cid:11).x; (cid:28)/ P X (cid:11)a(cid:11).x; (cid:28)/ (cid:0)! P (cid:0)! 1 c Z d 4x j (cid:11).x; (cid:28)/a(cid:11).x; (cid:28) /; where the event current j (cid:11).x; (cid:28)/ c X (cid:11).(cid:28)/(cid:14)4 (cid:0)x P (cid:0) D X.(cid:28)/(cid:1) (3.8) is deﬁned at each (cid:28) with support restricted to the spacetime location of the event at x X.(cid:28)/. The standard Maxwell current, representing the full worldline traced out by evolution of the event X.(cid:28)/, is found from D J (cid:22).x/ D Z d (cid:28) j (cid:22).x; (cid:28)/ c Z d (cid:28) D X (cid:22).(cid:28)/(cid:14)4 (cid:0)x P (cid:0) X.(cid:28) /(cid:1) (3.9) as seen for example in [4, p. 612]. This integration is called concatenation [5] and can be un- derstood as the sum at x of all events occurring at this spacetime location over (cid:28). The choice of kinetic term for a ﬁeld theory is guided by three principles: it should be a Lorentz scalar, gauge invariant, and simple (bilinear in the ﬁelds with the lowest reasonable order of derivatives). From experience with the Maxwell theory, we ﬁrst consider the electro- magnetic action containing a term of the form f (cid:11)(cid:12) .x; (cid:28)/f(cid:11)(cid:12) .x; (cid:28) / originally proposed by Saad et al. [3]. However, low-energy Coulomb scattering trajectories calculated in this theory [6] can- not be reconciled with Maxwell theory or experiment (we return to this point in Section 4.1). A satisfactory theory is found by generalizing the kinetic term so that the action takes the form [7] Sem D Z d 4xd (cid:28) (cid:26) e c2 j (cid:11).x; (cid:28)/a(cid:11).x; (cid:28)/ Z ds (cid:21) 1 4c (cid:0) hf (cid:11)(cid:12) .x; (cid:28) /(cid:136).(cid:28) s/f(cid:11)(cid:12) .x; s/i(cid:27) ; (cid:0) where (cid:21) is a parameter with dimensions of time. This may be written more compactly as Sem D Z d 4xd (cid:28) (cid:26) e c2 j (cid:11).x; (cid:28)/a(cid:11).x; (cid:28)/ 1 4c (cid:0) (cid:136) .x; (cid:28) / f(cid:11)(cid:12) .x; (cid:28)/(cid:27) ; f (cid:11)(cid:12) (3.10) where f (cid:11)(cid:12) (cid:136) .x; (cid:28)/ Z ds (cid:21) D (cid:136).(cid:28) (cid:0) s/f (cid:11)(cid:12) .x; s/ is a superposition of ﬁelds, non-local in (cid:28). The ﬁeld interaction kernel is chosen to be (cid:136).(cid:28)/ (cid:14) .(cid:28) / (cid:0) D .(cid:24)(cid:21)/2(cid:14)00 .(cid:28) / Z d (cid:20) 2(cid:25) D h1 C .(cid:24)(cid:21)(cid:20)/2i e(cid:0) i(cid:20)(cid:28) ; where the factor (cid:20)1 1 2 C 2(cid:21) (cid:17) (cid:16) c5 c (cid:24) D (3.11) (3.12) 30 3. CLASSICAL ELECTRODYNAMICS insures that the low-energy Lorentz force agrees with Coulomb’s law. Integrating by parts the term in (3.10) produced by the factor (cid:14)00 .(cid:28) s/ in (3.11), (cid:0) Z d (cid:28)ds f (cid:11)(cid:12) .x; (cid:28)/(cid:14)00.(cid:28) s/f(cid:11)(cid:12) .x; s/ (cid:0) Z d (cid:28)ds (cid:16)@(cid:28) f (cid:11)(cid:12) .x; (cid:28)/(cid:17) (cid:14)0.(cid:28) s/f(cid:11)(cid:12) .x; s/ (cid:0) Z d (cid:28) (cid:16)@(cid:28) f (cid:11)(cid:12) .x; (cid:28)/(cid:17) @(cid:28) f(cid:11)(cid:12) .x; (cid:28) / D (cid:0) D (cid:0) so that Sem D Z d 4xd (cid:28) (cid:26) e c2 j (cid:11)a(cid:11) 1 4c (cid:0) f (cid:11)(cid:12) f(cid:11)(cid:12) .(cid:24)(cid:21)/2 4c C (cid:16)@(cid:28) f (cid:11)(cid:12) (cid:17) (cid:0)@(cid:28) f(cid:11)(cid:12) (cid:1) (cid:27) (3.13) and the higher derivative in (cid:28) is seen to break the 5D symmetry of f (cid:11)(cid:12) f(cid:11)(cid:12) to O(3,1), leaving the gauge invariance of f (cid:11)(cid:12) unaﬀected. It remains necessary to give meaning to raising and (cid:17)55f5(cid:11). Expanding lowering the 5-index through f 5 (cid:11) D f (cid:11)(cid:12) f(cid:11)(cid:12) f (cid:22)(cid:23)f(cid:22)(cid:23) 2(cid:17)55f (cid:22) 5 f5(cid:22) D C 1 as the sign of the f 2 we see that we may interpret (cid:17)55 any necessary interpretation as an element in a 5D metric. D (cid:6) 5 term in the action, sidestepping Variation of the electromagnetic action (3.10) with respect to the potentials a(cid:11).x; (cid:28)/ leads to the ﬁeld equations e c describing a non-local superposition of ﬁelds f (cid:11)(cid:12) j (cid:11).x; (cid:28)/. In order to remove (cid:136).(cid:28)/ from the LHS, we use the inverse function (cid:136) .x; (cid:28)/ j (cid:11).x; (cid:28)/ @(cid:12) f (cid:11)(cid:12) D (cid:136) .x; (cid:28) / sourced by the local event current (3.14) ’.(cid:28)/ D (cid:21)(cid:136)(cid:0) 1.(cid:28)/ (cid:21) Z d (cid:20) 2(cid:25) D 1 which satisﬁes i(cid:20)(cid:28) e(cid:0) .(cid:24)(cid:21)(cid:20)/2 D C 1 2(cid:24) (cid:28) e(cid:0)j j =(cid:24)(cid:21) Z ds (cid:21) ’ .(cid:28) (cid:0) s/ (cid:136) .s/ (cid:14).(cid:28)/ D Z d (cid:28) (cid:21) ’ .(cid:28) / 1: D Integrating (3.14) with (3.15), we obtain @(cid:12) f (cid:11)(cid:12) .x; (cid:28) / e c D Z ds ’ .(cid:28) s/ j (cid:11) .x; s/ (cid:0) e c D j (cid:11) ’ .x; (cid:28) / (3.15) (3.16) (3.17) which describes a local ﬁeld sourced by a non-local superposition of event currents. While the event current (3.8) has sharp support at one spacetime point, the current j (cid:11) ’ .x; (cid:28) / c Z ds 2(cid:24) D e(cid:0)j (cid:28) s =(cid:24)(cid:21) j (cid:0) X (cid:11).s/(cid:14)4 (cid:0)x P (cid:0) X.s/(cid:1) (3.18) 3.4. ENSEMBLE OF EVENT CURRENTS 31 can be interpreted as the current induced by a smooth ensemble of events distributed in a neigh- borhood (cid:21) of a spacetime point. This interpretation is discussed further in Section 3.4. Because the ﬁeld strengths are derived from potentials, the Bianchi identity @(cid:11)f(cid:12)(cid:13) @(cid:13) f(cid:11)(cid:12) @(cid:12) f(cid:13)(cid:11) 0 D C C (3.19) holds. We see that (3.17) and (3.19) are formally similar to Maxwell’s equations in 5D, and are known as pre-Maxwell equations. Expanding the ﬁeld equations in 4D tensor, vector and scalar components, they take the form @(cid:23) f (cid:22)(cid:23) 1 c5 @ @(cid:28) (cid:0) f 5(cid:22) e c D j (cid:22) ’ @(cid:22) f 5(cid:22) e c j 5 ’ D @(cid:22)f(cid:23)(cid:27) @(cid:23)f(cid:27)(cid:22) @(cid:27) f(cid:22)(cid:23) 0 D C C @(cid:23)f5(cid:22) @(cid:22)f5(cid:23) (cid:0) 1 c5 @ @(cid:28) C f(cid:22)(cid:23) 0 D (3.20) which when compared with the 3-vector form of Maxwell’s equations B (cid:0) r (cid:2) 1 c @ @t E D e c J E D r (cid:1) B 0 D r (cid:1) E r (cid:2) C e c 1 c J 0 @ @t B 0 D suggest that f 5(cid:22) plays the role of the electric ﬁeld, whose divergence provides the Gauss law, and f (cid:22)(cid:23) plays the role of the magnetic ﬁeld. It follows from (3.17) that @(cid:11)j (cid:11) @(cid:22)j (cid:22) D 1 c5 @ @(cid:28) C j (cid:11) 0 D (3.21) so that j 5 .x; (cid:28) / D c5 (cid:26) .x; (cid:28) / plays the role of an event density, and d d (cid:28) Z d 4x (cid:26) .x; (cid:28) / Z d 4x @(cid:22)j (cid:22) .x; (cid:28) / 0 D D (cid:0) shows the conservation of total event number over spacetime, in the absence of injection/removal of events at the boundary by an external process. ENSEMBLE OF EVENT CURRENTS 3.4 The function ’.(cid:28)/ smooths the current deﬁned sharply at the event, over a range determined 1 for all (cid:28), producing a current ensemble associated with a large by (cid:21). For (cid:21) very large, ’.(cid:28)/ section of the worldline, approximating the standard Maxwell current. For (cid:21) 0, we approach the limit ’.(cid:28)/=(cid:21) (cid:14).(cid:28)/ which restricts the source current to the instantaneous current produced by a single event. ! ! ’ 32 3. CLASSICAL ELECTRODYNAMICS Rewriting the current (3.18) as j (cid:11) ’ .x; (cid:28) / D Z ds’ .(cid:28) (cid:0) s/ j (cid:11) .x; s/ 1 2(cid:24) D Z ds e(cid:0)j s =(cid:24)(cid:21) j (cid:11) .x; (cid:28) j s/ (cid:0) (cid:0) we recognize j (cid:11) ’ .x; (cid:28) / as a weighted superposition of currents. Each of these currents originates s/ along the worldline, occurring before or after the event X (cid:22).(cid:28)/, depend- at an event X (cid:22).(cid:28) ing on the displacement s. The superposition may thus be seen [8] as the current produced by an ensemble of events in the neighborhood of X (cid:22).(cid:28)/, a probabilistic view encouraged by the functional form of the weight ’.s/. Consider a Poisson distribution describing the occurrence of independent random events produced at a constant average rate of 1=(cid:21)(cid:24) events per second. The average time between events is (cid:21)(cid:24) and the probability at (cid:28) that the next event will occur s=(cid:24)(cid:21)=(cid:24)(cid:21), which may be extended to positive following a time interval s > 0 is just ’.s/=(cid:21) and negative values of the displacement. The current j (cid:11) ’ .x; (cid:28) / is constructed by assembling a set of event currents j (cid:11) .x; (cid:28) s/ along the worldline, each weighted by ’.s/, the probability that the event occurrence is delayed from (cid:28) by an interval of at least . We will see that the causality relations embedded in the pre-Maxwell equations select the one event from this ensemble for which an interaction occurs at lightlike separation, preserving relativistic causality. e(cid:0) D (cid:0) s j j We may also regard j (cid:11) ’ .x; (cid:28) / as a random variable describing the probability of ﬁnding a current density at x at a given (cid:28). The correlation function for the event density is (cid:10)(cid:26) .(cid:28)/ (cid:26) .s/(cid:11) 1 N D Z d 4x (cid:26) .x; (cid:28) / (cid:26) .x; s/ ; where N is a normalization. In the case of an event X (cid:22).(cid:28)/ the unsmoothed event current (3.8) leads to D u(cid:22)(cid:28) with constant velocity u(cid:22), (cid:10)(cid:26) .(cid:28) / (cid:26) .s/(cid:11) c2 N D Z d 4x (cid:14)4 .x u(cid:28) / (cid:14)4 .x (cid:0) us/ (cid:0) D c2(cid:14)3 .0/ u0 N (cid:14).(cid:28) j j s/ (cid:0) showing that the currents at diﬀering times (cid:28) deﬁned in (3.18) the correlation becomes ⁄ s are uncorrelated. For the ensemble current Z d (cid:28) 0ds0d 4x ’.(cid:28) (cid:28) 0/’.s (cid:0) (cid:0) s0/(cid:14)4 (cid:0)x (cid:0) u(cid:28) 0(cid:1) (cid:14)4 (cid:0)x us0(cid:1) (cid:0) (cid:10)(cid:26)’ .(cid:28)/ (cid:26)’ .s/(cid:11) D D D c2 N c2(cid:14)3 .0/ N u0 j j c2(cid:14)3 .0/ N u0 4(cid:24) 2 j j Z d (cid:28) 0 ’.(cid:28) (cid:0) Z d (cid:28) 0 e(cid:0)j (cid:28) (cid:28) 0/’.(cid:28) 0 s/ (cid:0) =(cid:24)(cid:21) (cid:28) 0j s (cid:28) 0(cid:0) =(cid:24)(cid:21): j (cid:0)j (cid:0) Taking (cid:28) > s and evaluating the integral over three intervals punctuated by s, (cid:28) 0, and (cid:28) leads to (cid:10)(cid:26)’ .(cid:28) / (cid:26)’ .s/(cid:11) D (cid:21)c2(cid:14)3 .0/ N u0 4(cid:24) j j (cid:18)1 (cid:28) (cid:0) (cid:24)(cid:21) C s (cid:19) e(cid:0) .(cid:28) (cid:0) s/=(cid:24)(cid:21) 3.5. THE 5D WAVE EQUATION AND ITS GREEN’S FUNCTIONS 33 with a time-dependence characteristic of an Ornstein–Uhlenbeck process with correlation length (cid:21). This correlation suggests that the current ensemble may be seen as the set of instan- taneous currents induced by an event undergoing a Brownian motion that produces random displacement in (cid:28) under viscous drag along the worldline. 3.5 THE 5D WAVE EQUATION AND ITS GREEN’S FUNCTIONS Using (3.5) to expand (3.17) leads to the wave equation @(cid:12) f (cid:11)(cid:12) (cid:0) D (cid:0) @(cid:12) (cid:16)@(cid:11)a(cid:12) (cid:0) @(cid:12) a(cid:11)(cid:17) D @(cid:12) @(cid:12) a(cid:11) D (cid:18)@(cid:22)@(cid:22) (cid:17)55 c2 5 C (cid:19) a(cid:11) @2 (cid:28) e c j (cid:11) ’ ; D (cid:0) (3.22) where we work in the 5D Lorenz gauge @(cid:12) a(cid:12) 0. As discussed above, this form partially pre- D serves 5D symmetries broken by the O(3,1) symmetry of the event dynamics. A Green’s function solution to (cid:18)@(cid:22)@(cid:22) C (cid:17)55 c2 5 (cid:19) G.x; (cid:28)/ @2 (cid:28) (cid:14)4 .x/ (cid:14) .(cid:28) / D (cid:0) can be used to obtain potentials in the form a(cid:11) .x; (cid:28) / e c D (cid:0) Z d 4x0d (cid:28) 0 G (cid:0)x x0; (cid:28) (cid:0) (cid:0) (cid:28) 0(cid:1) j (cid:11) ’ (cid:0)x0; (cid:28) 0(cid:1) : (3.23) The Green’s function can be expressed as the Fourier transform G.x; (cid:28)/ 1 .2(cid:25)/5 Z C D d 5k eik(cid:11)x(cid:11) k(cid:11)k(cid:11) D 1 .2(cid:25)/5 Z C d 4k d (cid:20) ei.k x (cid:1) C c5(cid:17)55(cid:20)(cid:28)/ 1 (cid:17)55(cid:20)2 k2 C over an appropriate contour C . To break the 5D symmetry present in the wave equation, we leave the (cid:20) integration for last, writing G.x; (cid:28)/ 1 2(cid:25) D Z d (cid:20) eic5(cid:17)55(cid:20)(cid:28) (cid:129) (cid:0)x; (cid:17)55(cid:20)2(cid:1) ; where (cid:129).x; m2/ is Schwinger’s principal part Green’s function [9] associated with the Klein– Gordon equation for a particle of mass m. Carefully repeating the steps of Schwinger’s deriva- tion, while allowing (cid:17)55 to be positive or negative, we are led to G.x; (cid:28)/ 1 .2(cid:25)/2 D (cid:0) Z d (cid:20) eic5(cid:17)55(cid:20)(cid:28) (cid:20)(cid:14) (cid:0)x2(cid:1) (cid:18) (cid:0) C (cid:17)55x2(cid:1) (cid:0) @ 1=2(cid:17)(cid:21) : x2(cid:12) @x2 J0 (cid:16)(cid:20) (cid:12) (cid:12) (cid:12) Now performing the (cid:20) integration, the pre-Maxwell Green’s function becomes G.x; (cid:28)/ 1 2(cid:25) D (cid:0) (cid:14).x2/(cid:14).(cid:28)/ c5 2(cid:25) 2 @ @x2 (cid:18). (cid:0) (cid:17)55g(cid:11)(cid:12) x(cid:11)x(cid:12) / (cid:0) 1 q (cid:0) (cid:17)55g(cid:11)(cid:12) x(cid:11)x(cid:12) (3.24) 34 3. CLASSICAL ELECTRODYNAMICS 2 1. The ﬁrst term contains the O(3,1) scalars so that both terms have units of distance(cid:0) time(cid:0) x2 and (cid:28) separately, and is called GMaxwell. It has support at instantaneous (cid:28) and, as in Maxwell theory, along lightlike separations. The second term, called GCorrelation, has support determined by (cid:2) (cid:17)55(cid:17)(cid:11)(cid:12) x(cid:11)x(cid:12) (cid:0) 8 < : D (cid:0) (cid:0)x2 (cid:0)x2 c2 5 (cid:28) 2(cid:1) c2t 2 x2 c2 5 (cid:28) 2 > 0 ; (cid:17)55 D x2 C c2 5 (cid:28) 2(cid:1) (cid:0) c2 5 (cid:28) 2 > 0 (cid:0) 1 and spacelike separations for (cid:17)55 (cid:0) c2t 2 D (cid:0) (cid:0) 1 D ; (cid:17)55 1 D (cid:0) on timelike separations for (cid:17)55 1. Contributions from GCorrelation are generally smaller than those of GMaxwell and drop oﬀ faster with distance from the source. To avoid singularities, particular care must be taken in handling the distribution functions. The derivative in GCorrelation produces two singular terms D (cid:0) D GCorrelation .x; (cid:28) / c5 2(cid:25) 2 1 2 D (cid:0) (cid:18). x2 (cid:0) x2 (cid:0) (cid:0) (cid:0) c2 5 (cid:28) 2/ (cid:0) c2 5 (cid:28) 2(cid:1) 3=2 (cid:0) (cid:0) (cid:14) (cid:0) x2 (cid:0) x2 (cid:0) (cid:0) ! c2 5 (cid:28) 2(cid:1) 1=2 (cid:0) c2 5 (cid:28) 2(cid:1) but these singularities cancel when ﬁrst combined under integrals of the type (3.23) prior to applying the limits of integration. This order of operations expresses an aspect of the boundary conditions posed by Schwinger in deriving the Klein–Gordon Green’s function. THE MASS-ENERGY-MOMENTUM TENSOR (cid:11) x0 ! (cid:30) .x/ x(cid:11) D C (cid:14)0(cid:30) .x/ C (cid:14)x(cid:11) that leave the action invariant, a ﬁeld undergoes (cid:14)x(cid:30) .x/ (cid:30) .x/ C D (cid:14)0(cid:30) .x/ C C (cid:14)x(cid:11)@(cid:11)(cid:30) .x/ ; 3.6 Under transformations x(cid:11) (cid:30) .x/ (cid:30)0 (cid:0)x0(cid:1) D ! where is a variation in the form of the ﬁeld at a ﬁxed point x and (cid:14)0(cid:30) .x/ (cid:30)0 .x/ (cid:30) .x/ D (cid:0) is a variation induced in the ﬁxed form of the ﬁeld by the variation of x. The action undergoes (cid:14)x(cid:30) .x/ D (cid:14)x(cid:11)@(cid:11)(cid:30) .x/ (cid:14)Sem D Z (cid:131)0 d 4x0d (cid:28) 0L0 Z (cid:0) (cid:131) d 4x d (cid:28) L; where (cid:131) ! this becomes (cid:131)0 is the change of volume induced by the variation in x. Expanding the ﬁrst term, (cid:14)Sem D (cid:0) Z (cid:131) d 4x d (cid:28) .@(cid:11)L/ (cid:14)x(cid:11) Z C (cid:131) d 4x d (cid:28) @(cid:11) (cid:18)Lg(cid:11) @L @ .@a(cid:30)/ (cid:12) (cid:0) @(cid:12) (cid:30) .x/(cid:19) (cid:14)x(cid:12) Z (cid:0) (cid:131) d 4x d (cid:28) @(cid:11) (cid:18) @L @ .@a(cid:30)/ (cid:14)x(cid:12) (cid:14)(cid:12) (cid:30)(cid:19) ; where we used the Euler–Lagrange equations 3.6. THE MASS-ENERGY-MOMENTUM TENSOR 35 @L @(cid:30) (cid:0) @a (cid:18) @L (cid:19) @ .@a(cid:30)/ D 0: Since (cid:14)S D 0 and the variations are arbitrary, we obtain Noether’s theorem (cid:18)Lg(cid:11)(cid:12) @(cid:11) @L @ .@a(cid:30)/ (cid:0) @(cid:12) (cid:30) .x/(cid:19) @(cid:11)Q(cid:11)(cid:12) 0 D D for the conserved current Q(cid:11)(cid:12) . The electromagnetic Lagrangian can be written Lem D e c2 j (cid:11).x; (cid:28)/a(cid:11).x; (cid:28)/ (cid:0) 1 4c f (cid:11)(cid:12) (cid:136) .x; (cid:28)/f(cid:11)(cid:12) .x; (cid:28) / ; where f (cid:11)(cid:12) (cid:136) .x; (cid:28) / Z ds (cid:21) D (cid:136).(cid:28) (cid:0) s/ f (cid:11)(cid:12) .x; s/ is the non-local convolved ﬁeld. Under translations, (cid:14)x(cid:12) "(cid:12) D (cid:14)a(cid:11) 0 D (cid:0)! and so the conserved current is Q(cid:18) (cid:11)(cid:12) (cid:136) D @L @ (cid:0)@(cid:11)a(cid:13) (cid:1) @(cid:12) a(cid:13) (cid:0) Lg(cid:11)(cid:12) 1 c g(cid:11)(cid:12) (cid:18) 1 4 D f (cid:14)" (cid:136) f(cid:14)" e c j (cid:1) a(cid:19) (cid:0) 1 c (cid:0) f (cid:11)(cid:13) (cid:136) @(cid:12) a(cid:13) : This current may be made symmetric in the indices by adding the total divergence (cid:129)(cid:18) (cid:11)(cid:12) (cid:136) D 1 c @(cid:13) (cid:16)f (cid:11)(cid:13) (cid:136) a(cid:12) (cid:17) e c2 j (cid:11)a(cid:12) C 1 c D f (cid:11)(cid:13) (cid:136) @(cid:13) a(cid:12) ; where the second form follows from the inhomogeneous pre-Maxwell equation. Now, the sym- metric current is (cid:136) D Q(cid:18) (cid:11)(cid:12) (cid:18) (cid:11)(cid:12) (cid:136) C (cid:129)(cid:18) (cid:11)(cid:12) (cid:136) D (cid:18) (cid:11)(cid:12) (cid:136)0 C e c2 hj (cid:11)a(cid:12) j (cid:1) (cid:0) a g(cid:11)(cid:12) i ; where (cid:18) (cid:11)(cid:12) (cid:136)0 D 1 c (cid:20)f (cid:11)(cid:13) (cid:136) f (cid:12) (cid:13) C (cid:136) f(cid:14)"g(cid:11)(cid:12) (cid:21) f (cid:14)" 1 4 is the source-free current. By explicit calculation, using the homogeneous pre-Maxwell equation, we ﬁnd @(cid:11)T (cid:11)(cid:12) (cid:136) D (cid:0) e c2 f (cid:12) (cid:11)j(cid:11); 36 3. CLASSICAL ELECTRODYNAMICS where T (cid:11)(cid:12) (cid:136) D (cid:0) (cid:18) (cid:11)(cid:12) (cid:136)0 D 1 c (cid:20)f (cid:11)(cid:13) (cid:136) f (cid:12) (cid:13) (cid:0) g(cid:11)(cid:12) f (cid:14)" (cid:136) f(cid:14)" (cid:21) 1 4 (3.25) is the conserved mass-energy-momentum tensor. Writing the (cid:12) D 5 component of the conservation law @(cid:11)T (cid:11)5 (cid:136) D (cid:0) e c2 f 5(cid:11)j(cid:11) and using for the single particle current leads to j (cid:11).x; (cid:28)/ c X (cid:11).(cid:28)/(cid:14)4 (cid:0)x P (cid:0) D X.(cid:28)/(cid:1) @(cid:11)T (cid:11)5 (cid:136) D (cid:0) e c f 5(cid:11) .x; (cid:28) / X(cid:11).(cid:28)/(cid:14)4 (cid:0)x P (cid:0) X.(cid:28) /(cid:1) : Integrating the LHS over spacetime leaves the (cid:28)-derivative Z d 4x @(cid:11)T (cid:11)5 (cid:136) D Z d 4x @(cid:22)T (cid:22)5 (cid:136) C 1 c5 d d (cid:28) Z d 4x T 55 (cid:136) D 1 c5 d d (cid:28) Z d 4x T 55 (cid:136) and integrating the RHS gives e c (cid:0) Z d 4x f 5(cid:22) .x; (cid:28) / X(cid:22).(cid:28)/(cid:14)4 (cid:0)x P (cid:0) X.(cid:28)/(cid:1) D (cid:0) e c f 5(cid:22) .X.(cid:28)/; (cid:28) / X(cid:22).(cid:28)/: P Recognizing this expression from the ﬁfth Lorentz force equation d d (cid:28) (cid:18) (cid:0) 1 2 M x2(cid:19) P D (cid:17)55 ec5 c f 5(cid:22) x(cid:22) P the RHS and LHS combine as d d (cid:28) (cid:20)Z d 4x T 55 (cid:136) C (cid:17)55 (cid:18) (cid:0) 1 2 M x2(cid:19)(cid:21) P 0 D demonstrating that the total mass of ﬁelds and events is conserved. c2), we see that T 55 Since M x2 has units of energy ( P x2 P D (cid:0) (energy per 4D spacetime volume). (cid:136) has units of energy density 3.7 WORLDLINE CONCATENATION We saw in (3.21) that the source current satisﬁes @(cid:11)j (cid:11) ’ .x; (cid:28) / cannot be a divergenceless Maxwell current. However, Stueckelberg noticed that under the boundary condition 0, and so the vector part j (cid:22) ’ .x; (cid:28) / D j 5 ’ .x; (cid:28)/ 0 (cid:28) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! !(cid:6)1 3.7. WORLDLINE CONCATENATION 37 we have @(cid:22) Z d (cid:28) j (cid:22) ’ .x; (cid:28) / 1 c5 C Z d (cid:28) @(cid:28) j 5 ’ .x; (cid:28) / @(cid:22)J (cid:22).x/ 0; D D where using (3.16) we conﬁrm J (cid:22).x/ D Z d (cid:28) j (cid:22) ’ .x; (cid:28) / Z d (cid:28) Z ds (cid:21) D ’ .(cid:28) (cid:0) s/ j (cid:11) .x; s/ D Z ds j (cid:22) .x; s/ in agreement with (3.9). Again, this integration, called concatenation [5], represents the sum at the spacetime point x of all events occurring over time (cid:28). Saad and Horwitz [3] extended Stueckelberg’s argument, showing that under the additional boundary condition f 5(cid:22).x; (cid:28)/ 0 (cid:28) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! !(cid:6)1 (cid:28)-integration of the pre-Maxwell equations leads to Maxwell’s equations in the form @(cid:12) f (cid:11)(cid:12) .x; (cid:28) / e c D j (cid:11) ’ .x; (cid:28) / @(cid:140)(cid:11)f(cid:12)(cid:13)(cid:141) 0 D @(cid:11)j (cid:11) 0 D 9 >>>>>= >>>>>; (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)! Z d (cid:28) (cid:21) 8 (cid:136)(cid:136)(cid:136)(cid:136)(cid:136)< (cid:136)(cid:136)(cid:136)(cid:136)(cid:136): @(cid:23)F (cid:22)(cid:23) .x/ e c D J (cid:22) .x/ @(cid:140)(cid:22)F(cid:23)(cid:26)(cid:141) 0 D @(cid:22)J (cid:22).x/ 0; D where Z d (cid:28) (cid:21) Under concatenation, F (cid:22)(cid:23) become Maxwell ﬁelds while F 5(cid:22) decouples from the Maxwell sys- tem. In addition, integrating the Green’s function (3.24) for the pre-Maxwell wave equation f (cid:11)(cid:23).x; (cid:28)/: F (cid:11)(cid:23).x/ D Z d (cid:28) GMaxwell D.x/ D D (cid:0) 1 2(cid:25) (cid:14).x2/ Z d (cid:28) GCorrelation 0 D (3.26) recovers the 4D Maxwell Green’s function. When concatenating GCorrelation, the two singular terms arising from the derivative must once again be subtracted prior to applying the limits of integration. As we have seen, SHP electrodynamics can be understood as a microscopic theory of events interacting at time (cid:28). We saw in Section 3.6 that during these interactions, particles and pre-Maxwell ﬁelds may exchange mass under conservation of total mass-energy-momentum. As mentioned in Section 1.3, Feynman recognized that mass exchange of this type is also permitted, in principle, in QED. He interpreted integration over the evolution parameter, the ﬁnal step in Equation (1.3) that describes the quantum Green’s function for scalar particles, as extraction of asymptotic mass eigenstates from these complex interactions. In much the same way, we will see that concatenation—integration of the pre-Maxwell ﬁeld equations over the evolution 38 3. CLASSICAL ELECTRODYNAMICS parameter (cid:28)—extracts from the microscopic event interactions the massless modes in Maxwell electrodynamics, expressing a certain equilibrium limit when mass exchange settles to zero. Thus, we will frequently compare the concatenated form of results in pre-Maxwell electrodynamics with the corresponding formulation in Maxwell theory, as a means of maintaining contact with established phenomenology. 3.8 PCT IN CLASSICAL SHP THEORY We recall from Section 1.1 that Stueckelberg’s initial motivation for consideration of (cid:28)-evolution was his desire to formulate a classical electrodynamics that includes antiparticles and describes pair processes through the dynamic evolution of a single type of evolution x(cid:22).(cid:28)/. And as we saw in Section 2.3, particles and antiparticles diﬀer only in the direction of their t-evolution, p0c. In quantum ﬁeld x0.(cid:28)/, or equivalently the sign of the energy E speciﬁcally the sign of P theory the relationship of particles and antiparticles, characterized by a charge conjugation op- eration C , is signiﬁcantly diﬀerent. This operation is understood as a third discrete symmetry of the ﬁeld equations, along with the improper Lorentz symmetries—time reversal T and space reversal P —that we expect to hold for a Lorentz covariant system. An antiparticle is obtained by acting with C and T to produce a particle with both the sign of the charge and the temporal ordering of its evolution reversed. Operator implementation of C generally requires a quantum formalism with complex wavefunctions, and the combined C T operation is anti-unitary. D We require electrodynamics to be symmetric under the improper Lorentz transformations T and P , and ﬁrst ﬁnd the transformations of the ﬁelds under these operations. We then consider a C operation, which in Wigner’s original sense of “reversal of the direction of motion” [10], acts on the (cid:28)-evolution. The Lorentz equations in explicit three-vector form are M d 2x0 d (cid:28) 2 D d 2x d (cid:28) 2 D M (cid:20)e .t; x; (cid:28) / (cid:1) (cid:20)e .t; x; (cid:28) / e c e c d x d (cid:28) (cid:0) dx0 d (cid:28) C (cid:17)55 (cid:15)0 .t; x; (cid:28) /(cid:21) d x d (cid:28) (cid:2) b .t; x; (cid:28) / (cid:0) (cid:17)55 (cid:15) .t; x; (cid:28) /(cid:21) and under space inversion P x D (cid:0)x0; x(cid:1) xP D (cid:0)!P (cid:0)x0 P ; xP (cid:1) (cid:0)x0; x(cid:1) (cid:0) D become M M d 2x0 P d (cid:28) 2 D d 2xP d (cid:28) 2 D e c e c (cid:20)eP .tP ; xP ; (cid:28) / (cid:20)eP .tP ; xP ; (cid:28) / d xP d (cid:28) (cid:0) (cid:1) dx0 P d (cid:28) C (cid:17)55(cid:15)0 P .tP ; xP ; (cid:28) /(cid:21) d xP d (cid:28) (cid:2) bP .tP ; xP ; (cid:28) / (cid:0) (cid:17)55(cid:15)P .tP ; xP ; (cid:28) /(cid:21) so that M d 2x0 d (cid:28) 2 D d 2x d (cid:28) 2 D M 3.8. PCT IN CLASSICAL SHP THEORY 39 e c e c (cid:20) (cid:0) (cid:20) (cid:0) eP .tP ; xP ; (cid:28) / eP .tP ; xP ; (cid:28) / d x d (cid:28) (cid:0) (cid:1) dx0 d (cid:28) C (cid:17)55(cid:15)0 P .tP ; xP ; (cid:28) /(cid:21) d x d (cid:28) (cid:2) bP .tP ; xP ; (cid:28) / (cid:17)55 . (cid:15) .tP ; xP ; (cid:28) //(cid:21) : (cid:0) (cid:0) Invariance under P , understood as form invariance of the interaction, requires that eP .tP ; xP ; (cid:28) / (cid:15)0 P .tP ; xP ; (cid:28) / e .t; x; (cid:28) / (cid:15)0 .t; x; (cid:28) / D (cid:0) D bP .tP ; xP ; (cid:28) / (cid:15)P .tP ; xP ; (cid:28) / D D (cid:0) b .t; x; (cid:28) / (cid:15) .t; x; (cid:28) / and as we would generally expect, the vectors e and (cid:15) change sign, while the axial vector b and 0-component (cid:15)0 are unchanged. Under time inversion T , x D (cid:0)x0; x(cid:1) xT D (cid:0)!T (cid:0)x0 T ; xT (cid:1) (cid:0) (cid:0) D x0; x(cid:1) I we similarly write M M d 2x0 T d (cid:28) 2 D d 2xT d (cid:28) 2 D e c e c (cid:20)eT .tT ; xT ; (cid:28) / (cid:20)eT .tT ; xT ; (cid:28) / d xT d (cid:28) (cid:0) (cid:1) dx0 T d (cid:28) C (cid:17)55(cid:15)0 T .tT ; xT ; (cid:28) /(cid:21) d xT d (cid:28) (cid:2) bT .tT ; xT ; (cid:28) / (cid:0) (cid:17)55(cid:15)T .tT ; xT ; (cid:28) /(cid:21) so that M d 2x0 d (cid:28) 2 D d 2x d (cid:28) 2 D e c e c (cid:20) (cid:20) (cid:0) (cid:0) M eT .tT ; xT ; (cid:28) / eT .tT ; xT ; (cid:28) / d x d (cid:28) (cid:0) (cid:1) dx0 d (cid:28) C (cid:15)0 T .tT ; xT ; (cid:28) /(cid:1) (cid:21) (cid:17)55 (cid:0) (cid:0) d x d (cid:28) (cid:2) bT .tT ; xT ; (cid:28) / (cid:0) (cid:17)55(cid:15)T .tT ; xT ; (cid:28) /(cid:21) : Now form invariance requires eT .tT ; xT ; (cid:28) / (cid:15)0 T .tT ; xT ; (cid:28) / e .t; x; (cid:28) / (cid:15)0 .t; x; (cid:28) / D (cid:0) D (cid:0) bT .tT ; xT ; (cid:28) / (cid:15)T .tT ; xT ; (cid:28) / b .t; x; (cid:28) / (cid:15) .t; x; (cid:28) / D D and here we notice that (cid:15)0 and (cid:15) transform as expected for components of a 4-vector, but the transformations of e and b are opposite to the behavior generally attributed to the electric and magnetic 3-vectors under time inversion. This can be attributed to our having respected the independence of x0 .(cid:28) / as a function of (cid:28), not constrained by the mass-shell condition dx0 d (cid:28) D C 1 q1 (cid:0) .d x=dt/2 : 40 3. CLASSICAL ELECTRODYNAMICS In general, all of the ﬁeld components transform tensorially as components of the f (cid:22)(cid:23) and (cid:15)(cid:22). From the transformation properties for the ﬁeld strengths, we may deduce the transfor- mation properties of the 5-vector potential components. First, we have ei P D (cid:0) and so we conclude that ei H) @0ai P (cid:0) (cid:0) (cid:0) @i (cid:1) a0 P D (cid:0) (cid:0)@0ai @i a0(cid:1) (cid:0) (3.27) which is consistent with a0 P D a0 ai P D (cid:0) ai bi P D bi D "ij k@j ak : Similarly, so we see that ei T D (cid:0) ei H) @0ai T (cid:0) (cid:0) @i a0 T D (cid:0) (cid:0)@0ai (cid:0) @i a0(cid:1) again consistent with (3.27). For the second vector ﬁeld, a0 T D (cid:0) a0 ai T D ai (cid:15)i P D (cid:0) (cid:15)i H) @5ai P (cid:0) (cid:0) (cid:0) @i (cid:1) a5 P D (cid:0) (cid:0)@5ai (cid:0) @i a5(cid:1) along with ai P D (cid:0) ai leads to which is consistent with Similarly, a5 P D a5 (cid:15)0 P D (cid:15)0 D @5a0 (cid:0) @0a5: (cid:15)i (cid:15)i T D ai leads to H) @5ai T (cid:0) @i a5 T D @5ai (cid:0) @i a5 along with ai T D a5 T D Thus, the 4-vector and scalar components of the potential transform tensorially under space and time inversion. a5: The pre-Maxwell equations in 3-vector form, as given in (4.17) and (4.18), e (cid:0) r (cid:1) b (cid:0) r (cid:2) 1 c5 1 c @ @(cid:28) (cid:15)0 @ @t e e c j 0 ’ D e(cid:26)0 ’ @ @(cid:28) (cid:15) D e c j’ D 1 c5 (cid:15) C r (cid:1) 1 c @ @t (cid:15)0 D ec5 c (cid:26)’ (cid:0) e c r j 5 ’ D 1 c C (cid:15)0 @ @t (cid:15) (cid:17)55 1 c5 @ @(cid:28) e C 0 D r (cid:1) b D 1 @ c @t C (cid:17)55 1 c5 0 b 0 D @ @(cid:28) b 0 D e r (cid:2) (cid:15) (cid:0) r (cid:2) are seen to be invariant under P and T using the transformations of the ﬁelds, under the choices 3.8. PCT IN CLASSICAL SHP THEORY 41 j 0 P .tP ; xP ; (cid:28) / D j 0 .t; x; (cid:28) / j 0 T .tT ; xT ; (cid:28) / j 0 .t; x; (cid:28) / D (cid:0) jP .tP ; xP ; (cid:28) / D (cid:0) j .t; x; (cid:28) / jT .tT ; xT ; (cid:28) / j .t; x; (cid:28) / D j 5 P .tP ; xP ; (cid:28) / D j 5 .t; x; (cid:28) / j 5 T .tT ; xT ; (cid:28) / D j 5 .t; x; (cid:28) / ; where again the 4-vector and scalar components of the current transform tensorially under space and time inversion. In order to discuss charge conjugation, we must make another short digression into quan- tum mechanics. As in Section 3.1, we may write the Stueckelberg–Schrodinger equation as (cid:16)i@(cid:28) ec5 c C a5(cid:17) .x; (cid:28) / D 1 2M 1 2M (cid:16)p(cid:22) (cid:0) (cid:18)@(cid:22) e c e c a(cid:22)(cid:17) (cid:16)p(cid:22) ie c (cid:0) a(cid:22)(cid:19) (cid:18)@(cid:22) a(cid:22)(cid:17) .x; (cid:28) / ie c a(cid:22) (cid:0) (cid:19) .x; (cid:28) / (cid:0) D (cid:0) and, taking the complex conjugate, observe that this system will be form invariant under a charge conjugation C that operates as (cid:3).x; (cid:28)/ (cid:0) D e (cid:28) eC D (cid:0) C .x; (cid:28)/ (cid:28)C D (cid:0) a(cid:22) C .x; (cid:28)/ e .x; (cid:28)/ (cid:28) a(cid:22).x; (cid:28)/ a5.x; (cid:28)/ (cid:0)!C (cid:0)!C (cid:0)!C (cid:0)!C (cid:0)!C D a(cid:22).x; (cid:28)/ (cid:0) a5.x; (cid:28)/ (cid:0) a5 C .x; (cid:28)/ D (cid:0) if these transformations can be made consistent with the pre-Maxwell equations and Lorentz force. As we now show, this consistency can indeed be established. Leaving aside the quantum wavefunction and returning to classical mechanics, transformations of the potentials lead to ﬁeld strength transformations ek (cid:15)k (cid:15)0 D D @0ak D bk D (cid:17)55@(cid:28) ak (cid:17)55@(cid:28) a0 @ka0 (cid:0) "kij @i aj @ka5 @0a5 (cid:0) (cid:0) (cid:0)!C (cid:0)!C (cid:0)!C (cid:0)!C ek bk (cid:15)k (cid:15)0 (cid:0) (cid:0) so that this operation reverses the sign of tensor quantities carrying a scalar index. Under these transformations, the pre-Maxwell equations remain form invariant as long as (cid:0)j 0; j; j 5(cid:1) (cid:0)j 0; j; j 5(cid:1)C D (cid:0)j 0; j; j 5(cid:1) (cid:0) (cid:0)!C 42 3. CLASSICAL ELECTRODYNAMICS which is again a reversal of the scalar component. Similarly, the Lorentz force M M d 2x0 C d (cid:28) 2 C D d 2xC d (cid:28) 2 C D e c e c (cid:20)eC (cid:20)eC d xC d (cid:28)C (cid:0) (cid:1) dx0 C d (cid:28)C C (cid:21) (cid:17)55(cid:15)0 C d xC d (cid:28)C (cid:2) bC (cid:0) (cid:21) (cid:17)55(cid:15)C undergoes becoming M d 2x0 d (cid:28) 2 D d 2x d (cid:28) 2 D e c e c (cid:18) (cid:20)e (cid:1) (cid:20)e (cid:18) (cid:19) (cid:19) d x d (cid:28) (cid:0) dx0 d (cid:28) (cid:0) M (cid:17)55 (cid:0) (cid:21) (cid:15)0(cid:1) (cid:0) (cid:18) C (cid:0) (cid:0) d x d (cid:28) (cid:19) b (cid:2) (cid:0) (cid:17)55 . (cid:0) (cid:15)/(cid:21) M d 2x0 d (cid:28) 2 D (cid:0) d 2x d (cid:28) 2 D (cid:0) e c e c (cid:20)e (cid:20)e d x d (cid:28) (cid:0) (cid:1) dx0 d (cid:28) C (cid:17)55(cid:15)0(cid:21) d x d (cid:28) (cid:2) b (cid:0) (cid:17)55(cid:15)(cid:21) ; M thus implementing classical charge conjugation. We see that current conservation @(cid:22)j (cid:22) @(cid:28) j 5 0 D C @(cid:22)j (cid:22) . C @(cid:28) / (cid:0) (cid:0) j 5(cid:1) (cid:0) 0 D (cid:0)!C is preserved, but since j 5 is interpreted as the number of events in a localized spacetime volume at a given (cid:28), the meaning of j 5 j 5 must be examined carefully. In standard relativistic mechanics, the continuity equation leads to a conserved charge C D (cid:0) through integration over volume in space as @(cid:22)J (cid:22) 0 D (cid:0)! dQ d (cid:28) D d d (cid:28) Z d 3x (cid:0)eJ 0(cid:1) c Z d 3x D (cid:0) .eJ/ 0 D r (cid:1) and since J 0.x/ c Z d (cid:28) X 0.(cid:28)/ (cid:14)4.x P X.(cid:28)// (cid:0) cannot change sign in this approach, only the conjugation e versal. But in SHP, charge conservation follows from D e can account for charge re- ! (cid:0) @(cid:11)j (cid:11) 0 D (cid:0)! dQ d (cid:28) D d d (cid:28) Z d 4x (cid:0)ej 5(cid:1) D (cid:0) Z d 4x e @(cid:22)j (cid:22) c5 0; D where it is the event density j 5.x/ c X 5.(cid:28)/ (cid:14)4.x P (cid:0) D X.(cid:28)// D cc5 (cid:14)4.x X.(cid:28)// (cid:0) that cannot change sign. But the eﬀective charge of an event interacting through the Lorentz force is associated with 3.9. BIBLIOGRAPHY 43 ej 0.x/ ec X 0.(cid:28)/ (cid:14)4.x P (cid:0) D X.(cid:28)// X 0.(cid:28)/ according to Stueckelberg’s prescription. Thus, the oper- which can change sign through P ation e e is not a required symmetry. ! (cid:0) Following Stueckelberg, we disentangle the symmetries of the coordinate time t from those of the chronological parameter (cid:28) by making the following interpretations of the discrete reﬂections. 1. Space inversion covariance P implies certain symmetric relations between a given experi- ment and one performed in a spatially reversed conﬁguration. 2. Time inversion covariance T implies certain symmetric relations between a given experi- ment and one performed in a t-reversed conﬁguration, which is to say one in which ad- x0 > 0 is replaced by a trajec- vancement in t is replaced by retreat, and so a trajectory with P x0 < 0. Thus, we expect symmetric behavior between pair annihilation processes tory with P and pair creation processes. 3. Charge conjugation covariance C implies certain symmetric relations between a given ex- periment and one in which the events are traced out in the reverse chronological order and carry opposite charge. The operations P and T are improper Lorentz transformations and therefore must be symme- tries of any (spinless Abelian) relativistic electrodynamics. But we do not regard the operation C deﬁned here as connecting symmetrical dynamical evolutions. Rather, we associate the reversal of temporal order performed by C with the re-ordering of events performed by the observer in the laboratory, who interprets events as always evolving from earlier to later values of t. Thus, charge conjugation exchanges the viewpoint of the events under interaction with the viewpoint of the laboratory observer. The charge inversion (associated with the gauge symmetry) under this exchange reinforces the view of antiparticles in the laboratory, but does not inﬂuence the event dynamics. 3.9 BIBLIOGRAPHY [1] Born, M. and Wolf, E. 1999. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diﬀraction of Light, Cambridge University Press, Cambridge. 25 [2] Jackson, J. D. and Okun, L. B. 2001. Review of Modern Physics, 73:663. 25 [3] Saad, D., Horwitz, L., and Arshansky, R. 1989. Foundations of Physics, 19:1125–1149. 27, 29, 37 44 3. CLASSICAL ELECTRODYNAMICS [4] Jackson, J. 1975. Classical Electrodynamics, Wiley, New York. DOI: 10.1063/1.3057859. 29 [5] Arshansky, R., Horwitz, L., and Lavie, Y. 1983. Foundations of Physics, 13:1167. 29, 37 [6] Land, M. 1996. Foundations of Physics, 27:19. 29 [7] Land, M. 2003. Foundations of Physics, 33:1157. 29 [8] Land, M. 2017. Entropy, 19:234. http://dx.doi.org/10.3390/e19050234 32 [9] Schwinger, J. 1949. Physical Review, 75(4):651–679. https://link.aps.org/doi/10. 1103/PhysRev.75.651 33 [10] Wigner, E. P. 1959. Group theory and its application to the quantum mechanics of atomic spectra, Pure Applied Physics, Academic Press, New York (translation from the German). https://cds.cern.ch/record/102713 38 PART III Applications C H A P T E R 4 47 Problems in Electrostatics and Electrodynamics 4.1 THE COULOMB PROBLEM Introductory treatments of electromagnetism quite naturally begin with the static Coulomb force between two point charges at rest. However, in the framework of Stueckelberg, Horwitz, and Piron, this seemingly simple conﬁguration requires some clariﬁcation. A timelike event in its rest frame can be given with velocity so that this “static” event evolves uniformly in (cid:28) with coordinates X 2 P c2 D (cid:0) (cid:0)! .c; 0/ X P D X.(cid:28)/ .ct; X/ .c.t0 C D (cid:28)/; X0/ D and the displacement .ct0; X0/ at (cid:28) 0 plays a role in interactions with other events. Taking X0 0, so that the event simply evolves along the t-axis in its rest frame, the D associated event current is D j (cid:11) .x; (cid:28) / c x(cid:11)(cid:14)4 .x P (cid:0) D X.(cid:28)// (cid:0)! 8 (cid:136)(cid:136)(cid:136)< (cid:136)(cid:136)(cid:136): j 0 .x; (cid:28) / j .x; (cid:28) / D j 5 .x; (cid:28) / c2(cid:14) .ct c.t0 (cid:0) C (cid:28)// (cid:14)3 .x/ cc5(cid:14) .ct c.t0 (cid:0) C (cid:28)// (cid:14)3 .x/ D 0 D with support restricted to the spatial origin—as in Maxwell theory—and to the time t The source for the pre-Maxwell ﬁeld is the smoothed ensemble current t0 (cid:28). C D j (cid:11) ’ .x; (cid:28) / D Z ds ’ .(cid:28) s/ j (cid:11) .x; s/ (cid:0) (cid:0)! 8 (cid:136)(cid:136)(cid:136)< (cid:136)(cid:136)(cid:136): j 0 ’ D j’ D j 5 ’ D c’ .t .t0 (cid:0) C (cid:28)// (cid:14)3 .x/ 0 c5’ .t .t0 (cid:0) C (cid:28)// (cid:14)3 .x/ (4.1) which varies continuously in t, and as (cid:28) advances has its maximum at t (cid:28). The potential induced by this current may be found, as in (3.23), by integration with the Green’s function GCorrelation. We ﬁrst treat the Maxwell term, which (3.24), containing two terms, G GMaxwell D C t0 D C 48 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS produces a potential with the expected 1=R dependence, multiplied by a time-dependent form factor found from ’. We then ﬁnd the contribution from the correlation term which is scaled by the small factor c5=c and drops oﬀ as 1=R2. 4.1.1 CONTRIBUTION TO POTENTIAL FROM GMaxwell The leading term in the potential is Z d 4x0d (cid:28) 0 (cid:14) (cid:16)(cid:0)x Z cdt 0 (cid:14) (cid:16)c2 (cid:0)t ’ (cid:18)(cid:28) (cid:18)t (cid:0) t0 (cid:0) (cid:0) (cid:0) 2 t 0(cid:1) R c (cid:0) (cid:19)(cid:19) 2(cid:17) (cid:18) ret(cid:14).(cid:28) x0(cid:1) (cid:0) (cid:28) 0/’ (cid:0)t 0 (cid:0) x2(cid:17) (cid:18) ret’ (cid:0)t 0 .t0 (cid:0) (cid:28) 0/(cid:1) (cid:14)3 (cid:0)x0(cid:1) .t0 C (cid:28)/(cid:1) (cid:0) C e 2(cid:25) e 4(cid:25) e 4(cid:25)R 0 a0 .x; (cid:28) / a .x; (cid:28) / a5 .x; (cid:28) / D D D D D c5 c a0 .x; (cid:28) / ; (cid:0) D (cid:18) .x .ct; x/, this ﬁeld will grow as (cid:28) x0/ to select retarded spacetime causality, and write R where we insert (cid:18) ret . As D j R=c from be- observed from a spacetime point x t (cid:0) D ! (cid:28), the maximum low and then decrease. Since the time coordinate of the source is tevent D R=c, representing a delay equal to the signal tevent C occurs if the observer is located at time t transmission time at the speed of light. Put in a more familiar way, the time coordinate of the t event detected at time t is tevent D .c(cid:28) experienced by the test event becomes To study the “static” Coulomb problem, we consider a test event evolving uniformly at x ct test D 0 ; x/, where x is constant. Inserting these coordinates and using (3.15), the potential D tretarded D R=c. (cid:0) t0 x j C C t0 (cid:0) ’ (cid:18) (cid:0) (cid:129)t0 C (cid:19) R c D 1 2(cid:24) e 4(cid:25)R (cid:129)t0 e(cid:0)j R=c =(cid:24)(cid:21) j (cid:0) (4.2) a0 .x; (cid:28) / a5 .x; (cid:28) / D D e 4(cid:25)R c5 c a0 .x; (cid:28) / ; where (cid:129)t0 may take (cid:24) D ’ t test 0 (cid:0) 1=2 for c5=c 1, and so recover the Coulomb potential (cid:28) t0 deﬁnes the mutual t-synchronization between the events. From (3.12) we in the particular case that (cid:129)t0 Yukawa potential D a0 .x; (cid:28) / e 4(cid:25)R D R=c. By contrast, if (cid:129)t0 D a0 .x; (cid:28) / e 4(cid:25)R D e(cid:0) 2 R j =(cid:21)c j 0, then a0 takes the form of a (4.3) 4.1. THE COULOMB PROBLEM 49 suggesting a semi-classical interpretation in which the photons carrying the pre-Maxwell in- teraction have mass m(cid:13) c2 =(cid:21). Taking m(cid:13) to be smaller than the experimental error on the 18eV =c2) [1], we may estimate (cid:21) > 104 seconds. In this approximation mass of the photon (10(cid:0) (cid:21)c will be larger than any practical distance in the problems we consider. 2 (cid:132) (cid:24) The ﬁeld strength components found from the Yukawa-type potential with (cid:129)t0 f k0.x; (cid:28)/ @k e 4(cid:25)R 1 2(cid:24) D R=(cid:24)(cid:21)c e(cid:0) f k5.x; (cid:28)/ c5 c D f k0.x; (cid:28) / 0 are D so that the test event will undergo Coulomb scattering f ij .x; (cid:28)/ f 50.x; (cid:28)/ 0 D D M xk R D e c f k x(cid:23) (cid:23) P (cid:0) (cid:17)55 ec5 c f 5k e c f k0 (cid:18) x0 P (cid:17)55 C (cid:19) c2 5 c D (cid:0) according to the Lorentz force (3.4). Since the test event velocity is M x R D (cid:0) e2 2(cid:24) (cid:18)1 C (cid:17)55 (cid:16) 2(cid:19) (cid:17) c5 c e(cid:0) R=(cid:24)(cid:21)c ! r 4(cid:25)R D (cid:0) e2 1 D x.(cid:28) / P c5 (cid:17)55 (cid:0) c (cid:1) 2 r c5 c (cid:1) (cid:0) 2 C 1 C .c; 0/ this becomes R=(cid:24)(cid:21)c e(cid:0) 4(cid:25)R ! ; where we used (3.12) for (cid:24). Now suppose the source event were an antiparticle event evolving c. This would change the signs of a0.x; (cid:28) / and f k0.x; (cid:28) / but not X 0 backward in time with P the signs of a5.x; (cid:28)/ or f k5.x; (cid:28)/. We can thus write the Coulomb force for both cases as D (cid:0) F. C = (cid:0) / D (cid:7) e2 1 2 c5 c (cid:1) 2 r (cid:17)55 (cid:0) c5 c (cid:1) (cid:0) (cid:6) 1 C R=(cid:24)(cid:21)c e(cid:0) 4(cid:25)R ! ; where the upper sign is for a particle event and the lower sign is for an antiparticle event. Since (cid:17)55 1, this expression provides an experimental bound on c5=c, given by D (cid:6) (cid:27) (cid:0)e(cid:0) C (cid:27) .e(cid:0) C eC (cid:0)! e(cid:0) (cid:0)! e(cid:0) C e(cid:0) C eC(cid:1) e(cid:0)/ D 1 (cid:6) experimental error " 1 ’ (cid:7) 1 c5 c (cid:1) 2 (cid:17)55 (cid:0) c5 c (cid:1) (cid:0) C 2 2 # ; where (cid:27) is the total classical scattering cross-section at very low energy. The action (3.13) recovers the usual ﬁrst-order kinetic term f (cid:11)(cid:12) f(cid:11)(cid:12) in the limit (cid:21) 0, ! in which case D and the source of the pre-Maxwell ﬁeld reduces to j (cid:11) ’ .x; (cid:28)/ but ﬁnite, then from (4.2) we have ! lim 0 (cid:21) 1 (cid:24)(cid:21) e(cid:0)j (cid:28) =(cid:24)(cid:21) j (cid:14).(cid:28)/ j (cid:11).x; (cid:28) /. If we take (cid:21) very small ! a0 .x; (cid:28) / e 4(cid:25)R ’ (cid:0) (cid:21)(cid:14) (cid:18)(cid:129)t0 (cid:19) R c (cid:0) 50 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS for the potential experienced by the test event. Now the support of the potential is restricted to a lightline between the events, and for any synchronization (cid:129)t0 R=c there will be no inter- action. As we remarked in Section 3.3, a solution for Coulomb scattering can be found in this case [2], but the delta function potential leads to a discontinuous trajectory that is diﬃcult to reconcile with classical phenomenology. This discontinuity is a primary motivation for intro- ducing the interaction kernel. We mention in passing that this diﬃculty is not present in SHP quantum ﬁeld theory because the deﬁnition of asymptotic states with sharp mass implies the loss of all information about the initial t-synchronization of the scattering particles. ⁄ The signiﬁcance of the small (cid:21) limit appears in a number of places. As discussed in Sec- tion 3.4, (cid:21) characterizes the section of a worldline over which the event current is smoothed. In this sense, (cid:21) can be seen as the correlation length of a statistical process that assembles the cur- rent from an ensemble of events occurring along the trajectory. When (cid:21) is small, the interaction between an event trajectory and a test event is determined by a small number of points along the =(cid:21) 2 worldline, including only one point when (cid:21) (cid:132) D of the electromagnetic ﬁeld associated with the Yukawa-like potential (4.3) becomes large. 0. Moreover, the mass spectrum m(cid:13) c2 (cid:24) By contrast, if (cid:21) is large, then the source j (cid:11) ’ .x; (cid:28)/ of the pre-Maxwell ﬁeld is assembled from a large ensemble of events along the worldline, locally approximating the concatenation of the worldline performed in constructing the Maxwell current J (cid:22).x/. In this case, the mass spectrum m(cid:13) c2 =(cid:21) of the electromagnetic ﬁeld is small, approaching zero in the limit (cid:21) ! 2 (cid:132) (cid:24) . 1 From (3.16) and (4.1) the concatenated current is J 0 .x/ c Z d (cid:28) (cid:21) D ’ .t .t0 (cid:0) C (cid:28)// (cid:14)3 .x/ c(cid:14)3 .x/ D J .x/ 0 D describing a static Maxwell charge at the origin, and the concatenated potential is A0.x/ e 4(cid:25)R Z d (cid:28) (cid:21) D ’ (cid:18)(cid:28) (cid:18)t (cid:0) t0 (cid:0) (cid:0) R c (cid:19)(cid:19) e 4(cid:25)R D A .x/ 0 D describing the static Coulomb potential. As required, J (cid:22).x/ and A(cid:22).x/ are independent of t0 and invariant under a shift of the event x(cid:22).(cid:28)/ along the time axis. The microscopic interaction between the events is thus seen to be sensitive to the t-synchronization (cid:129)t0 of the interacting events, a parameter not accessible by the standard Coulomb law. CONTRIBUTION TO POTENTIAL FROM GCorrelation 4.1.2 Up to this point, we have treated only the potential found from the leading term GMaxwell in the Green’s function. To consider the potential found from GCorrelation again we take as source the 0 and approximate ’.(cid:28) 0 (cid:0) event X c(cid:28); 0/, but simplify the calculation by taking t0 .ct0 D C D s/ (cid:21)(cid:14).(cid:28) 0 (cid:0) D s/ so that a0 .x; (cid:28) / D (cid:0) D (cid:0) e Z d 4x0d (cid:28) 0 GCorrelation (cid:0)x c (cid:21)ec Z d (cid:28) 0 GCorrelation (cid:0).ct c(cid:28) 0; x/; (cid:28) (cid:28) 0(cid:1) : (cid:0) (cid:0) 4.1. THE COULOMB PROBLEM 51 x0; (cid:28) (cid:0) (cid:0) (cid:28) 0(cid:1) c2(cid:21)(cid:14) (cid:0)ct 0 c(cid:28) 0(cid:1) (cid:14)3 (cid:0)x0(cid:1) (cid:0) We introduce the function g.s/ to express terms of the type (cid:16).x (cid:0) (cid:0) X.s//2 c2 5 .(cid:28) C (cid:0) s/2(cid:17) D (cid:0) (cid:16)..ct; x/ (cid:0) .cs; 0//2 c2 5 .(cid:28) C (cid:0) s/2(cid:17) D c2g .s/ ; where and g .s/ .t (cid:0) D s/2 R2 c2 (cid:0) c2 5 c2 .(cid:28) (cid:0) (cid:0) s/2 D C s2 Bs A C C (cid:22)2 D c2 5 c2 C (cid:0)1 (cid:0) D (cid:22)2(cid:1) B 2 (cid:0)t (cid:0) D (cid:0) (cid:22)2(cid:28) (cid:1) R2 c2 (cid:0) t 2 (cid:0) A D (cid:22)2(cid:28) 2 so that the potential can be written as a .x; (cid:28) / D (cid:21)ec5 2(cid:25) 2c3 .c; 0; c5/ Z ds (cid:20) 1 2 (cid:18) .g .s// g3=2 .s/ (cid:0) (cid:14) .g .s// g1=2 .s/ (cid:21) (cid:18) .t s/ : (cid:0) The zeros of g .s/ are found to be B (cid:0) (cid:6) pB 2 2C (cid:0) s (cid:6) D 4AC D (cid:22)2(cid:28)(cid:1) (cid:0)t (cid:0) (cid:6) r R2 c2 .1 .1 (cid:0) (cid:0) (cid:22)2/ (cid:22)2/ (cid:22)2 .t (cid:28)/2 (cid:0) C (4.4) and since we assume (cid:22)2 < 1 there will be roots for any values of t and R. In addition, the condition (cid:18) ret (cid:18).t Attempting to set t < s s/ requires t > s. leads to D (cid:0) (cid:0) (cid:22)2(cid:28) (cid:1) (cid:0)t (cid:0) (cid:0) t < q R2 c2 .1 .1 (cid:22)2 .t (cid:28)/2 (cid:0) C (cid:22)2/ (cid:0) (cid:22)2/ (cid:22)2 .t (cid:0) (cid:0) (cid:28) /2 > R2 c2 ) (cid:0) and so t leads to s (cid:0) (cid:21) is a condition of integration for the (cid:18) term. Similarly, attempting to set t > s C (cid:22)2(cid:28) (cid:1) (cid:0)t (cid:0) C t > leading to the condition q R2 c2 .1 .1 (cid:22)2 .t (cid:28) /2 (cid:0) C (cid:22)2/ (cid:0) (cid:22)2/ (cid:22)2 .t (cid:0) (cid:0) (cid:28)/ > R2 c2 ) (cid:0) (cid:18).g.s// (cid:18).t s/ 0 ⁄ (cid:0) ) s (cid:0) (cid:20) s t s C (cid:20) (cid:20) 52 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS from which a .x; (cid:28) / (cid:21)ec5 2(cid:25) 2c3 D (cid:16)1; 0; c5 c (cid:17) (cid:18) 1 2 s (cid:0) Z (cid:0)1 ds 1 g3=2 .s/ (cid:0) Z 1 ds (cid:0)1 (cid:14) .g .s// g1=2 .s/ (cid:18) .t (cid:0) s/(cid:19) : Using the well-known form [3] Z dx Bx C .C x2 C where we notice from (4.4) that 2 .2C s B/ C Bx ; A/1=2 C A/3=2 D q.C x2 C 4AC q D (cid:0) B 2 B (cid:0) (cid:0) pB 2 2C (cid:0) s (cid:0) D 4AC B (cid:0) D p (cid:0) (cid:0) 2C q ) p q (cid:0) (cid:0) D 2C s (cid:0) C B and so 1 2 s (cid:0) Z ds (cid:0)1 1 g3=2 .s/ D D D B / (cid:0) 2C s (cid:0) C qg1=2 .s (cid:0) q p (cid:0) qg1=2 .s 1 qg1=2 .s (cid:0) (cid:0) / C p (cid:0) (cid:0) 2C s B C qg1=2 .s/ 2pC (cid:12) (cid:12) (cid:12) (cid:12)(cid:0)1 B/2 .2C s (cid:0) C 1 2 / C (cid:22)2 p1 (cid:22)2/ (cid:0) C (cid:22)2 .t (cid:0) : (cid:28) /2 (4.5) R2 c2 .1 (cid:0) The second term is and using the identity we can evaluate Z 1 ds (cid:0)1 (cid:14) .g .s// g1=2 .s/ (cid:18) .t s/ (cid:0) Z ds f .s/ (cid:14) .g .s// f .s(cid:0)/ g0 .s(cid:0)/ j j (cid:12) (cid:12) (cid:12) (cid:12)s(cid:0)D D 1.0/ g (cid:0) Z 1 ds (cid:0)1 (cid:14) .g .s// g1=2 .s/ (cid:18) .t s/ (cid:0) D (cid:18) .t / g0 .s j (cid:0) / s (cid:0) (cid:0) g1=2 .s j (cid:0) / D g0 .s j (cid:0) / j 1 g1=2 .s : / (cid:0) Since (cid:0)C s2 D (cid:0) we see that this term cancels the singularity in the ﬁrst term, leaving g0 .s 2C s (cid:0) C (cid:0) C (cid:0) C A(cid:1)0 Bs D D B (cid:0) / q p (cid:0) 1 2 s (cid:0) Z (cid:0)1 ds 1 g3=2 .s/ (cid:0) Z 1 ds (cid:0)1 (cid:14) .g .s// g1=2 .s/ (cid:18) .t s/ (cid:0) D 1 2 R2 c2 .1 (cid:0) p1 (cid:22)2/ (cid:0) C (cid:22)2 (cid:22)2 .t (cid:28)/2 (cid:0) 4.2. LIÉNARD–WIECHART POTENTIAL AND FIELD STRENGTH 53 and a .x; (cid:28) / (cid:21)e 4(cid:25) 2 .c; 0; c5/ c5 c D r1 c5 c (cid:17) (cid:0) c5 c c5 c c2 .t : (cid:28) /2 R2 (cid:16)1 (cid:0) We notice that the potential has units of (cid:21)c=distance2 1/distance, as does the potential as- sociated with GMaxwell. This contribution to the potential is smaller by a factor of c5=c than the Yukawa potential found in (4.3), and drops oﬀ faster with distance, as 1=R2 compared to 1=R. This term may be neglected when the contribution from GMaxwell is signiﬁcant, but as we will see in Section 4.7.1, it may lead to qualitatively important phenomena when the leading term vanishes. D C (cid:0) 4.2 LIÉNARD–WIECHART POTENTIAL AND FIELD STRENGTH We now consider an arbitrary event X (cid:11) .(cid:28) / for which the smoothed current is j (cid:11) ’ .x; (cid:28) / D c Z ds ’ .(cid:28) s/ X (cid:11) .s/ (cid:14)4 (cid:140)x P (cid:0) (cid:0) X .s/(cid:141) and the Liénard–Wiechert potential found from GMaxwell is a(cid:11) .x; (cid:28) / D D e 2(cid:25)c e 2(cid:25) Z d 4x0d (cid:28) 0(cid:14) (cid:16)(cid:0)x x0(cid:1) 2(cid:17) (cid:18) ret(cid:14) (cid:0)(cid:28) (cid:0) (cid:28) 0(cid:1) j (cid:11) ’ (cid:0)x0; (cid:28) 0(cid:1) (cid:0) Z ds ’ .(cid:28) s/ X (cid:11) .s/ (cid:14) (cid:16).x P (cid:0) (cid:0) X .s//2(cid:17) (cid:18) ret; (4.6) where (cid:18) ret imposes retarded x0 causality. Writing the line of observation as z(cid:22) x(cid:22) (cid:0) D X (cid:22).s/ (cid:0)! z2 (cid:140)x (cid:0) D X .s/(cid:141)2 and using the identity we obtain Z ds f .s/ (cid:14) (cid:140)g .s/(cid:141) f .(cid:28)R/ g0 .(cid:28)R/ j D j ; (cid:28)R D g(cid:0) 1 .0/ a(cid:11) .x; (cid:28) / e 4(cid:25) D ’ .(cid:28) (cid:28)R/ (cid:0) X (cid:11) .(cid:28)R/ P X (cid:22) .(cid:28)R// ; X(cid:22) .(cid:28)R/(cid:12) P (cid:12) .x(cid:22) (cid:12) (cid:12) (cid:0) (4.7) (4.8) where the retarded time (cid:28)R satisﬁes z2 (cid:140)x (cid:0) D X.(cid:28)R/(cid:141)2 0 D (cid:18) .x (cid:0) X .(cid:28)R// 1: D 54 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS Introducing the notation for velocity u(cid:22) X (cid:22) .(cid:28) / D P (cid:12)(cid:22) D X (cid:22) P c u5 X 5 D P D c5 and the scalar length the potential becomes R D 1 2c d d (cid:28)R (cid:140)x (cid:0) X .(cid:28)R/(cid:141)2 z(cid:22)u(cid:22) z c D j (cid:12) j (cid:1) D (cid:0) a(cid:22) .x; (cid:28) / e 4(cid:25)R D ’ .(cid:28) (cid:0) (cid:28)R/ (cid:12)(cid:22) a5 .x; (cid:28) / e 4(cid:25)R D ’ .(cid:28) (cid:28)R/ (cid:0) c5 c ; (4.9) (4.10) where R is nonnegative because u(cid:22) is timelike and z(cid:22) is lightlike. Thus, a(cid:22) .x; (cid:28) / takes the form of the usual Liénard–Wiechert potential from Maxwell theory multiplied by the factor ’ .(cid:28) (cid:28)R/ which separates out the (cid:28)-dependence of the ﬁelds. To calculate the ﬁeld strengths, we need derivatives of the Liénard–Wiechert potential. (cid:0) Since d d (cid:28)R ’ .(cid:28) (cid:28)R/ (cid:0) D (cid:0) 1 2(cid:24) d d (cid:28) (cid:28) e(cid:0)j (cid:28)R (cid:0) =(cid:24)(cid:21) j " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21) D (cid:0) ’ .(cid:28) (cid:28)R/ ; (cid:0) where " .(cid:28) / D signum.(cid:28)/, we obtain the (cid:28)-derivative 1 c5 @(cid:28) a(cid:22) .x; (cid:28) / 1 c5 D 4(cid:25) e u j z j (cid:1) ’ .(cid:28) P (cid:0) (cid:28)R/ u(cid:22) D (cid:0) e 4(cid:25)c5 ’ .(cid:28) u j (cid:28)R/ (cid:0) z (cid:1) j " .(cid:28) (cid:28)R/ u(cid:22) (cid:0) (cid:24)(cid:21) directly from (4.10). The spacetime derivative is most conveniently found by applying the identity (4.7) to expression (4.6) @(cid:22)a(cid:12) .x; (cid:28) / D D e 2(cid:25) e 2(cid:25) e 2(cid:25) Z ds ’ .(cid:28) s/ X (cid:11) .s/ (cid:18) ret @(cid:22)(cid:14) (cid:16).x P (cid:0) Z ds ’.(cid:28) s/ (cid:0) Z ds ’.(cid:28) (cid:0) X (cid:12) .s/ (cid:18) ret (cid:14)0 h.x P X (cid:12) .s/ (cid:140)x(cid:22) .x X .s/ P s/ P (cid:0) (cid:0) X (cid:22) .s/(cid:141) X .s// (cid:0) (cid:1) D (cid:0) X .s//2(cid:17) (cid:0) X .s//2i (cid:140)2 .x(cid:22) (cid:18) ret d ds (cid:14) h.x X (cid:22) .s//(cid:141) X .s//2i (cid:0) (cid:0) and integrating by parts to obtain @(cid:22)a(cid:12) .x; (cid:28) / e 2(cid:25) e 4(cid:25) D D d ds d ds Z ds 1 u j z j (cid:1) " ’.(cid:28) " ’.(cid:28) (cid:0) (cid:0) X (cid:22) .s/(cid:141) X .s// # (cid:18) ret (cid:14) h.x X .s//2i (cid:0) s/ P X (cid:12) .s/ (cid:140)x(cid:22) X .s/ .x P (cid:0) (cid:1) z(cid:22).s/u(cid:12) .s/ # (cid:0) s/ : u z (cid:1) (cid:28)R s D 4.2. LIÉNARD–WIECHART POTENTIAL AND FIELD STRENGTH 55 Using z(cid:22) P D (cid:0) u(cid:22) R P D (cid:0) d d (cid:28) z u (cid:1) c D c(cid:12)2 z (cid:1) P(cid:12) (cid:0) we ﬁnd the ﬁeld strengths as f (cid:22)(cid:23).x; (cid:28)/ ’ .(cid:28) e 4(cid:25) D (cid:0) R (cid:28)R/ (cid:26) .z(cid:22)(cid:12)(cid:23) z(cid:23)(cid:12)(cid:22)/ (cid:12)2 (cid:0) R2 (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c z(cid:22)(cid:12)(cid:23) z(cid:23)(cid:12)(cid:22) (cid:0) R (cid:16)z(cid:22) P(cid:12)(cid:23) (cid:0) z(cid:23) P(cid:12)(cid:22)(cid:17) R .z(cid:22)(cid:12)(cid:23) C cR2 (cid:0) z(cid:23)(cid:12)(cid:22)/ (cid:16) P(cid:12) z(cid:17) 9 = (cid:1) (cid:0) (4.11) f 5(cid:22).x; (cid:28)/ c5 e 4(cid:25) D ’ .(cid:28) (cid:0) cR (cid:28)R/ (cid:26) (cid:0) z(cid:22)(cid:12)2 C R2 (cid:12)(cid:22)R (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c ; (cid:12)(cid:22)Rc2=c2 5 R z(cid:22) C z(cid:17) z(cid:22) (cid:16) P(cid:12) (cid:1) cR2 C : 9 = ; (4.12) It is convenient to express the ﬁelds as elements of a Cliﬀord algebra [4] with basis vectors e(cid:11) e(cid:12) (cid:1) D (cid:17)(cid:11)(cid:12) e(cid:11) e(cid:12) ^ D e(cid:11) (cid:10) e(cid:12) (cid:0) e(cid:12) (cid:10) e(cid:11) (4.13) and Cliﬀord product Separating spacetime and scalar quantities as e(cid:11)e(cid:12) e(cid:11) e(cid:12) (cid:1) D C e(cid:11) ^ e(cid:12) : X.(cid:28)/ D d X (cid:22).(cid:28)/e(cid:22) @(cid:22)e(cid:22) D X 5 @5 c5(cid:28) D 1 c5 @(cid:28) D and writing (cid:15)(cid:22) D f 5(cid:22), the ﬁeld strength tensors f D 1 2 f (cid:22)(cid:23) e(cid:22) e(cid:23) ^ f 5 D f 5(cid:22) e5 e(cid:22) e5 (cid:15) ^ D ^ are Cliﬀord bivectors, (3.5) takes the form In this notation, the pre-Maxwell equations (3.20) are f d a ^ D (cid:15) @5a (cid:0) D (cid:0) da5: e c j’ d (cid:0) (cid:1) f d @5(cid:15) (cid:0) D f ^ 0 D d d ^ (cid:1) (cid:15) e c j 5 ’ (cid:15) D @5f 0; D C (4.14) 56 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS where we may evaluate d (cid:1) f and similar terms using the Cliﬀord identity (cid:1) Deﬁning the dimensionless quantities associated with acceleration P(cid:12) D (cid:0) ^ (cid:1) (cid:1) a .b c/ .a b/ c .a c/ b: Q D (cid:0) z P(cid:12) (cid:1) c W D P(cid:12)R (cid:0) c (cid:12)cQ D (cid:0) P(cid:12) .(cid:12) (cid:1) z/ (cid:0) c X=c, D R (cid:12) (cid:16) P(cid:12) z(cid:17) (cid:1) the ﬁeld strengths become f .x; (cid:28)/ e 4(cid:25) D ’ .(cid:28) (cid:28)R/ (cid:0) z R3 ^ (cid:26)(cid:12) (cid:18)(cid:12)2 (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c R(cid:19) (cid:0) W (cid:27) (cid:15).x; (cid:28)/ ’ .(cid:28) c5 c e 4(cid:25) D (cid:0) R (cid:28)R/ (cid:26) (cid:0) (cid:12)R z(cid:12)2 C R2 (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c (cid:18) z R C (cid:19) (cid:12) c2 c2 5 (cid:0) (cid:27) zQ R2 in which the factors ’ .(cid:28) (cid:28)R/ and " .(cid:28) (cid:0) (cid:0) (cid:28)R/ contain the (cid:28)-dependence. Since Z d (cid:28) (cid:21) ’ .(cid:28)/ 1 D Z d (cid:28) (cid:21) (cid:0) ’ .(cid:28)/ " .(cid:28)/ (cid:24)(cid:21) D Z d (cid:28) (cid:21) ’0 .(cid:28)/ 0 D (cid:28)R/ the concatenated ﬁelds are found by replacing ’ .(cid:28) 0, in agreement with the standard Maxwell result. We mention again that these ﬁeld strengths were obtained us- ing only the leading term GMaxwell in the Green’s function, and neglect the smaller contributions from GCorrelation. Although the neglected terms vanish under concatenation, they may dominate the dynamics when the leading contribution is zero. In particular, while GMaxwell has support on the lightcone, GCorrelation has timelike or spacelike support (depending on the choice of (cid:17)55) and so becomes signiﬁcant in self-interactions. 1 and " .(cid:28) (cid:28)R/ ! ! (cid:0) (cid:0) Taking (cid:21)c (cid:29) imate R and neglecting mass transfer, so that (cid:12)2 u2=c2 D D (cid:0) 1, we may approx- f .x; (cid:28)/ e 4(cid:25) D (cid:0) ’ .(cid:28) (cid:28)R/ (cid:0) z R3 ^ .(cid:12) C W / (4.15) (cid:15).x; (cid:28)/ c5 c e 4(cid:25) D ’ .(cid:28) (cid:28)R/ (cid:0) z .1 (cid:12)R (cid:0) Q/ R3 (cid:0) and split the ﬁeld strengths into the short-range retarded ﬁelds f ret e 4(cid:25) that drop oﬀ as 1=R2, and the radiation ﬁelds ^ R3 D (cid:0) ’ .(cid:28) (cid:28)R/ (cid:0) (cid:12) z (cid:15)ret c5 c e 4(cid:25) D ’ .(cid:28) z (cid:28)R/ (cid:12)R (cid:0) R3 (cid:0) f rad e 4(cid:25) D (cid:0) ’ .(cid:28) (cid:28)R/ (cid:0) z W ^ R3 (cid:15)rad c5 c e 4(cid:25) D (cid:0) ’ .(cid:28) (cid:28)R/ (cid:0) zQ R3 associated with acceleration that drop oﬀ as 1=R. 4.3. ELECTROSTATICS 57 As elements of a Cliﬀord algebra, the ﬁeld strengths admit geometrical interpretation. The (cid:12) in f ret represents the plane spanned by the velocity (cid:12) and the line of observation z. factor z Similarly, we recognize ^ (cid:12)R z (cid:0) D (cid:0) (cid:12)2z (cid:12) .z (cid:12)/ (cid:1) .z (cid:12)/ (cid:12) (cid:1) ^ D (cid:0) C representing the projection of (cid:12) onto the z f ret e 4(cid:25) D (cid:0) ’ .(cid:28) (cid:28)R/ (cid:0) for the retarded ﬁelds. Similarly, using (cid:0) z (cid:12) ^ R3 (cid:12) plane, and so we have (cid:15)ret c5 c f ret (cid:12) (cid:1) D .b a (cid:1) ^ c ^ d / D .a (cid:1) b/ c d .a (cid:1) (cid:0) ^ c/ b d .a (cid:1) C ^ d / b c ^ and z2 D 0, we see that ^ in f rad represent the projection of z onto the volume spanned by z, (cid:12), and P(cid:12). Similarly, (cid:15)ret is proportional to zQ z/z=c, the projection of z onto the acceleration P(cid:12). . P(cid:12) D ^ (cid:1) D (cid:1) z W (cid:16)z (cid:12) ^ P(cid:12)(cid:17) z ELECTROSTATICS 4.3 The covariant equivalent of a spatially static charge is a uniformly evolving event X .(cid:28)/ u(cid:28) D D (cid:0)u0(cid:28); u(cid:28) (cid:1) X with constant timelike velocity P time axis as t the ﬁeld strengths are essentially kinematical in structure. (cid:12)c, which in its rest frame simply advances along the (cid:12)0(cid:28). As a result, and given the geometrical interpretation of the Cliﬀord forms, D D D u Writing the timelike velocity (cid:12) in terms of the unit vector O(cid:12) (cid:12) (cid:12)2 < 0 (cid:12) 1 j O(cid:12) D j O(cid:12)2 D (cid:0) (cid:12)2 (cid:12) D (cid:0) j 2 j the observation line z can be separated into components k D (cid:0) O(cid:12) (cid:16) z O(cid:12) (cid:1) z(cid:17) z ? D z C O(cid:12) (cid:16) O(cid:12) (cid:1) z(cid:17) which satisfy z2 ? D z2 k D O(cid:12)2 (cid:16) z2 O(cid:12) 2 2 (cid:16) z(cid:17) O(cid:12) (cid:1) C 2 z(cid:17) (cid:1) (cid:16) O(cid:12) 2 z(cid:17) (cid:16) O(cid:12) (cid:1) (cid:16) O(cid:12) D D (cid:0) 2 z(cid:17) (cid:1) (cid:0) 2 (cid:16) O(cid:12) j 2 z(cid:17) (cid:1) (cid:12) D (cid:0) j j z/2 .(cid:12) (cid:1) (cid:12) D j z2 k D (cid:0) 2 : z(cid:17) (cid:1) 2 z2 k (4.16) 58 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS The condition of retarded causality z2 D c2(cid:28) 2 R(cid:12)2 (cid:0) 2c(cid:28)R(cid:12) x2 x (cid:1) C 0 D relates the ﬁeld to the location of the event along the backward lightcone of the observation point. This implicit choice of (cid:28)R and its gradient d.z2/ 0 D D 2 (cid:0)c2(cid:28)Rd (cid:28)R(cid:12)2 c(cid:28)R(cid:12) cd (cid:28)R(cid:12) x (cid:1) C x(cid:1) D (cid:0) (cid:0) 2 (cid:140)cRd (cid:28)R z(cid:141) C lead to the following expressions: d (cid:28)R z cR D (cid:0) d / (cid:28)R .(cid:12) (cid:1) D (cid:12) (cid:12) (cid:1) (cid:1) d .(cid:12) z/ (cid:1) D d (cid:0)(cid:12) x (cid:1) (cid:0) (cid:12)2(cid:28)R(cid:1) D z z D 1 .(cid:12) (cid:1) .z d / (cid:28)R (cid:1) (cid:12)2z D (cid:0) (cid:12)2(cid:12) (cid:12) 2 C n (cid:12) (cid:12) Rn (cid:0) D z/ (cid:12) (cid:0) (cid:12) z (cid:1) (cid:12)2z(cid:3) z2 cR D 0 D (cid:0) (cid:12)2(cid:12) (cid:12) (cid:12) (cid:12) z ? cR z ? d 1 Rn D . (cid:0) 1/n (cid:0) n (cid:2).(cid:12) (cid:1) .(cid:12) z/ (cid:12) z/n (cid:0) 2 C d z (cid:1) .x d (cid:1) (cid:0) D d x (cid:1) (cid:0) D c(cid:12) (cid:1) d (cid:28)R (cid:1) c(cid:12)(cid:28)R/ 3 z D (cid:12) d z ^ D d d z ^ O D d ^ ^ z z j .x (cid:0) c(cid:12)(cid:28)R/ cd (cid:28)R (cid:12) ^ D (cid:0) D ^ R 1 z j j D (cid:0) j (cid:12) z z ^ R (cid:0) O ^ z z j j (cid:12) z ^ O R : 2 D (cid:0) Using these expressions, the pre-Maxwell equations (4.14) can be easily veriﬁed for the case of ’"=(cid:24)(cid:21), the exterior derivative of f a uniform velocity event [5]. For example, recalling ’0 D (cid:0) is e 4(cid:25) (cid:12) R3 (cid:12)2 ^ z (cid:12) ^ cR2 (cid:18)’ .(cid:28) ’0 .(cid:28) (cid:28)R/ (cid:28)R/ (cid:19) f d d z C D (cid:0) (cid:0) ^ ^ which produces terms of the type: d’.n/ .z ^ ^ (cid:12)/ D (cid:0) ’.n C 1/ z cR ^ .z u/ 0 D ^ d .z (cid:12)/ .d z/ (cid:12) ^ ^ D ^ ^ D (cid:0) (cid:12) z ^ R ^ (cid:12) 0 D (cid:20)d (cid:21) 1 Rn .z ^ ^ u/ D " (cid:0) n (cid:12) (cid:12) Rn (cid:12)2(cid:12) (cid:12) 2 C # z ? .z ^ ? ^ u/ 0 D and thus we recover d f ^ 0 D from kinematics. It is convenient to write the ﬁeld strengths in 3-vector and scalar form .e/i f 0i D .b/i D "ij kf j k .(cid:15)/i f 5i D (cid:15)0 D f 50 for which the ﬁeld equations split into four generalizations of the 3-vector Maxwell equations 4.3. ELECTROSTATICS 59 e (cid:0) r (cid:1) b (cid:0) r (cid:2) 1 c5 1 c @ @(cid:28) (cid:15)0 @ @t e (cid:0) D 1 c5 e c j 0 ’ D e(cid:26)0 ’ @ @(cid:28) (cid:15) D e c j’ b r (cid:1) e C r (cid:2) 1 c 0 b D @ @t 0 D and three new equations for the ﬁelds (cid:15) and (cid:15)0 (cid:15) C r (cid:1) 1 c @ @t (cid:15)0 D e c j 5 ’ D 1 c C (cid:15)0 ec5 c (cid:26)’ (cid:17)55 1 c5 @ @(cid:28) b (cid:15) (cid:0) 0 D r (cid:2) @ @t (cid:15) (cid:17)55 1 c5 @ @(cid:28) e C 0: D r (4.17) (4.18) Writing d e0@0 D C r and f e0 e ^ C D 1 2 f j kej ^ ek we ﬁnd that d f ^ 0 D (cid:0)! 8 (cid:136)< (cid:136): b 0 D r (cid:1) e C r (cid:2) 1 c @ @t b 0 D expressing the absence of electromagnetic monopoles. In the rest frame of a charged event, we may set point x .ct; x/ D 1 t P D ! (cid:12) D e0, so for an observation z2 0 D (cid:0)! 8 (cid:136)(cid:136)(cid:136)(cid:136)< (cid:136)(cid:136)(cid:136)(cid:136): R z (cid:28)R t D j x c j .x (cid:0) e0 c(cid:28)Re0/ D (cid:0) (cid:1) .c .t (cid:0) D (cid:0) (cid:28)R/ ; x/ D x j D j R .e0 x/ C O and the ﬁeld strengths reduce to f .x; (cid:28)/ e 4(cid:25) D ’ .(cid:28) (cid:28)R/ (cid:0) e0 x ^ O R2 (cid:18)1 C " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c R(cid:19) e0 ^ D e.x; (cid:28) / (cid:15).x; (cid:28)/ c5 c e 4(cid:25) D ’ .(cid:28) x (cid:28)R/ (cid:26) O R2 C (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)cR (cid:20)e0 (cid:18)1 (cid:19) c2 c2 5 C x(cid:21)(cid:27) : C O 60 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS We thus ﬁnd that the magnetic ﬁeld b is zero, while e 4(cid:25) e D (cid:18) ’ .(cid:28) (cid:0) R2 (cid:28)R/ ’0 .(cid:28) (cid:28)R/ (cid:19) x O (cid:0) R c5 c e (cid:15) D and (cid:15)0.x; (cid:28)/ D (cid:0) ’0 .(cid:28) (cid:0) R (cid:28)R/ (cid:18) c5 c C (cid:19) : c c5 (cid:0) e 4(cid:25) (4.19) (4.20) Because we obtained f .x; (cid:28)/ using only the leading term GMaxwell in the Green’s function, we expect errors on the order of the neglected term GCorrelation. In particular, we notice that (cid:18)@(cid:22)@(cid:22) (cid:17)55 c2 5 C (cid:19) GMaxwell @2 (cid:28) (cid:14)4 .x/ (cid:14) .(cid:28)/ D (cid:0) 1 2(cid:25) (cid:17)55 c2 5 (cid:0) (cid:14).x2/ (cid:14)00.(cid:28)/; where the second term on the right is canceled when GCorrelation is included in the wave equation. As a result, calculating (cid:15) D r (cid:1) c5 c e 4(cid:25) (cid:18)’ .(cid:28) (cid:0) (cid:28)R/ (cid:14)3 .x/ ’00 .(cid:28) (cid:0) cR (cid:0) (cid:28)R/ (cid:19) ; where we use . x=R2/ O D r (cid:1) 4(cid:25)(cid:14)3.x/, and 1 c @ @t (cid:15)0 D e 4(cid:25) ’00 .(cid:28) (cid:0) cR (cid:28)R/ (cid:18) c5 c C (cid:19) c c5 leads to the Gauss law as 1 c @ @t (cid:15)0 C r (cid:1) (cid:15) D c5 c e 4(cid:25) ’ .(cid:28) (cid:0) (cid:28)R/ (cid:14)3 .x/ c c5 e 4(cid:25) C ’00 .(cid:28) (cid:0) cR (cid:28)R/ exposing an error at the order of (cid:14)00.(cid:28) (cid:28)R/. (cid:0) We now consider a long straight charged line oriented along the z-axis, with charge per unit length (cid:21)e. In cylindrical coordinates x .(cid:26); z/ (cid:26) .x; y/ D the ﬁelds (cid:15) and e are found by replacing R along the z-axis to ﬁnd D D (cid:26) D p(cid:26)2 (cid:26) D px2 y2 C z2 in (4.19) and (4.20) and integrating (cid:26) O C (cid:21)e 4(cid:25) e D Z dz 0 ’ (cid:18)(cid:28) B B @ t (cid:0) .(cid:26)2 C C .(cid:26)2 z2/1=2 c C (cid:19) (cid:18)(cid:28) ’0 z2/3=2 (cid:0) t (cid:0) C c .(cid:26)2 .(cid:26)2 z2/1=2 c C (cid:19) 1 z2/ C .(cid:26) (cid:26); z/ O C C A (cid:15)0 D (cid:0) (cid:21)e 4(cid:25) c5 c Z dz ’0 (cid:18)(cid:28) t C (cid:0) c .(cid:26)2 .(cid:26)2 z2/1=2 c C (cid:19) : z2/1=2 C To get a sense of these expressions, we may use (3.15) to approximate ’.x/ permits us to easily carry out the z-integration to obtain D (cid:21)(cid:14).x/ which 4.3. ELECTROSTATICS 61 (cid:21)(cid:21)e 2(cid:25) e D 0 B @ (cid:18) .t c (cid:16).t (cid:0) (cid:26)=c (cid:0) (cid:28) /2 (cid:0) (cid:28)/ (cid:26) (cid:0) (cid:26)2=c2(cid:17) 3=2 (cid:0) (cid:14) .t q.t (cid:26)=c (cid:0) (cid:28) /2 (cid:28) / (cid:0) (cid:26)2=c2 (cid:0) (cid:0) 1 (cid:26) C A O which vanishes (cid:28) > (cid:28)R D t (cid:26)=c as required for retarded causality. Since (cid:0) Z d (cid:28) (cid:21) ’ .(cid:28)/ 1 D Z d (cid:28) (cid:21) ’0 .(cid:28) / 0 D the concatenated electric ﬁeld is found as (cid:21)e 4(cid:25) Z d (cid:28) (cid:21) e.x; (cid:28)/ E.x/ D D Z dz in agreement with the standard expression. 1 z2/3=2 C .(cid:26)2 .(cid:26) (cid:26); z/ O D (cid:21)e 2(cid:25)(cid:26) . (cid:26); 0/ O To obtain the ﬁeld of a charged sheet in the x y plane with charge per unit area (cid:27), it is convenient to start from the potential from a charged event, and integrating over x and y with R z2. Thus, px2 y2 (cid:0) D C C ’ (cid:18)(cid:28) t q.x 1 c x0/2 .y a0.x; (cid:28)/ (cid:27)c 4(cid:25) D Z dx0dy0 (cid:0) y0/2 .c5=c/a0.x; (cid:28)/. Changing to radial coordinates .x; y/ (cid:0) C cq.x (cid:0) x0/2 .y C C (cid:0) (cid:0) y0/2 C z2(cid:19) C z2 .(cid:26); (cid:18)/ we obtain and a5.x; (cid:28)/ D a0.x; (cid:28)/ (cid:27)c 4(cid:25) D Z d(cid:18)d(cid:26) ’ (cid:16)(cid:28) t (cid:0) C cp(cid:26)2 1 c p(cid:26)2 z2 C C which by change of variable (cid:16) z2 becomes 1 c p(cid:26)2 D a0.x; (cid:28)/ C (cid:27)c 2 D Z 1 z j =c j ’ .(cid:28) t (cid:0) C (cid:16)/ d (cid:16): ! z2(cid:17) We calculate the ﬁelds from e.x; (cid:28)/ a0 D (cid:27) 2 ’ (cid:18)(cid:28) t (cid:0) C (cid:19) j z c j z r j j D (cid:27) 2 D (cid:0)r ".z/’ (cid:18)(cid:28) t (cid:0) C (cid:19) z j c j z; O where (cid:15).x; (cid:28)/ D .c5=c/e.x; (cid:28)/ and (cid:15)0 D D 1 c @(cid:28) a0 (cid:17)55 c5 (cid:27) (cid:18)(cid:17)55 c C c c5 (cid:0) @t a5 1 c D (cid:19) ’ (cid:18)(cid:28) c5 c (cid:19) @(cid:28) a0 (cid:18)(cid:17)55 t (cid:0) C c c5 c5 (cid:0) c z (cid:19) : j c j 62 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS By concatenation, we recover Z d (cid:28) e.x; (cid:28)/ E.x/ D Z d (cid:28) D (cid:27) 2 ".z/’ (cid:18)(cid:28) t (cid:0) C (cid:19) j z c j (cid:27) 2 z O D ".z/ z O in agreement with the Maxwell ﬁeld from a charged sheet. We notice that, as expected, the space part of the electric ﬁelds change sign at the plane of the sheet, pointing out at each side. Consequently, an event passing through a charged sheet of equal sign will decelerate in space on its approach and then accelerate as it retreats. However, unlike the ﬁeld of a point event, the temporal part (cid:15)0 is an even function of spatial distance and so the event may accelerate along the time axis on both its approach to the charged sheet and its retreat. In such a case, the spatial motion will asymptotically return to its initial condition, while the event acquires a net temporal acceleration, corresponding to a shift in energy and mass. PLANE WAVES 4.4 From the wave equation (3.22) for j (cid:11).x; (cid:28)/ transform [6] D 0 we may write the ﬁeld in terms of the Fourier f (cid:11)(cid:12) .x; (cid:28)/ 1 .2(cid:25)/5 D Z d 5k eik xf (cid:11)(cid:12) .k/ (cid:1) 1 .2(cid:25)/5 D Z d 4k d (cid:20) ei.k (cid:1) x C k0x0 C (cid:17)55c5(cid:20)(cid:28)/f (cid:11)(cid:12) .k; (cid:20)/; where (cid:20) k5 (cid:17)55k5 D is understood to represent the mass carried by the plane wave, much as k0 and k represent energy and 3-momentum. This interpretation is supported by the wave equation which imposes the 5D constraint D k(cid:11)k(cid:11) k2 (cid:0) D .k0/2 C (cid:17)55(cid:20)2 0 D H) (cid:17)55(cid:20)2 .k0/2 k2 (cid:0) D (4.21) expressing (cid:20) in terms of the diﬀerence between energy and momentum. Under concatenation, the ﬁeld becomes F (cid:11)(cid:12) .x/ Z d (cid:28) (cid:21) D f (cid:11)(cid:12) .x; (cid:28)/ D Z d 4k .2(cid:25)/4 eik(cid:22)x(cid:22) 1 (cid:21)c5 f (cid:11)(cid:12) .k; 0/ Z d 4k .2(cid:25)/4 eik(cid:22)x(cid:22) D F (cid:11)(cid:12) .k/ and recovers the 4D mass-shell constraint k(cid:22)k(cid:22) domain, the sourceless pre-Maxwell equations take the form D 0 for the Maxwell ﬁeld. In the transform (cid:17)55(cid:20)(cid:15)0 0 k0b D 0 D k (cid:1) k e (cid:2) (cid:0) e (cid:0) (cid:15) (cid:0) k (cid:2) b k (cid:1) D 0 k (cid:1) (cid:15) b k (cid:2) C k0(cid:15)0 0 D (cid:17)55(cid:20)(cid:15) (cid:0) k0e k0(cid:15) k(cid:15)0 (cid:0) (cid:0) 0 D 0 D (cid:20)b 0 D (cid:20)e (cid:0) C 4.4. PLANE WAVES 63 which can be solved by taking (cid:15) and e ? k as independent 3-vector polarizations, and writing e k D (cid:17)55 (cid:20) k0 (cid:15) k (cid:15) ? D (cid:20) k0 e ? (cid:15)0 D 1 k0 k (cid:15) k (cid:1) 1 k0 b D k e ? (cid:2) for the remaining ﬁelds. Unlike Maxwell plane waves, for which E, B, and k are mutually orthog- onal, the pre-Maxwell electric ﬁelds e and (cid:15) have both transverse and longitudinal components. 0, we ﬁnd that e, b, and k become mutually orthogonal and (cid:15) becomes a decoupled When (cid:20) longitudinal polarization parallel to k. ! We use (3.11) to write the convolved ﬁeld as f (cid:11)(cid:12) (cid:136) .x; (cid:28)/ Z ds (cid:21) D (cid:136).(cid:28) (cid:0) s/f (cid:11)(cid:12) .x; s/ where D 1 1 .2(cid:25)/5 Z d 4k d (cid:20) ei.k (cid:1) x (cid:0) k0x0 (cid:17)55c5(cid:20)(cid:28)/f (cid:11)(cid:12) C (cid:136) .k; (cid:20)/; f (cid:11)(cid:12) (cid:136) .k; (cid:20)/ .(cid:24)(cid:21)c5(cid:20)/2 C f (cid:11)(cid:12) .k; (cid:20)/ D introduces a multiplicative factor that will appear once in each ﬁeld bilinear of T (cid:11)(cid:12) the 3-vector ﬁelds, the mass-energy-momentum tensor components are (cid:21) (cid:136) . In terms of e(cid:136) (cid:2)e (cid:1) b (cid:1) C b(cid:136) C (cid:17)55 (cid:0)(cid:15) (cid:15)(cid:136) (cid:1) C (cid:15)0(cid:15)0 (cid:136)(cid:1)(cid:3) T 00 (cid:136) D T 0i (cid:136) D T 50 (cid:136) D T 5i (cid:136) D T 55 (cid:136) D 1 2c 1 c 1 c 1 c 1 2c (cid:0)e b(cid:136) (cid:2) C (cid:17)55(cid:15)0(cid:15)(cid:136)(cid:1) i e (cid:15)(cid:136) (cid:1) (cid:0)(cid:15) b(cid:136) (cid:2) C i (cid:15)0e(cid:136)(cid:1) (cid:15)(cid:136) (cid:2)(cid:15) (cid:1) (cid:0) (cid:15)0(cid:15)0 (cid:136) C (cid:17)55 .e e(cid:136) b (cid:1) (cid:0) (cid:1) b(cid:136)/(cid:3) : For the plane wave, the energy density is 1 c (cid:16)e2 T 00 (cid:136) D .(cid:24)(cid:21)(cid:20)/2 (cid:21) b2(cid:1), is equivalent in form to the energy density in Maxwell theory (cid:17)55(cid:15)2 k ? C C (cid:17) 1 which, since e2 ? D 1 2 (cid:0)e2 ? C (cid:18) 00 1 2c D (cid:0)E2 B2(cid:1) C with the addition of the independent polarization (cid:15) . The mass density is found to be k T 55 (cid:136) D (cid:20)2 ck2 0 (cid:16)e2 ? C (cid:17) (cid:17)55(cid:15)2 k 1 C .(cid:24)(cid:21)(cid:20)/2 (cid:21) (cid:20)2 k2 0 D T 00 (cid:136) 64 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS expressing energy density scaled by the squared mass-to-energy ratio for the ﬁeld. The energy ﬂux—the standard Poynting 3-vector—is T 0i (cid:136) (cid:0)! T0 (cid:136) D k k0 T 00 (cid:136) expressing the energy density T 00 malized to energy. Comparing the proportionality factor to that for a free particle (cid:136) ﬂowing uniformly in the direction of the momentum nor- k k0 (cid:0)! p E=c D 1 c M d x=d (cid:28) M dt =d (cid:28) D v c which will not generally be a unit vector unless (cid:20) The mass ﬂux vector—a second Poynting 3-vector—can be written D 0, as it must be for Maxwell plane waves. T 5i (cid:136) (cid:0)! T5 (cid:136) D k (cid:20) T 55 (cid:136) expressing the mass density T 55 ized to mass. Finally, (cid:136) ﬂowing uniformly in the direction of the momentum normal- so that T 5(cid:22) (cid:136) can be written as T 50 (cid:136) D k0 (cid:20) T 55 (cid:136) D (cid:20) k0 T 00 (cid:136) T 5(cid:22) (cid:136) D k(cid:22) (cid:20) T 55 (cid:136) D (cid:20)k(cid:22) k2 0 T 00 (cid:136) (cid:136) ﬂowing in the direction of the 4-momentum. In this sense, T 50 expressing the mass density T 55 (cid:136) 0, as is the case represents the ﬂow of mass into the time direction. We notice that when (cid:20) for Maxwell plane waves, k=k0 becomes a unit vector and T 5(cid:11) 0, so that mass density and ﬂow vanish. The interpretation of plane waves carrying energy and momentum (energy ﬂux) uniformly to inﬁnity is thus seen to generalize to mass ﬂow, where mass is best understood through (4.21) as the non-identity of energy and momentum. (cid:136) D (cid:0)! Suppose that a plane wave of this type impinges on a test particle in its rest frame, de- 0, the wave will interact with the event through the .c(cid:28); 0; c5(cid:28) /. Since scribed by x(cid:11).(cid:28)/ Lorentz force (3.6) and (3.7) as D x P D M x(cid:22) .(cid:28) / R D e c (cid:2)f (cid:22) 0.x; (cid:28)/ x0 .(cid:28)/ P C c5f (cid:22) 5.x; (cid:28)/(cid:3) d d (cid:28) . (cid:0) 1 2 M x2/ P D (cid:0) ec5 c (cid:17)55(cid:15)0 x0 P which for (cid:15) k ⁄ 0 t R D (cid:0) (cid:17)55e ) c5 Mc2 (cid:1) 1 k0 k (cid:15) 0 becomes k ⁄ k (cid:15) k (cid:1) e M x R D (cid:16)1 he ? C c5 c (cid:20) k0 (cid:17) (cid:16) (cid:15) k c5 c C C (cid:17)55 (cid:20) k0 (cid:17)i 4.5. RADIATION FROM A LINE ANTENNA 65 d d (cid:28) . (cid:0) 1 2 M x2/ P (cid:17)55ec5 k (cid:15) 1 k0 D (cid:0) showing that the incident plane wave will initially accelerate the test event in such a way as to transfer mass. If the plane wave is a far ﬁeld approximation to the radiation ﬁeld of an accelerating charge, then the resulting picture describes the transfer of mass by the radiation ﬁeld between charged events. k (cid:1) 4.5 RADIATION FROM A LINE ANTENNA The radiation from a dipole antenna is treated generally in Maxwell theory [7] by approximating the oscillating current as the separable current density J .x; t / D J .x/ ei!t J .x/ i!(cid:26) 0; D C r (cid:1) where the second equation expresses represents current conservation, and of course we take the real parts of all physical quantities. This approximation may be justiﬁed by posing a collection of oscillating charges with position 4-vectors Xn .(cid:28)/ D (cid:0)ctn .(cid:28) / ; anei!(cid:28) (cid:1) which for nonrelativistic motion includes tn.(cid:28)/ for this collection is t D D (cid:28) for each particle. The Maxwell current J .x; t / X n D Z d (cid:28) c Xn .(cid:28)/ (cid:14)4 .x P (cid:0) Z d (cid:28) i! canei!(cid:28) (cid:14) .ct Xn .(cid:28)// c(cid:28) / (cid:14)3 (cid:0)x anei!(cid:28) (cid:1) (cid:0) (cid:0) X n " X n D D i! an(cid:14)3 (cid:0)x (cid:0) anei!t (cid:1) # ei!t so that replacing the term in square brackets with its time average over one cycle of oscillation T 2(cid:25)=! we obtain D J .x; t / " 1 T T Z 0 ’ dt X n i! an(cid:14)3 (cid:0)x (cid:0) anei!t (cid:1) # ei!t J .x/ ei!t : D Thus, J .x/ approximates the time-dependent current density by a time averaged static conﬁgu- ration in space, rendering the antenna problem tractable. To treat the dipole antenna in SHP electrodynamics [8] we cannot make use of this ap- proximation because the microscopic current j .x; t; (cid:28) / c X n D Xn .(cid:28) / (cid:14)4 .x P (cid:0) Xn .(cid:28) // X n D i! anei!(cid:28) (cid:14) .t (cid:28)/ (cid:14)3 (cid:0)x (cid:0) (cid:0) anei!(cid:28) (cid:1) 66 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS is not integrated over (cid:28), and so time averaging cannot be performed in any meaningful way. Instead, in analogy to this approximation, we pose a current of the form c (cid:2)(cid:26)0 .x/ C (cid:26) .x/ ei!t (cid:3) (cid:30) .(cid:28) t/ (cid:0) J .x/ ei!t (cid:30) .(cid:28) t/ (cid:0) j 0 .x; (cid:28) / j .x; (cid:28) / j 5 .x; (cid:28) / D D D c5 c j 0 .x; (cid:28) / c5 (cid:2)(cid:26)0 .x/ C D (cid:26) .x/ ei!t (cid:3) (cid:30) .(cid:28) t/ ; (cid:0) where (cid:26)0 .x/ is a background event density. The function (cid:30) .(cid:28) t / expresses a correlation be- tween t and (cid:28), inserted by hand in place of a time averaging procedure. In this sense, the re- placement (cid:0) j .x; t; (cid:28) / (cid:0)! J .x/ ei!t (cid:30) .(cid:28) t/ (cid:0) may be less precise than the comparable approximation in Maxwell theory, and we must be attentive to artifacts introduced by the model. In analogy to (3.15), we choose (cid:30) .(cid:28) t/ (cid:0) D 1 2(cid:27) (cid:28) e(cid:0)j t =(cid:27) j (cid:0) Z d! 2(cid:25) D (cid:136) .!/ ei!.(cid:28) t / (cid:0) (cid:136) .!/ 1 .(cid:27)!/2 D 1 C which imposes a correlation (cid:28) t (cid:0) ’ (cid:27) through (cid:30) .(cid:28) t/ (cid:0) (cid:0)! 8 < : strong correlation: (cid:27) weak correlation: (cid:27) 0 ) large (cid:30) .(cid:28) (cid:0) t (cid:0) ) ! ! t/ (cid:14) .(cid:28) t/ ! (cid:0) (cid:28) evenly distributed: ) t (cid:28) D Notice that in the strong correlation limit, the potential found from the Green’s function a .x; (cid:28) / D D e 2(cid:25) e 4(cid:25)c Z d 3x0d.ct 0/ (cid:14) (cid:16)(cid:0)x 1 ei!(cid:28) Z d 3x0 (cid:0) 2 x0(cid:1) (cid:0) (cid:14) (cid:18)(cid:28) c2 (cid:0)t t C (cid:0) 2(cid:17) J (cid:0)x0(cid:1) ei!t 0(cid:14) (cid:0)(cid:28) x0j (cid:19) J (cid:0)x0(cid:1) t 0(cid:1) (cid:0) x j (cid:0) c t 0(cid:1) (cid:0) x j x0j (cid:0) describes a Coulomb-like potential oscillating in (cid:28) simultaneously across spacetime, rather than !t /. This suppression of the expected wavelike behavior a wave propagating with phase .kr can be characterized by the dimensionless parameter (cid:0) 1 !(cid:27) D T 2(cid:25)(cid:27) D antenna period correlation time which we take to be small but greater than zero. The total number of events in this system at time (cid:28) is found from the spacetime integral 4.5. RADIATION FROM A LINE ANTENNA 67 N .(cid:28)/ D D D where Z d 4x j 5 .x; (cid:28) / 1 c5 Z d 3x (cid:26)0 .x/ Z dt (cid:30) .(cid:28) N ei!(cid:28) N0 C 1 C .(cid:27)!/2 ; t/ (cid:0) C Z d 3x (cid:26) .x/ Z dt ei!t (cid:30) .(cid:28) t/ (cid:0) Z d 3x (cid:26)0 .x/ N0 D Z d 3x (cid:26) .x/ N D given as a background event number with an oscillating perturbation. We must have to unsure that the event number remains positive. Similarly, the total charge is given by N0 > N .(cid:27)!/2 1 C Q .(cid:28)/ Q0 D C 1 Q ei!(cid:28) .(cid:27)!/2 ; C eN0 and Q eN , so that the total charge does not change sign, which would sug- where Q0 gest pair creation and annihilation processes. Since the background density (cid:26)0.x/ is independent of t and (cid:28), conservation of the 5D current becomes D D 1 c @ @t j 0 0 D 1 c5 @ @(cid:28) j C j 5 D (cid:26) .x/ C r (cid:1) t/(cid:3) (cid:0) C r (cid:1) J .x/ ei!t (cid:30) .(cid:28) t / (cid:0) @ (cid:2)(cid:0)ei!t (cid:1) (cid:30) .(cid:28) @t (cid:26) .x/ ei!t @ @(cid:28) (cid:30) .(cid:28) t/ (cid:0) J .x/(cid:141) ei!t (cid:30) .(cid:28) t/ (cid:0) C r (cid:1) C (cid:140)i!(cid:26) .x/ so that D i!(cid:26) C r (cid:1) J 0 D (cid:0)! e Z d 3x J .x/ e Z d 3x x J D r (cid:1) D (cid:0) e Z d 3x x .i!(cid:26)/ and we identify Z d 3x x e (cid:26) .x/ p D i!p Id d O D as the dipole moment p of the charge distribution (cid:26) .x/, so that i!p can be written as a constant current I along a dipole of length d in the direction O Z d 4x J .x/ ei!t (cid:30) .(cid:28) d. The total current density is J .(cid:28) / t/ e c D (cid:0) D i! pei!(cid:28) .(cid:27)!/2 1 C 68 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS representing an oscillating dipole. The induced potential found from the Green’s function GMaxwell is a(cid:11) .x; (cid:28) / e c D Z d 3x0 1 x (cid:0) x0j 4(cid:25) j j (cid:11) (cid:18)c (cid:18)t x j (cid:0) c (cid:0) x0j (cid:19) ; x0; (cid:28) (cid:19) so that writing x r r, we make the far ﬁeld approximation O D R x (cid:12) (cid:12) (cid:0) D x0(cid:12) (cid:12) D (cid:16)r 2 C 2 (cid:0)x0(cid:1) 2r r O (cid:1) (cid:0) 1=2 x0(cid:17) r r (cid:0) O (cid:1) x0 ’ and the dipole approximation k (cid:12) (cid:12) r O (cid:1) x0(cid:12) (cid:12) < kd 2(cid:25)d D (cid:21) (cid:28) eik r (cid:1) O x0 1 ) 1 ’ x0 r r (cid:0) O c (cid:1) (cid:18)1 r c ’ r (cid:0) O x0 (cid:1) O (cid:19) d r ’ r c to obtain a0 .x; (cid:28) / Q0 4(cid:25) r C Q 4(cid:25) r ’ e(cid:0) i .kr !t / (cid:30) (cid:16)(cid:28) (cid:0) t (cid:0) C (cid:17) r c a .x; (cid:28) / ik 4(cid:25) r p ’ e(cid:0) i .kr !t / (cid:30) (cid:16)(cid:28) (cid:0) t (cid:0) C (cid:17) r c a5 .x; (cid:28) / c5 c D a0 .x; (cid:28) / : We deﬁne the spherical wave factor e(cid:0) (cid:31) .x; (cid:28) / D i .kr !t / (cid:0) 4(cid:25) r (cid:30) (cid:16)(cid:28) t (cid:0) C (cid:17) r c and split the ﬁeld strengths into spacetime and polarization factors, as b e (cid:15) D r (cid:2) 1 c D (cid:0) @ @t (cid:17)55 D (cid:15)0 D (cid:17)55 a b (cid:31) D b a (cid:0) r @ @(cid:28) a (cid:0) @ @(cid:28) a0 1 c5 1 c5 a0 D c5 c r 1 c (cid:0) @ @t Q0 r 4(cid:25) r 2 O c5 c D a0 e (cid:31) Cb Q0 r 4(cid:25) r 2 O b b e b (cid:15) b (cid:15) (cid:31) Cb D D ikId "1 r O d (cid:2) O D (cid:0) ik"1 (cid:16)Q r O (cid:0) Id d(cid:17) O ik h "1Q r O C i"2Id di O a5 (cid:15) 0(cid:31) D b (cid:15) 0 b D ik h i"2i Q; "1 C c5 c c5 c where we used 1=kr 1 and deﬁne (cid:28) "1 1 C D R=c/ ".(cid:28) (cid:0) t C i!(cid:27) "2 (cid:17)55 D (cid:0) ".(cid:28) c c5 (cid:0) t C !(cid:27) R=c/ : 4.5. RADIATION FROM A LINE ANTENNA 69 We drop the static Coulomb terms produced by Q0, as these do not contribute to radiation. Since !(cid:27) 1 but small tends to suppress wavelike behavior, but c5=c z the polarizations then d leave "2 unchanged. Taking the orientation of the antenna to be O simplify to 1 [9], we approximate "1 D O (cid:28) ’ (cid:24) ik .Q ik h e ’ b (cid:15) 0 b ’ Id z/ O i"2i Q (cid:0) r O c5 c C r O z (cid:2) O b b (cid:15) b ikId ’ (cid:0) ik h ’ c5 c Q r O C i"2Id zi O (cid:15)(cid:22). Such terms are and we notice that terms containing 1=!(cid:27) appear only in the components of b t/, and can be understood as the contribution artifacts of modeling the time correlation by (cid:30).(cid:28) to the ﬁelds required to impose this correlation across spacetime. As was seen for plane waves, these ﬁelds will accelerate a test event initially at rest through the Lorentz force in such a way as to transfer mass to the event. (cid:0) The mass-energy-momentum tensor will contain bilinear ﬁeld combinations of the type T (cid:11)(cid:12) 1 c D (cid:18)f (cid:11)(cid:13) (cid:136) f (cid:12) (cid:13) (cid:0) (cid:136) f(cid:14)"g(cid:11)(cid:12) (cid:19) f (cid:14)" 1 4 Re h(cid:0)A(cid:11) i B(cid:11) (cid:1) (cid:31)i C (cid:0)! and it is convenient to separate the resulting products as T (cid:11)(cid:12) all terms containing 1=!(cid:27). We designate T (cid:11)(cid:12) 0 C D i D(cid:12) (cid:17) (cid:31)i Re h(cid:16)C(cid:12) C (cid:1) (cid:27) , where T (cid:11)(cid:12) T (cid:11)(cid:12) (cid:27) includes S .x; (cid:28) / C .x; (cid:28) / X .x; (cid:28) / D D D k2 (cid:30) (cid:0)(cid:28) k2 (cid:30) (cid:0)(cid:28) k2 (cid:30) (cid:0)(cid:28) t (cid:0) 4(cid:25) r C t (cid:0) 4(cid:25) r C t (cid:0) 4(cid:25) r C 2 r c (cid:1) ! 2 r c (cid:1) ! 2 r c (cid:1) ! sin2 .kr !t / (cid:0) cos2 .kr !t / (cid:0) 2 sin .kr (cid:0) !t / cos .kr !t / (cid:0) and note that these functions drop oﬀ as 1=r 2 and so will produce nonzero surface integrals at large r, as is characteristic of radiation ﬁelds. Using these functions, the components of T (cid:11)(cid:12) are 0 Id cos (cid:18)/2 2 .Id /2 (cid:16)1 C Id cos (cid:18) / z O C (cid:18)Id .Id (cid:0) .cos (cid:18) /2(cid:17) Q cos (cid:18)/ C C (cid:0) (cid:0) 2(cid:17)55 (cid:16) 2 (cid:17) Q2(cid:21) S .x; (cid:28) / (cid:17)55 (cid:16)Q 2(cid:19) (cid:17) r(cid:21) S .x; (cid:28) / O c5 c c5 c T 00 0 D T0 0 D T 50 0 D T5 0 D T 55 0 D (cid:20).Q 1 2 C (cid:20)Id .Q c5 c c5 c .Q .Q Q Q 1 2 (cid:17)55 .Q (cid:0) (cid:0) (cid:0) Id cos (cid:18)/ S .x; (cid:28) / Id cos (cid:18)/ S .x; (cid:28) / r O Id cos (cid:18)/2 S .x; (cid:28) / T 50 0 r O D 70 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS all of which have spacetime dependence S .x; (cid:28) /. The components of T (cid:11)(cid:12) (cid:27) are T 00 (cid:27) D 1 2 h"2 2 h.Id /2 C Q2i C .x; (cid:28) / (cid:17)55 (cid:0) c5 c "2Q (cid:140)Q C Id cos (cid:18)(cid:141) X .x; (cid:28) /i T0 (cid:27) D (cid:0) (cid:17)55 c5 c "2Q (cid:20)Id (cid:18)X .x; (cid:28) / (cid:17)55 C c c5 C .x; (cid:28) /(cid:19) Q X .x; (cid:28) / z O C r(cid:21) O T 50 (cid:27) D (cid:0) "2Id .Id (cid:0) Q cos (cid:18)/ X .x; (cid:28) / T5 (cid:27) D (cid:0) "2 hId (cid:140)Q (cid:0) Id cos (cid:18)(cid:141) (cid:16).Id /2 z O C Q2(cid:17) ri X .x; (cid:28) / O (cid:0) T 55 (cid:27) D 1 2 h"2 2 (cid:16).Id /2 (cid:0) Q2(cid:17) C .x; (cid:28) / c5 c C "2Q .Q (cid:0) Id cos (cid:18) / X .x; (cid:28) / i whose spacetime dependence is determined by C .x; (cid:28) / and X .x; (cid:28) / and is thus out of phase with the T (cid:11)(cid:12) 0 . As expected from the transfer of mass made possible by the ﬁelds (cid:15)(cid:22), we ﬁnd a nonzero mass density T 55 and mass ﬂux T0 and T5 into time and space. Moreover, integrating over a sphere of radius r, the net mass ﬂux into space will be of the form Z d (cid:127) r 2 T5 0 r O (cid:1) Z d (cid:127) r 2 c5 c hQ r O (cid:1) r 2 k2 (cid:30) (cid:0)(cid:28) P D D D D Q c5 c k2c5 4(cid:25)c .Q Id .cos (cid:18)// S .x; (cid:28) / ri O (cid:0) r c (cid:1) 2 ! t (cid:0) 4(cid:25) r C sin2 .kr (cid:0) !t / Z d (cid:127) (cid:140)Q Id cos (cid:18) (cid:141) (cid:0) Q2 (cid:16)(cid:30) (cid:16)(cid:28) t (cid:0) C 2 (cid:17)(cid:17) r c sin2 .kr !t / (cid:0) and thus nonzero wherever (cid:28) r=c. Just as the energy radiated by a Maxwell dipole antenna must be provided by the ampliﬁer that drives the oscillating current density, the mass radiated by an SHP antenna is continuously provided by an ampliﬁer that creates events and drives them into the antenna. ’ (cid:0) t For a center-fed antenna of length d oriented along the z-axis, the charge density may be described by where (cid:26) .x/ ( (cid:14) .x/ (cid:14) .y/ (cid:26)z .z/ D 0 ; z d 2 (cid:20) (cid:20) ; otherwise; (cid:0) d 2 (cid:26)z.z/ 1 2 D (cid:140)(cid:26)z.z/ (cid:26)z. z/(cid:141) (cid:0) C C 1 2 (cid:140)(cid:26)z.z/ (cid:26)z. z/(cid:141) (cid:0) .z/ (cid:26) C .z/ (cid:26) (cid:0) C D (cid:0) divides the charge density into even and odd parts. The total oscillating charge is 4.5. RADIATION FROM A LINE ANTENNA 71 Z d 3x e(cid:26) .x/ Q D d 2 2e Z 0 D dz (cid:26) .z/ C and the dipole moment is Id d O D i!e Z d 3x x(cid:26) .x/ 2ie! z O D d 2 Z 0 dz z (cid:26) .z/ (cid:0) C describes a net charge Q driven symmetrically into the left and right segments showing that (cid:26) of the antenna, while (cid:26) describes a dipole moment produced by shifting charge from one (cid:0) antenna segment into the other segment. Since Q eN , we see that the ampliﬁer driving net charge into the antenna must be driving new events into the antenna as well, accounting for the radiated mass. Taking Q 0 so that the ampliﬁer shifts charged events between antenna segments without injecting new events, the ﬁelds reduce to D D ikId e b (cid:15) 0 b D (cid:0) 0 D z O b b (cid:15) b ikId r O z (cid:2) O D (cid:0) k"2Id z O D so that the eﬀect of the waves on a test event at rest reduces to d d (cid:28) . (cid:0) 1 2 M x2/ P D (cid:0) e(cid:17)55c5(cid:15)0 0 D and there is no transfer of mass. Similarly, the components of become T (cid:11)(cid:12) 0 T 00 0 D T0 0 D T 50 0 D T5 0 D T 55 0 D .Id /2 (cid:18)1 .Id /2 (cid:0) (cid:0) 1 2 (cid:0) cos (cid:18) cos2 (cid:18)(cid:19) S .x; (cid:28) / z O r (cid:1) S .x; (cid:28) / C O 0 0 1 2 (cid:17)55 .Id /2 cos2 (cid:18) S .x; (cid:28) / describing no transfer of mass into space or time. 72 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS The components of T (cid:11)(cid:12) (cid:27) also simplify to T 00 (cid:27) D T0 (cid:27) D T 50 (cid:27) D T5 (cid:27) D T 55 (cid:27) D 2 (cid:19) 1 2 (cid:18) c !c5 (cid:30)0 (cid:30) 0 .Id /2 C .x; (cid:28) / (cid:30)0 (cid:30) .Id /2 X .x; (cid:28) / (cid:17)55 c !c5 T 50 . z O (cid:18) c !c5 1 2 r/ (cid:0) O (cid:30)0 (cid:30) 2 (cid:19) .Id /2 C .x; (cid:28) / ; (cid:0) "R=(cid:27) with (cid:30)0=(cid:30). These expressions involve no transfer of energy but do where we replaced describe nonzero transfer of mass into space and time directions. Once again, we understand this transfer as an artifact of the time correlation model that enters through the derivative of t/, rather than an inherent feature of radiation from an oscillating charge. In particular, (cid:30) .(cid:28) all of the nonzero terms in the expression for mass conservation contain (cid:30)0, so that these terms are separately conserved among themselves. To see this we expand (3.25) as (cid:0) @(cid:11)T (cid:11)5 e c D (cid:0) f 5(cid:11)j(cid:11) (cid:0)! 1 c @ @t T 50 T5 1 c5 @ @(cid:28) C T 55 e c (cid:15)(cid:22)j(cid:22) D (cid:0) C r (cid:1) which becomes 1 c @ @t T 50 (cid:27) C r (cid:1) T5 (cid:27) C 1 c5 @ @(cid:28) (cid:0)T 55 0 C T 55 (cid:27) (cid:1) D (cid:0) e c (cid:15)(cid:22) (cid:27) j(cid:22) (4.22) T5 0 D 0. We also write the ﬁeld as (cid:15)(cid:22) because T 50 (cid:27) because it contains the factor "2. Finally, 0 D we note that because T 55 0 depends on (cid:28) only through the factor of (cid:30)2 in S .x; (cid:28) /, the derivative @(cid:28) T 55 0 must similarly contain (cid:30)0. Thus, each term in (4.22) enters through the derivative of the time correlation model, and these terms are conserved among themselves with no corresponding energy transfer. Integrating the energy Poynting vector T0 over the surface of a sphere of radius r we must evaluate T0 r O (cid:1) D D D r O (cid:0) cos (cid:18) .Id /2 .Id /2 .Id /2 sin2 (cid:18) S .x; (cid:28) / (cid:0) (cid:0) cos2 (cid:18) z O C O 1(cid:1) S .x; (cid:28) / C (cid:1) (cid:0) r (cid:1) S .x; (cid:28) / to ﬁnd the instantaneous radiated power 4.6. CLASSICAL PAIR PRODUCTION 73 P D D D D Z d (cid:127) r 2 .Id /2 S .x; (cid:28) / sin2 (cid:18) .Id /2 r 2 k2 (cid:30) (cid:0)(cid:28) 2 r c (cid:1) ! t (cid:0) 4(cid:25) r C sin2 .kr !t / Z 0 (cid:0) 2(cid:25) (cid:25) d(cid:30) Z 0 d(cid:18) sin3 (cid:18) .Id /2 k2 (cid:30) (cid:0)(cid:28) 2 ! r c (cid:1) t (cid:0) 4(cid:25) C sin2 .kr !t / (cid:0) 8(cid:25) 3 k2.Id /2 6(cid:25) (cid:16)(cid:30) (cid:16)(cid:28) t (cid:0) C r c (cid:17) sin .kr 2 !t /(cid:17) : (cid:0) Since we have assumed that 1=!(cid:27) is small, we may take (cid:30) (cid:0)(cid:28) over one cycle of the wave, so that the average radiated power over one cycle is C (cid:0) t r c (cid:1) as eﬀectively constant k2.Id /2 6(cid:25) P N ’ (cid:16)(cid:30) (cid:16)(cid:28) t (cid:0) C r c (cid:17)(cid:17) 2 1 T T Z 0 dt .sin .kr !t //2 (cid:0) k2.Id /2 12(cid:25) D (cid:16)(cid:30) (cid:16)(cid:28) t (cid:0) C 2 (cid:17)(cid:17) r c which agrees with the standard result up to the factor of (cid:30)2. The neutral antenna radiates energy in agreement with the Maxwell result and radiates no mass (leaving aside the derivatives of the arbitrarily chosen function (cid:30)). CLASSICAL PAIR PRODUCTION 4.6 A standard technique for pair creation in the laboratory is the two-step process by which An- derson [10] ﬁrst observed positrons in 1932: high energy electrons are ﬁrst scattered by heavy nuclei to produce bremsstrahlung radiation, and electron/positron pairs are then created from the radiation ﬁeld. The Bethe-Heitler mechanism [11] describes this technique as the quantum process, e(cid:0) Z e(cid:0) Z Z (cid:13) (cid:13) C C involving a quantized radiation ﬁeld and the external Coulomb ﬁeld of the nuclei. We now calculate the classical trajectories that produce this two-step process, as shown in Figure 4.1. (cid:0)! (cid:0)! eC e(cid:0) C C C C Z (cid:0)! Because the electromagnetic interaction is instantaneous in (cid:28), we may take both stages of the Bethe-Heitler process as occurring at (cid:28)2: (1) the scattering of particle-2 by a nucleus Eout > 0) and (2) the absorption of the resulting bremsstrahlung radiation at t1 (Ein > 0 Eout > 0). In the Stueckelberg picture, the E < 0 (antiparticle) by particle-1 at t2 (Ein < 0 trajectory of particle-1 must have been produced at the earlier chronological time (cid:28)1 < (cid:28)2. To examine the conditions that might produce this initial negative energy trajectory, we describe particle-1 scattering in the Coulomb ﬁeld of another nucleus at t t3 and emerging with neg- ative energy moving backward in t. (cid:0)! D 74 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS Figure 4.1: Bethe–Heitler mechanism in classical electrodynamics. In the laboratory, where events are recorded in the order determined by clock t, the process t1 and emitting bremsstrahlung, followed by the appear- t3, the antiparticle encounters another t2 of a particle/antiparticle pair. Then at t appears as particle-2 scattering at t ance at t particle causing their mutual annihilation. D D D Our analysis is carried out in three parts. We ﬁrst consider the Coulomb scattering of a slow incoming particle by an oppositely charged nucleus. To produce the pair annihilation observed at (cid:28)1, the outgoing particle must have E < 0, while at (cid:28)2 the interaction must lead to E > 0. We identify the condition that allows the energy of the outgoing particle to change sign. In the second part, we compute the radiation ﬁeld produced by the acceleration of the scattered particle at (cid:28)2 using the Liénard–Wiechert potential for an arbitrary trajectory. In the third part we again use the Lorentz force to treat the acceleration of the E < 0 particle absorbing the radiation at (cid:28)2, and ﬁnd the condition for its return to an E > 0 trajectory. (cid:0) With the function ’.(cid:28) (cid:28)1/ in the ﬁeld strengths, the Lorentz force is a set of coupled nonlinear diﬀerential equations. By taking the correlation time (cid:21) to be small we may again ap- proximate ’.(cid:28) (cid:21)c and out- going scattering trajectories are easily obtained by integration of the Lorentz force. This solution provides a reasonable qualitative description of the classical Bethe–Heitler process, which may be reﬁned by numerical solution of the exact Lorentz force equations. (cid:28)1/, so that interactions are limited to a range R (cid:21)(cid:14).(cid:28) (cid:28)1/ (cid:25) (cid:24) (cid:0) (cid:0) tZE>0E>0E>0E>0ZE<0τ1τ2>τ1τ2t3t2t1particle−1particle−1particle−2(anti)particle−1Initially (at time (cid:28) ! (cid:0)1 rated. We set the nucleus at rest at the origin of the laboratory frame, 4.6. CLASSICAL PAIR PRODUCTION 75 ), the target nucleus Z and incoming particle are widely sepa- and from some point x the line of observation XZ .(cid:28) / D .ctZ; xZ/ D .c; 0/ (cid:28) z x (cid:0) D XZ .(cid:28) / D .ct; x/ (cid:0) .c; 0/ (cid:28) satisﬁes z2 D .c.t (cid:0) (cid:28)/; x/2 0 D (cid:0)! c.t (cid:28)/ (cid:0) D R D j x j (cid:0)! z D R (cid:16)1; R(cid:17) ; O where R is the scalar length deﬁned in (4.9) as u z (cid:1) c D (cid:0) (cid:0) XZ P (cid:1) z .c; 0/ R (cid:16)1; R(cid:17) O (cid:1) c D (cid:0) c R: D For the observation point we use the location of the incoming particle-1, approaching the nu- cleus on the trajectory x D Xin .(cid:28) / D .ct; x/ u(cid:28) s C D tin .c; v; 0; 0/ (cid:28) D P C (cid:0)st ; 0; sy; 0(cid:1) ; where d d (cid:28) u D .ct; x; y; z/ dx d (cid:28) D dx tin dt P v tin P D tin P D dt d (cid:28) D 1 (cid:0) (cid:12)2 p1 v=c. The scattering takes place in the plane z and (cid:12) we can write the spatial distance between the incoming particle and the target as 0 and since the nucleus is at the origin, D D R .(cid:28) / x j D D j px2 y2 q(cid:0)v 2 tin(cid:28) (cid:1) P s2 y : C D C Putting (cid:21) so that (cid:28)1 is determined from the causality conditions for the initial trajectories, R.(cid:28)1/, the support of the ﬁelds is narrowly centered around the retarded time (cid:28)1, (cid:25) (cid:140)Xin .(cid:28)1/ (cid:0) XZ .(cid:28)1/ (cid:141)2 0 D X 0 in .(cid:28)1/ (cid:0) X 0 Z .(cid:28)1/ > 0: These equations have the solution (cid:28)1 D v 1 tin (cid:0)1 P (cid:0) (cid:17)2 v(cid:1) (cid:18)(cid:17)vst qs2 t (cid:0) C s2 y (cid:0)1 (cid:0) (cid:19) (cid:17)2 v(cid:1) qs2 t (cid:0) v s2 y ; (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!v (cid:28) c 76 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS where we introduce the smooth parameter (cid:17)v D (cid:18)1 1 v (cid:0) (cid:19) 1 tin P (cid:26) 0; v 1; v (cid:0)! 0 c: D D Notice that the 0-component st of the impact parameter must be positive in order for the in- teraction to take place. The location of the incoming particle at the time of interaction is now where x .(cid:28)1/ R R O D t .(cid:28)1/ tin(cid:28)1 D P C st =c; R D 1 1 (cid:0) (cid:17)2 v (cid:18)(cid:17)vqs2 t (cid:0) s2 y (cid:0)1 (cid:17)2 v(cid:1) (cid:0) C (cid:19) st st (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!v (cid:28) c (cid:16)(cid:17)vst C R O D s2 y (cid:0)1 t (cid:0) (cid:17)vqs2 qs2 st C (cid:17)2 v(cid:1); (cid:0)1 (cid:0) t (cid:0) s2 y (cid:0)1 (cid:0) v(cid:1) sy; 0(cid:17) (cid:17)2 (cid:0) (cid:17)2 v(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!v (cid:28) c s 1 0 @ s2 y s2 t ; sy st 1 A : ; 0 (cid:0) Applying the Coulomb potential calculated in Section 4.1.1, the potential induced by the target nucleus in this approximation is a0 .x; (cid:28) / (cid:21) Ze 4(cid:25)R D (cid:14) .(cid:28) (cid:28)1/ (cid:0) ai 0 D a5 .x; (cid:28) / c5 c D a0 .x; (cid:28) / so that the nonzero ﬁeld strengths ei D f 0i D @0ai (cid:0) @i a0 f 5i (cid:15)i D D @5ai (cid:0) @i a5 (cid:15)0 D @5a0 (cid:0) @0a5 are e D (cid:0)r a0 (cid:15) D (cid:0)r a5 D c5 c e where we used @ @t (cid:14).(cid:28) (cid:28)1/ (cid:0) D (cid:18) dt d (cid:28) (cid:15)0 D (cid:17)55 c5 (cid:18)1 C c2 5 c2 1 tin P (cid:19) @(cid:28) a0; @ @(cid:28) tin (cid:14).(cid:28) (cid:0) (cid:28)1/ : 1 (cid:19)(cid:0) t D The nucleus and the incoming particle have opposite charge, so the Lorentz force M x0 R D (cid:0) M x R D (cid:0) e c e c (cid:0)f 0i xi P C f 05 x5(cid:1) P D (cid:0) e c (cid:0)e x (cid:1) P (cid:0) (cid:17)55c5(cid:15)0(cid:1) (cid:16)f k0 x0 P C f k5 x5(cid:17) P D (cid:0) e c (cid:0)ec t P (cid:0) (cid:17)55c5(cid:15)(cid:1) on the incoming particle becomes (cid:21)Ze2 Mc2 (cid:21)Ze2 M (cid:20) x P (cid:18) t P t R D x R D (cid:19) @(cid:28) (cid:21) (cid:14) .(cid:28) (cid:28)1/ (cid:0) 4(cid:25)R c2 5 c2 1 tin P (cid:14) .(cid:28) (cid:18)1 C (cid:1) r (cid:0) (cid:19) c2 5 c2 r (cid:17)55 (cid:0) (cid:28)1/ : (cid:0) 4(cid:25)R The delta function enables immediate integration of the force equations as 4.6. CLASSICAL PAIR PRODUCTION 77 tf P tin (cid:0) P D (cid:21)Ze2 Mc2 (cid:28)1 (cid:21)=2 C Z d (cid:28) (cid:20) x P (cid:1) r (cid:0) (cid:18)1 C (cid:28)1 (cid:21)=2 (cid:21)Ze2 Mc2 P (cid:21) Mc2 (cid:0) x .(cid:28)1/ Ze2 4(cid:25)R2 P (cid:1) r D D (cid:0) 1 4(cid:25)R x .(cid:28)1/ R (cid:1) O (cid:19) @(cid:28) c2 5 c2 1 tin P (cid:21) (cid:14) .(cid:28) (cid:28)1/ (cid:0) 4(cid:25)R xf P xin (cid:0) P D (cid:21)Ze2 M (cid:28)1 (cid:21)=2 C Z d (cid:28) (cid:18) t P (cid:0) (cid:17)55 (cid:19) c2 5 c2 r (cid:14) .(cid:28) (cid:28)1/ (cid:0) 4(cid:25)R (cid:21) M D (cid:0) (cid:21)=2 (cid:28)1 (cid:0) Ze2 4(cid:25)R2 (cid:18) t .(cid:28)1/ P (cid:0) (cid:17)55 (cid:19) c2 5 c2 R; O where the velocities are evaluated at the interaction point as t; (cid:0)P x(cid:1) .(cid:28)1/ P D 1 2 h(cid:0)P t; x(cid:1)f C P t; (cid:0)P x(cid:1)in P i : We introduce the dimensionless parameter for Coulomb scattering (cid:21) Mc Ze2 4(cid:25)R2 D (cid:21)c R (cid:2) Ze2 4(cid:25)R ge D 1 Mc2 D correlation length impact parameter (cid:2) interaction energy mass energy (4.23) (4.24) which appears in (4.23) and (4.24) as the factor controlling the strength of the interaction. Writing 1 2 we can expand the Lorentz force as components in the form Rx ge O 1 2 (cid:11)x (cid:11)y D D Ry ge O 2 3 2 1 (cid:11)x (cid:11)y (cid:11)x (cid:11)y 0 1 1 0 c tf P xf P yf P and solve for the ﬁnal velocity, 4 4 5 3 2 5 D 4 1 (cid:11)x (cid:11)y (cid:0) (cid:0) (cid:11)x (cid:0) 1 0 3 2 5 4 0 0 0 tin c P v tin P 0 3 5 C 2(cid:17)55 c2 5 c2 2 4 0 (cid:11)x (cid:11)y 3 5 c 2 3 6 4 tf P xf P yf P where we neglect c2 7 5 D 1 5 =c2 tin. (cid:28) P 1 1 4 g2 e (cid:0) 8 2 (cid:136)(cid:136)< 6 4 (cid:136)(cid:136): c v tin P tin P 0 3 tin ge P 7 5 (cid:0) 2 6 4 v c c Rx O Rx O Ry O 3 7 5 C 1 4 g2 tin e P 2 6 6 4 c v (cid:16) R2 O 2v R2 x (cid:0) O y Ry Rx O O (cid:17) 3 7 7 5 9 >>= >>; ; (4.25) 78 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS Before considering pair annihilation, we examine the low velocity and low interaction energy limit of this result. Taking j D the initial velocity reduces to x jP v c (cid:28) tin P ! 1 (cid:17)v 0 ! ge 1 (cid:28) the ﬁnal velocity becomes Xin .(cid:28)/ P ! .c; v; 0; 0/ ; tf P tin (cid:25) P xf P x (cid:25) P (cid:0) gec R O and the scattering angle can be found as 0 s D @ s2 y s2 t ; sy st 1 A ; 0 1 (cid:0) R O R st D cos (cid:18) R gec O (cid:0) x xf (cid:12) (cid:12) (cid:12) jP (cid:12)P j If we also wish to impose the nonrelativistic condition for conservation of energy, we obtain a new constraint in the form gec (cid:0) xf (cid:12) (cid:12) (cid:12) (cid:12)P xf P xf (cid:12) (cid:12) (cid:12)P x (cid:1) P x (cid:12) jP Rx O x (cid:1) P D D D v j : x2 P x2 P v2 x2 f D D P h x P (cid:0) D gec 2 Ri O ) 2v Rx O D gec in which case 1 xf (cid:12) (cid:12) (cid:12)P (cid:12) Now, using the deﬁnition of ge we ﬁnd cos (cid:18) D hv gec Rxi O 1 (cid:0) D R2 x: 2 O (cid:0) cot (cid:18) 2 D r 1 1 cos (cid:18) cos (cid:18) D Ry O Rx D O C (cid:0) sy st 2v gec D 2st (cid:21)v (cid:2) 4(cid:25)M v2sy Ze2 which recovers the Rutherford scattering formula if 2st (cid:21)v D 1: (4.26) R .(cid:28)1/ which we assumed to be comparable to (cid:21)c. Since we But for low energy we have st c in this low velocity case, (4.26) cannot be maintained. This result is unsur- cannot have v prising because the short-range potential cannot provide an adequate model of nonrelativistic Rutherford scattering. D (cid:24) Removing these restrictions and returning to the relativistic case, the condition for pair tf < 0 for some value of P annihilation at (cid:28)1 is that particle-1 scatters to negative energy, that is ge which we call g1. From (4.25), 1 (cid:0) tf P tin D P Rx g1.v=c/ O 1 4 g2 1 1 (cid:0) 1 4 g2 1 C 4.6. CLASSICAL PAIR PRODUCTION 79 and we see that for small values of g1, Since v < c and Rx < 1, the numerator has discriminant tf P tin (cid:0)! P (cid:21) 1: .vRx=c/2 1 < 0 (cid:0) and so is positive deﬁnite. The denominator becomes negative when 1 4 1 (cid:0) g2 1 < 0 ) g1 D correlation length impact parameter (cid:2) interaction energy mass energy > 2 and since we take the correlation length (cid:21)c approximately equal to the impact parameter R, the requirement for pair annihilation is Ze2 4(cid:25)R > 2 Mc2 meaning that the interaction energy is greater than the mass energy of the annihilated particles. As g1 approaches 2 from below tf P decreases from large negative values, taking the limiting value tf becomes very large. After g1 passes this critical value, P tin (cid:0)P D (cid:0) so that the outgoing trajectory is timelike for all values of g1 > 2. (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!g1 !1 H) Ef 2(cid:1) tf P C (cid:0) .Ein 2Mc2/ C Having found the condition for pair annihilation at time (cid:28)1 we now consider the scattering at time (cid:28)2, which we also treat as an incoming particle approaching a nucleus of opposite charge. Therefore we may apply the general expression (4.25). Particle-2 approaches a second nucleus along some trajectory x(cid:22) f .(cid:28)/ with posi- tive energy. The scattering and acceleration of particle-2 produces a radiation ﬁeld which can be evaluated at some point of observation y(cid:22) using the Liénard-Wiechert potential for an arbitrary trajectory. in.(cid:28)/ and emerges from the interaction along trajectory x(cid:22) The support of ’.(cid:28) (cid:28)2/ is narrowly centered on (cid:28)2, and so the line of observation z(cid:22) (cid:0) must be a lightlike vector, which we write as z(cid:22) x(cid:22) .(cid:28)2/ y(cid:22) (cid:26) D We express the initial and ﬁnal 4-velocities of the scattered particle as D D D (cid:0) (cid:26)(cid:22) O (cid:26) O .1; (cid:26)/ ; O (cid:26)2 O 1: and deﬁne (cid:12)in xin=c D P (cid:12)f xf =c D P (cid:129)(cid:12) (cid:12) .(cid:28) / P(cid:12) .(cid:28) / (cid:12) .(cid:28)2/ D D D D N(cid:12) (cid:12)f (cid:0) (cid:12)in C (cid:129)(cid:12) (cid:14) .(cid:28) (cid:12)in (cid:129)(cid:12) (cid:18) .(cid:28) (cid:28)2/ (cid:28)2/ (cid:0) (cid:0) (cid:2)(cid:12)f 1 2 D (cid:12)in(cid:3) : C 80 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS From (4.11) and (4.12) express the radiation ﬁelds produced by an arbitrary trajectory as (cid:28)2/F 5(cid:22) (cid:16)z; (cid:12); P(cid:12)(cid:17) ; (cid:28)2/F (cid:22)(cid:23) (cid:16)z; (cid:12); P(cid:12)(cid:17) e’.(cid:28) e’.(cid:28) f (cid:22)(cid:23) rad D (cid:0) f 5(cid:22) rad D (cid:0) (cid:0) where F (cid:22)(cid:23) 2 (cid:16)z ^ P(cid:12)(cid:17) (cid:26) D 4 .z (cid:0) ^ 4(cid:25)c(cid:26)3 (cid:22)(cid:23) (cid:12)/ (cid:16) P(cid:12) (cid:1) z(cid:17) 3 5 F 5(cid:22) 2 4 z(cid:17) z (cid:16) P(cid:12) (cid:1) 4(cid:25)c(cid:26)3 3 5 c5 c D (cid:22) (cid:1) z and (cid:26) (cid:12) is the scalar distance from the scattered particle to the point of observation. D (cid:0) As pictured in Figure 4.1, the radiation emitted by the scattering of particle-2 is absorbed by the negative energy particle-1 arriving at y(cid:22). Using the Lorentz force equations we calculate the change in velocity of particle-1 caused by the incoming radiation. Since each term in the y(cid:22).(cid:28)2/ of (cid:28)2/ and ’.0/ ﬁeld strengths contains P(cid:12).(cid:28)/ P particle-1 is 1=2, the change in velocity (cid:129)(cid:12) (cid:14) .(cid:28) D D (cid:0) (cid:129) y(cid:22) P D D e Mc e2 Mc Z 1 (cid:0)1 Z 1 d (cid:28) hf (cid:22)(cid:23) rad y(cid:23) P C d (cid:28) ’.(cid:28) (cid:0) (cid:28)2/ h f (cid:22)5 rad y5i P F (cid:22)(cid:23) (cid:16)z; (cid:12); P(cid:12)(cid:17) (cid:0) (cid:0)1 e2 2Mc (cid:20)F (cid:22)(cid:23) (cid:0)z; N(cid:12); (cid:129)(cid:12)(cid:1) y(cid:23) P (cid:17)55c5F 5(cid:22) (cid:16)z; (cid:12); P(cid:12)(cid:17)i y(cid:23) P (cid:17)55c5F 5(cid:22) (cid:0)z; N(cid:12); (cid:129)(cid:12)(cid:1) (cid:0) (cid:21) (4.27) D (cid:0) C expressed in terms of the velocity change (cid:129)(cid:12) and average velocity N(cid:12). These are found from (4.25) to be (cid:129)(cid:12) D (cid:0) 1 ge tin 1 e P 4 g2 (cid:0) 2 6 6 4 (cid:12) Rx O Rx O Ry O 3 7 7 5 1 2 g2 e tin 1 e P 4 g2 C 1 (cid:0) 2 6 6 4 (cid:12) 1 R2 (cid:12) x O Ry Rx O O 3 7 7 5 N(cid:12) D 1 1 tin 1 e P 4 g2 (cid:0) 2 4 1 (cid:12) 0 3 5 (cid:0) 1 1 2 ge tin 1 e P 4 g2 (cid:0) 2 6 6 4 (cid:12) Rx O Rx O Ry O 3 7 7 5 1 4 g2 e 1 4 g2 e C 1 (cid:0) (cid:12) tin P 2 6 6 4 0 R2 y (cid:0) O Ry Rx O O 3 7 7 5 ; where now O of scattering. Since particle-2 scatters at (cid:28)2 to an E > 0 outgoing trajectory, we may take v and so we set ge R is the unit vector from the second nucleus to incoming particle-2 at the moment c 0 for this interaction. g2 < 1 and g2 (cid:28) From (4.27) the Lorentz force acting on particle-1 at (cid:28)2 can be written D 2 (cid:25) y(cid:22) f C P e2 2Mc " .z ^ (cid:129)(cid:12)/ (cid:26) ^ N(cid:12)(cid:1) .(cid:129)(cid:12) (cid:0)z (cid:0) 4(cid:25)c(cid:26)3 z/ (cid:1) y(cid:22) in (cid:0) D P e2 2Mc " .z ^ (cid:129)(cid:12)/ (cid:26) (cid:0)z (cid:0) 4(cid:25)c(cid:26)3 (cid:22)(cid:23) # z/ (cid:1) yin (cid:23) P (cid:22)(cid:23) # y(cid:23)f P ^ N(cid:12)(cid:1) .(cid:129)(cid:12) 4.6. CLASSICAL PAIR PRODUCTION 81 neglecting the term .c2 5 =c2/F 5(cid:22). Making the simplifying choice O R 1 2 Rx g2 O v (cid:18) (cid:20)1 (cid:129)(cid:12) tin P (cid:19)(cid:21) (cid:26)x O C (cid:0) (cid:26) z (cid:1) D D (cid:0) z N(cid:12) (cid:1) (cid:26) (cid:1) O D 0, we ﬁnd tinv(cid:26) g2 P Rx; O where again we take g2 2 (cid:25) 0. Deﬁning a second dimensionless factor for radiation gR D 1 2 e2 4(cid:25)(cid:26) 1 Mc2 D 1 2 interaction energy mass energy using (cid:2).z ^ and now taking (cid:12) (cid:25) (cid:129)(cid:12)/ (cid:26) (cid:1) (cid:0) .(cid:129)(cid:12) z/ (cid:0)z ^ N(cid:12)(cid:1)(cid:3) y/ (cid:129)(cid:12)(cid:26) .z (cid:0) (cid:1) P z/ (cid:2)(cid:0) N(cid:12) y(cid:1) z (cid:1) P 0, the Lorentz force splits into the 0-component y/ (cid:26) (cid:1) P .(cid:129)(cid:12) z .(cid:129)(cid:12) y (cid:1) P D (cid:0) (cid:1) (cid:0) .z y/ N(cid:12)(cid:3) (cid:1) P y0 f (cid:0) P R g2gR O yf (cid:1) P y0 in C D P R g2gR O yin (cid:1) P and the space component yf P (cid:0) g2gR h(cid:16) R O yf (cid:17) (cid:1) P (cid:26) O C (cid:16) y0 (cid:26) f (cid:0) O P yin P yf (cid:17) (cid:1) P Ri O D g2gR h(cid:16) C R O yin(cid:17) (cid:1) P (cid:26) O C (cid:0) y0 (cid:26) in (cid:0) O P Ri : yin(cid:1) O (cid:1) P We write the velocity of incoming negative energy particle-1 as y0 in < P D and write the Lorentz force in components, with g yin P (cid:26) (cid:1) O (cid:0) 1 2 6 6 4 (cid:0) (cid:0) 1 g g Rx O Ry O 1 Rx g O (cid:26)x O g Rx O Rx (cid:26)y O O (cid:0) (cid:0) g (cid:0) (cid:0) g Ry g O Ry (cid:26)x O O Ry (cid:26)y O g O 3 7 7 5 2 6 4 y0 f P yxf P yyf P 3 7 5 D (cid:0) 1 (cid:0) 0 D 2 6 6 4 yin yin R j O D jP ) P g2gR, as 1 0 0 3 g g Rx O Ry O 1 0 0 1 7 7 5 2 6 4 y0 i P yxi P yyi P 3 g yi jP j 7 5 C 3 7 5 2 6 4 1 (cid:26)x O (cid:26)y O so that the ﬁnal velocity of particle-1 after absorbing the radiation is " y0 f P yf P # 1 " D 1 g2 (cid:0) y0 in P yin jP R j O # 2g " C 1 (cid:0) g2 g2 " C 1 g2 (cid:0) yin jP j yin C jP yin y0 R in O P y0 in C jP P y0 (cid:26) 2 2 in O P j yin jP C # # (cid:26) j O R j O g3 " C 1 g2 (cid:0) # : yin jP yin jP j (cid:26) j O 82 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS The 0-component is y0 f D P approximated at low velocity as 1 1 C (cid:0) g2 y0 in C g2 P 2 g C 1 g2 C g2 g (cid:0) yin jP j y0 f (cid:25) P 1 1 C (cid:0) g2 y0 in D (cid:0) g2 P (cid:11) y0 in; P where g2 D (cid:11) (cid:11) 1 1 ) (cid:11) D (cid:0) 1 1 C (cid:0) g2 g2 C (cid:0) is written so that (cid:11) > 1 for a positive energy timelike particle. The exact ﬁnal velocity of the scattered particle is # " y0 f P yf P 1 " (cid:11) (cid:0) 2 D (cid:0) y0 in P yin jP R j O # p(cid:11)2 C " 1 (cid:0) 1 " (cid:11) C 2 (cid:0) yin y0 in C jP P y0 (cid:26) 2 2 in O P C j yin jP " r (cid:11) (cid:11) 1 1 C (cid:0) yin jP yin jP j (cid:26) j O # # y0 R in O P yin jP j yin C jP # (cid:11) (cid:0) R j O (cid:26) j O 1 C 2 (cid:11) (cid:21) 1 (cid:0) : yin jP j with 0-component y0 f D (cid:0) P (cid:11) y0 in (cid:0) P 1 (cid:20)1 (cid:11) C 2 C 3 (cid:0) p(cid:11)2 A pair creation event is observed at (cid:28)2 for (cid:11) > 1 which requires that g2gR > 1 g D (cid:0)! e2 4(cid:25)(cid:26) > 2Mc2 g2 ; where g2 < 1 and so the energy absorbed from the bremsstrahlung emitted from the scattering at (cid:28)2 must be at least the total mass of the particle creation event observed in the laboratory. This provides a classical equivalent of the Bethe–Heitler mechanism in Stueckelberg–Horwitz–Piron electrodynamics. 4.7 PARTICLE MASS STABILIZATION As we have seen, under the right circumstances a particle and an interacting pre-Maxwell ﬁeld may exchange mass. In practical examples, such as pair creation and annihilation, the mass shift will be symmetric under evolution, so that the initial and ﬁnal masses will be equal. As another model of mass shift, consider an event propagating uniformly on-shell as x .(cid:28)/ u(cid:28) D D (cid:0)u0; u(cid:1) u2 c2 D (cid:0) until it passes through a dense region of charged particles inducing 4.7. PARTICLE MASS STABILIZATION 83 where X .(cid:28)/ is a small stochastic perturbation. If the typical distance scale between force centers is d then the perturbation will be roughly periodic with a characteristic period x .(cid:28) / u(cid:28) D C X .(cid:28) / ; j a fundamental frequency d u j a very short distance a moderate velocity D D a very short time, !0 D 2(cid:25) j u j d D very high frequency, and an amplitude on the order of for some macroscopic factor (cid:11) < 1. The perturbation can be represented in a Fourier series X (cid:22) .(cid:28) / j j (cid:24) (cid:11)d X .(cid:28) / Re X n D an ein!0(cid:28) (cid:11)d Re X n D n ein!0(cid:28) s(cid:22) with four-vector coeﬃcients an D where the sn represent a normalized Fourier series (s(cid:22) 0 (cid:24) but the perturbed velocity n; sn(cid:1) (cid:11)dsn D D (cid:11)d (cid:0)s0 (cid:11)d (cid:0)cst n; sn(cid:1) ; 1). The perturbed motion is of scale d , x(cid:22) .(cid:28) / P D u(cid:22) X (cid:22) .(cid:28) / C P D u(cid:22) (cid:11) u j j C Re X n 2(cid:25) n s(cid:22) n iein!0(cid:28) is of macroscopic scale (cid:11) turbed mass is u j . The unperturbed mass is m j M x2 .(cid:28) / =c2 P D D (cid:0) M and the per- m D (cid:0) M x2 .(cid:28) / P c2 M c2 D (cid:0) u C M 1 ’ 4(cid:25) (cid:11) C u j j Re X n (cid:11) Re X n u j j n iein!0(cid:28) ! ; n st 2(cid:25) n sn iein!0(cid:28) ! 2 where we neglect terms in (cid:11)2. This kind of interaction may produce a macroscopic mass shift m (cid:0)! m (cid:18)1 (cid:19) (cid:129)m m C (cid:129)m m D 4(cid:25) (cid:11) u j j Re X n n st n iein!0(cid:28) that remains signiﬁcant after the interaction. Two approaches have been suggested to explain why such mass shifts are not observed: one involving a self-interaction of the particle and its radiation ﬁeld under mass shift, and the second a more general argument in statistical mechanics. 84 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS SELF-INTERACTION 4.7.1 We consider an arbitrarily moving event X (cid:22).(cid:28)/ at the origin of a co-moving frame so that X .(cid:28) / .ct .(cid:28) / ; 0/ X .(cid:28) / P (cid:0)c t .(cid:28)/ ; 0(cid:1) P D D M D M X 2=c2 P t 2 can only result from a change in energy through and a change in mass m P D (cid:0) 1. The Green’s function permits us acceleration of t. We say that the event is on-shell if to compute the ﬁeld at some point x induced by the evolving event. If the motion at time (cid:28) X.(cid:28) (cid:3)/ along the trajectory of produces an observable ﬁeld at time (cid:28) (cid:3) > (cid:28) at some point x the event itself, then the event will experience a self-force. Because GMaxwell 0 on the event’s timelike trajectory, only a contribution from GCorrelation can produce such a self-interaction, and, as seen from (3.24), only if (cid:17)55 We approximate ’.(cid:28) 0 (cid:0) s/ as in Section 4.1.2, introduce the function g.s/ 1. (cid:21)(cid:14).(cid:28) 0 (cid:0) D C s/ D D D D t P to express terms of the type c2g .s/ (cid:16)(cid:0)X.(cid:28) (cid:3)/ 2 X.s/(cid:1) (cid:0) c2 5 .(cid:28) (cid:3) s/2(cid:17) (cid:0) D C D (cid:0) c2 (cid:18) (cid:0)t (cid:0)(cid:28) (cid:3)(cid:1) 2 t .s/(cid:1) (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) and write a(cid:11) (cid:0)X (cid:0)(cid:28) (cid:3)(cid:1) ; (cid:28) (cid:3)(cid:1) (cid:21)ec5 2(cid:25) 2c3 D Z ds X (cid:11).s/ P 1 2 (cid:18) .g.s// .g.s//3=2 (cid:0) (cid:14) .g.s// .g.s//1=2 ! (cid:18) ret for the self-ﬁeld experienced by the event. We designate the two terms as For an event evolving uniformly on-shell we have a(cid:11) (cid:0)X (cid:0)(cid:28) (cid:3)(cid:1) ; (cid:28) (cid:3)(cid:1) a(cid:11) (cid:18) C a(cid:11) (cid:14) : D t (cid:0)(cid:28) (cid:3)(cid:1) (cid:28) (cid:3) D g.s/ (cid:18)1 c2 5 c2 (cid:0) D (cid:19) .(cid:28) (cid:3) s/2 (cid:0) and using identity (4.7) are led to a (cid:0)X (cid:0)(cid:28) (cid:3)(cid:1) ; (cid:28) (cid:3)(cid:1) D 0 (cid:21)ec5 2(cid:25) 2c3 .c; 0; c5/ Z ds (cid:18) (cid:0)(cid:28) (cid:3) (cid:18) (cid:18)(cid:18)1 (cid:19) .(cid:28) (cid:3) (cid:0) (cid:19) .(cid:28) (cid:3) (cid:0) (cid:18)(cid:18)1 B B B @ c2 5 c2 c2 5 c2 1 2 (cid:0) (cid:0) s(cid:1) (cid:0) s/2(cid:19) 3=2 (cid:0) s/2(cid:19) (cid:14) (cid:18)(cid:18)1 (cid:18)(cid:18)1 (cid:0) (cid:0) c2 5 c2 c2 5 c2 (cid:19) .(cid:28) (cid:3) (cid:0) (cid:19) .(cid:28) (cid:3) (cid:0) s/ 2(cid:19) 1=2 s/ 2(cid:19) 1 C C C A (cid:21)ec5 .c; 0; c5/ D 2(cid:25) 2c3 (cid:18)1 3=2 (cid:19) c2 5 c2 (cid:0) (cid:28) (cid:3) Z ds (cid:0)1 0 @ 1 2 1 .(cid:28) (cid:3) (cid:0) s/ 3 (cid:0) (cid:14) .(cid:28) (cid:3) (cid:0) (cid:12) (cid:12) (cid:12) s/ (cid:18) .(cid:28) (cid:3) (cid:0) s/2(cid:12) (cid:12) (cid:12) .(cid:28) (cid:3) (cid:0) s/ 1 A : 4.7. PARTICLE MASS STABILIZATION 85 (cid:28) (cid:3) Z ds (cid:0)1 1 .(cid:28) (cid:3) (cid:0) s/ 3 D 1 2 .(cid:28) (cid:3) (cid:0) (cid:12) (cid:12) (cid:12) (cid:12) s/ 2 (cid:28) (cid:3) (cid:0)1 D lim (cid:28) (cid:3) s ! 1 2 .(cid:28) (cid:3) (cid:0) s/ 2 Since and (cid:28) (cid:3) Z ds (cid:0)1 (cid:14) .(cid:28) (cid:3) (cid:0) s/ (cid:18) .(cid:28) (cid:3) (cid:0) s/2 .(cid:28) (cid:3) (cid:0) s/ D lim (cid:28) (cid:3) s ! (cid:18) .(cid:28) (cid:3) (cid:0) .(cid:28) (cid:3) (cid:0) s/ s/2 D lim (cid:28) (cid:3) s ! 1 2 s/2 .(cid:28) (cid:3) (cid:0) we ﬁnd that for uniform on-shell motion a (cid:0)X (cid:0)(cid:28) (cid:3)(cid:1) ; (cid:28) (cid:3)(cid:1) D (cid:21)ec5 2(cid:25) 2c3 .c; 0; c5/ lim (cid:28) (cid:3) s ! 1 2 .(cid:28) (cid:3) (cid:0) 1 2 s/ 2 (cid:0) s/2 .(cid:28) (cid:3) (cid:0) ! 0 D the self-force vanishes. X i In general, because P D 0 and a(cid:11) .X .(cid:28) (cid:3)/ ; (cid:28) (cid:3)/ does not depend on X i , we have ai 0 D @i a0 @i a5 0 D D ) f (cid:22)(cid:23) f 5i 0 D D and so the ﬁeld reduces to f 50 @5a0 @0a5 (cid:0) D 1 c5 D a0 @(cid:28) (cid:3) 1 c C @t a5; where the partial derivative @(cid:28) (cid:3) only acts on the explicit variable (not on t .(cid:28) (cid:3)/ or (cid:18) ret). Similarly, the velocity P X (cid:11).s/ is constant with respect to @(cid:28) (cid:3). Inserting the potential we ﬁnd @5a0 (cid:18) (cid:0) @0a5 (cid:18) D 3(cid:21)ec5 4(cid:25) 2c3 c5 c Z ds (cid:18) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) (cid:20).t .(cid:28) (cid:3)/ (cid:0) (cid:14) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) t .s//2 s/2(cid:21) c2 5 c2 .(cid:28) (cid:3) (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) (cid:0) s/2(cid:19) (cid:20).t .(cid:28) (cid:3)/ t .s//2 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) 3=2 s/2(cid:21) (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) 5=2 (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) ; (cid:21)ec5 2(cid:25) 2c3 c5 c (cid:0) Z ds where (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) t.s/.(cid:28) (cid:3) D P s/ (cid:0) (cid:0) (cid:0)t (cid:0)(cid:28) (cid:3)(cid:1) (cid:0) t .s/(cid:1) 86 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS characterizes the energy acceleration in the rest frame, which will be associated with mass shift. Similarly, the derivatives of a(cid:14) produce @5a0 (cid:14) (cid:0) @0a5 (cid:14) D (cid:0) (cid:21)ec5 2(cid:25) 2c3 c5 c Z ds (cid:21)ec5 2(cid:25) 2c3 c5 c (cid:0) Z ds (cid:14) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) (cid:18).t .(cid:28) (cid:3)/ (cid:0) (cid:18).t .(cid:28) (cid:3)/ 2(cid:14)0 t .s//2 (cid:0) t .s//2 (cid:0) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) (cid:0) 3=2 s/2(cid:19) c2 5 c2 .(cid:28) (cid:3) (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) s/2(cid:19) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) 1=2 (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) and combining terms we ﬁnd where f 50 (cid:18) D 3(cid:21)e 4(cid:25) 2 c2 5 c4 Z ds f 50 (cid:14) D (cid:0) (cid:21)e (cid:25) 2 c2 5 c4 Z ds f 50 (cid:14) 0 D (cid:0) (cid:21)e (cid:25) 2 c2 5 c4 Z ds f 50 f 50 (cid:18) C f 50 (cid:14) C f 50 (cid:14) 0 ; D (cid:18) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) (cid:20).t .(cid:28) (cid:3)/ (cid:0) (cid:14) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) t .s//2 (cid:0) s/2(cid:21) c2 5 c2 .(cid:28) (cid:3) (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) 3=2 (cid:20).t .(cid:28) (cid:3)/ (cid:0) (cid:18).t .(cid:28) (cid:3)/ (cid:14)0 t .s//2 (cid:0) t .s//2 (cid:0) s/2(cid:21) c2 5 c2 .(cid:28) (cid:3) (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2(cid:19) (cid:18).t .(cid:28) (cid:3)/ t .s//2 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) 1=2 s/2(cid:19) (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) (4.28) 5=2 (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) (4.29) (cid:18) ret (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) : (4.30) Notice that if the particle remains at constant velocity (in any uniform frame), then x0 .(cid:28)/ u0(cid:28) D (cid:0)! (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) u0 c D .(cid:28) (cid:3) s/ (cid:0) (cid:0) (cid:18) u0 c (cid:28) (cid:3) (cid:0) u0 c s(cid:19) 0 D and so the self-force f 50 vanishes. For any smooth t .(cid:28) /, we may approximate t (cid:0)(cid:28) (cid:3)(cid:1) t .s/ (cid:0) D t .s/ C P t.s/.(cid:28) (cid:3) t.s/.(cid:28) (cid:3) s/ C (cid:0) D P s/ 1 2 R C t.s/.(cid:28) (cid:3) (cid:0) 1 2 R t.s/.(cid:28) (cid:3) s/2 (cid:0) C s/2 (cid:0) C o (cid:0).(cid:28) (cid:3) s/3(cid:1) (cid:0) o (cid:0).(cid:28) (cid:3) s/3(cid:1) (cid:0) (cid:0) t .s/ 4.7. PARTICLE MASS STABILIZATION 87 so the function (cid:129) (cid:0)(cid:28) (cid:3); s(cid:1) t.s/.(cid:28) (cid:3) D P s/ (cid:0) (cid:0) (cid:0)t (cid:0)(cid:28) (cid:3)(cid:1) (cid:0) t .s/(cid:1) D (cid:0) 1 2 R t.s/.(cid:28) (cid:3) s/2 (cid:0) C o (cid:0).(cid:28) (cid:3) s/3(cid:1) (cid:0) is nonzero only when the time coordinate accelerates in the rest frame, equivalent to a shift in the particle mass. As a ﬁrst-order example, we consider a small, sudden jump in mass at (cid:28) 0 characterized D by t .(cid:28)/ D (cid:28) .1 8 < : C ; ; (cid:28) < 0 (cid:28) > 0 (cid:12)/ (cid:28) ) t .(cid:28) / P D 1 1 8 < : C ; (cid:28) < 0 (cid:12) ; (cid:28) > 0 and calculate the self-interaction. Since (cid:18) ret enforces t.(cid:28) (cid:3)/ > t.s/, it follows that (cid:28) (cid:3) < 0 ) s < 0 t.(cid:28) (cid:3)/ ) P t.s/ D P D 1 ) (cid:129).(cid:28) (cid:3); s/ 0: D Similarly, (cid:28) (cid:3) > 0 and s > 0 t.(cid:28) (cid:3)/ ) P t.s/ D P (cid:12) 1 C D ) (cid:129).(cid:28) (cid:3); s/ 0: D But when (cid:28) (cid:3) > 0 and s < 0, (cid:129).(cid:28) (cid:3); s/ t.s/.(cid:28) (cid:3) D P s/ (cid:0) (cid:0) (cid:0)t (cid:0)(cid:28) (cid:3)(cid:1) t .s/(cid:1) (cid:0)(cid:28) (cid:3) s(cid:1) (cid:0) (cid:0) (cid:2).1 C D (cid:0) (cid:12)/ (cid:0)(cid:28) (cid:3)(cid:1) s(cid:3) (cid:0) D (cid:0) (cid:12)(cid:28) (cid:3) and f 50 can be found from the contributions (4.28)–(4.30). Writing g .s/ D (cid:0)t (cid:0)(cid:28) (cid:3)(cid:1) (cid:0) 2 t .s/(cid:1) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2 (cid:0).1 C D (cid:12)/ (cid:28) (cid:3) (cid:0) 2 s(cid:1) c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) s/2 and solving for g.s(cid:3)/ 0, we ﬁnd D s(cid:3) D 0 B @ 1 C 1 1 C A (cid:12) c5 c (cid:0) (cid:28) (cid:3) > (cid:28) (cid:3) so that g.s/ > 0 in the region of interest s < 0 < (cid:28) (cid:3) and there will be no contribution from the terms (4.29) or (4.30). Thus, f 50 f 50 (cid:18) D . (cid:0) D (cid:12)(cid:28) (cid:3)/ 3(cid:21)e 4(cid:25) 2 c2 5 c4 0 Z ds (cid:0)1 1 (cid:0) c2 5 c2 .(cid:28) (cid:3) (cid:0) 5=2 s/2(cid:21) (cid:20).t .(cid:28) (cid:3)/ t .s//2 (cid:0) 1 . D (cid:12)(cid:28) (cid:3)/ (cid:0) 3(cid:21)e 4(cid:25) 2 c2 5 c4 0 Z ds (cid:0)1 (cid:20)..1 (cid:12)/ (cid:28) (cid:3) (cid:0) C s/2 c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) : 5=2 s/2(cid:21) 88 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS Shifting the integration variable as x (cid:28) (cid:3) (cid:0) D s the integral becomes 0 Z ds (cid:0)1 1 (cid:20)..1 (cid:12)/ (cid:28) (cid:3) (cid:0) C s/2 c2 5 c2 .(cid:28) (cid:3) (cid:0) (cid:0) 5=2 D (cid:0) s/2(cid:21) (cid:28) (cid:3) Z 1 dx Bx C ; A/5=2 .C x2 C where C 1 (cid:0) D c2 5 c2 B D 2(cid:12)(cid:28) (cid:3) 2 (cid:0)(cid:12)(cid:28) (cid:3)(cid:1) A D which can be evaluated using the well-known form [3] Z .C x2 dx 2.2C x Bx A/5=2 D 3qpC x2 C C C B 2. We ﬁnally ﬁnd the ﬁeld strength in the form C C A C x2 B/ C Bx (cid:18) 1 Bx where q 4AC D (cid:0) f 50 (cid:21)e 4(cid:25) 2 D 1 5 .(cid:12)(cid:28) (cid:3)/3 Q (cid:18)(cid:12); c2 c2 5 c2 (cid:19) ; where Q (cid:18)(cid:12); c2 5 c2 (cid:19) is the positive, dimensionless factor 8C q (cid:19) ; A C C 1 1 Q (cid:18)(cid:12); (cid:19) c2 5 c2 D 2 6 6 6 6 6 6 6 6 6 6 6 6 4 3=2 (cid:19) 2 (cid:18)1 c2 5 c2 (cid:0) 0 B B B B B 1 B B B B B B B @ C C C C C C C C C C C C A 1=2 (cid:19) (cid:18)1 c2 5 c2 (cid:0) 0 B B B @ 1 C (cid:12) (cid:18)1 (cid:19) c2 5 c2 (cid:0) C C C A (cid:0) 2 1 6 6 4 2(cid:12) (cid:12)2 C c2 5 c2 1 (cid:0) C c2 5 c2 1 (cid:0) (cid:12)2 c2 5 c2 0 B B @ c2 5 c2 1 C (cid:12) c2 5 c2 1 (cid:0) 1=2 3 7 7 5 1 C C A C (cid:18)1 (cid:0) c2 5 c2 (cid:19) 1=2 2 6 6 4 1 C 2(cid:12) (cid:12)2 c2 5 c2 1 (cid:0) C c2 5 c2 1 (cid:0) 3 7 7 7 7 7 7 7 7 7 7 7 5 3=2 3 7 7 5 4.7. PARTICLE MASS STABILIZATION 89 which is seen to be ﬁnite for c5 < c, with Q (cid:18)(cid:12); (cid:19) c2 5 c2 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!c5 ! 0 2 1 (cid:0) (cid:140)1 C 1 2(cid:12) C (cid:12) (cid:12)2(cid:141)1=2 ! 0: D C Since f (cid:22)(cid:23) D 0, the Lorentz force induced by this ﬁeld strength is then M x(cid:22) R D ef (cid:22)(cid:11) x(cid:11) P D ef (cid:22)5 x5 P ef 5(cid:22) x5 P D (cid:0) D (cid:0) (cid:17)55ef 5(cid:22) x5 P D (cid:0) ef 5(cid:22)c5 and since f 5i 0 D M M xi R x0 R 0 D D (cid:0) c5ef 50 D 8 (cid:136)< (cid:136): 0 ; (cid:28) (cid:3) < 0 (cid:21)e2 4(cid:25) 2 (cid:0) 1 c5 .(cid:12)(cid:28) (cid:3)/3 Q (cid:18)(cid:12); c2 5 c2 (cid:19) ; (cid:28) (cid:3) > 0 which causes the 0-coordinate to decelerate. When the event returns to on-shell propagation the function (cid:129).(cid:28) (cid:3); s/ and ﬁeld strength f 50 again vanish. The mass decay can also be seen in the Lorentz force for the mass d d (cid:28) (cid:18) (cid:0) 1 2 M x2(cid:19) P ef 5(cid:22) x(cid:22) P D ef 50 x P D ecf 50 t P D (cid:0) D (cid:0) (cid:21)e2 4(cid:25) 2 c 5 .(cid:12)(cid:28) (cid:3)/3 Q (cid:18)(cid:12); c2 c2 5 c2 (cid:19) t: P We notice that if (cid:12) < 0 then f 50 changes sign so that the self-interaction results in damping or anti-damping to push the trajectory toward on-shell behavior. Although this model is approx- imate, it seems to indicate that the self-interaction of the event with the ﬁeld generated by its mass shift will restore the event to on-shell propagation. 4.7.2 STATISTICAL MECHANICS In Section 3.4 we saw that a particle, as observed through its electromagnetic current, can be interpreted as a weighted ensemble of events ’.s/x(cid:22).(cid:28) s/ selected from a neighborhood of event x(cid:22).(cid:28)/ (along a single timelike trajectory) determined by ’.s/. Here we model a particle as an ensemble x(cid:22) i .(cid:28)/ of N mutually interacting event trajectories given at a single (cid:28). Construct- ing the canonical and grand canonical ensembles without an a priori constraint on the total mass of the system, the total mass of the particle is determined by a chemical potential. Under perturbation, such as collisions for which the ﬁnal asymptotic mass of an elementary event is not constrained by the basic theory, the particle returns to its equilibrium mass value. Here we provide here a brief summary of the full model given in [12, 13]. C As described in Section 2.5, we ﬁrst construct a canonical ensemble by extracting a small subensemble (cid:128)s (the particle system) from its environment (cid:128)b (the bath ensemble). Summing 90 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS over all possible partitions of energy and mass parameter between the particle and bath (cid:128).(cid:20); E/ D D Z d (cid:127)bd (cid:127)sd (cid:20)bd (cid:20)s(cid:14).Kb (cid:20)b/(cid:14).Ks (cid:20)s/(cid:14).Es Eb C (cid:0) E/(cid:14).(cid:20)s (cid:20)b C (cid:0) (cid:20)/ (cid:0) (cid:0) Z d (cid:20)0dE 0(cid:128)b.(cid:20) (cid:20)0; E (cid:0) (cid:0) E0/(cid:128)s.(cid:20)0; E 0/ in which both mass and energy may be exchanged. We suppose that the integrand has a max- imum over both variables (cid:20)0; E 0, providing an equilibrium point for the system. By analyzing the partial derivatives, it can be shown that no saddle point conﬁguration is possible in the neighborhood of the maximum. The conditions for equilibrium can then be written and 1 (cid:20)0; E E0/ (cid:0) (cid:128)b.(cid:20) (cid:0) 1 (cid:20)0; E E0/ (cid:0) (cid:128)b.(cid:20) (cid:0) @(cid:128)b @E @(cid:128)b @(cid:20) .(cid:20) (cid:0) (cid:20)0; E (cid:0) E0/ max j D 1 (cid:128)s.(cid:20)0; E 0/ @(cid:128)s @E .(cid:20)0; E 0/ max j (cid:17) 1 T .(cid:20) (cid:0) (cid:20)0; E (cid:0) E0/ max j D 1 (cid:128)s.(cid:20)0; E 0/ @(cid:128)s @(cid:20) .(cid:20)0; E/ max j (cid:17) 1 T(cid:20) ; deﬁning temperature in the usual way, and a new eﬀective “mass temperature” T(cid:20). Writing Sb.(cid:20); E/ D ln (cid:128)b.(cid:20); E/ Ss.(cid:20); E/ D ln (cid:128)s.(cid:20); E/ it follows that at maximum @Sb @E D @Ss @E D 1 T @Sb @(cid:20) D @Ss @(cid:20) D 1 T(cid:20) : By additivity of entropy, the total entropy of the system is independent of (cid:20)0; E 0 in the neigh- borhood of the maximum, and for (cid:20)0 and E0 small compared to (cid:20) and E, (cid:128)b.(cid:20) (cid:20)0; E E0/ D in this neighborhood. Then (cid:0) (cid:0) eSb .(cid:20) (cid:0) (cid:20)0;E (cid:0) E 0/ (cid:138) eSb .(cid:20);E / (cid:20)0 (cid:0) @Sb @(cid:20) (cid:0) E 0 @Sb @E eSb .(cid:20);E /e(cid:0) (cid:20) 0T(cid:20) e(cid:0) E 0T D (cid:128).(cid:20); E/ D Z d (cid:20)0dE 0(cid:128)s.(cid:20)0; E 0/eSb .(cid:20);E /e(cid:0) (cid:20) 0T(cid:20) e(cid:0) E 0T eSb .(cid:20);E / Z d (cid:127)se(cid:0) Ks T(cid:20) e(cid:0) Es T D leading to the partition function QN .T(cid:20); T / D Z d (cid:127)e(cid:0) K T(cid:20) e(cid:0) E T ; where the overall factor Sb.(cid:20); E/ cancels out in any computation of average values. The Helmholtz free energy A is deﬁned through QN .T(cid:20); T / D A.T(cid:20) ;T /=T e(cid:0) Z d (cid:127)e(cid:0) K=T(cid:20) e.A E /=T (cid:0) 1 D 4.7. PARTICLE MASS STABILIZATION 91 from which it follows that A E D h i C T @A @T D h E i (cid:0) T S S D (cid:0) @A @T and K h i D (cid:0) T 2 (cid:20) T @A @T(cid:20) : Under the canonical distribution, corresponding to an equilibrium of both heat and mass, with- out exchange of particles with the bath, we therefore obtain a mean value for , the eﬀective i center-of-mass mass of the subensemble, which is determined by T(cid:20) and T . K h Computing the ﬂuctuations in energy, one ﬁnds (cid:10).E E (cid:0) h /2(cid:11) i D T 2 @ E h @T i (cid:10).K K (cid:0) h /2(cid:11) i D T(cid:20) 2 @ K h @T(cid:20) i showing that the mean mass rises with the mass temperature. (Since K is proportional to a neg- T(cid:20) is a positive number, to be identiﬁed with a “mass temperature.”) ative mass in this metric, Repeating the above for the grand canonical ensemble, in which the system (particle) en- semble may exchange events and volume with the bath, one decomposes the full microcanonical in terms of its canonical subsets (cid:0) QN .V; T; T(cid:20)/ N X 0 Ns D D Z d (cid:127)se(cid:0) Ks =T(cid:20) e(cid:0) Es =T QN Ns .V (cid:0) (cid:0) Vs; T; T(cid:20)/; where Kb K (cid:0) D Ks and Eb D Vs; T; T(cid:20)/ (cid:0) D Z d (cid:127)be(cid:0) Kb =T(cid:20) e(cid:0) Eb =T Es. Making the usual identiﬁcations QN Ns .V (cid:0) E (cid:0) @A @V D (cid:0) P @A @N D (cid:22) and deﬁning the new mass chemical potential leads to the grand partition function @A @K D (cid:0) (cid:22)(cid:20) Q.V; T; T(cid:20)/ eVP =T D D N X 0 Ns D zNs QNs .T; Ks; Es/; where QNs .T; Ks; Es/ D Z d (cid:127)s(cid:16)Ks e(cid:0) Es =T e(cid:22)=T z D e(cid:0) O (cid:22)(cid:20) =T : (cid:16) D 92 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS It follows that @ @z Modifying the Helmholtz free energy for the grand canonical ensemble, ln Q: ln Q @ @(cid:16) K h N h i D i D z (cid:16) A N D h i T ln z K C h i T ln (cid:16) (cid:0) T ln Q leads to Q It follows that the internal energy is e(cid:0) A=T z<N >(cid:16)<K> : D U E (cid:17) h A N (cid:0) h (cid:22) i C i D (cid:18)(cid:22)(cid:20) (cid:19) T T(cid:20) C K h i C T ln Q T 2 @ @T C ln Q and using the thermodynamic relation U A C D T S one ﬁnds S D @ @T .T ln Q/ (cid:18) (cid:22)(cid:20) C T C (cid:19) 1 T(cid:20) K h i (cid:0) (cid:22) T h N : i Finally, the Maxwell relations are S D (cid:0) (cid:18) @A @T (cid:19)(cid:12) (cid:12) (cid:12) (cid:12)V; N K ; i h i h P D (cid:0) (cid:18) @A @V (cid:19)(cid:12) (cid:12) (cid:12) (cid:12)<N >;<K>;T At the critical point in (cid:22) D @A N h i i @ K h @A K h i @ (cid:18)(cid:22)(cid:20) (cid:19) : T T(cid:20) C D (cid:0) @A K h i @ 0 D T T(cid:20) D (cid:0) (cid:22)(cid:20) (cid:0)! (4.31) and so (cid:22)(cid:20) is positive since T(cid:20) is negative. The particle in this model is a statistical ensemble which has both an equilibrium energy and an equilibrium mass, controlled by the temperature and chemical potentials, thus assuring asymptotic states with the correct mass. The thermodynamic properties of this system, involve the maximization of the integrand in the microcanonical ensemble, where both the energy and the mass are parameters of the distribution. A critical point in the free energy is made available by the interplay of the equilibrium requirements of the canonical ensemble (where the total mass of the system is considered variable) as for the energy, and the equilibrium requirements of the grand canonical ensemble (where a chemical potential arises for the particle number). The particle mass is controlled by a chemical potential, so that asymptotic variations in the mass can be restored to a given value by relaxation to satisfy the equilibrium conditions. 4.8. SPEEDS OF LIGHT AND THE MAXWELL LIMIT 93 SPEEDS OF LIGHT AND THE MAXWELL LIMIT 4.8 As discussed in Section 3.7, concatenation—integration of the pre-Maxwell ﬁeld equations over the evolution parameter (cid:28)—extracts from the microscopic event interactions the massless modes in Maxwell electrodynamics, expressing a certain equilibrium limit when mass exchange settles to zero. In this picture, the microscopic dynamics approach an equilibrium state because the boundary conditions hold pointwise in x as (cid:28) , asymptotically eliminating interactions that ! 1 cannot be described in Maxwell theory. The Maxwell-type description recovered by concatenat- ing the microscopic dynamics may thus be understood as a self-consistent summary constructed a posteriori from the complete worldlines. We have assumed that 0 c5 < c and we must check that SHP theory remains ﬁnite 0. First we notice that c5 appears explicitly three times in the pre-Maxwell equations (cid:20) as c5 (3.20) ! @(cid:23) f (cid:22)(cid:23) 1 c5 (cid:0) @(cid:28) f 5(cid:22) e c D j (cid:22) ’ @(cid:22) f 5(cid:22) e c D j 5 ’ D c5 c e(cid:26)’ @(cid:22)f(cid:23)(cid:26) @(cid:23)f(cid:26)(cid:22) @(cid:26)f(cid:22)(cid:23) 0 @(cid:23)f5(cid:22) @(cid:22)f5(cid:23) @(cid:28) f(cid:22)(cid:23) 0 C D C twice in the form 1 @(cid:28) and once multiplying the event density (cid:26)’. The derivative term poses c5 no problem in the homogeneous pre-Maxwell equation, which is satisﬁed identically for ﬁelds 1 derived from potentials. Speciﬁcally, the ﬁelds f5(cid:22) contain terms of the type @5a(cid:22) @(cid:28) a(cid:22) that c5 0. However, cancel the explicit (cid:28)-derivative of f(cid:22)(cid:23), evaluated before passing to the limit c5 the homogeneous equation does impose a new condition through D ! C D (cid:0) 1 c5 c5 (cid:0)@(cid:23)f5(cid:22) @(cid:22)f5(cid:23)(cid:1) @(cid:28) f(cid:22)(cid:23) 0 @(cid:28) f(cid:22)(cid:23) 0 (cid:0) C D requiring that the ﬁeld strength f (cid:22)(cid:23) become (cid:28)-independent in this limit. For the ﬁelds derived (cid:28)R/ unless we simul- in Section 4.2 this condition is violated by the multiplicative factor ’.(cid:28) taneously require c5 1, using (3.12) 1=c5 (cid:24) D for (cid:24). This requirement eﬀectively spreads the event current j (cid:11) ’ uniformly along the particle worldline, recovering the (cid:28)-independent particle current , in which case ’.x; (cid:28)/ (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)!c5 ! (cid:0) 1=2(cid:24) ! 1 ) ! ! D (cid:21) 0 0 j (cid:22) ’ .x; (cid:28) / j 5 ’ .x; (cid:28) / Z ds ’ .(cid:28) Z ds ’ .(cid:28) D D @(cid:22)j (cid:22) ’ .x; (cid:28) / C s/ j (cid:22) .x; s/ s/ j 5 .x; s/ @(cid:28) j 5 ’ .x; (cid:28) / (cid:0) (cid:0) 1 c5 (cid:0)! (cid:0)! (cid:0)! Z ds 1 (cid:1) j (cid:22) .x; s/ J (cid:22).x/ D Z ds j 5 .x; s/ @(cid:22)J (cid:22) .x/ 0 D associated with Maxwell theory. Generally, because the (cid:28)-dependence of the potentials and ﬁelds is contained in ’, the condition (cid:21) eliminates all the terms in the pre-Maxwell equations containing @(cid:28) . Similarly, the photon mass m(cid:13) =(cid:24)(cid:21)c2 must vanish. ! 1 (cid:24) (cid:132) 94 4. PROBLEMS IN ELECTROSTATICS AND ELECTRODYNAMICS We saw that f 5(cid:22) is generally proportional to c5 for ﬁelds of the Liénard–Wiechert type. Therefore, we can write the inhomogeneous pre-Maxwell equations in the ﬁnite form @(cid:23) f (cid:22)(cid:23) e c D j (cid:22) ’ @(cid:22) (cid:18) 1 c5 f 5(cid:22)(cid:19) e c D (cid:26)’; where we see that f 5(cid:22) decouples from the ﬁeld f (cid:22)(cid:23) that now satisﬁes Maxwell’s equations. To ﬁnd the limiting form of the electromagnetic interactions, we consider an arbitrary event X (cid:22) .(cid:28)/, which induces the current j (cid:11) ’ .x; (cid:28) / D c Z ds ’ .(cid:28) s/ X (cid:11) .s/ (cid:14)4 (cid:140)x P (cid:0) (cid:0) X .s/(cid:141) : From the ﬁeld strengths found in Section 4.2 the Lorentz force on a test event moving in the ﬁeld induced by this current can be written M x(cid:22) R D e c (cid:2)f (cid:22) (cid:23).x; (cid:28)/ x(cid:23) P C f 5(cid:22).x; (cid:28)/ x5(cid:3) P e2 4(cid:25)c D (cid:28) e(cid:0)j (cid:0) (cid:28)R =(cid:24)(cid:21) j F (cid:22) (cid:23).x; (cid:28)/ 1 x(cid:23) P C F 5(cid:22).x; (cid:28)/ c2 5 C .c5=c/2 ; where F (cid:22)(cid:23).x; (cid:28)/ e 4(cid:25)R D (cid:26) .z(cid:22)(cid:12)(cid:23) z(cid:23)(cid:12)(cid:22)/ (cid:12)2 (cid:0) R2 (cid:0) " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c z(cid:22)(cid:12)(cid:23) z(cid:23)(cid:12)(cid:22) (cid:0) R (cid:16)z(cid:22) P(cid:12)(cid:23) (cid:0) z(cid:23) P(cid:12)(cid:22)(cid:17) R C .z(cid:22)(cid:12)(cid:23) z(cid:23)(cid:12)(cid:22)/ (cid:16) z(cid:17) P(cid:12) (cid:1) (cid:0) F 5(cid:22).x; (cid:28)/ e 4(cid:25)cR (cid:26) (cid:0) D z(cid:22)(cid:12)2 C R2 (cid:0) (cid:12)(cid:22)R (cid:0) R2 " .(cid:28) (cid:28)R/ (cid:0) (cid:24)(cid:21)c z(cid:22) C (cid:12)(cid:22)Rc2=c2 5 R 9 = ; 0, we see that c2 and c5 In the limit (cid:21) 5 action reduces to the (cid:28)-independent expression ! 1 ! z(cid:17) z(cid:22) (cid:16) P(cid:12) (cid:1) cR2 C : 9 = ; F 5(cid:22).x; (cid:28)/ ! 0, and so the Lorentz force inter- M e2 4(cid:25)c recovering the Lorentz force in the standard Maxwell form. The parameter c5=c thus provides a continuous scaling of Maxwell’s equations and the Lorentz force to the standard forms in Maxwell theory. The combined limit (cid:21) 0 restricts the possible dynamics in SHP and c5 to those of Maxwell theory, as a system in (cid:28)-equilibrium [9]. ! 1 x(cid:22) R (cid:23).x/ x(cid:23) P F (cid:22) ! D 4.9 BIBLIOGRAPHY 4.9. BIBLIOGRAPHY 95 [1] Tanabashi, M., Hagiwara, K., Hikasa, K., Nakamura, K., Sumino, Y., Takahashi, F., Tanaka, J., Agashe, K., Aielli, G., Amsler, C., Antonelli, M., Asner, D. M., Baer, H., Banerjee, S., Barnett, R. M., Basaglia, T., Bauer, C. W., Beatty, J. J., Belousov, V. I., Beringer, J., Bethke, S., Bettini, A., Bichsel, H., Biebel, O., Black, K. M., Blucher, E., Buchmuller, O., Burkert, V., Bychkov, M. A., Cahn, R. N., Carena, M., Ceccucci, A., Cerri, A., Chakraborty, D., Chen, M. C., Chivukula, R. 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Royal Society of London, A(146):83. 73 [12] Horwitz, L. P. 2017 Journal of Physics: Conference Series, 845:012026. http://stacks.i op.org/1742-6596/845/i=1/a=012026 89 [13] Horwitz, L. P. and Arshansky, R. I. 2018. Relativistic Many-Body Theory and Statistical Mechanics, 2053–2571, Morgan & Claypool Publishers. http://dx.doi.org/10.1088/ 978-1-6817-4948-8 DOI: 10.1088/978-1-6817-4948-8. 89 C H A P T E R 5 Advanced Topics 97 5.1 ELECTRODYNAMICS FROM COMMUTATION RELATIONS In (2.1) we introduced an unconstrained 8D phase space .x(cid:22); p(cid:22)/ along with Poisson brackets for which x(cid:22); p(cid:23) f g D @x(cid:22) @x(cid:21) @p(cid:23) @p(cid:21) (cid:0) @x(cid:22) @p(cid:21) @p(cid:23) @x(cid:21) D g(cid:22)(cid:23).x/ D in curved spacetime. In 1990, Dyson [1] published a 1948 attempt by Feynman to derive the Lorentz force law and homogeneous Maxwell equations starting from Euclidean relations (cid:8)xi ; pj (cid:9) (cid:14)ij on 6D phase space. Several authors noted that the derived equations have only Galilean symmetry, and so are not actually the Maxwell theory, leading to a number of in- teresting theoretical developments. Tanimura [2] generalized Feynman’s derivation to Lorentz covariant form and obtained expressions similar to Maxwell theory, but including a ﬁfth elec- tromagnetic potential, a scalar evolution parameter that cannot be identiﬁed with proper time, absence of reparameterization invariance, and violations of the mass-shell constraint. His result can be identiﬁed with SHP electrodynamics. Signiﬁcantly, Hojman and Shepley [3] proved that the existence of quantum commutation relations is a strong assumption, suﬃcient to determine a corresponding classical action, from which this system can be derived. We generalize Tan- imura’s result to curved spacetime and show that this approach to SHP provides the ﬁnal step in Feynman’s program. Using the technique of Hojman and Shepley, we show that SHP elec- trodynamics follows as the most general interacting system consistent with the unconstrained commutation relations we have assumed [4]. We begin with the commutation relations among the quantum operators for (cid:22); (cid:23) 0; 1; ; D (cid:0) (cid:1) (cid:1) (cid:1) D (cid:140)x(cid:22); x(cid:23)(cid:141) 0 D D 1, and suppose equations of motion m(cid:140)x(cid:22); x(cid:23)(cid:141) P g(cid:22)(cid:23).x/ i (cid:132) (5.1) m x(cid:22) R D F (cid:22).(cid:28); x; x/: P We regard these quantities as operators in a Heisenberg picture, so that the ﬁeld equations and the Lorentz force may be interpreted, in the Ehrenfest sense, as relations among the expectation values which correspond to relations among classical quantities. It follows that (cid:140) x(cid:22); q.x/(cid:141) P D i (cid:132) m @q @x(cid:22) (5.2) 98 5. ADVANCED TOPICS for any function q.x/. Diﬀerentiating (5.1) with respect to (cid:28) we ﬁnd and so deﬁne W (cid:22)(cid:23) D (cid:0) x(cid:23)(cid:141) P C m(cid:140)x(cid:22); x(cid:23)(cid:141) R i (cid:132) D @(cid:26)g(cid:22)(cid:23).x/ x(cid:26) P m(cid:140) x(cid:22); P W (cid:23)(cid:22) by W (cid:22)(cid:23) D m2 i (cid:132) (cid:140) x(cid:22); P x(cid:23)(cid:141) : P (5.3) From (5.1) and the Jacobi identity, (cid:140) x(cid:21); (cid:140) x(cid:22); P x(cid:23) (cid:141) (cid:141) P (cid:140) x(cid:22); (cid:140) P x(cid:23); x(cid:21) (cid:141) (cid:141) P (cid:140) x(cid:23); (cid:140) x(cid:21); P x(cid:23) (cid:141) (cid:141) P C C D 0 we ﬁnd that (cid:140) x(cid:21); W (cid:22)(cid:23) (cid:141) Deﬁning f (cid:22)(cid:23) D (cid:0) (cid:16)(cid:140) (cid:140) x(cid:21); m2 i D (cid:132) f (cid:23)(cid:22) by x(cid:22) (cid:141); P x(cid:23) (cid:141) P C (cid:140) x(cid:22); (cid:140) x(cid:21); P x(cid:23) (cid:141) (cid:141)(cid:17) P i (cid:132) D (cid:16)@(cid:23)g(cid:21)(cid:22) (cid:0) @(cid:22)g(cid:21)(cid:23)(cid:17) : f (cid:22)(cid:23) W (cid:22)(cid:23) (cid:0) D m D.@(cid:23)g(cid:21)(cid:22) @(cid:22)g(cid:21)(cid:23)/ x(cid:21)E ; P (cid:0) (5.4) where the brackets ::: h i represent Weyl ordering, we ﬁnd (cid:140)x(cid:27) ; f (cid:22)(cid:23)(cid:141) 0; D which shows that f (cid:22)(cid:23) is independent of x. When lowering indices, we deﬁne P and from we may show that x(cid:22) P D h g(cid:22)(cid:23).x/ x(cid:23) P i (cid:2) x(cid:22); P x(cid:23)(cid:3) P D hDg(cid:22)(cid:21) x(cid:21)E ; (cid:10)g(cid:23)(cid:26) P x(cid:26)(cid:11)i P leading to the Bianchi relation f(cid:22)(cid:23) D g(cid:22)(cid:21)g(cid:23)(cid:26)f (cid:21)(cid:26) D (cid:0) m2 i (cid:132) (cid:140) x(cid:22); P x(cid:23)(cid:141) P (5.5) Rearranging Equation (5.1) and using (5.3) and (5.4), we see that @(cid:22)f(cid:23)(cid:26) @(cid:23)f(cid:26)(cid:22) @(cid:26)f(cid:22)(cid:23) 0: D C C where m(cid:140)x(cid:22); x(cid:23)(cid:141) R D i (cid:132) m f (cid:22)(cid:23) 2i (cid:132)h C (cid:128) (cid:23)(cid:21)(cid:22) x(cid:21) P ; i (cid:128) (cid:23)(cid:21)(cid:22) 1 2 D (cid:0) .@(cid:22)g(cid:21)(cid:23) @(cid:21)g(cid:22)(cid:23) C (cid:0) @(cid:23)g(cid:21)(cid:22)/ 5.1. ELECTRODYNAMICS FROM COMMUTATION RELATIONS 99 is the Levi–Civita connection. We now deﬁne g(cid:22) through the equation F (cid:22) m x(cid:22) R D D g(cid:22).x; x; (cid:28)/ P C h f (cid:22)(cid:23) x(cid:23) P i (cid:0) m h (cid:128) (cid:22)(cid:21)(cid:23) x(cid:21) P x(cid:23) P i and it follows that (cid:140)x(cid:21); g(cid:22)(cid:141) D D D (cid:140)x(cid:21); f (cid:22)(cid:141) i (cid:132) m 0 f (cid:21)(cid:22) (cid:0) f (cid:22)(cid:23)(cid:140)x(cid:21); x(cid:23)(cid:141) P D(cid:128) (cid:22)(cid:26)(cid:21) 2 i (cid:132) C C x(cid:26)E P C i (cid:132) m m (cid:128) (cid:22)(cid:23)(cid:26) (cid:140)x(cid:21); f (cid:22)(cid:23) (cid:14)(cid:21) x(cid:23)(cid:141) P (cid:23) (cid:0) i x(cid:26) P (cid:132) (cid:128) (cid:22)(cid:23)(cid:26) x(cid:23)(cid:140)x(cid:21); P C D(cid:16)(cid:128) (cid:22)(cid:23)(cid:26) (cid:14)(cid:21) x(cid:26) (cid:23) P C x(cid:26)(cid:141) P (cid:128) (cid:22)(cid:23)(cid:26) (cid:17)E x(cid:23) (cid:14)(cid:21) (cid:26) P so that g(cid:22) is also independent of x. We may write the force as P g(cid:22) f (cid:22)(cid:23) C h x(cid:23) P i D m h x(cid:22) R C D(cid:128) (cid:22)(cid:21)(cid:23) x(cid:21) P x(cid:23)Ei P D m x(cid:22) D P D(cid:28) and since we lower the index of g(cid:22) to ﬁnd m x(cid:22) R D m d d (cid:28) h g(cid:22)(cid:23) ; x(cid:23) P i x(cid:26) P We write the ﬁrst term on the right-hand side as (cid:0) h g(cid:23) D g(cid:23)(cid:21) f (cid:21)(cid:26) g(cid:23)(cid:21) f (cid:21) g(cid:23)(cid:21) (cid:128) (cid:21)(cid:26)(cid:27) m h x(cid:26) P x(cid:27) P : i i C g(cid:23)(cid:21) f (cid:21) m g(cid:23)(cid:21) h x(cid:21) R D i D m g(cid:23)(cid:21) d d (cid:28) h g(cid:21)(cid:26) x(cid:26) P i D m x(cid:23) R C m g(cid:23)(cid:21) @(cid:27) g(cid:21)(cid:26) h x(cid:26) P x(cid:27) P : i Since the indices (cid:26) and (cid:27) of @(cid:27) g(cid:21)(cid:26) occur in symmetric combination, we may write so that 1 2 .@(cid:27) g(cid:21)(cid:26) @(cid:26)g(cid:21)(cid:27) / (cid:128) (cid:21)(cid:26)(cid:27) D (cid:0) C 1 2 C @(cid:21)g(cid:26)(cid:27) g(cid:23) m x(cid:23) R D C 1 2 m @(cid:23)g(cid:21)(cid:26) h x(cid:21) P x(cid:26) P i (cid:0) h f(cid:23)(cid:21) g(cid:21)(cid:26) x(cid:26) P : i Using (5.2) and (5.5) we obtain x(cid:22); g(cid:23)(cid:141) (cid:140) P m(cid:140) x(cid:22); P x(cid:23)(cid:141) R D i (cid:132) m (cid:0) m(cid:140) x(cid:22); P x(cid:23)(cid:141) R D i (cid:132) m (cid:0) @(cid:23)g(cid:21)(cid:26).f(cid:22)(cid:21) (cid:28) 1 2 i @(cid:22)@(cid:23)g(cid:21)(cid:26) C (cid:132) @(cid:22).f(cid:23)(cid:21) g(cid:21)(cid:26)/ x(cid:26) P C i (cid:28) 1 @(cid:22)@(cid:23)g(cid:21)(cid:26) 2 C (cid:132) .@(cid:22)g(cid:21)(cid:26)/f(cid:23)(cid:21) x(cid:26) P (cid:0) (cid:0) x(cid:21) P i x(cid:26) (cid:132) 2m P i m2 f(cid:23)(cid:21) g(cid:21)(cid:26) f(cid:22)(cid:26) (cid:132) i x(cid:26) x(cid:21) (cid:132) m P P i @(cid:22)f(cid:23)(cid:21)g(cid:21)(cid:26) (cid:132) m x(cid:26) P (cid:0) (cid:29) .@(cid:23)g(cid:21)(cid:26)/f(cid:22)(cid:21) x(cid:26) P x(cid:21)f(cid:22)(cid:26)/ C P x(cid:26) P i m2 f(cid:23)(cid:21) g(cid:21)(cid:26) f(cid:22)(cid:26) (cid:132) (cid:29) : C 100 5. ADVANCED TOPICS Finally, antisymmetrization with respect to the indices (cid:22) and (cid:23) gives x(cid:22); g(cid:23)(cid:141) (cid:140) P x(cid:23); g(cid:22)(cid:141) (cid:140) P (cid:0) D D i (cid:132) m (cid:0) D.@(cid:22)f(cid:23)(cid:21) (cid:0) @(cid:23)f(cid:22)(cid:21)/g(cid:21)(cid:26) x(cid:26)E P D.@(cid:22)f(cid:23)(cid:21) @(cid:23)f(cid:21)(cid:22)/ x(cid:21)E P C (cid:10).@(cid:22)f(cid:23)(cid:26) @(cid:23)f(cid:26)(cid:22)/ x(cid:26)(cid:11) P C x(cid:22)(cid:141) R i (cid:132) m x(cid:23)(cid:141) R x(cid:23); (cid:140) P (cid:0) x(cid:23)(cid:141) P (cid:140) x(cid:22); P d d (cid:28) f(cid:22)(cid:23) (cid:0) (cid:0) i (cid:132) m m(cid:140) m x(cid:22); P d d (cid:28) i (cid:132) m i (cid:132) m D (cid:0) D (cid:0) (cid:2)(cid:10).@(cid:26)f(cid:22)(cid:23) @(cid:22)f(cid:23)(cid:26) C @(cid:23)f(cid:26)(cid:22)/ x(cid:26)(cid:11) P C C @(cid:28) f(cid:22)(cid:23)(cid:3) and so using the Bianchi identity for f(cid:22)(cid:23), @(cid:22)g(cid:23) @(cid:23)g(cid:22) (cid:0) @f(cid:22)(cid:23) @(cid:28) D 0: C Regarding these equations in the Ehrenfest sense, we may summarize the classical theory as m x(cid:22) D P D(cid:28) D m(cid:140) x(cid:22) R C (cid:27) (cid:22)(cid:21)(cid:23) x(cid:21) P x(cid:23)(cid:141) P D f (cid:22)(cid:23) g(cid:22) x(cid:23) P C @(cid:22)f(cid:23)(cid:26) @(cid:22)g(cid:23) C (cid:0) @(cid:23)f(cid:26)(cid:22) @(cid:26)f(cid:22)(cid:23) 0 D C @(cid:23)g(cid:22) @f(cid:22)(cid:23) @(cid:28) D 0: C Introducing the deﬁnitions xD (cid:28) D @(cid:28) @D D f(cid:22)D fD(cid:22) g(cid:22) : D D (cid:0) We may then combine the inhomogeneous ﬁeld equations as @(cid:11)f(cid:12)(cid:13) @(cid:12) f(cid:13)(cid:11) @(cid:13) f(cid:11)(cid:12) 0 D C C (5.6) (cid:1) (cid:1) (cid:1) ; D), which shows that the two form f is closed on the formal (D (for (cid:11); (cid:12); (cid:13) = 0; 1)- dimensional manifold .(cid:28); x/. Hence, if this manifold is contractable, then f is an exact form da. The Lorentz which can be obtained as the derivative of some potential with the form f force equation becomes D C m x(cid:22) D P D(cid:28) D m(cid:140) x(cid:22) R C (cid:128) (cid:22)(cid:21)(cid:23) x(cid:21) P x(cid:23)(cid:141) P D f (cid:22)(cid:23).(cid:28); x/ x(cid:23) P C g(cid:22).(cid:28); x/ f (cid:22) (cid:12) .(cid:28); x/ x(cid:12) : P D (5.7) Following Dyson and Feynman, we observe that given Equation (5.6), the two-form f (cid:11)(cid:12) is determined if we know functions (cid:26) and j (cid:22) such that D(cid:11) f (cid:22)(cid:11) j (cid:22) D D(cid:11) f d(cid:11) (cid:26); D 5.1. ELECTRODYNAMICS FROM COMMUTATION RELATIONS 101 where D(cid:11) is the covariant derivative. By denoting (cid:26) pactly as j d , these equations can be written com- D D(cid:11) f (cid:12) (cid:11) j (cid:12) ; D (5.8) 0. D where, due to the antisymmetry of f (cid:12) (cid:11), we see that j (cid:12) is conserved as D(cid:11)j (cid:11) D(cid:11)j (cid:11) 0 : D By comparing the Lorentz force (5.7) with (3.6), and the ﬁeld Equations (5.6) and (5.8) with (3.19) and (3.17), we see conclude that the assumption of unconstrained commutation relations leads to a ﬁeld theory equivalent to classical SHP electrodynamics. In Sections 3.2 and 3.3 we found the Lorentz force and ﬁeld equations from an action principle. Hojman and Shepley [3] set out to prove that the assumed commutation relations are suﬃcient to establish the existence of a unique Lagrangian of electromagnetic form. To accomplish this goal, they demonstrate a new connection between the commutation relations and well-established results from the inverse problem in the calculus of variations, a theory which concerns the conditions under which a system of diﬀerential equations may be derived from a variational principle. We consider a set of ordinary second-order diﬀerential equations of the form Fk.(cid:28); q; q; P q/ R D 0 qj P D dqj d (cid:28) qj R D d 2qj d (cid:28) 2 j; k 1; (cid:1) (cid:1) (cid:1) D ; n: Under variations of the path q.(cid:28)/ the function Fk.(cid:28); q; q; P q.(cid:28)/ dq.(cid:28)/ (cid:0)! C d C q.(cid:28)/ q.(cid:28)/ (cid:0)! P q.(cid:28)/ P q.(cid:28)/ P d d (cid:28) d 2 d (cid:28) 2 dq.(cid:28)/ q/ admits the variational one-form deﬁned by R q.(cid:28)/ R q.(cid:28)/ R (cid:0)! R dq.(cid:28)/ q.(cid:28)/ q.(cid:28)/ D R D P C C C d dFk @Fk @qj dqj C D @Fk qj d @ P qj P @Fk qj d @ R qj R C and the variational two-form dqkdFk @Fk @qj dqk ^ D dqj where the 3n path variations .dqk; d (cid:1) (cid:1) (cid:1) independent. The system of diﬀerential equations Fk.(cid:28); q; q; P exists a two-form (cid:127)2.dq; d qk; d P D 1; ; n are understood to be linearly q/ is called self-adjoint if there R q/ such that for all admissible variations of the path, P d qj P ^ C @Fk qj dqk @ R d qj ; R ^ C @Fk qj dqk @ P qk/ for k R dqkdFk.dq/ d d (cid:28) D (cid:127)2.dq; d q/: P 102 5. ADVANCED TOPICS Through integration by parts, one may show [5] that such a two-form exists and is unique up to an additive constant, if and only if @Fi qk D @ R @Fk @ qi D P @Fk @qi D @Fi qk C @ P @Fi @qk (cid:0) @Fk qi @ R d d (cid:28) 1 2 d d (cid:28) (cid:20) @Fi qk C @ R (cid:20) @Fi @ qk (cid:0) P (cid:21) @Fk qi @ R @Fk qi @ P (5.9) (5.10) (5.11) (cid:21) ; known as the Helmholtz conditions [6, 7]. Introducing the notation dqk (cid:12) (cid:14) D @ @qk (cid:12) qk (cid:12) D (cid:18) d d (cid:28) (cid:12) (cid:19) qk 0; 1; 2; (cid:12) D it follows that (cid:14)2 dqk (cid:12) ^ dql (cid:11) D @2 @qk (cid:12) @ql (cid:11) D 0; which permits the equivalence of a set of self-adjointness diﬀerential equations to a Lagrangian formulation to be easily demonstrated [8]. Varying the Lagrangian L, (cid:14)L D @L @qk dqk C @L qk @ P d qk P (cid:20) D (cid:0) d d (cid:28) @L qk C @ P @L @qk (cid:21) dqk d d (cid:28) (cid:18) @L qk @ P C dqk(cid:19) Fkdqk D d d (cid:28) C (cid:127)1 so that (cid:14)2 0 D H) (cid:0) dqk(cid:14)Fk d d (cid:28) C (cid:14)(cid:127)1 D (cid:0) dqk(cid:14)Fk d d (cid:28) C (cid:127)2 0 D which demonstrates self-adjointness. Conversely, self-adjoint of Fk requires that dqk(cid:14)Fk d d (cid:28) (cid:127)2 0 and since (cid:14)2 0, (cid:0) D D d d (cid:28) (cid:127)2 (cid:14) d d (cid:28) D (cid:127)1: Therefore, dqk(cid:14)Fk 0 D d d (cid:28) (cid:0) (cid:127)2 D (cid:14) (cid:18)dqkFk d d (cid:28) (cid:0) (cid:19) (cid:127)1 (cid:14)L D by variation of L under (cid:28)-integration, one obtains the diﬀerential equations Fk 0. D For the second-order equations considered here, it follows [5] from self-adjointness that the most general form of Fk is Fk.(cid:28); q; q; P q/ R D Akj .(cid:28); q; q/ P qj R C Bk.(cid:28); q; q/: P (5.12) 5.1. ELECTRODYNAMICS FROM COMMUTATION RELATIONS 103 To see this, notice that Fk is independent of d 3qi =dt 3, so that the right-hand side of (5.10) must qi . Inserting (5.12) into (5.9)–(5.11), one ﬁnds the Helmholtz conditions on be independent of R Akj and Bk Aij Aj i D @Bi qj C @ P @Bi @qj (cid:0) @Bj @ qi D P @Bj @qi D 2 (cid:20) @ @Akj @Aij qi qk D @ @ P P qk @ (cid:21) Aij @qk qk @ @qk @(cid:28) C P (cid:20) @ @(cid:28) C P 1 2 (cid:21) (cid:18) @Bi qj (cid:0) @ P (cid:19) @Bj qi @ P along with the useful identity @Aij @qk (cid:0) @Akj @qi D 1 2 @ qj P @ (cid:18) @Bi qk (cid:0) @ P @Bk qi @ P (cid:19) : In the domain of invertibilty of the Aj k, one can write (5.12) as Fk.(cid:28); q; q; P and the Helmholtz conditions become Akj .(cid:28); q; q/(cid:140) P q/ R D qj R f j (cid:141) (cid:0) f j .(cid:28); q; q/ P D (cid:0) .A(cid:0) 1/j kBk Aij Aj i D Aij # D D(cid:28) @f k qi @ P Aj k 1 2 D (cid:0) Aik D 1 2 D D(cid:28) " Aik @f k qj (cid:0) @ P @Akj qi @ P Aj k @Aij @ " qk D P @f k Aik qj C @ P @f k @qj (cid:0) Aj k @f k @qi ; # @f k qi @ P (5.13) (5.14) (5.15) where D D(cid:28) D @ @(cid:28) C P qk @ @qk C is the total time derivative subject to the constraint f k @ qk @ P The identity (5.13) becomes qk R (cid:0) f k.(cid:28); q; q/ P D 0 : (5.16) @Aij @qk (cid:0) (cid:20) @ qk @ P Within the domain of applicability of the inverse function theorem, (5.16) is equivalent to (5.12), and the Helmholtz conditions become the necessary and suﬃcient conditions for the existence qi .Ak nf n/(cid:21) : @Akj @qi D (cid:0) @ qj @ P .Ainf n/ (5.17) @ @ 1 2 (cid:0) P 104 5. ADVANCED TOPICS of an integrating factor Aj k such that Fk D Akj .(cid:28); q; q/(cid:140) P qj R (cid:0) f j (cid:141) D d d (cid:28) (cid:18) @L qk @ P (cid:19) @L @qk : (cid:0) (5.18) Employing this apparatus, Hojman and Shepley prove that given the quantum mechanical commutation relations the classical function has an inverse (cid:140)xi .(cid:28)/; xj .(cid:28)/(cid:141) P i Gij ; (cid:132) D gij Gij D lim 0 (cid:132)! !ij .g(cid:0) 1/ij D which satisﬁes the Helmholtz conditions. Following Santilli, we take the function A(cid:22)(cid:23) g(cid:22)(cid:23).x/ to be a Riemannian metric independent of tomatically. Since g(cid:22)(cid:23) does not depend on D x, so that Equation (5.14) is satisﬁed au- P x(cid:22), Equation (5.15) becomes P D D(cid:28) g(cid:22)(cid:23) and Equation (5.17) becomes x(cid:27) @ @x(cid:27) g(cid:22)(cid:23) D P 1 2 (cid:20) @f(cid:22) x(cid:23) (cid:0) @ P @f(cid:23) x(cid:22) @ P (cid:21) D (cid:0) Acting on (5.19) with @=@ (cid:21) @g(cid:22)(cid:23) @x(cid:27) (cid:0) @g(cid:27)(cid:23) @x(cid:22) : D @ (cid:0) 1 2 @ x(cid:23) P (cid:20) @f(cid:22) x(cid:27) (cid:0) @ P @f(cid:27) x(cid:22) @ P x(cid:27) and exchanging ((cid:23) P g(cid:22)(cid:27);(cid:23) 1 2 D (cid:0) (cid:27)), we obtain $ (cid:20) @2f(cid:22) x(cid:27) @ @ P x(cid:23) C P @2f(cid:27) x(cid:22)@ P x(cid:23) P @ (cid:21) ; (5.19) (5.20) (5.21) where g(cid:22)(cid:27);(cid:23) D @g(cid:22)(cid:27) =@x(cid:23). Combining (5.20) and (5.21), we ﬁnd 1 2 @2f(cid:22) x(cid:27) @ @ P x(cid:23) D (cid:0) P 1 2 .g(cid:22)(cid:23);(cid:27) g(cid:22)(cid:27);(cid:23) C (cid:0) g(cid:27)(cid:23);(cid:22)/ D (cid:0) (cid:128)(cid:22)(cid:27)(cid:23); where (cid:128)(cid:22)(cid:27)(cid:23) is the Levi-Civita connection. Thus, the most general expression for f(cid:22).(cid:28); x; x/ is P f(cid:22) (cid:128)(cid:22)(cid:23)(cid:27) x(cid:23) P x(cid:27) P (cid:0) D (cid:0) (cid:26)(cid:22)(cid:23).(cid:28); x/ x(cid:23) P (cid:0) (cid:27)(cid:22).(cid:28); x/: (5.22) Now from (5.19) we ﬁnd x(cid:27) @g(cid:22)(cid:23) P @x(cid:27) D 1 2 (cid:2)2(cid:128)(cid:22)(cid:23)(cid:27) x(cid:27) P C 2(cid:128)(cid:23)(cid:22)(cid:27) x(cid:27) P C (cid:26)(cid:22)(cid:23) C (cid:26)(cid:23)(cid:22)(cid:3) 5.1. ELECTRODYNAMICS FROM COMMUTATION RELATIONS 105 and using we ﬁnd that all terms except for those in (cid:26)(cid:22)(cid:23) cancel, so that .(cid:128)(cid:22)(cid:23)(cid:27) (cid:128)(cid:23)(cid:22)(cid:27) / x(cid:27) P g(cid:22)(cid:23);(cid:27) x(cid:27) P D C We now apply Equation (5.16) which becomes (cid:26)(cid:22)(cid:23) 0 D C (cid:26)(cid:23)(cid:22) : 1 2 D D(cid:28) g(cid:23)(cid:27) @f (cid:27) (cid:20)g(cid:22)(cid:27) x(cid:23) (cid:0) @ P (cid:20) @f(cid:22) D 1 x(cid:23) (cid:0) @ D(cid:28) 2 P @f (cid:27) x(cid:22) @ P @f(cid:23) x(cid:22) @ P (cid:21) (cid:21) D D using (5.22) to expand the left-hand side, 1 2 D D(cid:28) (cid:20) @f(cid:22) x(cid:23) (cid:0) @ P @f(cid:23) x(cid:22) @ P (cid:21) D (cid:0) 1 2 D D(cid:28) (cid:20) @ x(cid:23) @ P g(cid:22)(cid:27) @f (cid:27) @x(cid:23) (cid:0) g(cid:23)(cid:27) f(cid:22);(cid:23) f(cid:23);(cid:22) (cid:0) (cid:0) @f (cid:27) @x(cid:22) g(cid:22)(cid:27);(cid:23)f (cid:27) g(cid:23)(cid:27);(cid:22)f (cid:27) : C (5.23) (cid:16)(cid:128)(cid:22)(cid:21)(cid:27) x(cid:21) P x(cid:27) P C (cid:27)(cid:22).(cid:28); x/(cid:17) (cid:0) C (cid:20)2.(cid:128)(cid:22)(cid:23)(cid:21) x(cid:27) @ @x(cid:27) C g(cid:23)(cid:27);(cid:22)/f (cid:27) x(cid:21) (cid:0) P x(cid:21) (cid:128)(cid:23)(cid:22)(cid:21)/ P f (cid:27) @ x(cid:27) @ P (cid:26)(cid:22)(cid:23);(cid:28) (cid:0) x(cid:27) .g(cid:22)(cid:21);(cid:23)(cid:27) P (cid:0) (cid:0) 1 D 2 D(cid:28) (cid:18) @ @(cid:28) C P .g(cid:22)(cid:27);(cid:23) D (cid:0) D (cid:0) D (cid:0) x(cid:21) P (cid:23)/(cid:21) (cid:21) (cid:26)(cid:23)(cid:22) (cid:26)(cid:22)(cid:21).(cid:28); x/ .(cid:22) (cid:0) $ (cid:26)(cid:22)(cid:23) C (cid:0) (cid:19) h.g(cid:22)(cid:21);(cid:23) g(cid:23)(cid:21);(cid:22)/ x(cid:21) P C (cid:26)(cid:22)(cid:23)i (cid:0) g(cid:23)(cid:21);(cid:22)(cid:27) / x(cid:21)(cid:26)(cid:22)(cid:23);(cid:21); C P (5.24) where (cid:26)(cid:22)(cid:23);(cid:28) D 2.(cid:128)(cid:22)(cid:23)(cid:21) @(cid:26)(cid:22)(cid:23)=@(cid:28), and we have used (cid:128)(cid:23)(cid:22)(cid:21)/ x(cid:21) P (cid:0) x(cid:21). g(cid:23)(cid:21);(cid:22) D P (cid:0) x(cid:21).g(cid:22)(cid:21);(cid:23) 2 P D g(cid:22)(cid:21);(cid:23) C g(cid:23)(cid:21);(cid:22)/ : C (cid:0) g(cid:23)(cid:22);(cid:21) g(cid:22)(cid:21);(cid:23) g(cid:23)(cid:21);(cid:22) (cid:0) (cid:0) C g(cid:22)(cid:23);(cid:21)/ Again using (5.22) we have f(cid:22);(cid:23) D (cid:0) D (cid:0) (cid:20)(cid:128)(cid:22)(cid:21)(cid:27) x(cid:21) P (cid:20)(cid:128)(cid:22)(cid:21)(cid:27);(cid:23) x(cid:27) P C (cid:26)(cid:22)(cid:21).(cid:28); x/ x(cid:21) P C (cid:27)(cid:22).(cid:28); x/(cid:21) ;(cid:23) x(cid:21) P x(cid:27) P C (cid:26)(cid:22)(cid:21);(cid:23) x(cid:21) P C (cid:21) (cid:27)(cid:22);(cid:23) so that the right-hand side of (5.23) is f(cid:22);(cid:23) f(cid:23);(cid:22) (cid:0) (cid:0) g(cid:22)(cid:27);(cid:23)f (cid:27) g(cid:23)(cid:27);(cid:22)f (cid:27) D (cid:0) C (cid:20).(cid:128)(cid:22)(cid:21)(cid:27);(cid:23) D (cid:128)(cid:23)(cid:21)(cid:27);(cid:22)/ x(cid:21) x(cid:27) P P g(cid:23)(cid:27);(cid:22)/f (cid:27) : (cid:0) .g(cid:22)(cid:27);(cid:23) (cid:0) (cid:0) .(cid:26)(cid:22)(cid:21);(cid:23) (cid:26)(cid:23)(cid:21);(cid:22)/ x(cid:21) P C (cid:27)(cid:22);(cid:23) (cid:0) (cid:0) (cid:21) (cid:27)(cid:23);(cid:22) C 106 5. ADVANCED TOPICS Now canceling common terms, we are left with which, because the @(cid:26)(cid:22)(cid:23) @(cid:28) C P x(cid:21)(cid:26)(cid:22)(cid:23);(cid:21) x(cid:21).(cid:26)(cid:22)(cid:21);(cid:23) (cid:26)(cid:23)(cid:21);(cid:22)/ (cid:27)(cid:22);(cid:23) (cid:27)(cid:23);(cid:22) (cid:0) D P (cid:0) x(cid:21) are arbitrary, is equivalent the two expressions P @(cid:26)(cid:22)(cid:23) @(cid:28) D @(cid:27)(cid:22) @x(cid:23) (cid:0) @(cid:27)(cid:23) @x(cid:22) @(cid:22)(cid:26)(cid:23)(cid:21) @(cid:21)(cid:26)(cid:22)(cid:23) C C C @(cid:23)(cid:26)(cid:21)(cid:22) 0: D Therefore, we may identify f(cid:22)(cid:23) (cid:26)(cid:22)(cid:23) D (cid:0) and f5(cid:22) (cid:27)(cid:22) D (cid:0) showing that SHP electrodynamics is the most general interaction consistent with the uncon- strained commutation relations. Moreover, these commutation relations are suﬃcient to establish the existence of an equiv- alent Lagrangian for the classical problem associated with the quantum commutators. We ob- serve that in ﬂat space (5.18) implies (cid:17)(cid:22)(cid:23)(cid:140)M x(cid:23) R (cid:0) f (cid:23)(cid:141) D d d (cid:28) (cid:18) @L x(cid:22) @ P @2L x(cid:22)@ P x(cid:23) x(cid:23) R P (cid:19) (cid:0) C @L @x(cid:22) @2L x(cid:23) x(cid:22)@x(cid:23) P P @ @2L x(cid:22)@(cid:28) (cid:0) P @L @x(cid:22) C @ D @ so that the solution M (cid:17)(cid:22)(cid:23) D @ @2L x(cid:22)@ P x(cid:23) P (cid:17)(cid:22)(cid:23)f (cid:23) (cid:0) D @ @2L x(cid:23) x(cid:22)@x(cid:23) P P @2L x(cid:22)@(cid:28) (cid:0) P @L @x(cid:22) C @ is unique. Therefore, we see that L may consist of the quadratic term integrated from the ﬁrst expression, plus terms at most linear in x(cid:22). Thus, we may write the Lagrangian P e c which is the SHP event Lagrangian (3.3) in ﬂat space. This demonstrates that SHP electro- dynamics represents the conditions on the most general velocity dependent forces that may be obtained from a variational principle. a(cid:22).(cid:28); x/ ec5 c x(cid:22) P x(cid:22) P x(cid:22) P 1 2 a5 M C D C L CLASSICAL NON-ABELIAN GAUGE THEORY 5.2 A classical non-Abelian gauge theory was given by Wong [9] possessing the following structure: m R(cid:24)(cid:22) I P F(cid:22)(cid:23) F(cid:22)(cid:23) F(cid:22)(cid:23) (cid:2) @(cid:22)F(cid:22)(cid:23) A(cid:22) D gA(cid:22) C Aa(cid:22)I a I.(cid:28)/ P(cid:24) (cid:23) P(cid:24) (cid:22) I (cid:2) @(cid:23)A(cid:22) (cid:0) gF(cid:22)(cid:23) (cid:1) gA(cid:22) @(cid:22)A(cid:23) j(cid:23) Fa(cid:22)(cid:23)I a D D (cid:0) D D (cid:0) D gA(cid:22) A(cid:23) (cid:2) C (cid:140)I a; I b(cid:141) "abcIc; i (cid:132) D 5.2. CLASSICAL NON-ABELIAN GAUGE THEORY 107 where (cid:24) (cid:22).(cid:28)/ is the particle worldline and the I a.(cid:28)/ are an operator representation of the gener- ators of a non-Abelian gauge group. From the form of the ﬁeld f(cid:22)(cid:23), one has the inhomogeneous equation D(cid:22)F(cid:23)(cid:26) D(cid:23)F(cid:26)(cid:22) D(cid:26)F(cid:22)(cid:23) C 0 D with covariant derivative .D(cid:22)F(cid:22)(cid:23)/a C D @(cid:22)Fa(cid:22)(cid:23) (cid:0) " bc a Ab(cid:22)Fc(cid:22)(cid:23) : Lee [10] followed Feynman’s method, supplementing the phase space commutation relations with I P gAi I xi P 0 (cid:140)I a; I b(cid:141) i "abcIc (cid:140)xi ; I a.t/(cid:141) 0 (cid:132) D D for i 1; 2; 3, and arrived at the Wong’s equations in Newtonian form. Tanimura [2] gen- eralized Lee’s derivation to D-dimensional ﬂat Minkowski space and a general gauge group satisfying D C D (cid:2) (cid:140)I a; I b(cid:141) f ab c I c i (cid:132) D I a P D F ab c Ab(cid:22).x/ x(cid:22)I c P (5.25) for (cid:28)-independent ﬁelds. We now extend the presentation of Section 5.1 by generalizing the Helmholtz condi- tions to take account of classical non-Abelian gauge ﬁelds according to Wong’s formulation. To achieve this, we associate with variations dq of the path q.(cid:28) /, a variation dI a of the genera- tors I a, which may be understood as the variation of the orientation of the tangent space under q.(cid:28)/ dq.(cid:28)/. The explicit form of this variation follows from (5.25): for small d (cid:28), q.(cid:28)/ ! C dI a D f ab c (cid:140)Ab(cid:22).(cid:28); x/ dx(cid:22) C (cid:30)b.(cid:28); x/d (cid:28)(cid:141)I c; (5.26) where we have allowed an explicit (cid:28)-dependence for the gauge ﬁeld, and have included a Lorentz MaI a undergoes the scalar gauge ﬁeld (cid:30)a, in analogy with the Abelian case. The quantity M variation of the path D .(cid:28); x/ .(cid:28) C (cid:0)! d (cid:28); x C dx/ according to d M .dMa/I a (cid:18) @Ma @(cid:28) d (cid:28) D D x(cid:22)(cid:19) I a R f bc a Ab(cid:22)Mc (cid:21) I adx(cid:22) C Ma.dI a/ @Ma @x(cid:22) dx(cid:22) C Ma(cid:140)f ab C f bc a (cid:30)bMc @Ma x(cid:22) I ad @ P D(cid:22)Mdx(cid:22) C C @Ma x(cid:22) x(cid:22) d @ C P R (cid:30)bd (cid:28)(cid:141)I c @Ma x(cid:22) d @ C P c Ab(cid:22) dx(cid:22) (cid:21) I ad (cid:28) C (cid:20) @Ma @x(cid:22) (cid:0) x(cid:22) R C @Ma x(cid:22) I ad @ C R @M x(cid:22) x(cid:22) d @ P P C x(cid:22) P C @M x(cid:22) d @ R x(cid:22) R (cid:20) @Ma D @(cid:28) (cid:0) D(cid:28) Md (cid:28) D 108 5. ADVANCED TOPICS in which the spacetime part of the covariant derivative D(cid:22) has the form D and a similar covariant derivative for the (cid:28) component appears which contains (cid:30)a. (cid:0) .D(cid:22)F(cid:23)(cid:26)/a @(cid:22)Fa(cid:23)(cid:26) f bc a ab(cid:22)Fc (cid:23)(cid:26) Now, the entire structure of self-adjoint equations follows with the replacements @x(cid:22) (cid:0)! so that the Helmholtz conditions become @ D(cid:22) @ @(cid:28) (cid:0)! D(cid:28) ; A(cid:22)(cid:23) D A(cid:23)(cid:22) D D(cid:28) A(cid:23)(cid:27) A(cid:22)(cid:23) D (cid:0) @f (cid:27) x(cid:22) @ P (cid:21) D 1 2 D D(cid:28) (cid:20)A(cid:22)(cid:27) @f (cid:27) x(cid:23) (cid:0) @ P @A(cid:22)(cid:23) @A(cid:27)(cid:23) x(cid:27) D x(cid:22) @ @ @f (cid:27) P P (cid:20)A(cid:22)(cid:27) A(cid:23)(cid:27) x(cid:23) C @ P A(cid:22)(cid:27) D(cid:23)f (cid:27) @f (cid:27) x(cid:22) @ P A(cid:23)(cid:27) D(cid:22)f (cid:27) ; 1 2 (cid:21) (5.27) (5.28) (5.29) (cid:0) where is the total (cid:28) derivative subject to D D(cid:28) D D(cid:28) x(cid:27) D(cid:27) C P C f (cid:27) @ x(cid:27) @ P Since Hojman and Shepley’s argument relates only to the commutation relations among the coordinates, not to the structure of the forces, their result carries over unchanged. x(cid:22) R (cid:0) fa(cid:22).(cid:28); x; x/I a P D 0: In ﬂat spacetime, with A(cid:22)(cid:23) g(cid:22)(cid:23) (cid:17)(cid:22)(cid:23) D D D constant, (5.27) is trivially satisﬁed and (5.28) becomes @f(cid:22) x(cid:23) C @ P @f(cid:23) x(cid:22) D @ P 0 H) @2f(cid:22) x(cid:23)@ @ P x(cid:21) C P @ @2f(cid:23) x(cid:22)@ P x(cid:21) D P 0: (5.30) Recalling the identity (5.17), we may also write (since the metric carries no group indices) @2f(cid:23) x(cid:21) D x(cid:22)@ P P and so the most general form of fa(cid:22) is @2f(cid:22) x(cid:23)@ P x(cid:21) (cid:0) P @ @ 0 (cid:0)! @2f(cid:22) x(cid:23)@ @ P x(cid:21) D P 0; where (5.30) requires that fa(cid:22)(cid:23) 0. Finally, applying (5.29) leads to fa(cid:22) fa(cid:22)(cid:23).(cid:28); x/ x(cid:23) P C ga(cid:22).(cid:28); x/; (5.31) D fa(cid:23)(cid:22) C (cid:21) D D(cid:23)f(cid:22) D D 1 2 D D(cid:28) (cid:20) @f(cid:22) x(cid:23) (cid:0) @ P @f(cid:23) x(cid:22) @ P D(cid:22)f(cid:23) (cid:0) 1 2 D D(cid:28) .D(cid:28) (cid:140)fa(cid:22)(cid:23) fa(cid:23)(cid:22)(cid:141) (cid:0) D(cid:23)fa(cid:22)(cid:21) x(cid:21) P C D(cid:23)ga(cid:22) (cid:0) D(cid:22)fa(cid:23)(cid:21) x(cid:21) P C D(cid:22)ga(cid:23) x(cid:21)D(cid:21)/fa(cid:22)(cid:23) C P x(cid:21).D(cid:23)fa(cid:22)(cid:21) D P D(cid:22)fa(cid:23)(cid:21)/ D(cid:23)ga(cid:22) D(cid:22)ga(cid:23) (cid:0) C (cid:0) 5.2. CLASSICAL NON-ABELIAN GAUGE THEORY 109 and since x(cid:22) is arbitrary, we obtain P D(cid:21)fa(cid:22)(cid:23) C D(cid:28) fa(cid:22)(cid:23) D(cid:22)fa(cid:23)(cid:21) C D(cid:22)ga(cid:23) (cid:0) C D(cid:23)fa(cid:21)(cid:22) D(cid:23)ga(cid:22) 0 0 D D for the ﬁelds fa(cid:22)(cid:23) and ga(cid:22). Now, in analogy to the Abelian case, we may write 1 2 and applying the Euler-Lagrange equations, we obtain Aa(cid:22).(cid:28); x/I a.(cid:28)/ x(cid:22) P x(cid:22) P M C D L x(cid:22) P (cid:30)a.(cid:28); x/I a.(cid:28)/ C d d (cid:28) (cid:2)m x(cid:22) P C Aa(cid:22)I a(cid:3) D @ @x(cid:22) (cid:140)Aa(cid:23)I a @Aa(cid:23) @x(cid:22) P x(cid:23)I a x(cid:23) P C (cid:30)aI a(cid:141) @(cid:30)a @x(cid:22) I a: C C M I a x(cid:22) R @Aa(cid:22) @x(cid:23) P @Aa(cid:22) @(cid:28) C Rearranging terms and using (5.26) to express P x(cid:23) @x(cid:22) P @Aa(cid:22) @x(cid:23) P x(cid:23)(cid:19) I a (cid:20)(cid:18) @Aa(cid:23) Aa(cid:22) P x(cid:23)I a x(cid:22) R M D C (cid:0) (cid:0) I a Aa(cid:22) P D I a, we ﬁnd I a(cid:21) @(cid:30)a @x(cid:22) I a (cid:0) @Aa(cid:22) @(cid:28) I a C (cid:20)(cid:18) @Aa(cid:23) x(cid:23) @x(cid:22) P D (cid:0) @Aa(cid:22) @x(cid:23) P x(cid:23)(cid:19) I a (cid:0) Aa(cid:22)f ab c .Ab(cid:23) (cid:30)b/I c(cid:21) x(cid:23) P C @(cid:30)a @x(cid:22) I a (cid:0) @Aa(cid:22) @(cid:28) I a C (cid:20) @Aa(cid:23) D @x(cid:22) (cid:0) @Aa(cid:22) @x(cid:23) C f bc a Ab(cid:22)Ac(cid:23) (cid:21) x(cid:23)I a P (cid:20) @(cid:30)a @Aa(cid:22) C @x(cid:22) (cid:0) @(cid:28) C f bc a Ab(cid:22)(cid:30)c (cid:21) I a: Comparing this with (5.31), we may express the ﬁeld strengths in terms of the potentials as f(cid:22)(cid:23) (cid:20) @Aa(cid:23) D @x(cid:22) (cid:0) @Aa(cid:22) @x(cid:23) C f bc a Ab(cid:22)Ac(cid:23) g(cid:22) (cid:20) @(cid:30)a @Aa(cid:22) D @x(cid:22) (cid:0) @(cid:28) C f bc a Ab(cid:22)(cid:30)c (cid:21) x(cid:23)I a P (cid:21) I a; from which it follows that the ﬁeld equations are satisﬁed. Introducing the deﬁnitions xD (cid:28) D @(cid:28) @D D f(cid:22)D fD(cid:22) g(cid:22); D D (cid:0) the ﬁeld equations and Lorentz force assume the form where M x(cid:22) R f (cid:22)(cid:23) a x(cid:23)I a P D C @(cid:11)f(cid:12)(cid:13) @(cid:12) f(cid:13)(cid:11) @(cid:13) f(cid:11)(cid:12) 0 C a I a g(cid:22) C a I a f (cid:22)(cid:23) D x(cid:23) P C D f (cid:22) a DI a xD P x(cid:12) ; f (cid:22) a(cid:12) P D f(cid:11)(cid:12) (cid:20) @Aa(cid:12) D @x(cid:11) (cid:0) @Aa(cid:11) @x(cid:12) C f bc a Ab(cid:11)Ac(cid:12) (cid:21) I a recovers the usual relationship of the ﬁeld strength tensor to the non-Abelian potential. 110 5. ADVANCED TOPICS 5.3 EVOLUTION OF THE LOCAL METRIC IN CURVED SPACETIME General relativity has been summarized as: “Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve.” [11] The action of space on matter is expressed in equations of motion describing geodesic evolution with respect to a local metric g(cid:22)(cid:23).x/. Such equations were found from a Lagrangian in (3.6) and from canonical commuta- tion relations in (5.7). They can also be described in a Hamiltonian formulation on the phase space of position and momentum, an approach amenable to the canonical quantum dynamics for general relativity developed in [12, 13]. To express the action of matter on space, we look to Einstein equations that relate the local metric to sources of mass and energy, which evolve dynamically with (cid:28). We therefore consider a (cid:28)-dependent metric that may also evolve along with its sources. One possible approach, proposed by Pitts and Schieve [14, 15], is to develop general relativity on the 5D manifold .x(cid:22); (cid:28)/, introducing an ADM-type foliation with (cid:28) as a preferred time direction. In the approach followed here, we adhere to the restriction imposed in SHP electrodynamics, maintaining the role of (cid:28) as external, non-dynamical parameter throughout. General relativity treats the interval between a pair of instantaneously displaced points in spacetime (cid:14)x2 D g(cid:22)(cid:23)(cid:14)x(cid:22)(cid:14)x(cid:23) .x2 (cid:0) D x1/2 as an invariance of the manifold. To transform geometry into dynamics, a particle trajectory maps an arbitrary parameter (cid:16) to a continuous sequence of events x(cid:22).(cid:16)/ in the manifold. For any timelike path we may put (cid:16) proper time, and although the path consists of instantaneous displacements in a 4D block universe, “motion” is observed through changes in x0.s/ with proper time. Treating the sequence as a function, the invariant interval can be written D D s (cid:14)x2 D g(cid:22)(cid:23)(cid:14)x(cid:22)(cid:14)x(cid:23) g(cid:22)(cid:23) D dx(cid:22) ds dx(cid:23) ds (cid:14)s2 suggesting a dynamical description of the path by the action Z ds S D 1 2 g(cid:22)(cid:23) dx(cid:22) ds dx(cid:23) ds x2 P D (cid:0) which removes the constraint c2 associated with the usual square root form. A physical event x(cid:22).(cid:28)/ in SHP theory occurs at time (cid:28) and chronologically precedes events occurring at subsequent times. The physical picture that emerges in SHP electrodynamics can thus be understood as describing the evolution of a Maxwell–Einstein 4D block universe deﬁned at time (cid:28) to an inﬁnitesimally close 4D block universe deﬁned at (cid:28) 0, evolution slows to zero, recovering Maxwell theory as an equilibrium limit. The form of the gauge ﬁelds draws our attention to idea that while geometric relations on spacetime, such as O(3,1) invariance, are deﬁned within a given block universe, the dynamics operate through the d (cid:28). As c5 ! C 5.3. EVOLUTION OF THE LOCAL METRIC IN CURVED SPACETIME 111 (cid:28)-dependent gauge interaction, and in this sense are deﬁned in the transition from one 4D block manifold to another. We therefore consider the interval between an event x(cid:22).(cid:28)/ and an event a subsequent time, and expand as dx(cid:22) x(cid:22).(cid:28) (cid:14)(cid:28)/ x(cid:22).(cid:28)/ D N x(cid:22).(cid:28) N C (cid:0) C (cid:14)(cid:28)/ occurring at a displaced spacetime location at dx2 g(cid:22)(cid:23)(cid:14)x(cid:22)(cid:14)x(cid:23) g5(cid:23)(cid:14)x(cid:23)(cid:14)x5 g55(cid:14)x5(cid:14)x5 g(cid:11)(cid:12) .x; (cid:28) / (cid:14)x(cid:11)(cid:14)x(cid:12) D C referred to the coordinates of x. This interval contains both the geometrical distance (cid:14)x(cid:22) between two neighboring points in one manifold, and the dynamical distance (cid:14)x5 c5(cid:14)(cid:28) between events occurring at two sequential times. This leads to the Lagrangian D C D L D 1 2 Mg(cid:11)(cid:12) .x; (cid:28)/ x(cid:11) P x(cid:12) P and equations of motion x(cid:22) D P D(cid:28) D R x(cid:22) 0 D (cid:128) (cid:22) x(cid:11) (cid:11)(cid:12) P x(cid:12) P C x5 P D x5 D(cid:28) D R 0 D (cid:128) 5 x(cid:11) (cid:11)(cid:12) P x(cid:12) ; P C where (cid:128) (cid:13) we do not treat x5.(cid:28)/ quantities, not elements of a 5D tensor. This symmetry breaking of 5D through the prescription (cid:11)(cid:12) is the standard Christoﬀel symbol in 5D. But as in the electrodynamic Lagrangian, c5(cid:28) as a dynamical variable, and take the 5-index to denote scalar 4D+1 is expressed (cid:0)! (cid:17) (cid:128) (cid:22) 5(cid:11) D 1 2 g(cid:22)(cid:23) .@5g(cid:23)(cid:11) @(cid:11)g(cid:23)5 (cid:0) C @(cid:23)g(cid:11)5/ (cid:128) 5 (cid:11)(cid:12) (cid:17) 0 (5.32) which extends the geodesic Equations (3.6) and (5.7) to 5D. We deﬁne n.x; (cid:28)/ to be the number of events (non-thermodynamic dust) per spacetime volume, so that is the 5-component event current, and j (cid:11) .x; (cid:28) / (cid:26).x; (cid:28)/ x(cid:11).(cid:28)/ P D D M n.x; (cid:28)/ x(cid:11).(cid:28)/ P (cid:11)j (cid:11) r D @j (cid:11) @x(cid:11) C j (cid:13) (cid:128) (cid:11) (cid:13)(cid:11) D @(cid:26) @(cid:28) C r (cid:22)j (cid:22) 0 D is the continuity equation. Generalizing the 4D stress-energy-momentum tensor to 5D, the mass-energy-momentum tensor [16, 17] is T (cid:11)(cid:12) Mn x(cid:11) P x(cid:12) P D (cid:26) x(cid:11) P x(cid:12) P D (cid:0)! ( T (cid:22)(cid:23) T 5(cid:12) Mn D x5 D P x(cid:23) x(cid:22) P P x(cid:12) (cid:26) P D x(cid:23) P (cid:26) x(cid:22) D P c5j (cid:12) 112 5. ADVANCED TOPICS combining T (cid:22)(cid:23) with j (cid:11), and is conserved by virtue of the continuity and geodesic equations. The Einstein equations are similarly extended to G(cid:11)(cid:12) R(cid:11)(cid:12) D 1 2 (cid:0) Rg(cid:11)(cid:12) 8(cid:25)G c4 T(cid:11)(cid:12) ; D where the Ricci tensor R(cid:11)(cid:12) and scalar R are obtained by contracting indices of the 5D curva- ture tensor R(cid:14) (cid:13)(cid:11)(cid:12) . Since conservation of T (cid:11)(cid:12) depends on prescription (5.32), we must similarly suppress (cid:128) 5 0. Working through the (cid:11)(cid:12) when constructing the Ricci tensor to insure 4D r(cid:12) G(cid:11)(cid:12) D algebra we ﬁnd that R(cid:22)(cid:23) (cid:0)R(cid:22)(cid:23)(cid:1) and obtain D R(cid:22)5 R55 1 c5 1 c5 D D @(cid:28) (cid:128) (cid:21) (cid:22)(cid:21) (cid:0) @(cid:21)(cid:128) (cid:21) (cid:22)5 C (cid:27)5(cid:128) (cid:27) (cid:128) (cid:21) (cid:22)(cid:21) (cid:0) (cid:27)(cid:21)(cid:128) (cid:27) (cid:128) (cid:21) (cid:22)5 @(cid:28) (cid:128) (cid:21) 5(cid:21) (cid:0) @(cid:21)(cid:128) (cid:21) 55 C (cid:27)5(cid:128) (cid:27) (cid:128) (cid:21) 5(cid:21) (cid:0) (cid:27)(cid:21)(cid:128) (cid:27) (cid:128) (cid:21) 55 as new components. The weak ﬁeld approximation [11] is generalized to 5D as g(cid:11)(cid:12) (cid:17)(cid:11)(cid:12) h(cid:11)(cid:12) C D (cid:0)! @(cid:13) g(cid:11)(cid:12) D @(cid:13) h(cid:11)(cid:12) 2 (cid:0)h(cid:11)(cid:12) (cid:1) 0 (cid:25) leading to R(cid:11)(cid:12) 1 2 Deﬁning Nh(cid:11)(cid:12) ’ (cid:16)@(cid:12) @(cid:13) h(cid:13) h(cid:11)(cid:12) D @(cid:11)@(cid:13) h(cid:13) @(cid:13) @(cid:13) h(cid:11)(cid:12) @(cid:11)@(cid:12) h(cid:17) (cid:12) (cid:0) (cid:11) C 1 2 (cid:17)(cid:11)(cid:12) h, the Einstein equations become (cid:0) (cid:0) 16(cid:25)G c4 T(cid:11)(cid:12) @(cid:12) @(cid:13) Nh(cid:13) (cid:11) C @(cid:11)@(cid:13) Nh(cid:13) (cid:12) (cid:0) D @(cid:13) @(cid:13) Nh(cid:11)(cid:12) @(cid:11)@(cid:12) Nh (cid:0) R (cid:17)(cid:11)(cid:12) R(cid:11)(cid:12) ’ (cid:17)(cid:11)(cid:12) h(cid:11)(cid:12) : h ’ which take the form of a wave equation 16(cid:25)G c4 T(cid:11)(cid:12) @(cid:13) @(cid:13) Nh(cid:11)(cid:12) D (cid:0) D (cid:0) (cid:18)@(cid:22)@(cid:22) (cid:17)55 c2 5 C (cid:19) @2 (cid:28) Nh(cid:11)(cid:12) after imposing the gauge condition @(cid:21) Nh(cid:11)(cid:21) for this equation leads to D 0. Using the Green’s function GMaxwell from (3.24) Nh(cid:11)(cid:12) .x; (cid:28) / D 4G c4 Z d 3x0 T(cid:11)(cid:12) (cid:16)t (cid:0) x j x j (cid:0) x0jc x0j (cid:0) ; x0; (cid:28) (cid:17) relating the ﬁeld Nh(cid:11)(cid:12) .x; (cid:28) / to the source T(cid:11)(cid:12) .x; (cid:28) /. In analogy to the Coulomb problem, we take a point source X .cT .(cid:28)/; 0/ in a co-moving frame, with D T 00 D mc2 T 2(cid:14)3 .x/ ’ .t P (cid:0) T .(cid:28) // T (cid:11)i 0 D T 55 c2 c2 T 00; 5 D 5.3. EVOLUTION OF THE LOCAL METRIC IN CURVED SPACETIME 113 where ’.(cid:28)/ is the smoothing function (3.15). Writing M m ’ .t (cid:0) D T .(cid:28)// produces Nh00 .x; (cid:28) / 4GM T 2 c2R P D Nh(cid:11)i .x; (cid:28) / 0 D Nh55 .x; (cid:28) / 2 (cid:17)(cid:11)(cid:12) Nh and neglecting c2 so using h(cid:11)(cid:12) (cid:17)(cid:11)(cid:12) h(cid:12)(cid:13) the non-zero Christoﬀel symbols are D Nh(cid:11)(cid:12) (cid:0) 1 5 =c2 1, we see that h00 (cid:28) c2 c2 Nh00 5 D D Nh00. Since g(cid:11)(cid:12) h(cid:12)(cid:13) ’ 1 (cid:128) (cid:22) 00 D (cid:0) 2 1 (cid:128) (cid:22) 50 D 2c5 (cid:17)(cid:22)(cid:23)@(cid:23)h00 (cid:17)(cid:22)0@(cid:28) h00 1 2 (cid:128) (cid:22) 0i D (cid:128) (cid:22) 55 D (cid:0) (cid:17)(cid:22)(cid:23)@i h(cid:23)0 1 2 (cid:17)(cid:22)(cid:23)@(cid:23)h55 so the equations of motion split into .@(cid:28) h00/ t R D t P x C P (cid:1) . r h00/ t 2 P c2 2 x R D h00/ . r t 2: P In spherical coordinates, putting (cid:18) D (cid:25)=2, the angular and radial equations are 2 R P (cid:30) P R (cid:30) R C D 0 (cid:30) (cid:0)! P D L R MR2 (cid:0)! R L2 (cid:0) M 2R3 D (cid:0) GM t 2 R2 P T 2 P and the t equation is 2G@(cid:28) M t c2R P C 4GM T c2R P T R t P (cid:0) 2GM R R2c2 P T 2 P (cid:25) 2GM c2R (cid:18)1 C (cid:19) (cid:11) .(cid:28)/ 2 t R D (cid:11) .(cid:28) / P t; P where we neglect P R=c T P 1 C D (cid:25) (cid:11) .(cid:28) / 0 and @(cid:28) ’ 0 (taking (cid:21) large), and deﬁne (cid:25) T 2 2 (cid:0)! P 1 C ’ (cid:11) .(cid:28) / T (cid:0)! P T R ’ (cid:18)1 (cid:11) .(cid:28) / 2 (cid:19) P (cid:11) .(cid:28) / 2 : C In the Newtonian case, (cid:11) 0 1, but this t equation has the solution D exp (cid:20) 2GM c2R t P D t (cid:0)! P (cid:18)(cid:11) C D 1 (cid:11)2(cid:19)(cid:21) 4 t 2 (cid:0)! P T 2 P 1 C ’ (cid:18)1 1 2 C 2GM c2R (cid:19) (cid:11) which, since 2GM=c2R 1, leads ﬁnally to the radial equation in the form l 2 M 2R2 (cid:0) GM R (cid:18)1 1 2 C (cid:11) .(cid:28) /(cid:19)(cid:27) dK d (cid:28) D (cid:0) GM 2R d d (cid:28) D (cid:11) .(cid:28)/ : (cid:28) 1 2 d d (cid:28) (cid:26) 1 R2 2 P C We recognize K on the LHS as the Hamiltonian of the particle moving in this local metric. The mass ﬂuctuation of the point source is seen to induce a ﬂuctuation in the mass of a distant particle through the ﬁeld g(cid:11)(cid:12) .x; (cid:28)/, producing a small modiﬁcation of Newtonian gravity. 114 5. ADVANCED TOPICS Interactions in SHP electrodynamics form an integrable system in which event evolution generates an instantaneous current deﬁned over spacetime at (cid:28), and in turn, these currents induce (cid:28)-dependent ﬁelds that act on other events at (cid:28). We expect that in a similar way, a fully developed SHP formulation of general relativity will describe how the instantaneous distribution of mass at (cid:28) expressed through T(cid:11)(cid:12) .x; (cid:28)/ induces the local metric g(cid:11)(cid:12) .x; (cid:28)/, which, in turn, determines geodesic equations of motion for any particular event at x(cid:22).(cid:28)/. ZEEMAN AND STARK EFFECTS 5.4 As discussed in Section 2.4, reasonable solutions to the relativistic central force problem are obtained in a restricted Minkowski space (RMS) with ﬁxed unit vector n(cid:22) RMS.n/ x (cid:8)x (cid:140)x .x n/n(cid:141)2 0(cid:9) (cid:1) 2 (cid:0) (cid:21) D j invariant under O(2,1) but not general Lorentz transformations. Because quantum states are classiﬁed by their symmetry representations, Horwitz and Arshansky [18–20] generalized their solutions to the quantum central force problem to an induced representation of O(3,1). Studying the Lorentz transformations on n(cid:22) and the RMS(n), they found the generators h(cid:22)(cid:23) of O(3,1) for the combined space, formed a maximally commuting set of operators, and solved for eigenstates of these operators. The energy levels of these degenerate quantum states split in a constant elec- tromagnetic ﬁeld—the Zeeman and Stark eﬀects. To couple the electromagnetic ﬁeld to these states, we construct a gauge theory for the induced representation in its classical form [21, 22]. .0; 0; 0; 1/ so that the parameterization (2.5) describes RMS.n(cid:14)/. Given We denote n(cid:14) the Lorentz transformation n(cid:14) L.n/ n it follows that D D RMS.n(cid:22)/ and x 2 L.n/ x y D and so we may characterize the full spacelike region x transformation (cid:131) acts as n (cid:131) n and x n0 D ! (cid:131)L.n/T y D x0 D (cid:131) x D y RMS.n(cid:14)(cid:22)/ H) 2 LT .n/y by (cid:16) (cid:131) x , it follows that D D x0 D L.(cid:131)n/T L.(cid:131)n/ (cid:131) L.n/T y ! L.n0/T y0: D .n; y/. Since a Lorentz Thus, y transforms under the O(2,1) little group deﬁned through y y0 and since D(cid:0) (cid:28)-dependent, but one can show that since d=d (cid:28) is Lorentz-invariant and commutes with (cid:131) D(cid:0) D n(cid:14), the little group preserves RMS(n(cid:14)). We have taken L.n.(cid:28)// to be ! 1.(cid:131); n/n(cid:14) D(cid:0) D D L.(cid:131)n/ (cid:131) L.n/T 1.(cid:131); n/ y 1.(cid:131); n/ D is form-invariant. Representing the Lorentz transform (cid:131) D D(cid:0) 1.(cid:131); n/ D(cid:0) 1.(cid:131); n/ y y P C P . y/0 P (cid:131) 1 C D 1 2 !(cid:22)(cid:23) M(cid:22)(cid:23) o.!2/ C d d (cid:28) (cid:140)D(cid:0) 1.(cid:131); n/ y(cid:141) x x0 as ! W .M(cid:22)(cid:23)/(cid:27)(cid:21) (cid:17)(cid:27)(cid:22)(cid:17)(cid:21)(cid:23) (cid:17)(cid:27)(cid:23)(cid:17)(cid:21)(cid:22) (cid:0) D 5.4. ZEEMAN AND STARK EFFECTS 115 .n0; y0/ can be represented as (cid:131) the Lorentz transform N (cid:16) W D .n; y/ ! and the generators are found as 1 (cid:131) N D (cid:16)0 D 1 2 C !(cid:22)(cid:23) X (cid:22)(cid:23) o.!2/ C X(cid:22)(cid:23) D (cid:0) (cid:0)xT M(cid:22)(cid:23) x r C nT M(cid:22)(cid:23) n(cid:1) r D (cid:0) (cid:0)yT LM(cid:22)(cid:23)LT y r C nT M(cid:22)(cid:23)D(cid:1) ; where we introduce L.@=@n(cid:22)/LT S(cid:22) D D(cid:22) . D n/(cid:22) r C yT S(cid:22) y : r It is easily shown that for a function of x alone (even as n varies with (cid:28)) D(cid:22) acts as a kind of D(cid:22)f .L.n/T y/ covariant derivative with D(cid:22)f .n; y/ (cid:17) (cid:16) ; P(cid:16) g f As a classical Lagrangian on the phase space 0. we put D L 1 2 1 2 M (cid:0) x2 P M h. y P D D (cid:26)2 n2(cid:1) C P n(cid:27) S(cid:27) y/2 C C P e . A.x/ (cid:31).n// V .x2/ x P (cid:1) (cid:26)2 n2i P C C n C P (cid:1) e h. y P (cid:0) n(cid:27) S(cid:27) y/ C P A.n/.y/ (cid:31).n/i n C P (cid:1) (cid:0) V .x2/; (cid:1) where (cid:26) is a length scale required because n is a unit vector, A.n/ little group, and we used D LA transforms under the x P D LT y P LT y C P D LT (cid:16) y P L LT y(cid:17) P LT . y P D C n(cid:27) S(cid:27) y/ : C P This L is scalar and represents a generalized Maxwell electrodynamics including n as a new dynamical degree of freedom. The conjugate momenta are found to be p(cid:22) (cid:25)(cid:22) D D @L y(cid:22) D @ P @L n(cid:22) D @ P M (cid:16) y(cid:22) P M (cid:0)(cid:26)2 n(cid:27) S(cid:27) y(cid:22) C P C eA.n/(cid:17) n(cid:22) P yT S(cid:22)p e(cid:31)(cid:1) C (cid:0) having used the antisymmetry of the matrices S(cid:22). The Hamiltonian is obtained from the La- grangian as K y D P (cid:1) p n C P (cid:1) (cid:25) (cid:0) L D 1 2M (cid:16)p (cid:0) 2 eA.n/(cid:17) 1 2Md 2 .P (cid:0) C e(cid:31)/2 V; C where P (cid:31) tion produced by a Lorentz transformation (cid:14)(cid:16) yT S(cid:27) p . Taking A.n/ (cid:25)(cid:27) C D D D 0 and applying Noether’s theorem to the varia- 2 !(cid:22)(cid:23)X(cid:22)(cid:23) (cid:16) we obtain the conserved quantities 1 h(cid:22)(cid:23) D p(cid:26)X(cid:22)(cid:23)y(cid:26) C (cid:25) (cid:26)X(cid:22)(cid:23)n(cid:26) D D yT (cid:2)L.n/M(cid:22)(cid:23)LT (cid:3) p nT M(cid:22)(cid:23)P C 116 5. ADVANCED TOPICS which satisfy Poisson brackets (cid:8)h(cid:22)(cid:23); K(cid:9) 0. D Now interpreting p and (cid:25) as quantum operators, so that p(cid:22) @ @y(cid:22) i (cid:132) D (cid:25)(cid:22) @ @n(cid:22) i (cid:132) D P(cid:22) D(cid:22) i (cid:132) D the h(cid:22)(cid:23) are precisely the Lorentz generators found by Horwitz and Arshansky for solutions .x; (cid:28)/ to the Stueckelberg–Schrodinger equation i@(cid:28) 0. This system is invariant under U.1/ gauge transformations K and satisfy (cid:2)h(cid:22)(cid:23); K(cid:3) D D ie(cid:130).(cid:16)/= e(cid:0) (cid:132) ! A.n/ (cid:22) (cid:0)! A.n/ (cid:22) C @ @y(cid:22) (cid:130) (cid:31)(cid:22) (cid:31)(cid:22) C (cid:0)! D(cid:22)(cid:130): For interactions cyclic in n, we may put RMS.n/ with ﬁxed n, so the classical and quantum dynamics reduce to n P D 0 for the classical system which remains within L D L0 D 1 2 M y2 P (cid:0) V K D K0 D (cid:0) 2 (cid:132) 2M @ @y(cid:22) @ @y(cid:22) C V and quantum wavefunctions satisfy D(cid:22) in perturbation theory by expressing a constant ﬁeld strength F (cid:22)(cid:23) as D 0. The Zeeman and Stark eﬀects are thus obtained A(cid:22).x/ 1 2 D (cid:0) F (cid:22)(cid:23)x(cid:23) (cid:31)(cid:22).n/ D (cid:26) A(cid:22).n/ D (cid:0) (cid:26) 2 F (cid:23) (cid:27) n(cid:27) and writing D for the potential in RMS(n(cid:14)). To ﬁrst order in e, the Hamiltonian is just D (cid:0) A.n/ (cid:22) .y/ L(cid:22)(cid:23)A(cid:23).LT y/ .LF LT y/(cid:22) 1 2 F(cid:22)(cid:23)X (cid:22)(cid:23) K D K0 e 4M C 4m F(cid:11)(cid:12) X (cid:11)(cid:12) so that the Zeeman eﬀect follows from e 2m B kLk splitting the en- ergy levels along the diagonal component Lk of angular momentum. For the Stark eﬀect, we put e 2m EkAk, where Ak is a boost, and to reproduce the phenomenol- 4m F(cid:11)(cid:12) X (cid:11)(cid:12) e(cid:15)(cid:22)x(cid:22), hinting ogy we must include an additional scalar potential V at the 5D gauge theory. A5, where A5 2m F0i X 0i 4m Fij X ij D (cid:0) ! ! ! D C D V e e e e 5.5 CLASSICAL MECHANICS AND QUANTUM FIELD THEORY Although quantum ﬁeld theory diﬀers from classical mechanics in both methodology and re- sults, classical SHP electrodynamics presents a number of interesting qualitative implications for QED. 5.5. CLASSICAL MECHANICS AND QUANTUM FIELD THEORY 117 D As seen in Sections 1.3 and 3.1, the Stueckelberg–Schrodinger equation is ﬁrst-order in (cid:28), and the Hamiltonian operator is a Lorentz scalar, so that manifest covariance is preserved throughout the second quantization procedure. In constructing canonical momenta, the kinetic term for the ﬁelds f (cid:11)(cid:12) (cid:136) f(cid:11)(cid:12) formed from the cross derivatives of a(cid:11) leads to momentum ﬁelds (cid:25)(cid:22) @(cid:28) a(cid:22) but no (cid:25)5 component, because @(cid:28) a5 does not appear in f(cid:11)(cid:12) . In Dirac quantization for gauge theories [23], one inserts a momentum (cid:25)5 conjugate to a5 and a Lagrange multiplier 0. The secondary constraint (that the primary constraint to enforce the primary constraint (cid:25)5 commutes with the Hamiltonian) leads to the Gauss law @(cid:22)f 5(cid:22) .ec5=c/j 5. But because this system is ﬁrst-order, one may apply the Jackiw quantization scheme [24], in which we ﬁrst eliminate the constraint from the Lagrangian by solving the Gauss law, and then construct the Hamiltonian from the unconstrained degrees of freedom, which are the matter ﬁelds and the transverse electromagnetic modes. Since the momentum modes are not constrained to be lightlike, as we saw for plane waves in Section 4.4, there can be three transverse polarization modes. The resulting system is amenable to both canonical and path integral quantization. D D In canonical quantization, one ﬁnds the propagator G.x; (cid:28)/ for the matter ﬁelds as the vacuum expectation value of (cid:28)-ordered operator products (equivalent to a Fourier transform of the momentum representation with a Feynman contour). The propagator enforces (cid:28)-retarded causality, with G.x; (cid:28)/ 0 for (cid:28) < 0, so that SHP quantum ﬁeld theory is free of matter loops. Extracting the propagator for a sharp mass eigenvalue recovers the Feynman propagator for the Klein–Gordon equation. D As in classical mechanics, quantum systems evolve as (cid:28) increases, with advance or retreat of x0 treated on an equal footing. Perturbation theory is constructed in an interaction picture obtained by a unitary transformation constructed from the scalar interaction Hamiltonian and (cid:28). As a result, this method has been shown [25] to circumvent the Haag no-go theorem [26], summarized as, “Haag’s theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction.” [27] As seen in Section 4.7, particles interacting through the electromagnetic ﬁeld can ex- change mass. The treatment of Moller scattering leads to a cross-section identical to the standard QED result for spinless particles when mass exchange is absent. When mass is exchanged, the usual pole in the cross-section at 0o splits into a zero and two poles close to but away from the forward beam axis, providing a small experimental signature (and one very diﬃcult to observe). Because there are no matter loops in this theory, the problem of renormalization reduces to treatment of photon loops in the matter ﬁeld (gauge and vertex factors become unity by the Ward identities). Mass renormalization can be absorbed into the ﬁrst order mass term (cid:3)i@(cid:28) in the quantum Lagrangian. To remove singularities from the loop contributions to the matter propagator in standard QED, some regularization scheme is required. However in SHP QED, the ﬁeld interaction kernel (3.11) places a multiplicative factor h1 in the photon propagator. This factor acts as a mass cut-oﬀ rendering the theory superrenormalizable. Un- like a momentum cut-oﬀ, this factor leaves the Lorentz and gauge symmetries of the original 1 .(cid:24)(cid:21)(cid:20)/2i(cid:0) C 118 5. ADVANCED TOPICS theory unaﬀected, recalling Schwinger’s motivation for his “proper time method” discussed in Section 1.3. 5.6 BIBLIOGRAPHY [1] Dyson, F. J. 1990. American Journal of Physics, 58:209–211. https://doi.org/10.1119/ 1.16188 97 [2] Tanimura, S. 1992. Annals of Physics, 220:229–247. http://www.sciencedirect.com/ science/article/pii/000349169290362P 97, 107 [3] Hojman, S. A. and Shepley, L. C. 1991. Journal of Mathematical Physics, 32:142–146. ht tps://doi.org/10.1063/1.529507 97, 101 [4] Land, M., Shnerb, N., and Horwitz, L. 1995. Journal of Mathematical Physics, 36:3263. 97 [5] Santilli, R. M. 1990. Foundations of Theoretical Mechanics I, Springer-Verlag. 102 [6] Helmholtz, H. 1887. Journal für die Reine Angewandte Mathematik, 100:137. 102 [7] Darboux, G. 1894. Leçons sur la Théory Générale des Surfaces, 3, Gauthier-Villars. 102 [8] Dedecker, P. 1950. Bulletin de l’Académie Royale des Sciences de Belgique Classe des Sciences, 36:63. 102 [9] Wong, S. K. 1970. Nuovo Cimento, 65A:689. 106 [10] Lee, C. R. 1950. Physics Letters, 148A:36. 107 [11] Misner, C. W., Thorne, K. S., and Wheeler, J. A. 1973. Gravitation, W.H. Freeman and Co., San Francisco, CA. 110, 112 [12] Horwitz, L. P. 2019. Journal of Physics: Conference Series, 1239. https://doi.org/10. 1088%2F1742-6596%2F1239%2F1%2F012014 110 [13] Horwitz, L. P. 2019. The European Physical Journal Plus, 134:313. https://doi.org/10. 1140/epjp/i2019-12689-7 110 [14] Pitts, J. B. and Schieve, W. C. 1998. Foundations of Physics, 28:1417–1424. https://do i.org/10.1023/A:1018801126703 110 [15] Pitts, J. B. and Schieve, W. C. 2001. Foundations of Physics, 31:1083–1104. https://do i.org/10.1023/A:1017578424131 110 [16] Saad, D., Horwitz, L., and Arshansky, R. 1989. Foundations of Physics, 19:1125–1149. 111 [17] Land, M. 2019. Journal of Physics: Conference Series, 1239. https://doi.org/10.1088% 2F1742-6596%2F1239%2F1%2F012005 111 5.6. BIBLIOGRAPHY 119 [18] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:66. 114 [19] Arshansky, R. and Horwitz, L. 1989. Journal of Mathematical Physics, 30:380. [20] Horwitz, L. P. 2015. Relativistic Quantum Mechanics, Springer, Dordrecht, Netherlands. 114 [21] Land, M. and Horwitz, L. 1995. Jounal of Physics A: Mathematical and General, 28:3289– 3304. 114 [22] Land, M. and Horwitz, L. 2001. Foundations of Physics, 31:967–991. 114 [23] Dirac, P. 1964. Lectures on Quantum Mechanics, Yeshiva University, New York. 117 [24] Jackiw, R. 1993. https://arxiv.org/pdf/hep-th/9306075.pdf 117 [25] Seidewitz, E. 2017. Foundations of Physics, 47:355–374. 117 [26] Haag, R. 1955. Kong. Dan. Vid. Sel. Mat. Fys. Med., 29N12:1–37. Philosophical Magazine Series, 746, 376. 117 [27] Streater, R. F. and Wightman, A. S. 1964. PCT, Spin, Statistics, and All That, Princeton University Press. 117 Authors’ Biographies 121 MARTIN LAND Martin Land was born in Brooklyn in 1953. He grew up in the New York City area, strongly inﬂuenced by his mother, a social worker who worked with Holocaust survivors, and his father, a second-generation engineer in small manufacturing businesses associated with the garment industry. In his school years he cleaned swimming pools and stables, worked as a carpenter on a construction site, and expedited orders in the garment center. In 1972, he entered Reed College in Portland, Oregon, where he received a Kroll Fellowship for original research which per- mitted him to devote an extra year to extensive study in the humanities along with his specialization in physics. After com- pleting his BA in 1977, he returned to New York City where he received an M.S. in electrical engineering from Columbia University in 1979 as a member of the Eta Kappa Nu engineering honor society. He joined Bell Laboratories, developing special- ized hardware for ﬁber optic communication with application in computer networks and video transmission. In 1982, he worked as a telecommunications engineer at a major Wall Street bank. Returning to theoretical physics at Hebrew University in Jerusalem, he worked with Eliezer Ra- binovicci on supersymmetric quantum mechanics to receive a second M.S. in 1986. In 1985, he married Janet Baumgold, a feminist therapist and co-founder of the Counseling Center for Women. Following a year devoted to full-time fatherhood and another in compulsory national service, he began working toward a Ph.D. in high energy physics with Lawrence Horwitz at Tel Aviv University in 1988. He elaborated many aspects of the classical and quantum theories known as Stueckelberg-Horwitz-Piron (SHP) theory, producing a dissertation developing the SHP quantum ﬁeld theory. Concurrently with his doctoral work, he was on the research faculty of the Computer Science Department at Hebrew University, developing specialized hardware for parallel computing. After submitting his dissertation in 1995, he taught communications engineering for three years at the Holon Institute of Technology, before joining the Depart- ment of Computer Science at Hadassah College in Jerusalem, teaching computer architecture, microprocessors, embedded systems, and computer networking. He was a founding member of the International Association for Relativistic Dynamics (IARD) in 1998 and has served as IARD president since 2006. In parallel to his activities in physics and computer science, he has 122 AUTHORS’ BIOGRAPHIES enjoyed a long collaboration with Jonathan Boyarin of Cornell University in various areas of the humanities, critical theory, and Jewish studies. This collaboration has allowed him to communi- cate contemporary thinking in physics, especially notions of time associated with SHP theory, to scholars in other ﬁelds as modern context for philosophical consideration of temporality. AUTHORS’ BIOGRAPHIES 123 LAWRENCE P. HORWITZ Lawrence Paul Horwitz was born in New York City on Oc- tober 14, 1930. He lived in Westchester County until 1934, then went to London where his father founded and managed a chain of womens wear shops, called the Richard Shops, and then returned to the United States in 1936. After a few years in Brooklyn, NY, his family moved to Forest Hills in Queens, NY, where he learned tennis and attended Forest Hills High School, a school dedicated to teaching students how to think, where he came to love physics. He then went to the College of Engineering, New York University, where he studied Engi- neering Physics and graduated summa cum laude with a Tau Beta Pi key and the S.F.B. Morse medal for physics. He met a young lady, Ruth Abeles, who arrived from Germany in the U.S. in 1939 and became his wife before moving on to Harvard University in 1952 with a National Science Foundation Fellowship. He received his doctorate at Harvard working under the supervision of Julian Schwinger in 1957. He then worked at the IBM Watson Research Laboratory where he met Herman Goldstine, a former assistant to John von Neumann and, among other things, explored with him octononic and quaternionic Hilbert spaces from both physical and mathematical points of view. He then moved on to the University of Geneva in 1964, becoming involved in scattering theory as well as continuing his studies of hypercomplex systems with L. C. Biedenharn and becoming involved in particle physics with Yuval Neeman at CERN. He became full professor at the University of Denver in 1966–1972; he then accepted a full professorship at Tel Aviv University. After stopping for a year to work with C. Piron at the University of Geneva on the way to Israel, he has been at Tel Aviv Univer- sity since 1973, with visits at University of Texas at Austin, Ilya Prigogine Center for Statistical Mechanics and Complex Systems in Brussels, and at CERN, ETH (Honggerberg, Zurich), University of Connecticut (Storrs, CT), IHES (Bures-sur-Yvette, Paris), and Institute for Ad- vanced Study (Princeton, NJ), where he was a Member in Natural Sciences, 1993, 1996, 1999, 2003 with short visits in August 1990, and January 1991, working primarily with S. L. Adler. He is now Professor Emeritus at Tel Aviv University, Bar Ilan University, and Ariel University. His major interests are in particle physics, statistical mechanics, mathematical physics, theory of unstable systems, classical and quantum chaos, relativistic quantum mechanics, relativistic many body theory, quantum ﬁeld theory, general relativity, representations of quantum theory on hypercomplex Hilbert modules, group theory and functional analysis, theories of irreversible quantum evolution, geometrical approach to the study of the stability of classical Hamiltonian systems, and to the dark matter problem, and classical and quantum chaos. He is a member of the American Physical Society (Particle Physics), Swiss Physical Society, European Physi- cal Society, International Association for Mathematical Physics, Israel Physical Society, Israel Mathematics Union, European Mathematical Society, International Quantum Structures As- 124 AUTHORS’ BIOGRAPHIES sociation, Association of Members of the Institute for Advanced Study, and the International Association for Relativistic Dynamics.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8672399.pdf&bkn=8672398&pdfType=book	Ancient Hindu Science Its Transmission and Impact on World Cultures Copyright © 2019 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Ancient Hindu Science: Its Transmission and Impact on World Cultures Alok Kumar www.morganclaypool.com ISBN: 9781681735306 ISBN: 9781681735313 ISBN: 9781681735320 paperback ebook hardcover DOI 10.2200/S00906ED1V01Y201903ENG034 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #34 Series ISSN Print 1939-5221 Electronic 1939-523X Ancient Hindu Science Its Transmission and Impact on World Cultures Alok Kumar State University of New York at Oswego SYNTHESIS LECTURES ON ENGINEERING #34 CM&cLaypoolMorganpublishers&ABSTRACT To understand modern science as a coherent story, it is essential to recognize the accomplish- ments of the ancient Hindus. They invented our base-ten number system and zero that are now used globally, carefully mapped the sky and assigned motion to the Earth in their as- tronomy, developed a sophisticated system of medicine with its mind-body approach known as Ayurveda, mastered metallurgical methods of extraction and puriﬁcation of metals, includ- ing the so-called Damascus blade and the Iron Pillar of New Delhi, and developed the science of self-improvement that is popularly known as yoga. Their scientiﬁc contributions made im- pact on noted scholars globally: Aristotle, Megasthenes, and Apollonius of Tyana among the Greeks; Al-Birūnī, Al-Khwārizmī, Ibn Labbān, and Al-Uqlīdisī, Al-Jāh. iz among the Islamic scholars; Fa-Hien, Hiuen Tsang, and I-tsing among the Chinese; and Leonardo Fibbonacci, Pope Sylvester II, Roger Bacon, Voltaire and Copernicus from Europe. In the modern era, thinkers and scientists as diverse as Ralph Waldo Emerson, Johann Wolfgang von Goethe, Jo- hann Gottfried Herder, Carl Jung, Max Müller, Robert Oppenheimer, Erwin Schrödinger, Arthur Schopenhauer, and Henry David Thoreau have acknowledged their debt to ancient Hindu achievements in science, technology, and philosophy. The American Association for the Advancement of Science (AAAS), one of the largest scientiﬁc organizations in the world, in 2000, published a timeline of 100 most important sci- entiﬁc ﬁnding in history to celebrate the new millennium. There were only two mentions from the non-Western world: (1) invention of zero and (2) the Hindu and Mayan skywatchers astro- nomical observations for agricultural and religious purposes. Both ﬁndings involved the works of the ancient Hindus. The Ancient Hindu Science is well documented with remarkable objectivity, proper citations, and a substantial bibliography. It highlights the achievements of this remarkable civilization through painstaking research of historical and scientiﬁc sources. The style of writing is lucid and elegant, making the book easy to read. This book is the perfect text for all students and others interested in the developments of science throughout history and among the ancient Hindus, in particular. KEYWORDS Hindu science, History of science, Vedic science, Hindu religion, Ancient Indian science, Indian science and technology v This book is dedicated to my parents, Late Ganga Saran Sarswat, father and Late Shanti Devi, mother. They taught me virtues of life. Contents vii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Multicultural Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The Ancient Hindu Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 About the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 2 The Building Blocks of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Geography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 The Power of Questioning: Śāstrārtha (Debate) to Acquire Knowledge . . . . . 17 Respect for Knowledge: The Role of a Guru . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Smr. ti (Memory), An Answer to Book Burning . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Yoga and Meditation for Self-Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 3 The Hindu Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1 The Hindu Numerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.1 The Word-Numerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1.2 The Place-value Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 From Śūnyatā and Neti-Neti to Zero and Inﬁnity (Ananta) . . . . . . . . . . . . . . . 32 3.2 3.3 The Binary Number System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 The Fibonacci Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.5 The Square-root Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.6 3.6.1 Sum of a Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6.2 Sum of a Series with (cid:134)n2 and (cid:134)n3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6.3 Solution to a Quadratic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.7.1 Transforming a Square into a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.7.2 Height of a Tall Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 viii 4 5 6 7 3.7.3 The Value of (cid:25) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.8 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.9 Trigonometry: From Jyā to Sine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.10 Diﬀusion of Hindu Mathematics to Other Cultures . . . . . . . . . . . . . . . . . . . . 50 3.10.1 The Middle East . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.10.2 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10.3 Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.10.4 Support of Pope Sylvester II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.1 Heliocentric Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1.1 Ujjain, Greenwich of the Ancient World . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1.2 Diurnal Motion of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2 Hindu Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 Hindu Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.4 Diﬀusion of Hindu Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4.1 The Middle East . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4.2 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.4.3 Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Space (Ākāśa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2 5.3 Matter and Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.1 Conservation of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Atom (Paramān. u) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.4 5.5 Gravitation and Ocean Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1 Mining and Metallurgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.1.1 The Iron Pillar of New Delhi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.2 Wootz or Damascus Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Fermentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.3 Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.1 7.2 Sacred Rivers and Mountains: Ecological Perspectives . . . . . . . . . . . . . . . . . . 118 Sacred Tulsī and Sacred Cow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 ix 7.2.1 Vegetarianism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Life in Plants: Similarities with Humans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.3 8 Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.1 Doctors, Nurses, Pharmacies, and Hospitals . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Ayurveda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.2 8.2.1 Pañca-karma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 8.3.1 Plastic Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.3.2 Cataract Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.3.3 Carpenter Ants Suturing and Leech Therapy . . . . . . . . . . . . . . . . . . . 141 8.4 Hindu Medicine in Other World Cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.3 9.1 9 The Global Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Impacts during the Ancient and Medieval Periods . . . . . . . . . . . . . . . . . . . . . 149 9.1.1 Impact on Arabia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.1.2 Impact on China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 9.1.3 Impact on Greek Science and Philosophy . . . . . . . . . . . . . . . . . . . . . . 151 Impacts During the Modern Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 9.2.1 Emerson and Thoreau–Two Celebrated American Scholars . . . . . . . . 156 9.2.2 Impact on Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 9.2 A Timeline of the Hindu Manuscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Preface xi I was raised in Haridwar, a famous Indian city that is known for religion, philosophy, mysticism, and the Ganges river. I heard about the greatness of India often as a child from my father who was a learned man. I did not notice about this greatness in the scientiﬁc literature that was a part of my academic curricula. It created a great emotional dilemma to me. Why India, with so much philosophy, intellect, and prosperity, could not make a substantial contribution to science? I found the answer only after I came to America and had access to good library facilities in California. The history of science as we know from the textbooks is simply incomplete. By writing this book and other books, I am trying to ﬁll these gaps. It is not possible to provide details of the achievements of the ancient Hindus in one introductory book. Their contributions are enormous and this book presents only the ‘tip of the iceberg,’ as the phrase goes. I have chosen only those topics that are interesting to me and I have some knowledge. The accomplishments of the ancient Hindus span many ﬁelds. In mathematics, they in- vented our base-ten number system and zero that are now used globally, carefully mapped the sky and assigned motion to the Earth in their astronomy, developed a sophisticated system of medicine with its mind-body approach known as Ayurveda, mastered metallurgical methods of extraction and puriﬁcation of metals, including the so-called Damascus blade and the Iron Pillar of New Delhi, and developed the science of self-improvement that is popularly known as yoga. Their scientiﬁc contributions made impact on noted scholars from all over the world, Aristotle, Megasthenes, and Apollonius of Tyana among the Greeks; Al-Birūnī, Al-Khwārizmī, Ibn Labbān, and Al-Uqlīdisī, Al-Jāh. iz among the Islamic scholars; Fa-Hien, Hiuen Tsang, and I-tsing among the Chinese; and Leonardo Fibbonacci, Pope Sylvester II, Roger Bacon, Voltaire and Copernicus from Europe. Their testimony about Hindu science provide a clear sense of the immense contributions of the ancient Hindus. In the modern era, thinkers and scientists as diverse as Ralph Waldo Emerson, Johann Wolfgang von Goethe, Johann Gottfried Herder, Carl Jung, Max Müller, Robert Oppenheimer, Erwin Schrödinger, Arthur Schopenhauer, and Henry David Thoreau have acknowledged their debt to ancient Hindu achievements in science, technology, and philosophy. In this book, I have used scientiﬁc norms of analysis and have sorted out the hard facts from fantasy. In other words, the analysis here is rational and objective. For important state- ments, I have provided citations to the peer-reviewed literature. This can help the readers to investigate further, if needed. No culture or civilization has prospered to great heights without knowing and preserving their historic and existing knowledge base. Preserving knowledge is a process in which all gen- xii PREFACE erations must participate otherwise the knowledge become prone to be lost forever. This is my mindset in writing this book. After I was done with the manuscript of one of my previous books, Sciences of the Ancient Hindus: Unlocking Nature in the Pursuit of Salvation, I submitted it to an internationally renowned publisher. After about two years of review process, the publisher agreed to publish the book provided I drop the term Hindus from the title and replace with Indian. One reviewer warned me of “the deeply contested nature of the adjective Hindu and its association with a particular kind of nationalist politics” in India. This was prior to Narendra Modi’s government in India. I have no involvement in Indian politics now nor I ever had one at any stage. I have lived most of my adult life in America. I rejected the suggestion since I wanted to be truthful. It has been a challenging and rewarding experience for me to write this book. I hope the readers enjoy reading this book as much as I have enjoyed writing it. Only the readers can judge the validity of this endeavor. Alok Kumar March 2019 Acknowledgments xiii After I completed my book, Sciences of the Ancient Hindus, I told my wife that I would not be writing another book on this topic. I said so since writing a book is a long arduous journey. It was diﬃcult for me to conduct research for the book in the absence of a network of collaborators and proper academic support. I had to work on that book during my oﬀ hours from the job and the family-life suﬀered in the process. Much was changed after I published the above-mentioned book. My family and I realized that this book was not just another academic publication. The book struck a chord with the readers and we were inspired to observe it. It changed our mindset. As a result, when I was approached by the editors of Morgan and Claypool Publishers, I readily accepted their oﬀer. Any arduous task becomes much simpler with a network of capable people to assist. I would like to thank the following people for their assistance: • My wife, Kiran Singh-Kumar, daughter, Aarti Kumar, and mother-in-law, Chaya Singh, provided me constant encouragement and assistance. They are the silent heroes in this project. • My brother, Nand Kishore Sharma, sister-in-law, Bina Sharma, and sister, Pushpa Sharma, who take so much pride in knowing my achievements. • Dr Ved Chaudhary, President of Educators’ Society for Heritage of India (ESHA); Dr Deen Khandelwal, Founder-President, Hindu University of America; Dr Ambalavanar Somaskanda, a medical doctor from Rochester; and Dr. John Kares Smith, my colleague from SUNY Oswego, for reading the ﬁrst draft of the book. They made corrections on the draft, provided valuable suggestions to improve the book, and, above all, provided encouragement. • Chris Hebblethwaite, librarian, who tirelessly searched databases to collect relevant infor- mation for me. His oﬃce was my ﬁrst stop when I could not ﬁnd a speciﬁc information. • Dr. John Zielinski, my colleague in the physics department, who often goes for long walks with me on campus. He was always a willing participant in any discussion related to this book. • Editors, Jeanine Burke and Joel Claypool, for providing me with excellent tips for eﬀective writing. xiv ACKNOWLEDGMENTS I have tried hard to avoid printing and scholarly mistakes. However, if some remain, please bring them to my notice ([email protected]). If you like the book, the credit goes to the people mentioned above. I am responsible for the errors. Alok Kumar March 2019 C H A P T E R 1 Introduction 1 “The ﬁrst nation (to have cultivated science) is Hind. This is a powerful nation having a large population, and a rich kingdom. Hind is known for the wisdom of its people. Over many cen- turies, all the kings of the past have recognized the ability of the Hindus in all branches of knowledge.”1 This was the conclusion that S. ā‘id al-Andalusī (1029–1070) made in his book, T. abaqāt al-‘Umam (Book of the Categories of Nations), in 1068. S. ā‘id lived in Spain and com- piled perhaps the ﬁrst popular book on the global history of science. S. ā‘id analyzed the scholarly contributions of various nations, chose eight nations that were well versed in sciences, and ranked Hind at the top of the list. The people that were described in his book for their contributions to science are: the Hindus, the Persians, the Chaldeans, the Greeks, the Romans, the Egyptians, the Arabs and the Hebrews. S. ā‘id was a Muslim, a historian of science, and a mathematician with interest in astronomy. S. ā‘id, his father, and his grandfather served as religious judges (qād. i) in Spain. In his role as judge, S. ā‘id mastered the sciences of jurisprudence and law, implemented the Sharia law in resolving conﬂicts, served as a mediator, and also supervised and audited the public works. Obviously, such roles were entrusted to persons of repute and inﬂuence. One of his students, Azarquiel (Arzachel or Zarqālī), is known for the famed Toledan Tables. These astronomical tables were used to predict the movements of the Sun, Moon and planets relative to the ﬁxed stars. In the view of S. ā‘id, “[t]he Hindus, as known to all nations for many centuries, are the metal (essence) of wisdom, the source of fairness and objectivity. They are peoples of sublime pensiveness, universal apologues, and useful and rare inventions.” In giving examples of such rare inventions, S. ā‘id mentioned the disciplines of mathematics, astronomy, medicine, and the invention of chess. S. ā‘id’s book was quite popular during the medieval period. During the colonial period, however, the book lost its repute, its contents did not ﬁt well with the colonial agenda, and it was conveniently forgotten. It was introduced to the English-speaking world in 1991.2 S. ā‘id was familiar with the contributions of the Egyptians, Greeks and Romans to science. Yet, while comparing the signiﬁcance of their contributions to science, he chose Hind to be the top nation in science. This is in contrast to what we teach today in sciences. Did S. ā‘id commit an 1Salem and Kumar, 1991, p. 11. In the original manuscript, the same term, Hind, is used to deﬁne the geographical region and the people. In today’s context, the medieval term Hind describes the present India, Pakistan, Bangladesh, Nepal, and Afghanistan, popularly also known as the Greater India. 2Salem and Kumar, 1991. I was reading the scientiﬁc literature produced during the medieval world while researching for my book, Sciences of the Ancient Hindus. I noticed that S. ā‘id’s book was cited by several medieval scholars. I tried to acquire the book and did not succeed. This led to more eﬀorts and ﬁnally the original Arabic version was acquired, authenticated and published with proper translation and annotations. 2 1. INTRODUCTION honest scholarly mistake by placing Hind, also popularly called Bharat, India, and Hindustan, at the top of his list? Was he the only scholar to rank Hind at the top among all other nations in science? What are the important contributions of the Hindus to science? Further, in year 2000, many events were organized and some landmarks were set to cele- brate the new millennium. The American Association for the Advancement of Science (AAAS) tried to compile a list of the top 100 scientiﬁc ﬁndings that made signiﬁcant impacts on the world. It was a major undertaking where quite a few historians of science were involved. Only two discoveries were selected from the non-Western world: (1) invention of zero and (2) the astronomical observations of the Hindu and Mayan skywatchers for agricultural and religious purposes. Both ﬁndings involved the works of the ancient Hindus. Why did the Hindus invent zero as a mathematical entity? What was the connection of astronomical observations with agri- cultural and religious purposes? Did they make any interesting astronomical observations in the process? These are some of the questions that this book has tried to answer. After going through its pages, readers will be able to make their own judgments on these issues. 1.1 THE MULTICULTURAL SCIENCE While covering the ancient and medieval periods, most science courses focus on inventions and discoveries from Greece and Europe. Students learn that scientiﬁc rational thinking orig- inated with the Greeks around the seventh century BCE, and ﬂourished there for about 800 years. Greek philosopher-scientists such as Thales (624–546 BCE), Pythagoras (562–500 BCE), Democritus (460–370 BCE), Hippocrates (460–370 BCE), Plato (427–347 BCE), Aristotle (386–322 BCE), and Archimedes (287–212 BCE) are responsible for most basic ideas in sci- ence. The period after the beginning of the Common era is deﬁned as the Dark Ages (475–1000 CE) or the Middle Ages (475 CE to the Renaissance). The term, the Dark Ages, signiﬁes the lack of intellectual and scientiﬁc activities in Europe. After the fourteenth century, the Europeans reacquainted themselves with the scientiﬁc tradition of the Greeks that led to the European Renaissance. In relation to the Renaissance period, we learn about Galileo, Faraday, Newton, Kepler, and Boyle who lived in Europe. There are not many examples of scientists, discoveries, or inventions that have any connection to Asia, Africa, and Latin America. Science evolves out of human necessities and curiosities. With the growth in science, our lives are constantly changing/improving in myriad ways. The Earth that was considered to be boundless by our ancestors can now be traveled around in a day or two. We have landed on the Moon and are planning our visit to Mars. We can easily make a telephone call to our loved ones halfway around the Earth for a nominal expense. The increased food demand in the past century is met by the green revolution. The life expectancy is increasing all over the world. Most civilizations in the past have found material beneﬁts and intellectual satisfaction in attempting to understand the world’s physical and biological phenomena. Science was bound to prosper in most cultures. The question is why it did not happen in Asia, Africa, the Middle East, and Latin America. Or, may be our science textbooks are simply providing incomplete information. 1.1. THE MULTICULTURAL SCIENCE 3 Indeed, this popular version of our history of science is full of gaps that are ﬁnally catch- ing the attention of scholars. A major gap was ﬁrst demonstrated by Joseph Needham (1900– 1995) with his multi-volume book, Science and Civilisation in China. Needham was a British biochemist and historian who raised the famous question, popularly known as the Needham question: “Why did modern science, the mathematization of hypotheses about Nature, with all its implications for advanced technology, take its meteoric rise only in the West at the time of Galileo [but] had not developed in Chinese civilisation or Indian civilisation?” Needham an- swered this question in his book with a speciﬁc focus on China and proved that the history of science that we teach in science courses is simply incomplete. No such major eﬀort to compile Indian science has taken place so far for a variety or reasons. The present book is a small eﬀort to ﬁll that gap. Roger Bacon (1214–1294), a noted Franciscan natural philosopher from England, wrote a book, The Opus Majus, under the instruction of Pope Clement IV (1190–1268). The main purpose of the book was to improve the training of missionaries to Christianize distant ethnic lands.3 This book clearly establishes that India was a leader in science. Bacon knew the works of Ibn al-Haytham (Alhazen)4 (965–1040 CE), Al-Battānī (858–929 CE), and Ibn Sīnā (980– 1037 CE) from the Middle East. He also knew about the Hindu science from his days in the University of Paris.5 Geoﬀrey Chaucer (c. 1343–in the Prologue of his Canterbury Tales6, writes about a physi- cian who was well versed with the works of Serapion the Elder of Syria, al-Rāzī and Ibn Sīnā of Persia, along with the works of Hippocrates, Rufus of Ephesus, Dioscorides and Galen: “With us ther was a Doctour of Phisyk In al this world ne was ther noon him lyk To speke of phisik and surgerye, 3Roger Bacon was not the only one who worked tirelessly to produce a book to assist the training of missionaries to Christinize India. Max Müller, Professor of Comparative Philology, Robert Boyle, Director of the East India Company, and Monier Monier-Williams, Boden Professor of Sanskrit in Oxford University, are some other noted scholars who produced literature or used their resources to assist missionaries to Christinize India. Monier-Williams even candidly wrote that the purpose of translation was to aid in “the conversion of the natives of India to the Christian religion.” (Goldberg, 2010, p. 28.) Another person who made a signiﬁcant impact to achieve this goal was Lord T. B. Macaulay (1800–1859), member of the Supreme Council of India. In this capacity, in his Minute on Indian Education, he suggested the British empire to introduce western-based reforms in Indian schools. This document became quite successful. Macaulay believed that (1) “a single shelf of a good European library was worth the whole native literature of India and Arabia” and (2) “all the books written in the Sanscrit [Sanskrit] language are less valuable than what may be found in the most paltry abridgments used at preparatory schools in England.” With this mindset, the education policy of India was framed during the colonial period. Lord Macaulay’s reforms largely remained in place in India even after the independence. 4The year 2015 was declared as the “Year of Light” by the United Nations to emphasize the importance of light science and to celebrate 1,000 years of Ibn al-Haytham’s book, Kitāb al-Manazir, a book on optics. Several centuries later, many noted scientists, such as Roger Bacon, Robert Grosseteste, Leonardo Da Vinci, Galileo Galilei, Christiaan Huygens, René Descartes, Johannes Kepler, and Issac Newton, had studied optics from a Latin translation or the original Arabic copy of his book. Some of them wrote their own books on optics later. 5Smith, a chapter, The Place of Roger Bacon in the History of Mathematics, in the book by Little, 1914, p. 156. 6The Canterbury Tales, Prologue, 411–413, 429–432. It is interesting to note the evolution of the English language in the past millennium. 4 1. INTRODUCTION Wel knew he the olde Esculapius, And Deiscorides, and eek Rufus, Old Ypocras, Haly, and Galien, Serapion, Razis, and Avicen” England, France, Spain, Portugal, and the Netherlands controlled most of the world dur- ing the eighteenth century. Popular literature was produced and disseminated by European na- tions to support their dream of domination. In this literature, Egypt, India, Persia, and China entered the scientiﬁc age only through their interactions with the Europeans. Thus, the histories of Asians, Africans, and other indigenous peoples often appear only after their encounter with the Europeans.7 Though the British and French governments were brainwashing these ethnic civilizations with their propaganda, they were recruiting their best scholars and scientists to learn from these ethnic cultures. For example, when Napoleon Bonaparte (1769–1821) invaded Egypt, he took about 150 biologists, mineralogists, linguists, mathematicians, and chemists with him to learn Egyptian science. This group included mathematician Jean-Baptiste Joseph Fourier, mineralo- gist Déodat Guy Grater de Dolomieu, and botanical artist Pierre Joseph Redouté.8 Why did Napoleon take the best scientists of France to Egypt in a war? Napoleon had brought 400 ships, 40,000 soldiers, and 167 scientists, engineers, and artists to Alexandria. In less than a month, he lost to the British soldiers led by Admiral Horatio Nelson. Yet his mission was a magniﬁ- cent triumph. The savants (as French scientists and philosophers were called) had uncovered an invaluable treasure of relics in Egypt, including the Rosetta Stone, and established the Institut d’Égypte in Paris, the ﬁrst institution in the world devoted to Egypt’s ancient culture. Thus, in Western literature, the history of Asians, Africans, or the indigenous peoples of the Americas often appears to begin only after their encounter with European people. Science is thus Eurocentric and incomplete in the process. This omission of the non-Western literature in the history of science is “deeply unjust to other civilizations. And unjust here means both untrue and unfriendly, two cardinal sins which mankind cannot commit with impunity,” writes Joseph Needham.9 The failure to mention multicultural contributions in present-day science education has been noted by many scholars who have provided examples after examples of historical gaps in their books.10 For example, the Greek philosopher Leucippus (born ca. 490 BCE) or his disciple Democritus (born 470 BCE) are generally credited for being the originators of the atomic theory. The contemporaneous Indian philosopher Kan. āda, who lived sometime between 7This topic caught the attention of scholars during the later part of the twentieth century. However, considerably more research is needed to better understand the contributions of other civilizations. For more information, consult Baber, 1996; Goonatilake, 1984, 1992; and Said, 1978 and 1993. 8For more information, read Brier, 1999. 9Needham in Nakayama and Sivin, 1973, p. 1. 10Bernal, 1971, Harding, 1991, 1994; Needham, 1954–99; Rashed, 1996; and Teresi, 2002. This knowledge is yet to be incorporated appropriately in introductory science textbooks. 1.1. THE MULTICULTURAL SCIENCE 5 the sixth to tenth centuries BCE, is simply ignored in most science texts. Henry Margenau (1901–1997), a noted philosopher-physicist who served as Eugene Higgins Professor of Physics and Natural Philosophy at Yale University, pointed to this gap in his book, Physics and Philosophy, and wrote, “But the most remarkable feature . . . which I have never seen in American textbooks on the history of science is the atomic theory of philosopher Kanada [Kan. āda].”11 This is not an American issue, as listed by Henry Margenau; it is an academic issue that is global in scope. Kan. āda’s work is still not covered in science texts even in India, the region where he was born and lived. As mentioned earlier, the colonial education pattern established by Lord Macaulay still continues in India, a sad reﬂection of the still pervasive colonial mindset of Indian academia. Although progress is being made, it is at a very slow pace. We have a long way to go to establish science as a truly global enterprise. A signiﬁcant number of articles and books have been published in the last 25 to 30 years to add contributions from Islamic countries, includ- ing an Encyclopedia of the History of Arabic Science.12 The scholarship on the Indian, Egyptian, and Mayan civilizations is still highly incomplete. Our new knowledge on Islamic science and Chinese science happened due to the large inﬂux of money and human resources from China and the Middle East. In contrast, the governments from Latin American countries, India, and Egypt have not allocated much resources for this cause. We need another Joseph Needham(s) to raise resources and preserve the knowledge of these civilizations. The time is now. India, Egypt, Baghdad, and Persia were centers of learning, along with Athens and Rome, during the ancient and/or early medieval periods. For example, the place-value system to write numbers that was invented by the Hindus is central to the growth of mathematics. Many of the medicinal treatments, surgical procedures, and anatomical knowledge came to the West from the Caraka-Sa ˙mhitā and the Suśruta-Sa ˙mhitā of India, the Edwin Smith Surgical Papyrus, the Ebers Papyrus, and the Kahun Papyrus of Egypt, and the Book of Healing and the Canon of Medicine of Ibn Sīnā of Persia. Similarly, the modern astronomy owes a lot to the works of Āryabhat.a I (ca. 500) from India and al-Khwārizmī from Baghdad. The Islamic inﬂuence on science is evident from the Arabic terms that are commonly used in science: alcohol, Aldebaran, algebra, almanac, alkali, algorithm, Altair, azimuth, Betelgeuse, calendar, Deneb, magazine, monsoon, nadir, ream, and zenith are all derived from the Arabic language. These words have become a part of the Western heritage and are listed in most English dictionaries. A similar list of Sanskrit words in English is provided in Chapter 9. The three crucial inventions that inﬂuenced the modern world came from China: paper, gunpowder, and magnetic compass. Paper remained the most important tool for documentation for over a millennium after it was recently replaced by digital electronic technologies. Magnetic compass allowed traveler to navigate through an ocean while the gunpowder became a tool of conquest and subjugation after its use was discovered for making guns and cannons.13 11Margenau, 1978, p. XXX. 12Hogendijk and Sabra, 2003; Kennedy, 1970; King, 1983 and 1993; Kunitzsch, 1989 and 1983; Rashed, 1996; Saliba, 1994; Samsó, 1994; and Selin, 1997 and 2000. 13The list of such contributions is long, and is covered by Kumar, 2014; Montgomery and Kumar, 2015. 6 1. INTRODUCTION 1.2 THE ANCIENT HINDU SCIENCE As mentioned in the previous section, the modern place-value notation system (base 10) that is used to represent numbers, is Hindu in origin. In this system we write, for example, eleven as one and one, side by side (11). The one on the left is in the second place, as we count from the right to left. The magnitude of this one (1) on the left is equal to ten. Any number in this place has to be multiplied by ten. Practically all cultures invented their own number system: the Greeks, Romans, Egyptians, Babylonians, Mayans, and Chinese. The Greeks, the Romans, and the Egyptians did not use a place-value notational system although they did use base-10 system. In their systems, eleven was written as ten and one (for example, XI in the Roman system). The Hindu place-value notation system made it possible to write very large numbers and simpliﬁed mathematical calculations; therefore, it prevailed over the other systems. Just imagine reading the values of various stocks in a newspaper. It is easy to ﬁgure out that a number with three digits will be greater than a number with two digits. Similarly, a number with four digits will be greater than a number with three digits. It provides a quick comparison which is not possible with other systems. It also allows much faster arithmetical calculations. Nicolaus Copernicus (1473–1543) in his book, On the Revolutions, used Hindu numerals in mathematical computations to provide a heliocentric model of the solar system. He noted the usefulness of this system over the Roman or Greek numeral system for quick computations. Copernicus was not the ﬁrst one to use Hindu numerals. Several hundred years before him, Leonardo Fibonacci (1170–1250) wrote a popular book, Liber Abaci, and introduced the Hindu methods of numeration and computation to the Western world. S. ā‘id al-Andalusī wrote about the presence of this numeral system in Spain during the eleventh-century. (Read Chapter 3). Trigonometry deals with relationships involving lengths and angles of right-angled tri- angles. Such mathematical relationships are highly applicable in the disciplines of architecture, mathematics, physics, and astronomy. With the work of Āryabhat.a I (ca. 500), trigonometry began to assume its modern form. He used the half chord of an arc and the radius of a circle to deﬁne the sine of an angle.14 The origin of the subject of trigonometry and word “sin,” used to deﬁne trigonometric function “sin” (pronounced as sine), can be traced to the Sanskrit language. (Read Chapter 3). About a millennium before Copernicus, Hindu astronomer Āryabhat.a I assigned mo- tion to the earth. He considered motion of the planets and considered stars to be stationary. Āryabhat.a I used the analogy of a boatman in a river, observing objects on the shore moving backward, to explain the apparent motion of the Sun and other stars. He explained the con- cept of relative motion many centuries before its more formal discussion by the noted Parisian scholar Nicholas Oresme in the fourteenth century.15 Interestingly, Copernicus used more or less the same analogy of a boatman to explain the apparent motion of the Sun in his book, On the Revolutions (Book 1, Chapter 8). (Read Chapter 4). 14Clark, 1930; Kumar, 1994. 15Kumar and Brown, 1999. 1.2. THE ANCIENT HINDU SCIENCE 7 The ancient Hindus deﬁned the age of the universe to be of the order of billions of years. This large number assigned to the age of the universe intrigued Carl Sagan, a noted astrophysicist who is famed for his Cosmos TV series. He wrote: “The Hindu dharma is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an inﬁnite, number of deaths and rebirths. It is the only dharma in which time scales correspond to those of modern scientiﬁc cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long, longer than the age of the Earth or the Sun and about half the time since the Big Bang.” (Read Chapter 4.) The ancient Hindus deﬁned standards for physical measurements of space (length), mass, 4 second, as noted by and time. The smallest unit of time used in India was of the order of 10(cid:0) al-Bīrūnī, the Islamic scholar who visited India during the eleventh century. These standards were prevalent in India at least 500–1000 years before al-Bīrūnī. Similarly, multiple standards of length were also deﬁned and, in Mārkan. daya-Purān. a, the size of an atom was deﬁned of 9 meter. Kaut.ilya (4th century BCE) deﬁned various lever arms and scale-pans the order of 10(cid:0) for balances for diﬀerent range of weights. Superintendents were assigned to stamp labels for diﬀerent weight-standards for public use to prevent cheating. Traders who did not use these stamped standard weights in business transactions were ﬁned. Kan. āda, in his Vaiśes. ika-sūtra, deﬁned the concept of atom while discussing the distinctive properties of diﬀerent matters and considering inﬁnite divisions of matters. (Read Chapter 5). Caraka, Suśruta, and Kaut.ilya documented chemical transformations where oxidation, reduction, calcination, distillation, and sublimation were explained. Caraka, in his Caraka- Sa ˙mhitā, lists gold, copper, lead, tin, iron, zinc, and mercury in making drugs. Mining was a highly organized activity among the ancient Hindus. Kaut.ilya deﬁnes the role of mining for a sound economy. The Iron Pillar near Qutub-Minar in New Delhi is a testimony to metal forg- ing of the ancient Hindus. The pillar, although about 1600 years old and weathering the heat, humidity, and rain in the open air, is still rust-free. We only hope that the car manufacturers of today can learn this ancient technology from India to make better rust-free cars. Hardened steel was also produced to allow a warrior to enter in a battleﬁeld without worrying about breaking or bending his sword. This steel, though invented in India, is popularly known as Damascus steel. The Europeans ﬁrst learned of this process from Damascus where it was called “steel of India.” King Poros of Sindh, a province of India (now in Pakistan), after receiving a gift of life from Alexander the Great, gave 6,000 pounds of steel as precious gift to Alexander. (Read Chapter 6). Plants have life; they try to protect themselves from the predators or attract bees for pol- lination purposes. At a time when human activities are destroying the ecology, the ecological perspectives of the ancient Hindus are relevant where rivers, mountains, plants, and animals are deemed sacred. The principle of ahi ˙msā as a moral principle and its consequences on global warming and world hunger are discussed in the chapter on biology. (Read Chapter 7). The so-called plastic surgery and cataract surgery ﬁnd its roots in the surgical skills of the ancient Hindus. The role of a doctor and a patient, the design of a hospital, the role of food and 8 1. INTRODUCTION and the quality of air and water were considered by the ancient Hindus. They emphasized the body-mind approach to medicine and evolved ayurveda or “science of life,” a system of medicine. (Read Chapter 8). Ralph Emerson, Henry Thoreau, Leonardo Fibonacci, Schrödinger, Tolstoy, Tesla, Goethe, Schopenhaur, Robert Oppenheimer, Brian David Josephson (known for Josephson junction in physics) are some of the leading western thinkers who studied the scholarly work of ancient Hindus and formed their own worldview based on it. Similarly, on the east of In- dia, Xuanzang (also known as Hiuen Tsang), Faxian (also known as Fa-Hien or Fa-Hsien), Yijing (also known as I-Ching, I-Tsing) were the leading scholars in China. These scholars are as much known for their wisdom as their arduous journeys to India to collect scholarly books. Similarly, on the West of India, Al-Jāh. iz, (ca. 776–868 CE), al-Khwārizmī (ca.800–847 CE), al-Uqlīdisī (ca. 920–980 CE) and Ibn Labbān (ca. 971–1029 CE), all noted Islamic philoso- phers, are known as much for their scholarly activities as for their eﬀorts to introduce Hindu wisdom to the Middle East. These Islamic scholars were quite honest in writing their books, as they should be, and openly acknowledged their gratitude to the Hindus. (Read Chapters 3, 4, and 9). 1.3 ABOUT THE BOOK This book explains the religious, social and cultural contexts that allowed some distinctive in- ventions and discoveries in Hindu science. For the Hindus, the disciplines of physics, chemistry, mathematics, astronomy, and medicine were sacred. A mastery of either of these disciplines al- lowed a person to achieve moks. a (liberation from the cycle of birth and death), the highest goal of life for any Hindu. This book primarily deals with the ancient period when the sacred books of the Hindus were composed(Vedas, Upanis. ads, and Purān. as) and ends after the work of Āryabhat.a I, the ﬁfth-century. Therefore, the works of Brahmagupta, Bhāskara, and Mādhava, all prominent Hindu natural philosophers, are not included. Later contributions are covered in a few selective cases to know the impact of the ancient period. Since the works of the ancient Hindus took many centuries to become known to the Arabs and then to the Europeans, the later accounts from these cultures are discussed. For example, al-Bīrūnī’s work during the eleventh century is discussed in relation to Āryabhat.a I’s work. The works of Emerson, Thoreau, Schrödinger, and Oppenheimer are discussed in connection to Vedanta or the Bhagavad-Gītā. Similarly, the work of Jagdish Chandra Bose related to plants is discussed in relation to Mahābhārata, an epic, where life in plants is explained in detail. Copernicus’ comment about the usefulness of the place-value notation and his work in astronomy are discussed, although the works were done during the sixteenth-century. The religious philosophy of the ancient Hindus may have played a crucial role in the in- vention of zero. The ancient Hindus tried to explain the nature of God that is devoid of all 1.3. ABOUT THE BOOK 9 attributes (Nirgun. a-swarūpa or amūrta). This religious and philosophical approach of attribute negation or nothingness (śūnyatā) led them to the mathematical entity of inﬁnite and zero. In Chapter 2, readers will also learn the role of śāstrārtha (debate or discussion on the meaning of sacred texts) in resolving personal, social, and religious disputes. Conﬂicts were resolved without any rancor or violence. Even marriages were arranged using this practice (svaya ˙mvara). Also, the ancient Hindu literature was mostly written as poetry in lucid stories that are rich in similes and metaphors in order to facilitate its memorization and oral trans- mission. As a result, despite the destruction of libraries in the Indian peninsula after the Islamic invasion, this knowledge remained intact to a large extent. Pythagoreans in Greece also practiced orality to preserve their knowledge, like the ancient Hindus. “Why do they call it by this name?” This etymological question is often asked by curious students. The epistemology and origins of various words and concepts that are commonly used in science texts, such as the so-called Arabic numerals, the zero, the trigonometric function “sine,” algebra, and algorithm, are explained in this book. Information on these developments demonstrates the migration of knowledge from one culture to another and helps the readers to understand the multicultural nature of science. The worldwide use of the Hindu numerals is perhaps a great triumph of the ancient Hin- dus. Although Hindu numerals were not accepted at ﬁrst, rivalries had ensued in Arabia and Europe, decrees were issued against their use; their practical merit and their usefulness in math- ematical calculations ﬁnally established their supremacy and they gradually became prevalent worldwide. Leonardo Fibbonacci (1170–1250) is well known for Fibbonacci’s Sequence. How- ever, little is known about his gratitude to the ancient Hindus, as he had clearly acknowledged in Liber Abaci. Kan. āda’s book, Vaiśes. ika-Sūtra, deﬁnes the nature of time and space, conservation of mat- ter, gravitation, and the concept of the atom. Time is a commonly used word in our daily con- versation. However, its nature is enigmatic and subtle. Readers will learn the subtleties in the concept of time in Chapter 5. They will also learn the concept of the atom, as suggested by Kan. āda, and its comparison with Democritus’ atom. This book is written primarily for readers who are trained in the Western knowledge sys- tem and are interested in learning about Hindus’ contributions to science. Many references are deliberately chosen from the primary sacred literature of the Hindus as well as authentic sec- ondary sources from the Western sources. Such a selection is made to counter a general skepti- cism demonstrated by some Western scholars concerning Hindu accounts of their history. These Western scholars generally complain that scholars in the East tend to stretch their imaginations to suit their views and do not provide logical steps and facts when deriving their conclusions. A hallmark of this book is in the documentation of the scholarly comments and acknowledge- ments made by Greeks, Persians, Egyptians, Arabs, Chinese, and Europeans in support of the scientiﬁc achievements of the ancient Hindus. Salient features of this book are in providing 10 1. INTRODUCTION cross-cultural perspectives and comparisons, and portraying a coherent picture of the scientiﬁc contributions of the ancient Hindus. This book is not encyclopedic or compendious. It is not possible to achieve that in such a small introductory work since the ancient Hindu literature is vast. This book presents only the “tip of the iceberg,” as the saying goes. I have chosen only those topics where my knowledge and interests lie. Several Sanskrit and Hindi words are now commonly used in English and have entered in English dictionaries. However, their English spellings in some cases are not in accordance with the system of transliteration. As these words are in common use in the English-speaking world, using any other spelling might create confusion for a broad range of readers. For this reason, we have kept the popular usage in some cases. For example, the spelling of the word “ayurveda,” as mentioned in most dictionaries, is incorrect; the proper spelling is āyurveda. For Sanskrit terms that are not present in most English dictionaries, diacritic marks have been retained. To keep the book readable, simple, and enjoyable to non-scholars in the ﬁeld, an amalgamated system of popular spelling as well as proper spelling is used. It is a common practice among scholars dealing with non-English literature. I have used scientiﬁc norms of analysis and have sorted out the hard facts from fantasy. In other words, the analysis here is rational and objective. In philosophy and mysticism, there are several areas where the ancient Hindu literature stands abreast with the later concepts in science, such as causality and duality (or dualism). But these concepts are not covered in this book, because the borderline between facts and opinion is hazy.16 Duality, as deﬁned in the concept of the Creator and the creation as two independent entities, in Hindu philosophy, is quite diﬀerent from the de-Broglie’s Wave-Particle Duality of matter. The parallelism between ancient theories and modern science is fascinating to read; but in many cases, this is where the connection ends. The works of noted Noble Laureate physicists such as Brian Josephson and Erwin Schrödinger do pose an interesting dilemma in which their beliefs, based on the ancient Hindu literature, played a signiﬁcant role in their discoveries in science.17 In the Lawrence Livermore Laboratory in California, the Shiva Target Chamber is a 20- laser-beam facility to study laser fusion. This facility was constructed in 1977. Edward Teller, the father of the hydrogen bomb and a designer of this facility, explained the design of the chamber in the following words: “Laser light is brought in simultaneously from ten pipes on the top and ten pipes on the bottom. Compression and nuclear reaction occurs in a tiny dot at the middle of the sphere. Apparatus practically ﬁlling a whole building feeds the twenty pipes, or the arms of the god Shiva [Śiva]. According to Hindu Creed, Shiva [Śiva] had three eyes: two for seeing, and one (usually kept closed) to emit annihilating radiation. The Hindus obviously knew about 16The Tao of Physics by Fritzof Capra, The Wu Li Masters by Gary Zukav, and Mysticism and the New Physics by Michel Talbot are examples of such works. These books are bestsellers for their insights. These are scholarly works that brought together the disciplines of religion and science. 17Read Capra, 1980; Josephson, 1987; Restivo, 1978 and 1982; Schrödinger, 1964; Talbot, 1981; and Zukav, 1979. 1.3. ABOUT THE BOOK 11 lasers.”18 Is it really true that the Hindus “knew about lasers”? Perhaps not. In my mind, what Teller has mentioned is a mere conceptual notion of Hindus in an immensely powerful laser like light that can destroy every thing in an instant, like the third eye of Lord Śiva, but it cannot be cited as a historical fact or an established theory. The term Hindu was commonly used in science texts in the last century.19 The leading journals of science, like The American Mathematical Monthly, ISIS,20 Islamic Culture, Science, and The Mathematical Gazette and many books used the term Hindu science in the past. However, such usage is less these days since some authors are concerned about the reaction of the readers.21 For example, Philip Goldberg, in his bestseller book, American Veda, avoided the term Hindu because he was concerned that “many potential readers would miscontrue the nature of the book.”22 In my previous book, Sciences of the Ancient Hindus, a reviewer warned me of “the deeply contested nature of the adjective Hindu and its association with a particular kind of national politics” in India. I have ignored such concerns. I do not have any involvement with the politics of India, nor do I want to push any political agenda through this book. The Vedas, the Upanishads, and Purān. as are the sacred books of the Hindus. I want my book to be based in truth. Once the readers realize the truthfulness of my assertions, I am conﬁdent that such myopic criticisms will disappear. “A class in arithmetic would be pleased to hear about the Hindoos [Hindus] and their invention of the ’Arabic notation’,” suggested Cajori.23 “They will marvel at the thousands of years which elapsed before people had even thought of introducing into the numeral notation that Columbus-egg—the zero.”24 It is this Columbus-egg, the zero, that is captivating the historians of science in AAAS as they include zero among the top 100 scientiﬁc ﬁnds that made signiﬁcant impact in human history, as discussed earlier. 18Teller, 1979, p. 216. 19Datta, 1927; Hammett, 1938; Herschel, 1915; Karpinski, 1912; Mukhopādhyāya, 1994; Ray, 1919 and 1956; Renfro, 2007; Royle, 1837; Saidan, 1965; Seal, 1915; Zimmer, 1948. 20It is a mere coincidence that this term is also associated with a terrorist organization. The journal ISIS is a premier journal of the history of science. 21I am pleased that there are no such concerns with Islam and Buddhism where a good number of new book titles are published every year with explicit mention of religion. 22Goldberg, 2010, p. 2–3. 23Cajori, 1980, p. 3. Florian Cajori (1859–1930) was a professor and the ﬁrst chair in history of mathematics at the University of California at Berkeley. Many of his books on the history of mathematics are still a landmark. 24Cajori, 1980, p. 3. Columbus-egg, a term that Cajori related to the invention of zero, refers to a brilliant discovery or idea that looks simple after fact. C H A P T E R 2 13 The Building Blocks of Science As explained in the ﬁrst chapter, human necessities play an important role in the evolution of science. People set up their goals based on their personal needs or the needs of the society and achieve them with the help of science. What were the geographical, social, and religious conditions that allowed the growth of science among the ancient Hindus? How did the ancient Hindus preserve their scientiﬁc knowledge and transmit it to the following generations? How people who contributed to Hindu science were treated in their society? These are important questions that need to be explored to understand the social, cultural, and religious contexts of the development of science among the ancient Hindus. The sciences of the ancient Hindus were an essential and integral part of their religious practices. An important tenet of Hinduism is in the transmigration of soul which is deﬁned in so many ways in the Vedas and Upanis. ads. This doctrine tells us that the soul is immortal and it transmigrates or reincarnates from one life form to another.1 Our deeds in this life decide our fate in the next life. Therefore, the notion of rebirth is tightly coupled with the notion of karma (action) that provides a great incentive toward leading a moral life minimizing wrong deeds. Pythagoras, Socrates, Empedocles, Plato, Plotinus, Apollonius, and other Pythagorean philosophers also believed in the transmigration and immortality of the soul. “The soul is neither born, nor dies. This one has not come from anywhere, has not become anyone. Unborn, constant, eternal, primeval, this one is not slain when the body is slain. If the slayer think to slay, if the slain think of himself slain, both these understand not. This one slays not, nor is slain,” suggests Kathā-Upanis. ad.2 “Either as a worm, or as a moth, or as a ﬁsh, or as a bird, or as snake, or as a tiger, or as a person, or as some other in this or that condition, he is born again here according to his deeds, according to his knowledge,” suggests Kaushītaki-Upanis. ad.3 The goal of life is to avoid this cycle of birth and death and achieve liberation (moks. a). As a mother nourishing her children, gives capāti (chapāti or rotī, a ﬂat bread) and dāl (lentils) to one, and khicad. ī (a rice and lentil preparation) and yogurt to another; similarly, according to their needs, the Hindu religion oﬀers four major choices to human rational minds, and allows individuals to choose their own path to liberation: 1. Karma-yoga (the Path of Action, Selﬂess Service to Humanity) 1Atharvaveda, 12: 2: 52. 2Kathā-Upanis. ad, 2: 18, 19. 3Kaushītaki-Upanis. ad, 1: 2. 14 2. THE BUILDING BLOCKS OF SCIENCE 2. Bhakti-yoga (the Path of Devotion or Love to God) 3. Jñāna-yoga (the Path of Knowledge of Ultimate Truth) 4. Rāja-yoga (the Path of Yoga and Meditation) All paths are equally eﬀective. It is up to an individual to select the appropriate path for himself or herself. Jñāna-yoga (Jñāna means knowledge), the path relevant here, encourages an individual to understand the ultimate truth by raising such questions as, “Who am I?”, “Why am I here?”, or “What is the purpose of my life?” This mode of Socratic questioning allows self-introspection; the person discovers the ultimate truth from within. Like Socrates suggested in Greece, the Bhagavad-Gītā tells us that one can ﬁnd knowledge from within and perfect it by yoga: “There is no better means of achieving knowledge; in time one will ﬁnd that knowledge within oneself, when one is oneself perfected by yoga.”4 “We contemplate that adorable glory of the deity, that is in the earth, the sky, the heaven! May He stimulate our mental power.”5 This hymn is the popular Gāyatri-mantra that is chanted over and over by millions of Hindus as a ritual prayer every day. The mind is the primal source of our knowledge. Our ﬁve senses would not function with- out the mind. It is the mind that unravels most of the obstacles that we face from day to day. One can even achieve liberation (moks. a) through the exercise of mind to comprehend the ultimate truth. For this reason, knowledge has always remained so central to the Hindus. If knowledge is the key to salvation, then the issue of ownership of knowledge and deﬁning spatio-temporal attributes associated with knowledge become trivial issues. Therefore, the ancient Hindus did not care much to deﬁne the period or author of their knowledge. This practice contrasts greatly with the Western tradition. As Charles Eliot elucidates: “They [Hindus] simply ask, is it true, what can I get from it? The European critic, who expects nothing of the sort from the work, racks his brain to know who wrote it and when, who touched it up and why?”6 Hindu tradition has subordinated the pride of authorship, invention, or discovery to the self-satisfaction one gains from discovering the truth and sharing it with the world in the spirit of selﬂess service to humanity. While this avoids the cult of personality, it results in a lack of chronological records of discoveries and inventions. This explains why Hindus had developed such a vast literature yet there is no chronological records, so valued by the Western historians. The ancient Hindus did not separate the disciplines of astronomy, mathematics, chem- istry, physics, yoga, and medicine from moral codes, prayers, and the so-called divine literature. These scientiﬁc disciplines were labeled as sacred disciplines, necessary to know the ultimate knowledge. The Chāndogya-Upanis. ad cites an incidence in which the vagabond saint, Nārada, approaches another sage, Sanatkumāra, to learn about the ultimate knowledge—a knowledge 4Bhagavad-Gītā, 4: 38. 5R. gveda, 3: 62: 10. 6Eliot, 1954, vol. 1, p. LXVII. Charles Norton Edgecumbe Eliot (1862–1931) was a botanist, linguist, and diplomat. He was the British ambassador to Japan and was ﬂuent in 16 languages and could converse in another 20 languages, including Sanskrit. 2. THE BUILDING BLOCKS OF SCIENCE 15 that could provide him freedom from sa ˙msāra (worldly manifestation) and lead to liberation (moks. a). As all good teachers do, Sanatkumāra asked Nārada to apprise his existing knowledge base, so that an appropriate lesson can be designed. Nārada pointed out astronomy (Naks. atra- vidyā) and mathematics (rāsi-vidyā), along with logic, history, grammar, ﬁne arts, and the four Vedas as the knowledge that he had already mastered in his eﬀorts to achieve moks. a.7 In Hindu tradition, secular knowledge (aparā-vidyā) is considered to be helpful in achiev- ing liberation, along with spiritual knowledge (parā-vidyā), as advised in Mun. d. aka-Upanis. ad.8 When Śaunaka, a seeker, went to A ˙ngirās, a teacher, and asked: “By knowing which a man comes to know the whole world.” A ˙ngirās’ reply included a long list of disciplines, such as as- tronomy, the sacred Vedas, Sanskrit grammar, etymology and metrics, as suggested in Mun. d. aka- Upanis. ad.9 The natural philosophy of Hindus fulﬁlls the spiritual needs of people as well as their need for rational thinking. It is for this reason that Ārybhat.a I, in his book Āryabhat. īya, cov- ering astronomy, mathematics, and physics, suggested that one can achieve Brahman (moks. a) by becoming well versed in the disciplines of astronomy, physics, and mathematics.10 Similarly, Kan. āda, in his book Vaiśes. ika-sūtra, deﬁned the physical properties of matter and suggested that the knowledge is helpful in achieving moks. a.11 Also, the Agni-Purān. a suggests that knowledge of the human anatomy can also lead to moks. a. “Said the God of Fire: Now I shall describe the system of veins and arteries [Nād. ī-cakra] that are to be found in the human body. A knowledge of these [arteries and veins] leads to a knowledge of the divine Hari [God].”12 Scientiﬁc activities had important functions that were valued in the ancient Hindu society. For example, the role of astronomers was to ﬁx the calendar, to set dates of religious festivals, and to predict eclipses and other astronomical events. These disciplines and duties became as important as composing and promoting moral codes. Learning human anatomy and functions helped in treating diseases in people and animals. Knowing science had another important function: One way to know about the Creator (God) is to learn about God’s creation. Science is an important tool to learn the physical prop- erties of the created universe. Creation is the physical phenomenon that can tell us about the Creator. For this reason, Albert Einstein once wrote: “I maintain that the cosmic religious feel- ing is the strongest and noblest motive for scientiﬁc research. Thus, science became a tool to learn about the God. . . in this materializtic age of ours the serious scientiﬁc workers are the only profoundly religious people.”13 7Chāndogya-Upanis. ad, 7: 1: 2–4. 8Mun. d. aka-Upanis. ad, 1: 1: 3–5. 9Mun. d. aka-Upanis. ad, 1: 1: 5 10Āryabhat. īya, Daśgītika, 13. “Whoever knows Daśgītika Sūtra [ten verses] which describes the movements of the Earth and the planets in the sphere of the asterisms passes through the paths of the planets and asterisms [stars] and goes to the higher Brahman [God].” 11Vaiśes. ika-Sūtra, 1: 1: 4. 12Agni-Purān. a, 214: 1–5. 13Einstein, 1930. 16 2. THE BUILDING BLOCKS OF SCIENCE Progress in science has never been a hindrance to spiritual growth in the history of Hin- duism. Knowing the truth was the main focus. Thus, science could grow freely and indepen- dently and no artiﬁcial boundaries within the moral codes limited the scientists in their investi- gations. This led al-Mas‘udī (d. 957 CE), an Islamic historian during the tenth century, to write that science and technology were established without the aid of religious prophets in India. In his opinion, wise men could deduce the principles without the need of religion. It is not the prophets who dictated the domain of science, it was the logic, intuition, and experience of dili- gent observers who contributed to the domain of science. Al-Mas‘udī considered Hind (India) as the land of “virtue and wisdom.”14 This is in contrast to prolong periods in some parts of the world where a chasm existed between science and religion and people had to make a choice between the two. It is well known that Bruno and Michael Servetes were burned to death and Galileo was imprisoned when their scientiﬁc beliefs were in conﬂict with the religious doctrines during the Inquisition period in Europe. The lofty heights reached by the ancient Hindus in the realm of philosophy and religion are well recognized and extensive literature exists on these topics.15 However, not much is known in the popular literature about their contributions to the natural sciences. The sciences of the ancient Hindus are embedded in their religious books, along with other disciplines. In ancient India, the various domains of knowledge, including science and religion, progressed hand-in- hand and grew under the shelter of one another. Religion ﬂourished with the help of science and science ﬂourished with the multi-faceted development of religion. 2.1 GEOGRAPHY The current boundaries of India lie in the Northern Hemisphere between 8(cid:14)40N to 37(cid:14)60N lati- tudes and from 68(cid:14)70 E to 97(cid:14)250 E longitudes. Thus, the latitudinal as well as the longitudinal extent of India is about 29 degrees. Although India accounts for only 2.4 per cent of the world’s total land area, it sustains 16 percent of the world population. The Tropic of Cancer (23(cid:14)300 N) divides the country into two equal halves: (1) the southern half lies in the tropical zone while the northern half belongs to subtropical zone. India has the Himalayan mountain range in the north, Vindhya mountain range in the middle, Indian Ocean in the south, Thar desert and Pun- jab plain in the west, forested mountains in the north-east, and tropical and watershed region of the Indo-Gangetic Plain in the east. The high Himalayan mountain range, with the tallest peak of mount Everest, blocks the frigid wind from the Tibetal Plateau and augurs temperate climate in the north. The south, in contrast, is always warm and humid. Thus, the geography of India provided all diﬀerent kinds of climate. With this geography comes vast mineral resources, and a great diversity of ﬂora and fauna. It was easy for its inhabitants to meet their basic needs for food and shelter. The climate allowed a lifestyle where they could be close to the nature. The high population density in India is sus- 14Khalidi, 1975, p. 102–106. 15Dasgupta, 1922–1955; Durant, 1954; and Radhakrishnan, 1958. 2.2. THE POWER OF QUESTIONING 17 tainable due to the favorable climatic conditions. Ralph Waldo Emerson (1803–1882 CE), an eminent American philosopher and poet, who lived in the northeast region of America where the temperature during the winter season is frigid, wrote: “The favor of the climate, making sub- sistence easy and encouraging an outdoor life, allows to the Eastern nations a highly intellectual organization, - leaving out of view, at present, the genius of Hindoos [Hindus] (more Orient in every sense), whom no people have surpassed in the grandeur of their ethical statement.”16 Emerson carefully studied the Hindu literature, including Vedas, Upanis. ads, Bhagavad-Gītā, and the works of Kālidāsa, a poet. Hindu philosophy was the source of Emerson of his transcenden- talism and helped him in his quest to deﬁne a truly representative man. Ancient India had acquired great fame as a society rich in spiritual as well secular dimen- sions. Therefore, it was visited by many travelers from Greece, Rome, China, and Arabia during the ancient and early medieval periods who provided accounts of the prosperity in the region. An early account is from Megasthenes (350–290 BCE), an ambassador of Seleucus I who ruled India for a short period. Megasthenes writes that the Indians, “having abundant means of subsis- tence, exceed in consequence the ordinary stature, and are distinguished by their proud bearing. They are also found to be well skilled in the arts, as might be expected of men who inhale a pure air and drink the very ﬁnest water.”17 Megasthenes is emphatic that the region never suf- fered from “famine” and “general scarcity in the supply of nourishing food.”18 Strabo (63 BCE - 21 CE), a Greek geographer and traveler, also visited India and found that the country was “abounding in herbs and roots,”19 indicating prosperity. The Chinese traveler Yijing (or I-tsing; 643–713 CE), who lived in India for about 22 years, mostly in Nalanda, a center of learning in modern Bihar, wrote: “. . . ghee [clariﬁed butter], oil, milk, and cream are found everywhere. Such things as cakes and fruit are so abundant that it is diﬃcult to enumerate them here.”20 Yijing visited India to acquire knowledge and carried some 400 Sanskrit texts back with him to China.21 Most Chinese, Greek, Persian, Arabian, and European documents written in diﬀerent periods testify to the prosperity of the Indus-Sarsvatī Valley region. It is only after the later part of the British occupation, in the late nineteenth century that the region suﬀered from hunger and poverty due to colonial exploitation. 2.2 THE POWER OF QUESTIONING: ŚĀSTRĀRTHA (DEBATE) TO ACQUIRE KNOWLEDGE Curiosity raises questions and questions lead to ideas and creativity. The power of questioning as a learning tool goes far back into history. The Socratic dialog is a standard tool for learning where 16Emerson, 1904, vol. 8, p. 239. For more information, read Acharya, 2001. 17McCrindle, 1926, p. 30. 18McCrindle, 1926, p. 31. 19Strabo, 15: 1: 22 20Takakusu, 1966, p. 44. 21Takakusu, 1966, p. xvii. 18 2. THE BUILDING BLOCKS OF SCIENCE the answer of a question is a question. Socrates (470–399 BCE) didn’t give lectures or write books. He propagated a dialectical technique in which he led his students by asking appropriate questions that demanded critical thinking to arrive at the correct answer. Socrates’ questions revealed the ways in which his student’s thinking was dogmatic and in error. A good question is an excellent way to start a conversation. Good questions lure people to open up about themselves and divulge their thoughts and feelings. Questions are also instru- mental in allowing you to introspect yourself and ﬁnd answers. In a group, questions promote discussion. Questions have the ability to spawn more questions. This process is a hallmark of learning and has been an essential ingredient of Hindu thought. In some religions, unquestioning faith in their scriptures is emphasized and used as the yardstick to judge the person’s spirituality. In contrast, in Hinduism, asking questions is a com- mon norm. The Bhagavad-Gītā, a sacred book of the Hindus, is a narrative dialog between prince Arjuna and Lord Kr.s.n. a. Arjuna was not fearful in asking tough questions; he was not fearful of being deﬁned as a person with no faith. He bluntly asked, “Why should I ﬁght with my own family members?” Kr.s.n. a, by fulﬁlling Arjuna’s curiosity, could teach the concepts of dharma, duty, and moks. a. The Bhagavad-Gītā is not the only book with such dialogs in the Hindu cor- pus; Maitreyī, in Br. hadāran. yaka-Upanis. ad, raises question about the futility of wealth and love for self. The sacred Rāmāyan. a is the compilation of questions asked by sage Vālmīki and answers by Nārada Muni. Henry David Thoreau, (1817–1862 CE), an American philosopher, naturalist, and au- thor, praised the Hindus for their openness to new ideas. “The calmness and gentleness with which the Hindoo [Hindu] philosophers approach and discourse on forbidden themes is ad- mirable.”22 Thoreau wrote this statement after his studies of the Vedas and Upanis. ads. Truthful- ness, goodness, and beauty, as marked in satya ˙m, śiva ˙m, and sundara ˙m [Only truth is beneﬁcial and beautiful], have always been the guiding principles for the Hindus. Interrogation, cross-examination, debate, symposium, and discussion were well deﬁned tools practiced from the ancient period among the Hindus. In the Hindu tradition, scholastic debate (vāda) is practiced not only for the disciplines of philosophy; it is also for sciences and religion. Questioning is a powerful tool of investigation to discover unchartered territory of knowledge. Usually multiple possibilities are probed when people try to resolve a question. How do you select one possible solution over the others? How do you decide, when diﬀerent people support diﬀerent solutions? A debate is a way in which scholars can present their cases; such debates can easily ﬁlter novices from scholars. The practice of debate was so ingrained and valued among the Hindus that it was used as one of the eight ways in which a woman could select a groom for herself. Prospective grooms debated with established scholars or among a group of prospective grooms in public on various issues to win the bride. It was this practice that led 22Thoreau, 1906, vol. 2, p. 3. 2.2. THE POWER OF QUESTIONING 19 Gautama (who later became Lord Buddha) to debate Arjuna, as mentioned in Lalitvistara, an ancient book (See Chapter 3).23 The Br. hadāran. yaka-Upanis. ad narrates an episode in which King Janaka decided to donate one thousand cows to the best Brahmin. Yājñavalkya, a revered saint, took all the cows and thus infuriated several other holy men who also needed the gift for their livelihood. To resolve the matter, a debate ensued and Yājñavalkya had to demonstrate his superior intellectual abilities by answering questions posed by other holy men.24 Sages like Aśvala, Jāratkārava Ārtabhāga, Bhujyu Lāhyāyani, Us.hasta Cākrāyan. a, and Kahola Kaus.ītakeya debated with him and asked questions on philosophical subjects to which Yājñavalkya provided convincing replies. They all lost the debate one-by-one. These sequence of debate was chosen by the rank of these scholars. In the end came Gārgi Vācaknavī, the daughter of sage Vācaknu who was in the lineage of sage Gārga, and took her name from the lineage and her father. But, she also lost to Yājñavalkya.25 A healthy śāstrārtha (debate or discussion) is an essential element and practice in the Hindu religion. It has led to the idea of “monism”—there is only one existence (God)—as well as the idea of “dualism”—there are two separate realities, Him (God) and me (my soul). The quest to know the ultimate truth led to the evolution of various systems of knowledge which outwardly seem to be divergent. The Hindu tradition allowed divergent opinions to coexist and established śāstrārtha as a means to resolve scholarly diﬀerences. Each person was allowed to test and discover the truth in his/her own way. Debate was considered a good way to eﬀectively formulate the thought process, a good way to understand the subject matter, and to become established among scholars. Forty-four diﬀerent forms of debates or discussions are described in the Caraka-Sa ˙mhitā, demonstrating debate as a highly evolved system.26 This book advises to decide the purpose of the debate in advance: For example, is it for curiosity or to subjugate the opponent? The latter purpose of subjugation was practiced in the special situations, e.g., śāstrārtha for marriage. The Sanskrit term ānuvīks. ikī, deﬁned as investigation through reasoning, has a long tra- dition among the ancient Hindus. It is a tool of investigation that is applicable in all aspects of learning: scientiﬁc, religious, and social. The earliest text on economics, Arthaśāstra of Kaut.ilaya, lists27 ānuvīks. ikī as one of the four cognitive (vidyā) disciplines, along with trayī (vedic learn- ing), dan. d. anīti (jurisprudence), and vārttā (economics). Ānuvīks. ikī is considered as a “source of all knowledge” or a “means for all activities,” and a “foundation for all social and religious duties.” “When seen in the light of these sciences, the science of ānuvīks. ikī is most beneﬁcial to the world, keeps the mind steady and ﬁrm in weal and woe alike, and bestows excellence of foresight, speech, and action. Light to all kinds of knowledge, easy means to accomplish all 23Bays, 1983, p. 224. 24The Br. hadāran. yaka-Upanis. ad, 3: 1. 25In contrast to many cultures, females could excel in philosophy and science among the ancient Hindus. The practice continues even today. 26Caraka-Sa ˙mhitā, Vimānasthāna, 8: 27. 27King, Richard, 1999, p. 34; Arthaśāstra, 1: 2: 6–7. 20 2. THE BUILDING BLOCKS OF SCIENCE kinds of acts and receptacle of all kinds of virtues, is the science of ānuvīks. ikī ever held to be,” suggests Kaut.ilaya.28 The medical treatise Caraka-Sa ˙mhitā emphasizes the importance of debate and discus- sion in the learning process. “Discussion with a person of the same branch of science increases knowledge and brings happiness. It contributes toward the clarity of understanding, increases dialectical skills, broadcasts reputation, dispels doubts regarding things heard. . . Hence it is the discussion with men of the same branch of science, that is applauded by the wise.”29 The Caraka- Sa ˙mhitā suggests yukti or heuristic reasoning as a valid and independent means of knowledge. Medical practitioners were advised to free themselves from bias and search for the truth dispas- sionately.30 According to Caraka, discussions can be friendly or hostile. In the Hindu tradition, even hostile discussions were an organized tradition in which scholars with diﬀering opinions shared their point of view, and debated with each other.31 The rule was to avoid any “celebration for the victor” or “any insult to the loser.”32 Since knowing truth was the purpose of a debate, it was the knowledge that became central and not the person. This discouraged a feeling of triumph or defeat for the participants. It was suggested that all assertions in a debate should be made in a polite manner. A person in anger can do anything to win, even inappropriate actions. Therefore, wise people debate in a polite manner.33 This chapter of the Caraka-Sa ˙mhitā reminds us of the Robert’s Rules of Order that were established in the West centuries later, in the nineteenth century.34 2.3 RESPECT FOR KNOWLEDGE: THE ROLE OF A GURU Hinduism does not enforce any undue restraint upon the freedom of human reasoning, the freedom of thought, or the will of an individual. Hindus’ respect for knowledge is inherent in the core values of the religion. Respect for learning is obvious from the status that was bestowed on gurus. A festival, guru-pūrn. imā, is celebrated every year when Hindus oﬀer thanks, love, and devotion to their gurus. This festival falls on the full moon day (pūrn. imā) in the month of Ās. ād. ha ( June - July). The Śvetāśvatara-Upanis. ad tells us that the Vedic knowledge is automatically revealed to a person who has the deepest love for God and the same love toward his teacher.35 28Arthaśāstra, 1: 2: 6–7. 29Caraka-Sa ˙mhitā, Vimānasthāna, 8: 15. 30Caraka-Sa ˙mhitā, Sūtrasthānam, 25: 32. 31Caraka-Sa ˙mhitā, Vimānasthāna, 8: 16. 32Caraka-Sa ˙mhitā, Vimānasthāna, 8: 17. 33Caraka-Sa ˙mhitā, Vimānasthāna, 8: 22–23. 34Henry Martyn Robert (1837–1923) was an engineering oﬃcer in the U.S. Army. In 1875, he self-published a book, The Pocket Manual of Rules of Order for Deliberative Assemblies, in two parts. The book gained popularity and the ﬁrst formal edition was published in 1876 with a new title: Robert’s Rules of Order. The book is still a classic and frequently consulted by groups for smooth interactions and discussion. 35Śvetāśvatara-Upanis. ad, 6: 23. 2.3. RESPECT FOR KNOWLEDGE: THE ROLE OF A GURU 21 In Hindu tradition, gurus36 have a very high status that is comparable to parents and God. For example, Kabir, a famous medieval poet, shared a situation where his guru and God both appeared before him at the same time. In the Hindu tradition, dignitaries are greeted and honored by the host by touching their feet in the order of their comparative stature. Kabir’s dilemma was who should he greet ﬁrst, his guru or God? Kabir quickly resolved this dilemma as he realized that the guru should be the ﬁrst one since he (guru) enabled him to see God.37 Gurus shared their own personal experiences with disciples, guided disciples in their interactions with the community, taught social rules, taught various intellectual disciplines, and most important of all, became the spiritual guides of disciples. It was the guru who assigned a skilled trade or profession varn. a, later known as jāti (or caste), to a disciple after the completion of his or her education. Hindus divided the human lifespan of 100 years into four stages (āśrama): brahmacarya (learning stage), gr. hastha (householder stage), vānaprastha (stage of teaching, and doing com- munity service) and sanyasa (stage of contemplation and renunciation). Brahmacarya is the ﬁrst stage of life where a child, after the infancy stage, joins gurūkula (gurū = teacher, kula = home or lineage), boarding school run by a guru in a natural environment (or forest). Parents left their children here in the care of the guru, to live in the school compound with the family of their guru and not with their parents to get appropriate education suited to their aptitude and inclinations. Irrespective of the social and economic status of the parents, each child had to live at the same standard of living as the guru’s family. This allowed disciples to live near the guru, who could observe ﬁrsthand aptitudes and inclinations of disciples. The disciples understood the complex- ities of life quickly because of their continued association with the guru. Young children not only gained content-based knowledge from their guru, they also learned virtuous lifestyles and ethics. This system worked quite well for the ancient Hindus and they excelled in the sciences, along with other skill trades and disciplines.38 Gurus were considered to be authority ﬁgures, but were not considered infallible. It was considered a healthy practice for the disciples to raise questions about gurus’ teachings to under- stand reality in their own way. The Prasna-Upanis. ad (Prasna = question), one of the principal Upanis. ads, is entirely based on the questioning between disciples and their teacher. The role of the guru was and still is paramount to most Hindus. It does not stop after the brahmacarya stage; it continues for the rest of the life. Carl Jung, a noted psychoanalyst, emphasized the importance of the guru in the following words: “. . . practically everybody of a certain education, at least, has a guru, a spiritual leader who teaches you and you alone what you 36Śiks. ak, ācārya, śrotriya Upādhyāya, purohit are other words for guru. 37Guru Govind dāū khare, kāke lāgu pāya, balihārī guru āpnu jin Govind diyo batāya. My teacher and God are in front of me. Whom should I prostrate ﬁrst? It has to be the guru who taught me to recognize God. 38Joshi, 1972. 22 2. THE BUILDING BLOCKS OF SCIENCE ought to know. Not everybody needs to know the same thing and this kind of knowledge can never be taught in the same way.”39 Some of the famous teachers in Hindu history are Kaut.ilya (ﬂ. 300 BCE), teacher of Candragupta Maurya (reigned c. 321–297 BCE) and Vasis.t.ha (pre-historic), teacher of Lord Rāma. Kaut.ilya laid the rules of administration for Candragupta, especially for psychological warfare, political philosophy, and economics, which are compiled in his book, Arthaśāstra. It was Kaut.ilya’s strategies that ended the Greek rule in a western state of India (now in Pakistan). Similarly, it was Vasis.t.ha who convinced King Daśaratha to allow Lord Rāma to relinquish the worldly comforts of his palace and live in a forest to protect sage Viśvāmitra’s gurukula from rāks. asa (evil mongers). 2.4 SMR. TI (MEMORY), AN ANSWER TO BOOK BURNING In the gurukulas, the ancient Hindus memorized their literature (mostly poetry) verbatim. The spoken words, not the written words, have been the basis of literary and scientiﬁc traditions of the Hindus. The people who memorized the texts were highly respected as they became the tools that could keep the tradition alive. This tradition continues even today. People who memorized Vedas or Upanis. ads are highly respected in today’s Hindu society.40 This memorization tradition was facilitated by composing their literature in Sanskrit either in stories or in poetry with a rhythm or pattern. Stories have characters with links with each other. Similarly, it is much easier to memorize a poem than a prose due to the rhythm. Sanskrit grammar was developed by Hindus to facilitate composition of poetry. Even math problems were composed in beautiful poetry in Sanskrit. The ﬁrst written accounts in India are from the period of Aśoka (r. 269–232 BCE), the third emperor in line of the Mayura dynasty. He erected stone obelisks with his edicts inscribed in the stones rock edicts all over India. These edicts are useful guide to life in ancient India. However, such inscriptions or manuscripts are limited in number. Yijing (also I-tsing, 635–713), a Chinese traveler who visited India, was impressed when he met people who could recite hundreds of thousands of verses of Vedas. “The Vedas have been handed down from mouth to mouth, not transcribed on paper or leaves. In every generation there exist some intelligent Brahmans who can recite 100,000 verses . . . This is far from being a myth, for I myself have met such men,” writes Yijing.41 39Jung, Carl, CW Letters, 1973, vol. 1, p. 237. Jung (1875–1961) was an inﬂuential psychiatrist and thinker of the twentieth century. Hindu philosophy played an important role in his theories on symbolism and the unconscious mind. 40Vedi (or Bedi), Dvivedi, Trivedi, and Caturvedi are common last names (surnames) among brahmins, the people who were entrusted to preserve the Vedas. These names literally symbolize the number of Vedas memorized by them. Dwi means two and Dwivedi is the surname of a person who has memorized two Vedas. Similarly, tri and catur mean three and four, respectively. Thus, Trivedi and Caturvedi are the people who have memorized three or four Vedas, respectively. Of course, today these surnames are inherited from father to children without any connection to memorization. 41Takakusu, 1966, p. 182. I have thought of this statement along with the people who memorized Vedas in India. Suppose, it takes 10 seconds to narrate one verse. To narrate 100,000 verses, this equals to one million seconds. One million seconds equal a period of non-stop chanting for more than 11 days. How can one remember voluminous texts that take more than 11 days to read? Obviously, the person had to breathe in between, take rest, eat food, and sleep. This means that, in a rough 2.4. SMR. TI (MEMORY), AN ANSWER TO BOOK BURNING 23 Al-Bīrūnī, an Islamic scholar who lived in India for some thirteen years during the eleventh century, wrote of the importance of poetic literature in popularizing science: “By com- posing their books in metres [poetry] they [Hindus] intend to facilitate their being learned by heart, and to prevent people in all questions of science ever recurring to a written text, save in case of bare necessity. For they think that the mind of man sympathizes with everything in which there is symmetry and order, and has an aversion to everything in which there is no or- der. Therefore, most Hindus are passionately fond of their verses, and always desirous of reciting them, even if they do not understand the meaning of words, and the audience will snap their ﬁngers in token of joy and applause. They [Hindus] do not want prose compositions, although it is much easier to understand them.”42 During the Islamic invasion of India, libraries were burnt. As an example, the libraries in Nalanda and Vikramsila were destroyed around 1200 CE by Bhkhtiyar Khilji. However, most of the sacred literature of the Hindus was easily reproduced because Hindus had memorized the poetic verses of their sacred literature. The ﬁctional novel Fahrenheit 451 by American writer Ray Bradbury dramatizes this feat. The title is based on the temperature at which paper catches ﬁre. This novel deals with a futurist society where books were outlawed and ﬁremen burned books. A small group of people countered this situation by memorizing books. The tradition of memorization of sacred texts (or lack thereof ) had a profound outcome for world cultures. Comparatively speaking, when the textual riches of Alexandria, China, Baghdad, and Rome were ﬂamed, the glory of these cultures dissipated like smoke in the sky. In contrast, the Hindus could still salvage much of their textual riches.43 Memorization was facilitated by the abundant use of polysemous words in Sanskrit to maintain rhythm and tone. In some situations, the meanings of a word are so divergent that multiple interpretations can be made of the same sentence. It creates a dilemma. What is the original intended meaning of a verse? To make matter complex, the authors of the Hindu lit- erature deliberately intended multiple meanings of their verses, depending on the expertise of a person. A layperson as well as a scholar could enjoy the hymns. As a result, scholars today argue with each other to validate their own interpretations. The problem becomes tense when a native interpretation is deemed biased by a foreign experts. In contrast to Catholicism, Ju- daism, and Islam, the contemporary Hindu literature is mostly produced by non-practitioners. For example, Max Müller, Monier-Williams, and Rudyard Kipling were devout Christians who translated the sacred Hindu texts with the intent of changing the religious landscape of India. Even after a century has elapsed, their translations are still popular in US, UK and Europe. estimate, the person memorized a text that took about 25–30 days to narrate. Is it possible? Historical documents support such memorization. 42Sachau, 1964, vol. 1, p. 137. 43Montgomery and Kumar, 2000. 24 2. THE BUILDING BLOCKS OF SCIENCE 2.5 YOGA AND MEDITATION FOR SELF-IMPROVEMENT Our physical body and mind are the basic instruments for all our actions, perceptions, and thoughts. It is the body and mind (popularly deﬁned as two separate entities) that are the ba- sic tools of our knowledge, virtues, and our happiness. In the modern culture, more emphasis is placed on the body. Gyms are popularly becoming a place where people go for exercise and sculpt their bodies for self improvement. Our icons are the supermodels and superathletes. What about the mind? Or, more importantly, a unison of body and mind? The ﬁrst organizing principle underlying human movements and postures is our existence in the gravitational ﬁeld. The earth’s gravitational ﬁeld has an inﬂuence on every movement we make. The combination of the nervous system and skeletal muscles functioning together in gravity forms the basis of various yoga postures.44 The practice of yoga perhaps is the most cost-eﬀective and non-invasive treatment in many medical conditions. It is the most integrated science of self improvement where body and mind are both nourished that allows people to reach their fullest potential. The Sanskrit term yoga comes from the root ‘yuj’ which means “union,” “join” or “balance.” The term “union” deﬁnes the union of our physical self and the mind for some, while for others, a union of self with the divine. However, in both unions, a person transcends from everyday mundane existence to his/her fullest potential that leads to the understanding of the unity of all living creatures and ultimately to moks. a—an ultimate goal for all Hindus. Body and mind are the vehicles for the Hindus that allowed them to liberate their soul from the cycle of birth and death. Body and mind are the Siamese twins that create synergy for this ultimate goal of liberation. Yoga is all about balance; it is a balance of mind and body, a balance of strength and ﬂexibility, a balance in a particular posture, even a balance in breathing from left and right nostrils that harmonizes the left and right brains. It is a philosophy; it is a way of life. It helps to avoid sickness. It helps a person to reach his/her best potential. Yoga is perhaps the oldest system of personal development that is eﬀective.45 Although the Vedas were the ﬁrst to mention the importance of yoga, the Upanis. ads were the ﬁrst to provide a systematic form of yoga. The ﬁrst major treatise of yoga known to us is Patañjali’s Yoga-Sūtra. The Indus seals of Harappa and Mohenjo-daro depicting human ﬁgurines in lotus postures in a meditative state provide archaeological support for the existence (Figure 2.1).46 In Patañjali’s yoga-sūtra, yoga is deﬁned as a system of eight limbs (as. t. ā ˙nga-yoga):47 “Restraint (yama), observance (niyama), posture (āsana), breath-control (prān. āyāma), sense- 44Coulter, 2001, 23. 45Coulter, 2001; Cowen, 2010; Eliade, 1969; Feuerstein, 1989; Iyengar, 1966; and Kulkarni, 1972. For a beginner who is interested in the medical aspects of yoga, Coulter’s book is good. For the philosophical aspects, consult Eliade’s book. 46Worthington, 1982, p. 9. 47Patañjali’s yoga-sūtras, 1: 40. 2.5. YOGA AND MEDITATION FOR SELF-IMPROVEMENT 25 Figure 2.1: A monk sitting in a lotus posture in a meditative state (taken from Wikimedia). withdrawal (pratyāhāra), concentration (dhāran. ā), meditative-absorption (dhyāna) and enlight- enment (samādhi) are the eight members [of Yoga].”48 Yoga postures (āsana) are an outcome of biomimicry practiced by the ancient Hindus. They observed various life forms—small and big, their life styles, the ways they exercised, the ways they cured themselves, the ways they relaxed, and the ways they avoided sickness. These studies evolved into a system of medicine called Ayurveda (science of life). It is no coincidence that many āsana are named after animals. The names of various postures are either based on their geometry or their similarity to an object, bird or animal. The following are some popular āsana: dhanura-āsana (bow posture), garud. a-āsana (eagle posture), krounc-āsana (heron posture), makar-āsana (crocodile posture), man. dūka-āsana (frog posture), mayur-āsana (peacock posture), padma-āsana (lotus posture), trikon. a-āsana (triangle posture), vakra-āsana (curved posture), and hala-āsanas (plough posture). Yoga is also a science that is cognizant of the bones, muscles, joints, organs, glands and nerves of the human body (biology). It uses the physics of balance in designing postures, the physics of motion and balance to allow changes in postures and a deep understanding of the strength and connectivity of various muscles to make the body strong and ﬂexible. At the same 48Patañjali’s Yoga-Sūtra, 2: 29. 26 2. THE BUILDING BLOCKS OF SCIENCE time it is based on a deep understanding of the power and functioning of the mind (psychology) in controlling the thought processes (meditation) for optimum or holistic health. The word yoga has appeared in the R. gveda to deﬁne the yoking, connection, achieving the impossible.49 By yoga, one gains contentment, endurance of the pairs of opposites, and tranquility, tells the Maitreyī-Upanis. ad.50 “When cease the ﬁve senses, together with the mind, and the thoughts do not stir. That, they say, is the highest course. This they consider as yoga, ﬁrm holding back of the senses. Then one becomes undistracted. Yoga, truly, is the origin and end,” suggests the Kathā-Upanis. ad.51 In other words, yoga is alpha and omega of the art of self-improvement. Here “origin and end” means that yoga is essentially involved in knowledge and experi- ence; it is a process at all stages. Yoga is advocated for the knowledge or realization of the self (ātman).52 Patañjali equated yoga with samādhi (tranquil state) in the very ﬁrst verse of his book. Yoga is not a mere abstract speculation of human mind; it is real with a concrete referent: “[This supreme ecstasy] is near to [him who is] extremely vehement [in his practice of Yoga].”53 Our body and mind are intimately linked. If the muscles of our body are toned and relaxed, it is easier for our mind to relax. Similarly, if our mind is anxious, it directs stimuli to our physical body and changes the chemical composition and physical state of our muscles. The outcome is the drainage of physical and emotional energies. The ancient Hindus realized the intimate link of mind and body, and formulated exercises for both. The physical body received its vital energies through yogic postures (āsana), while mind gained its vital energies through meditation. An active organ receives a larger ﬂow of blood than an inactive organ. Blood is an essential ingredient for the proper functioning of the various organs of body, and these organs get enriched due to a higher and more eﬃcient transfusion of oxygen through our lungs. The yoga postures work on the body frame as well as on the internal organs, glands, and nerves. Most joints and organs are put into isometric or other ranges of motions. Most people take short and shallow breaths throughout the day using their chest. This kind of breathing does not allow our “lungs to expand and soak up the oxygen.”54 Although hyperventilation or heavy breathing can be useful in the short term by boosting sympathetic nervous system activity, a better way to breathe is using the abdomen and diaphragm, called the belly breath and take slow and steady breaths. You need to use your diaphragm, which is the muscle underneath your lungs. When the diaphragm ﬂexes, it pulls down and opens the lower lobes of your lungs, allowing more air inside. Chest breathing comes from stress; it is a reaction to stress. 49R. gveda, 1: 34: 9; 3: 27: 11; 7: 67: 8; 10: 114: 9; Dasgupta, 1963, vol. 1, p. 226. 50Maitreyī-Upanis. ad, 6: 29. 51Kathā-Upanis. ad, 6: 10–11. 52Kathā-Upanis. ad, 2: 12; Mun. d. aka-Upanis. ad, 3: 2: 6; Śvetāśvatara-Upanis. ad, 1: 3: 6–13; Maitreyī-Upanis. ad, 6: 18, 19, 27. 53Patañjali’s Yoga-Sūtra, 1: 21. 54Dollemore, Giuliucci, Haigh, Kirchheimer and Callahan, 1995, p. 152; Gilbert, 1999a and 1999b. 2.5. YOGA AND MEDITATION FOR SELF-IMPROVEMENT 27 All yoga exercises start with basic deep breathing techniques along with proper āsanas. It serves two purposes: ﬁrst, to bring an optimum amount of oxygen into the lungs; second, to control the mind by controlling the breath. Deep breathing is not the fast pumping action of our lungs where we take a fast deep breath and puﬀ it out; it involves a controlled rhythmic action to ﬁll the lungs with air, to retain it for a brief period, and slowly exhale. The whole process has four parts: inhalation (pūraka), retention (kumbhaka), exhalation (recaka), and suspension (kumbhaka). The word meditation derives from a Latin word, mederi, which means to heal. It is the healing of a mental aﬄiction caused by psychological stress. Managing our thought processes is a key to managing the stress that aﬀects our lives. Meditation can help a person ﬁnd new ideas and practical answers to problems. It gives ample stillness to the mind to think properly in order to make proper judgments. It helps the mind to control emotion without suppression but with an outlet where the emotional waste could be discarded in order to become more at peace with the world. For this reason, the Maitreyī-Upanis. ad considers meditation as essential to realize God, along with knowledge (vidyā) and austerity (tapas).55 Meditation is a process of knowing for the Hindus. The Sanskrit words that reﬂect medita- tion are: cintan, dhyāna, or manana. Nowhere in the world was the art of meditation as perfected as was done by the ancient Hindus. The Śvetāsvetara-Upanis. ad tells us that meditation and yoga are the way to know the self-power (ātma-śakti) of God within us.56 The Chāndogya-Upanis. ad tells us that all people who achieved greatness in the past did so with the help of meditation.57 The practice of concentration (ekāgratā or dhārn. a) is the endeavor to control the two generative sources of mental ﬂuidity: sensory activity (indriya) and subconscious activity (sam. skāra).58 It is diﬃcult to achieve pursuit of one object (ekāgratā, single-mindedness) with a tired body or restless mind, and with unregulated breathing. Meditation can decrease our reaction time, increase alertness and improve the eﬃciency of a person. Insomnia, headache, lack of appetite, shaking of the hands and other symptoms can be either reduced or nearly eliminated. It also helps in asthma, anxiety, high blood pressure, back pain, heart disease, etc. Concentration of the mind acts like a focusing lens (convex lens) of Sun’s rays. It concentrates thought and invokes miraculous powers to the mind’s activities. The only way to understand the impact of yoga is to go through the experience. The diaphragmatic movements provide a “massaging action to the heart” as well as to the inferior vena cava as the latter passes through the diaphragm, thus propelling the blood forward toward the heart and can be labeled as the “second heart.”59 In the Universidade Federal de São Paulo, Brazil, Danucalov et al. investigated the changes in cardiorespiratory and metabolic intensity resulting from prān. āyāma and meditation during the same hatha yoga session. Nine 55Maitreyī-Upanis. ad, 4: 4. 56Śvetāsvetara-Upanis. ad, 1: 3. 57Chāndogya-Upanis. ad, 7: 6: 1. 58Eliade, 1975, p. 62. 59Thomas, 1993; taken from Gilbert, 1999a 28 2. THE BUILDING BLOCKS OF SCIENCE yoga instructors were subjected to analysis of the air exhaled during the three periods, each of 30 minute duration: rest, respiratory exercises, and meditation. The oxygen uptake and carbon dioxide output were proven to be statistically diﬀerent during the active sessions (prān. āyāma and meditation) compared to the rest phase. In addition, the heart rate showed decreased lev- els during rest as compared to meditation. Therefore, the results from this study suggest that meditation reduces the metabolic rate while the prān. āyāma techniques increases it.60 Researches have shown that yoga can help people suﬀering from asthma, heart disease, high blood pressure, type 2 diabetes, and obsessive-compulsive disorder, lower their dosage of medications, and sometimes eliminate the use of medication.61 Practicing yoga not only relieves temporary symptoms such as headaches, sinus pressure and hot ﬂashes, but it can also improve health during more serious medical conditions such as cancer, diabetes, anxiety, and heart dis- ease, to name a few. “Yoga is not a panacea, but it is powerful medicine indeed for body, mind, and spirit,” suggests Dr. McCall, a medical doctor who studied and practiced the eﬀects of yoga.62 60Danucalov et al., 2008. 61McCall, 2007, p. 43. 62McCall, 2007, p. XIX. C H A P T E R 3 29 The Hindu Mathematics “Of the development of Hindu mathematics we know but little. A few manuscripts bear testi- mony that the Indians had climbed to a lofty height, but their path of ascent is no longer trace- able,” wrote Cajori in his book, A History of Mathematics.1 This indicates the status of scholarship on Hindu mathematics in 1893 when Cajori ﬁrst published this book. However, the scholarship of the last hundred years has ﬁlled many gaps in our understanding of Hindu mathematics. Most mathematics textbooks are devoid of historical anecdotes and stories. Mathematics is taught as a discipline that someday somehow appeared in fully developed form. Therefore, students of mathematics do not learn much about the dynamic aspect of the discipline. This led George Sarton, a leading historian of science and chemistry in the twentieth-century, a former professor at Harvard University, to write, “if the history of science is a secret history, then the history of mathematics is a doubly secret, as secret within a secret.”2 Mathematics is also the discipline where the non-Western cultures have made signiﬁcant contributions. Mathematics owes a lot to its Hindu and Middle Eastern roots.3 3.1 THE HINDU NUMERALS The number system that we use today in most of the civilized world has come to us from the ancient Hindus. This system of counting is so simple that it is diﬃcult to realize its profundity and importance.4 Young children all over the world are generally taught this counting system ﬁrst and the alphabet of their native language later. Children are taught to write eleven as one and one (11), written side-by-side, which they learn without much diﬃculty. “Our civilization uses it unthinkably, so to speak, and as a result we tend to be unaware of its merits. But no one who considers the history of numerical notations can fail to be struck by the ingenuity of our system, because its use of the zero concept and the place-value principle gives it an enormous advantage over most of the other systems that have been devised through the centuries.”5 1Cajori, 1980, p. 83. 2Taken from Dauben, Joseph W., Mathematics: a Historian’s Perspective, a chapter in the book by Chikara, Mitsuo and Dauben, 1994, p. 1. 3Bag, 1979; Colebrooke, 1817; Datta and Singh, 1938; Ifrah, 1985; Joseph, 1991; Rashed, 1996; Smith, 1925; Srini- vasiengar, 1967. 4Ifrah, 1985, p. 428. Ifrah’s book is still one of the most engaging and scholarly book on numerals in various ethnic cultures. The other noted books are by Calinger, 1999; Cook, 1997; Katz, 1993; Smith, 1925; Smith and Karpinski, 1911; Suzuki, 2002. 5Ifrah, 1985, p. 428. 30 3. THE HINDU MATHEMATICS Several civilizations such as the Egyptians, Chinese, and Romans used the additive deci- mal systems although their symbols were diﬀerent. In their system, multiple repetition of sym- bols were used and added to increase magnitude. Thus, in the Roman system, X means 10 and XX becomes (10 + 10) = 20. Also, XVI amounts to 10 + 5 + 1 = 16. The Romans also used 1), respectively. subtractive symbolism where IX and IL represents 9 (as 10 1) and 49 (as 50 (cid:0) (cid:0) 3.1.1 THE WORD-NUMERALS In an oral tradition, numbers are chosen as words that can be used in a narrative. This happened with the ancient Hindus where words representing numbers were chosen in verses of the sacred literature. The word-numerals in Sanskrit language are written similar to the way numbers are written in German language. For example, 23 is called three and twenty (drei und zwanzig) in German while twenty and three in the English system. Similarly, fourteen is called vier-zehn (four and ten) and ﬁfty-three is called drei und fünfzig (three and ﬁfty). In the Sanskrit language, the mother language of all Indo-European languages, the language of the Vedas, twelve is written as two and ten,6 34 as four-thirty,7 53 as three and ﬁfty,8 77 as seven and seventy.9 just like the German system. For compound numerals, the number of higher order was placed as qualiﬁer and the lower as qualiﬁed. For example, eleven is deﬁned as ten qualiﬁed by the addition of one, thus giving eka-dasa, translated as one-ten. The number 720 is denoted as seven-hundred-twenty10 and the number 60,099 is written as sixty-thousand-nine-ninety11 in the R. gveda. The R. gveda mentions “three thousand and three hundred and nine-thirty (3339)”12 as the count of people in a yajna, a holy gathering where worshipping is done around ﬁre. The Atharvaveda deﬁnes a hundred, thousand, myriad, hundred-million.13 Similarly, consistent with the practice in the R. gveda, the Baudhāyana-śulbasūtras expressed the number 225 as (200 and 5 and 20)14 and the number 187 as (100 + 7 + 80).15 For the numbers provided in the Vedas and Śulbasūtras, the following points are clearly established: 1. The numbers from one to ten have speciﬁc names. 2. After ten, speciﬁc words are designated to 20, 30, . . . 100. All other numbers in between are deﬁned as a combination of these words. 6R. gveda, 1: 25: 8. 7R. gveda, 1: 162: 18; R. gveda, 10: 55: 3. 8R. gveda, 10: 34: 8. 9R. gveda, 10: 93: 15. 10R. gveda, 1: 164: 11. 11R. gveda, 1: 53: 9. 12R. gveda, 10: 52: 6. 13Atharvaveda, 8: 8: 7. 14Baudhāyana-śulbasūtras, 16: 8. 15Baudhāyana-śulbasūtras, 11: 2. 3.1. THE HINDU NUMERALS 31 3. After 100, new words are assigned to 1,000, 10,000, 100,000, etc. 4. In word numerals, numbers between 10 and 20 were deﬁned as a number above ten and then 10. For example, 12 is deﬁned as 2 and 10 (dvi-daśa). A similar practice was made for other numbers. For example, 99 is written as (9 + 90), 76 as (6 + 70), etc. The ancient Hindus wondered about the total number of atoms in the universe, the age of the universe, size of atom, etc. To deﬁne these physical quantities, they used really large numbers as well as really small numbers. Al-Bīrūnī, an Islamic philosopher who lived in India during the eleventh-century, criticized the Hindus for their passion for large numbers: “I have studied the names of the orders of the numbers in various languages with all kinds of people with whom I have been in contact, and have found that no nation goes beyond thousand. The Arabs, too, stop with the thousand, which is certainly the most correct and the most natural thing to do. Those, however, who go beyond the thousand in their numeral system are the Hindus, at least in their arithmetical technical terms.”16 This criticism of al-Bīrūnī demonstrates that the ancient Hindus were simply much ahead of their time. I am fairly conﬁdent that if al-Bīrūnī were to write his book today, he would not criticize the Hindus for their fondness of large numbers. Al-Bīrūnī mentioned 1019 as the largest number used by the Hindus. 3.1.2 THE PLACE-VALUE NOTATIONS The Greeks, Egyptians, and Romans, did not use place-value notations in writing numbers while the Babylonians, Chinese, Mayans, and Hindu, did use. The Babylonian system was base-sixty while the Mayan system was base-twenty. The current place-value system (also called position- value system) that is base-10 is Hindu in origin. This is certain. The uniqueness of the Hindu system lies in the fact that the position of a number qualiﬁes its magnitude. Tens, hundreds, or thousands were not represented by diﬀerent signs; they are represented by using digits in diﬀerent positions. For example, the one is in second place in 10 (ten), in third place in 100 (hundred), and in fourth place in 1,000 (thousand). In a positional- or place-value system, a number, represented as x4x3x2x1 can be con- structed as follows: x1 .x2 C (cid:2) 101/ .x3 C (cid:2) 102/ .x4 C (cid:2) 103/ Where x1, x2, x3, and x4 are nonnegative integers that have magnitudes less than the chosen base (ten in our case). As you may have noticed, the magnitude of a number increases from right to left. For example, the number 1234 will be written as Similarly, 16Sachau, 1964, vol. 1, p. 174. .3 4 C (cid:2) 101/ .2 (cid:2) C 102/ .1 (cid:2) C 103/ 1:2345 1 C D 2 10 C 3 102 C 4 103 C 5 104 32 3. THE HINDU MATHEMATICS In India, Āryabhat.a I (born 476 CE) used a positional value system in describing numbers, did not even bother to explain much about it, and claimed it to be ancient knowledge. This indicates that the system was prevalent then.17 The earliest written record of the place-value notation comes from Vāsumitra, a leading ﬁgure of Kaniska’s Great Council. According to Xuan Zang (also known as Hiuen Tsang, 602– 664), Kusāna King Kaniska (144–178 CE) called a convocation of scholars to write a book, Mahāvibhāsa. Four main scholars under the chief monk, named Pārśva, wrote the book in 12 years. Vāsumitra was one of the four scholars. In this book, Vāsumitra tried to explain that matter is continually changing as it is deﬁned by an instant (time), shape, mass, etc. As time is continually changing, therefore, matter is diﬀerent in each situation although its appearance and mass do not change. He used an analogy of the place-value notation to emphasize his point. Just as location of digit one (1) in the place of hundred is called hundred (100) and in place of thousand (1,000) is called thousand, similarly matter changes its state (avasthā) in diﬀerent time designations.18 New explanations are generally given in terms of known and established facts. Thus, the very reason Vāsumitra used place-value notation as an example to deﬁne change in matter es- tablishes that the place-value notation was considered as an established knowledge during the early Christian era. In modern perspective, just imagine reading the values of various stocks in a newspaper. In a quick scan, you can recognize easily that 1089 is greater than 951. All you need to see is that the ﬁrst number has four digits while the second number has only three. This is enough for a quick comparison. In contrast, in the Roman numerals, XC (90) is ﬁve times more in magnitude than XVIII (18). This is not easy to ﬁgure out in a quick glance. Also, mathematical operations of multiplication, division, addition and subtraction become much simpler in a place- value notation. 3.2 FROM ŚŪNYATĀ AND NETI-NETI TO ZERO AND INFINITY (ANANTA) Zero and inﬁnity are perhaps two grandest concepts ever invented in mathematics. Zero is one of the top hundred discoveries/inventions ever produced in history, as listed by American Asso- ciation for the Advancement of Science in its ﬂagship journal, Science, in year 2000. It is the last numeral invented by the Hindus that prompted the natural philosophers to dump the abacus. It became much easier to perform calculations on a tablet or paper. “In the simple expedient of 17Āryabhat. īya, Gola, 49–50. 18Ruegg, 1993; Sinha, 1983, p. 130. 3.2. FROM ŚŪNYATĀ AND NETI-NETI TO ZERO AND INFINITY (ANANTA) 33 cipher [zero], which was permanently introduced by the Hindus, mathematics received one of the most powerful impulses,” writes Cajori in his book A History of Mathematics.19 Zero is a numeral and it has the same status as any other numerals, all in the absence of any magnitude. The presence of zero indicates a speciﬁc absence of the symbols of 1, 2, . . . , 9 at that location. Zero is thus a sign that deﬁnes no value or a missing value in a particular location in a number. It also deﬁnes the starting point in measurements, such as the coordinate axes, meter sticks, stop watches, and thermometers. Zero is the denial of number in a particular location and gains its meaning from digits that are on the left of it. Zero plays the role of a number and at the same time signiﬁes the metaphysical reality of the absence of substance (emptiness). In Hindu philosophy, the terms śunyata and neti-neti deﬁne emptiness which evolved into a mathematical reality in the form of zero, as explained later. Zero, as a “void,” is an integral part of the Hindu philosophy. The nirgun. a-rūpa (nonmanifested-form, amūrta-rūpa) of God is worshiped by the Hindus. In this form, no at- tributes can be assigned to God. Nothingness (śūnyatā, emptiness or void) as such, in Hindu tradition, has a substance; it is not an absence of everything with 100% mathematical certitude; it is an absence of all attributes that are within the realm of māyā (illusion of the manifested world). In the nirgun. a manifestation, God is beyond any attributes yet the source of all. He is nowhere and yet everywhere. The mathematical symbol zero has similar qualities. Zero has no magnitude and, therefore, is present in every number as a a. It shows its presence when associated with a number in the decimal system. D C 0 The concept of neti-neti (not this, not that; essential for nirgun. a-rūpa, as we cannot assign any particular attribute to God) dates back to the Vedic and Upanis. adic periods. The Br. hadāran. yaka-Upanis. ad explains the Supreme God (ultimate reality) by deﬁning God as the absence of all the attributes (neti-neti).20 The absence of a number in place-value notation has a meaningful function. It does not have a similar usefulness in any other system that is not place-value. For example, the location of two digits 5 and 4 can be ﬁfty four (54), ﬁve hundred four (504), ﬁve hundred forty (540), etc., depending on the location of the two digits. It is only natural to assign a symbol—a circle or a dot—for this absence of a number, for convenience. This is how zero became so central to the place value system and mathematics. The concept of zero was known in ancient India philosophically during the Upanis. ad- period. We do know that zero was used as mathematical entity in Chandāh. -sūtra. When did it become, along with a philosophical entity, to mathematical reality is not clearly established. In a short aphorism, to ﬁnd the number of arrangements of long and short syllables in a meter containing n syllables, zero is deﬁned: “[Place] two when halved, when unity is subtracted then 19Cajori 1980, p. 147; Accounts on the invention of zero are provided by Bronkhorst, 1994; Datta, 1926; Gupta, 1995; Kak, 1989, 1990; Ruegg, 1978. Ruegg has provided perhaps the best review that includes philosophical insights and historical developments. 20Br. hadāran. yaka-Upanis. ad, 3: 9: 26. 34 3. THE HINDU MATHEMATICS (place) zero . . . multiply by two when zero . . .”21 Pi ˙ngala was the younger brother of eminent grammarian Pān. ini, who lived near Peshawar around 2850 BCE22 King Devendravarman of Kalinga, Orissa inscribed his deed on a copper plate in 681 CE. This deed provides an archaeological evidence of place-value notation. It lists twenty as two and zero (20) in a place-value notation.23 In the Chaturbhuj Temple, Gwalior Fort, in Gwalior, India, a plaque is mounted where 270 number is listed with zero as a symbol. The plaque is about 1500 years old. The Bakhshālī manuscript mentions śūnya for zero at hundreds of places in the text.24 By the seventh-century, this concept already reached in the Far-East, where inscriptions of zero, in writing 605, is carved on a sandstone. This stone was discovered at the archaeological site of Trapang Prei, in Kratie province, in northeastern Cambodia. By the eighth-century, the concept of zero was already in China. Zero is mentioned and symbolized as a dot in Chapter 104 of the Kaiyun Zhanjing (Astronomico-astrological Canon), a book written during the reign of Kaiyun (713–741 CE): “Each individual ﬁgure is written in one piece. After the nine, the ten is written in the next row. A dot is always written in each empty row and all places are occupied so that it is impossible to make a mistake and the calculations are simpliﬁed.”25 The dot is an obvious reference to zero. This book was written by Qutan Xida (Gautama Siddārtha), an Indian scholar who settled in China, between 718 and 729 CE during the Tang dynasty.26 This book also contains Āryabhat.a’s sine tables. When the Arabs learned about zero, they literally translated the Sanskrit word śūnya (empty) into sifr (empty) in Arabic. “While the Arabs, as we have learned, did not invent the cipher [zero], they nevertheless introduced it with the Arabic numerals into Europe and taught Westerners the employment of this most convenient convention, thus facilitating the use of arithmetic in everyday life . . . al-Khwārizmī . . . was the ﬁrst exponent of the use of numerals, including the zero, in preference to letters. These numerals he called Hindu, indicating the In- dian origin.”27 Leonardo Fibonacci (1170–1250) called zero as zephir, in Latin, in his book, Liber Abaci.28 Adelard of Bath (1080–1152) used the term cifrae in his translation of al-Khwārizmī’s 21Pi ˙ngala’s Chandāh. -sūtra, 7: 28, 29, 30; Datta and Singh, 1938, vol. 1, p. 75. This quotation does not indicate the origin of number zero but provides a testimony that the zero was used as a mathematical number in India. Similar accounts of zero are also made elsewhere in the same manuscript (Chandāh. -sūtra, 3: 2 and 17; 4: 8, 11, and 12; 18: 35, 44, 48 and 51). 22Shyam Lal Singh, Pi ˙ngala Binary Number, in the book by Yadav and Mohan, 2011, p. 121. 23Filliozat, 1993. 24Hayasi, 1995, p. 210, 213. The Bakhshālī manuscript consists of seventy fragmentary leaves of birch bark and is presently preserved in the Bodleian Library at Oxford University. The original size of a leaf is estimated to be about 17 cm wide and 13.5 cm high, containing mathematical writings. The manuscript was accidentally found in 1881 near a village, Bakhshālī, that is now near Peshawar in Pakistan. It is currently preserved in Bodleian Library at Oxford University. In his detailed analysis, Hayasi assigns the seventh century CE as the date when this manuscript was written. However, recently researchers at the Bodelian library at Oxford University investigated an old copy of Bakhshālī manuscript and found it to be written during the third or fourth century using carbon-dating—some ﬁve hundred earlier than previously thought. For more information, http://www.bodleian.ox.ac.uk/news/2017/sep-14. 25Martzloﬀ, 1997, p. 207 26Yoke, 1985, p. 83 27Hitti 1963, p. 573. 28Horadam, 1975; Sigler, 2002, p. 17. 3.3. THE BINARY NUMBER SYSTEM 35 Zīj al-Sindhind.29 The word zero in the English language evolved from the terms in Latin and Italian. Opposite to the nirgun. a-rūpa approach to deﬁne God, the ancient Hindus tried to assign attributes connected to God. Once you start the process of assigning attributes, there is no limit; you can continue for ever. This led to the concept of inﬁnity. For this reason, in the ancient literature of the Hindus, God is also named as ananta (inﬁnity). The Br. hadāran. yaka Upanis. ad (5: 1) tells us: “The world there is full; The world here is full; Fullness from fullness proceeds. After taking fully from the full, It still remains completely full.” When you take away something from a given quantity, it becomes less. Simple arithmetic dictates this. However, it all fails when we deal with inﬁnity. You subtract something from inﬁnity, it still remains inﬁnity. So when you take away “fully from the full,” the remaining is still the same, inﬁnity. In Surya Prajnapati, a text that was written around 400 BCE, numbers are deﬁned as enumerable, innumerable, and inﬁnite. This text deﬁned inﬁnity in one direction, inﬁnity in two directions (inﬁnity in area), inﬁnity in three directions (inﬁnity in volume), and perpetually inﬁnite. 3.3 THE BINARY NUMBER SYSTEM A system in which numbers are represented as linear combinations of powers of two (2) is called the binary number system. This is a positional-numeral system employing only two kinds of bi- nary digits, namely 0 and 1. The importance of this system lies in the convenience of representing decimal numbers using a two-state system in computer technology. A simple “on-oﬀ ” or “open- closed” system can eﬀectively represent a number. Similarly, a set of condensers “charged” or “not-charged” can represent a number, or a set of two diﬀerent voltages on a device can eﬀec- tively represent a number. For this reason, the binary number system is popular in electronic circuitry. The presence of a binary number system is an example of the place-value notational system. 1). In the binary system, we write 3 In this system, the number 3 can be written as (1 as 11. To understand the system, a few examples are provided in Table 3.1. 21 C (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) C C C C C .0 .1 .1 .1 26/ 25/ 23/ 28/ 27/ Using this system, a somewhat larger number 444 is represented as 110111100 [(1 (cid:2) 24/ .1 0]. To convert a number into a binary number, divide the number by two. If there is one as remainder, then write one (1). If it is divisible, then write zero. For example, to write 45 in the binary system, let us divide by two: 45 the remainder is 0. Let us write 0. 11 1. 5 the remainder is 0. Let us write 0. 2 1. 2. The resultant is 11 and (cid:4) 2. The resultant is 5 and the remainder is 1. Let us write 2. The resultant is 1 and 1. The resultant is 0 and the remainder is 1. Let us write (cid:4) 2. The resultant is 2 and the remainder is 1. Let us write 1. 2 2. The resultant is 22 and the remainder is 1. Let us write 1. 22 22/ 21/ .0 .1 C C C (cid:4) (cid:4) (cid:4) (cid:4) (cid:2) (cid:2) (cid:2) 29Neugebauer, 1962, p. 18. 36 3. THE HINDU MATHEMATICS Table 3.1: Decimal Numbers and Their Binary Equivalent By taking the ﬁrst quotient 1 and the remainders in the reverse order, we can write 45 (cid:2) C C .0 .1 24/ in binary number: 101101. This number implies .1 (cid:2) 23/ 25/. This converts to (1 + 4 + 8 + 32) and equals to 45. Interestingly, this rule is provided in Pi ˙ngala-Sūtra (8: 24–25) in a cryptic language which is nicely explained by Barend A. van Nooten using history documents that provided commentary to Pi ˙ngala’s verse.30 Recently, Shyam Lal Singh has explained the rules of poetic metrics in an article, Pi ˙ngala Binary Numbers, in the book, Ancient Indian Leaps into Mathematics.31 .1 .0 .1 C C C (cid:2) (cid:2) (cid:2) (cid:2) 20/ 21/ 22/ The ancient Hindus carefully deﬁned the methodology to write hymns which involved the study of language and prosody. This allowed a verse to have speciﬁc rhythm (metrical structure) in chanting. The ﬁrst comprehensive treatise that is known to us was written by Pi ˙ngala, called Chandāh. -sūtra (or Candāh) or Chandāh. -śāstra.32 In Sanskrit, the science of versiﬁcation (prosody) consists of verse feet, padas, that are composed of syllables: light (laghu) and heavy (guru). A knowledge of metrics is essential which is determined by the permutations and combinations of short and long syllables. Each verse usually consists of a set of four quarter verses, called pādas. All verses contain the same number of syllables. For example, most verses in the Sanskrit language are either 8-, 11-, or 12-syllabic. 30van Nootan, 1993. Barend A. van Nooten is a former professor of Sanskrit at the University of California at Berkeley. He is known for his co-authored books, Rigveda: A Metrically Restored Text and The Sanskrit Epics. 31Yadav and Mohan [Editors], 2011. 32Weber, 1863; taken from van Nooten, 1993, also reproduced in Rao and Kak, 1998. Decimal NumbersBinary Equivalent1 = (0 × 21) + 1012 = (1 × 21) + 0103 = (1 × 21) + 1114 = (1 × 22) + (0 × 21) + 01005 = (1 × 22) + (0 × 21) + 11016 = (1 × 22) + (1 × 21) + 01107 = (1 × 22) + (0 × 21) + 11118 = (1 × 23) + (0 × 22) + (0 × 21) + 010009 = (1 × 23) + (0 × 22) + (0 × 21) + 1100110 = (1 × 23) + (0 × 22) + (1 × 21) + 0101011 = (1 × 23) + (0 × 22) + (1 × 21) + 1101115 = (1 × 23) + (0 × 22) + (1 × 21) + 1111117 = (1 × 24) + (0 × 23) + (0 × 22) + (0 × 21)+ 1100013.4. THE FIBONACCI SEQUENCE 37 These quarters, (pādas), which are again subdivided into various groups or subgroups, depending on the number syllables (aks. ara) in each quarter and the placement of short and long syllables. The vowels, such as a, i, u, r., and l. are short syllables while ā, e, ai, ī, o, au, and ū are long syllables. There are some more rules to deﬁne the short and long syllables which are beyond the scope of this book.33 Pi ˙ngala gave the following rule: “(Place) two when halved” “when unity is subtracted then (place) zero;” “multiply by two when zero;” “square when halved.”34. It was van Nootan’s expertise in Sanskrit metrics that allowed him to discover this unique binary system. In this system, each syllable is assigned a numerical value, based on its position in the meter. The work of Pi ˙ngala in Candāh. -sūtra deﬁnitely shows that he knew the place-value system of numeric notations and used a binary numerical base, and not base-10.35 The discovery of binary numbers is generally attributed to Gottfried Leibniz (1646–1716 CE) at the end of 17th century. Leibniz is said to have come up with the idea when he interpreted Chinese hexagram depictions of Fu Hsi in I-Ching (The Book of Changes) in terms of a binary code.36 Pi ˙ngala, in van Nooten’s views, did not provide the further applications of the discovery. However, this knowledge was available to Sanskrit scholars of meterics.37 “Unlike the case of the great linguistic discoveries of the Indians which directly inﬂuenced and inspired Western linguistics, this discovery of the theory of binary numbers has so far gone unrecorded in the annals of the West,” remarks van Nooten. 3.4 THE FIBONACCI SEQUENCE Leonardo Fibonacci (1170–1250) was an Italian mathematician who popularized Hindu nu- merals in the Western world by writing a book, Liber Abaci. This book played an important role in the growth of mathematics in Europe. Fibonacci came in contact with Hindu mathematics during his stay in Bugia, located on the Barbary Coast of Africa. In Fibonacci’s own account, his father was a public oﬃcial there to help the visiting Pisan merchants there. His father wanted Fibonacci to learn mathematics for “a useful and comfortable future.” He arranged some lessons in mathematics for the young Fibonacci from well known scholars. This is how Leonardo learned about Hindu numerals. Leonardo recognized the superiority of this new system over his native Roman numeral system and wrote the above-mentioned book about it. The Fibonacci sequence is connected with cumulative growth, and plays a role in various number games and natural phenomena, including a botanical phenomenon called phyllotaxis 33For more information, read Singh, Shyam Lal, Pi ˙ngala Binary Numbers, in the book, Ancient Indian Leaps into Mathe- matics. Van Nooten, 1993 and Datta and Singh, 1962 are the other resources to understand this system. 34Datta and Singh, 1962, vol. 1, p. 76; van Nooten has provided a slightly diﬀerent translation. However, both systems provide similar results. 35van Nooten, 1993 36Loosen and Vonessen, 1968, p. 126–131; reference taken from van Nooten, 1993. 37van Nooten, 1993. 38 3. THE HINDU MATHEMATICS where the arrangement of leaves on a system is studied.38 The seeds-pattern in a sunﬂower follow the Fibonacci sequence. The following is the problem that Fibonacci posed in Liber Abaci that is well known today as the Fibonacci sequence: “A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also. Because the above written pair in the ﬁrst month bore, you will double it; there will be two pairs in one month. One of these, namely the ﬁrst, bears in the second month, and thus there are in the second month 3 pairs; of these in one month 2 are pregnant, and in the third month 2 pairs of rabbits are born, and thus there are ﬁve pairs in the month; in this month 3 pairs are pregnant, and in the fourth month there are 8 pairs, of which 5 pairs bear another 5 pairs; these are added to the 8 pairs making 13 pairs in the ﬁfth month; these 5 pairs that are born in this month do not mate in this month, but another 8 pairs are pregnant, and thus there are in the sixth month 21 pairs; to these are added the 13 pairs that are born in the seventh month; there will be 34 pairs in this month; to this are added the 21 pairs that are born in the eighth month; there will be 55 pairs in this month; to these are added the 34 pairs that are born in the ninth month; there will be 89 pairs in this month; to these are added again the 55 pairs that are born in the tenth month; there will be 144 pairs in this month; to these are added again the 89 pairs that are born in the eleventh month; there will be 233 pairs in this month. To these are still added the 144 pairs that are born in the last month; there will be 377 pairs, and this many pairs are produced from the above written pair in the mentioned place at the end of the one year.”39 Based on the assumptions, at the beginning of the second month, there will be two pairs. After the second month, there will be three pairs. In the third month there will be 5 pairs. In the consecutive month 8, 13, 21, 34, 55, 89, 144, 233, and 377 pairs will be there. Thus, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and 377 pairs of rabbits will be available. As one can notice, in this number sequence, Also, xn xn D 1 (cid:0) C xn 2 (cid:0) xn 1 C (cid:2) xn 1 (cid:0) D x2 n C . (cid:0) 1/n It was the French mathematician Édouard Lucas (1842–1891) who assigned this mathe- matical series as “the Fibonacci sequence.” Later, an Oxford botanist, A. H. Church, recognized that the number of seeds in the spiral patter of sunﬂower head match with the Fibonacci sequence numbers. In 1963, an International Fibonacci Society was formed to study related topics.40 In India, this sequence appeared in the science of hymn-composing, or metrics, just like the binary numbers that were discussed in the previous section. In one particular category, the 38For more information, see Hoggatt, 1969. 39Sigler, 2002, p. 404–405. 40Gies and Gies, 1969, p. 81–83. 3.5. THE SQUARE-ROOT OPERATION 39 number of variations of meters having 1, 2, 3, . . . morae (syllabic instant) are 1, 2, 3, 5, 8, 13, . . ., respectively, the so-called Fibonacci numbers. Ācārya Virāhanka (lived sometime between 600–800 CE), Gopāla (before 1135 CE) and Hemachandra (ca. 1150 CE) had provided this sequence before it was suggested by Leonardo Fibonacci. To understand this metrical science, a knowledge of Sanskrit is required. Readers can get more information on this from the work of Permanand Singh that is published in a prestigious journal, Historia Mathematica. He concludes that “the concept of the sequence of these numbers in India is at least as old as the origin of the metrical sciences of Sanskrit and Prakrit poetry.”41 3.5 THE SQUARE-ROOT OPERATION The approximate value of the square root of the number 2 can be calculated using an arithmetical equation that is an alternative form of the Pythagorean theorem, as explained later in Section 3.8. This theorem is provided in several Śulbasūtras.42 If we apply the expression to a square of side 1 in any unit system, we can ﬁnd the value of p2. According to this theorem, the diagonal of a right-angle triangle with two equal sides (a) is D (cid:2) For a = 1, this gives us the approximate value of p2. 4 (cid:0) C (cid:2) 3 3 L a a a 3 C a 4 (cid:2) 34 p2 L D 1 C D 1 4 (cid:2) (cid:2) 577 408 34 D 1 3 C 3 p2 1 (cid:2) D 4 (cid:0) 3 1:41 This is the accepted value. If one tries to get higher accuracy in the results, the value is correct to the ﬁfth decimal place, 1.41421. After the ﬁfth decimal place, the value given in this formula is slightly higher (1.4142156) than the actual value (1.4142135). Professor John F. Price of the University of New South Wales, Australia, provides the rationale of this formula in Baudhayana Śulbasūtra.43 According to him, we know the value of p2 is between 1 and 2. If we equate p2 to 1 or 2 and square both sides we get 2 on one side while 1 or 4 on the other side. Using similar considerations, we know that p2 will be less than .1 1 3 /, Therefore, our ﬁrst initial approximation is 1 2 / and more than .1 C C C If we improve this value by adding a small term (x) to our value of p2, square both sides, (cid:25) p2 1 1 3 assume x2 to be quite small and neglect it, we go through the following sequence: 41Singh, 1985. 42Baudhayāna-Śulbasūtra, 2: 12; Āpastambā-Śulbasūtra, 1: 6; and Kātyāyana-Śulbasūtra, 2: 9. 43Price, in Gorini, 2000, p. 46–55. 40 3. THE HINDU MATHEMATICS p2 1 C D 1 3 C x D 4 3 C x 2 (cid:19) (cid:18) 4 3 2 D (cid:18) 4 3 2 D 8 3 x C 2 (cid:19) x2 C 8 3 x C 1 (cid:2) 4 In our next approximation, x D 3 p2 1 C (cid:25) 1 3 C 3 1 (cid:2) y 4 C This reduces to Again, square and ignore y2 term. The next step yields p2 4 3 C 3 D 1 (cid:2) y 4 C 16 9 C 9 2 D 1 2 9 16 C 4 4 C y (cid:18) 2 4 (cid:2) 3 C 3 (cid:2) (cid:2) (cid:2) If we simplify this equation and calculate y, we get (cid:19) 4 2 (cid:2) If we continue further, the next approximation will be y D (cid:0) 3 1 4 34 (cid:2) (cid:2) L 1 C D 1 3 C 3 1 (cid:2) 4 (cid:0) 3 1 4 (cid:2) (cid:2) 34 (cid:0) 3 4 (cid:2) (cid:2) 1 34 (cid:2) 577 2 (cid:2) This will give us p2 = 1.414213562374, a value accurate up to the thirteenth place. This approximation was done by David W. Henderson of Cornell University44 and Price45. It is inter- esting that the Śulbasūtra does mention that the value is only approximate and a little bit higher than the actual value (saviśes. a).46 This process is called the method of successive approximations in most mathematics books, a modern technique. 44Read, Square Roots in the Śulba Sūtras by Henderson, in Gorini, 2000, p. 39–45. 45Price, John F., Applied Geometry of the Śulba Sūtras, in the book by Gorini, 2000, p. 46–55. 46Read, Square Roots in the Śulba Sūtras by Henderson, in Gorini, 2000, p. 39–45. This process continues with more terms added. It always remains only an approximate value. Depending on the type of accuracy we need in everyday situation, the ancient Hindus felt appropriate to stop after reading to the ﬁfth place of the decimal. Henderson also compares the popular “divide-and-average” method, also called the Newton’s method, with the Baudhayāna’s method and concludes that Baudhayāna’s method “uses signiﬁcantly fewer computations” than the Newton’s method to reach the same order of accuracy. 3.6. ALGEBRA 41 3.6 ALGEBRA Al-Khwārizmī, Muhammad ibn Mūsā is one of the earliest known astronomers and mathemati- cians from the glorious period of Baghdad/Islam. He was native to the Khwarizm Region in Persia, as the name suggests. He later moved to Baghdad and served in the court of al-Mamūn (813–833 CE). His best known works are: Kitāb al-jabr wa‘l Muqābala (The Book of Manipula- tion and Restoration), Kitāb al Hisāb al-Hindī (Book of Indian Mathematics), and Zīj al-Sindhind (Astronomy Table from India). The last two books are obviously the works of the Hindus as the titles suggest. Even the third book was based on the work of the Hindus. The impact of al- Khwārizmī was so great in Europe that the title of his one book became synonymous with the theory of equations. The word “algebra” stemmed from the word al-jabr which appeared in the title of al-Khwārizmī’s book. Al-jabr literally means bone-setting, indication manipulation of equations. Al-Khwārizmī played a crucial role as a disseminator of science. Latinization of his name took many forms: from algorizmus to algoritmus to algorithmus. The mathematical term, algorithm, has possibly stemmed from his Latinized name.47 1 John Wallis (1616–1703), an English mathematician, taught at Oxford University, wrote a book, A Treatise of Algebra both Historical and Practical in 1685. He is credited with introducing . In this book, he writes: “However, it is not unlikely that the Arabs, the symbol for inﬁnity, who received from the Indians the numerals ﬁgures (which the Greeks knew not), did from them also receive the use of them, and many profound speculations concerning them, which neither Latins or Greeks did know, till that now of late we have learned them from thence. From the Indians also they might learn their algebra, rather than from Diophantus, (who only of the Greeks wrote of it, and he but late, and in a method very diﬀerent from theirs) . . . And the name they [Arabs] gave it (Al-gjabr W‘al-mokabala) seems to have no aﬃnity with any Greek name . . . ”48 By the ﬁfth century CE, the following are some of the rules that were known to the ancient Hindus. All these rules are taken from Āryabhat. īya. Āryabhat.a I did not provide the derivation of the rules in most cases and called the knowledge ancient. 47For more information, read Crossley and Henry, 1990; Hughes, 1989; King, 1983; Sesiano, in the book by Selin, 1997. 48Wallis, 1685, page 4, Chapter 2. 42 3. THE HINDU MATHEMATICS 3.6.1 SUM OF A SERIES “The desired number of terms minus one, halved, then increase by the number of the preceding terms (if any), multiply by the common diﬀerence between the terms, and then increase by the ﬁrst term of the (whole) series. The result is the arithmetic mean (of the given number of terms). This multiplied by the given number of terms is the sum of the given terms. Alternatively, multiply the sum of the ﬁrst and last terms by half the number of terms.”49 This rule can be mathematically written for a series with initial term a and common dif- ference between terms as d . mathematically, it can be written as .a a C C d / C :::(cid:140)a C .n (cid:0) 1/d (cid:141) The sum of the series for n terms is: Sn D n (cid:20)(cid:18) n 1 (cid:19) d (cid:0) 2 a(cid:21) C n 2 (cid:140)a .a .n (cid:0) C C 1/d /(cid:141) (cid:140)first term last term(cid:141) C D n 2 D These results are correct. 3.6.2 SUM OF A SERIES WITH (cid:134)n2 AND (cid:134)n3 “The continued product of the three quantities viz, the number of terms, number of terms plus one, and twice the number of terms increased by one when divided by 6 gives the sum of the series of squares of natural numbers. The square of the sum of the series of natural numbers gives the sum of the series of cubes of natural numbers.”50 Mathematically, the above verse translates as follows: 32 For the series 12 C correct value for all values of n. Similarly, for the series 13 33 23 22 C C C ::: n2, the sum equals to n.n to .1 2 3 C C ::: C C ::: C C n/2. This reduces to h n.n C 2 C n3, according to Āryabhat.a I, the sum equals which provides correct result. C 2 1/ i 1/.2n 6 C C 1/ . This provides the 3.6.3 SOLUTION TO A QUADRATIC EQUATION Āryabhat.a I also gave the solution of a complex money-transaction problem: “Multiply the sum of the interest on the principal and the interest on this interest by the time and by the principal. Add to this result the square of the half of the principal. Take the square-root of this. Subtract 49Āryabhat. īya, Gan. itpada, 19. 50Āryabhat. īya, Gan. itpada, 22. 3.7. GEOMETRY 43 half the principal and divide the remainder by the time. The result will be the interest on the principal.”51 The problem can be written as follows: “A certain amount of money (P for principal money) was given on loan for one month with unknown interest x. The unknown interest x that was accrued in one month was again loaned for time T months. On the completion of this period, the original interest x and the interest on this interest, all together, became I . Find out the rate of interest x on the amount P . The answer provided by Āryabhat.a I is as follows: pIP T C .P =2/2 T (cid:0) P =2 x D The solution provided by Āryabhat.a I is correct. 3.7 GEOMETRY The ancient Hindus used an elaborate knowledge of geometry for the construction of altars for religious purposes, for arranging various battalions of soldiers in wars, and for planning the design of their cities.52 In scientiﬁc warfare, a smaller army can prevail with proper geometri- cal constructions in achieving their tactical goals. For example, Pān. d. ava in Mahābhārata used their much smaller army and these tactical geometrical constructions against a much larger army of Kaurava. Cakravyūha was an important geometrical construction of the placements of war- riors to trap enemy warriors during the period of Mahābhārata. Abhimanyu, son of Arjuna, as mentioned in Mahābhārata, knew how to break and enter into the geometrical fortiﬁcation of cakravyūha. However, he did not know the ways to come out of it. He was trapped and lost his life. In Mahābhārata war, multiple geometrical constructions, deﬁned by their similarity to mostly animal or object shapes, were used in organizing soldiers to ﬁght. The word śulba means a chord, a rope, or a string and Śulbasūtra signiﬁes geometry using strings. The Śulbasūtra are not the books of geometry or mathematics; these books deal mostly with rituals. The knowledge of geometry and mathematics is used to perform the rituals. One can consider them as the “ﬁrst applied geometry text in the world” to “combine geometry and numerical techniques.”53 3.7.1 TRANSFORMING A SQUARE INTO A CIRCLE “If it is desired to transform a square into a circle, (a cord of length) half the diagonal (of the square) is stretched from the center to the east (a part of it lying outside the eastern side of the square); with one-third (of the part lying outside) added to the remainder (of the half diagonal), the (required) circle is drawn.”54 51Āryabhat. īya, Gan. itpada, 25. 52Datta, 1932; Kulkarni, 1983; Sarasvati Amma, 1979; Sen and Bag, 1983; Staal, 1999; Thibaut, 1875. 53Henderson, in Gorini, 2000 54Baudhayāna-Śulbasūtra, 2: 9. 44 3. THE HINDU MATHEMATICS Let PQRS be the given square and O is the center of the square (see Figure 3.1). The half diagonal OP is drawn and an arc PAQ is formed, implying OP = OA. A circle of radius OB (r) is drawn where OB = OC + CB and CB = 1 3 CA. This implies that OB = OC + 1 This equals OB = OC + 1 Let 2a be the side of square PQRS, 3 CA. 3 (OA - OC). r a C D 1 3 .p2a a/ (cid:0) a(cid:140)1 r D C 1 3 .p2 1/(cid:141) (cid:0) The area of the circle is (cid:25) r 2 with the area of the given square (4a2). D .2 r a 3 D 3:14(cid:140) a 3 .2 p2/ C p2/(cid:141)2 C 4:06a2. This is in rough agreement D Figure 3.1: Transforming square into a circle of the same area. Hindus’ mathematical books did not provide axioms and postulates; the mathematical rules are based on experimental veriﬁcation. As a result, some rules are only approximately cor- ABPQSRCOrect. Seidenberg tried to assign a possible period for the general use of geometry among the Hindus but realized, “no matter how far we go back in ’history’, we ﬁnd geometrical rituals.”55 3.7. GEOMETRY 45 3.7.2 HEIGHT OF A TALL OBJECT “(When two gnomons of equal height are in the same direction from the lamp-post), multiply the distance between the tips of the shadows (of the two gnomons)[CD] by the (larger [GD] or shorter [EC]) shadow and divide by the larger shadow diminished by the shorter one [GD - EC]: the result is the upright (i.e., the distance of the tip of the larger [BD] or shorter shadow [BC] from the foot of the lamp-post). The upright multiplied by the height of the gnomon and divided by the (larger or shorter) shadow gives the base (i.e. height of the lamp-post).”56 Mathematically, and BD D CD GD (cid:2) GD - EC AB h BC (cid:2) EC D D h (cid:2) GD CD EC (cid:0) The proof of this theorem is as follows (see Figure 3.2). Let AB be the unknown height that we want to ﬁnd out. We place a gnomon of height h at point E. This gives us the shadow EC. Now we place the same gnomon or another one of the same size at point G. This gives us shadow GD. Figure 3.2: Determining height of a tall object using a small stick. Using similar triangles, AB h D BC EC D BD GD 55Seidenberg, 1962. 56Āryabhat. īya, Gan. itapada,16. For more information, read Mishra and Singh, 1996; and Shukla and Sarma, 1976, p. 58. ABECGDHhhF46 3. THE HINDU MATHEMATICS As given before, Since, BD = BC + CD, AB D h BC (cid:2) EC BC EC D BD GD BC CD C GD BC CD C BC BC EC GD EC D D CD BC D GD EC 1 C CD BC D GD EC (cid:0) 1 CD BC D GD EC (cid:0) EC Therefore, BC D CD GD EC EC (cid:2) (cid:0) AB h BC (cid:2) EC D D h (cid:2) GD CD EC (cid:0) Thus, by measuring the lengths of shadows at two diﬀerent locations for a stick, one could measure the height of the unknown object. Or, by aligning the stick in such a way that one could see the top of the object in line with the top of stick while looking from the ground level from two diﬀerent locations, one could measure the height of the unknown object. 3.7.3 THE VALUE OF (cid:25) The Greek letter (cid:25) (pronounced as pi) indicates the ratio of the circumference of a circle to its diameter that is a constant for any circle. The ancient Hindu books generally provide two values of (cid:25): one for rough calculations and second for precise measurements. The knowledge of (cid:25) is useful in the construction of altars, wheels of a cart, the metallic rims of a wheel, and in geometry. The Mānava-Śulbasūtra provided the value of (cid:25) to be 3.2: “The ﬁfth part of the diameter added to the three times the diameter gives the circumference (of a circle). Not a hair of length is left over.”57 This provides the value of circumference, C , from diameter, D, as, 3.8. THE PYTHAGOREAN THEOREM 47 16 5 This gives a value of (cid:25) which is close to the actual value of 3.14. Since the purpose of these D 5 C 3:2D 3D D D D D C books was to prepare altars, these calculations were good enough for that purpose. Āryabhat.a I gave the value of (cid:25) that is correct to the fourth decimal place: “Add four to hundred, multiply by eight, and add sixty two thousand. The result is approximately the circum- ference of a circle [C] of which the diameter [D] is twenty thousand.”58 Mathematically, we know that C I’s method, is equal to: (cid:140).4 (cid:25) D D C (cid:25) D. Therefore, the value of (cid:25), based on Āryabhat.a 100/ 8(cid:141) (cid:2) 20; 000 C 62; 000 62; 832 20; 000 D D 3:1416 This is equal to the presently accepted value of 3.1416, for up to 4 decimal places. Āryabhat.a I called this value to be approximate. This makes sense since the value of (cid:25) can only be determined approximately since the ratio of circumference to diameter is not evenly divisive; it can have an innumerable number of signiﬁcant ﬁgures. It is an endeavor for many mathe- maticians to calculate a more precise value of (cid:25). The value of (cid:25) to a large number of signiﬁcant ﬁgures is commonly used to check the speed, eﬃciency, and the accuracy of computers. 3.8 THE PYTHAGOREAN THEOREM The so-called Pythagorean theorem connects the three sides of a right-angle-triangle with the relation, D where a, b, and c are the base, perpendicular, and hypotenuse, respectively of a right- angle triangle (see Figure 3.3). Pythagoras, a Greek philosopher is said to be the originator of the theorem sometime during sixth century BCE C a2 b2 c2 Let us provide a few statements from the Śulbasūtra that indicate the understanding of the Pythagorean theorem among the Hindus: 57Mānava-Śulbasūtra, 11: 13. 58Āryabhat. īya, Gan. itapada, 10. Also, Read Hayashi et al., 1989 and Kulkarni, 1978a. The work of Hayasi et al. has a good review of the later developments on the issue in India. For example, Madhav (14th century) calculated the value of (cid:25) that was correct to eleven places. 48 3. THE HINDU MATHEMATICS Figure 3.3: A right-angled triangle, PQR. “The diagonal of a square produces double the area (of the square). It is p2 (dvikaran. ī) of the side of the square (of which it is the diagonal).”59 The word dvikaran. ī literally means “that which produces 2,” implying the twice area of the square constructed using dvikaran. ī as one side in comparison to the original square. “The diagonal (of a right angle triangle) of which the breadth is pada and the length 3 padas is p10 padas.”60 “The diagonal (of a right triangle) of which the breadth is 2 pada and the length is 6 pada is p40 pada.”61 The Baudhayāna-Śulbasūtra provides another rule for a right-angle triangle: “The areas (of the squares) produced separately by the length and the breadth of a rectangle together equal the area (of the square) produced by the diagonal.”62 Similar rules are given elsewhere in the ancient Hindu literature: “The areas (of the squares) produced separately by the length and the breadth of a rectangle together equal the area (of the square) produced by the diagonal. By the understanding of these (methods) the construction of the ﬁgures as stated (is to be accomplished).”63 59Āpastambā-Śulbasūtra, 1: 5. 60Kātyāyana-Śulbasūtra, 2: 4. 61Kātyāyana-Śulbasūtra, 2: 5. 62Baudhayāna-Śulbasūtra, 1: 48. 63Āpastambā-Śulbasūtra, 1: 4. QacbPRIIIIII3.9. TRIGONOMETRY: FROM JYĀ TO SINE 49 There is a curious similarity between Baudhayāna and Pythagoras on the so-called Pythagorean theorem. It is important to understand that Baudhayāna’s work was compiled at least around 1700 BCE, while the Pythagorean theorem was compiled over a millennia later, i.e., around sixth-century BCE.64 There are indications that Pythagoras perhaps came in contact with India or Indian wisdom. The Pythagorean theorem is mostly given in terms of geometry in most cultures. However, among the Hindus, they used a mathematical expression for the Pythagorean theorem which is unique to them. Several Śulbasūtras provided a arithmetical method to ﬁnd the diagonal of a right-angled triangle with two equal sides: “The measure is to be increased by its third and this (third) again by its own fourth less the thirty-fourth part (of the fourth); this is (the value of ) the diagonal of a square (whose side is the measure).65 Mathematically, for a right-angled triangle with two equal sides of length a, the hy- potenuse is equal to L a D C a 3 C 3 a (cid:2) a 4 4 (cid:0) 3 34 (cid:2) (cid:2) No other culture has provided a similar mathematical form to calculate the hypotenuse. 3.9 TRIGONOMETRY: FROM JYĀ TO SINE Trigonometry is a branch of science which deals with speciﬁc functions of angles and their application to calculations in geometry. The sine function, as deﬁned in trigonometry, is essential to the study of geometry. For a right-angle-triangle, if (cid:18) is the acute angle of a right triangle, the mathematical symbol sin, pronounced as sine, of (cid:18) is the ratio of the side opposite (b) and b the hypotenuse (c). Mathematically, sin (cid:18) c . Why do we call this function sine? Who chose this word for the scientiﬁc community for what reason? What is the meaning of this word? These are simple questions that intrigue curious minds when they ﬁrst learn about this trigonometric function. The answer is as follows: The sine function was called jyā by Āryabhat.a I. Al-Khwārizmī, when borrowed this concept, chose an Arabic that is similar in pronunciation. He used geib or jaib for this term. This word has a speciﬁc meaning: fold or pocket. The Latin word for pocket or fold is sinus, and, thus, the term sine for this trigonometric function evolved. D “The most signiﬁcant contribution of India to medieval mathematics is in trigonometry. For a circle of unit radius the length of an arc is a measure of the angle it subtends at the center [center] of the circle. The Greeks, to facilitate calculations in geometry, tabulated values of the chord of arcs. This method was replaced by Hindu mathematicians with half chord of an arc, known as sine of the angle . . . No inﬂuence on the West was exerted by the development in India . . . Thus, methods had been known in India were not rediscovered until 1624 by the 64Seidenberg, 1962. It is likely that the date assigned by Seidenberg will be revised with new scholarship. 65Baudhayāna-Śulbasūtra, 2: 12; Āpastambā-Śulbasūtra, 1: 6; and Kātyāyana-Śulbasūtra, 2: 9. 50 3. THE HINDU MATHEMATICS French mathematician Claude-Gaspar Bachet, sieur de Méziriac,”66 suggests the Encyclopedia Britannica (see Figure 3.4). Figure 3.4: Āryabhat.a I’s method to deﬁne an arc. Āryabhat.a I used the half chord on an arc, deﬁned the sine function and gave a table of 21; 600 sines of the angles. In his book, the circumference of a circle was divided into 360 equal segments. He also divided the quadrant of a circle into 24 equal parts. The smallest is thus 2250 or 3(cid:14)450. Āryabhat.a I deﬁned jyā (or sin (cid:18)) for a circle of radius, R, of 3438 units. What is the mystery behind this strange number 3438? Well, we know that there are 21600 minutes of arc in a circle of 360 degrees. If we divide this number by 2(cid:25), we get 3437.74 = 3438. A consequence of this is that if angle (cid:18) is measured in minutes of arc and is small, then 3438 sin (cid:18) is approximately equal to (cid:18). For example, for a 5-degree angle, the angle comes out to be 300 in minutes. R sin (cid:18) = 3438 sin (300) = 299.6 = 300, implying that R = 3438 is similar to using radians instead of degrees in modern mathematics, where we have that sin x is approximately equal to x.67 In Table 3.2, a comparison of Āryabhat.a I’s values with the modern values is provided. 60 D (cid:2) 3.10 DIFFUSION OF HINDU MATHEMATICS TO OTHER CULTURES 3.10.1 THE MIDDLE EAST Owing their gratitude to the Hindus, numerals were always called arqam hindiya in the Middle East, meaning the Hindu numerals.68 These numerals were known as Hindu numerals through- out the medieval period in the Arab world and are known so even today. Al-Jāh. iz, (ca. 776–868 CE), al-Khwārizmī (ca.800–847 CE), al-Uqlīdisī (ca. 920–980 CE) and Ibn Labbān (ca. 971– 1029 CE), several famous natural philosophers from the Middle East or nearby regions, have testiﬁed to the Hindu origin of the so-called Arabic numerals. 66Encyclopedia Britannica, vol. 23, p. 605, 1989. 67For more details, read Achar, 2002; Clark, 1930; Hayasi, 1997; and Shukla and Sarma, 1976. 68Sarton, 1950. ABCORh = R sin (λ/2) = R sin θhθλTable 3.2: Āryabhat.a I’s and Modern sine values 3.10. DIFFUSION OF HINDU MATHEMATICS 51 Interestingly, in conformity with Arabic tradition, these numerals were called Hindu all through the medieval and early Renaissance periods in Europe by their top scholars. Adelard of Bath (1116–1142 CE) and Roger Bacon (1214–1292 CE) in England, Leonardo Fibonacci (1170–1250 CE) in Italy, S. ā‘id Al-Andalusī (1029–1070 CE) and Ibn Ezra (11th century CE) in Spain, and Voltaire (1694–1778 CE) in France called them Hindu numerals. They were la- AngleĀryabhata I's ValueModern sine value × 34383°45’2252257°20’44944911°15’67167115°0’89089018°45’1105110522°30’1315131526°15’1520152130°0’1719171933°45’1910191037°30’2093209241°15’2267226645°0’2431243148°45’2585258452°30’2728272856°15’2859285960°0’2978297763°45’3084308367°30’3177317671°15’3256325675°0’3321332178°45’3372337282°30’3409340986°15’3431343190°0’3438343852 3. THE HINDU MATHEMATICS beled Arabic only after the sixteenth century by some.69 This was the beginning of the colonial period. Why the Hindu numerals got changed to Arabic numerals is a mystery in the history of mathematics. Did it happen due to a coincidence or was it a result of complex political ambitions of the West? This is a curious mystery that is not yet resolved. Today, most textbooks call these numerals the Hindu-Arabic numerals. Al-Jāh. iz, (776–868 CE), a well-known Arab theologian and natural philosopher, at- tributed the origin of numerals to the Hindus.70 Using Hindu numerals, Kūshyār Ibn Labbān (ca. 971–1029 CE) wrote a book on Hindu arithmetic, Principles of Hindu Reckoning,71 which became quite popular during the eleventh-century Islamic world. Kūshyār ibn Labbān was pri- marily an astronomer from Jilan, a village in Persia on the south of Caspian Sea, and wrote his manuscripts in Arabic. He started his book with the following sentence: “In the name of Allāh, the Merciful and Compassionate. This book on the principle of Hindu arithmetic is an arrange- ment of Abu al-Hasan Kushyār bin [Ibn] Labbān al-Jīlī, may God have mercy on him.”72 In the time of communal tensions around the world, Labbān’s book sets an example for all—a Muslim who wrote a book on the Hindu arithmetic with the mercy of Allāh. It is com- pletely in line with the doctrines of Prophet Mohammad who suggested that his followers travel around the world for knowledge: “You should insist on acquiring knowledge even if you have to travel to China.” Ibn Sīnā (980–1037 CE), a noted Persian scholar of the eleventh century mentions that the Hindu method of calculation was common in Persia during his period. Even merchants with small businesses used the Hindu mathematical methods for calculations. Ibn Sīnā himself learned such methods from a vegetable merchant, Mahmūd al-Massāhī.73 Ibn Sīnā was a proliﬁc writer with books on medicine, metaphysics, natural philosophy, and mathematics. He explained the Greek works of Aristotle, Plato, and Plotinus within the framework of Islam. Since the Greek numerals were already in use in Arabia when the Hindu numerals were introduced, both numeral systems competed with each other. Lobbies were formed where the superiority of one system over the other was debated/discussed. Severus Sebokht (died, 662 CE), a Syrian natural philosopher mentioned of such a rivalry between the Greek and Hindu numerals. 74 “I will omit all discussion of the science of the Hindus, a people not the same as Syrians, their subtle discoveries in the science of astronomy, discoveries which are more ingenious than those of the Greeks and the Babylonians; their valuable method of calculation; their computing 69Clark, 1929, p. 217. 70Pellat, 1969, p. 197; Levy and Petruck, 1965, p. 6. 71Levy and Petruck, 1965. 72Levy and Petruck, 1965. 73Gohlman, 1974, p. 21 and 121. 74Wright, 1966, p. 137. Sebokht was born in Nisibis in Persia and taught Greek philosophy in Syria. Later, he became the bishop of the convent of Ken-neshre (Qenneshre), a center of Greek learning in Upper-Euphrates in West-Syria. He had a good grasp of various sciences and wrote on astronomy, geography, and mathematics. His manuscripts are preserved in museums in London and Paris. Sebokht believed in the universal nature of science and was of the opinion that many cultures, not just the dominant Greeks, contributed to the Arab scientiﬁc pool. 3.10. DIFFUSION OF HINDU MATHEMATICS 53 that surpasses description. I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they have reached the limits of sci- ence, should know these things, they would be convinced that there are also others [Hindu] who know something.”75 This quotation is a proof that the Hindu numerals were in practice in Arabia by the seventh-century. Also, by the seventh century, people started to discard the Greek numerals in favor of the Hindu numerals in Arabia. Al-Uqlidīsī (920–980 CE, also written as Uklidisi, meaning ‘the Euclid-man’ for his role as copyist of Euclid’s work) in his book, Kitāb al-Fusūl f ī al-hisāb al-Hindī deﬁned the Hindu numeral system and explained Hindu arithmetic: “I have looked into the works of the past arithmeticians versed in the arithmetic of the Indians [Hindus, in the original] . . . We can thus dispense with other works of arithmetic. The reader who has read other works will realize this fact and thus adhere to this work and prefer it to others, new or old, for it contains more than any other books of this kind.”76 The title of the above book indicates that the book contained the mathematics of the Hindus. According to al-Uqlidīsī, “even the blind and the weak sighted will ﬁnd in our explanations and summaries something to beneﬁt from without toil or cost, by the will and help of God.”77 He mentioned the use of the dust-board abacus for the Hindu arithmetic [hisāb al-Ghubār, hisāb al-takht (board), al-Hisāb al-Hindī or Hisāb al-turāb (dust)].78 This kind of board became so popular for mathematical calculations, arithmetic was called Hisāb al-Ghubār, meaning mathematics of the dust-board. This term was common in the medieval Spain.79 On the practicality of a dust board in mathematical calculations, al-Uqlidīsī writes, “If some persons dislike it because it needs the takht (board), we say that this is a science and technique that needs a tool.”80 Al-Khwārizmī wrote a book in the Arabic language on the use of Hindu numerals, Kitāb al-hisāb al-Hindī. Although the original book in the Arabic language has been lost, its Latin translation by Robert of Chester has survived.81 A thirteenth century manuscript from Spain has been found recently which is more complete than the ﬁrst Latin translation. This manuscript along with its German translation was published by Menso Folkerts in 1997.82 Al-Khwārizmī’s book is a compilation of the mathematical procedures used by the Hindus, as acknowledged by himself.83 Adelard of Bath (1080–1152 CE), an English philosopher, mathematician, and 75Datta and Singh, pt. 1, p. 96; Clark, 1929, p. 220. 76Saidan, 1978, p. 35. 77Saidan, 1978, p. 189. This book was composed in Damascus in 952–953 CE and a 1186 CE manuscript has survived. Read Burnett, 2006. 78Saidan, 1978, p. 12. 79Read, Salem and Kumar, 1991. 80Saidan, 1978, p. 35; Saidan has also compiled a list of books on Hindu-Arabic arithmetic that were in the Arab world. See, Saidan, 1965. 81Hughes, 1989. 82Folkerts, Menso, Die älteste Lateinische Schrift über das Indische Rechnen nach al-H. wārizmī, Übersetzung und Kommentar von M. Fokerts under Mitarbeit von Paul Kunitzsch, Bayerische Akademie der Wissenschaften, Philosophisch-historische Klasse, Abhandlungen, Neue Folge, Heft 113, 1997. Taken from Folkerts, 2001. 83Folkerts, 2001. Al-Khwārizmī was perhaps the most inﬂuential Islamic philosopher in Europe before the European Renaissance. The mathematical terms sine, algorithm, and zero are attributed to him. 54 3. THE HINDU MATHEMATICS scientist, translated al-Khwārizmī’s astronomical tables, that had been previously revised by al- Majrīt.ī (d. 1007 CE), from Arabic to Latin. These tables included tables of sine, and, thus, the sine function was introduced to the Latin world.84 Further, this Latin translation was translated into English by O. Neugebauer.85 It is this English translation that is our major source of al- Khwārizmī’s knowledge in astronomy and trigonometry. Trigonometry was introduced to the Arab world by India.86 Al-Battānī, Abu ‘Abd Allāh Muhammad ibn Jābir ibn Sinān al-Raqqī al-Harrānī al-Sābi‘ (858–929 CE) used the half-cord (that leads to sine function) instead of the chord in his book Kitāb al-Zīj(Book of Tables) fol- lowing the examples of his predecessors who used the Hindu method rather than the Greek method.87 Al-Battānī’s Zīj was translated into Latin by Robert of Ketton and Plato of Tivoli during the twelfth century. This table was also translated into Spanish under the patronage of Alfonso X.88 3.10.2 CHINA Yoshio Mikami, in his book, The Development of Mathematics in China and Japan, wrote of the Indian inﬂuence on Chinese mathematics: “Things Indian exercised supremacy in art and liter- ature, in philosophy, in the mode of life and the thoughts of the inhabitants, in everything. It is even said, astronomy and calendrical arts had also felt their inﬂuence. How then could arith- metic remain unaﬀected? No doubt the Chinese studied the arithmetical works of the Hindoos [Hindus].”89 On the popularity of Indian literature in China, Mikami wrote: “we read in history, the Indian works were read in translation ten times more than the native [Chinese] classics, a fact that vividly tells how the Indian inﬂuence had swept over the country [China].”90 The biggest export of India to China is deﬁnitely the religion founded on the teaching of Lord Buddha, Buddhism. When Buddhism was introduced to China, this country was already an old civilization with a powerful tradition and history. Philosophers such as Confucius guided Chinese society with their philosophies. Confucianism mostly deals with ethical rules that are applicable to this world; it does not deal with the spiritual life. Buddhism ﬁlled that niche to allow people to think about the “ultimate questions” of life, liberation, etc. There was a contrast in the intentions of these visitors who came from China in comparison to the Europeans. Most Chinese travelers visited India for their spiritual pursuits while Marco Polo and Vasco de Gamma visited to collect wealth. For example, Xuan Zang (b. 603 CE, also known as Hiuen Tsang, Huan Chwang, Yuan Chwang, Hiouen Thsang, and Hsuan Tsang)91 studied in Nālandā and carried books on twenty-two horses on his way back to China. He build a pagoda in Xian, 84Sarton, 1931, vol. 2, p. 167. 85Neugebauer, 1962. 86Needham and Ling, 1959, vol. III, p. 108. 87Dictionary of Scientiﬁc Biographies, vol. I, p. 508 88Julio Samsó in Selin, 1997 89Mikami, 1913, p. 57. 90Mikami, 1913, p. 57. 91Bernstein, 2001, p. 22. 3.10. DIFFUSION OF HINDU MATHEMATICS 55 China to house the books. Kumārjīva, an Indian scholar, went to Chang-an in 401 CE and served as “Grand Preceptor” of an enormous translation project involving thousands of monks and scholars that advanced the philosophy of the great Indian philosopher Nāgārjuna.92 He was from the Andra Pradesh region and was the founder of the Madhyāmika (Middle Path) school of Buddhism. This school became popular in China under the name Sanlun. Nāgārjuna was based in Nālanda University. Ch’u-t’an Hsi-ta from Tang’s Court translated a Sanskrit text into Chinese and intro- duced decimal notation and the arithmetic rules during the early eighth century. His work was continued further by Yijing (or I-tsing, 643–713 CE), under the order of the emperor.93 (See Chapter 2.) The trigonometric term jyā, as deﬁned by Āryabhat.a I, was called ming in China.94 In the section, Tui yueh Chien Liang Ming (On the prediction of the Moon’s positions) of Chiu-Chih- li, an astronomical book that is based on Sanskrit works, chia is the term used in this book to deﬁne the trigonometric function sine which is an obviously a minor change in pronunciation of the term jyā.95 The term ming may have been adopted from the title of this book later as the book became popular in China. In 718 CE, a new calender, called Jiuzhi li (Nine Upholder Calendar), was compiled in China.96 This calendar is based on Varāhamihira’s Pañca Siddhānta and contains a table of sines and the Hindu numeral zero in the form of a dot (bindu).97 3.10.3 EUROPE Monk Vigilia of the monastery of Albelda in the Rioja, Asturias (an autonomous community in Spain), in 976 CE, made a copy of the Etymologies that was originally written by Isidore of Seville (560–636 CE). In this copy, the monk provided information about the Hindu numerals with the following remark: “We must know that the Indians have a most subtle talent and all other races yield to them in arithmetic and geometry and the other liberal arts. And this is clear in the nine ﬁgures with which they are able to designate each and every degree of each order (of numbers).”98 S. ā‘id al-Andalusī (1029–1070 CE), a Spanish scholar of the eleventh century, writes about the Hindu numerals and arithmetic: “That which has reached us from their [Hindus’] work on numbers is Hisāb al-Ghubār (dust board arithmetic) which was simpliﬁed by Abū Jā‘far Muh- mmad ibn Mūsā al-Khwārizmī. This method of calculating is the simplest, fastest, and easiest method to understand and use and has a remarkable structure. It is a testimony to the intelligence of the Hindus, the clarity of their creativity, and the power of their inventiveness.”99 92Bernstein, 2001, p. 95 93Sarton, 1927, vol. 1, p. 513. 94Martzloﬀ, 1997, p. 90 and 100. 95Sen, 1970 96Yoke, 1985, p. 162 97Yoke, 1985, p. 162. 98Burnett, 2006. 99Salem and Kumar, 1991, p. 14. 56 3. THE HINDU MATHEMATICS S. ā‘id al-Andalusī was not the only one in Spain to write about the dominance of India in the sciences. Rabbi Abrahm Ibn Ezra (1096–1167 CE), a poet, scholar, and author of numer- ous books on grammar, philosophy, medicine, astronomy, astrology and mathematics, wrote on the ways the Hindu numerals were introduced in Arabia. Ibn Ezra mainly lived in Spain and translated al-Bīrūnī’s and al-Khwārizmī’s work into Hebrew. Ibn Ezra mentions the role of the Jewish scholars in bringing a Hindu scholar, named Kanaka, who taught place-value notations to the Arabs.100 Leonardo Fibonacci (1170–1250 CE) is well known for his contributions in arithmetic and geometry. He is also known for the Fibonacci Sequence. He learned the Hindu mathemat- ics from the Arabs and popularized Hindu numerals in the western world. “Of all the methods of calculation, he [Fibonacci] found the Hindu [method] to be unquestionably the best,”101 concludes Cajori in his studies. Fibonacci attributed the numerals correctly to the Hindus. Fi- bonacci wrote a statement in this book which erases any confusion about his knowledge of the Hindu numerals: “The nine Indian ﬁgures are: 9 8 7 6 5 4 3 2 1. With these nine ﬁgures, and with the sign 0 . . . any number may be written, as is demonstrated below.”102 He further writes to explain the place value notation: “The ﬁrst place in the writing of the numbers begins at the right. The second truly follows the ﬁrst to the left. The third follows the second. . . . the nine ﬁgures that will be in the second place will represent as many tens . . . the ﬁgure that is in the third place denotes the number of hundreds. . . if the ﬁgure four is in the ﬁrst place, and the unit in the second, thus 14, undoubtedly xiiii will be denoted . . if the ﬁgure of the unit is in the ﬁrst place, and the ﬁgure four in the second, thus 41, xli will be denoted.”103 Fibonacci was fascinated with Hindu mathematics. “. . . the art of the nine Indian ﬁgures, the introduction and knowledge of the art pleased me so much above all else, and I learned from them, whoever was learned in it, from nearby Egypt, Syria, Greece, Sicily and Provence, and their various methods, to which locations of business I traveled considerably afterward for much study, and I learned from the assembled disputations,” writes Fibonacci.104 Leonardo used the mathematical knowledge of the Hindus for business transactions from one currency to another, investment of money, calculation of simple and compound interest, and in deﬁning the rules of barter. Fibonacci found the prevalent Roman numerals inferior to the Hindu numerals. The purpose of writing his book Liber Abaci was to introduce the Romans to the very best available tools of mathematical calculations and their applications. Fibonacci started the book with the following sentence: “You, my Master Michael Scott, most great philosopher, wrote to my Lord about the book on numbers which some time ago I composed and transcribed to you; whence complying with your criticism, your more subtle examining circumspection, to the honor of you and many others I with advantage corrected this 100Goldstein, 1996. 101Cajori, 1980, p. 121. 102Boncompagni, 1857–1862; Horadam, 1975. 103Sigler, 2002, p. 17–18. 104Sigler, 2002, p. 15–16. 3.10. DIFFUSION OF HINDU MATHEMATICS 57 work. In this rectiﬁcation I added certain necessities, and I deleted certain superﬂuities. In it I present a full instruction on numbers close to the method of the Indians whose outstanding method I chose for this science.”105 Roger Bacon (1214–1294 CE), a noted Franciscan natural philosopher from England, studied at Oxford University and the University of Paris. Several manuscripts about the Hindu mathematics were available in French at the University of Paris that were read by Bacon.106 Ba- con emphasized the role of mathematics for Europe in his Opus Majus and deemed it “necessary to the culture of the Latins”107 Fibonacci’s Liber Abaci was published thirteen years prior to the birth of Bacon. As an adult, this book became known to Bacon. Bacon suggested that people should study mathematics from “all the sages of antiquity” and chastised them for being “ig- norant” of its “usefulness.”108 Bacon felt that mathematics is “the gate and key” to learn other sciences. In his view, a study of mathematics was essential for a study of philosophy that, in turn, was essential for the study of theology. Therefore, mathematics “has always been used by all the saints and sages more than all other sciences,”109 and is essential for theology and to know about the creatures and other creations.110 Thus, mathematics, in the mind of Roger Bacon, was a tool to know more about theology or to know about God’s creations. This is similar to how Nārada viewed mathematics to achieve salvation (Chapter 2). The triumph of the Hindu numeral system over the Roman numerals precipitated neither rapidly nor without conﬂict. It was not easy to discard the Roman numerals as they were deeply rooted in the system. Initially, the new Hindu system was mixed with the Roman by some where place value notation was practiced using Roman symbols. For example, 1482 was written as M.CCCC.8II, whereas 1089 was written as I.0.VIII.IX.111 In the twelfth and early thirteenth century, it was common to write numbers below 360 in Arabic, Greek or Latin symbols and the numbers above 360 in Hindu numerals.112 In 1299 CE, the City Council of Florence forbade the use of Hindu numerals in oﬃcial accounting books. Similarly, as late as the ﬁfteenth century, the mayor of Frankfurt issued an order to the master calculators to abstain from the use of the Hindu numerals.113 Some even tried to create a parallel system with the ﬁrst nine Roman numerals. For example, H. Ocreatus, a student of Adelard of Bath, tried to create this system which could have been appropriate scientiﬁcally. However, it did not catch on among the scholars.114 As late 105Sigler, 2002. Michael Scot was Leonardo’s mentor. 106Smith, a chapter, The Place of Roger Bacon in the History of Mathematics, in the book by Little, 1914, p. 156. 107Bacon, 1928, vol. 1, p. 27. 108Bacon, 1928, vol. 1, p. 27. 109Bacon, 1928, vol. 1, p. 116. 110Bacon, 1928, vol. 1, p. 195. 111Gupta, 1983; Menninger, 1970, p. 287. In the number 1482, an amalgamation of the Roman and Hindu system is practiced. The number 1 represents 1000 and M is the corresponding symbol. Similarly, C represents 100. The second number 1089 is written in place-value notations with Roman symbols for diﬀerent numbers. As mentioned earlier, symbols can easily be changed without compromising quality. 112Burnett, 2006. 113Gazalé, 2000, p. 48. 114Burnett, 2006 58 3. THE HINDU MATHEMATICS as the eighteenth century, the National Audit Oﬃce (Cour des Comptes) in France was still using Roman numerals in their accounting.115 As mentioned earlier, the Arabic term geib or jaib is a metamorphosed form of the term jyā used by the Hindus. The Arabic word jaib has multiple meanings: pocket, fold, or bosom. Adelard of Bath used the term elgeib for the trigonometric function sine, following the word used by al-Khwārizmī who use geib or jaib for this term.116 Rabbi Ben Ezra (born c. 1093), of Toledo, Spain, also used a similar term, al-geib, for this trigonometric function.117 Eventually, Gherardo of Cremona (ca. 1114–1187 CE, sometimes also spelled as Gerard or Gerhard, born in Carmona, Spain) literally translated the Arabic term into Latin and used the term sinus to deﬁne the operation.118 The term sinus means bosom, fold, or pocket in Latin. Pocket or bosom has nothing to do with the trigonometric function. However, this term has been in use for about a millennium. In 1631, Richard Norwood (1590–1675), a British mathematician and surveyor, pub- lished a book on trigonometry where the word sine was used for this trigonometric function and the symbol “s” was used to depict the function in his mathematical equations.119 In 1634, the French mathematician Pierre Hérigone (1580–1643) became the ﬁrst person to use the symbol “sin” for sine and the practice has continued since then.120 David Eugene Smith has provided an excellent review of sine function.121 3.10.4 SUPPORT OF POPE SYLVESTER II Pope Sylvester II was instrumental in popularizing the Hindu numerals, in his life as Gerbert d’Aurillac (945–1003 CE), his name prior to becoming pontiﬀ. He was born in a poor family in France and was ﬁrst educated at Aurillac, France. He later moved to Catalonia, Spain. He visited the cities of Barcelona, Seville, and Cordova in Spain which were leading centers of learning during the period. Gerbert became the headmaster of the cathedral school at Reims, later became the archbishop of Reims and then of Ravenna in Italy. His education in France and Spain in Latin grammar, science, and mathematics and his political astuteness, allowed him to become the hundred forty-sixth pope. With the patronage of Otto III of Saxony, on April 9, 999, he was elected as pontiﬀ and chose Pope Sylvester II as his new name. It was an important period for Christianity as it was about to complete one thousand years since the birth of Christ. Pope Sylvester II is known for his eﬀorts to translate Greek and Arabic texts on natural philosophy into Latin. He raised the proﬁle of natural philosophy and reinforced intellectual aspects of theology in the mainstream activities of the Church. 115Sarton, 1950. 116Neugebauer, 1962, p. 44, 45. 117Goldstein, 1996. 118Smith, 1925, vol. II, p. 616. 119Smith, 1925, vol. II, p. 618. 120Smith, 1925, vol. II, p. 618. 121Smith, 1925, vol. II, p. 614–619. 3.10. DIFFUSION OF HINDU MATHEMATICS 59 Pope Gerbert had a unique training: monastic life from Christian teachers, pagan life from Latin classics, and academic learnings (astronomy and mathematics) from the Muslim teachers of tenth century Spain. His interests included literature, music, philosophy, theology, mathematics and the natural sciences. He became familiar with the Hindu numerals during his stay in Spain. Later, he wrote and taught in his own school in Rheims about the Hindu numerals with its positional notations and rules related to the arithmetical operations.122 Gerbert used the nine signs of the Hindus to construct his abacus and “gave the multiplication or the division of each number, dividing and multiplying their inﬁnite numbers with such quickness that, as for their multiplication, one could get the answer quicker than he could express in words.”123 Gerbert wrote ﬁve books dealing with science and mathematics that are now lost. What we know about Gerbert is from the writings of his students, particularly Richer, the son of a French nobleman,124 and through his letters.125 Richer later became a monk in St. Rémy of Rheims and wrote a popular book on the history of France, Historia Francorum.126. Nikolai Bubnov, a Russian scholar, extensively studied the works of Gerbert and published a book about his contributions to mathematics, in Latin.127 Recently, another book on the life of Gerbert was published by Pierre Riché in French.128 In one letter that was written to Constantine, monk of Fleury in 980 CE, Gerbert ex- plained the Hindu numerals and mathematics to his monk friend using the abacus that was pop- ular in Spain. Following are the excerpts of the letter: “Do not let any half-educated philosopher think they [Hindu numerals and mathematics] are contrary to any of the arts or to philosophy. . . For, who can say which are digits, which are articles, which the lesser numbers of divisors, if he disdains sitting at the feet of the ancient?”129 Richer described Gerbert’s abacus in the following words: “in teaching geometry, indeed, he expended no less labor [than in teaching astronomy]. As an introduction to it he caused an abacus, that is, a board of suitable dimensions, to be made by a shield maker. Its length was divided into 27 parts [columns] on which he arranged the symbols, nine in number, signify- ing all numbers. Likewise, he had made out of horn a thousand characters, which indicated the multiplication or division of each number when shifted about in the 27 parts of the abacus. [He manipulated the characters] with such speed in dividing and multiplying large numbers that, in view of their very great size, they could be shown [seen] rather than be grasped men- tally by words. If anyone desires to know this more thoroughly let him read his book which he 122Lattin, 1961. 123Darlington, 1947. 124Darlington, 1947. 125Lattin, 1961. 126Richer, 1964–67. 127Bubnov, 1899. 128Riché, 1987. 129Lattin, 1961, p. 45. 60 3. THE HINDU MATHEMATICS wrote to Constantine, the grammaticus; for there he will ﬁnd these matters treated completely enough.”130 Another disciple of Gerbert, Bernelinus, has described his abacus as consisting of a smooth board with a uniform layer of blue sand. For arithmetical purposes, the board was divided into 30 columns, of which 3 were reserved for fractions. These 27 columns were grouped with three columns in each group. These were marked as C (cenlum), D (decem), and S (singularis) and M (monas). Bernelinus gave the nine numerals and suggested that the Greek letters could also be used instead.131 Pope Sylvester lived in a period that is before the times of Fibonacci of Italy and Roger Bacon of England, both credited for the introduction of the Hindu numerals in Europe. Un- fortunately, Pope Sylvester II died in 1003, less than four years after he was crowned as Pope. He was a champion of scientiﬁc scholarships along with his usual duties as a religious leader. ********* In summary, this chapter provides a brief sketch of the contributions of the Hindus, and reminds us of the mathematical tools that were perfected by the Hindus more than a thousand years ago and which have become a part of mainstream mathematics. “Think of our notation of numbers, brought to perfection by the Hindus, think of the Indian arithmetical operations nearly perfect as our own, think of their elegant algebraic methods, and then judge whether the Brahmins on the banks of the Ganges are not entitled to some credit,” questions Cajori.132 The answer is deﬁnitely in the aﬃrmative. 130Lattin, 1961, p. 46. The 27 columns in his abacus is an interesting number. The ancient Hindus divided the ecliptic circle into 27 parts. (Read 4.2) 131Cajori, 1980, p. 116. 132Cajori, 1980, p. 97. C H A P T E R 4 Astronomy 61 As mentioned in Chapter 1, the American Association for the Advancement of Science (AAAS) ranked Hindus’ contributions to astronomy among the top 100 scientiﬁc discoveries in human history. This recognition was a result of careful and systematic observations of the sky by the ancient Hindus. They noticed changes in the positions of some luminaries (planets, meteors, comets) against the ﬁxed background of other luminaries (stars), tried to know the shape of the Earth, looked for an explanation for the various phases of the Moon, the changing seasons, de- signed their own luni-solar calendar, assigned motion to the earth in their cosmological model, and correctly assigned the age of the universe of the order of billions of years. Once scientiﬁc observations were made and conclusions were drawn, the ancient Hindus documented the facts into stories or poetic verses. For example, a story was written in which Rohin. ī (Aldebaran; a star in constellation Taurus), the celestial female deer, was pursued by the stars (male) of Orion, labeled as the celestial stag. Sirius in his role as a hunter pins Orion with his arrow to protect Aldebaran. The line that connects Sirius with Aldebaran go through the Belt of Orion, indicat- ing the arrow’s ﬂight. This story is provided in the R. gveda.1 Similarly, the Big Dipper or Ursa Major, with seven stars was labeled as saptrishi mandal (group of seven sages). The Sanskrit word for astronomy is khagola-śāstra. Another term, jyotis. a-śāstra (astrology) covers considerable astronomy too. Hindu astronomy partly ﬂourished out of the need to per- form religious rituals on proper days at particular times that were governed by the positions of the Sun or the Moon with respect to various constellations. The ancient Hindus performed rites at sunrise and sunset, at the rising and setting of the Moon, and at other well-deﬁned entrances of the Moon or the Sun into particular constellations. These needs required keen observations and mapping of the sky. A special class of priests (khagola-śāstri, scholars of the sky) made obser- vations of astronomical events, including the motions of the planets, and documented them in their hymns.2 The Yajurveda mentions Naks. atra-daraśa3 as the term for astronomer. This term is made up of two words: naks. atra means constellation or a prominent star and daraśa means seer or observer, signifying a person who studies astronomy. The Chāndogya-Upanis. ad mentions naks. atra-vidyā (knowledge of constellations or astronomy) as a discipline. Most Hindu festivals are governed by astronomical events. For example, Sa ˙mkrānti, an important festival in India, is 1Krupp, October 1996. Krupp is an internationally known astronomer and works at the Griﬃth Observatory in Los Angeles. Krupp failed to provide a proper reference in his article. I have not been able to trace it in the R. gveda. However, knowing the reputation of Krupp, I have decided to share it with the reader. 2see Brennard, 1988; Burgess, 1893; Paramhans, 1991; Saha and Lahri, 1992; Shukla and Sarma, 1976; Somayaji, 1971; Subbarayappa and Sarma, 1985. 3Yajurveda, 30: 10. 62 4. ASTRONOMY celebrated on the day when the Sun moves (apparent motion) away from one rāśi (zodiac) and enters in a new zodiac. There are 12 zodiac signs and, therefore, twelve Sa ˙mkrānti festivals every year. The most popular of these festivals is makar-Sa ˙mkrānti. This is the day when the Sun moves from the dhanu zodiac (Sagittarius) to makar (Capricorn) zodiac. On this day, the Hindus visit temples, fast for the day, donate money to needy people, feed hungry people, and some bathe in the holy rivers. This religious need required regular scientiﬁc observations of the constellations and the apparent motion of the Sun. The ancient Hindus designed sophisticated instruments to facilitate their observations. Yukio Ōhashi, a Japanese scholar, based on his research, notice the following instruments that the Hindus had for astronomical observations during the period of Āryabhat.a I:4 1. Chāyā-yantra (Shadow-Instrument) 2. Dhanur-yantra (semi-circle instrument) 3. Yas.t.i-yantra (staﬀ ) 4. Cakra-yantra (circular instrument) 5. Chatra-yantra (umbrella instrument) 6. Toya-yantrān. i (water instrument) 7. Ghat.ikā-yantra (clepsydra) 8. Kapāla-yantra (clepsydra) 9. Śa ˙nku-yantra (gnomon) The Taittirīya-Brāhman. a advised the khagola-śāstris to the study the stars before sunrise to ﬁgure out the exact time of the rituals. “The position of an auspicious star [relative to the Sun] has to be determined at sunrise. But when the Sun rises, that star would not be visible. So, before the Sun rises, watch for the adjacent star. By performing the rite with due time adjustment, one would have performed the rite at the correct time.”5 The ancient Hindus knew the shape of the Earth as spherical from the earliest periods. The Śatapatha-Brāhman. a, an ancient book of the Hindus, mentions the spherical shape of the earth: “. . . womb is spherical and moreover this terrestrial world doubtless is spherical in shape.”6 In his book Geography, Strabo (ca. 63 BCE - 25 CE), a Greek traveler and historian, mentions that the Indians, like the Greeks, believed in the spherical shape of the Earth: “According to the Brachmanes, the world . . . is of a spheroidal ﬁgure.7 4Ōhashi, 1994. 5Taittirīya-Brāhman. a, 1: 5: 2: 1. 6Śatapatha-Brāhman. a, 7: 1: 37. 7Strabo, 15: 1: 59. 4. ASTRONOMY 63 Al-Bīrūnī (973–1050 CE) also aﬃrms this view: “According to the religious traditions of Hindus, the Earth on which we live is round.”8 The key word in this quotation is “traditions.” There is about a thousand years of time gap between Strabo and al-Bīrūnī. Since the Vedic period, the Earth was considered to be spherical. Al-Bīrūnī also quoted the Hindu astronomers to indicate that the size of the Earth was very small in comparison to the visible part of the universe:9 “These are the words of Hindu astronomers regarding the globular shape of heaven and earth, and what is between them, and regarding the fact that the earth situated in the center of the globe, is only a small size in comparison with the visible part of heaven.” Āryabhat.a I used an analogy of a kadamba ﬂower (neolamarckia cadamba) (Figure 4.1) to demonstrate the distribution of various life forms on the Earth: “Half of the sphere of the Earth, the planets, and the asterisms is darkened by their shadows, and half, being turned toward the Sun, is lighted according to their size. The sphere of the earth, being quite round, situated in the center of space, in the middle of the circle of asterisms [constellations or stars], surrounded by the orbits of the planets, consists of Earth, water, ﬁre, and air. Just as the ball formed by a kadamba ﬂower is surrounded on all sides by blossoms just so the Earth is surrounded on all sides by all creatures terrestrial and aquatic.”10 Figure 4.1: Kadamba ﬂower (taken from Wikimedia). There are numerous accounts in the Hindu literature indicating that the Moon gets its luminosity from the Sun. The R. gveda tells us that “He [the Moon] assumed the brilliancy of the Sun,”11 “He [the Moon] is adorned with Sun’s beams . . .,”12 or, “the Sun-God Savitar bestows his sunlight to his Lord, the Moon.”13 The Yajurveda (Śukla) also tells us that “the Moon whose rays are the Sun’s ray.”14 Al-Bīrūnī (973–1050 CE), in stating the Hindu view that planets are illuminated by the Sun, wrote: “the Sun aloft is of ﬁery essence, self-shining, and ’per accidens’ illuminates other 8Sachau, 1964, vol. 1, p. 233. 9Sachau, 1964, vol. 1, p. 269. 10Āryabhat. īya, Gola, 5–7. 11R. gveda, 9: 71; 9. 12R. gveda, 9: 76: 4. 13R. gveda, 10: 85: 9; Atharvaveda, 14: 1: 9. 14Yajurveda(Śukla), 18: 40. 64 4. ASTRONOMY stars when they stand opposite to him.”15 “The Moon is watery in her essence,” writes Al-Bīrūnī. “therefore the rays which fall on her [Moon] are reﬂected, as they reﬂect from the water and the mirror toward the wall.”16 Varāhamihira stated that, in the words of al-Bīrūnī: “The Moon is always below the Sun, who throws his rays upon her, and lit up the one half of her body, whilst the other half remains dark and shadowy like a pot which you place in the sunshine. The one half which faces the Sun is lit up, whilst the other half which does not face it remains dark.”17 “If the Moon is in conjunction with the Sun [new moon], the white part of her turns toward the Sun, the black part toward us. Then the white part sinks downward toward us slowly, as the Sun marches away from the Moon.”18 The above statements from al-Bīrūnī demonstrate that the ancient Hindus knew that the moonlight in the night sky is actually the reﬂected sunlight. The night sky does not have the Sun. If so, how could it illuminate the Moon? Based on the statements provided, the ancient Hindus had the understanding of the changing geometry of the Earth, the Moon, and the Sun. Information to support this argument is provided later, especially in relation to Rāhu and Ketu. The ancient Hindus knew that the Sun does not dissolve after the sunset. The Sun does not set or rise. (Section 4.1.) Al-Bīrūnī states that “every educated man among Hindu theologians, and much more so among their astronomers, believes indeed that the Moon is below the Sun, and even below all the planets.”19 Āryabhat.a I (Figure 4.2) explained the geometry of the solar system and the universe: “Half of the globe of the Earth, the planets, and the stars are dark due to their own shadows; the other halves facing the Sun are bright in proportion to their sizes.”20 “Beneath the stars are Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon, and beneath these is the Earth . . .”21 This observation of the heavenly objects, as given by Āryabhat.a I, is correct for an observer on the Earth. The apparent path of the Sun as viewed from the Earth against the background of stars is called the ecliptic. This path results from the Earth’s motion around the Sun against the backdrop of the celestial sphere. The Moon with its changing phases moves around the Earth in a plane that is close to the ecliptic plane. The plane of the Moon lies 5(cid:14) north or south of the ecliptic plane. The two points at which the Moon’s path crosses the elliptic plane, known as the descending and ascending nodes. The nodal points are not ﬁxed and move along the ecliptic plane of the Earth’s motion. The ancient Hindus called them Rāhu and Ketu, respectively. The rotational periods of Rāhu and Ketu as deﬁned in Hindu astrological charts, the horoscopes, are 15Sachau, 1964, vol. 2, p. 64. 16Sachau, 1964, vol. 2, p. 66. 17Sachau, 1964, vol.2, p. 66. 18Sachau, 1964, vol. 2, p. 67. 19Sachau, 1964, 2, p. 67. 20Āryabhat. īya, Gola, 5. 21Āryabhat. īya, Kālakriyā, 15. 4. ASTRONOMY 65 Figure 4.2: Āryabhat.a I statue on the premise of the Inter-University Center for Astronomy and Astrophysics, Pune, India (taken from Wikimedia) the same as that of these nodal points. These two nodes are diametrically opposite to each other and so are the Rāhu and the Ketu in the horoscope. These nodal points describe the relation of the Moon and the Sun to the Earth. Along with the individual eﬀects of the Sun and Moon, there is also a collective eﬀect exhibited by the Sun and the Moon, as noticed in lunar and solar eclipses. The solar eclipse and the lunar eclipse can be explained with the help of these nodal points. The ancient Hindus knew this fact and tried to explain eclipses by the motion of Rāhu and Ketu, the two nodal points. The R. gveda mentions solar eclipse22 which is a common observation in most cultures. An explanation for the cause was warranted. In Hindu scriptures, as given in the Ādi-parva of Mahābhārata, eclipses are described as the swallowing of the Sun or the Moon by two demons, Rāhu or Ketu. As the story goes, once the gods decided to churn the ocean to get the divine nectar (amr. ta) to become immortal. As amr. ta came out from the churning process, all gods started to drink it. A demon took the guise of a god and drank amr. ta too. When he gulped it, the Sun and the Moon recognized him. They both warned Lord Vis.n. u about his transgression. Lord Vis.n. u acted promptly and slit his throat. By then, however, amr. ta had already entered in his body and, therefore, he could not die. His head is called Rāhu and torso Ketu. Ever since there has been a long lasting feud of Rāhu and Ketu with the Sun and the Moon. They chase them across the sky and try to swallow them. Whenever Rāhu or Ketu succeed, an eclipse occurs. An eclipse is therefore symbolizes a momentary victory of Rāhu and Ketu over the Sun or the 22R. gveda, 5: 40: 5–9. 66 4. ASTRONOMY Moon. In essence, it is a temporary victory of evil over good. Therefore, eclipse is considered as an inauspicious occasion in Hindu scriptures. Hindus, therefore, pray during an eclipse and bathe in their holy rivers to purify themselves afterward. The Chāndogya-Upanis. ad provided an account of the lunar eclipse: “From the dark, I go to the varicolored. From the varicolored, I go to the dark. Shaking oﬀ evil, as a horse his hairs; shaking oﬀ the body, as the Moon releases itself from the mouth of Rāhu.”23 Here “varicolored” is indicative of the corona rings that appear during an eclipse. The mention of Rāhu is indicative of the role of the nodal points. The Atharvaveda provides the cause of a solar eclipse: “Peace to us during lunar eclipse, peace to us during the period when Rāhu swallow the Sun.”24 Āryabhat.a I used scientiﬁc terms and explained the cause of solar and lunar eclipses as the Moon blocks the Sun or the Earth comes in between the Sun and the Moon. He also provided the method to calculate the area of the Moon or the Sun that would be aﬀected during an eclipse: “The Moon obscures the Sun and the great shadow of the Earth obscures the Moon.”25 This is a clear indication that the geometry of eclipse was known to Āryabhat.a I. “When at the end of the true lunar month the Moon, being near the node, enters the Sun, or when at the end of the half-month the Moon enters the shadow of the Earth that is the middle of the eclipse which occurs sometimes before and sometimes after the exact end of the lunar month or half-month.”26 “Multiply the distance of the Sun by the diameter of the Earth and divide (the product) by the diﬀerence between the diameters of the Sun and the Earth: the result is the length of the shadow of the Earth (i.e., the distance of the vertex of the Earth’s shadow) from the diameter of the Earth (i.e., from the center of the Earth).27 Thus, Length of the Earth0s Shadow Sun0s distance Sun0s diameter D Earth0s diameter Earth0s diameter (cid:2) (cid:0) “The diﬀerence between the length of the Earth’s shadow and the distance of the Moon from the Earth multiplied by the diameter of the Earth and divided by the length of the Earth’s shadow is the diameter of the Earth’s shadow (in the orbit of the Moon).”28 Al-Bīrūnī conﬁrms that the cause of solar and lunar eclipse was known to the Hindus. “It is perfectly known to the Hindu astronomers that the Moon is eclipsed by the shadow of the Earth, and the Sun is eclipsed by the Moon.”29 23Chāndogya-Upanis. ad, 8: 13: 1. 24Atharvaveda, 19: 9: 10. 25Āryabhat. īya, Gola, 37. 26Āryabhat. īya, Gola, 38. 27Āryabhat. īya, Gola, 39, taken from Shukla and Sarma, 1976, p. 152. 28Āryabhat. īya, Gola, 40. 29Sachau, 1964, vol. 2, p. 107. 4.1. HELIOCENTRIC SOLAR SYSTEM 67 4.1 HELIOCENTRIC SOLAR SYSTEM Most planetary models during the ancient period considered a geocentric system where the Earth remained stationary, like in the Ptolemy’s model. Planets moved around the earth in epicyclic motions in these models. Āryabhat.a I, on the contrary, came up with a detailed and innovative model of the solar system in which the Earth was in axial motion. With the known spherical shape of the Earth, Āryabhat.a I assigned diurnal motion to the Earth, and was able to explain the repeated occurrence of day and night. He somehow knew the time diﬀerence between various locations on earth: “Sunrise at Lanka (Sri-Lanka) is sunset at Siddhapura, mid-day at Yavakoti (or Yamakoti, Indonesia), and mid-night at Romaka (Rome).”30 With the current knowledge, we can safely say that Āryabhat.a I somehow knew the longitudes of these locations and could correctly infer the time diﬀerences. The above statement is remarkable since it involves information that requires simultaneous observation. Needless to say, Āryabhat.a I had no way to make a phone call since the phones were not available. Similarly, all other means to contact with people in Rome was not possible for a person sitting in India. The only possibility is to predict it using geometry and astronomy in which the relative motion of the Sun and the Earth, including its shape, is known to the person. This is similar to what Eratosthenes did when he made simultaneous measurements at Syene and Alexandria, both in Egypt, to measure the size of the Earth.31 Several Hindu scriptures indicate that the Sun constantly illuminates the Earth. Sunrise or sunset happen depending on the side of the Earth illuminated by the Sun at that particular instant. Following are some of representative statements: “Actually the Sun neither rises nor sets. . . When the Sun becomes visible to people, to them He [the Sun] is said to rise; when He [the Sun] disappears from their view, that is called his [the Sun] setting. There is in truth neither rising or setting of Sun, for he is always there; and these terms merely imply his presence and his disappearance,” suggests Vis. n. u-Purān. a.32 “He [the Sun] never sets or rises. When [we] think that he is setting, he is only turning round, after reaching the end of the day, and makes night here and day below. Then, when [we] think he is rising in the morning, he is only turning round after reaching the end of the night, and makes day here and night below. Thus, he (the Sun) never sets at all,” suggests the Āitareya-Brāhman. a.33 “Never did the Sun set there nor did it rise. . . the Sun neither rises nor sets. He who thus knows this secret of the Vedas, for him, there is perpetual day,”34 suggests the Chāndogya- Upanis. ad. 30Āryabhat. īya, Gola, 13. The locations of Siddhapura is not known. Assuming Āryabhat.a I to be correct, this longitude falls somewhere in the continent of America, near Mexico. 31Brown and Kumar, 2011. 32Vis. n. u-Purān. a, 2: 8. 33Āitareya-Brāhman. a, 14: 6; taken from Subbarayappa and Sarma, 1985, p. 28. 34Chāndogya-Upanis. ad, 3: 11: 1–3; taken from Subbarayappa and Sarma, 1985, p. 28. Some translators have translated the text somewhat diﬀerently. However, in most translations, “Sun never sets” is stated. 68 4. ASTRONOMY 4.1.1 UJJAIN, GREENWICH OF THE ANCIENT WORLD Sri Lanka was used as a reference point because the prime meridian of Ujjain, a city in India, (Longitude 75(cid:14)430E, Latitude 23(cid:14)130N) intersects the equator near Sri Lanka. The location of Ujjain played an important role in astronomy during the ancient and medieval periods. Ujjain was the Greenwich of the ancient and medieval world and most ancient astronomers in India and Arabia used this city as a reference point for their astronomical observations. Āryabhat.a I deﬁned the distance between Ujjain and Sri Lanka as one-sixteenth of the Earth’s circumference in the north direction.35 This gives the latitude of Ujjain as 360 16 = 22(cid:14)300 which is quite close to the actual number. A diﬀerence of 1(cid:14) in latitude creates an error of 69 miles in distance. Therefore, the value given by Āryabhat.a I for the latitude diﬀers with the actual value by 430 which is equivalent to less than 50 miles. People in most metropolitan cities would agree that this is a small distance. For example, suburban sites in New York or Los Angeles can be 50 miles away from the city center and still would be considered as a part of these cities. Since the settlements around Ujjain have evolved over the last thousand years, it may easily be the distance of modern city center and the ancient location of the observatory. During the medieval period, Ujjain was considered as the prime meridian in the Middle East. More details on Ujjain is provided in Section 4.4. 4.1.2 DIURNAL MOTION OF THE EARTH Āryabhat.a I assigned diurnal motion to the Earth and kept the Sun stationary in his astronomical scheme. According to Āryabhat.a I the motion of the stars that we observe in the sky is an illusion. To explain the apparent motion of the Sun, Āryabhat.a I used an analogy of a boat in a river. “As a man in a boat going forward sees a stationary object moving backward just so in Sri-Lanka a man sees the stationary asterisms (stars) moving backward exactly toward the West.”36 Āryabhat.a I Āryabhat.a I was the Head at the famous Nālandā University near modern Patna. He composed a book, Āryabhat. īya, dealing with mathematics (gan. ita-pada), spheri- cal astronomy (gola-pada), and time-reckoning (kāla-kriyā-pada). The book was composed in 499 CE by Āryabhat.a I when he was only 23 years old. His work made a major impact in India for several centuries as the following writers like Brahmgupta (born around 598 CE) and Varāhamihira (505–587 CE) wrote extensive commentaries on his work. Āryabhat. īya is an invaluable document for the historians of science; it provides an account of the ancient sciences of the Hindus. The content of this book was not a new knowledge created by Āryabhat.a I. He was emphatic to not take the credit and labeled the content of his book as “old knowledge.” 35Āryabhat. īya, Gola, 14; Shukla and Sarma, 1976, p. 123–126. 36Āryabhat. īya, Gola, 9; to read more about Āryabhat.a I, read Hooda and Kapur, 1997; and Shukla and Sarma, 1976. 4.1. HELIOCENTRIC SOLAR SYSTEM 69 Āryabhat. īya has 118 metrical verses subdivided into four chapters. The ﬁrst chap- ter, Daśa-gītikā has ten verses and provided astronomical constants. The second chapter is on mathematics. The third chapter is on time-reckoning, and the fourth chapter concerns spherical astronomy. In this book, Āryabhat.a I provided the value of (cid:25) as approximately equal to 3.1416, the solution of indeterminate equations and quadratic equations, theory of planetary motions, and calculations of the latitudes of planets. And most important of all, a millennium before Copernicus, he assigned axial motion to the Earth in his astronomical model and kept the stars stationary. In Āryabhat.a I’s honor, the ﬁrst artiﬁcial satellite of India was launched in 1975 and was named after him. The International Astronomical Union has also named a lunar crater after Āryabhat.a I in 1979. The interpretation is that a person standing on the equator, that rotates from the west to the east, would see the asterisms (constellations) moving in the westward motion. This clear grasp of Earth’s rotational motion is splendidly explained in the analogy of a boat man by Āryabhat.a I. Interestingly, about one millennium after Ārybahat.a I, Copernicus used a similar argu- ment to assign motion to the Earth. “For when a ship is ﬂoating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In that same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating.”37 This similarity be- tween Ārybahat.a I’s statement and Copernicus’ statement is intriguing. Did Copernicus know of the work of Āryabhat.a I? This issue is not clearly resolved as yet. However, there is a possibility of Copernicus knowing the work of Āryabhat.a I, as discussed in Section 4.4. **** Once the rotational (axial or spin) motion of the Earth is established, what kind of issues it creates to explain the observed phenomena? Why do we have diﬀerent seasons? Does it lead to the heliocentric theory of solar system? Let us investigate further to answer these questions. With spin motion assigned to the Earth, a set of other questions immediately arise: Is there a motion of the Sun? This question pops up since there is no longer a necessity to explain day and night with the Sun’s motion. According to Āryabhat.a I, the Earth spins on its axis like a merry-go-round. However, we do not experience any ﬂy-away feeling on the Earth as we do on a merry-go-round. The spin motion of the Earth also creates problems to explain ﬂights of ﬂying birds. How do they go back to their nest with the Earth spinning so fast, especially if they ﬂy to the West? Assigning any motion to the Earth seems contrary to human experiences. It is a much bigger triumph to assign any kind of motion to the Earth than to just add orbital motion to the already known spinning (rotational) motion of the Earth. 37Copernicus’ On the Revolution, Book 1, Chapter 8; Copernicus, 1978, p. 16. 70 4. ASTRONOMY This leads to the next question. If day and night are due to the Earth spinning in one place, why do we have diﬀerent seasons? Why do we observe northward or southward motions of the Sun? Āryabhat.a I considered constellations and stars to be stationary in the sky and attributed their apparent motion to the moving Earth. Can the Sun be also stationary like other stars? No where did Āryabhat.a I struggle in dealing with such questions in his book. His statements are fairly conclusive and straight forward. In summary, the axial rotation of the Earth compli- cates the simplicity of the geocentric system. On the contrary, in a heliocentric system, the axial rotation is a necessity. In describing the spin motion of the Earth, Āryabhat.a I makes another explicit statement, “The revolutions of the Moon multiplied by 12 zodiac are signs [rāśi]. The signs multiplied by 30 are degrees [360(cid:14)]. The degrees multiplied by 60 are minutes. . . . The Earth moves one minute in a prān. a.”38 Āryabhat.a I provided the following deﬁnition of prān. a, a unit of time: “One year consists of twelve months. A month consists of thirty days. A day consists of sixty nād. ī. A nād. ī consists of sixty vinād. ikā. Sixty long syllables or six prān. as make a sidereal vinād. ikā. This is the division of time.”39 Let us transcribe it in a modern set of standards. Assuming a day to be 24 hours long with a 360(cid:14) rotation (86,4000), one nād. ī comes out to be 1,4400, vinād. ikā equals to 240, and prān. a comes out to be four seconds. Therefore, Āryabhat.a I’s statement can be modiﬁed as follows: “The Earth rotates by an angle of one minute (10) in 4 seconds.” One minute in angle multiplied by 21,600 gives us 360(cid:14). Thus, 4 seconds multiplied by 21,600 should give us the time that is equal to one day (or 24 hours). This is the case when we multiply the two numbers and change the units to hours. Therefore, not only Āryabhat.a I assigned spin motion to the Sun, he also correctly provided the speed of the spin. Āryabhat.a I makes explicit statement elsewhere: “The Earth rotates through [an angle of ] one minute of arc in one prān. a.”40 Āryabhat.a I provided the periods of revolution for diﬀerent planets, the Moon, and the Sun in one yuga: “In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth 1,582,237,500, of Saturn 146,564, of Jupiter 364,224, of Mars 2,296,824, of Mer- cury and Venus the same as those of the Sun. of the Moon’s apogee, 4,88,219; of [the śighrocca (conjunction)] of Mercury, 1,79,37,020; of (the śighrocca) of Venus, 70,22,388; of (the śighrocca) of the other planets, the same as those of the Sun; of the Moon’s ascending node in the opposite direction (i.e., westward), 2,32,226. These revolutions commenced at the beginning of the sign Aries on Wednesday at sunrise at Sri Lanka (when it was the commencement of the current yuga.)”41. Yuga is an important concept in Hindu cosmology, as given in the Hindu scriptures (Section 4.3). 38Āryabhat. īya, Dasgītika, 4. 39Āryabhat. īya, Kālakriyā, 2. 40Āryabhat. īya, Dasgītika, 6. 41Āryabhat. īya, Dasgītika, 3–4 4.1. HELIOCENTRIC SOLAR SYSTEM 71 The “Moon’s apogee” deﬁnes the point of the Moon’s orbit when it is farthest from the Earth. The śighrocca of a planet is the imaginary body which is supposed to revolve around the Earth with the heliocentric mean velocity of the planet. Shukla and Sarma have done a careful analysis of these periods in their translation of Āryabhat. īya, calculated the sidereal period in terms of days, and compared them with the modern values.42 (Table 4.1.) Table 4.1: Mean motion of the planets As one can notice, all values are quite close to the modern accepted values. Interestingly, the period of Mercury and Venus are explicitly considered equal to the Sun by Āryabhat.a I. Since Mercury and Venus are the only two planets inside the Earth’s orbit, their orbital period, as observed from the Earth, comes close to that of the Sun. Obviously, this observation is in a geocentric system. Was it because Āryabhat.a I believed in the geocentric solar system or because it was a prevalent practice of the period to describe motion as viewed from the Earth? In the very next verse, Āryabhat.a I erased any doubt about the two diﬀerent motions assigned to Mercury and Venus. Thus, the sidereal period of Mercury and Venus comes out to 87.97 and 224.70 days, in the calculation of Shukla and Sarma.43 This compares well with the modern values of 87.97 and 224.70, respectively for Mercury and Venus. Thus, Āryabhat.a I provides one statement in the geocentric system while the other in the heliocentric system with the Earth as the point of observation. This has intrigued astronomers through the ages. 42Shukla and Sarma, 1976, p. 7. 43Shukla and Sarma, 1976, p. 7. PlanetRevolutions in 4,320,000 YearsSidereal PeriodĀryabhaṭa ISidereal PeriodModernsSun4,320,000365.25868365.25636Moon57,753,33627.3216727.32166Moon’s apogee488,2193,231.987083,232.37543Moon’s asc. node232,2266,794.749516,793.39108Mars2,296,824686.99974686.9797Śighrocca of Mercury17,937,02087.9698887.9693Śighrocca of Venus7,022,388224.69814224.7008Jupiter364,2244,332.272174,332.5887Saturn146,56410,766.0646510,759.20172 4. ASTRONOMY According to a detailed analysis given by B. L. van der Waerden,44 the motion of Mercury and Venus as given by Āryabhat.a I were in a heliocentric model.45 Van der Waerden makes the following assertions to back up his conjecture that Āryabhat.a I proposed a heliocentric model and not a geocentric model:46 1. In a geocentric system, there is no need to assume axial rotation for the Earth as most observations, though wrong, are easier to explain. However, in a heliocentric system, we are forced to think of axial rotation. Āryabhat.a I clearly argue for the axial rotation of the Earth and provides accurate period for the axial motion. 2. In the Midnight system of Āryabhat.a I, the apogees (farthest point from the earth) of the Sun and Venus are both at 80(cid:14), and their eccentricities (a measure of astronomical orbit deviation from circularity) are also equal. This fact can be explained by assuming that the system was originally derived from a heliocentric system.47 “In genuine epicycle theory for Venus, the eccenter carrying the epicycle is independent of the Sun’s orbit. Its apogee and eccentricity are determined from observations of Venus, whereas the apogee and eccentricity of the Sun are determined from eclipse observations. The probability that the apogee and eccentricity of Venus coincide with those of the Sun is very small.”48 3. The periods of revolution for the outer planets are essentially the same in the geocentric and heliocentric models. It is the planetary periods of the inner planets, Mercury and Venus, that separates the two theories. In a geocentric theory, these two periods will essentially be the same as the solar period. However, in a heliocentric system, these periods are quite dif- ferent. Āryabhat.a did assign diﬀerent periods for the Sun, Mercury and Venus, indicating a heliocentric system. 4. The revolutions of Mercury and Venus considered by Āryabhat.a I are heliocentric revolu- tions, not geocentric. These periods provided by Āryabhat.a I have “no importance what- soever” in a geocentric system.49 Based on the descriptions given in Āryabhat. īya, Van der Waerden concludes that “it is highly probable that the system of Āryabhat.a [I] was derived from a heliocentric theory by setting the center of the Earth at rest.”50 The reason for this kind of torturous path in the work 44B. L. van der Waerden (1903–1996) was a proliﬁc author with several books on algebra, geometry, and astronomy to his credit. He taught at the University of Leipzig in Germany, the University of Amsterdam in the Netherlands, and the University of Zurich in Switzerland. 45van der Waerden, The Heliocentric System in Greek, Persian, and Hindu Astronomy, in the book by King and Saliba, 1987, p. 534. 46van der Waerden, The Heliocentric System in Greek, Persian, and Hindu Astronomy, in the book by King and Saliba, 1987, p. 530–535. 47van der Waerden, in the book by King and Saliba, 1987, p. 532. 48van Waerden, in the book by King and Saliba, 1987, p. 531. 49Van Waerden in the book by King and Saliba, 1987, p. 534. 50Van der Waerden in the book by King and Saliba, 1987, p. 534. 4.1. HELIOCENTRIC SOLAR SYSTEM 73 of Āryabhat.a I is perhaps due to an overwhelming tendency among all early astronomers and their students, in the words of Van der Waerden, “to get away from the idea of a motion of the Earth.”51 In the history of astronomy, for convenience purposes, astronomers did transform the heliocentric theory into equivalent geocentric one. This was done by Tycho Brahe when he transformed Copernican heliocentric model into a geocentric one.52 Van der Waerden’s conclusion that Āryabhat.a I proposed a heliocentric model of the so- lar system has received independent support from other astronomers.53 For example, Hugh Thurston came up with a similar conclusion in his independent analysis. “Not only did Āryabhat.a believe that the Earth rotates, but there are glimmerings in his system (and other similar Indian systems) of a possible underlying theory in which the earth (and the planets) orbits the Sun, rather than the Sun orbiting the earth.”54 The evidence used by Thurston is in the periods of the outer planets and the inner planets. Āryabhat.a basic planetary periods are relative to the Sun which is not so signiﬁcant for the outer planets. However, it is quite important for the inner planets (Mercury and Venus). The motion that Āryabhat.a I assigned to the Earth is not a mere speculation of modern astronomers. Āryabhat.a I’s thesis was well known in the Middle East even after six centuries. Al-Bīrūnī (973–1050 CE) erroneously criticized Hindu astronomers for assigning motion to the Earth (Figure 4.3). He referred to the work of Varāhamihira, a Hindu astronomer, to support his idea of the geocentric universe: “If that were the case, a bird would not return to its nest as soon as it had ﬂown away from it toward the west,”55 and “stones and trees would fall.”56 In the ﬁrst drawing, Figure 4.3, the bird ﬂies to the West and leave his nest. After a while, when he comes back, the nest has moved considerably due to the motion of the Earth. This was the argument of al-Bīrūnī against the moving Earth. A similar argument was used by Aristotle (384–322 BCE) to favor his theory of the geocentric universe. Al-Bīrūnī’s criticism validates the work of Āryabhat.a I in India and its existence in the Middle East prior to the eleventh century. After viewing various possibilities of the motion of the Earth, al-Bīrūnī favored the sta- tionary Earth: “The most prominent of both modern and ancient astronomers have deeply stud- ied the question of the moving of the Earth, and tried to refute it. We, too, have composed a book on the subject called Miftah-ilm-alhai‘a (Key of astronomy), in which we think that we have surpassed our predecessors, if not in the words, at all events in the matter.”57 This depicts that at least some six centuries after the heliocentric theory was proposed by Āryabhat.a I, the Islamic philosophers from Arabia still could not grasp the idea of moving Earth. 51Van der Waerden in the book by King and Saliba, 1987, p. 530. 52Van der Waerden in the book by King and Saliba, 1987, p. 530. 53Billard, 1977; Thurston, 1994 and 2000. 54Thurston, 1994, p. 188. 55Sachau, 1964, vol. 1, p. 276. 56Sachau, 1964, vol. 1, p. 277. 57Sachau, 1964, vol. 1, p. 277. 74 4. ASTRONOMY Figure 4.3: Al-Bīrūnī’s argument against Āryabhat.a’s assignment of the motion of the earth. (Designed with the help of David Valentino) Science texts still do not cover Āryabhat.a’s work along with the work of Copernicus. The opponents of Āryabhat.a’s heliocentric system are totally silent in providing explanation to why Āryabhat.a assigned spin motion to the earth and not struggled to explain the simple astronomical observations with this spin motion. Also, why the periods of Mercury and Venus are not equal to the period of the Sun, as it should be in a geocentric system. Obviously, a lot more research on Āryabhat. īya is needed to resolve this issue. 4.2 HINDU CALENDAR Pañcā ˙nga (Pañcā = ﬁve and a ˙nga = limb, meaning ﬁve-limbed) is the term used for the Hindu al- manac. The ﬁve limbs are: day (vāra), date (tithi), naks. atra (asterism), yuga (period), and kāran. ā (half of tithi). Pañcā ˙nga is popular even today among the Hindus. Hindu priests use it for pre- dicting eclipses, deﬁning time of various rituals, including marriage, casting horoscopes, and for solemn entrance into a house (gr. ah-praveśa) or business. Hindu families commonly use Pañcā ˙nga to check the day of fasting, auspicious times for worshiping, and days of festivals. Most cultures have calendars that are either based on the motion of the Moon or the Sun. The regular appearance of the new or the full moon forms a basis of most lunar calendars, like the Islamic calendar. Solar calendars are based on the cyclic motion of the Sun in diﬀerent zodiacs that is due to the orbital motion of the Earth around the Sun. The Hindu calendar is luni-solar in which the months are based on the motion of the Moon while the year is deﬁned by the Sun. A year is the time the Earth takes to complete one revolution around the Sun, starting 4.2. HINDU CALENDAR 75 from Mes. a (Aries). This calendar is similar to the Jewish or Babylonian calendar that are also luni-solar. In the Hindu Calendar, a month is divided into two equal parts, known as paks. a, each of roughly ﬁfteen days depicting the waxing and waning of the Moon. The paks. a starting from the new moon to the full moon is considered the bright-half (Śukla-paks. a) while the second part starting from a full moon to a new moon, is known as the dark-half (Kr. s. n. a-paks. a).58 The new moon day, when the longitude of the Sun and Moon are equal, is called amāvāsya. The full moon night, when the Sun and the Moon are 180(cid:14) out of phase, is known as pūrn. imā. It gives a mean lunar year to be 354 days 8 hours 48 minutes and 34 seconds. A day (vāra) begins at sunrise. The date (tithi) is indicative of the position of the Moon relative to the Sun. A month (māsa) starts and ends on amāvāsya (meaning dwelling together, implying conjunction of the Sun and the Moon, the new moon). The word amāvāsya is used in Atharvaveda59 which signiﬁes that the ancient Hindus knew the cause of the new moon during the Vedic period. The days in between amāvāsya and pūrn. imā are counted as numbers: ekādaśī (eleventh day of the fortnight), caturthī (fourth day of the lunar fortnight), etc. The ecliptic circle was divided into 27 parts, each consisting of 13(cid:14)200, called naks. atra. To understand the features of the Hindu calendar, let us compare it with the Western cal- endar that is popular internationally. The Western calendar, also called the Gregorian calendar, was proposed by Pope Gregory XIII in 1582. It was a modiﬁed form of the calendar estab- lished by Julius Caesar, known as the Julian calendar. This calendar was based on the Egyptian calendar of the period. The Catholic kingdoms adopted the Gregorian calendar soon after its inception. However, England resisted its use and adopted it in 1752, under some resistance from the Protestant majority. The Western calendar is irregular and inconvenient to use because: 1. There exists no easy way to ﬁgure out the date of a particular day from simple observations. 2. Diﬀerent months have diﬀerent numbers of days. This creates diﬃculties in the business world where, at times, monetary transactions are made based on the day devoted to a particular task. 3. Because the span of a month is diﬀerent for diﬀerent months, performance records are diﬃcult to compare. 4. There is a problem of the leap year. One has to remember the year to decide the number of days in the month of February. There is no possible way to ﬁgure it out using astronomical observations. One has to remember the empirically deﬁned rules to ﬁgure this out. Most people use the Western calendar since their childhood and are not familiar with alternatives, they do not realize its weaknesses. In the lunar calendar, one year equals 354 days 58see Arthaśāstra, 108. 59deﬁned in Atharvaveda, 7: 79. 76 4. ASTRONOMY and, in the solar calendar, one year is roughly equal to 365 days. The diﬀerence of 11 days in a year can cause radically diﬀerent seasons for the same month in two years in a lunar calendar that are about 15–17 years apart from each other. This is the case with the Islamic calendar. Āryabhat.a I explained the civil and sidereal days: “The revolutions of the Sun are solar years. The conjunctions of the Sun and the Moon are lunar months. The conjunctions of the Sun and Earth are [civil] days. The rotations of the Earth are sidereal days.”60 This deﬁnes the sidereal day as the period from one star-rise to the next, civil days as one sun-rise to the next, and the lunar month, or synodic month, as from one new moon to the next new moon. The ancient Hindus, who knew both the lunar and solar calendars, realized that 62 solar months are equal to 64 lunar months. Therefore, they added one extra month after every 30–35 months. The R. gveda described the Moon as “the maker of months” (māsa-krt).61 “True to his holy law, he knows the twelve Moons with their progeny: He knows the Moon of later birth,”62. Here “the twelve Moons with their progeny” means the twelve months and “the Moon of the later birth” means the 13th month, the supplementary or the intercalary month of the luni-solar calendar. This is a clear indication of the luni-solar calendar during the R. gvedic-period. The Atharvaveda also mentions the 13th month in some years. “He [Sun] who meets out the thirteenth month, constructed with days and nights, containing thirty members, . .”63 The creation of 13th month or the intercalary month of thirty days is ascribed to the Sun, the Moon being the originator of the ordinary months of the year. This is a clear indication that the thirteenth month was added to keep up with the seasons since it is ascribed to the Sun. Al-Bīrūnī explained the Hindu luni-solar calendar in his book, Alberuni’s India: “The months of the Hindus are lunar, their years solar; therefore their new year’s day must in each solar year fall by so much earlier as the lunar year is shorter than the solar (roughly speaking, by eleven days). If his precession makes up one complete month, they act in the same way as the Jews, who make the year a leap year of thirteen months . . . The Hindus call the year in which a month is repeated in the common language malamasa [malamāsa]. Mala means the dirt that clings to the hand. As such dirt is thrown away out of the calculation, and the number of months of a year remains twelve. However, in the literature, the leap month is called adhimāsa.”64 Kaut.ilya (ca. 300 BCE), in his Arthaśāstra, mentions a separate intercalary month and calls it malamāsa.65 This month is generally added every third year.66 In the Hindu calendar, most of the festivals have religious, social, and seasonal importance. In societies where the lunar calendar is in practice, the seasonal festivals are not much celebrated. India is an agricultural country where approximately 65% of the population still lives in villages. 60Āryabhat. īya, Kālakriyā, 5. 61R. gveda, 1: 105: 18. 62R. gveda, 1: 25: 8. 63Atharvaveda, 13: 3: 8. 64Sachau, 1964, vol. 2, p. 20. 65 Arthśāstra, 60; Shamasastry, 1960, p. 59. 66Arthaśāstra, 109; Shamasastry, 1960, p. 121. 4.2. HINDU CALENDAR 77 During the Holī festival, a big ﬁre is burned every year to symbolize the death of Holikā, the aunt of Lord Dhruva. People bring a sample of their harvest, and place it over a ﬁre to roast the wheat or barley seeds which they tie to sugarcane. They share these seeds and sugarcane with friends and family members and decide whether the crop of wheat, barley and cane sugar is ready for harvest or not. During Daśaharā, the quality of barley and wheat seeds is tested in a social gathering; people carry sprouted seeds and share them with their friends. Similarly, after the monsoon season from July to September, one needs to get ready for the winter in India. Cleaning spider webs, dusting rooms, painting walls, and decorating the houses are common chores before Dīpāvalī (Dīvālī). Most Hindu festivals are deﬁned either by the position of the Moon or the Sun. Makara- Sa ˙mkrānti (the Sun enters the sign of Makara (Capricorn) constellation in its northward jour- ney), Gan. eśa-caturthī (fourth day of the Moon, starting from amāvāsya, the new moon), Kr. s. n. a- Janmās. t. amī (eighth day of the Moon) are all deﬁned by the phase of the Moon or the Sun in a particular constellation. Basant-Pañcamī (ﬁfth day of the new Moon), Rām-Navamī (a day to honor Lord Rāma, falls on the ninth day of the new moon), Guru-pūrn. imā (a day to honor teachers, always fall on the full moon), and Nāga-Pañcamī (a day to honor snakes, falls on the ﬁfth day of the new moon) are some of these festivals that are deﬁned by the Moon. The Moon is seen in the sky on almost all nights unless it is close to the Sun. The position of the Sun can be ﬁxed against a constellation only a little before sunrise or after sunset—the time when the sunlight is too weak to suppress the light of other stars. Hindu astronomy, unlike Western astronomy, mapped the sky with the phases of the Moon rather than with the stars. It simpliﬁed their calculations—at full moon, the position of the Sun can automatically be given by that of the Moon. Similarly, the position of the Sun can easily be determined with the diﬀerent phases of the Moon. The following are the months in the Hindu calendar: 1. Caitra (March-April) 2. Vais. ākha (April-May) 3. Jyais. t. ha (May-June) 4. Ās. ād. ha ( June-July) 5. Śrāvan. a ( July-August) 6. Bhādrapad (August-September) 7. Āśvina or Kwār (September-October) 8. Kārttika (October-November) 9. Agarhayana or Aghan (November-December) 78 4. ASTRONOMY 10. Paus. a (December-January) 11. Māgha ( January-February) 12. Phālguna (February-March) The names of the months are derived from the names of the naks. atra (star or constellation) in which the Sun dwells (or nearby). Xuan Zang (or Hiuen Tsang), a Chinese traveler who visited India during the seventh century, and al-Bīrūnī who traveled in India during the eleventh century also used the similar names for various months in India.67 Nothing was more natural for the sake of counting days, months, or seasons than to ob- serve the twenty-seven places which the Moon occupied in her passage from any point in the sky back to the same point. The location of the Moon and its shape provided the tithī (date) as well as the particular time in the night sky for astute observers. This procedure was considerably easier than determining the Sun’s position either from day to day or from month to month. As the stars are not visible during daytime and barely visible at sunrise and sunset, the motion of the Sun in conjunction with certain stars was not an easily observable task. On the contrary, any Vedic shepherd was able to decide day and time easily with the observation of the Moon. The ancient Hindus formulated a theory of creation which was cyclic in nature. The uni- verse followed a cycle of manifestated and non-manifestated existence. A new unit of time, yuga, was chosen to deﬁne the period of this cycle. The yuga system is based on astronomical considerations, and is frequently mentioned and explained in the Purān. ic literature. In the yuga system of the Hindus, a mahā-yuga (mahā means big in the Sanskrit language) is divided into four yugas: Satya or Kr. ta, Tretā, Dvāpar, and Kali. The spans of Satya-yuga, Tretā- yuga, Dvāpara-yuga, and Kali-yuga are in the ratio 4: 3: 2: 1. According to the Hindu scriptures, life on the Earth diminishes in goodness as we go from Satya- to Kali-yuga. At present, we live in the age of Kali-yuga that started in 3102 BCE of the Julian Calendar. A Kali-yuga is equal to 432,000 solar years. A maha-yuga is equal to 4 + 3 + 2 + 1 = 10 Kali-yuga, equivalent to 4,320,000 solar years. Seventy maha-yuga constitute a manvantara and fourteen manvantara constitute one kalpa. A kalpa is the duration of the day of Brahmā, the creator of the universe. The night is equally long and the creation dissolves into the unman- ifested form during the night of Brahmā. After that, it starts again.68 Thus, the total cycle of creation is about 8.5 billion years. It is this number that caught the attention of Carl Sagan, after recognizing this number to be so close to number accepted by modern science which is also of the order of billion of years. In contrast, just two centuries ago, a large number of scientists or scholars in the West considered earth to be just six thousand years old. 67For Hiuen Tsang, see Beal, book II, p. 72; for al-Bīrūnī, see Sachau, vol. 1, p. 217. 68Garud. a-Purān. a, Chapter 233. 4.3. HINDU COSMOLOGY 79 4.3 HINDU COSMOLOGY The R. gveda raises questions about the creation: “What was the tree, what wood, in sooth, pro- duced it, from which they fashioned forth the Earth and Heaven?”69 Or, “What was the place whereon he took his station? What was it that supported him? How was it? Whence Visvakar- man [God], seeing all, producing the Earth, with mighty power disclosed the heaven.”70 In Hindu theory of creation, matter was not created from nothing, as the Bhāgavad-Gītā (2: 16) tell us: “Nothing of non-being comes to be, nor does being cease to exist.” The R. gveda gives an account of creation and explains the state of the universe just before the blast: “Then was neither non-existent nor existent: there was no realm of air, no sky beyond it. What covered in, and where? And what gave shelter? Was water there, unfathomed depth of water? Death was not then, nor was there aught immortal: no sign was there, the day’s and night’s divider. That one thing, breathless, breathed by its own nature: apart from it was nothing whatsoever. Darkness there was: at ﬁrst concealed in darkness this all was indiscriminate chaos. All that existed then was void and formless: by the great power of warmth was born that unit.”71 The R. gveda uses the analogy of a blast furnace of a blacksmith to explain the creation process: “These heavenly bodies produced with blast and smelting, like a smith. Existence, in an earlier age of Gods, from non-existence sprang. Thereafter were the regions born. This sprang from the productive power.”72 This is quite similar to the Big-Bang Theory in which the universe was created with a Big Bang, like a bomb explosion. The Srimad-Bhāgvatam provides a description of the process of creation in which the whole universe was in noumenal form and came to existence under the desire of the Creator (God). The existence will continue for a period of time before the universe would again go back to its noumenal form of matter. This will form a cyclic (oscillating) process will continue forever.73 The concept of matter that cannot be experienced was not a part of science only 100 years ago. Today, the issues of dark matter and energy as a form of matter are scientiﬁc realities. The Bhagavad-Gītā describes the creation of the universe as a transformation of noumenal matter into matter: “From the noumenal all the matter sprung at the coming of the day; at this coming of the night they dissolve in just that called the noumenal.”74 For the Hindus, the end of each creation comes with heat death, somewhat similar to the accelerated global warming which is causing concerns to modern scientists. This process of destruction is described in the Vis. n. u-Purān. a. “The ﬁrst, the waters swallow up the property of Earth, which is the rudiment of smell; and Earth, deprived of its property, proceeds to destruc- tion. Devoid of the rudiment of odor, the Earth becomes one with water. The waters then being much augmented, roaring, and rushing along, ﬁll up all space, whether agitated or still. When 69R. gveda, 10: 31: 7 70R. gveda, 10: 81: 2. 71R. gveda, 10: 129: 1–4. 72R. gveda, 10: 7: 2, 3. 73Srimad-Bhāgvatam, 3, 11–12. 74Bhāgavad-Gītā, 8: 8. 80 4. ASTRONOMY the universe is thus pervaded by the waves of the watery element, its rudimental ﬂavor is licked up by the element of ﬁre, and, in consequence of the destruction of the rudiments, the waters themselves are destroyed. Deprived of the essential rudiment of ﬂavor, they become one with ﬁre, and the universe is therefore entirely ﬁlled with ﬂame, which drinks up the water on ev- ery side, and gradually overspreads the whole of the world. While space is enveloped in ﬂame, above, and all around, the element of wind seizes upon the rudimental property, or form, which is the cause of light; and that being withdrawn, all becomes of the nature of air.”75 Al-Bīrūnī used the views of Varāhamihira, a ﬁfth century Hindu philosopher, to explain the Hindu view of creation. “It has been said in the ancient books that the ﬁrst primeval thing was darkness, which is not identical with the black color, but a kind of non-existence like the state of a sleeping person.”76 “Therefore, they [Hindu] do not, by the word creation, understand a formation of something out of nothing.”77 “By such a creation, not one piece of clay comes into existence which did not exist before, and by such a destruction not one piece of clay which exists ceases to exist. It is quite impossible that the Hindus should have the notion of a creation as long as they believe that matter existed from all eternity.”78 Let us sum up the Hindus’ theory of creation as provided above: There was a void in the beginning. This void was not the one that we perceive in a strict physical sense; this void was full of energy, in analogy, similar to the ﬁelds of modern physicists. The voluminous writings in Hindu literature does not describe the special creation as arising out of nothing. Almost all the scriptures of the Hindus, including the earliest R. gveda, advocate that the present form of the universe evolved from the noumenal form of matter. “Void” or “nonexistence” is like the noumenal matter or dark matter proposed by the mod- ern scientists and philosophers; like the wavefunctions of Schrödinger to explain the microscopic reality that cannot be experienced but, when squared, gives the probability of existence of a par- ticle. The noumenal matter is beyond the senses’ experience but gives rise to a manifested form of matter with a blast under the desire of God.79 The language used to describe the process of creation in the Vedas is at least four thousand years old. The account of the Hindu theory of creation by al-Bīrūnī is about 1,000 years old. Yet, there are striking similarities in the modern theory of creation and the Hindu theory of creation. In both theories, the present universe was created with a blast. In addition, the ancient Hindus believed that the creation process is cyclic in nature, i.e. it goes through the cycle of creation and destruction. The destruction will start with 75Vis. n. u-Purān. a, 6: 4. 76Sachau, 1964, vol. 1, p. 320. 77Sachau, 1964, 1, p. 321. 78Sachau, 1964, vol. 1, p. 323. 79Kant deﬁned the term, noumenon, which means a thing that cannot be perceived and can only be inferred from experi- ence. It is a product of intellectual intuition, like the interaction of electrical ﬁelds that gives rise to a force on a charge particle when placed near other charge particles. Such intuitions are an integral part of most religions as well science where realities are deﬁned from inferred experiences. The analogy mentioned above is an eﬀort to describe nonexistence of the ancient Hindus by sharing similar concepts in physics. However, we are dealing with two diﬀerent domains of knowledge and the nonexistence of the ancient Hindus is not the dark matter or Schrödinger’s wavefunction. 4.4. DIFFUSION OF HINDU ASTRONOMY 81 an increase in heat that will give rise to an increase in the water levels of the oceans. Eventually, the heat will become so high that it will destroy all life forms. Since everything animated in the universe should have a cause or the beginning, what was the beginning of the void or the beginning of the noumenal matter? Instead of drawing a picture of the beginning of the universe, the Hindus exposed the limit of human inquiry. The R. gveda says: “Who verily knows and who can here declare it, whence it was born and whence comes this creation? The Gods are later than this world’s production. Who knows then whence it ﬁrst came into being? He, the ﬁrst origin of this creation, whether he formed it all or did not form it, Whose eye controls this world in highest heaven, He verily knows it, or perhaps He knows not.”80 In this way, the R. gveda exposes the limits of human inquiries to deﬁne the ﬁrst cause of creation. 4.4 DIFFUSION OF HINDU ASTRONOMY The sacred books of the Hindus and Āryabhat.a I’s and Brahmgupta’s books on astronomy reached the Middle East and China, and caused a spurt of new books on astronomy in these regions. With the inﬂuence of the Middle East in Europe, it also indirectly impacted there too. Several noted European astronomers, including Copernicus and Kepler, read translations of the books from the Middle East that were based on Hindu astronomy. 4.4.1 THE MIDDLE EAST If we had to choose just ten astronomy books in human history, Zīj al-Sindhind of al-Khwārizmī (c. 800–850 CE) would be among these books. Al-Khwārizmī, Abu Ja‘far Muh. ammad ibn Mūsā (ca. 800–847 CE) was a member of al-Ma‘mun’s Bayt al-Hikma. The motion of seven celestial bodies, the mean motions, and the positions of apogee and the nodes are described in his Zīj al-Sindhind.81 As the title indicates, this book was based on Hindu astronomy. The contents and the mathematical procedures82 used by al-Khwārizmī in his book agree well with Brahmsphuta- siddhanta(composed in 628 CE) of Brahmgupta, a Hindu astronomer.83 “al-Khwārizmī’s . . . treatise on astronomy was . . . a set of tables concerning the movements of the Sun, the Moon and the ﬁve known planets, introduced by an explanation of its practical use. Most of the parameters adopted are of Indian origin, and so are the methods of calculation described, including in particular use of the sine,” concludes Régis Morelon in his analysis.84 al- Khwārizmī’s book has been translated into English by Neugebauer.85 This book of al-Khwārizmī 80R. gveda, X: 129: 6–7; for more information on Hindu cosmology, see Jain, 1975 and Miller, 1985. 81Translated by Neugebauer, 1962. 82Goldstein, 1967; Kennedy and Ukashah, 1969. 83Salem and Kumar, 1991, p. 47. 84Régis Morelon, Eastern Arabic Astronomy Between the Eighth and the Eleventh Centuries, in the book by Roshdi Rashed, 1996, vol. 1, p. 21. He taught in CNRS in Paris for many years and later served as director of IDEO (Dominican Institute of Oriental Studies) in Cairo from 1984 to 2008. 85Neugebauer, 1962. 82 4. ASTRONOMY became one of the most documented books of astronomy in Europe during the medieval period. The famous Toledo Tables and the Alfonsine Tables were based on this book. In the title of his book, al-Khwārizmī has acknowledge Hindus’ contribution to astronomy. Several medieval and modern historians have written about the connection of Zīj al-Sindhind to Hindu astronomy. “Three Indian astronomical texts are cited by the ﬁrst generation of Arab scientists: Aryab- hatiya [Āryabhat. īya], written by Aryabhata [Aryabhat.a I] in 499 [CE] and referred to by Arab authors under the title al-arjabhar; Khandakhadyaka by Brahmgupta (598–668 CE), known in Arabic under the title Zīj al-arkand; and Mahasidhanta [Mahāsiddhānta], written toward the end of the seventh or at the beginning of the eighth century, which passed into Arabic under the title Zīj al-Sindhind,” writes Régis Morelon.86 A multitude of Zījs were written in India and Afghanistan ﬁrst, and in Persia and Baghdad later. A typical Zīj covered information on trigonometry; spherical astronomy; solar, lunar, and planetary mean motions; solar, lunar and planetary latitudes, parallax, solar and lunar eclipses, and geographical coordinates of various locations, particularly to locate qibla.87 “The Arabic text is lost and the work has been transmit- ted through a Latin translation made in the twelfth century by Adelard of Bath from a revision made in Andalusia by al-Majrīt.ī (d. 1007 CE).”88 Al-Khwārizmī even used metamorphosed Sanskrit terms in his astronomical calculations. For example, for the rules when ﬁnding the sizes of the Sun, the Moon and the Earth’s shadow, al-Khwārizmī used the term elbuht, that comes from the Sanskrit word bhukti where the shadows on the Earth from the Sun and the Moon was observed at the same time daily, indicating the mathematical processes were essentially taken from Hindu astronomy.89 S. ā‘id al-Andalusī (1029–1070 CE) writes that “a person originally from Hind came to Caliph al-Mans.ūr in A.H. 156 [773 CE] and presented him with the arithmetic known as Sindhind for calculating the motion of stars. It contains ta‘ādyal [equations] that give the posi- tions of stars with an accuracy of one-fourth of a degree. It also contains examples of celestial activities such as the eclipses and the rise of the zodiac and other information. . . . Al-Mans.ūr ordered that the book be translated into Arabic so that it could be used by Arab astronomers as the foundation for understanding celestial motions. Muhammad ibn Ibrahim al-Fazārī accepted the charge and extracted from the book that astronomers called al-Sindhind. . . . This book was used by astronomers until the time of Caliph al-Ma‘mūn, when it was abbreviated for him by Abu Ja‘far Muh. ammad ibn Mūsā al-Khwārizmī, who extracted from it his famous tables, which were commonly used in the Islamic world.”90 86Régis Morelon, General Survey of Arabic Astronomy, in the book by Roshdi Rashed, 1996, vol. 1, p. 8. 87King, in the book by Selin, 1997, p. 128; Mercier in Selin, 1997, p. 1057. Zij is a common term used in Arabic for tables and qibla is the direction of Kaaba (Mecca) from your location. 88Régis Morelon, Eastern Arabic Astronomy Between the Eighth and the Eleventh Centuries in the book by Roshdi Rashed, 1996, vol. 1, p. 21; see also Toomer, G. J., 1973, Dictionary of Scientiﬁc Biographies, vol. 7, p. 360. 89Neugebauer, 1962, p. 57; Goldstein, 1996. 90Salem and Kumar, 1991, p. 46–47. This tells us that Europeans were aware that al-Khwārizmī’s work was taken from Hindu astronomers. 4.4. DIFFUSION OF HINDU ASTRONOMY 83 Caliph al-Mans.ūr was a ruler of Baghdad and his Abbasid dynasty was known for its respect of knowledge. He established Bayt al-Hikma (House of Wisdom) which became a model for other empires in Arabia and Europe. The House of Wisdom was a court or school where scholars worked in history, jurisprudence, astronomy, mathematics, and medicine, etc. These scholars were supported by Caliph al-Mans.ūr and, in return, they helped the Caliph in his personal and kingdom aﬀairs. It was a practice of the rulers of Abbasid dynasty to patronize scholars from foreign lands. With time, Baghdad became a center of learning. Scholars from the nearby regions visited Baghdad to acquire knowledge. Abū Ma‘sher, Jafar ibn Moh. ammad ibn Amar al-Balkhī (787–886 CE), a Persian as- tronomer who mostly lived in Baghdad, also mentioned Kanaka’s role in Baghdad. He labeled Kanaka as the foremost astronomer among all the Indians of all times.91 We do not know much about Kanaka. Most of the information about him has come from the manuscripts written later in Arabia, the Mediterranean region and Europe. Apparently, Kanaka made his impact outside India. In Persia, under the Sasanids (226–651 CE), observational astronomy was practiced under the inﬂuence of Indian and Greek astronomy. We know from al-Hashīmī (ﬂ. ninth century) that Shāh Anūshirwān compared the work of Ārybahat.a I’s Arkand with Ptolemy’s Almagest. He found Āryabhat.a I’s work better than Ptolemy’s. Thus, the king asked his astronomers to compile a Zīj on Āryabhat.a I’s system. This is how the “Royal tables” (Zīj al-Shāh) were compiled.92 Al- Mans.ur, while deciding the auspicious time for the foundation of the capital Baghdad, asked his astronomers to use a Pahlavi version of Zīj al-Shāh to calculate this time.93 Like the Greenwich observatory in England has become a standard location to deﬁne the time and longitude of various locations in the world, al-Khwārizmī used Arin (Ujjain), the Greenwich of the ancient and medieval worlds, as the central place of the Earth.94 This is an important piece of information. Almost any point on the Earth can be chosen as a standard for this. Al-Khwārizmī could have chosen Baghdad as the prime meridian, his place of residence. However perhaps due to the prevalent practice in Arabia and al-Khwārizmī’s dependence on the Hindu astronomical tables, he preferred to choose Ujjain. It is the city that was also chosen by Āryabhat.a I and Brahmgupta, from whom al-Khwārizmī derived his work, as zero meridian. al-Khwārizmī deﬁned one sidereal year equal to 365.15302230 days. This is exactly the same value used by Brahmgupta.95 In Al-Khwārizmī’s book, the “era of ﬂood” was the era of Kaliyuga (February 17, 3102 BCE). Al-Khwārizmī’s elwazat, a procedure to calculate the mean positions of the planets, was similar to the ahargan. a method of Hindu astronomy.96 91Pingree, 1968, p. 16. 92van der Waerden, The Heliocentric System in Greek, Persian, and Hindu Astronomy, in the book by King and Saliba, 1987; Régis Morelon, General Survey of Arabic Astronomy, in the book by Roshdi Rashed, 1996, vol. 1, p. 8. On a diﬀerent note, under Anūshirwān’s reign, chess was introduced from India, and the famous book, Kalilah and Dimnah was translated. 93David King, in the book by Selin, 1997, p. 126; F. Jamil Ragep, in the book by Selin, 1997, p. 395. 94Neugebauer, 1962, p. 10, 11. 95Neugebauer, 1962, p. 131. 96Sen, 1970. 84 4. ASTRONOMY 4.4.2 CHINA The inﬂuence of the Hindu thought on China can be judged by the fact that, between 67 CE and 518 CE, in less than ﬁve centuries, some 1,432 works in 3,741 fasciculi were translated from Sanskrit to Chinese and were cataloged in 20 disciplines.97 By 433 BCE, the Chinese as- tronomers recorded a system of 28 hsiu (lunar mansions or Moon stations) marked by a promi- nent star or constellation. The Moon traveled past and lodged in each of these mansions. This system probably originated from the Hindu system of 28 naks. atra (star or constellation).98 The Vedas provide a complete list of these naks. atra. One diﬀerence between these two systems is that whereas the Hindus named their naks. atra after their gods, the Chinese honored their emperors, queens, princes, and even bureaucrats by assigning their names to stars. The Navagraha-siddhānta (Nine Planet Rule), a popular Indian astronomy book, was trans- lated into Chinese as Kaiyuan Zhanjing in 718 CE by Indian astronomer Gautama Siddhārtha (Qutan Xida, his Chinese name). This book is still preserved in a collection from the Tang pe- riod. It contains the Indian calendar, known as navagr. aha (nine houses; used for the ﬁve planets, the Sun, the Moon, and the two nodal points, Rāhu and Ketu). This calendar was known as Ji- uzhi li (Nine Upholder Calendar) in China.99 This calendar is based on Varāhamihira’s Pañca Siddhānta that was written during the sixth century. It contains the astronomical tables along with the methods to calculate an eclipse. It has a table of sines and the Hindu numeral zero in the form of a dot (bindu).100 The Chinese, in following the Hindu tradition, also used nine planets in their astronomical work that included the Sun, the Moon, Mercury, Venus, Saturn, Jupiter, Mars, and the ascending and descending nodes known as Rāhu and Ketu in the Hindu work.101 In May 1977, a tomb of an Indian astronomer from the Gautama family was excavated at Chang-an county in modern Shaanxi province. This tomb had manuscripts and inscriptions that has provided valuable information about Gautama clan. As a result of this excavation, we now know that Gautama Siddhārtha was not the only famous person in Gautama clan. Gau- tama Zhuan also played an important role in the Bureau of Astronomy and at the Tang court. He got married to a Chinese woman and the following generations were assimilated into the Chinese culture.102 During the Tang Dynasty (618–907 CE), three schools of Indian astronomical systems were based in China to guide the emperors. These schools are: Siddhārtha school, Kumāra school, and Kaśyapa school.103 At least two experts from the Siddhārtha school served as Di- rector of the astronomical bureau during Tang dynasty. It is important to mention that these directors were crucial for emperors in their day-to-day activities as they had to ﬁnd auspicious 97Gupta, 1981; Mukherjee, 1928, p. 32, taken from Gupta, 1981. 98Sarma, 2000. 99Yoke, 1985, p. 162 100Yoke, 1985, p. 162. 101Bagchi, 1950, p. 169 and Yoke in Selin, 1997, p. 78. 102Sen, Tansen, 1995. 103Yoke in Selin, 1997, p. 110. 4.4. DIFFUSION OF HINDU ASTRONOMY 85 times for rituals and government actions, consult the director on astrological matters, and even take advice on dealing with people. This is perhaps the most powerful position, after the emperor himself. This position was occupied by Hindus for several generations during the Tang dynasty. This fact tells a lot about the status of Hindu astronomy and Hindus in China. Amoghavajra (Chinese name, Bukong), a brahmin from India arrived in China in 719 at the age of 15 with his uncle. In 741, he went back to India and again returned to China in 746. He was given the title of Zbizang by the Tang Emperor Xuanzong (713–756). In 759 CE, Amoghavajra wrote Xiu yao jing (Lunar mansion and planet sutra). A commentary to this work by Yang Jingfeng mentioned the three Indian schools of astronomy prevalent in China and occupants of powerful Bureau of Astronomy: “Those who wish to know the positions of the ﬁve planets adopt Indian calendrical methods. One can thus predict what hsiu (a planet will be traversing). So we have the three clans of Indian calendar experts, Chia yeh ( Jia ye Kasyapa), Chhu than (Qutan Gautama) and Chu mo lo ( Jiu mo lo Kumara), all of them hold oﬃce at the Bureau of Astronomy. But now most use is made of the calendrical methods of Master Chhu than chuan (Qutan zhuan) together with his Great Art.”104 Another person from this clan, Gautama Rahula, was the director of astronomy between 627 to 649, and compiled two calendars viz. Jingweili and Guangzaili. As the family settled down in China, marry the Chinese, they are not labeled as Indian in Chinese records. Rāhu (Chiao chhu) and Ketu (chiao chung) were frequently mentioned in the Chinese texts written during and after the Tang Dynasty (618–907 CE).105 The book, Qi Yao Rang Zai Jue (Formulae for Warding oﬀ Calamities According to the Seven Luminaries), was compiled by an In- dian Buddhist monk, Jin Ju Zha, in China. This book has detailed ephemerides of Rāhu and Ketu. According to this book: “The luminary E Luo Shi Rāhu is also known by the following names: The Yellow Standard (Huang Fan), The Head of the God of Eclipse (Shi Shen Tou), Su- perposition (Fu), and The Head of the Sun (Tai Yang Shou). It always moves invisibly and is never seen when it meets the Sun or the Moon, an eclipse occurs; if the meeting is at a new moon or a full moon, then an eclipse necessarily occurs; when it is opposite to the Sun or the Moon, there will also be an eclipse.”106 In summary, the text supports the following points: 1. Rāhu and Ketu are invisible luminaries. 2. The motion of Rāhu and Ketu have a bearing on the occurrence of eclipses. 3. The theory depicted in the tales of Rāhu and Ketu is diﬀerent than the ancient theory of eclipses in China. 4. Rāhu and Ketu execute a uniform motion against the background of ﬁxed stars and its speed does not vary. 104Deshpande, 2015; Sen, 1995. A similar account is also provided by Needham and Ling, 1959, vol. 3, p. 202 and Yoke, in Selin, 1997, p. 78. 105Needham and Ling, 1959, vol. 3, p. 416. 106Wei-xing, 1995. 86 4. ASTRONOMY 4.4.3 EUROPE As mentioned earlier, during the eleventh century, the European scholars in Spain knew that al- Khwārizmī’s work in the Middle East was an extension of Hindu astronomy. S. ā‘id al-Andalusī, a prominent scholar from Spain, provided ample information about the work of Āryabhat.a I, Brahmgupta, etc. He believed that the Hindus’ work on astronomy formed the basis for Arab astronomy,107 as mentioned in the previous subsection. S. ā‘id al-Andalusī was not the only person stating this fact. Rabbi Abraham Ibn Ezra (1096–1167 CE) provided a similar story of this transfer of knowledge from India to Arabia.108 Ibn Izra was based in Spain and wrote about Hindu mathematician and astronomer, Kanaka, who shared his knowledge and allowed the Arabs to know about Hindu astronomy: “The scholar, whose name was Kanaka, was brought to the king, and he taught the Arabs the basis of numbers, i.e., the nine numerals. Then, from this scholar with the Jew as Arabic-Indian interpreter, a scholar named Jacob b. Sharah translated a book containing the tables of seven planets [ﬁve planets, the Sun, and the Moon]. . .”109 Abū Ishaq Ibrāhim ibn Yahya al-Naqqash, better known as al-Zarqalī (ca.1029–1087 CE), a Spanish astronomer who worked under S. ā‘id al-Andalusī, compiled the famous Toledan Tables that are based on the Sindhind system.110 “One of the ﬁrst Latin authors to use tables of Arabic origin was Raymond of Marseilles. In 1141 [CE], he composed a work on the motions of the planets, consisting of tables preceded by canons and an introduction in which he claims to draw on al-Zarqāllu [Zarqalī].111 Prior to al-Zarqalī, around 960 CE, ‘Arīb bin Sa‘īd and Mozarab bishop Rabī b. Zayd compiled the Calendar of Códoba for al-H. akam II after his accession to the caliphate. The calendar provided the dates when the Sun enters in diﬀerent zodiacs. These dates are provided according to the Sindhind and used the mathematics of Brahmgupta.112 “The Toledan tables are a composite collection, including the parts taken from the tables of al-Zarqāllu [Zarqalī] alongside extracts from al-Khwārizmī (notably the planetary latitudes), elements from Al-Battānī (in particular, the tables of planetary equations), and yet other parts derived from the Almagest or the Handy Tables of Ptolemy.”113 The Toledan tables were translated by Gerard of Cremona114 and played an important role in the growth of European astronomy. Al-Zarqalī is not the only person in Europe who studied and wrote astronomy books on the Hindu system of Sindhind. Al-Majrīt.ī (d. 1007 CE) also modiﬁed the Sindhind of al- 107Salem and Kumar, 1991 108Goldstein, 1967, p. 1478. 109Goldstein, 1996. 110Sarton, 1927, vol. I, p. 759. 111Henri Hugonnard-Roche, Inﬂuence of Arabic Astronomy in the Medieval West, in the book by Roshdi Rashed,1996, vol. 1, p. 287; also see, Toomer, 1968. 112Juan Vernet and Julio Samsó, Development of Arabic Science in Andalusia, in the book by Roshdi Rashed,1996, vol. 1, p. 250–251. 113Henri Hugonnard-Roche, Inﬂuence of Arabic Astronomy in the Medieval West, in the book by Roshdi Rashed, 1996, vol. 1, p. 289. 114Henri Hugonnard-Roche, Inﬂuence of Arabic Astronomy in the Medieval West, in the book by Roshdi Rashed, 1996, vol. 1, p. 292. 4.4. DIFFUSION OF HINDU ASTRONOMY 87 Khwārizmī. A student of al-Majrīt.ī, Ibn al-Samh. (979–1035 CE), composed a zij that was based on the Sindhind system.115 Another student of al-Majrīt.ī, Ibn al-Saﬀār, also authored a brief astronomical table that was based on the Sindhind system.”116 The third scholar from Spain, Ibn al-Ādāmi also compiled the astronomical tables known as Kitab Naz. m al-‘Iqd (Book on the Organization of the Necklace) that was completed after his death by his student al-Qāssim bin Moh. ammad ibn Hashim al Madā’inī, better known as al-’Alawī, in 950 CE. “This book contains all that was known about astronomy and the calculation of the motions of the stars according to the system of the Sindhind, including certain aspects of the trepidant motions of the celestial bodies, which were never mentioned before,” writes S. ā‘id al-Andalusī.117 It is the Latin version of al-Khwārizmī’s text that was used by Adelard of Bath, a British scientist and Arabist of the early twelfth century, to teach Henry Plantagenet, the future King Henry II of England.118 Thus, the work of the Brahmins on the banks of Ganges became the subject matter of learning to the Royalty in England. Alfonso X, King of Castile119 (1252–1284 CE) gathered a group of Muslims, Jewish, and Christian scholars in the tradition of Bayt al Hikma or House of Wisdom of Baghdad. These schol- ars translated the earlier works in Arabic that were based on Hindu astronomy and compiled them into a single book in the Castilian language, called the Alfonsine Tables. This book reached Paris in the early 14th century and was translated into Latin. Soon the book spread throughout Europe and used as computing tool by European astronomers.120 Thus, medieval astronomy in Europe was a derived and improved mixture of Hindu, Persian, and Arabic contributions. It is established that a bound volume of the Alfonsine Tables was owned by Copernicus and he did copy planetary latitudes from these tables.121 The extent to which Copernicus was in debt of the Hindu science is a matter of interpretation and debate. However, there is no dispute that he did use Hindu numerals and mathematics in his calculations. His dependence on Hindu astronomy is an open question which only the future scholarships will ascertain. Johannes Kepler gave his table of parallax of the Moon which is essentially identical with the theory of parallax given in Khandakhadyaka of Brahmgupta.122 The theory of Brah- mgupta was proposed about one millennium before Kepler. A possible connection could be al-Khwārizmī’s book on Hindu astronomy, Zīj al-Sindhind. This book quite popular in Europe when Kepler was learning astronomy in his youth. 115Salem and Kumar, 1991, p. 64. 116Salem and Kumar, 1991, p. 65. 117Salem and Kumar, 1991, p. 53. 118Burnett, 1997, p. 31. 119Castile is presently a part of Spain. As a side note, soaps made from olive oil and sodium hydroxide or any hard soap from fat or oil are called Castile soaps. It is the legacy of this region. 120Chabás, 2002; King and Saliba in the book by Gingerich, 1993. 121Swerdlow and Neugebauer, 1984, p. 4 and Chabás, 2002. 122Neugebauer, 1962, p. 124. This is the conclusion of Neugebauer (1899–1990), a noted historian of science, who was trained in Gröningen, Germany, and taught at Brown University, USA. C H A P T E R 5 Physics 89 Physics deals with matter and energy and their interactions. Measurements are central to the growth of physics and length (space), time, and mass, are the three most important physical quantities, called the fundamental quantities. Most other physical quantities are generally ex- pressed in their terms of mass, length, and time. For example, speed is measured in miles per hour (or kilometer per hour) and involves a measurement of space (distance) and time. This means that a car moving with 65 miles/hour moves 65 miles (one measurement) in one hour (second measurement). Similarly, force is measured in terms of mass, length, and inverse-square of time. Therefore, for convenience purposes, most civilization deﬁned standards for these fundamental quantities. The ancient Hindus also methodically and carefully deﬁned these standards. 5.1 SPACE (ĀKĀŚA) Space is a three dimensional matrix into which all objects are situated and move without produc- ing any interaction between the object and the space. In the classical sense, space allows a physical ordering of objects without any reference to time. Objects appear to be near or distant due to this physical ordering. In the Newtonian (classical) world, where objects move with speeds much smaller in comparison to the speed of light, space and time are independent of each other, and are considered as separate fundamental quantities. In the relativistic world, where objects move 108 m/s), space and time do not with a velocity that is comparable to the velocity of light (3 have their independent status; they are integrated and form a new space-time (spatio-temporal) reality. In the present context, only the classical picture of space and time as two independent realities are considered. (cid:2) Ākāśa is one of the terms used to describe “space” in the Sanskrit language. According to the Chāndogya-Upanis. ad, space was the ﬁrst entity in the creation of the universe. To a question, “To what does the world go back?,” the Chāndogya-Upanis. ad answers: “To space, all things are created from space and they dissolve into space. Space alone is greater than any manifestation; space is the ﬁnal goal.”1 The Chāndogya-Upanis. ad identiﬁed space as an entity that contains the Sun, the Moon, and other material objects: “In Space are both the Sun and the Moon, light- ening, the stars, and ﬁre. Through space one calls out; through Space one hears; through Space one answers. In Space one enjoys himself. In space one is born. Reverence Space.”2 Thus, even the heavenly objects were a part of something larger and more basic than them; this was space 1Chāndogya-Upanis. ad, 1: 9: 1. 2Chāndogya-Upanis. ad, 7: 13: 1–2. 90 5. PHYSICS that encompassed humans, sound, the Sun, the Moon, and the stars. It is space that provides individuality to objects as they are recognized based on the space they occupy: “Space is the accomplisher of name and form (individuality).”3 The Vaiśes. ika-Sūtra of Kan. āda explained the attribute of space: “That which gives rise to such cognition and usage as, this is remote from this, is the mark of space.”4 Thus, distance is an attribute of space. Kan. āda considered the various directions (east, west, north, south) as the attributes of space.5 A standard of length is imperative for any measurement of space. The Mārkan. daya-purān. a provides the following standards of length: “A minute atom, a para-suks. ma, the mote in a sun- beam, the dust of the earth, and the point of a hair, and a young louse, and a louse, and the body of a barley-corn; men say each of those things is eight times the size of the preceding thing. Eight barley-corns equal an “a ˙ngula” (ﬁnger-breadth), six ﬁnger-breaths are a “pada” (step), and twice that is known as bitasti; and two spans make a cubit measured with the ﬁngers closed in at the root of the thumb; four cubits make a bow, a “dan. d. a” (stick), and equal to two “nadikayaga;” two thousand bows make a “gavyūti;” and four times that are declared by the wise to be a “yojna;” this is the utmost measure for the purpose of calculation.”6 9 meter which is strikingly closer to the actual value (of the order of 10(cid:0) In Sanskrit, “pāda,” literally meaning a human step. If we consider “pāda” to be equal to one foot and calculate the size of an atom using Mārkan. daya-purān. a, its value comes out to be 2.9 10(cid:0) Kaut.ilaya, the teacher and Prime Minister of Chandragupta Maurya (Candragupta, reigned, 322–298 BCE) deﬁnes several standards of length in his book, Arthaśāstra7 that are compiled in Table 5.1. 10 m). (cid:2) 5.2 TIME It is easy to measure time. Most people carry a watch and some of these watches can be bought for just a few dollars. To deﬁne the nature of time is comparatively a lot diﬃcult task. Despite consistent eﬀorts for at least two millenniums, it is still an open question. In other words, it is a lot easier to set a standard for time; it is a lot diﬃcult to set an abstract deﬁnition of time that can exemplify its nature.8 Time and action (event) are related with each other. Events are the basis of time. Time deals with the order and the duration of events. Since events are discrete in nature, this makes time discrete in nature. If there is a sequence of events at a deﬁnite time interval, careful mea- surements of such a body constitutes a clock. In simple words, time divides two events from one another. What happens when events move faster and the time between the two events becomes 3Chāndogya-Upanis. ad, 7: 14: 1. 4Vaiśes. ika-Sūtra, 2: 2: 10. 5Vaiśes. ika-Sūtra, 2: 2: 11–13. For this book, I have used a Hindi edition by Pundit Shriram Sharma Ā ¯carya. 6Mārkan. deya-purān. a, 49: 37. 7Arthaśāstra, Chapters 106–107; Book 2, Chapter 20; Shamasastry, 1960, p. 117. 8For the history of time and clocks, read Balslev, 1983; Panikkar, 1984; and Prasad, 1992. Table 5.1: A Standard of Length from Kaut.ilaya’s Arthaśāstra 5.2. TIME 91 smaller and smaller? Do we have continuous events and, therefore, continuous time? Philoso- phers have considered the question as to whether time is continuous or discrete for ages, without coming to a deﬁnite conclusion. Any temporal existence is evolved with time and vice-versa. It is time that is the origin of the ﬁrst cause, as the Atharvaveda tells us: “Time created living things and ﬁrst of all, Prajāpati.”9 In Hindu scriptures, “Prajāpati” is the ﬁrst God created who, in turn, created the present uni- verse. In this view, it is time that unfolds the spatio-temporal universe and divides the past from the present and the future. “In time, texts are produced—what is, and what is yet to come.”10 “Time is the supreme power in the universe.”11 The Maitreyī-Upanis. ad relates time to the mūrta (existent) world. “There are two forms of Brahmā: Time and Timeless. That which is before the Sun is Timeless and that which begins 9Atharvaveda, 19: 53: 10. 10Atharvaveda, 19: 54: 3. 11Atharvaveda, 19: 54: 6. 8 paramāṇavah, atoms1 particle thrown oﬀ by the wheel of a chariot8 particles1 likṣā (egg of louse or young louse)8 likṣā1 yūka (louse of medium size)8 yūka1 yava (barley of medium size)8 yava1 aṅgula (ﬁnger breadth)4 aṅgula1 dhanurgṛaha8 aṅgula1 dhanurmuṣaṭi12 aṅgula1 vitasti14 aṅgula1 or pāda2 vitasti1 aratni or prajāpatya hasta (arm-length)42 aṅgula1 kiṣku (forearm)54 aṅgula1 hasta used in measuring timber forests.84 aṅgula1 vyama4 aratini1 rajju (rope)10 daṇḍa1 rajju2 rajju1 a3 rajju1 nivartana66.5 nivartana1 goruta4 goruta1 yojna.92 5. PHYSICS with the Sun is Time.”12 This quotation states that the Sun was created with the creation of universe and that time existed only after the creation. Prior to the creation, time did not exist, in the absence of any event. “[A]nything before the Sun” deﬁnes the period before the physical manifestation of the world, the situation before the Big Bang, when matter was in noumenal form, and no events were possible. Therefore, time could not have existed in the absence of events. Only after the creation, matter became accessible to experience. The Vaiśes. ika-Sūtra considered time as an entity that exists only in the manifested world (non-eternal), like in the Maitreyī-Upanis. ad mentioned above. “The name Time is applicable to a cause, in as much as it does not exist in eternal substances and exists in noneternal sub- stances.”13 Therefore, time can only be noticed in a dynamic world (temporal world) where events are happening and serve as distinguishing factors. In a void, after this temporal world dissolves into “darkness” or “non- existence,” time cannot exist.14 The Vis. n. udharmotra-Purān. a explains the subtlety of time and its quantized nature: “if one pierces 1,000 lotus petals (put on top of each other) with a needle, the foolish man thinks that they are pierced simultaneously, but in reality they were pierced one after the other and the subtle diﬀerence between the instants in which the successive petals have been pierced represents the subtlety of time.”15 Āryabhat.a I explains the nature of time and deﬁnes a method to measure it: “Time, which has no beginning and no end, is measured by (the movements of ) the planets and the asterisms on the sphere.”16 To measure time, the apparent motion of the Sun deﬁned the events; sunrise and sunset were two easily observed events. A scale based on the average-solar day was estab- lished by the ancient Hindus. The duration of an average day was divided into several segments that became a standard of time. To measure the magnitude of time, a simple method is deﬁned in the Srimad- Bhāgvatam.17 (Table 5.2.) The duration of “nād. ikā” is measured as follows: “Take a copper vessel measuring six “pala;” make a hole into the copper vessel by a pin made of gold of which the length shall be four ﬁngers and measure four “ma ˙sa” (unit of mass). Put the vessel on water. The time taken to make the vessel ﬁlled with the water and sink constitutes one nād. ikā.” If we consider the average length of a day to be 12 hours then the smallest unit of time, “trasaren. u,” comes out to be about 1.7 4seconds.18 10(cid:0) Within the accuracy of a solar clock, the method provided in the Srimad-Bhāgvatam for the measurement of time is fairly good. All factors that can inﬂuence a measurement are provided—the size of the copper vessel, the size of the hole is deﬁned from the length of the gold pin and its weight that deﬁnes the diameter of the pin, and the type of liquid. (cid:2) 12Maitreyī-Upanis. ad, 6: 15. 13Vaiśes. ika-Sūtra, 2: 2: 9. 14see R. gveda, 10: 129: 1–4; see Chapter 4. 15Vis. n. udharmotra-Purān. a, 1: 72: 4–6. 16Āryabhat. īya, Kalākriya, 11. 17Srimad-Bhāgvatam, 3: 11: 6–11. 18Srimad-Bhāgvatam, 3: 11: 6–11. Table 5.2: A Standard of Time from Srimad-Bhāgvatam 5.2. TIME 93 Table 5.3 deﬁnes a standard of time provided in Kaut.ilaya’s Arthaśāstra.19 One nālika is deﬁned as the time during which one adhaka (a measurement of mass) of water passes out of a pot through an aperture of the same diameter as that of a wire of 4 a ˙ngula and made of 4 ma ˙sa (measurement of mass) of gold. The length and mass of gold deﬁnes the diameter of the wire. Here, trut.i comes out to be 0.06 s, if we assume 1 day to be 12 hours. Table 5.3: A Standard of Time from Kaut.ilaya’s Arthaśāstra (cid:2) (cid:2) 60/=.88; 473; 600/ Al-Bīrūnī explained that the smallest unit of time used in India was an. u that is equal to 4 seconds.20 He did not see a use of such a small (24 60 unit for time, just like he did not like the Hindus to deﬁne large numbers. “The Hindus are foolishly painstaking in inventing the most minute segment of time, but their eﬀorts have not 9s) or femto- resulted in a universally adopted and uniform system.”21 With nano-second (10(cid:0) 9:766 10(cid:0) D (cid:2) 19Arthaśāstra, 107; Shamasastry, 1960, p. 119. 20Sachau, 1964, vol. 1, p. 337. 21Sachau, 1964, vol. 1, p. 334. 3 trasareṇu1 truti100 truti1 bedha3 bedha1 lāva3 lava1 nimeṣa3 nimeṣa1 kṣaṇa5 kṣaṇa1 kāṣṭha15 kāṣṭha1 laghu15 laghu1 nāḍikā or daṇḍa2 nāḍikā1 muhūrta6 or 7 daṇḍa1 prahara (one-fourth of a day or night)2 truṭi1 lava2 lava1 nimeṣa5 nimeṣa1 kāṣṭha30 kāṣṭhā1 kalā40 kalā1 nālika2 nālika1 muhūrta15 muhūrta1 day or night94 5. PHYSICS second (10(cid:0) ahead of their time. 15s) prevalent in scientiﬁc works today, it simply shows that the Hindus were simply 5.3 MATTER AND MASS In order to deﬁne and distinguish matter, Kan. āda deﬁnes matter (padārtha) into six categories.22 1. Substance (dravya) 2. Quality (gun. a) 3. Action (karma) 4. Generality (sāmānya) 5. Individuality (viśes. a) 6. Inherence (samavāya) Matters of diﬀerent materials have diﬀerent attributes. For example, identical sizes of iron and cotton would have diﬀerent weights. Apples can have diﬀerences in their colors and yet be called apples. It is the assembly of attributes that deﬁnes matter. Table 5.4 deﬁnes the attributes of matter as deﬁned by Kan. āda. Table 5.4: Attributes of matter from Vaiśes. ika-Sūtra (1: 1: 6) To explain what he meant by diﬀerent attributes of matters, Kan. āda provides examples: Earth has the attributes of color, taste, and touch;23 water has the attributes of color, taste, touch, ﬂuidity, and viscidity;24 ﬁre with color, and touch;25 air has the attribute of touch;26 while space 22Vaiśes. ika-Sūtra, 1: 1: 4. 23Vaiśes. ika-Sūtra, 2: 1: 1. 24Vaiśes. ika-Sūtra, 2: 1: 2. 25Vaiśes. ika-Sūtra, 2; 1: 3. 26Vaiśes. ika-Sūtra, 2; 1: 4. 1.color (rūpa)10.priority (paratva)2.taste (rasa)11.posteriority (aparatva)3.smell (gandha)12.intellect (buddhi)4.touch (sparśa)13.pleasure (sukha)5.number (saṅkhyā)14.pain (duḥkha)6.measure (parimāṇa)15.desire (icchā)7.individuality (pṛthaktā)16.aversion (dveṣa)8.conjunction (saṁyoga)17.volition (prayatnaḥ)9.disjunction (vibhāga)5.3. MATTER AND MASS 95 has no such properties.27 While analyzing air, Kan. āda concludes that “air is a substance since it has action and attributes.”28 “Air is matter, but its non-perception, in spite of being substance, is due to the non-existence of color in it.”29 With the non-perception of air, Kan. āda deﬁnes reality beyond appearance. Not all that exists in the world is visible to human eyes. In his attempt to clarify a diﬀerence between space and air, Kan. āda used the attribute of touch which is absent in space: “Air has the property of touch while space does not have such a property.”30 To support that air is matter, Kan. āda argued that a breeze can easily move the leaves of grass.31 Thus, air, though invisible, can exert force and move things. Kaut.ilaya’s Arthaśāstra provided standards of mass and suggested that the standards should be made of iron or stones, available in Magdha and Mekala, both parts of Central India. A replacement could be of objects that do not change their physical conditions. These standards should not contract or expand when wet, and a change of temperature should not aﬀect them.32 For a measurement of mass, Kaut.ilaya deﬁned balances with diﬀerent lever arms and scale- pans for a range of masses:33 With the fulcrum in the middle, two identical pans hang on both sides of the fulcrum at equal distances. Standard appropriate masses are placed on one side and the unknown mass on the other so that the beam is balanced when the device is suspended by the fulcrum. Kaut.ilaya provides descriptions of sixteen types of such balances. He suggested diﬀerent balances for diﬀerent accuracy: “public-balance” (vyāvahārikā), “servant-balance” (bhājini) and “harem-balance” (antah. pura-bhājini).34 Superintendents were assigned to stamp mass-standards for public use to avoid cheating, and money was charged for such services.35 Traders were not allowed to use their own standards, and were ﬁned if found guilty of doing so.36 Much before Kaut.ilaya, a beam balance with two identical pans of metallic copper or bronze hanging from each end of the beam and a fulcrum in the middle have been found in Harappa and Mohenjodaro archaeological excavations. The beams are thicker in the middle around fulcrum and tapered at the end where pans are suspended. Most pans have three sym- metrical holes to suspend using strings. The diameter of these pans range from 5.50 to 8.25 cm. From Lothal, Gujrat, even teracotta pans have been excavated. Some micro-balances with stan- dard weights ranging from 0.89 to 1.2 g were also excavated.37 27Vaiśes. ika-Sūtra, 2; 1: 5. 28Vaiśes. ika-Sūtra, 2: 1: 12. 29Vaiśes. ika-Sūtra, 4: 1: 7. 30Vaiśes. ika-Sūtra, 2: 1: 4, 5. 31Vaiśes. ika-Sūtra, 5: 1: 14. 32Arthaśāstra, 103; Book 2, Chapter 19; Shamashastri, 1960, p. 113. 33Arthaśāstra, 103; Book 2, Chapter 19; Shamasastri, 1960, p. 114. 34Arthaśāstra, 104; Book 2, Chapter 19; Shamasastri, 1960, p. 114. 35Arthaśāstra, 105; Book 2, Chapter 19; Shamasastri, 1960, p. 116. 36Arthaśāstra, 105; Book 2, Chapter 19; Shamasastri, 1960, p. 116. 37Sharma and Bhardwaj, 1989. 96 5. PHYSICS 5.3.1 CONSERVATION OF MATTER Conservation of matter is a fundamental law in physics that was introduced by John Dalton (1766–1844 CE) in 1803. Einstein’s mass-energy relation added energy to the conservation of mass since mass can be transformed into energy and vice-versa. Mass and energy are two dif- ferent manifestations of the same reality. Therefore, the law of conservation of matter is now transformed into a broader law of conservation of energy to incorporate mass-energy transfor- mations. Conservation of matter, in the ancient Hindu literature, is an extension of the theory of reincarnation. The ancient Hindus noted that life is a continual process and birth and death are just two diﬀerent stages of life. In an extension of birth and death to the inorganic world, they believed that matter, like the soul, cannot be destroyed or created; only a transformation from one form to another is possible. As discussed in Chapter 4, the possibility of creation from “nothing” is rejected by the ancient Hindus. The Vaiśes. ika-Sūtra tells us that a substance is produced from other substances.38 Mixing or separation of diﬀerent substances creates new substances and it is impossible to create matter from “nothing.”39 In his attempt to explain the properties of air, Kan. āda suggests the law of conservation of matter that is strikingly similar to the deﬁnition accepted by the scientists about hundred years ago. “Matter is conserved. Since air and ﬁre are made up of atoms, these are also conserved.”40 Kanada also makes an explicit statement that “molecules and materials are eternal,” implying that they are conserved.41 The Sanskrit term nitya is used to deﬁne that atoms and matter are conserved. The most common translation of nitya is “eternal,” deﬁning something that will exist forever. This essentially means that atoms are eternal or conserved. 5.4 ATOM (PARAMĀN. U ) Karl Marx (1818–1883), the father of communism, wrote his doctoral thesis on the diﬀerences of the philosophies of Democritus and Epicurus in 1841. While studying the life of Democritus, Karl Marx suggested that Democritus came in contact with Indian gymnosophists and the con- cept of atom was already present in India during that period. Karl Marx was not the ﬁrst person to indicate this. The connection of the Greek philosophers with India has been accepted by some scholars through out in antiquity and the medieval world. This is also the view of Diogenes Lu- cretius (First Century BCE; IX: 35) whom Marx studied extensively for his work. Marx writes, “Demetrius in the Homonymois [Men of the Same Name] and Antisthenes in the Diadochais [Suc- cessions of Philosophers] report that he [Democritus] traveled to Egypt to the priests in order to 38Vaiśes. ika-Sūtra, 1: 1: 23 and 27. 39Vaiśes. ika-Sūtra, 1: 1: 25 and 28. 40Vaiśes. ika-Sūtra, 7: 1: 4; 7: 1: 19–20. 41Vaiśes. ika-Sūtra, 7: 1: 8. 5.4. ATOM (PARAMĀN. U ) 97 learn geometry, and to the Chaldeans in Persia, and that he reached the Red Sea. Some maintain that he also met the gymnosophists in India . . .”42 Kan. āda’s atomic theory was formulated sometime between the sixth century BCE and tenth century BCE.43 Kan. āda was from Pabhosa, Allahabad, and was perhaps the ﬁrst atomist in India.44 His theory was quite popular in ancient and medieval India. The Vāyu-Purān. a, Padma- Purān. a, Mahābhārata, and Srimad-Bhāgvatam list Kan. āda’s work and bear infallible testimony to the antiquity and popularity of the Vaiśes. ika-Sūtra. In Kan. āda’s theory, the combination of molecules (an. u) is possible and the non-perception of atoms disappears when they amass together to become bigger.45 This indirectly deﬁnes limits to the resolving power of human eyes. The smallest state of matter is paraman. u (atom) which cannot be seen. These atoms aggregate to form the world we see. The shape of atoms is spher- ical.46 Two atoms combine to form a dyad. Three dyads of the same type form a triad which is large enough in size to be visible, ‘as motes in a sunbeam.’ Lucretius, who wrote about the con- nection of Democritus and India, used a similar analogy to show how invisible objects become visible.47 The above statement of combination of atoms tells us that “atoms possess an innate propensity to aggregate. This idea is thus a forerunner of the modern concept of van der Waal forces,” suggests Prof. S. K. Bose of the University of Notre Dame in Indiana, USA.48 In his views, Vaiśes. ika-Sūtra “recognizes the existence of properties of the composite body that result from the manner in which the atoms are put together and organized.” As an example, one can use the diﬀerence between water as liquid vs. soild. Both have the same atoms. However, the distinct properties of the bulk materials are diﬀerent. The attributes such as color, taste, smell, and touch of earth, water, ﬁre, and air are non- eternal on account of their substrata.49 These attributes disappear with the disappearance of their substance. Some attributes of the substrata are prone to change in its combinative (chemical action; pākajah) causes under the action of heat.50 Thus, odor, ﬂavor, and touch are attributes of atom in the Vaiśes. ika-Sūtra whereas Democritus denied such connections. The Greek atoms possessed only minimal properties: size, shape, and weight.51 The invisibility of an object, as we divide it into small parts, can simply be observed from the experience of wet clothes hung in air. The water in clothes can be seen and experienced with 42Marx, 1841, The Diﬀerence Between the Democritean and Epicurean Philosophy of Nature, 1841, Doctoral Thesis, Part 1, Chapter 3, online version. 43Sinha, 1911, p. VI; Sarsvati, 1986, p. 302; Subbarayappa, 1967. A recent paper by Karin Preisendanz assigns the second century CE to the commentary of Candrananda on Vaiśes. ika-Sūtra. 44Sarasvati, 1986, p. 295. 45Vaiśes. ika-Sūtra, 4: 1: 6; 7: 1: 9–11. 46Vaiśes. ika-Sūtra, 7: 1: 20. The statement of Kan. āda is pretty clear. On the other hand, it was not at all possible for the ancient scholars to see an atom. How can you deﬁne a shape for something that you cannot even see? This statement is presented here to promote further scholarship on this issue. 47Bose, 2015. This article provides an excellent review of atomism in diﬀerent cultures. 48Bose, 2015. 49Vaiśes. ika-Sūtra, 7: 1: 2. 50Vaiśes. ika-Sūtra, 7: 1: 6. 51Horne, 1960. 98 5. PHYSICS touch. As the sunlight and air dry the cloth, the moisture escapes from the cloth and becomes invisible. The same water drops that were visible to the human eye disappear with extended exposure to air and sunlight. Thus, smallness of an object causes this invisibility, as suggested by Kan. āda. Continual division of matter does not lead it to disappear from existence, as it becomes invisible. It is for this reason “an absolute non-existence of all things is not possible because an atom remains in the end.”52 The Vāyu-Purān. a suggested a similar ultimate division of matter, “A paramān. u (atom) is very subtle. It cannot be seen by the eye. It can be imagined. What cannot be (ultimately) split in the world should be known as atom.”53 The Srimad-Bhāgvatam suggested a theory of the atom that is similar to Kan. āda’s: “That which is the ultimate division of matter, that which has not gone through any change, that which is separated from others, and that which helps the perception of objects, that which remains after all is gone, - all those go under the name of parām. anu (atom).54 “Two atoms make one an. u (molecule) and three an. u make one trasaren. u. This trasaren. u is discovered in the line of solar light that enters into a room through a window and due to its extreme lightness such trasaren. us couresth the way to sky.”55 Cyril Bailey (1871–1957), a British philologist, analyzed Kan. āda’s theory in his book, The Greek Atomists and Epicurus. In his view, “It is interesting to realize that at an early date Indian philosophers had arrived at an atomic explanation of the universe. The doctrines of this school were expounded in the Vaicesika Sutra [Vaiśes. ika-Sūtras] and interpreted by the aphorisms of Kanada [Kan. āda]. While, like the Greek Atomists, they reached atomism through the denial of the possibility of inﬁnite division and the assertion that indivisible particles must ultimately be reached in order to secure reality and permanence in the world, there are very considerable diﬀerences between the Indian doctrines and that of the Greeks.”56 On the relation of atoms and matter in Kan. āda’s system and its similarity to Greek atomism, Bailey continues, “Kanada [Kan. āda] works out the idea of their combinations in a detailed system, which reminds us at once of the Pythagoreans and in some respects of modern science, holding that two atoms combined in a binary compound and three of these binaries in a triad which would be of a size to be perceptible to the senses.”57 There are marked diﬀerences between Kan. āda and Democritus. Atoms, as deﬁned by Kan. āda, are indestructible, indivisible, and have the minutest dimension. In the case of Dem- ocritus, atoms of all elements (substances) are made up of just one substance; they diﬀer only in regards to form, dimension, position, etc. These atoms were indivisible, like Kan. āda sug- gested, and had inﬁnite shapes and, therefore, inﬁnite types of substances.58 The roots of Indian atomism were epistemological and based on empiricism and observation while those of Greek 52Nyāya-sūtra, 4: 2: 16. 53Vāyu-Purān. a, 2: 39: 117. 54Srimad-Bhāgvatam, 3: 11: 1. 55Srimad-Bhāgvatam, 3: 11: 5. 56Bailey, 1928, p. 64. 57Bailey, 1928, p. 65. 58McDonell, 1991, p. 11–12. atomism were ontological or a priori.59 Kan. āda gained knowledge of atoms through empiricism, intuition, logic, observation, and experimentation. 5.5. GRAVITATION AND OCEAN TIDES 99 5.5 GRAVITATION AND OCEAN TIDES The Vaiśes. ika-Sūtra suggested that objects fall downward when dropped as a result of gravity. “The falling of water, in absence of conjunction, is due to gravity,”60 and “ﬂowing results from ﬂuidity.”61 Kan. āda used gurutva word, in Sanskrit, for heaviness or gravity; gurutvākars. an. (im- plying attraction of the earth) is the Hindi term for the gravitational force today. To elaborate the gravitational properties, Kan. āda wrote: “In absence of conjunction, falling results from gravity.”62 In the absence of any conjunction, due to gravity, only downward motion is possible: “In absence of propulsive energy generated by action, falling results from gravity.”63 Kan. āda also explained why water should fall due to gravitational eﬀect, even though it goes up in the form of rain-clouds during the evaporation process: “The Sun’s rays cause the ascent of wa- ter, their conjunction with air.”64 Kan. āda explains the upward motion of the objects: “Throwing upward is the joint product of gravity, volition, and conjunction.”65 An example is the upward motion of water in a tree.66 Al-Bīrūnī (973–1050 CE) explains the shape of the Earth and force of attraction between the Earth and human: “The diﬀerence of the times which has been remarked is one of the results of the roundity of the earth, and of its occupying the center [center] of the globe. . . the existence of men on earth is accounted for by the attraction of everything heavy toward its center [center], i.e., the middle of the world.”67 He continues, “. . . we say that the earth on all its sides is the same; all people on earth stand upright, and all heavy things fall down to earth by a law of nature, for it is the nature of the earth to attract and to keep things. . . .”68 Al-Bīrūnī provides an analogy of a kadamba ﬂower (Fig. 4.1) to describe humans on the Earth. In this analogy, spikes are like humans. The force of gravitation allows humans to live on all sides of the Earth where nothing is up or down. He ascribed this knowledge to Varāhmihir (505–587 CE).69 As mention in Chapter 4, Āryabhat.a I also knew this because he used the same analogy. He said that there was no “up” or “down” side of the Earth. What this means is that, from its location in the great vastness of space, among the immense number of stars and 59Horne, 1960 60Vaiśes. ika-Sūtra, 5: 2: 3. 61Vaiśes. ika-Sūtra, 5: 2: 4. 62Vaiśes. ika-Sūtra, 5: 1: 7. 63Vaiśes. ika-Sūtra, 5: 1: 18. 64Vaiśes. ika-Sūtra, 5: 2: 5. 65Vaiśes. ika-Sūtra, 1: 1: 29. 66Vaiśes. ika-Sūtra, 5: 2: 7. 67Sachau, 1964, 1, p. 270. 68Sachau, 1964, vol. 1, p. 272. 69Sachau, 1964, vol. 1, p. 272. 100 5. PHYSICS other celestial bodies, it is impossible to designate an “up” or “down” side, or direction, with the Earth. Ocean tides are noticed since antiquity. Is it a phenomenon like the overﬂow spill of water in cup? Do we have a similar eﬀect in the ocean? Vālmīki, in his famous epic Rāmāyan. a, connects high ocean tides to the full moon: “the roaring of the heaving ocean during the fullness of the Moon.”70 The Vis. n. u-Purān. a clearly suggests that the amount of water is not increased: “In all the oceans the water remains at all times in the same quantity, and never increases or diminishes; but like the water in a pot, which, expands with heating, so the water of the ocean expand and contract with the phase of the Moon.”71 The Matsya-Purān. a also gives a similar picture, “When the Moon rises in the East, the sea begins to swell. The sea becomes less when the Moon wanes. When the sea swells, it does so with its own waters, and when it subsides, its swelling is lost in its own water . . . the store of water remains the same. The sea rises and falls, according to the phases of the Moon.”72 This is an excellent analogy that indicates that there is an expansion in water during high tides in the ocean and the quantity of water in the ocean does not increase or decrease with a change in the phase of the Moon. Additionally, this also explains that the Hindus knew the thermal expansion of matter.73 Al-Bīrūnī claims that “the educated Hindus determine the daily phases of the tides by the rising and setting of the Moon, the monthly phases by the increase and waning of the Moon . . .”74 Johannes Kepler (1571–1630 CE) is generally credited with suggesting the correlation of ocean tides with the phases of the Moon. Kepler lived about ﬁve centuries after Al-Bīrūnī and more than at least a millennium after the Vis. n. u-Purān. a was written. Since the Moon and the Sun are so far away from the Earth, it was diﬃcult for scientists of that period to comprehend the theory of ocean tides. Newton’s action-at-a-distance later described its validity. 70Vālmīki’s Rāmāyan. a, 2: 6: 27. 71Vis. n. u-Purān. a, 2: 4. 72Matsya-Purān. a, 123: 30–34. 73The expansion of matter with an increase in temperature has been known to modern scientists only from the last 2–3 hundred years. 74Sachau, 1964, 2, p. 105. C H A P T E R 6 Chemistry 101 Chemistry, like medicine, evolved primarily as a science of rejuvenation among the ancient Hin- dus. Suśruta deﬁned chemistry (Rasāyana-tantra) as the science “for the prolongation of human life, and the invigoration of memory and the vital organs of man. It deals with the recipes that enable a man to retain his manhood or youthful vigor up to a good old age, and which generally serve to make the human system immune to disease and decay.”1 Soma—the elixir of life—was produced with a knowledge of chemistry, and is mentioned in the R. gveda and Atharvaveda.2 Soma is a tonic to rejuvenate a person and to slow down the aging process. The Atharvaveda suggests: “Invest this Soma for long life, invest him for great hearing power.”3 Rasāyana is the rejuvenation therapy in ayurveda which was practiced to prolong life. This therapy is used to replenish the rasa (soup or sauce) and other dhātus (element) in our physical body.4 Caraka explains the purpose of rasāyana: “Long life, excellent memory and intelligence, freedom from disease, a healthy glow, good complexion, a deep powerful voice, strong bodily and sensory powers, and beauty can be obtained from rasāyana.”5 Caraka and Suśruta deﬁne calcination, distillation, and sublimation processes in the chem- ical transformation or puriﬁcation of metals.6 Caraka mentions gold, copper, lead, tin, iron, zinc, and mercury used in drugs and prescribed various ointments made from copper sulphate, iron sulphate, and sulfur, for external application in various skin diseases.7 The oxides of copper, iron, lead, tin and zinc were also used for medicinal purposes. All these metals are native to the Indian Peninsula. Thin sheets of gold, silver, and iron were treated with salts and alkali in the prepara- tion of drugs by Caraka.8 The Chāndogya-Upanis. ad tells us of the alloys (reaction or joining) of gold with salt (borax), silver with gold, tin with silver, and copper with lead.9 Poisons and the drugs to counter poison were developed. The Mahābhārata, Rāmāyan. a, and Kaut.ilaya’s Arthaśāstra mention chemical weapons (astra) that were used in wars. For exam- ple, Kaut.ilaya provided a recipe of poison gas that was deadly: “The smoke caused by burning the powder of śatakardama, uchchidi ˙nga (crab), karavira (nerium odorum), kat. utumbi (a kind of 1Suśruta-Sa ˙mhitā, Sūtrasthanam, 1: 10. 2R. gveda, 10: 57: 3–4; R. gveda, 9: 62: 1; R. gveda, 9: 2: 1; R. gveda, 8: 2: 1; Atharvaveda, 19: 24: 3. 3Atharvaveda 29: 24: 3. 4Caraka-Sa ˙mhitā, Cikitsāstānam, 1: 5 5Caraka-Sa ˙mhitā, Cikitsāstānam, 1: 6–7. 6Biswas and Biswas, 1996 and 2001; Ray, 1948; and Bhagvat, 1933. 7Ray, 1956, p. 61–62. 8Ray, 1956, p. 62. 9Chāndogya-Upanis. ad, 4: 17: 7. 102 6. CHEMISTRY bitter gourd), and ﬁsh, together with chaﬀ of the grains of madana and kodrave (paspalam scro- biculatum), or with the chaﬀ of the seeds of hastikarn. a (castor oil tree) and palāśa (butea frondosa) destroys animal life as far as it is carried oﬀ by the wind.”10 Several deadly poisons were also concocted using complicated procedures: “The smoke caused by burning the powder made of the mixture of the dung and urine of pigeons, frogs, ﬂesh-eating animals, elephants, men, and boars, the chaﬀ and powder of barley mixed with kāsīsa (green sulphate of iron), rice, the seeds of cotton, kut. aja (nerium antidysentericum), and kośātaki (luﬀa pentandra), cow’s urine, the root of bhān. di (hydroeotyle asiatica), the powder of nimba (nimba meria) śigru (hyperanthera morunga), phan. irjaka (a kind of basil or tulsī plant), kshibapiluka (ripe coreya arborea), and bhā ˙nga (a common intoxicating drug), the skin of a snake and ﬁsh, and the powder of the nails and tusk of an elephant, all mixed with the chaﬀ of madana and kodrava (paspalam scrobiculatum) or with the chaﬀ of the seeds of hastikaran. a (castor oil tree) and palāśa (butea frondosa) causes instantaneous death wherever the smoke is carried oﬀ by the wind.”11 One can notice that the concoction is fairly complicated to produce and the ingredients are not so common. The dung of pigeons, frog, and skin or a snake are not common items in most chemical preparations. However, this is how most drugs/poisons were made during the ancient and medieval periods. The ancient Hindus used metal, minerals, gems and jewels to treat obstinate incurable diseases. Complex chemical transformations were performed before a concoction was prepared. Metals were converted into bhasms using oxidation or reduction processes. In some cases, these were transformed into biologically active nanoparticles.12 The concept of reducing particle size for improving the eﬀectiveness of a drug is as old as the Caraka-Sa ˙mhitā. In some cases, metals are heated at a high temperature and quenched with plant extracts. In this process, ﬂakes or metal turn into a ﬁne nano-size powder with new chemical structure and properties. To understand if the process was achieved or not, one criterion was that the bhasmas should be lusterless. Al- Bīrūnī provides the accounts of alchemical practices of the Hindus.13 “They [the Hindus] have a science similar to alchemy which is quite peculiar to them. They call it Rasāyana, a word composed with rasa, i.e., gold.14 It means an art which is restricted to certain operations, drugs, and compound medicines, most of which are taken from plants. Its principles restore the health of those who are ill beyond hope, and give back youth to fading old age, so that people become again what they were in the age near puberty; white hair becomes black again, the keenness of the senses is restored as well as the capacity for juvenile agility, and even for cohabitation, and the life of people in this world is even extended to a long period.”15 10Arthaśāstra, 411; Book 14, Chapter 1; Shamasastri, 1960. p. 442. 11Arthaśāstra, 411; Book 14, Chapter 1; Shamasastri, 1960. p. 442–443. 12Chaudhary and Singh, 2010; Sarkar and Chaudhary, 2010 13Sachau, vol. 1, p. 187–193. 14Al-Bīrūnī is mistaken in translating rasa as gold. Since gold is used in some recipes in Rasāyana, it may have caused him to make this mistake. 15Sachau, vol. 1, p. 188–189. 6.1. MINING AND METALLURGY 103 “In India the earliest allusions to alchemical ideas appear in the Atharva Veda (Athar- vaveda), where mention is made of the gold which is born from ﬁre,” writes C. J. Thompson, in his book The Lure and Romance of Alchemy.16 The R. gveda mentions surā as an intoxicating drink that was used along with soma. Today, surā is a term used in India for alcoholic drinks. The Arthaśāstra of Kaut.ilaya gives recipes for fermented alcoholic drinks made from rice (similar to Sake, a popular Japanese drink), sugarcane (similar to rum), grapes (similar to wine), and various spices. Suśruta wrote a complete chapter on the elixirs for rejuvenation of humans and suggested recipes for people to become immune to disease and decay.17 Cyavanaprāśa is a very popular tonic for rejuvenation in India. The name has stemmed from the name of Cayavana r. s. i (seers) who rejuvenated his body with the help of Aśvin Kumāras, two Vedic doctors. This is mentioned at several places in the R. gveda.18 People in northern In- dia take Cyavanaprāśa as a precautionary measure particularly in the winter season against the common cold and cold-related symptoms. The use of Cyavanaprāśa is fairly ancient as Caraka has referred to it for rejuvenation.19 Caraka provided several recipes for making iron tonics in his Caraka-Sa ˙mhitā. The process of making these elixirs is known as the killing of metal in Sanskrit, and the ﬁnal product is called bhasma. To accomplish the killing of iron, Caraka recommended the use of ﬁne thin plates of iron with āmlā (a fruit) extract and honey for one year in an underground pot; it reduces iron to a ferrous compound. Also, Caraka mentioned the conversion of yellow gold into a red colloidal form using plant extract, before being used as a tonic. Many of these reactions were done to make the metals nontoxic. Suśruta devoted one whole chapter on the use of alkalis (ks. āra) in various diseases and noticed its corroding, digestive, mucous destroying, and virile potency destroying properties.20 6.1 MINING AND METALLURGY The ancient Hindus excelled in mining and metallurgical processes. In Persia, due to the high quality of the so-called Damascus steel that was originally produced in Hind, steel was called “foulade Hind,” indicating the steel of India. Similarly, after the conquest of Poros, Alexander the Great received steel as the precious gift that the Greeks did not have. (Read Section 6.2.) Aristotle, in his book, On Marvelous Things Heard, writes that Indian-copper is known to be good and is indistinguishable from gold.21 This mention was made perhaps to acknowledge the high quality of the Indian bronze made from copper that was “indistinguishable from gold” due to the mixing of zinc and other metals or minerals. 16Thompson, 1932, p. 54. 17Suśruta-Sa ˙mhitā, Cikitsāstānam, 27: 1. 18R. gveda, 5: 74: 5 and 6; R. gveda, 7: 71: 5. 19Caraka-Sa ˙mhitā, Cikitsāstānam, 1: 74. 20Suśruta-Sa ˙mhitā, Sūtrasthānam, Chapter 11. 21Aristotle, On Marvelous Things Heard, 49, part of Aristotle’s Minor Work. 104 6. CHEMISTRY The smelting operation is deﬁned in R. gveda22 where ore was dumped into ﬁre and bellows were used to fan the ﬁre. A good example of its existence is the theory of creation, as shared in Chapter 4, provided in R. gveda, where the analogy of a smelting device was used to describe the creation of the universe. The Atharvaveda tells us that the chest of the earth contains gold, indi- cating gold mines and mining operation.23 Most ancient metals such as iron, copper, gold, silver and lead were naturally available in various parts of India.24 The remains of Mohenjo-daro and Harappa contain metallic sheets and pottery that are inscribed. Bronze, copper, iron, lead, gold, and silver were used to make axes, daggers, knives, spears, arrow heads, swords, drills, metal mir- rors, eating and cooking utensils, and storage utensils. The 10 centimeter high Mohenjo-daro’s dancing girl is made of copper with armful of bangles (Figure 6.1). Out of the 324 objects from these archaeological sites that have been analyzed, about 184 objects are of pure copper25 and four archaeological copper processing kilns are discovered at Harappa, Lothal, and Mohenjo- daro’s sites.26 The timber from an old mine in Hutti, Karnataka was collected at a depth of about 200 meters and was carbon dated. It was concluded that the mining process was carried out in this mine around 4th century BCE.27 Ktesias, a Greek traveler who lived in Persia during the 5th century BCE, mentions of the vast amount of gold mined from “high-towering moun- tains.”28 He also mentions a congealing processing to get quality gold.29 Several ancient Greek historians, such as Herodotus, Ktesias, Arrian, and Megasthenes, mentioned the use of metals in India.30 The chemical analysis of the brass artifacts from Taxila (third-fourth century BCE) reveal that 35–40 percent zinc content in these artifacts, giving a golden appearance to them. This was achieved by mixing zinc with copper. It is quite natural to assume that a metallurgical process was practiced to get pure zinc. Zinc is found as sphalerite, a sulphide of zinc. This ore is ﬁrst converted into an oxide in a combustion process. This is further converted into zinc in a reduction process which is quite cumbersome. However, the smelting technicians found an innovative procedure to get pure zinc. In contrast, such extraction methods were practiced in Europe only around the sixteenth century.31 Zinc was smelted in a downward distillation process where the zinc vapors were swiftly cooled down to avoid reduction process that happens at a slightly higher temperature. The main concern is that the zinc oxide needs a minimum temperature of 1150 degree Celsius for the 22R. gveda, 9: 112. 23Atharvaveda, 12:1:6. 24Agarwal, 2000; Biswas and Biswas, 1996. 25Lahiri, 1995. 26Agrawal, 2000, p. 40. 27Radhakrishna and Curtis, 1991, p. 23–24. 28McCrindle, 1973, p. 16, 17. 29McCrindle, 1973, p. 68. 30Bigwood, 1995. 31Subbarayappa, 2013 p. 299. 6.1. MINING AND METALLURGY 105 Figure 6.1: The dancing girl of Mohenjo-daro. (Taken from Wikimedia). reduction of oxide while the boiling point of zinc is 900 degree Celsius. Thus, it vaporizes and escapes. The excavated furnaces at Zawar, in Udaipur district, Rajasthan, have two chambers, top and bottom, separated by a thick perforated brick plate. The top chamber is sealed from the top, forcing vapor to go to the lower chamber which was ﬁlled with water. Water reduced 106 6. CHEMISTRY the temperature and solidiﬁed zinc. Even today, this area is known for mining operations and Hindustan Zinc Ltd. is still in operation there.32 The copper statue of Buddha in Sultanganj (Figure 6.2), Bihar, is over 2.3 m high, 1 m wide, and weighs over 500 kg. It was found in 1864 in the North Indian town of Sultanganj, Bhagalpur district, Bihar, by an East India Company engineer. Today, the statue is housed in Birmingham Museum and Art Gallery, Birmingham, England. The statue was made using a technique which is popularly known as ‘lost wax technique’. It is a method of metal casting in which a molten metal is poured into a mold, mostly of clay, that is created by means of a wax model ﬁrst. Once the soft clay solidiﬁes, the whole assembly is baked, melting the wax and extracted. This clay mold is then used for metal casting. The Painted Grey Ware of the Gangetic Valley were manufactured around 600 BCE.33 Two glass bangles found at Hastinapur, near New Delhi, are from the 1100–800 BCE period. The bangles are made from soda-lime-silicate glass with ornamental coloring from iron. Similar bangles of green color were also found elsewhere in northern India.34 Glass bangles are the ornamental jewelry that are worn by Hindu ladies even today. Beads of green glass with cuprous oxide coloring were found in Taxila belonging to the 700–600 BCE period.35 Kaut.ilya realized the importance of mining to the state economy. He suggested that “mines are the source of treasury; from treasury comes the power of government.”36 He described various metallic ores and mining operations along with the processes of distillation, reﬁnement, and quality control. Kaut.ilya even deﬁned the duties of the Director of mining: “must possess the knowledge of the science dealing with copper and other minerals (sulbadhātu-śāstra), expe- rienced in the art of distillation and condensation of mercury (rasapāka) and of testing gems, aided by experts in mineralogy and equipped with mining laborers and necessary instruments, the Director of mines shall examine mines which, on account of their containing mineral excre- ment, crucibles, charcoal, and ashes, may appear to have been once exploited or which may be newly discovered on plains or mountain slopes possessing mineral ores, the richness of which can be ascertained by weight, depth of color, piercing smell, and taste.”37 Kaut.ilaya provided clues for ﬁnding good locations for mining: observe soil, stones, or water that appears to be mixed with metal and the color is bright or if the object is heavy or with strong smell, this indicates the possibility of a mine nearby.38 He provides techniques to locate glass, gold, silver, iron, and copper mines.39 Mining operations were leased to private investors at a ﬁxed rate.40 According to him, the head of mining operations must know metal- 32Subbarayappa, 2013, p. 300; Srinivasan, 2016. 33Dikshit, 1969, p. 3. 34Dikshit, 1969, p. 3. 35Dikshit, 1969, p. 4. 36Arthaśāstra, 85; Book 2, Chapter 12; Shamasastri, 1960. p. 89. 37Arthaśāstra, 82; Book 2, Chapter 12; Shamasastri, 1960. p. 83. 38Arthaśāstra, 82; Book 2, Chapter 12; Shamasastri, 1960. p. 84. 39Arthaśāstra, 82; Book 2, Chapter 12; Shamasastri, 1960. p. 84. 40Arthaśāstra, 83; Book 2, Chapter 12; Shamasastri, 1960. p. 86. 6.1. MINING AND METALLURGY 107 Figure 6.2: Statue of Buddha from Sultanganj. (Taken from Wikimedia.) lurgy, chemistry, and the reﬁnery processes.41 This tells us that metallurgy was an established discipline during the third century BCE in India. Kaut.ilaya deﬁned the ethical rules of conduct for goldsmiths. Severe penalties were prescribed for goldsmiths who fraudulently adulterated gold. Any mixing of inexpensive impurities of tin, copper, and brass during the melting process of gold and silver was considered a crime and the criminals were prosecuted. Thieves of mineral products were punished with a ﬁnancial penalty that was eight times the value of the stolen products.42 41Arthaśāstra, 81; Book 2, Chapter 12; Shamasastri, 1960. p. 83. 42Arthaśāstra, 83; Book 2, Chapter 12; Shamasastri, 1960. p. 86. 108 6. CHEMISTRY Kaut.ilaya described gold, silver, arsenic, copper, lead, tin, and iron ores and their pu- riﬁcation processes.43 Coins, as currency, were used in business transactions during his period. Compositions of diﬀerent coins are deﬁned in Kaut.ilaya’s book,44 and rules of punishment are deﬁned for people making counterfeit coins.45 Kaut.ilaya also explained the methods to catch manufacturers of counterfeit coins46 and deﬁned a penalty for the coin-examiner to accept a counterfeit coin into the treasury.47 Sixteen gold standards based on the percentage of gold content in a specimen, that is similar to the current “carat” system, were deﬁned by Kaut.ilaya. Copper was mixed with gold to form an alloy of diﬀerent carat standards.48 Several gold alloys were deﬁned by Kaut.ilaya that were blue, red, white, yellow, and parrot (green) in colors. This was achieved by the processing of gold with rock salt, lead, copper, silver, mercury, etc. The processes of chemical reactions were well-deﬁned with exact proportions of each element or compound.49 Gold-plating and other metal-plating procedures are deﬁned using amalgams, heating processes, rock salt, mica, wax, etc.50 Kaut.ilaya also deﬁned color, weight, characteristics, hammering, cutting, scratching, and rubbing as tools to test precious stones.51 6.1.1 THE IRON PILLAR OF NEW DELHI The Iron Pillar near Qutab-Minar in New Delhi is a testimonial to the metal forging skills of the ancient Hindus (Figure 6.3). The pillar marks the renunciation of kingly duties and the beginning of aesthetic life for King Candra. We know of this from the inscription on the pillar. The inscription is dated between 400–450 CE and the inscribed letters have minimal corrosion despite 1600 years of weathering in the open air.52 Air, heat, and heavy rains of Northern India have not caused signiﬁcant rusting of the pillar, even with high heat and humid weather from July to September. The pillar is indisputably a long standing permanent record of the excellent metallurgical skills and the engineering skills of the ancient Hindus. King Candra is most likely the famous King Candragupta Vikramāditya II (375–413 CE) and the current site of the pillar was chosen by Tomar King Ana ˙ngpāla who erected it on the site of a temple. In 1739 CE, Nadir Shah occupied the city and decided to break the pillar using cannons and failed. Several spots where the cannon balls hit the pillar are still marked.53 43Arthaśāstra, 93; Book 2, Chapter 14; Shamasastri, 1960. p. 98. 44Arthaśāstra, 84; Book 2, Chapter 2; Shamasastri, 1960. p. 86–87. 45Arthaśāstra, 59; Book 2, Chapter 5; Shamasastri, 1960. p. 57, 58. 46Arthaśāstra, 212; Boook 4, Chapter 4; Shamasastri, 1960. p. 239. 47Arthaśāstra, 203; Book 4, Chapter 1; Shamasastri, 1960. p. 230. 48Arthaśāstra, 86; Book 2, Chapter 13; Shamasastri, 1960. p. 90. 49Arthaśāstra, 88; Book 2, Chapter 13; Shamasastri, 1960. p. 92. 50Arthaśāstra, 92; Book 2, Chapter 14; Shamasastri, 1960. p. 97. 51Arthaśāstra, 92; Book 2, Chapter 14; Shamasastri, 1960. p. 97. 52Balasubramaniam, 2001. 53Balasubramaniam, 2001; Balasubramaniam, Prabhakar and Shanker, 2009. 6.1. MINING AND METALLURGY 109 Figure 6.3: The Iron Pillar of New Delhi. (Taken from Wikimedia.) The pillar is about 7.16 m long (23 feet, 6 inches) with a 42.4 cm (16.4 inches) diameter near the bottom and about 30.1 cm (11.8 inches) at the top. It weighs over six tons. The pillar is a solid body with a mechanical yield strength of 23.5 tons per square inch and ultimate tensile strength of 23.9 tons per square inch. It is made of wrought iron. There is no other pillar from the early medieval period of that size anywhere else in the world.54 The composition of the wrought iron is as follows:55 carbon 0.15%, silicon 0.05%, sulfur 0.005%, manganese 0.05%, copper 0.03%, nickel 0.05%, nitrogen 0.02%, phosphorous 0.25%, and 99.4% pure iron. Iron of such purity is not naturally available in Indian mines. This composition is a strong indication of an iron reﬁning process in the making of this pillar. The pillar has a coating of a thin protective layer of Fe3O4 using salts and quenching. The excavation of the buried portion revealed that the base of the pillar was covered by a sheet of lead, about 3 mm in thickness. This absence of rusting in not unique to the Iron Pillar. The iron beams of the Sun Temple in coastal 54Lal, B. B., On the Metallurgy of the Meharauli Iron Pillar, in the book by Joshi and Gupta, 1989, p. 25 and 26; Balasubramaniam, 2001. 55Biswas and Biswas, 1996, vol. 1, p. 394. 110 6. CHEMISTRY Orissa and the Iron Pillar of Dhar (Madya Pradesh), both in relative higher humidity regions, do not show much rusting either. This is perhaps due to a higher phosphorus content of the iron. The Sun Temple of Kon. ārka, a ninth century construction, in Orissa has 29 iron beams of various dimensions used in its construction. The largest beam is 10.5 meter (35 feet) in length and about 17 cm (about 7 inches) in width with a square cross-section and is about 2669 kg (6000 lbs.) in weight.56 Iron nails are used to connect stone pieces. The composition of the iron beams and nails is similar to those of the famed Iron Pillar of Delhi. Similarly, the iron pillar of Dhar is about thousand years old and has little or no rusting.57 The pillar is 7.3 tons in mass and 42 feet long. Dhar is an old capital of Malwa which is about 60 km from the well known city of Indore. The pillar was possibly constructed by King Bhoja (1010–1053 CE) and currently lies in three parts in front of Lāt. mosque in Dhar. King Bhoja was well versed in metallurgy and wrote a book on metallurgical processes and metal weapons, called Yuktikalpataru. Bahadur Shah, a Muslim king, captured the region and decided to move the erected pillar to Gujrat. In the process of digging ground to take out the pillar, it fell down and was broken into pieces, as we know from the memoirs of Emperor Jahāngir. The pillar has been weathering the monsoons of India for over a thousand years and has little rusting. The surface of the pillar is coated with a thin optically dull layer and on top of it is another thick layer of optically bright material. Professor R. Balasubramaniam of the Indian Institute of Technology, Kanpur, India has compiled a nice summary of the history of the pillar and its chemical constitution.58 Recent researches have ﬁgured out the process on why the pillars do not rust. The main reason is the mixing of phosphorus with iron. Once the surface of iron is rusted, it becomes porous and allows phosphorus to react with other chemical compounds which reduces to phos- phoric acid. This acid interacts with iron to form dihydrogen phosphate. The chemical reactions are as follows:59 2H3PO4 Fe C ! Fe.H2PO4/2 ! This further dissociates into two forms: C 2H3PO4 FeO Fe.H2PO4/2 H2 H2O C C 3Fe.H2PO4/2 Fe3.PO4/2 4H3PO4 C ! Fe.H2PO4/2 FeHPO4 H3PO4 C ! Both of these phosphates are amorphous and insoluble in water. These amorphous phos- phates reorganize themselves into crystalline ferric phosphate, and drastically reduces the poros- 56Ray, 1956, p. 212. 57Balasubramaniam and Kumar, 2003. 58Balasubramaniam, 2002. 59Balasubramaniam, 2001. ity of the surface. This large reduction in porosity reduces any further rusting of the iron.60 Thus, it is the phosphorus content of the pillar that does the trick, making the pillar to be rust free. Can we use the same technology in making car bodies which are prone to rusting in cold regions where salt is used on roads? 6.2. WOOTZ OR DAMASCUS STEEL 111 6.2 WOOTZ OR DAMASCUS STEEL The word steel comes from the Old High German (German language, around 11th century CE) word stahal which is related to the Sanskrit word stakati, meaning “it resists”61 or “strike against.” Sword-making was a popular use of this steel due to its hardness. Steel is an alloy of iron containing 0.10 to 1.5% carbon in the form of cementite (Fe3C).62 The properties of steel vary greatly with a minor change in carbon content, along with other elements. Metals such as manganese, silicon, chromium, molybdenum, vanadium, or nickel are purposely mixed in the process depending on the desired outcome. For example, stainless steel has approximately 12% or more chromium content. Steel was prepared and used in India for various purposes from the ancient period.63 Ktesias, who was at the court of Persia during the 5th century BCE, mentioned the two high quality Indian steel swords that were presented to him. One sword was presented by the King of Persia and the other by King’s mother, Parysatis.64 Nearchus (ﬂ. 360–300 BCE), an oﬃcer in the army of Alexander the Great, mentions that the Indians generally carried a broad three cubit long sword with them.65 King Poros, a king from Punjab, lost a major battle with Alexander the Great and was imprisoned. He was brought to the court and Alexander asked him how he should be treated now. Poros replied: like a king. This surprised Alexander and the ensuing conversation between them made him realize the futility of wars. Alexander decided to release Poros and gave his kingdom back to him. This was a highly unusual move from Alexander. Usually defeated kings wer slaughtered or imprisoned. Poros was grateful to receive a gift of life and wanted to show his gratitude to Alexander the Great. Porus wanted to gift something that was precious and Alexander did not have—more precious than gold, gems, or spices. He opted to give 100 talents (6000 pounds)66 of steel as a precious gift to Alexander, as we know from the accounts of Quintus Curtius (9: 8: 1), a Roman historian during the ﬁrst century CE who wrote a biography of Alexander the Great. Steel was called ferrum candidum, meaning white iron, by Curtius.67 60Balasubramaniam, 2001. 61Le Coze, 2003. 62Bhardwaj, 1979, p. 159. 63Prakash and Igaki, 1984. 64Fragments, 1: 4; McCrindle, 1973, p. 9. 65Bigwood, 1995. 66Casson, 1989, p. 114. 67Casson, 1989, p. 114. 112 6. CHEMISTRY The Periplus Maris Erythraei text, written around 40–70 CE,68 provides information on the importation of steel to the Roman empire. It was subjected to a custom duty under Marcus Aurelius (121–180 CE) and his son Commodus (161–192 CE).69 During the period of Empe- rior Justinian (482–565 CE) of Rome, the Digest of the Roman Law, (39, 15, 5–7) was compiled to run the state. Indian iron (Ferrum Indicum) is in the list of objects that were subject to im- port duty.70 Similarly, iron was taxed and traded in Alexandria, Egypt in the early ﬁrst century CE and was called koos. Steel is called wuz in the Gujrati language, and Wooku (or ukku) in the Kannada language, a prominent language in South India.71 Perhaps this explains the origin of wootz, the Syrian word for steel. This word was new to the Syriac literature and appeared late in chronology. The Arabs called steel Hundwáníy, meaning Indian.72 This word perhaps evolved into andanic or ondanique for swords and mirrors, used by the medieval writers. This also led to the words alhinde [or al-Hind, meaning India] and alinde [for steel mirror] in Spain.73 The best steel in Persia was called foulade Hind, meaning steel of India. Another kind of steel, jawābae Hind, meaning a Hindu answer, was also popular because it could cut a steel sword.74 Steel was called wootz in India and was traded in the form of castings (cakes) of the size of ice-hockey pucks.75 Persians made swords from wootz and these swords were later erro- neously known as Damascus swords.76 As is the case with the Arabic numerals, the Europeans learned about steel-making in the Middle East during the War of the Crusades in 1192 CE.77 By noticing the remarkable hardness and strength, they became interested in knowing the secrets of making ultra-high carbon steel. The European did not know at that time that the manufacturing process had originated in India. Archaeological sites in the Periyar district of Tamil Nadu, which date back to about 250 BCE, provide indications of crucibles used to mix iron and carbon for the steel-making pro- cess.78 Varāhmihir, during the sixth century CE, wrote a chapter on swords (khad. galaks. anam) in his Br. hat-Sa ˙mhitā (50: 23–26), and provided a recipe for the hardening of steel. His processes used chemical techniques as well as heating and quenching. Swords treated with these processes did not “break on stones” or become “blunt on other instruments,” as reported by Varāhmihir.79 Steel production was very much limited due to the high consumption of fuel and the required high temperature for melting. The situation prevailed until 1850 CE, when high tem- 68Casson, 1989, p. 7. 69Casson, 1989, p. 114. 70Schoﬀ, 1915. 71Agarwal, 2000, p. 198; Biswas and Biswas, 1996, vol.1, p. 121, Le Coze, 2003. 72Schoﬀ, 1915. 73Schoﬀ, 1915. 74Royle, 1837, p. 47. 75Sherby and Wadsworth, 2001 76Sherby and Wadsworth, 2001 77Joshi, Narayan, R., Tough Steel of Ancient India, p. 293, in the book by Sharma and Ghose, 1998. 78Agarwal, 2000, 197; Prakash and Igaki, 1984. 79Biswas and Biswas, 1996, vol. 1, p. 276. 6.3. FERMENTATION 113 perature furnace technology improved. Thus, the use of steel was largely for making blades for knives, daggers, and swords. With proper processing, these steels can be made to a strength that is about ﬁve times greater than that of the strongest wrought iron.80 Damascus steel has an attractive swirling surface pattern that is an outcome of the cooling process. The patterns result from the alignment of the Fe3C particles that form on the surface during the cooling process.81 Thus, Damascus swords became famous for their hardness and could absorb blows in combat without breaking. It did not fail a Middle Age warrior during combat. Making wootz steel is complex process as even minute impurities change the outcome. Temperature and the cooling period also aﬀect the quality of steel. Giambatlista della Porta (1535–1615), an Italian scholar from Naple, in 1589 CE wrote on the importance of temper- ature in treating wootz, and suggested to avoid “too much heat.”82 Oleg D. Sherby and Jeﬀrey Wadsworth, two researchers from Stanford University, ﬁgured out that a slow equilibrium cool- ing is the best way to produce quality steel. When iron and carbon (1.3–1.9%) are heated to 1200(cid:14)C, they reach a molten state and the slow cooling allows the carbon to diﬀuse through the iron to form white cementite patterns that result from alignment of the Fe3C (cementite) parti- cles. With polishing, the Fe3C particles appear white in the near black steel matrix. The carbide particles serve the role of strengthening without making the metal brittle.83 The blade was hard- ened by heating it to 727(cid:14)C which allows a change in the crystal structure. Iron molecules that were distributed as body-centered ferrite begin to form a face-centered lattice. The blade was then quenched in water.84 If the heating was done above 800(cid:14)C before quenching, it made the metal brittle. Michael Faraday (1791–1867), a fellow of the Royal Society and discoverer of many elec- tromagnetic discoveries, tried to duplicate Damascus steel and incorrectly concluded that alu- minum oxide and silica additions contributed to the properties of the steel. Faraday and Stodart also attempted to make steel by alloying nickel and noble metals like platinum and silver. All their eﬀorts were of no avail. Thus, the steel-making technology of ancient India alluded even great European scientists till the nineteenth-century.85. 6.3 FERMENTATION The R. gveda mentions fermentation of barley, a key ingredient in beer: “A mixture of a thick juice of soma with barley powder.”86 In another place, there is a mention of fermented alcoholic drink which took about 15 days of processing. “Fifteenth day old highly intoxicating soma,”87 which 80Sherby and Woodworth, 2001 81For more information, please read, Sache, 1994; Figiel, 1991. 82Smith, 1982. 83Sherby and Wadsworth, 1985. 84Sherby and Wadsworth, 1985. 85Faraday, 1819; Stodart and Faraday, 1822; Day, 1995 86R. gveda IX: 68: 4. 87R. gveda X: 27: 2. 114 6. CHEMISTRY probably refers to the broth fermented in the vat for 15 days. The Yajurveda-Śukla tells us about various kinds of alcoholic drinks:88 “Âtithya’s sign is Mâsara, the Gharm’s symbol Nagnahu. Three nights with Surâ poured, this is the symbol of the Upasads. Emblem of purchased Soma is Parisrut, foaming drink eﬀused.” Elsewhere in the same book, the fermentation process is mentioned. “Like shuttle through the loom the steady ferment mixes the red juice with the foaming spirit.”89 Here Nagnahu is root of a plant that is used as yeast, Parisrut is a kind of beer, and Surâ is another word for liquor. The Chāndogya-Upanis. ad tells us that drinking liquor on a regular basis is as bad as stealing gold, killing a Brahmin, or having an aﬀair with your teacher’s wife.90 Elsewhere, ﬁve extremely wealthy and immensely learned householders decided to examine the following two questions: What is our self (ātman)? What is brahman? They decided to visit Aśvapati Kaikeya, a highly learned scholar, to teach them about these two questions. Aśvapati Kaikeya tells his visitors that “no one drinks” in his kingdom, indicating the presence of alcoholic beverages.91 Caraka mentions some 84 diﬀerent kinds of alcoholic liquors.92 For the fermentation, Caraka mentions the following sources of sugar: sugarcane juice, gud. a (jaggery), molasses, honey, coconut water, sweet palmyra sap and mahua ﬂowers. Some sweet fruits such as grape, date, mango, banana, apricot, jackfruit, rose-apple, jāmun, pomegranate, kādamba, bilva, etc. are also used in the fermentation. Similarly, rice and barley were used from the grain category for fermentation. By the time of Kaut.ilaya, the superintendent of liquor was designated to su- pervise this industry. The manufacturing of liquor and controlled liquor traﬃc in and out of village boundaries were monitored.93 Liquor shops were required to have beds and seats and the rooms were ﬁlled with the scents of ﬂowers. Some recipes for liquor making are also provided: “Medaka is manufactured with one dron. a (measure of capacity, volume) of water, half an ād. haka (unit of mass) of rice, and three prasthas (mass) of kin. va (ferment).”94 Some ferments were used for medicinal purposes. Kaut.ilaya suggested that patients should learn the preparation of these aris. t. a (fermented and distilled liquor and medicine) from physi- cians. He has even provided several recipes: “one hundred pala of kapittha (Feronia Elephantum), 500 pala (mass) of sugar, and one prastha (mass) of honey form āsava.”95 Some hard liquors with rice and lentils were also suggested: “one dron. a of either boiled or unboiled paste of māsa (Phrase- olus Radiatus), three parts more of rice, and one kars.a of morata (Alangium salviifolium) and the like form kin. va (ferment).”96 Additives were mixed in order to improve the taste or appearance 88Yajurveda-Śukla, 19: 13–15. 89Yajurveda-Śukla, 19: 83. 90“A man who steals gold, drinks liquor, and kill a Brahmin; A man who fornicates with his teacher’s wife—these four will fall.” Chāndogya-Upanis. ad, 5: 10: 9. 91Chāndogya-Upanis. ad, 5: 11: 5. 92Achaya, 1991. 93Arthaśāstra, 119; Shamasastri, 1960. p. 131. 94Arthaśāstra, 120; Book 3, Chapter 25; Shamasastri, 1960. p. 133. 95Arthaśāstra, 120; Book 2, Chapter 25; Shamasastri, 1960. p. 132. 96Arthaśāstra, 120; Shamasastri, 1960. p. 133. of liquors. These additives were used sweeteners, spices, and astringents.97 The variety listed in Caraka-Sa ˙mhitā and Arthaśāstra is comparable or even better than the variety that is present in the market today. 6.3. FERMENTATION 115 97For more information, read Achaya, 1991; Prakash, 1961; and Singh et al., 2010. C H A P T E R 7 Biology 117 In the Caraka-Sa ˙mhitā, an early Hindu treatise on medicine, biology was considered the most important of all sciences. “The science relating to life is regarded by the philosophers as the most meritorious of all the sciences because it teaches mankind what constitutes their good in both the worlds [spiritual and physical].”1 Good health helps people to fulﬁll their four purposes in life: dharma (duty), artha (prosperity), kāma (sensuality), and moks. a (liberation).2 The ancient Hindus systematically studied various life forms and noticed inter- dependencies and commonness in them. It was due to these commonnesses between plants and animals that led Suśruta to suggest that new medical practitioners should dissect plants ﬁrst before they performed any dissection on animals or humans. About 739 plants and over 250 animals are mentioned in the ancient literature of the Hindus.3 The 24th chapter of Yajurveda has a large variety of birds, animals, and snakes mentioned. Plants and animals are characterized with respect to their utility, habitat, or some other special features: Four-footed, reptiles, claws, born from an embryonic sac, born from an egg, born from sprouts (plants), or domesticated.4 The botanical world was divided into grasses, creepers, shrubs, herbs, and trees.5 The R. gveda mentions the heart, lung, stomach, and kidneys. The Atharvaveda6 refers to the heart as a “lotus with nine gates,” a correct description of heart when held with its apex upwards. From this top view, one can observe nine openings in the heart: three in right atrium, four in the left atrium, and one in each of the right and left ventricles.7 Similarly, perhaps there is a mention of blood circulation in the Atharvaveda:8 “Who stored in him ﬂoods moving in all diverse directions and formed to ﬂow in rivers pink, rosy red, and coppery dark running in all ways in a man, upward and downward.” 1Caraka-Sa ˙mhitā, Sūtrasthānam, 1: 43. 2Caraka-Sa ˙mhitā, Sūtrasthānam, 1: 15. 3Kapil, 1970. 4Smith, 1991. 5Kapil, 1970; Smith, 1991. 6Atharvaveda, 10: 8: 43. 7Narayana, 1995; Rajgopal et al., 2002. 8Atharvaveda, 10: 2: 11. 118 7. BIOLOGY 7.1 SACRED RIVERS AND MOUNTAINS: ECOLOGICAL PERSPECTIVES Ecology (paryāvaran. a) primarily deals with the relationships of organisms with their environ- ment. The Hindus strongly believe in the mighty Earth as a living system that has several billion years of experience in developing processes that are sustainable and cyclic. It is the respect for the ecosystem that led the ancient Hindus to promote vegetarianism. Trees, mountains, rivers, and animals were worshiped by the ancient Hindus. Cutting trees, dumping waste products in a river, and killing animals are considered as sins. It is a common phrase in India that the God lives in every particle of the universe. (kan. a kan. a mei Bhagwān hai). The Bhagavad-Gītā9 sug- gests the omnipresence of God. Therefore, in the worldview of the Hindus, the ecology should be preserved and respected. The Manu-Smr. ti tells us that that all plants and animals have spe- ciﬁc functions and we must protect them: “Brahma, the God of Creation, has created all the plants and animals with speciﬁc characteristics and functions, and none should disturb these creatures.”10 The ancient Hindus considered nature (prakr. ti) as a living sacred entity. Nature is not a property that is owned by the humans for their use; on the contrary, humans are a part of nature. Nature is represented by its ﬁve forces: ākāśa (space or sky), vāyu (air), teja (ﬁre), ap (water) and pr. thivī (earth)—popularly known as pañcā-bhūta (ﬁve elements). All animate and inanimate objects in nature are made up of these ﬁve elements, including humans and animals. The ancient Hindus realized that they could neither control nature nor overpower its order; they just tried to live with it in a manner that was based on respect and appreciation for the natural forces and order. Rivers, mountains, and oceans were treated with reverence. It was not ethical to dump waste into a river or deplete a mountain of its trees. The ecosystem connects living beings with inanimate objects. For example, a little misuse of water, an inanimate object, has dire consequences to life forms that drink it. The geographical region of the Indus Valley and the surrounding area was considered sacred by the ancient Hindus. It was only natural for them to preserve the ecology of the region. The Earth is worshiped as mother; it is considered to be a devī (Goddess) and has numerous names: Bhūmi, Pr. thivī, Vasudha, and Vasundharā. Even today, India is personiﬁed as Bhārat- mātā (Mother India). The Earth is considered as mother and the inhabitants as her children, as suggested in the Atharvaveda,11, and supports people of all races and remains fertile, arable and nourisher of all.12 This chapter of the Atharvaveda does not discriminate between “us” and “them;” it includes everyone. Another verse in the same book suggests that the Earth caters to 9Bhagavad-Gītā, 7: 19; 13:13. 10Manu-Smr. ti, 1: 28: 39–35. 11Atharvaveda, 12: 1: 12. 12Atharvaveda, 12: 1: 11 7.2. SACRED TULSĪ AND SACRED COW 119 people of diﬀerent religions and languages.13. A request is made for Mother Earth to provide medicines, medicinal plants and prosperity,14 and prestige.15 Every day, hundreds of thousands of people visit Ganges [Ga ˙ngā] or Yamunā rivers and worship them. These rivers are considered to be puriﬁers of sins, and bathing in the sacred wa- ters is a popular activity which is also associated with a prayer. In the evenings, group āratī (prayer) is performed where people worship God by worshiping the river. As David Gosling, a nuclear physicist who has studied South Asian ecology, suggests that the Hindu traditions serve as an important model in “raising social and environmental awareness, underscoring the con- tinuities between past and present and their possible transformations within an environmental paradigm.”16 7.2 SACRED TULSĪ AND SACRED COW Trees and plants are highly eﬃcient chemical and pharmaceutical factories. Human survival is dependent on the quality of the foods provided by trees and plants. It is only natural to respect plant life and worship them. The respect that the Hindus bestow on plants can be observed by noticing stone deities placed under many trees with ﬂags and steamers adorning the branches. The mythological kalpavr. ks. a, a tree that fulﬁlls all human desires, is well known in Hindu tradi- tion. In their popular belief, each tree has a vr. ks. a-devatā, or tree-deity, who is worshiped by the Hindus with prayers and oﬀerings of water, ﬂower, sweets, and encircled by sacred thread. The sacred thread symbolizes the wishes of the praying person. For example, in the Mahābhārata, Sukra says: “Rubbed with the astringent powder of the hanging roots of the Banyan tree (Ficus bengalensis) and anointed with the oil of priyango (panicum italicum), one should eat the shashlika paddy mixed with milk, By so doing one gets cleansed of all sins.”17 The Padma-Purān. a advo- cated that planting trees was a simple way to reach nirvān. a (liberation), to escape the cycle of birth and death.18 Since the Hindus realized the common connection between plants, animals and humans, and the importance of trees for human life, it became a religious code to preserve plant life. Aśoka (reigned 272–232 BCE) issued a decree against the burning of forests.19 It was a hunting practice during the period to set ﬁre to grass and trees. As the animals got scared by the ﬁre and ran away to protect themselves, they were trapped and killed by the hunters. Thus, Aśoka’s decree simultaneously took care of plants as well as animals. Tulsī (ocimum sanctum) is perhaps the most sacred plant in Hindu households. It is like a small shrub from 30–60 cm in height. Tulsī is worshiped by the Hindus as goddess, just like 13Atharvaveda, 12: 1: 45 14Atharvaveda, 12: 1: 17 and 27 15Atharvaveda, 12: 1: 63 16Gosling, 2001, taken from Van Horn, 2006. 17Mahābhārata, Anuśāsana Parva, 10. 18Padma-Purān. a, Srs. t. i-Kān. d. a, Chapter 28: 19–22. 19Smith, 1964, p. 187. 120 7. BIOLOGY Laks.mī, Sītā, or Rādhā. It is common for the Hindus to worship a tulsī plant in the morning and feed it water while facing the Sun. When the Hindus die, people put Tulsī leaves, mixed with Ganges (Ga ˙ngā) water, in the mouth of the dead body for puriﬁcation. In most pujas (Hindu prayer), a nectar made from milk, honey, curd, and tulsī, called pancāmrt (meaning, nectar made from ﬁve substances), is given to all participants. In a Hindu wedding, the groom, his family members, and family friends generally go to bride’s house in a procession. In the midst of this joyous occasion, they ﬁrst go to a pipal or banyan tree and pray. Similarly, the bride and groom visit a tree as a couple and pray before they enter in their house after marriage. The sacred areas of most Hindu temples are surrounded by trees. The Hindus enforce sanctity for plants and animals by associating them with gods and goddesses. Swans are associated with Sarasvatī, mice with Lord Ganesha, snakes and bulls with Lord Śiva, lions with the Goddess Durgā, Lord Kr.s.n. a with snakes and cows, and monkeys with Lord Rāma. Cows are worshiped, so are snakes, and many other life-forms. The following is a list of some trees and their corresponding deities: Goddess Laks.mī in tulsī (Ocinlum sanctum), Goddess Śītalā in neem, God Vis.n. u in pīpal (Ficus religiosa), and Lord Śiva in Vata (Ficus in- dica).20 Similarly, in other interpretations, tulasī is beloved of Lord Kr.s.n. a; pīpal is inhabited by Brahmā, God Vis.n. u, and Lord Śiva; aśoka (Saraca indica) is dedicated to God Kāma; palāś, a tree, to the Moon; bakula (Mimusops elangi) to Lord Kr.s.n. a; and rudrāks. a (Eleaecarpus ganitrus) to Lord Śiva. “The Hindu spiritual heritage can provide new ways of valuing, thinking, and act- ing that are needed if respect for the nature is to be achieved and future ecological disasters are to be averted.”21 Feeding weak and old animals is considered a charitable act. Like the household dogs and cats in the Western world, all animals were bestowed a proper treatment by the Hindus.22 When Hindus eat food, they separate some food from their plate for birds, dogs, and cows. The ﬁrst chapāti usually goes to a cow and the last one to a dog in many Hindu households.23 The sanctity of cows in Hinduism is well known and much publicized in the West. In legends and popular stories, the Earth is said to assume the form of a cow, especially in times of distress, to implore the help of the gods. The sacredness of the cow represents an anomaly to social scientists who wonder why in a country with hungry population the cow is virtually untouched.24 The Mahābhārata tells us that the killing of a cow is wrong and has its bad conse- quences and causes a person to go to hell.25 The relationship between the cow and man is not competitive, but symbiotic. The cow augments the needs of human beings by providing them 20Dwivedi, 1997. 21Dwivedi, 1997 22Narayanan, 2001. 23Most Hindu families do not keep dogs as pets. Usually, each street has a few stray dogs that are patronized by the families living on that street. These dogs recognize people who live there and protect the street from strangers at night. Mahatama Gandhi used to say that the kindness of a culture can be judged by the way they treat animals. 24Weizman, 1974. 25 “All that kill, eat, and permit the slaughter of cows rot in hell for as many years as there are hairs on the body of the cow so slain.” (Mahābhārata, 13: 74: 4.) 7.2. SACRED TULSĪ AND SACRED COW 121 milk, bullocks, dung, and hides. Judging the value of Indian cattle by the western standards is inappropriate.26 Due to inherent diﬀerences in the value systems, such an evaluation generally leads to confusion or misleading conclusions. Kaut.ilaya’s Arthaśāstra instructed the director of forests, superintendent of cattles, horses, and elephants to prevent cruelty to animals and protection of wildlife. Punishments were in- ﬂicted on those who violated these rules. For example, killing an elephant was punished with death.27. Similarly, killing or injuring animals in reserve parks and sanctuary, especially those that were protected species, were punished:28 “Elephants, horses, or animals having the form of a man, bull or an ass living in oceans, as well as ﬁsh in tanks, lakes, channels and rivers; and such game birds . . . shall be protected from all kinds of molestation. Those who violate the above rule shall be punished ﬁrst with amercement. Animals useful for riding, milk, hair, or to stud were protected and hurting these animals was a crime.29 Because the earth is a closed system, we need processes that will sustain us in the long run. We need to ﬁnd eﬀective methods to deal with the population growth. We also must develop new technologies for food production, new family planning practices, and we must change our dietary choices. Christian J. Peters, a scientist from Tufts University, Boston, along with a team of several researchers from other universities, studies the environmental impact and food security of various diets. The purpose of this study is to compare the per capita land requirements and potential carrying capacity of the land base of the continental United States (U.S.) under a diverse set of dietary scenarios. This team considered ten diet scenarios using a biophysical simulation model. Eight of the diets complied with the 2010 Dietary Guidelines for Americans. Meat-eating diets turned out to be not good. The highest capacity turned out to be with lacto-vegetarian diet, even better than vegan diet.30 This is basically the diet of most Hindus. The ancient Hindus, in their analysis, observed a balance in prakr. ti (primal nature); every species plays an important role in the balance. This balance of prakr. ti was based on the knowl- edge gained through empiricism, intuition, and experimentation. Once a common connection between plants, animals, and humans was established, the coexistence of all living forms fol- lowed. Hanumāna, and Gan. apati (Gan. eśa), as well as trees, are revered widely by the Hindus.31 7.2.1 VEGETARIANISM Livestock production accounts for 70% of all agricultural land use and 30% of the land surface of the planet, excluding the polar ice-caps. The livestock business contributes about 4.6 to 7.1 26Harris, The Myth of the Sacred Cow, in Leeds and Vayda, 1965. 27Arthaśāstra 2: 2: 9; Shamasastry 50, p. 49. 28Arthaśāstra, 2: 26: 1; Shamasastry, 112, p. 135. 29Arthaśāstra,4: 13: 21; Shamasastry, 235, p. 263. 30Peters et al., 2016 31Mythological stories are associated with these gods. It may be demeaning to some that the Hindus gods have some animal attributes. However, most Hindus do not even think about that. Crowds in temples all over the India on Tuesday testify their reverence to Lord Hanumāna. Similarly, it is common for people to worship Lord Gan. eśa ﬁrst on any auspicious occasion. For more information, see Nelson, Lance [Editor], 1998; and Chapple and Tucker [Editors], 2000; Roy, 2005. 122 7. BIOLOGY billion tons of greenhouse gases each year to the atmosphere, which accounts for 15% to 24% of the total current greenhouse gas production, according to a report from the United Nations.32 The greenhouse gases released from livestock production is higher than from all forms of trans- portation combined. Yes, the climate change that the world is facing is directly connected to our dinner plate. To produce one pound of beef, a steer must eat sixteen pounds of grain and soy, the re- maining ﬁfteen pounds are used to produce energy for the steer to live.33 The production of one kilogram of beef in a US feedlot causes the emission of about 14.8 kg of CO2. In comparison, 1 gallon of gasoline emits about 2.4 kg of CO2.34 An average American’s meat intake is about 124 kg per year, the highest in the world. In comparison, the average for a global citizen is 31 kg a year.35 The Manu-Smr. ti tells us that people who give consent to killing, who dismember a living entity, who actually kill, who purchase or sell meat, who purify it, who serve it, and who eat the meat are all sinners.36 Bhīs.ma explains to Yudhis.t.hira that the meat of animals is like the ﬂesh of one’s own son, and a person who eats meat is considered a violent human being.37 The Mahābhārata38 also suggests that “dharma exists for the general welfare of all living beings; hence by which the welfare of all living creature is sustained, that is real dharma.” In the Hindi language, the word ācar-vicār (ācar = conduct, vicār = thought) signiﬁes the connection of mind and physical body. This term is commonly used to describe the nature of a person. Diet and the state of mind are closely related. The Vaiśes. ika-Sūtra suggests that “improper diet instigate violence.”39 The ancient Hindus, in their astute observation of prakr. ti (nature) noticed a distinct role of each life-form and the importance of the “balance” in prakr. ti was realized: “A man who does no violence to anything obtains, eﬀortlessly, what he thinks about, what he does, and what he takes delight in. You can never get meat without violence to creatures with the breath of life, and the killing of creatures with the breath of life does not get you to heaven; therefore, you should not eat meat. Anyone who looks carefully at the source of meat, and at the tying up and slaughter of embodied creatures, should turn back from eating any meat, ” suggests the Manu-Smr. ti.40 Aśoka (reigned 272–232 BCE), grandson of Chandragupta (Candragupta, reigned 324– 300 BCE), tried to sanctify animal life as one of his cardinal doctrines. The Greek and Aramaic edicts in Kandhar in Afghanistan show Aśoka’s resolute resolve against animal killing. “The King abstains from the slaughter of living beings, and other people including the king’s hunters 32Steinfeld, et al., 2006. 33Kaza, 2005. 34Subak, 1999 and Fiala, 2008. 35Fiala, 2008. 36Manu-Smr. ti, 5: 51–52. 37Mahābhārata, Anuśāsana Parva, 114: 11. 38Śānti Parva, 109: 10 39Vaiśes. ika-Sūtra, 6: 1: 7. 40Manu-Smr. ti, 5: 47–49. 7.3. LIFE IN PLANTS: SIMILARITIES WITH HUMANS 123 and ﬁshermen have given up hunting. And those who could not control themselves have now ceased not to control themselves as far as they could. . .”41 Aśoka issued the following decree as known in Rampurva text: “Those she-goats, ewes (adult female sheep) and sows (adult female pig), which are either pregnant or milch, are not to be slaughtered, nor their young ones which are less than six months old. Cocks are not to be caponed. Husks containing living beings should not be burnt. Forests must not be burnt either uselessly or in order to destroy living beings.”42 These were the moral codes, not only the administrative one for ruling. Kinship with nature became a basis of their kinship with God. Hindu nonviolence made such an impact on the Muslim King Jahāngīr (r. 1605–1627 CE) that, in 1618 CE, he took a vow of nonviolence. In 1622 CE, this vow was broken when he had to pick up his gun to save his own life and his reign against his own son Khurram. This was the period when rulers used cruelty against animals and humans to demonstrate their imperial authority. Jahāngīr took this vow after killing about 17,167 life forms in 37 years. He ordered Thursday and Sunday to be holidays against the slaughter of animals and animal eating—Sunday being the birthday of his father Akbar and Thursday as the day of his accession to the throne.43 Obviously, the ancient Hindus were not concerned with energy or water consumption issues when they propagated vegetarianism. However, they were concerned with long life, good health for themselves, morality, animal rights, and sustaining ecology. They studied nature and came up with relationships between various life forms: plants, animals, and humans. These sci- entiﬁc studies led them to deﬁne a life style that led them to vegetarianism. Their concerns have a newly found meaning in today’s world. Their life style, if adopted today, can easily take care of the energy crisis that the world is facing today, improve the quality of water, completely erase the problem of hunger for a while with the current population growth, and conserve ecology and nature. 7.3 LIFE IN PLANTS: SIMILARITIES WITH HUMANS The Manu-Smr. ti suggests that plants are susceptible to pain and pleasure. “There are various kinds of shrubs and bushy plants, and various kinds of weeds and grass, creepers and trailing plants, some of which grow from seeds and others from graft. Variously enshrouded by the quality of tamas (ignorance), the eﬀects of their own acts, they retain their consciousness inward, susceptible to pleasure and pain.”44 The Mahābhārata mentions a discourse between two monks, Bhr.gu and Bhārdvāja, on the epistemology of plants. Bhr.gu asks: “Sir, all plant-life and animals are guided by the same ﬁve primal elements (pañcabhūta). But I don’t see it in the plants. Plants do not possess body heat, do not move their parts, remain at one place, and do not seem to have the ﬁve elements. Plants 41Sircar, 1957, p. 45. 42Sircar, 1957, p. 73–74. For more information, please also see, Smith, 1964; Barua, 1946. 43Findley, 1987. 44Manu-Smr. ti, 1: 48–49. 124 7. BIOLOGY neither hear, nor see, nor smell, nor taste. They cannot feel the touch of others. Why then you call them a component of ﬁve elements? They do not seem to possess any liquid material in them, heat of body, any earth, any wind, and any empty space. How then can plants be considered a product of ﬁve elements?”45 To such questions, Bhārdvāja replied: “Though trees are ﬁxed and solid, they possess space within them. The blooming of the fruits and ﬂowers regularly take place in them. Body heat of plants is responsible for the dropping of ﬂower, fruit, bark, leaves from them. They sicken and dry up. This proves the sense of touch in plants. It has been seen that sound of fast wind, ﬁre, lightening aﬀect plants. It indicates that plants must have a sense of hearing. Climbers twine the tree from all sides and grows to the top of it. How can one proceed ahead unless it has sight? Plants therefore must have the vision. Diseased plants may be cured by speciﬁc fumigation. This proves that plants possess sense of smell and breathe. Trees drink water from their roots. They also catch diseases from contaminated water. These diseases are cured by quality water. This shows that they have a perception of taste. As we suck water through a tube, so the plants take water through their roots under the action of air in the atmosphere. Trees when cut produce new shoots, they are favored or troubled by certain factors. So they are sensitive and living. Trees take in water through roots. Air and heat combine with water to form various materials. Digesting of the food allows them to grow whereas some food is also stored.”46 A close analysis of the above lengthy discourse between Bhrgu and Bhārdvāja depicts that the Hindus believed of life in plants, metabolism in plants, a need of food in plants, diseases in plants, and possible cures of diseases in plants using medicine. All these properties are also peculiar to animals and humans. The above quotation also tells us the Hindus’ belief that plants are sensitive to sound, touch, and quality of irrigated-water just like humans. The R. gveda mentions the hearing qualities in plants: “All plants that hear this speech, and those that have departed away, Come all assembled and confer your healing power upon this herb.”47 Thus, though plants do not have organs like humans, they do have similar functions— they breathe, eat, sleep, listen, reproduce, and die similar to humans. The Br. hadāran. yaka-Upanis. ad compares a man to a tree: “A man is indeed like a mighty tree; his hairs are like his leaves and his skin is its outer bark. The blood ﬂows from the skin [of a man], so does the sap from the skin [of a tree]. Thus, blood ﬂows from a wounded man in the same manner as sap from the tree that is struck. His ﬂesh [corresponds to what is] within the inner bark, his nerves are as though the inner ﬁbers [of a tree]. His bones lie behind his ﬂesh as the wood lies behind the soft tissues. Marrow [of a human bone] resembles with the pith [of a tree].”48 The Chāndogya-Upanis. ad recognized the presence of life in plants. “Of this great tree, my dear, if someone should strike at the root, it would bleed, but still live. If someone should 45Mahābhārata, Śānti-Parva, 184: 6–18. 46 Mahābhārata, Śānti-Parva, 184: 10–18. 47R. gveda, 10: 97: 21 48Br. hadāran. yaka-Upanis. ad, 3: 9: 28. 7.3. LIFE IN PLANTS: SIMILARITIES WITH HUMANS 125 strike its middle, it would bleed, but still live. If someone should strike at its top, it would bleed, but still live. Being pervaded in ātman [soul or self ], it continues to stand, eagerly drinking in moisture and rejoicing. If the life leaves the one branch of it, then it dries up. It leaves a second; it dries up . . . Verily, indeed, when life has left it, this body dies.”49 The presence of life in plants and similarities between plants and humans are quite clearly deﬁned in the ancient Hindu literature. It was only natural for someone to test these ideas. A major attempt came from Sir J. C. Bose (1858–1937 CE) of Calcutta during the earlier parts of the twentieth century. Though Bose was trained in physics, he ventured into the discipline of botany and made valuable contributions. As a result of his contributions, Bose was knighted by the British monarchy in 1917 and was elected a Fellow of the Royal Society of London in 1920. He was thus the third Indian and the ﬁrst natural scientist from India to be so honored. The ﬁrst Indian to get elected as a Fellow of the Royal Society was Engineer, Adaseer Cursetjee, in 1841, and the second was mathematician Srinivas Ramanujan, elected in 1918. Bose demonstrated life essences in plants with his experiments during the late nineteenth century. His contributions are: 50 1. Power of response (reﬂex action) In a mimosa plant, if a single leaf is touched, all the leaves in the branch slowly close. Bose devised an instrument to study such a behavior in other plants. He concluded that all plants, like human beings, possess reﬂex actions. 2. Food Habits Bose demonstrated that plants need food, like humans; nourishment of a plant comes from its roots as well as from its body. Bose experimentally demonstrated that, like humans, plants nourish themselves from a distribution of nutrients through a continuous cycle of contraction and expansion of cells. If a poison is administered to a plant, it may succumb to it. On the removal of poison, it may gradually revive and become normal. Plants also sway abnormally like a drunk person if treated with an alcoholic substance and become normal when the cause is removed. 3. Mind Activity A sun-ﬂower plant adjusts itself throughout the day so that it always faces the Sun. Many other plants close their leaves during the night and turn to face a brighter light source if the light is not uniformly distributed, indicating a mind activity in plants. 4. Nerves Plants also have nerves and feel sensation through leaves, branches, or trunks. If certain areas of a plant are made numb with ice, less pain is felt in the plant. Scientiﬁc American, a popular science magazine in America, published an article on J.C. Bose and summarized his work in the following words: “By a remarkable series of experiments conducted with instruments of unimaginable delicacy, the Indian scientist [ J. C. Bose] has dis- covered that plants have a nervous system . . . With the possibilities of Dr. Bose’s crescograph, 49Chāndogya-Upanis. ad, 6: 12: 1–3. 50for more information, read Subrata Dasgupta, 1998. 126 7. BIOLOGY in less than quarter of an hour the action of fertilizers, foods, electric currents and various stim- ulants can be fully determined.”51 51Scientiﬁc American, April 1915. C H A P T E R 8 Medicine 127 Diseases are as old as life itself. Manu (progenitor of humanity), or Adam and Eve, must have also needed the science of medicine. The problems of colds, fever, headache, and exhaustion has been experienced by people at one time or another. The ancient Hindus developed a system that is popularly known as Ayurveda, literally translated as the science of life. According to Suśruta, a noted ancient Hindu surgeon, Brahmā (creator of the universe) was the ﬁrst to inculcate the principles of Ayurveda and taught it to Prajāpati. The Aśvin Kumaras, two brothers, learned from Prajāpati and taught it to Indra. Indra taught it to Dhanvantari who later taught it to Suśruta.1 Dhanavantari’s status in India is similar to Aesculapius in the Western world. Caraka, another ancient Hindu physician, considered Ayurveda to be eternal:2 “The science of life has always been in existence, and there have always been people who understood it in their own way: it is only with reference to its ﬁrst systematized comprehension or instruction that it may be said to have a beginning.” The R. gveda suggests the human life expectancy to be 100 years.3 The Yajurveda-Śukla tells everyone to aspire to have an active life till they reach 100.4 The Upanis. ads also suggest us that we should expect to live an active life for hundred years. “Even while doing deeds here, one may desire to live a hundred years,” suggests the Iśā-Upanis. ad.5 During the ancient period, in most cultures, the life expectancy was about 40 years of age. However, among the ancient Hindus, it was the second stage of life at that age. Marco Polo, when he visited India, has mentioned of the long life of the Hindus. The materia medica of the Indus-Sarasvatī region is particularly rich due to a large number of rain forests around the country. The Indian climate is unique, as all four seasons are experi- enced. The abundance of materia medica has been recorded by several foreigners who visited India during the ancient and medieval periods. Although India’s total land area is only 2.4% of the total geographical area of the world, today it accounts for 8% of the total global biodiversity with an estimated 49,000 species of plants of which 4,900 are endemic, implying their presence only in India or nearby regions.6 There are around 25,000 eﬀective plant-based formulations available 1Suśruta-Sa ˙mhitā, Sūtrasthānam, 1: 16. 2Caraka-Sa ˙mhitā, Sūtrasthānam, 30, 26–28. 3“That Indra for a hundred years may lead him safe to the farther shore of all misfortune.” R. gveda, 10: 161: 3. “With the most saving medicines which thou givest, Rūdra, may I attain a hundred winters.” The R. gveda, 2: 33: 2. As a comparison, the life expectancy among the ancient Egyptian was only about mid-thirties while for the Roman it was mid-forties. 4Yajurveda-Śukla, 40: 2. 5Iśā-Upanis. ad, 2. 6Ramakrishnappa, K., 2002. This report can be accessed at http://www.fao.org/DOCREP/005/AA021E/AA021e00.htm. 128 8. MEDICINE in Indian medicine. It is estimated that there are over 7,800 medicinal drug manufacturing units in India, which consume about 2,000 tonnes of herbs annually.7 The Caraka-Sa ˙mhitā lists 341 plants and plant products for use in medicine. Suśruta described 395 medicinal plants, 57 drugs of animal origin and 64 minerals and metals as therapeutic agents.8 The ancient Hindus understood that disease is a process that evolves over time. They tried to prevent diseases by using proper hygiene, a healthy lifestyle, a balanced diet, yoga, internal and external medicine, surgery, and prayer. Good health was considered as essential to achieve moks. a.9 Detailed experiments were performed to evolve new medical knowledge. For exam- ple, Suśruta selected a cadaver, cleaned it, and wastes were removed. Afterward, the body was wrapped in grass and placed in a cage to protect it from animals. The cage was then lowered into a river or a rushing stream of water. This was done to ensure constant cleaning. Once the decay process took a toll on the body, it was taken out of water. Skin, fat, and muscles were brushed away from the corpse with grass brushes, and the human anatomy was observed.10 In evaluating the diagnostic techniques of the ancient Hindus, Erwin Heinz Ackerknecht, in his book A Short History of Medicine, writes that “[d]iagnostic were highly developed. The In- dian healer used questioning, very thorough inspection (e.g., to diagnose pulmonary consump- tion from the loss of weight), touch (including observation of the pulse), and examination with other senses, such as tasting the urine for diabetes. Indians knew the sweet taste of diabetic urine long before Europeans did.”11 8.1 DOCTORS, NURSES, PHARMACIES, AND HOSPITALS During the Vedic period, doctors were divided into surgeons (śalya-vaidya) and physicians (bhis. ak).12 These doctors were well respected in the society. “He who stores herbs [medicine man] is like a king amid a crowd of men, Physician is that sage’s name, ﬁend-slayer, chaser of disease,” suggests the R. gveda.13 The inscriptions of King Aśoka (third century BCE) refer to the cultivation of medicinal plants and the construction of hospitals in his kingdom. The rock edict of Girinar in India, erected by Aśoka (r. 269–232 BCE), indicates that separate hospitals for humans and animals were built. Aśoka suggests ahi ˙msā in the treatment of all animals: “Meritorious is abstention from the slaughter of living beings.”14 Indeed, hospitals were build all over India from the earliest periods. 7Mukherjee and Wahile, 2006. 8Mukherjee and Wahile, 2006. Krishnamurthy has given quite a diﬀerent number for the medicinal plants. According to Krishnamurty, Suśruta deﬁned 793 plants for medical usages. Krishnamurthy (1991) has compiled the list of these plants in the ninth chapter of his book. Krishnamurthy, 1991. 9Caraka-Sa ˙mhitā, Sūtrasthānam, 1: 15–16. 10Rajgopal et al., 2002. 11Ackerknecht, 1982, p. 38. 12Mukhopādhyāya, 1994. 13R. gveda, 10: 97: 6. 14Sircar, 1957, p. 47. 8.1. DOCTORS, NURSES, PHARMACIES, AND HOSPITALS 129 Caraka deﬁnes following qualities of a doctor: good knowledge of the medical texts; ex- perienced in curing various diseases, skillful in the preparation of drugs, and their uses; good in quick thinking in diﬃcult situations; and good in hygiene.15 The doctor should also have control over his hands when in surgery or diﬃcult situations. A person with shaking hands is not a good surgeon.16 “Drugs are like nectar; administered by the ignorant, however, they become weapons, thunderbolt or poison. One should therefore shun the ignorant physician,” suggests Suśruta.17 Emphasizing constant practice in diagnosis, Suśruta suggests that “the physician who studies the science of medicine from the lips of his preceptor, and practices medicine after acquired experience in his art by constant practice is the true physician.”18 Caraka advised people to avoid incompetent doctors,19 as it can even aggravate their con- dition.20 Caraka has provided a detailed code of conduct for doctors which is similar to the Hippocratic Oath in the Western world.21 This code of conduct forbids doctors to indulge in money-making and lust: “He, who practices not for money nor for caprice but out of compas- sion for living beings is the best among all doctors.”22 And, most importantly, a doctor must continue to help his patients, despite adversity. This is the only way to save the life of a person.23 Physicians were instructed to be friendly, kind, eager to help underprivileged people, and re- main calm in diﬃcult diseases.24 “The underlined objective of a treatment is kindness. Kindness to another human being is the highest dharma. A doctor becomes successful and ﬁnds happiness with this objective.”25 Doctors were advised to concentrate only on the treatment of the patient and not on materializtic rewards, the patient was advised to reward the doctor with money that he can aﬀord and to be respectful toward the doctor.26 According to an ancient legend, Jivaka Kumarabhacca was a revered physician who pro- vided medical care to Lord Buddha and his disciples. Jivaka studied medicine under the leg- endary and revered physician Ātreya, in the city of Taxila. After many years of training, one day Jivaka decided to have his own independent practice and shared his views with his teacher. Ātreya decided to take an exam before he could allow Jivaka to have his own practice. He asked Jivaka to go around the āshram (monastery) and collect all plants with no medicinal value. Jivaka walked around and toiled to look for a plant with no medicinal value. After considerable eﬀorts and somewhat dejected, he went back to Ātreya with no plant in his hand and told him that he 15Caraka-Sa ˙mhitā, Sūtrasthānam, 9: 6. 16Caraka-Sa ˙mhitā, Sūtrasthānam, 29: 5–6. 17Suśruta-Sa ˙mhitā, Sūtrasthānam, 3: 51. 18Suśruta-Sa ˙mhitā, Sūtrasthānam, 4: 7 19Caraka-Sa ˙mhitā Sūtrasthānam, 9: 15–17. 20Caraka-Sa ˙mhitā, Sūtrasthānam, 16: 4. 21Caraka-Sa ˙mhitā, Vimānasthānam, 8: 13. 22Caraka-Sa ˙mhitā, Vimānasthānam, 8: 13. 23Caraka-Sa ˙mhitā, Sūtrasthānam, 1: 134. 24Caraka-Sa ˙mhitā, Sūtrasthānam, 9: 26. 25Caraka-Sa ˙mhitā, Cikitsāsthānam, 4: 63. 26Caraka-Sa ˙mhitā, Cikitsāsthānam, 4, 55. 130 8. MEDICINE could not ﬁnd even a single plant with no medicinal value. Ātreya was pleased with the answer and gave his blessing to Jivaka to start his own practice for the welfare of human beings. Caraka and Suśruta emphasized that a good doctor must have all needed equipment with him.27 Similarly, Suśruta suggested multitude of surgical tools, leeches, ﬁre for sanitizing tools, cotton pads, suture threads, honey, butter, oil, milk, ointments, hot and cold water, etc. for a surgeon. For the tools, roundhead-knife, scalpel, nail-cutter, ﬁnger-knife, lancet that is as sharp as the leaf of the lotus, single-edge knife, needle, bistoury, scissors of various shapes, curved bistoury, ax-shaped hammer, trocar, hooks, narrow-blade knife, toothpick, etc. Surgeon must know to hold these instruments properly for surgery28 and surgery should be avoided when one could eﬀectively use leeches to do the same job.29 “One who knows the text but is poor in practice gets confounded on seeing a patient; he is like a coward on the battle ﬁeld. One who is bold and dexterous but lacking in textual knowledge fails to win the approval of peers and risks capital punishment from the king. Having half-knowledge, implying either textual or practical knowledge, is a physician who is unﬁt for the job and is like a one-winged bird,” suggests Suśruta.30 In the views of Suśruta, a person with just theoretical knowledge in ayurveda only, is “like an ass that carries a load of sandal wood [without ever being able to enjoy its pleasing scent].”31 Suśruta advised that doctors must involve all ﬁve senses in the physical examination of the patient: inspection, palpation, auscultation (listening to the sound of the heart, lungs, etc.), taste, and smell.32 For incisions, surgeons were advised to use the tool rapidly only once to desirable depth.33 Obviously, this was done to avoid or minimize pain to patients. It was also advised that the surgeon must be courageous, must be quick in action and decision-making, self conﬁdent, should not sweat in tense situations, his hands should not shake, and he should have sharp instruments.34 Caraka advised doctors to diﬀerentiate between the diseases that can be cured and those that cannot be cured.35 He advised doctors to not treat patients with incurable diseases in ad- vanced stages and alleviate the suﬀering of the patient.36 Since disease is a process with various stages, he suggested that even serious diseases can be cured if caught in their early stages. Proper medication at the early stage and proper lifestyle is essential to control these serious ailments.37 27Caraka-Sa ˙mhitā, Sūtrasthānam, 16: 1; Suśruta-Sa ˙mhitā, Sūtrasthānam, 5: 6. 28Suśruta-Sa ˙mhitā, Sūtrasthānam, 8: 3–4. 29Suśruta-Sa ˙mhitā, Sūtrasthānam, 13: 3–4. 30Suśruta-Sa ˙mhitā, Sūtrasthānam, 3: 48–50 31Suśruta-Sa ˙mhitā, Sūtrasthānam, 4: 2 32Suśruta-Sa ˙mhitā, Sūtrasthānam, 10: 4. 33Suśruta-Sa ˙mhitā, Sūtrasthānam, 5: 7. 34Suśruta-Sa ˙mhitā, Sūtrasthānam, 5: 5–6. 35Caraka-Sa ˙mhitā, Sūtrasthānam, 18: 39. 36Caraka-Sa ˙mhitā, Sūtrasthānam, 18: 40–44. This is a sensitive issue that has moral, cultural, and moral implications. Most people incur major medical expenses in the last ﬁve years of their lives. Should we treat a patient with no or little chance of recovery? The Edwin Smith Papyrus has dealt with the same issue more than 3000 years ago in Egypt. This issue is still under discussion in many countries around the world. 37Caraka-Sa ˙mhitā, Sūtrasthānam, 18: 38. 8.1. DOCTORS, NURSES, PHARMACIES, AND HOSPITALS 131 It is essential for a doctor to recognize the disease by knowing the symptoms of the ailment. However, since the number of diseases is very large, a doctor should not feel ashamed if he can- not identify the disease from the symptoms.38 This is an example of honesty that is expected of all physicians. Doctors were responsible for treatment and were punished for wrongdoings. The penalty for such wrongdoings depended on the extent of damage. Humans received more attention than animals in their medical treatment.39 Physicians were not above the law; their greed and carelessness were checked with laws during the period of Chandragupta Maurya (Candragupta, reigned 322–298 BCE) in India.40 According to Caraka, the following are the four constituents that are crucial for the quick recovery of a patient: a qualiﬁed doctor, a quality drug, a qualiﬁed nurse, and a willing patient.41 This clearly signiﬁes the importance of nursing in medical care. The roles of a nurse are: the complete knowledge of nursing, skillful, aﬀection for the patient, and cleanliness.42 A good patient is deﬁned as someone with a good memory, follows the instructions of the doctor, free of fear, and can explain the symptoms of the disease well. This combination of doctor, nurse, drug, and patient is essential for a successful cure. Otherwise, the cure is incomplete.43 Patients were advised to ignore doctors who practice just for money, were not qualiﬁed, or were too proud of their status.44 Patients should go to a doctor who has studied śāstra (texts), is astute, is pure, understands the job well, has a good reputation, and has good control of his mind and body, suggested Caraka.45 A good doctor should be respected like a guru.46 “The patient, who may mistrust his own parents, sons, and relatives, should repose an implicit faith in his own physician, and put his own life into his hands without the least apprehension of danger; hence a physician must protect his patient as his own begotten child,” suggest Suśruta.47 Pharmacies prepared medicines as powders, pastes, infusions, pills, confections, or liquids using chemical techniques of oxidation, fermentation, and distillation. Pharmacists were trained in grafting, general care of plants, extract juices from ﬂowers, concocting various medical prepa- rations, and making medicinal bhasms and extracts. In providing the design of a hospital, Caraka suggests that it should have good ventila- tion and the rooms should be big enough for patients to walk comfortably. The rooms should not experience the intense glare of sunlight, water, smoke, and or dust. The patient should not experience any unpleasant sound, touch, view, taste, or smell. Expert chefs, masseuses, servants, 38Caraka-Sa ˙mhitā, Sūtrasthānam, 18: 45–46. 39Manu-Smr. ti, 9: 284. 40Kaut.ilaya’s Arthaśāstra, 144. 41Caraka-Sa ˙mhitā, Sūtrasthānam, 9: 3. 42Caraka-Sa ˙mhitā, Sūtrasthānam, 9; 8. 43Caraka-Sa ˙mhitā, Sūtrasthānam, 9: 9–13. 44Caraka-Sa ˙mhitā, Sūtrasthānam, 29: 12. 45Caraka-Sa ˙mhitā, Sūtrasthānam, 29: 13. 46Caraka-Sa ˙mhitā, Sūtrasthānam, 4: 51. 47Suśruta-Sa ˙mhitā, Sūtrasthānam, 25: 42–45. 132 8. MEDICINE nurses, pharmacists, and doctors should be hired to take care of the patients. Birds, deer, cows and other animals, along with singers and musicians should be kept in the hospital compound.48 Hospitals should have enough quality food in the storage room, stored drugs, and a com- pound with drug plants. The doctors must be intelligent in knowing the books as well as equip- ment. Only then, they were allowed to help a patient.49 8.2 AYURVEDA Ayurveda is the Hindu science of healing and rejuvenation which is curative as well as preventive. It is a holistic medicine that focuses on mind and body and a person needs to practice the doctrines of ayurveda when healthy to avoid sickness. Dietary measures and lifestyle changes are recommended to delay the aging process at the cellular level and to improve the functional eﬃciency of body and mind. The ancient Hindus recognized the self-healing capacity of our body and focused on creating a balance that allows the body to cure itself. Ayurveda is a combination of two words–āyur and veda. Āyur means the span of life while veda means unimpeachable knowledge or wisdom. Ayurveda signiﬁes life science for the well being of body and mind. This stemmed out of Hindus’ belief that health and disease co-inhere in body and mind. Ayurveda has its origin in the Vedas for the “principal elements of its gen- eral doctrines.”50 In the Hindu tradition, Ayurveda is considered as an Upa-Veda (subordinate Veda) that deals with medicine and medical treatment for good health, longevity, and elimina- tion of disease. It is considered to be in well-evolved form at the time of Atharvaveda. Suśruta wrote: “The Ayurveda originally formed one of the subsections of the Atharvaveda and originally consisted of 100,000 verses.”51 Ayurveda uses herbal medicine, dietetics, surgery, psychology, and spirituality to cure diseases. Pañca-karma (detoxiﬁcation of body), laxatives, herbal oil massages, and nasal thera- pies are some of the treatments. Though ancient in origin, it is still the most popular system of medicine in modern India. Several Indian universities provide doctoral degree programs in Ayurveda. These universities train doctors who practice throughout India and provide low cost medical care to poor people. These days, Banaras, Chennei, Haridwar, Lucknow, Patna, and Trivandrum are some of the prominent cities that house universities to train ayurvedic doctors. Caraka suggested that physical ailments should be cured by proper diet, changing daily routines that included moderate physical exercise,52 and medicine, while the mental diseases should be cured by self control, meditation, and even by charms (bhuta-vidyā).53 Caraka deﬁnes 48Caraka-Sa ˙mhitā, Sūtrasthānam, 15: 7. 49Caraka-Sa ˙mhitā, Sūtrasthānam, 16: 1. 50Filliozat, 1964, p. 188. 51Suśruta-Sa ˙mhitā, Sūtrasthānam, 1: 3. 52Caraka-Sa ˙mhitā, Sūtrasthānam, 7: 30. 53Caraka-Sa ˙mhitā, Sūtrasthānam, 1–8. 8.2. AYURVEDA 133 that the purpose of Ayurveda is to preserve the well-being of a healthy person and to get rid of the diseases of a sick person.54 In the ayurvedic tradition, the human body is considered as a conglomeration of ﬁve el- ements, known as mahābhūtas—earth (pr. thivī), air (vāyu), water (apah. ), ﬁre (tejas), and space (ākāśa). The ﬁve mahābhūtas produce seven dhātus: rasa (juice-plasma), rakta (blood), mām. sa (ﬂesh), medas (fat), asthi (bone), majjā (marrow), and śukra (reproductive ﬂuids in male and females).55 The ﬁve mahābhūta, or the seven dhātu, constitute the prakr. ti (attributes) of a per- son. These dhātu are a product of the ﬁve elements. When in equilibrium, these dhātus make a person happy and healthy. The various combinations of these dhātu constitute the tri-gun. as (three-attributes) in a person: sattva, rājas, tāmas. A person with dominant sattva values truth, and honesty; rājas value power, prestige, and authority. A tāmas dominant person lives in igno- rance, fear, and servility. The basic theory of Ayurveda rests on the three humors (tridos. a; tri = three, dos. a = the lit- eral meaning is defect, popularly known as elements)–Kapha (phlegm), a heat regulating system, and mucous and glandular secretion; vata (wind), a nerve force; and pitta (bile), metabolism and heat production. These three dos. a control the normal functions of a human body and a balance is necessary. The term dos. a is generally translated as “corrupting agents,” “defect,” or “imperfec- tion.” However, in Ayurveda, these dos. a are the keys to good health. The theory of dos. a is pretty complex as it “is aﬀected by an almost inﬁnite number of exogenous factors and combinations of factors that make up human ecology: diet, rate, time, and context of food consumption, cli- mate, direction of wind, age, behavioral patterns, rest, accidents, exercise, state of mind, and so forth.”56 An imbalance of these three dos. as causes most diseases. It is the purpose of all treat- ments to keep the balance of the dos. as by balancing the seven dhātus.57 The Suśruta-Sa ˙mhitā gives various symptoms of the deﬁciency of these tridos. as and their eﬀects on body.58 Balance is essential in the natural world and is a key concept in Hindu philosophy. It is the balance of body and mind in āsana that is crucial in yoga. It is the balance of tridos. as in ayurveda that is crucial in the well-being of a person, just like the yin and yang in Chinese philosophy. Therefore, before ayurvedic doctors look for the cure of a disease, they inquire about the patient, his/her constitution, eating habits, and nature to know the imbalance in dhātu. For example, in describing the cause of diabetes and its cure, Suśruta and Caraka attribute lack of exercise, laziness, sweet foods, alcoholic foods and beverages, elevation of kapha, and excess of newly harvested food grains as the cause. A continual balance of tridos. a results in contentment, longevity, and enlightenment. We eat food to nourish the seven dhātus in our body. By changing diet, people can change the equilibrium of dhātus and thus their attributes. Therefore, among the Hindus, it is a customary to describe the attributes of a person from a combination of two 54Caraka-Sa ˙mhitā, Sūtrasthānam, 30: 26. 55For the roles of these dhātu, read Suśruta-Sa ˙mhitā, Sūtrasthānam, Chapter 15. 56Alter, 1999; Lad, 1984; and Zysk, 1991. 57Caraka-Sa ˙mhitā, Sūtrasthānam, 16: 35–36. 58Suśruta-Sa ˙mhitā, Sūtrasthānam, Chapter 15. 134 8. MEDICINE words, ācar-vicār, describing the thinking and eating habits of a person. Suśruta suggested eating in moderation for a healthy life.59 Caraka clearly regulates the quantity of food that a person should eat: “The food must be digested in time and should not cause any inconvenience in activity of the person.”60 Patients should seek eﬀective drugs immediately after recognizing a sickness.61 Thus, quick diagnosis is the key in ﬁghting against a disease. Following are the typical drugs used in ayurveda: 1. Animal products (honey, milk, blood, urine, fat, horn, etc.) 2. Minerals and metals (salt, gypsum, alum, gold, lead, copper, iron, phosphorous, sulfur, potassium, calcium, iodine, lime, mud, precious stones, etc.) 3. Herbs and plants (for example, aloe vera, barley, beans, cinnamon, clove, coriander, cumin, black pepper, fenugreek, neem, etc.) In Ayurveda, metals are oxidized, reduced, and transformed into a chemical compound that is non-toxic, to be used as a drug.62 Several elements like gold, lead, copper, iron, phospho- rous, sulfur, potassium, calcium, and iodine are processed with physio-chemical techniques. Wa- ter, sunlight, milk, honey, and fermented extracts of fruits are also used as medicine in Ayurveda. For example, Drāks. aśava, that is an extract of grape and apple-vinegar along with several miner- als, with a speciﬁc fermentation technique, is perhaps the best natural medicine for indigestion. It cleans the blood, improves the functioning of kidneys and liver, improves the pH value of urine, and provides minerals. It is not only a curative medicine but could also be used on a regular basis as a preventive medicine for good health. Minerals are also used for curative purposes; śilājīta, perhaps the most important one, is a gelatine substance secreted from mountain stones during the scorching heat of June and July in Northern India, and contains traces of tin, lead, copper, silver, gold, and iron. Śilājīta has heat-producing and body purifying properties and is used in the treatment of diabetes, leprosy, internal tumor, and jaundice.63 The daily routine (dinacarayā) is crucial for good health. Caraka deals with the issue of life- style in great detail in the ﬁrst chapter of Caraka-Sa ˙mhitā.64 Suśruta also devoted a long chapter to prescribe a good lifestyle for a healthy person.65 Almost as a rule, it was considered good to get up early in the morning and practice yoga and meditation after toiletry functions and bath. To optimize health and as preventive measures for various body organs and for general health, dental cleaning with herbs, mouthwash, tongue scraping, daily bath, massage, clean clothes, 59Suśruta-Sa ˙mhitā, Sūtrasthānam, 46: 145. 60Caraka-Sa ˙mhitā, Sūtrasthānam, 5: 4. 61Caraka-Sa ˙mhitā, Sūtrasthānam, 11: 63. 62For more information, read Zimmer, 1948. 63Suśruta-Sa ˙mhitā, Cikitsāstānam, Chapter 13. 64Caraka-Sa ˙mhitā, Sūtrasthānam, sections 5, 7, and 8. 65Suśruta-Sa ˙mhitā,Cikitsāstānam, 24: 3–132. 8.2. AYURVEDA 135 good shoes, daily exercise, and good thought processes were suggested. The role of the mind was known to the ancient Hindus. Thus, they suggested good thought process as essential to good health. Mouth hygiene received much attention in ancient writings. Caraka suggested to brush the teeth twice a day66 and clean the tongue using a metallic scraper.67 He also suggests many herbs such as clove, cardamom, beetle nut, and nutmeg to keep in the mouth for a pleasant breath.68 Suśruta provides the following instructions for the hygiene of mouth. “A man should leave his bed early in the morning and brush his teeth. The tooth-brush should be made of a fresh twig of a tree or a plant grown on a commendable tract and it should be straight, not worm-eaten, devoid of any knot or at most with one knot only (at the handle side), and should be twelve ﬁngers in length and like the small ﬁnger in girth.”69 “The teeth should be cleansed daily with (a compound consisting of ) honey, powdered trikat. u, trivarga, tejovatī, saindhave and oil. Each tooth should be separately cleansed with the preceding cleansing paste applied on (the top of the twig) bitten into the form of a soft brush, and care should be taken not to hurt the gum any way during the rubbing process. This tends to cleanse and remove the bad smell (from the mouth) and uncleanliness (of the teeth) as well as to subdue the kapha (of the body). It cleanses the mouth and also produces a good relish for food and cheerfulness of mind,”suggests Suśruta.70 Afterward, the person should cleanse the tongue by scraping it with gold, silver, or wood foil.71 8.2.1 PAÑCA-KARMA Pañca-karma is an ayurvedic treatment to cleanse the body system to remove toxins. This treat- ment has three phases: purva-karma (preparation), pradhā-karma (main treatment), and paśca- karma or Uttara-karma (post-treatment).72 Before the actual process, a dietary and herbal treat- ment is prescribed to cleanse the intestinal system, reduce the excess or vitiated dos. as, and in- creasing the gastric ﬁre. In the oleation process, oily substances like sesame, ﬂaxseed, or mustard oil or ghee are taken internally or externally in massage and sudation (sweating) techniques are used. Ghee is clariﬁed butter by removing its water contents and milk solids. It becomes lactose- free and can be used by people with lactose intolerance. Ghee is antimicrobial and antifungal and, therefore, can be preserved without refrigeration for an extended period.73 The oleation process lubricates bodily tissues and should be taken in moderation especially people with kapha. The exact prescription in purva-karma depends on the individual and the diet includes simple foods 66Caraka-Sa ˙mhitā, Sūtrasthānam, 5: 71. 67Caraka-Sa ˙mhitā, Sūtrasthānam, 5: 74. 68Caraka-Sa ˙mhitā, Sūtrasthānam, 5: 76. 69Suśruta-Sa ˙mhitā, Cikitsāstānam, 24: 3. 70Suśruta-Sa ˙mhitā, Cikitsāstānam, 24: 6–7. 71Suśruta-Sa ˙mhitā, cikitsāsthānam, 24: 11–12. 72Ninivaggi, 2008, p. 207 73Ninivaggi, 2008, p. 209. 136 8. MEDICINE such as khicar. ī, a combination of basmati rice, split mung lentils and some mild spices, such as turmeric, cumin and coriander. The ﬁve actions of Pañca-karma are as follows: vamana, virecana, vasti, nasya, and rakta- moksha.74 These actions are provided by Suśruta. First, the body is detoxiﬁed by inducing vomit- ing using herbal mixture (vamana), then an herbal mixture is taken for numerous bowel move- ments (virecana), oil or herbs are administered anally for some time and expelled (vasti). Nasya is practiced by using neti-kriyā (luke warm water passed through the sinus) and oil is applied inside to clean the sinus system. In some special cases, the blood is puriﬁed or even taken out using needles, incisions, or by leeches.75. In the post-treatment, dietary and lifestyle lessons are provided to have balanced dinacaryā. Pañca-karma is advised for a variety of medical conditions: arthritis, rheumatism, respi- ratory disorders, gastrointestinal disorders, menstrual problems, obesity, etc. A team of Har- vard Medical School in Massachusetts conducted a clinical study of this practice to observe the role of psychosocial factors in the process of behavior change and salutogenic process. The 20 female participants underwent in a 5-day ayurvedic cleansing retreat program. Measurements were taken before the program, immediately after the program, and after three months for the quality of life, psychosocial, and behavioral changes. This study indicates that pañca-karma “may be eﬀective in assisting one’s expected and reported adherence to new and healthier behavior patterns.”76 8.3 SURGERY Suśruta, in his Suśruta-Sa ˙mhitā, describes some one hundred medical surgical instruments of metals in various shapes and sizes. These include probes, loops, hooks, scalpels, bone-nippers, scissors, needles, lancets, saws, forceps, syringes, rectal speculums, and probes. Many surgical operations including those for hernia, amputation, tumor, restoration of nose, skin grafting, extraction of cataracts, and caesarean section are described in the Caraka-Sa ˙mhitā and/or the Suśruta-Sa ˙mhitā. In both books, blunt as well as sharp tools depending on the needs are de- scribed. Some of these instruments are sharp enough to dissect a hair longitudinally.77 Suśruta performed lithotomy, cesarean section, excision of tumors, and the removal of hernia through the scrotum.78 New doctors practiced incisions ﬁrst on plants or dead animals. The veins of large leaves were punctured and lanced to master the art of surgery. Cadavers were advocated as an indis- pensable aid to the practice of surgery. Bandaging, amputations, and plastic surgery were ﬁrst practiced on ﬂexible objects or dead animals just as is done by medical students today. Suśruta 74Ninivaggi, 2008, p. 212. 75Ninivaggi, 2008, p. 219 76Conboy, Edshteyn, and Garivsaltis, 2009. 77For a detailed account of the tools, see Mukhopādhāya, 1994. 78Singh, Thakral, and Deshpande, 1970. It is an excellent article with basic information. 8.3. SURGERY 137 suggests that “a surgeon in seeking a reliable knowledge must duly prepare a dead body and carefully ascertain from his own eyes what he learned with books.”79 Suśruta classiﬁed surgery into eight parts: extraction of solid bodies, excising, incising, probing, scarifying, suturing, puncturing, and evacuating ﬂuid.80 He designed his surgical in- struments based on the shapes of the beak of various birds and the jaws of animals. In his attempt to explain surgery, Suśruta writes: “The scope of surgery, a branch of medical science, is to re- move an ulcer and extraneous substance such as fragments of hay, particles of stone, dust iron, ore, bone; splinters, nails, hair, clotted blood or condensed pus, or to draw out of the uterus a dead fetus, or to bring about safe parturitions in cases of false presentation, and to deal with the principle and mode of using and handling surgical instruments in general, and with the application of cautery and caustics, together with the diagnosis and treatment of ulcers.”81 All surgical procedures were deﬁned in terms of three stages of the process: Pre-operative measures, operation, post-operation measures. This included the preparation of the surgical room, the patient, and the tools. Starvation or mild dieting was advised on the day of surgery. Intoxicating beverages were advised to avoid the pain of surgery. In the post-operative mea- sures bandaging, redressing, healing and cosmetic restoration were also involved.82 Anesthesia, antiseptic, and sterile techniques were used by the ancient Hindus. Suśruta described fourteen diﬀerent kinds of bandages (bandha).83 On the harmful eﬀects of non-bandaging, Suśruta suggests that ﬂies and gnats are attracted to the wound. Foreign matters, such as dust and weeds can settle on the wound. Sweat, heat and cold can make the wound malignant.84 Suśruta advises doctors to clean wounds ﬁrst to get rid of dust, hairs, nails, loose pieces of bones, and other foreign objects before suturing to avoid suppuration. If not done, it can cause severe pain and other problems.85 Suśruta found innovative ways to perform various surgical procedures: horse hairs were used as suture material while black carpenter ants were used in closing incisions in soft tissues. Blood or pus was drawn from body by using leeches. The amputation of the leg and other body parts was done during the R. gvedic period. The R. gveda tells us that the lower limb of Queen Viśpalā was severed in King Khela’s battle. Āsvins connected an artiﬁcial limb to her at night and she was able to ﬁght the battle again:86 A neolithic 4000 year-old skeleton with a multiple-trepanated skull was recently found in Kashmir. The trepanation on this skull was perhaps accomplished using drills of various di- ameters and could be a result of an elaborate medico-ritual ceremonial procedure.87 Similarly, nearly perfect tiny holes as dental treatment were found in excavations in the Mehrgarh site, 79Suśruta-Sa ˙mhitā, Śarīrsthānam, 5: 6. 80Suśruta-Sa ˙mhitā, Sūtrasthānam, 5: 5 81Suśruta-Sa ˙mhitā, Sūtrasthānam, I: 4. 82Suśruta-Sa ˙mhitā, Sūtrasthānam, 5: 3. 83Suśruta-Sa ˙mhitā, Sūtrasthānam, 18: 14–18; also read Kutumbiah, 1962, p. 163. 84Suśruta-Sa ˙mhitā, Sūtrasthānam, 18: 23. 85Suśruta-Sa ˙mhitā, Sūtrasthānam, 25: 18. 86R. gveda, 1: 116: 15. 87Sankhyan and Weber, 2001. 138 8. MEDICINE near Baluchistan, that are about 7,500 to 9,000 years old. Eleven drilled molar crowns from nine adults were studied from this site. The drilled holes are about 1.3–3.2 mm in diameter and angled slightly to the occlusal plane, with a depth of about 0.5 to 3.5 mm.88 Cavity shapes were conical, cylindrical or trapezoidal. At least in one case, “subsequent micro-tool carving of the cavity wall” was performed after the removal of the tooth structure by the drill.89 In all cases, marginal smoothing conﬁrms that drilling was performed on a living person who later continued to chew on the tooth surfaces.90 Using the ﬂint drills that are similar to the ones found in Mehrgarh and using a bow-drill, the team of Coppa et al. could drill a hole in hu- man enamel in less than a minute. When Andrea Cucina, a researcher from the University of Missouri-Columbia, looked the cavities using an electron microscope, he found that the sides of the cavities were perfectly round to be caused by bacteria. He also noticed concentric groves left by the drill. According to him, some plants or other substances were put into the hole to prevent any further decay in the molars. These ﬁllings were decayed during the 9,000 years of seasoning.91 8.3.1 PLASTIC SURGERY In Rāmāyan. a, attractive and voluptuous Sūrpan. akhā, sister of Rāvan. a, tried to devour Lord Rāma, a married man. Lord Laks.man. a, younger brother of Lord Rāma, decided to cut oﬀ her nose and earlobes as punishment. King Rāvan. a took care of the problem by asking his surgeon to reconstruct the nose and earlobes of his sister.92 In time, nasal amputation also worked its way into the metaphors and the Hindi term Nāk kat gai (nose is chopped) implies that a person is insulted. Also, “saving nose” (nāk bacā lī) is a colloquial term meaning to go through diﬃcult circumstances without embarrassment. Suśruta described the technique to graft skin, presently known as “plastic surgery” as a general umbrella term. He repaired the nose or earlobes using an adjacent skin ﬂap. Today, this procedure is popularly called as “the Indian method of rhinoplasty”93 although no plastic is used in the process. Live ﬂesh from the thigh, cheek, abdomen, or the forehead was used to make the new artiﬁcial parts. This procedure was not practiced in the West until the second half of the 15th century in Sicily, an empire with considerable contact with Arabia.94 In England, the ﬁrst article on rhino- plasty appeared in the Gentleman’s Magazine in 1794, written by Colly Lyon Lucas, a British surgeon and member of the Medical Board at Madras, India.95 He described the process in 88Coppa et al., 2006 89Coppa et al., 2006 90Coppa et al., 2006 91Coppa et al, 2006. 92Brain, 1993. 93Sorta-Bilajac and Muzur, 2007. 94Pothula, 2001. 95Brain, 1993; Lucas, The Gentleman’s Magazine, 64, pt. 2, no. 4, 891–92, October, 1794. In this article, only the initials of the author are provided. 8.3. SURGERY 139 his letter to the Editor, describing the process as “long known in India” and not known to the British. Colly Lyon Lucas witnessed a case where a local Indian serving the British army, in the war of 1792 CE, was captured by King Tipu Sultan. Unable to defeat the British outright, the sultan tried to starve his enemies by ambushing the Indian bullock drivers who transported grain to the British. Tipu decided to humiliate the bullock drivers by mutilating their noses and ears. Lucas describes one such victim of this practice, the Mahratta bullock driver Cowasjee, who, on his capture, had his nose and one of his hands amputated by the sultan. After one year, this man decided to get his nose repaired. An operation was performed by the Indian doctors who took skin from the forehead and placed it on the nose in proper form. The whole process took about 25 days. The artiﬁcial nose looked “as well as the natural one” and the scar on the forehead was not very observable after a “length of time.” The procedure generated great interest among the British surgeons. Lucas writes:96 “For about 12 months he remained without a nose, when he had a new one put on by a man of the Brickmaker cast near Poonah [Poona]. This operation is not uncommon in India, and has been practiced from time immemorial.. . . A thin plate of wax is ﬁtted to the stump of the nose, so as to make a nose of good appearance. It is then ﬂattened, and laid on the forehead. A line is drawn round the wax, and the operator then dissects oﬀ as much skin as it covered, leaving undivided a small slip between the eyes. This slip preserves the circulation till an union has taken place between the new and old parts. The cicatrix of the stump of the nose is next pared oﬀ, and immediately behind this raw part an incision is made through the skin, which passes around both alae, and goes along the upper lip. The skin is now brought down from the forehead, and, being twisted half round, its edge is inserted into this incision, so that a nose is formed with a double hold above, and with its alae and septum below ﬁxed in the incision. A little Terra Japonica is softened with water, and being spread on slips of cloth, ﬁve or six of these are placed over each other, to secure the joining. No other dressing but this cement is used for four days. It is then removed and cloths dipped in ghee (a kind of butter) are applied.. . . For ﬁve or six days after the operation, the patient is made to lie on his back; and on the tenth day, bits of soft cloth are put into the nostrils, to keep them suﬃciently open. The artiﬁcial nose is secure, and looks nearly as well as the natural one; nor is the scar on the forehead very observable after a length of time.” In England, The ﬁrst operation of rhinoplasty was performed by Joseph Constantine Carpue on October 23, 1814, in front of a large group of surgical colleagues and his students. Carpue performed the second operation on an army oﬃcer who lost his nose during the Penin- sular War against Napoleon, and later wrote a monograph about it.97 In his book, A Short History of Medicine, the author Erwin Heinz Ackernecht states that “[t]here is little doubt that plastic surgery in Europe, which ﬂourished ﬁrst in medieval Italy, is a direct descendant of classic Indian surgery.”98 A well known European surgeon, who restored 96taken from Ang, 2005. 97Brain, 1993; Carpue, 1816; a brief summary of the history of this procedure in India is provided by Ang, 2005; Rana and Arora, 2002. 98Ackernecht, 1982. p. 41. 140 8. MEDICINE a lost nose, was Branca de Branca from Sicily, using Suśruta’s adjacent ﬂap method. His son, Antonio Branca, used tissue from the upper arm as the reparative ﬂap in his operations (around 1460), and “the Italian method” using a distant ﬂap was born. The method was most extensively described by Gaspare Tagliacozzi in his Chirurgia curtorum in 1597,99 almost two centuries prior to when the British learned. The following procedure was provided by Suśruta in the repair of a nose: “The portion of the nose to be covered should be measured with a leaf. A piece of skin of the required size should then be dissected from the cheek, and turned back to cover the nose. The part of the nose to which this skin is to be attached or joined, should be made raw, and the physician should join the two parts quickly but evenly and calmly, and keep the skin properly elevated by inserting two tubes in the position of nostrils, so that the new nose may look normal. When the skin has been properly adjusted a powder composed of licorice, red sandal-wood, and extract of barberry should be sprinkled on the part. It should be covered with cotton, and white sesame oil should be constantly applied. The patient should take some clariﬁed butter. When the skin has united and granulated, if the nose is too short or too long, the middle of the ﬂap should be divided and an endeavor made to enlarge or shorten it.”100 The Suśruta-Sa ˙mhitā demonstrated a procedure to mend an earlobe with a patch of skin- ﬂap scraped from the neck or the adjoining parts. “The modes of bringing about an adhesion of the two severed parts of an ear-lobe are innumerable; and a skilled and experienced surgeon should determine the shape and nature of each according to the exigencies of a particular case.”101 “A surgeon well-versed in the knowledge of surgery should slice oﬀ a patch of living ﬂesh from the cheek of a person devoid of ear-lobes in a manner so as to have one of its ends attached to its former seat. Thus, the part, where the artiﬁcial ear-lobe is to be made, should slightly scariﬁed (with a knife), and the living ﬂesh, full of blood and sliced oﬀ as previously directed, should be attached to it (so as to resemble a natural ear-lobe in shape).”102 Two thousand years after Suśruta, this operation essentially follows the same procedure. In these operations, “the Indians became masters in a branch of surgery that Europe ignored for another two thousands years,” acknowledges Majno, a well-known historian of medicine.103 Ilza Veith and Leo M. Zimmerman, in their book Great Ideas in the History of Surgery, make a similar conclusion: “It is an established fact that Indian plastic surgery provided basic pattern for Western eﬀorts in this direction.”104 99Sorta-Bilajac and Muzur, 2007. 100Suśruta-Sa ˙mhitā, Sūtrasthānam, 16: 46–51. 101Suśruta-Sa ˙mhitā, Sūtrasthānam, 16: 25. 102Suśruta-Sa ˙mhitā, Sūtrasthānam, 16: 4. 103Majno, 1975, p. 291. 104Veith and Zimmerman, 1993, p. 63. 8.3. SURGERY 141 8.3.2 CATARACT SURGERY The earliest form of cataract surgery, now known as ’couching,’ was ﬁrst introduced by the ancient Hindus. Suśruta explains the procedure in which a curved needle is used to push the opaque phlegmatic matter in the eye out of the way of vision.105 Immediately after the surgery, the eye is sprinkled with breast milk and clariﬁed butter. This procedure of the removal of cataract by surgery was also introduced into China from India. Two poets from the Tang dynasty, Bo Juyi (772–846 CE) and Liu Yuxi (772–842 CE), wrote about a brahmin removing the cataract using a golden probe.106 According to Guido Majno, a professor of pathology from the University of Massachusetts, the cataract operation described by Aulus Cornelius Celsus (25 BCE - 50 CE) is perhaps derived from Suśruta.107 Celsus was a celebrated Roman medical writer and physician. His book De Medicina was a standard book of medicine in Rome. 8.3.3 CARPENTER ANTS SUTURING AND LEECH THERAPY Suśruta used somewhat unconventional from the modern standards but highly successful meth- ods to take care of some surgical issues. In the treatment of intestinal surgery to remove obstruct- ing matter, Suśruta suggested to “bring the two ends of intestines that needed to join together. The intestines should be ﬁrmly pressed together and large black ants should be applied to grip them quickly with their claws. Then the bodies of the ants having their heads ﬁrmly adhering to the spots, as directed, should be severed and the intestines should be gently reintroduced into the original position and sutured up.”108 This may be a crude method for some. However, it was eﬀective procedure and worked well. The leeches were used to suck pus and blood in the cure of boils, tumors, and other similar diseases by Suśruta. He deﬁnes the types of leeches that should be used and provided details of the process. Leeches worked well when the patients were not ﬁt for operations and bleeding was an issue since, with leeches, almost no quality blood was lost.109 Suśruta ﬁrst describes twelve diﬀerent kinds of leeches and suggest to use only six types for the purpose of human treatment. Suśruta suggests that the “leeches should be caught with a piece of wet leather, or by some similar article, and then put in to a large-sized new pitcher ﬁlled with the water and ooze or slime of a pool. Pulverized zoophytes and powder of dried meat and aquatic bulbs should be thrown into the pitcher for their food, and blades of grass and leaves of water-plants should be put into it for them to lie upon. The water and the edibles should be changed every second or third day, and the pitchers should be changed every week.”110 “The aﬀected part [of the patient] should be sprinkled over with drops of milk or blood, or slight incisions should be made into it 105Suśruta-Sa ˙mhitā, Uttaratantra, 17–69: 55 , verses 55–69. 106Deshpande, 2008. 107Majno, 1975, p. 378. 108Suśruta-Sa ˙mhitā, Cikitsāsthānam, 14: 20–21. 109Suśruta-Sa ˙mhitā, Sūtrasthānam, Chapter 13 110Suśruta-Sa ˙mhitā, Sūtra-sthāna, 13: 15. 142 8. MEDICINE in the event of their refusing to stick to the desired spot. . . while sucking, the leeches should be covered with a piece of wet linen and should be constantly sprinkled over with cold water. A sensation of itching and of a drawing pain at the seat of the application would give rise to the presumption that fresh blood was being sucked, and the leeches should be forthwith removed. Leeches refusing to fall oﬀ even after the production of the desired eﬀect, or sticking to the aﬀected part out of their fondness for the smell of blood, should be sprinkled with the dust of powered rock salt.”111 To use these leeches again, Suśruta suggests that the “leeches should be dusted over with rice powder and their mouths should be lubricated with a composition of oil and common salt. Then they should be caught by the tail-end with the thumb and the foreﬁnger of the left hand and their backs should be gently rubbed with the same ﬁngers of right hand from tail upward to the mouth with a view to make them vomit or eject the full quantity of blood they had sucked from the seat of the disease. The process should be continued until they manifest the fullest symptoms of disgorging.”112 Using leeches for surgical procedures is not just an ancient practice. In 2004, the Food and Drug Administration in America cleared the use of leeches (Hirudo medicinalis) as a “med- ical device” appropriate for certain procedures. Today, surgeons use leeches often in procedures that require skin grafting or regrafting amputated appendages, such as ﬁnger or toes. If the veins do not ﬂow blood to the damaged region, leeches are used to ooze the blood so that the body’s own blood supply eventually gets established and the limb survives.113 Also, the saliva of leeches contains an anti-clotting agent, called hirudin, which allows the blood to ﬂow freely and avoid congested skin ﬂaps problem. It also has hyaluronidase, histamine-like vasodilators, collagenase, inhibitors of kallikrein and superoxide production, and poorly characterized anaes- thetic and analgesic compounds. Thus, the saliva is analgesic, anaesthetic and has histamine-like compounds.114 The therapy is pretty inexpensive, with each session taking about 40 minutes and leeches worth $7–10.115 For each session, a new group of leeches are used and dumped as in- fectious waste material after the treatment. In Germany alone, about 350,000 leeches were sold in 2001.116 Their use is even more prevalent now. In a study conducted at the Department for Internal and Integrative Medicine, University of Essen, Germany, sixteen people in the test group were recruited who endured persistent knee pain for more than six months and had deﬁnite radiographic signs of knee osteoarthritis. Ten out of sixteen proceeded with leech therapy and avoided conventional treatment while the remaining six tried only the conventional treatment. In all patients with leech therapy, no adverse eﬀect or local infection was observed. Some patients described the initial bite of leeches as painful. It was 111Suśruta-Sa ˙mhitā, Sūtrasthānam, 13: 18. 112Suśruta-Sa ˙mhitā, Sūtrasthānam, 13: 19–20. 113Michalsen et al., 2001; Michalsen et al., 2006; Rados, 2004. 114Michalsen et al., 2001; Oevi et al., 1992. 115Rados, 2004. 116Michalsen et al., 2001. 8.4. HINDU MEDICINE IN OTHER WORLD CULTURES 143 found that the group with leech therapy did considerably better than the group with conventional therapy. Their pain was reduced signiﬁcantly after three days and the good eﬀects lasted up to four weeks. Later, a second group with 52 people was was experimented with similar therapy that yielded similar results.117 8.4 HINDU MEDICINE IN OTHER WORLD CULTURES The Hindu medicine was popular in China, the Middle East, and Europe from the ancient period. Ktesias, a Greek physician who lived in the Persian court during the early ﬁfth-century BCE for some 17 years, wrote that the Indians did not suﬀer from headaches, or toothaches, or ophthalmia.118 They also did not have “mouth sores or ulcers in any part of their body.”119 Claudius Aelianus (175–235 CE), who lived during the period of Emperor Septimus Severus in Rome, preferred drugs from India in comparison to the Egyptian drugs. He wrote: “So let us compare Indian and Egyptian drug and see which of the two was to be preferred. On the one hand the Egyptian drug repelled and suppressed sorrow for a day, whereas the Indian drug caused a man to forget his trouble for ever.”120 This statement implies that the Indian herbs and drugs were well received by the Romans. Al-Bīrūnī (973–1050 CE) mentions the availability of an Arabic translation of Caraka- Sa ˙mhitā in the Middle East.121 As Arab medicine became popular in Europe, the name of Caraka is repeatedly mentioned in medieval-Latin, Arabic, and Persian literature on medicine.122 Al-Jāh. iz (ca. 776–868 CE), a Muslim natural philosopher from Arabia, acknowl- edged that the Hindus possess a good knowledge of medicine and “practice some remarkable forms of treatment.”123 “They were the originators of the science of ﬁkr, by which a poison can be counteracted after it has been used.”124 S. ā‘id al-Andalusī (d. 1070 CE) of Spain also acknowledged the vast knowledge of the Hindus in medicine. “They [Hindus] have surpassed all the other peoples in their knowledge of medical science and the strength of various drugs, the characteristics of compounds and the peculiarities of substances.”125 Nearby in England, Roger Bacon (1214–1292), a twelfth century natural philosopher, wrote a book for the Pope and noticed that the Indians “are healthy without inﬁrmity and live to a great age.”126 Marco Polo, an Italian traveler, also noticed the long lives of the Hindus. “[T]hese Brahmins live more than any other people in the world, and this comes about through little eating and drinking, and great abstinence which they practise [practice] 117Moore and Harrar, 2003. 118McCrindle, 1973, p. 18. 119McCrindle, 1973, p. 18. 120Aelianus, 1958, 4: 41. 121Sachau, 1964, p. XXVIII. 122Royle, 1837, p. 153. 123Pellat, 1969, p. 197. 124Pellat, 1969, p. 197. 125Salem and Kumar, 1991, p. 12. 126Bacon, 1928, Opus Majus, p. 372. 144 8. MEDICINE more than any other people. And they have among them regulars and orders of monks, according to their faith, who serve the churches where their idols are, and these are called yogis, and they certainly live longer than any others in the world, perhaps from 150 years to 200.”127 It is likely that Marco Polo was overstating their longevity in his reference to brahmins living upto to 150 to 200 years. However, the point remains. The Hindus were known to have lived long lives. “Hindoo [Hindu] works on medicine having been proved to have existed prior to Arabs, little doubt can be entertained,” writes John Forbes Royle (1798–1858), in his book Antiq- uity of Hindoo Medicine, to advocate the antiquity of Hindu medicine and its role in modern medicine.128 “We can hardly deny to them [Hindu] the early cultivation of medicine; and this so early, as, from internal evidence, to be second, apparently to none with whom we are ac- quainted. This is further conﬁrmed by the Arabs and Persians early translating of their works; so also the Tamuls [Tamils] and Cingalese [Singhalese, people of Sri-Lanka] in the south; the Tibetans and Chinese in the East; and likewise from our ﬁnding, even in the earliest of the Greek writers, Indian drugs mentioned by corrupted Sanscrit [Sanskrit] names. We trace them at still earlier periods in Egypt, and ﬁnd them alluded to even in the oldest chapters of the Bible.”129 Royle served as surgeon for the East India Company and lived in India. His interest in traditional botanical Hindu remedies of various diseases led him to write his classic book. Abu Yusuf Ya‘aub ibn Ishaq al-Kindī, popularly known as al-Kindī (ca. 800–870 CE), is considered to be the “philosopher of Arabia.” He was born and lived in Baghdad. He wrote a medical formulary, called Aqrābādhīn, which was translated by Martin Levey into English.130 While studying the materia medica deﬁned by al-Kindī, Levey concludes that about 13 percent comes from the Indian region. In his view, “many of the Persian materia medica may more prop- erly be considered to be Indian.”131 In that case, the Indian-Persian materia medica in al-Kindī’s work turns out to be about 31 percent.132 Alī B. Rabban Al-T. abarī (783–858 CE), a Persian physician from Tehran, who later lived in Baghdad serving Caliph al-Mutawakkil (reigned 847–861 CE) as his physician, wrote an encyclopedic book on medicine, Firdaws al-H. ikmah (Paradise of Wisdom).133 It was translated into English by Muh. ammad Zubair Siddiqi in 1928.134 This book contains some thirty-six chapters on Hindu medicine and refers to the works of noted Indian physicians/thinkers such as Caraka, Suśruta, Cān. akya (Kaut.ilaya), Mādhavakara, and Vagbhata II. Al-T. abarī mentions three dos. a and seven dhātu of ayurveda for medical treatments. This is in accordance with the tradition of ayurveda in India. 127Needham, 1981, p. 81. 128Royle, 1837, p. 62. 129Royle, 1837, p. 152. 130al-Kindī, 1966. 131al-Kindī, 1966, p. 20. 132Levey and al-Khaledy, 1967, p. 33. 133see Meyerhof, 1931; Dictionary of Scientiﬁc Biography, 13: 230. 134Siddiqi, 1928. 8.4. HINDU MEDICINE IN OTHER WORLD CULTURES 145 Max Meyerhof has written excellent accounts of al-T. abarī’s work and connected it with Suśruta-Sa ˙mhitā, Caraka-Sa ˙mhitā, the Nidāna and the As. t. ā ˙ngahr. dava-Sa ˙mhitā. The Nidāna is a work on pathology written by Mādhavakara. This work was translated into Arabic under the patronage of Hārun al-Rashīd. The As. t. ā ˙ngahr. dava-Sa ˙mhitā is the work of Vagbhata II.135 Max Meyerhof concludes the existence of Indian drugs in Arabic treatises: “We ﬁnd indeed, in the earliest Arabic treatises on medicine, the mention of many Indian drugs and plants which were unknown to Greeks, and all of them bearing Sanskrit names which had passed through the New Persian language.”136 Triphalā is a popular drug in India. The word Triphalā means “three-fruits” since the drug is made from three ingredients: haritaki or simply har (Terminalia chebula), bahera (Terminalis belerica), and āmalaki (Phyllanthus emblica). The Arabs used the term atrifal for triphalā that is similar in pronunciation, while the Chinese literally translated the term and called it san-teng, implying three herbs.137 These literary evidences are examples of the transmission of medical knowledge from India to Arabia and China. In studying the transmission of ayurvedic knowledge to China, Chen Ming, a Chinese scholar, suggests that “scholars of medical history have long been well aware of the Indian inﬂu- ence on Chinese medicine.”138 In providing examples of such knowledge, he cites the division of medicine into eight branches in Chinese books, as done by Caraka and Suśruta. Dharmaks.ema, a scholar, in his book Daban nie jing, followed the same division in 421 CE. Paramārtha (499– 569 CE) translated a Sā ˙mkhya text, jinqishilum, that refers to eight divisions of medical reme- dies. Sun Simiao (581–682), a medical writer and physician for the Sun and Tang dynasties, wrote about ayurvedic practices in his work Beiji Qianjin yao fang (Important medicinal formu- lae [worth] a thousand [pieces of ] gold). He mentions Jīvaka’s story, discussed in Section 8.1, that all plant life has medicinal value. Simiao is known for the text “On the Absolute Sincerity of Great Physicians,” popularly known as the Chinese Hippocratic Oath, written in the ﬁrst chapter of the above-mentioned book. This oath is still required reading for Chinese physicians. Simiao also attributed several medicinal formulations to Jīvaka: Jīvaka’s ball medicine for ten thousand illnesses, Jīvaka’s medicines for illnesses caused by evil spirits, Jīvaka’s soup, Jīvaka’s medicine for prolonging life without getting old. He introduced “chan” or “dhyāna (meditation) and yoga into China, and also introduced a particular massage technique and called it Brāhmin’s method.139 Tombs in Turfan (also Turpan, 42(cid:14)590N, 89(cid:14)110E, near the Silk Road) yield medical frag- ments in Sanskrit and Tocharian, the local language. Fragments of the ayurvedic texts, Bhela Sa ˙mhitā, Siddhasāra, and yoga-śataka, have been found in these tombs. The epitaph of Lüsbuai (Battalion Commander) Zhang Xianghuan (681 CE) mentions two ayurvedic physicians, Jī- 135Meyerhof, 1931 and 1937. 136Meyerhof, 1937. 137Mahdihassan, 1978. 138Ming, 2006. 139Deshpande, 2008. 146 8. MEDICINE vaka and Nāgārjuna. In his studies, Chen Ming concludes that “Indian medicine also inﬂuenced medical practices in Medieval Turfan.”140 Su Jing in the seventh century revised the Tang pharmacopoeia called or Xinxiu bencao (Newly revised materia medica) and noted down a remedy for Beriberi. He deﬁned the prescrip- tion as ‘Brahmin’s prescription’. In 752 AD, Wang Tao of the Tang dynasty wrote a large com- pendium, Waitai miyao fang (Medical secrets of an oﬃcial). This book again records a treatment of beriberi using the ‘Brahmin’s prescription’. Both of these records suggest that a successful cure for Beriberi came to China from India.141 140Ming, 2006. 141Deshpande, 2008. C H A P T E R 9 The Global Impact 147 The preceding chapters covered the multi-faceted concepts of Hindu science: numeral sys- tem with its place-value notations; mathematical processes that cover arithmetic, algebra, and trigonometry; the shape of the Earth and planetary motions; the constitution of matter; the properties of matter; standards for mass, length and time; and physical and chemical processes involved in the making of drugs, poisons, and new compounds, so-called plastic surgery, rust- free Iron Pillar, yoga, etc. These chapters basically cover most branches of modern science and provide the substantial contributions that the ancient Hindus made to science. Also, as men- tioned in Chapter 1, the rationale of why the American Association for the Advancement of Science (AAAS) decided to credit the Hindus for their knowledge in mathematics and astron- omy is also provided. These chapters also provided the global impact of speciﬁc discoveries and inventions of the ancient Hindus. The current chapter focuses only on some additional new information. If we need to mention just one thought that is central to Hinduism and which could play an important role in the future of humanity as it did in the past, it is a hymn of R. gveda: “To what is One, sages call by diﬀerent names.”1 The underlying meaning is that God is one and people call Him by diﬀerent names. Though this doctrine is not a part of science, it is perhaps the most timely message in view of the religious strife around the world. Al-Bīrūnī, an Islamic philosopher, understood this well when he wrote: “The Hindus believe with regard to God that he is one, eternal, without beginning and end, acting by free will, almighty, all-wise, living, giving life, ruling, preserving, . . .”2 It is due to the impact of this doctrine that the Hindus did not subjugate other religions and tried to spread their own message by winning the hearts of people. Christians, Jews, Zoroastrians, and Muslims found refuge in India at diﬀerent times in history and could ﬂourish there. Out of the currently 2.6 million population of Zoroastrians in the world, most live in India, a country of refuge. In contrast, elsewhere in world history, there have been more wars in the name of religion than on anything else. For the ancient (and modern) Hindus, exploring the truth, including science, was consid- ered helpful in achieving liberation (moks. a). Therefore, scientiﬁc investigations were encouraged through religious codes, as explained in Chapter 2. Long before the Christian era, the ancient Hindus had established an educational system which was comparable to the present university system. The intellectual centers of Nālandā (near Patna, India), Taxila (Taks.aśilā, near Islam- 1R. gveda, 6: 22: 46. 2Sachau, 1964, vol. 1, p. 27. 148 9. THE GLOBAL IMPACT abad, Pakistan), Kānchipuram (Tamilnadu, India), Vikramśilā (Bihar, India), Varanasi (Uttar Pradesh, India), and Valabhi (Gujrat, India) were perhaps the most well known during the an- cient period. Taxila was visited by Alexander the Great and later supported by Aśoka. It had a large number of stūpas (pillars) and monasteries. The center of Taxila was destroyed during the ﬁfth century by the Huns. Nālandā (near Patna, Bihar) is the place where Nāgārjuna and Āryabhat.a I taught. Nālandā was visited by three famous Chinese visitors: Faxian (or Fa-Hien), Xuan Zang (or Hiuen Tsang), and Yijing (or I-tsing). At one time, it had about 10,000 stu- dents, 1,500 teachers, and 300 classrooms. It was completely destroyed in 1193 by the army of Bakhtiyar Khilji. The library was set on ﬁre and, due to the extensive collection of books, it took over three months for the ﬁre to be extinguished. Other intellectual centers, such as in Varanasi, destroyed in 1194 CE by Qutb-ud-din Aibak, and Mathura, destroyed in 1018 CE by Mahmud of Ghazni, also suﬀered.3 Substantially greater eﬀort is required in order to unearth and fully comprehend the foun- dational stones of a vast intellectual treasure that we owe to the ancient Hindus. For some reason, the scholarship of the last century on Hindu science is scant and has not received the interest of scholars as it did during the nineteenth century. There are only a small number of courses on Hinduism in the West, while courses that focus on the anthropological studies of India and sen- sational issues, such as sati, the caste-system, eroticism in literature, human traﬃcking, etc. have been steadily growing. At the time of this writing, there is not even a single course in America that deals primarily with Hindu science. In contrast, the ancient Greeks, whose contributions to science were comparable to those of the Hindus, are covered in various courses in most univer- sities. The main reason is that most academic institutions are shaped by the interests of donors. It may sound ridiculous to some; however, it is the brutal reality of academia. Princeton Uni- versity oﬀered 13 courses just on Greece during the Spring 2008 semester. This is in part due to Stanley J. Seeger’s endowment to the university.4 Similar endowments for Hinduism are lacking and there is little or no support from the governments of various countries. This is not the case with other religions. Most of the knowledge of the ancient Hindus was transferred to the West via the Islamic domination of Europe. This transfer of knowledge is reminded by the Sanskrit words that are now a part of the English language in original or metamorphosed form. A list of these words makes a strong case for the Hindu science, as they are related to the scholarly tradition of the ancient Hindus. Numbers (two, three, six, seven, eight, and nine), pundit, guru, read, sine (as a trigonometric function), geometry, zero, sulfur, gold, silver, lead, uterus, yoga are some of the 3I have decided to avoid any description of the destruction that the ancient Hindus and their institutions had to deal with. The destruction of Baghdad by Hulagu Khan, the destruction of Spain during the Inquisition, and the destruction of Alexandria by a religious zealot group are some examples of how a country or a culture can be subdued. Most examples of destruction cited here outside the Indus-Valley region occurred for a short period. In contrast, the Hindus faced subjugation and destruction of their intellectual centers for nearly a millennium. It is magical the way India, with majority Hindu popula- tion, has bounced back in science and technology even after many centuries of foreign rule during Mogul and colonial period that tried to destroy the educational system of Hindus and extinguish their spirit to search for truth. 4Arenson, 2008. 9.1. IMPACTS DURING THE ANCIENT AND MEDIEVAL PERIODS 149 examples of the Sanskrit words in English.5 All cultures have words to deﬁne a scholar in their languages. However, it is the Sanskrit word “guru” or “pundit” that has prevailed in English. 9.1 IMPACTS DURING THE ANCIENT AND MEDIEVAL PERIODS During the ancient and medieval periods, the Hindu corpus attracted the great minds from all over the world, such as: Pythagoras, Apollonius of Tyana, and Plotinus from the Greek or Roman tradition; al-Bīrūnī, al-Fazārī, Ibn Sīnā, al-Jāh. iz, al-Khwārizmī, al-Mas‘udī, Kūshyār Ibn Labbān, and al-Uqlidīsī from the Islamic tradition; Faxian (Fa-Hien), Xuan Zang (or Hi- uen Tsang), and Yijing (or I-tsing) from the Chinese tradition; and Pope Sylvester, S. ā‘id al- Andalusī, Roger Bacon, Adelard of Bath, and Leonardo Fibonacci from the European tradition. The ancient Hindus invented the game of chess, called catura ˙nga in Sanskrit. The word signiﬁes “four members of an army”—elephants, horses, chariots, and foot soldiers. It was called al-śatranj in Arabic. In the game, a key move is made to trap the king, called eschec in French and “check” in English. This led to the word chess for the game. The game epitomizes the science of warfare that helped the ancient and medieval strategists in warfare. The role of horses, elephants, foot-soldiers, chariots, and the king are well deﬁned in a set conﬁguration. The main task was to protect your own king and kill the king of your enemy. S. ā‘id al-Andalusī, (died in 1070 CE) of Spain considered the discovery of chess as a testimony to the “clear thinking and the marvels of their [Hindu] inventions. . . . While the game is being played and its pieces are being maneuvered, the beauty of structure and the greatness of harmony appear. It demonstrates the manifestation of high intentions and noble deeds, as it provides various forms of warnings from enemies and points out ruses as well as ways to avoid dangers. And in this there is considerable gain and useful proﬁt.”6 Today, chess is played all over the world and international tournaments are conducted to select a world champion. 9.1.1 IMPACT ON ARABIA The work of al-Khwārizmī in Baghdad was made possible due to the discoveries and inventions of the ancient Hindus. Al-Khwārizmī work led to the inclusion of several new words in the English dictionary: algebra, zero, algorithm, sine function, to name a few. His books were read by established scholars in Europe, such as Copernicus, Adelard of Bath, and Leonardo Fibonacci, either in Arabic or in translation. Al-Khwārizmī’s main contributions were to compile Hindu 5amrita, Aryan, ashram, atman, acharya, ahimsa, bandana, basmati, candy, cheetah, cot, jackal, jungle, karma, kin, kun- dalini, lemon, mahout, man, Mandarin, mantra, maya, mix, namaste, nirvana, orange, pajamas, puja, samadhi, sapphire, shampoo, sugar, swastika, tantra, yoga, yogi, and zen are non-science representative words that are of Sanskrit in origin. The followers of Lord Kr.s.n. a celebrate festivals by carrying images of Him in a huge wagon all over India. Lord Kr.s.n. a’s another name is Jagan-nāth, the lord of the world. For Europeans, it was a waste of time and money for senseless devotion. Thus, the word juggernaut evolved to deﬁne large overpowering and destructive forces or objects. Similarly, thug and dacoit are also Sanskrit in origin. In some case the path of adoption is a bit convoluted. 6Salem and Kumar, 1991, p. 14. 150 9. THE GLOBAL IMPACT knowledge of mathematics and astronomy in his books, as indicated from the title of his books. It was the Hindu mathematical tools that allowed Copernicus to ﬁgure out his heliocentric solar system. Copernicus knew some mathematical tools of the ancient Hindus that he may have learned during his stay in Italy where people like Pope Sylvester and Leonardo Fibonacci had already documented the mathematics of the Hindus. As mentioned earlier, Copernicus opted to use Hindu arithmetic in writing his book, De revolutionibus orbium coelestium (On the Rev- olutions of the Heavenly Spheres). Copernicus is not the only celebrated scientist who was beneﬁted with the contributions of the ancient Hindus; the table of parallax of the Moon that was suggested by Johannes Kepler (1571–1630) was identical to the one given by Brahmgupta in Khan. d. a-Khādyaka almost a millennium ago, as inferred by Otto E. Neugebauer in his analysis.7 Khalīl wa Dimna is one of the celebrated books in the Islamic world. This book is based on an Indian book, the Pañca-tantra, meaning “ﬁve-principles.” The original Sanskrit book was written before the Christian era by Vis.n. u Sharma to educate the sons of an Indian king on human conduct and the art of governing (nīti) using animal fables. Burzuwaih (or Borzuy), a personal physician of Anoushiravan (ﬂ. 550 CE) of the Sassanid dynasty, made a trip to India to collect medicinal herbs for the king. He came back with the book and translated it into the Persian language. After the Islamic conquest of Persia, the book was translated by Ibn al- Muqaﬀa (8th century CE) into Arabic as Khalīl wa Dimna where Khalīl and Dimna are the two jackal characters in several stories in the book. All stories ended with a question and the next story was the answer of the previous question. These stories have ethical, social, and political wisdom. Khalīl wa Dimna became popular in the Middle East and was known in Europe by the eleventh century. S. ā‘id Al-Andalusī praised the contents of Khalīl wa Dimna in his book T. abaqāt al-‘Umam and correctly labeled Hind as the country of origin. In his view, the book is useful for the “improvement of morals and the amelioration of upbringing” and “is a book of noble purpose and great practical worth.”8 9.1.2 IMPACT ON CHINA Mandarin is one of the two most prominent languages in China and sets the norms of aristo- cratic communication—a language used by the upper class. It was the spoken language of the bureaucrats who were courteous and polite in their behavior. The word itself is derived from the Sanskrit word mantrin, meaning a minister or councilor. Even today in India, all cabinet min- isters are called mantrī and the Prime-minister is called Pradhān-mantrī, meaning the prime councilor. The Sanskrit language inﬂuenced the aristocrats of China who adopted the language. As a result, some Sanskrit words entered in the Chinese language. For example, ks. an. a (a mo- ment), śarīra (body) and nirvana in Sanskrit became chānā, shélizi, and niepān, respectively, in Chinese. Of course, the most signiﬁcant example of this inﬂuence is the fact that Buddhism 7Neugebauer, 1962, p. 124. 8Salem and Kumar, 1994, p. 14. 9.1. IMPACTS DURING THE ANCIENT AND MEDIEVAL PERIODS 151 became the most prominent religion in China without any war or conﬂict. This is in contrast to several other nations where people had to choose between their lives or their religion. Such was the inﬂuence of India on China. 9.1.3 IMPACT ON GREEK SCIENCE AND PHILOSOPHY Cyrus the Great (558–530 BCE) of Achaemenid Dynasty ruled all the way from Greece to the Indus River. Being part of a common empire, the Greeks learned about India. In 327 BCE, Alexander the Great fought back, regained Greece from Persia, and later controlled Persia and India. When the army of Alexander could go through hostile conditions to reach India, it was also possible for a lone scholar to visit India too. The historical documents provide information about the inﬂuence of Indian philosophy on two prominent Greek or Roman philosophers. Pythagoras Pythagoras advocated vegetarianism, metempsychosis (transmigration of the soul from one physical body to another, just as we cast oﬀ old clothes and wear new one), fasting as a way of puriﬁcation, chastity as a virtue, and the sanctity of animal life that must be honored. He promoted orality in the preservation of knowledge, monism as an ideology, and believed on the existence of a soul in plants, animals, and humans. The above-mentioned doctrines of Pythago- ras were essential to his school, and were practiced by his followers in the West for almost a millennium. These doctrines were new to Greece during the period of Pythagoras. Elsewhere, there is only one place in the world where all the above-mentioned doctrines existed prior to Pythagoras. This is the land of the Hindus, the Indus-Sarasvatī region. As is the case with the Hindu tradition, Pythagoras did not write any book since he contended that knowledge should be veiled from undesirable people; only oral communication was used to transfer knowledge. Apollonius of Tyana (15–100 CE), a noted Pythagorean philosopher, learned the doctrine of nonviolence or the sanctity of human and animal life in the tradition of Pythagoras who, in Apollonius’ view, was himself taught by Hindu philosophers. Philostratus quotes the words of Apollonius: “I did not sacriﬁce, I do not: I do not touch blood, even on the alter, since that was the doctrines of Pythagoras. . . it was the doctrines of the Naked Philosophers of Egypt and the Wise Men of India, from whom Pythagoras and his sect derived the seeds of their philosophy.”9 Apollonius correctly considered the Indian civilization to be much more ancient than the period of Pythagoras. “Pythagoras was anticipated by the Indians, lasts not for brief time, but for an endless and incalculable period,” opines Apollonius.10 Apollonius was a person of repute, visited India, and was compared with Jesus of Nazareth by some Christians during the early centuries of Christianity. Titus Flavius Clemens (c.150–215 CE), popularly known as Clement of Alexandria, was a Christian theologian who was familiar with classical Greek philosophy and literature. He 9Book 8, Chapter 7, 12; Philostratus, 1960, vol. 2, p. 339. 10Philostratus, 1960, vol. 2, p. 49. 152 9. THE GLOBAL IMPACT believed that the Greek philosophy had non-Greek origins. Similar to Apollonius, Clement, in his book Stromata (The Miscellanies), writes that Pythagoras went to Persia and came in contact with the Brahmins. In his view, Pythagoras learned philosophy from his interactions with these brahmins: “Pythagoras was a hearer of . . . the Brahmins.”11 Eusebius of Caesarea (263–339 CE), a Roman Christian historian, in his book Praeparatio Evangelica (Preparation for the Gospel) mentions Pythagoras’ visit to Babylon, Egypt and Persia. Similar to Apollonius of Tyana and Clement of Alexandria, Eusebius also shares the opinion that Pythagoras “studied under the Brahmans [or Brahmins],” and learned geometry, arithmetic, and music from these foreign lands. Eusebius is also quite clear in his statement that Pythagoras learned “nothing” from the Greek philosophers and “became the author of instruction to the Greeks in the learning which he had procured from abroad.”12 The visit of Pythagoras to India was conclusive in the mind of Voltaire (1694–1778) (pen name of Francois Marie Arouet) as he writes that “Pythagoras, the gymnosophist, may alone serve an incontestable proof that true science was cultivated in India. . . . It is even more prob- able that Pythagoras learned the properties of the right-angled triangle from the Indians, the invention of which was afterward ascribed to him.”13 According to Voltaire, “The Orientals, and particularly the Indians, treated all subjects under the veil of fable and allegory: for that reason Pythagoras, who studied among them, expresses himself always in parables.”14 Voltaire had no doubt about Pythagoras’ visit to India and wrote: “All the world knows that Pythagoras, while he resided in India, attended the school of Gymnosophists and learned the language of beasts and plants.”15 D. E. Smith, a noted historian who is known for his classic book, History of Mathematics, points out a resemblance between the Hindu and Pythagorean philosophies: “In spite of the as- sertions of various writers to the contrary, the evidence derived for the philosophy of Pythagoras points to his contact with the Orient. The mystery of the East appears in all his teaching . . . indeed his [Pythagoras’] whole philosophy savors much more of the Indian than of the Greek civilization in which he was born.”16 On a possible Indian inﬂuence on Pythagoras in comparison to Egyptian inﬂuence, H. W. Rawlinson (1810–1895 CE) concludes: “It is more likely that Pythagoras was inﬂuenced by India than by Egypt. Almost all the theories, religious, philosophical, and mathematical, taught by the Pythagoreans were known in India in the sixth century B.C. [BCE].”17 Rawlinson is the person who ﬁrst decoded cuneiform language of Babylon after discovering the Darius’ Behistun inscriptions. He also served the British empire and lived in India. 11Stromata, Book 1, Chapter 15. 12Praeparatio Evangelica, Book 10, Chapter 4. 13Voltaire, 1901, vol. 29, p. 174. 14Voltaire, 1901, vol. 24, p. 39. 15Voltaire, vol. 4, p. 47. 16Smith, 1925, vol. I, p. 72. 17Rawlinson, p. 5 in the book by Garratt, 1938. 9.1. IMPACTS DURING THE ANCIENT AND MEDIEVAL PERIODS 153 Plotinus Plotinus (205–270 CE), the founder of the Neo-Platonic school, attempted to visit India to learn from Brahmins while he was in Alexandria. He joined the army of Emperor Gordian III during his expedition to Persia in 242 CE against the Sassanians king, Sapor, in hopes of visiting India. This is obviously a major sacriﬁce for a philosopher to pick up weapons and ﬁght, just for learning from India. However, he was not the ﬁrst. Before Plotinus, Pyrrhon pursued a similar dream to visit India by joining Alexander’s army. Pyrrhon succeeded while Plotinus failed since Gordian III was assassinated in Mesopotamia, and Plotinus could not fulﬁll his dream of an Indian expedition.18 Plotinus moved to Antioch and later to Rome where he spent the rest of his life. Plotinus also did not write any book, following in the footsteps of Pythagoras and Socrates and the Hindus. Similar to the oral tradition of the Hindu, he only gave lectures while living in Rome. His lectures were later compiled by his followers under the title Enneads. Ammonius Sakkas, Plotinus’ teacher, was perhaps an Indian since his name is not a typical Greek name, and is similar to a Sanskrit name, where Śākya means a monk.19 Porphyry, a disciple of Plotinus, tells us that Plotinus “acquired such a mastery of philosophy, that he became eager to gain knowledge of the teaching prevailing among the Persians, as also among the Indians.”20 It is pretty clear that association with Ammonius kindled a desire in Plotinus to join Emperor Gordian’s military expedition to Persia and India. The inﬂuence of the Hindu philosophy on Neo-Platonism has been suggested by scholars over the years. Rawlinson writes: “It certainly appears probable that Neo-Platonism was aﬀected by Oriental [Hindu] philosophy . . . Hence we may suppose that the doctrines it inculcates, – abstinence from ﬂesh, subjection of the body by asceticism, and so on—are derived from Oriental [Hindu] sources.”21 Rawlinson concludes: “the debt of Neo-Platonism to Oriental sources is indisputable . . .” Plotinus “produced a new philosophical synthesis: Greek rationalism in the service of Oriental mysticism,” as suggested by Jean W. Sedlar.22 In Plotinus’ philosophy, the human soul is a part of the world-soul, implying that we all have divinity within us. When Plotinus was close to death, as we know from his student Porphyry, he said, “I am striving to give back the divine which is in me to the divine in the universe.”23 This implies that his individual soul will merge with the cosmic divine soul. This is the core essence of the Hindu philosophy of Aham brahmāsmi (I am the God), which is central to the Vedas and Upanis. ads24 and is currently propagated by the New Age movement in America. Thomas McEvilley, in his book The Shape of Ancient Thought, explored the Greek works and compared them with Indian thoughts. On the question of exchanges between these two cultures, McEvilley suggests that “[i]t can be argued that Plato was already Indianized through 18Sedlar, 1980, p. 292; McEvilley, 2002, p. 550. 19Sedlar, 1980, p. 292; Halbfass, 1988, p. 17. 20Gregorios, 2002, p. 17; McEvilley, 2002, p. 550. 21Rawlinson, 1926, p. 175. 22Sedlar, 1980, p. 292. 23MacKenna, 1956, sec. 1, p. 1. 24Br.hadāran. yaka Upanis.ad, 1: 4: 10. 154 9. THE GLOBAL IMPACT Orphic and Pythagorean inﬂuences, and on that basis alone some, at least, of his works cannot be regarded as ‘purely Greek thought.’ Plotinus, then may have received the Indian inﬂuence from Gymnosophists in Alexandria, or from the works of Plato, or both; it comes to the same thing: he was philosophizing in an Indianized tradition. It is not just a question of whether Plotinus’ philosophy was derived from India by him. Its major outlines, in the view presented in this book, had been derived from India almost a thousand years earlier and handed down through what might be called the Indianized, or Indian-inﬂuenced, strand of Greek philosophy, to which Plotinus emphatically belonged. He could, then, and perhaps would, have come up with his model of things without any additional Indian input in his lifetime, though it seems clear, in any case, that he had some.”25 IMPACTS DURING THE MODERN PERIOD 9.2 The literature of the ancient Hindus continued to attract modern scientists and philosophers: Ralph Waldo Emerson, Johann Wolfgang von Goethe, Johann Gottfried Herder, Aldous Hux- ley, Carl Jung, Max Müller, Robert Oppenheimer, Erwin Schrödinger, Arthur Schopenhauer, Nikola Tesla, Henry David Thoreau, and Hideki Yukawa, to name a few. These scholars found the origin or validity of their ideas in Hindu literature. “India has had a signiﬁcant impact upon the manner in which Europe has articulated, deﬁned, and questioned itself and its fundamen- tal and symptomatic concepts of theory, science and philosophy,” write Wilhelm Halbfass.26 This view is supported by the fact that many European philosophers, including Goethe, Jung, Herder, Humboldt, and Schopenhauer studied Hindu books and introduced Hindu concepts in their own works.27 Voltaire (Actual name, Francois-Marie Arouet; 1694–1778 CE), a French historian, philosopher, and dramatist, visited India, Egypt, and Arabia during the eighteenth century, and was well versed with the history of these regions. In the view of Voltaire, “As India supplies the wants of all the world but is herself dependent for nothing, she must for that very reason have been the most early civilized of any country. . .”28 In Voltaire’s view, Indian science was more ancient than Egyptian science. The recent excavations in Margarh are proving him right. Voltaire writes, “If the question was to decide between India and Egypt, I should conclude that the sciences were much more ancient in the former [India],”29 Voltaire is not alone in assign- ing priority to the Indians in comparison to Egypt. Benjamin Farrington, a noted historian of science, expressed similar views in his analysis of the Pythagorean Theorem. “The degree of this knowledge, and the possibility of this diﬀusion from a common center [center], are questions that may one day be answered with a conﬁdence that is now impossible. But when the answer is given, if it ever is, perhaps neither Babylon nor Egypt will appear as the earliest exponent of 25McEvilley, 2002, p. 550–551. 26Halbfass, 1988, p. 159. 27Sedlar, 1982 and 1980. 28Voltaire, 1901, vol. 29, p. 180. 29Voltaire, 1901, vol. 24, p. 41. 9.2. IMPACTS DURING THE MODERN PERIOD 155 civilization. The Nile and the Euphrates may have to yield place to the Indus [India].”30 This is in reference to the ancient Hindus’ Śulbasūtra that contains the so-called Pythagorean Theorem long before it was proposed by Pythagoras. “I am convinced that everything has come down to us from the banks of the Ganges, - astronomy, astrology, metempsychosis, etc. . . It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry. . .But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins’ science not been long established in Europe,” wrote Voltaire in a letter in 1775. Johann Gottfried Herder (1744–1803), a German philosopher and poet, considered the Ganges region as “the primordial garden” where human wisdom started and was nourished, and the birth place of all languages, the Sanskrit language being the mother. He also considered Sanskrit poetry as the mother of all other poetry, indicating Vedic literature as the source of most other poetry works elsewhere.31 Herder inﬂuenced another famous German philosopher and poet, Johann Wolfgang von Goethe (1749–1832 CE). Goethe’s interest in India came with his reading of Kālīdāsa’s famous works – Śakuntalā and Meghduta—and ﬂourished with his in- teraction with noted philosophers such as Johann Gottfried von Herder.32 Goethe even tried to learn Sanskrit to read Hindu literature.33 He tried to visit India, but without success.34 Goethe’s poor health did not allow him to take the arduous sea journey to India. His popular drama, Faust, was inspired by his reading of the German translation of Śakuntalā by Forster in 1791.35 He also wrote two ballads dealing with India: “Der Gott und die Bajadere” and “Der Paria.”36 Carl Gustav Jung (1875–1961), a Swiss psychiatrist and psychoanalyst who as a young man collaborated with Sigmund Freud on human psychology, was greatly inﬂuenced with Hindu scriptures. Jung’s contributions to psychology, dream analysis, and New Age movement are immense. Freud and Jung developed diﬀerences on the role of libido on human personality and that caused a break-up in their collaboration and personal friendship. Jung basically lost his social circle where he had not many colleagues to discuss his research. He sought refuge in the Hindu literature for philosophical ideas. The ancient works of Patañjali inﬂuenced Jung greatly. The books of the Hindus not only inﬂuenced his thinking but also provided Jung conﬁrming parallels for his independent insights. “In the absence of like-minded colleagues, Hinduism pro- vided him with evidence that his diﬀerences with Freud were founded on experiences shared by other human beings, therefore were not simply the products of a deranged mind,” writes Harold 30Farrington, 1969, p. 14. 31Patton, 1994, p. 207–208. 32Herder was called German Brahmin by some for his interest in Hinduism. Herder wrote Gedanken einiger Brahmanen (Thoughts of Some Brahmins) in 1792 which was based on Hitopadesha and the Bhagavad-Gītā. To read more about Herder and Hinduism, read Ghosh, 1990. 33Dasgupta, 1973, p. 21. 34Steiner, 1950, p. 1. 35Remy, 1901, p. 20. 36Remy, 1901, p. 20. 156 9. THE GLOBAL IMPACT Coward.37 Jung wrote two articles that directly dealt with his impression of India: “The Dream- like World of India” and “What India Can Teach Us.” Both articles were published in the journal Asia in the 39th volume in 1939. In the second article, Jung provided a very positive view of the Indian civilization. In his view, India was “more balanced psychologically than the West and hence less prone to the outbreaks of barbarism which at that time were only too evident” in Europe.38 It is suggested that the concept of “self,” as developed by Jung was largely based on the Upanis.adic notion of ātman.39 As Jung writes, “The East [India] teaches us another broader, more profound, and higher understanding - understanding through life.”40 According to Jung, the inﬂuence of Hindu literature is nothing new; such inﬂuences “may be found in the works of Meister Ekhart, Leibniz, Kant, Hegel, Schopenhauer, and E. von Hartmann.”41 9.2.1 EMERSON AND THOREAU–TWO CELEBRATED AMERICAN SCHOLARS Ralph Waldo Emerson (1803–1882) and Henry David Thoreau (1817–1862 CE) were two of the most celebrated American scholars of the nineteenth century. They proposed the philosophy of transcendentalism and thereby inﬂuenced generations of Americans and others worldwide. The worldviews of Emerson and Thoreau were inﬂuenced by the sacred books of the Hindus and other classics of India. Emerson was fond of reading the Bhagavad-Gītā and popularized the book among his friends by loaning his personal copy. This personal copy became quite worn in time due to its extensive use.42 Emerson shared his appreciation for the Hindu philosophy in the following language: “This belief that the higher use of the material world is to furnish us types or pictures to express the thoughts of the mind, is carried to its extreme by the Hindoos [Hindus] . . . I think Hindoo [Hindu] books are the best gymnastics for the mind.”43 Thoreau also wrote quite approvingly about the Hindus: “the Hindoos [Hindus] . . . possess in a wonder- ful degree the faculty of contemplation,” “their religious books describe the ﬁrst inquisitive & contemplative access to God,” or “their method is pure wisdom or contemplation.”44 Similar to the Hindu tradition, Thoreau promoted vegetarianism: “I believe that every man who has ever been earnest to preserve his higher or poetic faculties in the best condition has been particularly inclined to abstain from animal food, and from much food of any kind.”45 Russell B. Goodman, in his analysis of Emerson’s work, concludes that “Emerson’s phi- losophy, from his college days onward, grew up together with his knowledge of and interest in 37Coward, 1984. 38Clarke, 1994, p. 62. 39Nicholson, Hanson, Stewart, 2002, p. 116. 40Jung, Collected Works, vol. 13, p. 7. 41Jung, Letters, vol. 1, p. 87. 42Horton and Edwards, 1952, p. 118; taken from Gangadharan, Sarma and Sarma, 2000, p. 311. For more information on Emerson, read Acharya, 2001. 43Emerson, 1904, vol. 8, p. 14. 44Scott, 2007. 45Henry David Thoueau, Walden; or, Life in the Woods, Dover, 1995, p. 139. 9.2. IMPACTS DURING THE MODERN PERIOD 157 Hindu philosophical writings.”46 “His relationship with Hinduism, as with many other systems of thought, was transformative and respectful at once—reconstructive rather than deconstruc- tive.” At the youthful age of seventeen, Emerson wrote that during the ancient period in India “fair science pondered” and “sages mused.”47 Emerson wrote to John Chapman in May 1845 that he “very much want[ed]” the Bhagavad-Gītā to read the dialogs of Lord Kr.s.n. a and Arjuna.48 In August 1845, Emerson went to the mountains of Vermont and read the Vis. n. u-Purān. a. He commented that “[n]othing in theology is so subtle as this & the Bhagwat [perhaps Bhāgvat- purān. a].”49 Emerson’s poem “Hamatreya” is based on a passage from the Vis. n. u-Purān. a, and his essay “Immortality” is based on Kathā Upanis. ad. The beginning of his poem “Brahma” is also derived from Kathā Upanis. ad and the Bhagavad-Gītā, concludes Philip Goldberg, in his book American Veda.50 “The borrowings were not aesthetic embellishments; they were central to Emerson’s worldview.” Thoreau praised Hindu literature in his writing: “What extracts from the Vedas I have read fall on me like the light of a higher and purer luminary . . . It rises on me like the full moon after the stars have come out, wading through some far summer stratum of the sky.”51 A. K. B. Pillai, in his book Transcendental Self: A Comparative Study of Thoreau and the Psycho- Philosophy of Hinduism and Buddhism, evaluated the connections between the tenets of Hinduism and transcendentalism and concluded that “Walden is the closest to the Yogic system of all major American writings.”52 Walden is perhaps the most popular book of Thoreau. “Whenever I have read any part of the Vedas, I have felt that some unearthly and unknown light illuminated me. In the great teaching of the Vedas, there is no touch of sectarianism. It is of all ages, climes and nationalities, and is the royal road for the attainment of the Great Knowledge,” writes Thoreau.53 In Walden, a book written by Thoreau, he writes, “In the morning I bathe my intellect in the stupendous and cosmogonal philosophy of the Bhagvat-Geeta [Bhagavad-Gītā], since whose composition years of the gods have elapsed, and in comparison with which our modern world and its literature seem puny and trivial. . . I lay down the book and go to my well for water, and lo! there I meet the servant of the Brahmin, priest of Brahma [Brahmā] and Vishnu [Vis.n. u] and Indra, who still sits in his temple on the Ganges reading the Vedas, or dwells at the root of a tree with his crust and water jug. . . The pure Walden water is mingled with the sacred water of the Ganges.”54 46Goodman, 1990. 47Goodman, 1990. 48Rusk, 1939, vol. III, p. 288; taken from Goodman, 1990. 49Goodman, 1990. 50Goldberg, 2010, p. 34. 51Thoreau, 1906, 2: 4. 52Pillai, 1985, p. 4, 88. 53Goldberg, 2010, p. 39. 54Taken from Scott, 2007 158 9. THE GLOBAL IMPACT Thoreau and Emerson were the leaders of the American Transcendentalism movement of the nineteenth century.55 They were drawn to Hindu texts since they received support to their own way of thinking in these texts. “There is little doubt that both Emerson and Thoreau shared an overwhelming and sustained enthusiasm for Vedic literature and Vedāntic philosophy and be- came their ardent votaries,” concludes Sundararaman.56 This support for Hinduism by Emerson and Thoreau has also been noticed by others. Raj Kumar Gupta shares on the enthusiasm and struggle Emerson and Thoreau dealt with: “[i]n their fervent and enthusiastic admiration for Hindu idealism and spiritualism, Emerson and Thoreau lost sight of the fact that they were contrasting American practice with Indian theory.”57 In his analysis, Gupta made the following judgment about Emerson and Thoreau: “Hindu ideas and ideals are used to bring out, explicitly or by implication, the failures and deﬁciencies of nineteenth century American life and thought, and in an attempt to ﬁll the void and supply the deﬁciency. Thus, Hinduism represents not only ideals against which American values are judged and found wanting, but also a corrective and an antidote to those values.”58 9.2.2 IMPACT ON PHYSICS J. Robert Oppenheimer (1904–1967), an atomic physicist, director of the Manhattan Project, and the so-called father of the atomic bomb, not only read books of the ancient Hindus but even tried to learn the Sanskrit language to get the original intended meaning of them. While working with Ernest Lawrence in Berkeley, after he got his B.S. degree from Johns Hopkins University in 1933, he wrote to his brother Frank: “Lawrence is going to the Solvay conference on nuclei, and I shall have double chores in his absence . . . I have been reading the Bhagwad Gita [Bhagavad- Gītā] with Ryder and two other Sanskrists. It is very easy and quite marvelous. I have read it twice but not enough. . .”59 In another letter to his brother Frank, he writes, “Benevolences starting with the precious Meghduta [a book by Kālīdāsa] and rather too learned Vedas . . .”60 Within a year of study on the side, Oppenheimer became well versed in reading classics in Sanskrit on his own.61 It is obvious that reading of the sacred books of the ancient Hindus shaped Oppenheimer’s worldview and helped him in his researches in physics. Oppenheimer considered the Bhagavad-Gītā “the most beautiful philosophical song existing in any known tongue.” He kept a well-worn copy of it conveniently on hand on the bookshelf closest to his desk and often gave the book (in translation) to friends as a present.62 55Christy, 1932; Riepe, 1970. 56Sundararaman, David Thoreau: The Walden-R. s.i, in the book by Gangadharan, Sarma, and Sarma, 2000, p. 311. 57Gupta, 1986, p. 81. 58Gupta, 1986, p. 81. 59Smith and Weiner, 1980, p. 162. The reference alludes to Arthur W. Rider (1877–1938), a professor of Sanskrit at the University of California, Berkeley. 60Smith and Weiner, 1980, p. 180. 61Nisbet, p. 136. 62Royal, 1969, 64. 9.2. IMPACTS DURING THE MODERN PERIOD 159 In his condolence message upon the death of President Roosevelt, he asked people to have courage and continue with the task of the Manhattan Project at Los Alamos: “In the Hindu Scripture, in the Bhagwad Gita [Bhagavad-Gītā], it says, ‘Man is a creature whose substance is faith. What his faith is, he is.’ ”63 Most of his speech was taken from Bhagavad-Gītā. It is also well known that he started chanting the verses of Bhagavad-Gītā when he witnessed the test explosion of the atom bomb as director of the Manhattan Project. In the main verse, the aura of God is described as brighter than a thousand suns. It has led to a book an engaging and popular book on the atomic bomb with the same title.64 Brian Josephson (born 1940) received the Nobel Prize in physics in 1973 for his discov- ery of the Josephson quantum tunneling eﬀect in superconductors. SQUID (Superconducting Quantum Interference Device), a magnetometer to measure low magnetic ﬁelds, is a device that is based on the Josephson eﬀect. Josephson suﬀered from insomnia especially after he received Nobel Prize and was hooked on tranquilizers. In his attempt to protect his health, he started practicing transcendental meditation, as propagated by Maharshi Mahesh Yogi (1918–2008). These regular practices of meditation gave him “inner peace” and sound sleep. He is currently the director of the Mind-Matter Uniﬁcation Project at the Cavendish Laboratory in England and a regular practitioner of yoga and meditation. His current researches mostly deal with the uncommon subjects of science: consciousness, the role of the observer and mind in quantum me- chanics, analogies between quantum mechanics and Hindu mysticism, physics and spirituality, and yoga.65 Josephson believes that scientists “can enhance their abilities through meditation.”66 Erwin Schrödinger: the Guru of Dual Manifestations Erwin Schrödinger, a Nobel Laureate in physics and one of the prominent architects of modern physics, writes on the connectedness of the various events in nature in his book, My View of the World: “Looking and thinking in that manner you may suddenly come to see, in a ﬂash, the profound rightness of the basic conviction in Vedanta . . . Hence this life of yours is not merely a piece of the entire existence, but in a certain sense the whole. This, as we know, is what the Brahmins express in that sacred, mystical formula which is yet really so simple and so clear: Tat tvam asi (that is you). Or, again in such words as ‘I am in the east and in the west, I am below and above, I am this whole world.”’67 Vedanta is one of the six orthodox schools of Hindu philosophy. The word means “end of the Vedas,” reﬂecting concepts that are documented in the Upanis.ads. Tat tvam asi is a Sanskrit term that mentioned in the Chāndogya-Upanis. ad (6: 8: 7) and connects self with the ultimate reality. 63Smith and Weiner, 1980, p. 288. 64Jungk, Robert, 1958. He was an Austrian writer who wrote extensively on nuclear weapons. He even ran for the presi- dency of Austria in 1992 for the Green Party. 65Josephson, 1987. 66Horgan, 1995 67Schrödinger, 1964, p. 21. 160 9. THE GLOBAL IMPACT It is interesting to see similarities of Schrödinger’s philosophy of life that he derived from the books of the Hindus and the quantum mechanical wavefunction he created to deﬁne the microscopic reality. Though anecdotal, it is interesting to note the similarities between quantum mechanical waves and wavefunctions with its all pervading nature, as deﬁned by Schrödinger, with the all pervading (omnipresent) description of God. The wavefunction, though abstract, materializes itself in a region of space, in either its particle or its wave aspect, when squared (probability density). This is similar to the Nirgun. a-svarūpa (amūrta, without form) of God that manifests itself in human form (sagun. a-svarūpa) from time to time in diﬀerent regions. It is important to mention that these analogies are not real connections. However, they do play an important role in the thinking of the inventors, as mentioned in Chapter 1. Schrödinger’s worldview helped him in “hatching” scientiﬁc and mathematical ideas. Schrödinger was inﬂuenced with the philosophy of Arthur Schopenhauer (1788–1860). Several other noted European intellectuals and philosophers were inﬂuenced by Schopenhauer, including Immanual Kant, Friedrich Nietzsche, Thomas Mann, Sigmund Freud, Albert Ein- stein, Carl Jung, and Leo Tolstoy.68 Schopenhauer’s philosophy was greatly inﬂuenced by the teachings of Hinduism and Buddhism. He suggested a life style of negating desires, similar to Pythagoras and the Hindu philosophy. His book, The World as Will and Representation, empha- sizes the Upanis.adic teaching: Tat tvam asi (that is you). Schopenhauer had a dog named Atman (meaning soul in Sanskrit). Though Schopenhauer was popular in Europe, his philosophy was not popular among physicists. Schrödinger realized that his views may not be appreciated by his physicist colleagues: “I know very well that most of my readers, despite Schopenhauer and the Upanis.ads, while perhaps admitting the validity of what is said here as a pleasing and appropri- ate metaphor, will withhold their agreement from any literal application of the proposition that all consciousness is essentially one.”69 Observation is central to the growth of science. However, it provides a plurality of realities as the observation may diﬀer from person to person, depending on the aspects these observers are interested in. This creates multifarious realities. This plurality does not get much attention by scientists. Schrödinger did consider the issue of plurality in life. “For philosophy, then, the real diﬃculty lies in the spatial and temporal multiplicity of observing and thinking individuals. . . the plurality that we perceive is only an appearance; it is not real. Vedantic philosophy, in which this is fundamental dogma, has sought to clarify it by a number of analogies, one of the most attractive being the many faceted crystal which, while showing hundreds of little pictures of what is in reality a single existent object, does not really multiply that object.”70 Schrödinger believed in the advocacy of the Hindu philosophy of oneness: “In all the world, there is no kind of framework within which we can ﬁnd consciousness in the plural; this is simply something we construct because of the spatio-temporal plurality of individuals, but it is a false construction. . . 68Moore, 1992, p. 112 69Schrödinger, 1964, p. 29. 70Schrödinger, 1964, p. 18. 9.2. IMPACTS DURING THE MODERN PERIOD 161 The only solution to this conﬂict, in so far as any is available to us at all, is in the ancient wisdom of the Upanishads.”71 In his essay on The Diamond Cutter, Schrödinger writes: “The ego is only an aggregate of countless illusions, a phantom shell, a bubble sure to break. It is Karma. Acts and thoughts are forces integrating themselves into material and mental phenomena—into what we call objec- tive and subjective appearances . . . The universe is the integration of acts and thoughts. Even swords and things of metal are manifestations of spirit. There is no birth and death but the birth and death of Karma in some form or condition.”72 These statements led Walter Moore, who has written a book on the life of Schrödinger, to infer that Schrödinger “thought deeply about the teachings of Hindu Scriptures, reworked them into his own words, and ultimately came to believe in them.”73 Also, his worldview helped him in creating the wave-mechanics which is counterintuitive to Newtonian thinking: “Perhaps these thoughts recurred to Erwin when he made his great discovery of wave mechanics and found the reality of physics in wave motions, and also later when he found that this reality was part of an underlying unity of mind.”74 The philosophy of multiple representations of truth, thin boundaries between abstract thoughts (amūrtā), actual realities (mūrta) and universal consciousness played an important role in the science that Erwin Schrödinger created. Moore concludes, “Vedanta and gnosticism are beliefs likely to appeal to a mathematical physicist, a brilliant only child, tempted on occasion by intellectual pride. Such factors may help to explain why Schrödinger became a believer in Vedanta, but they do not detract from the importance of his belief as a foundation for his life and work. It would be simplistic to suggest that there is a direct causal link between his religious beliefs and his discoveries in theoretical physics, yet the unity and continuity of Vedanta are reﬂected in the unity and continuity of wave mechanics.”75 In the view of Moore, “Schrödinger and Heisenberg and their followers created a universe based on superimposed inseparable waves of probability amplitudes. This view would be entirely consistent with the Vedantic concept of the All in One.”76 * * * * * * * * Just think of the global impact of the eﬀorts of the ancient Hindus for knowing the ul- timate truth. They created disciplines that were for the welfare of all humanity. Hinduism has transcended the boundaries of what is called ’religion’ in the West and has permeated the whole world. Yoga is practiced by devoted Christians, Muslims, and atheists, without discrimination. It is currently prescribed in many hospitals in the Western world for pain management and cures of various diseases. The United Nations have declared June 21 as the “yoga day” which is being celebrated all over the world. 71Schrödinger, 1964, p. 31. 72taken from Moore, 1992, p. 114. 73Moore, 1992, p. 113. 74Moore, 1992, p. 114. 75Moore, 1992, p. 173. 76Moore, 1992, p. 173. 162 9. THE GLOBAL IMPACT Think of the kids that are schooled in Africa, Asia, or Europe. Everywhere in the civilized world, kids learn to count even before they learn the alphabet of their own language. In diﬀerent languages, the numbers may be named diﬀerently; but, they all use the same (base 10) mathe- matical principles (known as the decimal system) in counting and in arithmetic operations that were invented long ago by the ancient Hindus. These mathematical methods are so eﬀective and important, most kids learn them without ever inquiring about the alternatives. “The Indian system of counting has been the most successful intellectual innovation ever made on our planet. It has spread and been adopted almost universally, far more extensively even than the letters of the Phoenician alphabet which we now employ. It constitutes the nearest thing we have to a universal language,”77 writes John D. Barrow in his book, Pi in the Sky: Counting, Thinking, and Being. In dealing with numbers, the size of the atom conceived by the ancient Hindus comes 10m. For the age of the universe, they came up with a number that is of the order close to 10(cid:0) of a billion years. Both of these numbers were considered mere speculations and ridiculed by foreign scientists during the early medieval period. However, these numbers are in tune with the modern science now. Is this a coincidence? How can one reach such striking conclusions that were considered ridiculous by scientists just a century ago? For the Hindus, this information was valuable enough to be preserved in their most sacred books. How did they reach to these numbers? It is not an easy question to answer. The answer is perhaps in the role of the mind in the meditative state to learn the mysteries of nature that are not otherwise accessible through the faculties of the ﬁve senses we human beings are endowed with. This role of mind or conscious- ness is what Noble Laureate Brian Josephson is investigating these days at the University of Cambridge, London and has attracted the minds of Robert Oppenheimer, Erwin Schrödinger, and others. The social attitudes in India toward accepting new scientiﬁc theories were in contrast to those prevailing in Europe. Unlike Galileo and Copernicus, Āryabhat.a never faced any hostile sentiments or violent reaction from the priestly class or the possibility of any kind of persecution from the king when he assigned motion to the earth. On the contrary, invention and promotion of such ideas led a person to the greatest honor on earth while alive, and moks. a - ultimate goal of liberation - after death, as suggested by Āryabhat.a I. Thus, becoming an astronomer, a medical doctor, or a musician was as honoriﬁc profession as becoming a priest or swami. This is perhaps the reason why Caraka and Suśruta were so deeply involved in the medical research and practice and Āryabhat.a in astronomy and mathematics. Ultimately, they were working toward achieving moks. a, liberation of their soul. Multicultural Cooperation in Science Many intellectual centers in our history used multicultural approaches to learning. Damascus and Baghdad became leading centers of learning when they started attracting Greek, Indian, 77Barrow, 1992, p. 92. 9.2. IMPACTS DURING THE MODERN PERIOD 163 Persian, and Egyptian scholars. Similarly, Spain became a center of learning from the eighth century to the eleventh century, because it attracted scholars from all over the world.78 However, these centers eventually declined when the scholars were judged on ill-conceived grounds (race, gender, religion, or culture), rather than on the basis of merit. Such declines occurred in Spain, Egypt, the Middle East, and elsewhere in Europe. Modern science is international in character. Scientiﬁc ideas are studied and developed in many languages from all over the world. Thus, science education with a multicultural approach can be a broadening and humanizing experience. Multicultural approach teaches us how human beings are alike in the pursuit of knowledge. It inspires us to learn from each other and appreciate each other. It allows us to function as a cohesive society. However, so far, science education has not utilized this opportunity to its fullest potential. Preserving knowledge is a process in which all generations must participate or become susceptible to lose some valuable knowledge. Museums are created to slow down or stop this tide of entropy. However, they mostly secure artifacts and have limitations. Perhaps, libraries are the places where knowledge can be documented and preserved. However, these libraries are prone to destruction as we know from the history of Alexandria, Nālandā, and Taxila. Therefore, dissemination of knowledge to the next generation is a duty that each generation must involve in. This is called guru-r. n. a (debt to the guru) that each disciple owes to his or her own teacher to continue the tradition of knowledge, to carry forward the torch (light) of knowledge to the next generation. No culture or civilization has prospered to great heights without knowing and preserving their historic and existing knowledge base. This book is written to preserve the knowledge of the ancient Hindus and to recognize their rightful place in world history. Of course, it is only a small step; much more eﬀort needs to be exercised on a continual basis to research, disseminate and preserve this ancient knowledge of the Hindus from the earliest period of the Indus-Sarasvati civilization to the end of the last millennium when this knowledge was deliberately suppressed in the pursuit of colonial objectives. The twenty-ﬁrst century is the harbinger of free, open and honest pursuit of scientiﬁc knowledge in all its varied dimensions unfettered by dogma or national or cultural chauvinism. 78Salem and Kumar, 1991. A P P E N D I X A 165 Timeline of the Hindu Manuscripts A lack of well-accepted chronology is the weakest point of the Hindu manuscripts. There are several reasons for it: ﬁrst, the Hindu culture practiced orality to preserve their ideas unlike the Egyptian (papyrus) and Babylonians (clay tablets). It is diﬃcult to ﬁnd archaeological records in a oral culture. Second, the Hindu culture basically followed in the same tradition from the earliest periods. As discussed in Chapter 5, events are essential to deﬁne time not only in the physical sense but in cultural sense too. Events of atrocities, change in value system, change in prosperity, etc. are the landmarks of a culture. However, in the case of the Hindus, a similar pattern of prosperity and cultural traits continued for so long, the culture paid little or no attention to deﬁne events and time frame. We know that the R. gveda is the earliest book of the Hindu literature, and is certainly one of the earliest known manuscripts in human history. The ancient Hindus did not erect monu- ments to document history, until the period of Emperor Aśoka who reigned in India between 268 to 232 BCE. The ancient Hindus did not even mention the names of the authors in their books. Some Western historians look for a “hard-copy” or “hard-evidence” to accept a particular date for the antiquity of the Hindu manuscripts. Due to the prevalent oral tradition, such evi- dences are not possible with the ancient Hindus. Jessica Frazier, a Lecturer in Religious Studies at the University of Kent and a Fellow of the Oxford Center for Hindu studies, in her quest to deﬁne history, historiography, and timeline of various Hindu events, shares her experience in the following words: “The search for an Indian historiography is like the work of a geologist who must sift innumerable layers of compacted material, or perhaps better, a zoologist who can never stop seeking new species of history, and never assume that any given specimen will remain long in a single place or form.” She criticizes too much reliance on the accounts of travelers such as Herodotus and others who visited India and wrote their accounts. In her view, “[t]he ideal Western historian has classically been seen as an itinerant Godlike traveller.” These travellers had a limited exposure of the culture and wrote their view from their bird’s eye view. Even the astronomical observations of the heavenly bodies which should provide a linear scale of time fails because of “multiple parallel chronologies.” She concludes that, “‘while India’s Hindu past was ever-present in divine reality and recursive myth, it was nevertheless unreachable by accepted historiographical methods.”1 1Frazier, 2009. 166 A. TIMELINE OF THE HINDU MANUSCRIPTS During the colonial period, scholars in the West worked hard to deﬁne Hindu religion and culture in their eﬀorts to Christianize India. At that time in Europe, it was a prevalent belief among Christians that the world was created around 4004 BCE on one Friday afternoon. This was based on the genealogy presented in the book of Genesis, in the Bible, as concluded by Archbishop James Ussher (1581–1656 CE), who was also the Vice-Chancellor of the Trinity College in Dublin. In 1642, Dr. John Lightfoot (1602–1675 CE), then Vice Chancellor at the Cambridge University improved the calculation further and made it more precise to be 9 AM, October 23, 4004 BCE.2 These calculations were generally agreed on by the Western scholars at the beginning of the twentieth century. As a result, the Western scholars assigned dates to Vedas and upanis. ad that made sense to the misconstrued date of 4004 BCE. Once these dates were arbitrarily deﬁned, they have not been modiﬁed with current research. Al-Bīrūnī (973–1050 CE) noticed the problem of historiography in assigning actual dates to various events in the eleventh century and criticized the ancient Hindus: “Unfortunately the Hindus do not pay much attention to the historical order of things, they are very careless in relating the chronological succession of their kings.”3 Carl Jung (1875–1961 CE), a psychoanalyst and philosopher, aptly answered such crit- icisms of the absence of a chronological history in India, by attributing it to the antiquity of the Hindu civilization. “After all why should there be recorded history [in India]? In a country like India one does not really miss it. All her native greatness is in any case anonymous and im- personal, like the greatness of Babylon and Egypt. History makes sense in European countries where, in a relatively recent, barbarous, and inhistorical past, things began to shape up . . . But in India there seems to be nothing that has not lived a hundred thousand times before.”4 Even the ancient writers such as Caraka (around 600 BCE), Suśruta (around 1000 BCE), and Ārybhat.a I (5th century) do not represent the ﬁrst eﬀorts for most theories in their books; they all claim to be merely reproducing old ideas in new form. The ﬁrst book in the modern era on the Hindu sciences was published by Brajendranath Seal in 1915.5 Seal opted to deal with the absence of a proper chronology right in the ﬁrst paragraph of his Foreword. He basically assigned an umbrella period of 500 BCE to 500 CE to all Hindu manuscripts considered in his book. Bose et al in 1971 and Chattopadhyaya in 1986, two prominent books on the history of Hindu science, encountered the same issue. This situation has not improved much in the last century; we still cannot assign accurate dates for ancient manuscripts. The issue of antiquity can only be solved either from the artifacts of the ancient Hindus or from the astronomical maps provided in their oral literature. Previously, the maps provided in the Hindu oral literature were ignored by the scholars as they deﬁned the period of R. gveda to be more ancient than 1500 BCE, an arbitrary date assigned by Max Müller. Since the recent 2White, 1897, p. 9. 3Sachau, 1964, vol. 2, p. 10. 4Jung, Collected Works, vol. 10, p. 517. 5Seal, 1915 A. TIMELINE OF THE HINDU MANUSCRIPTS 167 excavations unearthed artifacts that are some 10,000 years old, a need for the revision of history is warranted.6 A massive eﬀort is needed to resolve this issue. Though the dates are not certain, there is a general acceptance about the chronological order of these books and periods can be assigned to these books, as listed in Table A.1. The content of my book will not change much with corrections in this table. Most conclusions will remain valid even with a diﬀerent chronology. Table A.1: The Antiquity of Hindu Books 6Kenoyar, 1998. ManuscriptDate of PeriodĀryabhaṭīya5th century CEBakhshālī ManuscriptSeventh Century CEBrāhmaṇasBetween 2000 - 1500 BCEMahābhārata BattleBetween 2449 BCE to 1424 BCEPingala’s Chandah SutraBetween 480 - 410 BCEPurāṇaBetween the Christian era and 11th centuryManu-Saṁhitā ,Between 500 - 100 BCECaraka-SaṁhitāAround 600 BCESuśruta-SaṁhitāAround 1000 BCEŚulbasūtraBetween 1700 BCE to 1000 BCEUpanishads800 to the beginning of the Christian eraVaiśesika-SūtraBetween 900 - 600 BCEVedasAround 1500 BCE or earlierReferences 169 [1] Atharvaveda: The Hymns of the Atharvaveda, Ralph T. H. Griﬃth, Chowkhamba Sanskrit Series, Varanasi, 1968. [2] Bhagavad-Gītā, S. Radhakrishnan, Unwin Paperbacks, London, 1948. [3] Caraka Sa ˙mhitā: The Caraka Sa ˙mhitā, Satyanārāyan. a Śāstrī, Chowkhamba Sanskrit Series, Varanasi, 1992, 2 volumes, in Hindi. 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In Oswego, Kumar has received the Chancellor’s Award for Excellence in Teaching, a life-time SUNY award, in 1997 and the President Award for Creative and Scholarly Activity or Research, a life-time award, in 2002. He is a fellow of the Alexander von Humboldt Foundation, Germany, and a NOVA/NASA fellow. Kumar is active in the ﬁelds of atomic physics, chemical physics, history of science, and science education. He has about 75 peer-reviewed publications, and has authored/coauthored three books: (1) Science in the Medieval World, (2) Sciences of the Ancient Hindus: Unlocking Nature in the Pursuit of Salvation, and (3) A History of Science in World Cultures: Voices of Knowledge. All three books deal with the cultural heritage studies in science, including the non-Western cultures. Kumar believes that, to understand modern science, it is essential to recognize that many of the most fundamental scientiﬁc principles are drawn from knowledge amassed by ancient civilizations. Kumar strongly believes that, in a gadget-ﬁlled world, scientiﬁc literacy is becoming an essential requirement for everyday life. It is the duty of a scientist to disseminate scientiﬁc knowl- edge to the general public. He has done so through articles and interviews in the popular media, making documentary ﬁlms on archaeological sites that are rich in science, oﬀering institutes for the underprivileged and underrepresented middle school students to pursue a career in science and technology, and lecturing about science for the general public. There are about 120 arti- cles/reports about his activities in the popular media. This includes press releases from Reuters, the Press Trust of India, articles in The Washington Post, Family Life, The Scientists, The Post Stan- dard, The Palladium Times, India Abroad, India West, The South Asian Times, Hinduism Today, AramcoWorld, Organiser, and radio interviews. 195 Index Abū Ma‘sher, 83 Adelard of Bath, 34, 51, 53, 57, 82, 87, 149 Agni-Purān. a, 15 Ahi ˙msā, 128 Al-Andalusī, S. ā‘id, 51, 55, 82, 86, 143, 149, 150 Al-Battānī, 3, 54, 86 Al-Jāh. iz, 8, 50, 52, 149 Al-Bīrūnī, 8, 23, 31, 56, 63, 64, 76, 80, 93, 99, 102, 147 Al-Khwārizmī, 8, 34, 50, 53, 81, 83, 87, 149 Al-Kindī, 144 Al-Majrīt.ī, 54, 82, 86, 87 Al-Mas‘udī, 16, 149 Al-T. abarī, 144 Al-Uqlidīsī, 53 Al-Uqlidīsī, 149 Almagest, 83, 86 Āpastambā-Śulbasūtra, 49 Apollonius of Tyana, 13, 149 Archimedes, 2 Aristotle, 2, 52, 73, 103 Arjuna, 19, 43 Arthaśāstra, 19, 22, 76, 90, 95, 101, 103, 106, 114 Āryabhat.a I, 5, 6, 8, 15, 41, 66, 68, 92 Aśoka, 22, 119, 128, 148 Atharvaveda, 13, 30, 75, 91, 101, 118, 132 Bakhshālī, 34 Baudhayāna-Śulbasūtra, 41 Bayt al-H. ikma, 81 Bhagavad-Gītā, 8 Bhagavad-Gītā, 79, 118, 157 Bhārdvāja, 123 Bhīs.ma, 122 Biomimicry, 25 Bonaparte, Napoleon, 4 Boyle, Robert, 2, 3 Brahmgupta, 68, 81–83, 87, 150 Cakravyūha, 43 Caraka-Sa ˙mhitā, 5, 7, 20, 101, 103, 117, 127, 128, 130, 132, 134, 136, 145 Chandāh. -sūtra, 33, 36 Chāndogya-Upanis. ad, 14, 27, 61, 67, 89, 90, 101, 114, 124 Clement of Alexandria, 151 Copernicus, 6, 69, 81, 87, 149, 150 da Vinci, Leonardo, 3 Daśaratha, 22 Daśaharā, 77 Democritus, 2, 4 Descartes, 3 Dhātu, 101, 144 Dincarayā, 134 Dolomieu, Déodat, 4 Babylon, 31, 52, 75, 154 Bacon, Roger, 3, 51, 57, 143 Egypt, 56, 96, 112, 130, 154 196 INDEX Emerson, 17, 154, 156 Eusebius, 152 Faraday, Michael, 2 Fibbonacci, 9 Fourier, Joseph, 4 Galileo, 2, 3, 162 Ga ˙ngā, 119, 120 Grosseteste, Robert, 3 Hippocrates, 2 Holī, 77 Huygens, Christiaan, 3 Ibn al-Haytham, 3 Ibn Labbān, 8, 50, 52, 149 Ibn Sīnā, 3, 5, 52, 149 Indus-Sarasvatī, 127 Janaka, 19 Kan. āda, 4, 7, 9, 90, 94–96, 99 Kanaka, 56, 83, 86 Kathā-Upanis. ad, 13, 26 Kātyāyana-Śulbasūtra, 48 Kaurava, 43 Kaut.ilaya, 19, 90, 95, 101, 108, 114, 131, 144 Kepler, 2, 3, 81, 87, 100, 150 Ketu, 64, 84 Khalīl wa Dimna, 150 Khandakhadyaka, 87 Khan. d. a-Khādyaka, 150 Kr.s.n. a, 120, 149, 157 Laks.man. a, 138 Laks.mī, 120 Lalitvistara, 19 Leucippus, 4 Macaulay, T. B., 3 Mahābhārata, 8, 43, 65, 97, 120, 122, 123 Manu-Smr. ti, 122, 123 Margenau, 5 Mārkan. daya-purān. a, 90 Megasthenes, 17 Monier-Williams, Monier, 3 Müller, Max, 3 Nāgārjuna, 55, 146 Nāgārjuna, 148 Naks. atra, 61, 78, 84 Nālandā, 54, 68, 147, 163 Nārada, 14, 57 Needham, 3 Newton, Isaac, 2, 3 Pañca-karma, 132, 135, 136 Pān. d. ava, 43 Paramān. u, 97, 98 Patañjali, 24, 26, 155 Plastic surgery, 136, 138 Plato, 2, 13, 52, 153 Plotinus, 13, 52, 149, 153 Polo, Marco, 144 Prakr. ti, 118, 121, 122, 133 Pr. thivī, 118, 133 Pythagoras, 2, 13, 47, 149, 155 Rāhu, 64, 66, 84, 85 Rāma, 22, 138 Rāvan. a, 138 Rāmāyan. a, 100, 101, 138 Redouté, Joseph, 4 R. gveda, 26, 61, 63, 65, 79, 81, 101, 103, 113, 124, 127, 128, 137, 147 Royle, John F., 144 Sanatkumāra, 14 Sanskrit, 3 Sarasvatī, 120 Śāstrārtha, 9, 19 Sebokht, 52 Śilājīta, 134 Sītā, 120 Śiva, 10, 120 Socrates, 13 Srimad-Bhāgvatam, 79, 92, 97, 98 Śulbasūtra, 40, 43, 47, 155 Sūrpan. akhā, 138 Suśruta-Sa ˙mhitā, 5, 101, 103, 127, 136, 140, 141, 145 Sylvester, Pope, 58, 60, 149, 150 T. abaqāt al-‘Umam, 1 Thales, 2 Thoreau, 18, 156 Upanis. ad, 127, 153 Vaiśes. ika-Sūtra, 7, 9, 15, 90, 92, 94, 96, 97, 99, 122 INDEX 197 Varāhamihira, 55, 64, 68, 73, 80, 84 Vāyu-Purān. a, 97, 98 Vedas, 15, 18, 30, 67, 80, 132, 158 Vis.n. u, 65, 120, 157 Vis. n. u-Purān. a, 67, 79, 100, 157 Viśvāmitra, 22 Yājñavalkya, 19 Yajurveda, 61, 114, 117 Yudhis.t.hira, 122 Yuga, 70, 78 Zarqālī, 1 Zīj al-Sindhind, 35, 41, 81, 82, 87
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=9340651.pdf&bkn=9340650&pdfType=book	Biologically Inspired Design A Primer Torben A. Lenau, Danmarks Tekniske Universitet Akhlesh Lakhtakia, The Pennsylvania State University As the existence of all life forms on our planet is currently in grave danger from the climate emergency caused by Homo sapiens, the words “sustainability” and “eco-responsibility” have entered the daily-use vocabularies of scientists, engineers, economists, business managers, industrialists, capitalists, and policy makers. Normal activities undertaken for the design of products and systems in industrialisms must be revamped. As the bioworld is a great resource for eco-responsible design activities, an overview of biologically inspired design is presented in this book in simple terms for anyone with even high-school education. Beginning with an introduction to the process of design in industry, the book presents the bioworld as a design resource along with the rationale for biologically inspired design. Problem-driven and solution-driven approaches for biologically inspired design are described next. The last chapter is focused on biologically inspired design for environment. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com store.morganclaypool.com L E N A U • L A K H T A K I A B I O L O G I C A L L Y I N S P I R E D D E S I G N : A P R I M E R M O R G A N & C L A Y P O O L Biologically Inspired Design A Primer Synthesis Lectures on Engineering, Science, and Technology Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Biologically Inspired Design: A Primer Torben A. Lenau and Akhlesh Lakhtakia 2021 Engineering Design: An Organic Approach to Solving Complex Problems in the Modern World George D. Catalano and Karen C. Catalano 2020 Integrated Process Design and Operational Optimization via Multiparametric Programming Baris Burnak, Nikolaos A. Diangelakis, and Efstratios N. Pistikopoulos 2020 The Art of Teaching Physics with Ancient Chinese Science and Technology Matt Marone 2020 Scientiﬁc Analysis of Cultural Heritage Objects Michael Wiescher and Khachatur Manukyan 2020 Case Studies in Forensic Physics Gregory A. DiLisi and Richard A. Rarick 2020 iv An Introduction to Numerical Methods for the Physical Sciences Colm T. Whelan 2020 Nanotechnology Past and Present Deb Newberry 2020 Introduction to Engineering Research Wendy C. Crone 2020 Theory of Electromagnetic Beams John Lekner 2020 The Search for the Absolute: How Magic Became Science Jeﬀrey H. Williams 2020 The Big Picture: The Universe in Five S.T.E.P.S. John Beaver 2020 Relativistic Classical Mechanics and Electrodynamics Martin Land and Lawrence P. Horwitz 2019 Generating Functions in Engineering and the Applied Sciences Rajan Chattamvelli and Ramalingam Shanmugam 2019 Transformative Teaching: A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam, Brooke Coley, and Audrey Boklage 2019 Ancient Hindu Science: Its Transmission and Impact on World Cultures Alok Kumar 2019 Value Rational Engineering Shuichi Fukuda 2018 v Strategic Cost Fundamentals: for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese 2018 Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw 2018 Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi 2018 Empowering Professional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimization (with illustrative case study problems and solutions), Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 vi The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 vii Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2021 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Biologically Inspired Design: A Primer Torben A. Lenau and Akhlesh Lakhtakia www.morganclaypool.com ISBN: 9781636390475 ISBN: 9781636390482 ISBN: 9781636390499 paperback ebook hardcover DOI 10.2200/S01064ED1V01Y202012EST014 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY Lecture #14 Series ISSN Print 2690-0300 Electronic 2690-0327 Biologically Inspired Design A Primer Torben A. Lenau Danmarks Tekniske Universitet Akhlesh Lakhtakia The Pennsylvania State University SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY #14 CM&cLaypoolMorganpublishers&ABSTRACT As the existence of all life forms on our planet is currently in grave danger from the climate emer- gency caused by Homo sapiens, the words “sustainability” and “eco-responsibility” have entered the daily-use vocabularies of scientists, engineers, economists, business managers, industrialists, capitalists, and policy makers. Normal activities undertaken for the design of products and sys- tems in industrialisms must be revamped. As the bioworld is a great resource for eco-responsible design activities, an overview of biologically inspired design is presented in this book in simple terms for anyone with even high-school education. Beginning with an introduction to the process of design in industry, the book presents the bioworld as a design resource along with the rationale for biologically inspired design. Problem- driven and solution-driven approaches for biologically inspired design are described next. The last chapter is focused on biologically inspired design for environment. KEYWORDS bioinspiration, biomimicry, biomimetics, bioreplication, bionik, bionics, nature- inspired design, circular economy, contraindicated performance, design for envi- ronment, eco-eﬃciency, engineered biomimicry, multifunctionality, sustainability xi Dedicated to sustainable societies Contents xiii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix 1 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 What is Design? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Design Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Design Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.1 Task Clariﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 Function Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.3 Design Brief and Product Speciﬁcation . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.4 Conceptual Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.5 Concept Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.6 Toward Detailed Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 3 Engineered Biomimicry: Solutions from the Bioworld . . . . . . . . . . . . . . . . . . . 21 3.1 The Case for Engineered Biomimicry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Engineered Biomimicry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 3.2.1 Bioinspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.2 Biomimetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Bioreplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Examples of Engineered Biomimicry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 Bioinspired Computational Techniques . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.2 Biomimetic Production of Human Insulin . . . . . . . . . . . . . . . . . . . . . 26 3.3.3 Bioreplicated Visual Decoys of Insects . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4 Design Teams for Bioworld Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5 3.3 xiv 4 5 6 7 Rationale for Biologically Inspired Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Energy Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1 4.2 Circular Economy of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3 Multifunctionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.4 Multicontrollability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.5 Suboptimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.6 Contraindicated Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.7 Problem-Driven Biologically Inspired Design . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.1 5.2 5.3 5.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Phases of Problem-Driven BID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 First Phase: Problem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.1 5.2.2 Second Phase: Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2.3 Third Phase: Understand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Fourth Phase: Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2.4 5.2.5 Fifth Phase: Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Engineers and Biologists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Solution-Driven Biologically Inspired Design . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1 6.2 6.3 6.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Examples of Solution-Driven BID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.2.1 Mycelium Bio-Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.2.2 Bombardier-Beetle Spray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.3 Tubercles for Flow Control 6.2.4 Abalone-Shell Armor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Steps for Solution-Driven BID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.3.1 Application Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.3.2 Eight-Step Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Biologically Inspired Design for the Environment . . . . . . . . . . . . . . . . . . . . . . . 77 7.1 Sustainability and the Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.2 Matter of Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Sustainable Practices from Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.3 xv 7.4 Circular Economy of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.5 Mutually Beneﬁcial Coexistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.6 Energy Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.7 Design Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.7.1 Environmental Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.7.2 Circular Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Impact Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.7.3 7.8 Grafting “Biologically Inspired Design” onto “Design for Environment” . . . . 87 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.9 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 xvii Preface This primer on biologically inspired design (BID) was initiated during a sabbatical semester spent by Akhlesh Lakhtakia at Danmarks Tekniske Universitet (DTU) during the second half of 2019, at the invitation of Torben A. Lenau. The close collaboration between both of us resulted not only in the descriptions of BID approaches and the case stories required to make the reading of this book interesting to undergraduate students enrolled for BID courses, but it also made a collaboration possible with Daniela C. A. Pigosso and Tim C. McAloone for grafting BID onto design for environment. The combination of the two design foci makes it possible to tap into the enormous knowledge bank that the bioworld represents and apply well-proven solutions in the quest to secure sustainable societies and ecosystems on our planet. Torben A. Lenau started in 2009 to teach BID to engineering students at DTU. More than 400 students have marched through the course since then. The course is focused on the problem-driven approach to BID illustrated by around a hundred case studies. The solution-driven approach to BID complements the problem-driven approach. Both are treated in two chapters in this book. They are described in suﬃcient detail to allow practi- tioners as well as students to follow and apply the approaches to their own BID activities. As this book explains BID in simple terms for anyone with even high-school education, we hope that not only engineering and design students but also members of the general public interested in sustainability will proﬁt from the time they will spend on reading this primer on BID. Torben A. Lenau and Akhlesh Lakhtakia January 2021 Acknowledgments xix Torben A. Lenau thanks the many students of Danmarks Tekniske Universitet (DTU) who took his course 41084 Biologically Inspired Design over the years for providing the empirical experience and contextual setting that stimulated the development of methodological support tools. He is also highly grateful for insightful discussions with and support from his wife Ingrid. Akhlesh Lakhtakia is grateful to the Trustees of The Pennsylvania State University for a sabbatical leave of absence, the Otto Mønsted Foundation for partial ﬁnancial support, and the Department of Mechanical Engineering, DTU for gracious hospitality in Fall 2019 semester. He also thanks Mercedes for wonderful spousal support during that period. Both of us are grateful to Daniela C. A. Pigosso and Tim C. McAloone for discussions on grafting biologically inspired design onto design for environment. We thank Patrick D. McAtee for several suggestions as well as for alerting us to several errors in a draft manuscript, and the staﬀ of Morgan & Claypool for splendid cooperation in producing this book. Torben A. Lenau and Akhlesh Lakhtakia January 2021 C H A P T E R 1 Deﬁnitions 1 “Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.” Lewis Carroll, Alice in Wonderland (1865) First things ﬁrst, we must begin with deﬁnitions. This is all the more necessary for a rapidly emerging area such as engineered biomimicry, which encompasses both basic research on outcomes and mechanisms of diverse phenomena displayed by living organisms and the appli- cation of fundamental principles uncovered by that basic research to devise useful processes and products [1]. Engineered biomimicry can thrive in an industrialism, which is a society replete with manufacturing industries for mass production of a diverse array of products. Biomimicry lies within the ambit of engineered biomimicry. Although the two terms are often used as synonyms of each other, biomimicry additionally incorporates the attributes of sustainability evinced by the bioworld. Sustainability is deﬁned as the maintenance of natural resources for ecological balance; hence, present-day needs are satisﬁed without endangering the ability of future generations to do the same [2]. Sustainability mandates the formation of those industrial ecosystems that are founded on the principles of circular economy. The main out- puts, byproducts, and wastes of every segment of a circular economy become inputs to one or more of the other segments of that economy, thereby minimizing the overall resource inputs to the circular economy [3]. The inter-relationships of engineered biomimicry, biomimicry, sus- tainability, and industrialism are schematically depicted in Fig. 1.1. Design and manufacture are the two main engineering activities in any industry. Accord- ingly, engineered biomimicry encompasses both biologically inspired design and manufacture, as depicted in Fig. 1.2. The scope of biologically inspired design is the formulation of de- sign strategies to reproduce desirable outcomes, mechanisms, and structures from the bioworld. A manufacturing action may or may not be provenanced in the bioworld. The history of Homo sapiens is marked by numerous approaches to the solution of engineer- ing problems based on solutions from the bioworld. These approaches of engineered biomimicry can be classiﬁed as bioinspiration, biomimetics, and bioreplication, as shown also in Fig. 1.2. The goal in bioinspiration is to reproduce a biological outcome without reproducing the underlying physical mechanism(s) and the biological structure(s). As an example, powered ﬂying machines were inspired by birds in self-powered ﬂight. But airplanes do not ﬂap their wings like birds, and the tails of birds are horizontal unlike the vertical tails of aeroplanes. Rotorcraft do 2 1. DEFINITIONS Figure 1.1: Engineered biomimicry and biomimicry within the contexts of sustainable actions and mass production. Figure 1.2: Conceptual anatomy of engineered biomimicry. SustainableactionsBiomimicryEngineeredbiomimicryIndustrialism(mass production)Engineered biomimicryBiomimeticsBioinspirationBiologicallyinspireddesignProductionBioreplication1. DEFINITIONS 3 not ﬂy like birds either. But these engineered structures do reproduce the natural outcome of moving from one location to another without being in physical contact with the ground. Biomimetics is the reproduction of a physical mechanism responsible for a speciﬁc func- tionality exhibited by a biological structure. The classic example of biomimetics is Velcro™ com- prising dense assemblies of hooks and loops, the former emulating the hooked barbs on a bur- dock seed and the latter the fur of a furry animal. When a furry animal brushes against a burdock seed, the hooks get fastened to the fur. The International Standards Origanization (ISO) has formulated a set of criteria for whether a product can be considered as biomimetic [4]. The crite- ria relate to the biomimetic design process which was applied to develop the product and require that (i) a function analysis has been performed on an available biological system, (ii) the essential mechanisms in that biological system have been abstracted into a model, and (iii) the model has been transferred and applied to design the product. Bioreplication is the direct replication of a structure found in a biological organism in order to reproduce one or more functionalities exhibited by the biological structure copied. Decoys created by nanoscale replication of the actual elytra of a female emerald ash borer for the purpose of sexually attracting male emerald ash borers provide an example of bioreplication [5]. The term biomaterial refers to either a material harvested from a biological organism to be used for the same purpose as in the organism or an artiﬁcial material used for a biological purpose. In the latter case, the term biocompatible material is also used. Bovine milk is a biomaterial of the ﬁrst kind, being produced in the bioworld as a nutrient for calves and also used by humans as food. Prostheses for human hips and knees are made of biomaterials of the second kind. Biomanufacturing uses a biological process to produce a synthetic product. Thus, syn- thetic insulin is produced by inserting the human insulin genes in open loops of bacterial DNA to close the latter, the closed loops are inserted in bacteria which multiply rapidly in a fermentation chamber, the insulin then being harvested from the bacteria being produced in that chamber. Escherichia coli and Saccharomyces cerevisiae are commonly used species of bacteria, but yeast, a fungus, often replaces the bacteria in this biomanufacturing process [6]. A speciﬁc biomanufac- turing process has at least one component that is either biomimetic or bioreplicatory. A structure is multifunctional if it can perform two or more distinct functions that are not highly related to each other [7]. An example of multifunctionality is displayed in the bioworld by skin, which contains the organism, deﬁnes its shape and size, hosts a variety of sen- sors, and may be used to camouﬂage as well as to advertise. The fuselage of an aircraft functions both as a thermal isolator and an acoustic isolator. The well-known Swiss Army™ knife is a multifunctional tool. The output of a multicontrollable structure can be controlled independently by more than one mechanisms [8]. As natural examples: the same sound can be uttered using two or three 4 1. DEFINITIONS diﬀerent conﬁgurations of the tongue and the buccal cavity, and multiple modes of locomotion can be used by an organism to propel itself from one location to another. 1.1 REFERENCES [1] A. Lakhtakia and R. J. Martín-Palma (Eds.), Engineered Biomimicry, Elsevier, Waltham, MA, 2013. DOI: 10.1016/c2011-0-06814-x. 1 [2] M. Mulligan, An Introduction to Sustainability: Environmental, Social and Personal Perspec- tives, 2nd ed., Routledge, Abingdon, Oxford, UK, 2018. DOI: 10.4324/978131588852. 1 [3] W. R. Stahel, Circular Economy: A User’s Guide, Routledge, Abingdon, Oxford, UK, 2019. 1 [4] ISO 18458:2015, Biomimetics—Terminology, Concepts and Methodology, International Standards Organization, Geneva, Switzerland, 2015. https://www.iso.org/standard/ 62500.html DOI: 10.3403/30274979. 3 [5] M. J. Domingue, A. Lakhtakia, D. P. Pulsifer, L. P. Hall, J. V. Badding, J. L. Bischof, R. J. Martín-Palma, Z. Imrei, G. Janik, V. C. Mastro, M. Hazen, and T. C. Baker, Bioreplicated visual features of nanofabricated buprestid beetle decoys evoke stereotypical male mating ﬂights, Proceedings of U.S. National Academy of Sciences, 111:14106–14111, 2014. DOI: 10.1073/pnas.1412810111. 3 [6] N. A. Baeshen, M. N. Baeshen, A. Sheikh, R. S. Bora, M. M. M. Ahmed, H. A. I. Ramadan, K. S. Saini, and E. M. Redwan, Cell factories for insulin production, Microbial Cell Factories, 13:141, 2014. DOI: 10.1186/s12934-014-0141-0. 3 [7] A. Lakhtakia, From bioinspired multifunctionality to mimumes, Bioinspired, Biomimetic and Nanobiomaterials, 4:168–173, 2015. DOI: 10.1117/12.2258683. 3 [8] A. Lakhtakia, D. E. Wolfe, M. W. Horn, J. Mazurowski, A. Burger, and P. P. Banerjee, Bioinspired multicontrollable metasurfaces and metamaterials for terahertz applications, Proceedings of SPIE, 10162:101620V, 2017. DOI: 10.1117/12.2258683. 3 C H A P T E R 2 What is Design? 5 It is not enough that we build products that function, that are understandable and usable, we also need to build products that bring joy and excitement, pleasure and fun, and, yes, beauty to people’s lives. Donald A. Norman (2004)1 2.1 INTRODUCTION Design has been around for as long as humans have created things. Design and making were not separate until the rise of the age of factories, since the craft-person designed the product while making it [1]. For example, a potter would make a pot by working with clay without ﬁrst making drawings. This was possible as long as the product was simple and the production process was implemented close to the people using the product. However, modern products are usually very complicated and are often produced at locations far away from their users’. This development engendered the need for more formalized design activity whereby designers analyze user needs and create documentation so that the product can be later man- ufactured by others elsewhere. The documentation must be detailed and accurate in specifying form, materials, dimensions, and other variable parameters. A design activity need not be formal and often it is not; however, it must be eﬀective. Methods and tools are therefore developed to improve the likelihood of matching user needs to a good new product whose production is cost eﬀective and which can be expediently disposed oﬀ after use. In writing this book, we expect that biologically inspired design will help designers in identifying good solution principles and even get detailed inputs for how to realize the product structure and functionality. Apart from ﬁnding solutions to functional needs, design is also about product appearance and the messages the product sends. This is clearly obvious for clothing and automobiles, because high premiums are paid for exclusive looks. Many automobiles are designed to communicate the impression of speed and power. This is done by borrowing design features from animals with those characteristics. For example, automobile headlights are designed to remind the bystander of the eyes of tigers or lions. Cute animals inspire children’s toys and sports equipment draw 1D.A. Norman, Introduction to this special section on beauty, goodness, and usability, Human-Computer Interaction, 19:311–318, 2004. 6 2. WHAT IS DESIGN? on visual inspiration from agile animals such as cheetahs. Biological inspiration for product appearance is a huge area, but this book is focused on how to utilize functional solutions found in the bioworld. 2.2 DESIGN THINKING The concept of design thinking is often invoked to distinguish design activities from scientiﬁc problem solving wherein underlying principles are uncovered systematically to ﬁnd optimal so- lutions. In contrast, design thinking requires multiple explorations to identify a range of possible solutions from which a satisfactory one is identiﬁed. The major diﬀerence in the thought processes of scientists and designers was exposed in an experiment more than four decades ago [2]. A group of ﬁfth-year students from architecture and a similar group from science were asked to arrange building blocks with colored sides with the goal of maximizing the number of sides of a speciﬁc color. The results suggested that science students selected blocks in order to discover the structure of the problem, whereas architecture students generated sequences of blocks until a combination proved acceptable. Design thinking is claimed to be suitable for solving an ill-posed problem by sketching several possible solutions to understand it from diﬀerent viewpoints [1, 3]. It calls for a mindset, as can be seen from analyzing the preferred ways of working of many designers. The mindset includes a strong user focus and the will to understand the core of the problem by generating a large space of many solutions. Several of these solutions will be visualized and even prototyped before a solution is ﬁnally selected for production. 2.3 THE DESIGN OBJECT From a ﬁrst look, it seems obvious that the product is the design object. However, further analysis clariﬁes that the design object also includes other elements such as single components or parts within the product; the overall system within which the product functions; and the non-material services associated with its merchandizing, use, and eventual disposal. When designing, the goal is to produce a thing to satisfy a need. This thing can be a phys- ical product such as a toothbrush or an automobile, or it can be a service such as linen laundry in a hotel. Clearly, the complexity of the design process varies with the type of the product or service to be designed. The delimitation of the design object is therefore important. The tooth- brush is a single component even though it is permanently assembled from a plastic handle and several clumps of brushing hairs. On the other hand, an automobile is a larger collection of single components that are conﬁgured in subsystems which together are assembled into the complete product: the automobile. However, an automobile is part of a larger system includ- ing gas stations, repair shops, roads, and parking spots, which together are necessary to provide the transportation functionality to the user. Furthermore, the product is part of a larger con- text which has a major impact on how the product is designed. Automobiles of diﬀerent types 2.4. DESIGN PROCESS 7 are made to satisfy needs in diverse contexts, as exempliﬁed by minivans to transport families with children, mobile homes for leisure activities, mobile workshops for mechanics, and taxis to transport visitors with luggage. The bioworld shows similar features. Organisms of many diﬀerent types co-exist in a mutualistic relationship system that is the prerequisite for the existence of a single organism in that system. In other words, the system comprises its constituent organisms as subunits with speciﬁc roles and interfaces to the rest of the organisms. Removal of organisms of a certain type from the system can seriously alter, and even demolish, the latter. In the same way, each organism consists of several organs and other subunits with speciﬁc roles and interfaces to the rest of the organism. When seeking inspiration from the bioworld, it is therefore beneﬁcial to also look at the larger system that the organism is part of. One major diﬀerence between the bioworld and design activity must be noted. A new feature in an organism arises in the bioworld as a result of random modiﬁcations of parental DNA. Most of these mutations are either inconsequential or harmful, but a certain mutation may confer reproductive success in the prevailing environment. That mutation becomes more prevalent in succeeding generations. A new species emerges in consequence of a succession of numerous mutations, which makes sudden innovation impossible in the bioworld [4], the oc- currence of elevated emergence rates of new species in the fossil record [5, 6] notwithstanding. For example, a marine species cannot evolve into an avian one through just one mutation. In contrast, although design activity is greatly limited by the availability of materials, tools, and expertise, disruptive innovation is possible by the interjection of a radically new concept. As an example, the emergence of the smartphones in 1992 from the predecessor telephones was a single-step achievement inasmuch as a smartphone possesses a touch screen, can email, store notes, keep a calender, and run diverse apps and widgets that would become widespread within a decade. Furthermore, smartphones began to provide very convenient access to the internet, thereby taking away a market segment from laptop manufacturers [7]. 2.4 DESIGN PROCESS While there is a general agreement that every design process starts with a user need and is expected to end with a solution, there are many models for structuring, organizing, and docu- menting design processes. The Pahl–Beitz model shown in Fig. 2.1 encompasses the following stages in sequence: task clariﬁcation, development of concepts (i.e., principal solutions), pre- liminary layout, deﬁnitive layout, and documentation [8]. Even though the model is sequential, it is recognized that many iterative loops will be made if the result of an activity is unsatisfactory. The Cross model shown in Fig. 2.2 is organized so the diﬀerent stages in a design activity form a circle [1]. The model makes it more apparent that design is an iterative activity wherein all decisions are revisited several times before a good ﬁnal solution is found. Both the Pahl–Beitz model and the Cross model require a function analysis to be undertaken before the design is speciﬁed. In the Pahl–Beitz model, function analysis takes place during concept development, 8 2. WHAT IS DESIGN? Figure 2.1: The Pahl–Beitz model of systematic design activity [8]. Analyze the market and company situationFind and select product ideasFormulate product proposalClarify the taskElaborate requirement listTaskMarket, company, economyInformationUpgrade and improvePlanning andclarifying the taskConceptual designEmbodiment designDetail designRequirements list(design speciﬁcation)Concept(principal solution)Preliminary layoutDeﬁnitive layoutProduct documentationSolutionPlan andclarifythe task:Develop theprincipalsolution:Develop theconstructionsolution:Deﬁne theconstructionstructure:Prepareproductionand operatingdocuments:Identify essential problemsEstablish function structuresSearch for working principles and working structuresCombine and ﬁrm up into concept variantsEvaluate against technical and economic criteriaPreliminary form design, material selection, and calculationSelect best preliminary layoutsReﬁne and improve layoutsEvaluate against technical and economic criteriaEliminate weak spotsCheck for errors, disturbing inﬂuences, and minimum costsPrepare the preliminary parts list and production and assembly documentsElaborate detail drawings and parts listComplete production, assembly, transport, and operating instructionsCheck all documents2.4. DESIGN PROCESS 9 Figure 2.2: The Cross model of systematic design activity [1]. with problem identiﬁcation linked to the search for working principles. In the Cross model, function analysis is used to analyze the overall design problem and break it into subproblems. A diﬀerence between the two models is the explicit focus on alternatives in the Cross model. Generating alternative solutions is an important way to ﬁgure out how the design problem is best solved. The Pahl–Beitz model, of course, recognizes this matter but the linear format of the model does not invite consideration of alternatives. Illustrated in Fig. 2.3, the Tjalve model is a sequential model of design activity contain- ing iterative loops [9]. With more emphasis on concept development than in the previous two models, the Tjalve model encompasses the stages of problem analysis; identiﬁcation of main functions; identiﬁcation of sub-functions and means; formulation of the basic structure of the product; quantiﬁcation of the product structure; delimitation of materials, dimensions, and sur- faces; and the overall form of the product. Whereas the Pahl–Beitz and Cross models are well suited for managing and coordinating design processes, the Tjalve model aims at guiding the designer in creative activities. Indeed, the Tjalve model deﬁnes the product in terms of ﬁve basic attributes. These are the structure of the product with its constituent elements and relations, along with the form, material, dimensions, and surface of each element. Thus, this model is a journey from an abstract description of the product using functions toward gradually more and more concrete descriptions of the overall structure and the constituent elements. Solutions are identiﬁed for each function, the arrangement of the solutions being called the basic structure. The basic structure is typically described using symbolic graphs rather than drawings illustrating the appearance of the prod- uct. The quantiﬁed structure developed thereafter contains dimensions as well as the physical arrangement of the constituent elements. RequirementsCharacteristicsObjectivesOpportunitiesStage ﬂowdirectionAlternativesEvaluationFunctionsImprovementOverallproblemOverallsolutionSub-problemSub-solutions10 2. WHAT IS DESIGN? Figure 2.3: The Tjalve model of systematic design activity [9]. The Tjalve model emphasizes the need for alternatives and gives detailed inspiration for how to systematically explore diﬀerent basic structures that will satisfy the functional require- ments. Several alternatives are also generated for the quantiﬁed structure, wherein the con- stituent elements can be conﬁgured diﬀerently in relation to each other. A useful division be- tween the total form of the product and the forms of the constituent elements allows for the search for partial solutions for single functions which later are combined into the total solution. Finally, the integrated-product-development model shown in Fig. 2.4 emphasizes that product design is not done in isolation but in parallel and close collaboration with market- and production-oriented activities [10]. While designers consider the type of product to design, the marketing team investigates competing products and determines whether there is room for a new MainfunctionsCriteriaProblemanalysisSub-functionsand meansBasicstructureQuantiﬁedstructureTotal formForm ofthe elementsMaterialDimensionSurface2.4. DESIGN PROCESS 11 Figure 2.4: The integrated-product-development model of systematic design activity [10]. product in the market, and the production team investigates diverse options for manufacturing the product. 2.4.1 TASK CLARIFICATION A design process can be initiated by many diﬀerent triggers [11]. A common trigger is the user need for a good solution, inadequate and barely adequate solutions being unsatisfactory. Another trigger is the introduction of a new technology, as exempliﬁed by the emergence of social media triggered by the introduction of smartphones. Yet another trigger is the economic aﬀordability of a technology. For instance, the low prices of eﬃcient batteries have caused a boom in the use of electrical scooters and bicycles. Once a user need has been identiﬁed, the design process has to be articulated. This is most often done either verbally or in writing, but a powerful alternative way is to provide diagrams. In order not to restrict the design process, the focus should be on highlighting the need but not on describing how it has been solved previously. This can be done by describing the consequences of satisfying the need through before/after pictures like the ones commonly used in advertise- ments for diet pills and other weight-reduction regimen. By visualizing the need, the designer avoids ﬁxation on existing solutions and becomes receptive to innovative solutions. Being readily understood, graphics are also eﬀective in communicating with stakeholders. Many design processes actually involve re-design of existing products. Re-design can be initiated either for improved functionality or to alleviate shortcomings experienced in existing products. A detailed analysis of how users behave in the situations calling for the use of a product Determiningthe basicneedDeterminingthe type ofproductConsiderationof producttypeUserinvestigationProductprincipledesignDeterminingtype ofproductionMarketinvestigationProductdesignphaseProductprinciplephaseInvestigationof needphaseRecognitionof needphaseProductionpreparationphaseExecutionphasePreliminaryproductdesignDeterminingproductionprinciplesPreparationfor salesModiﬁcationformanufacturePreparationforproductionSalesProductadaptationProduction543210TheNeed* INTEGRATED PRODUCT DEVELOPMENT12 2. WHAT IS DESIGN? Figure 2.5: Three stages in the use of a venﬂon catheter for injecting a polymer tube in a vein. (1) A metal needle labeled A penetrates the skin and guides a soft polymer tube labled B into the vein. (2) The metal needle is retracted and disposed of, leaving the polymer tube in the vein. (3) The polymer tube is ready for use. and interact with that product is typically carried out by the marketing department, but personal experiences of the designers will often lead to better results. Many companies therefore encour- age their designers to directly meet users in order to understand their needs and constraints as well as how the users will actually interact with the product. User contact is also valuable for getting feedback on design proposals comprising sketches and/or prototypes. An example of re-design is furnished by new types of the venﬂon catheter. A soft polymer tube in the venﬂon catheter is injected into a vein with the help of a stiﬀ metal needle, as shown in Fig. 2.5. The metal needle is retracted after the polymer tube is in place and is then disposed of. Nurses revealed in interviews that the retraction as well as the disposal of the metal needle are problematic for them. Not only have two extra processes to be carried out, but the sharp needle also represents a hazard. For this reason, the venﬂon catheter is nowadays equipped with a small safety device which prevents the nurse from touching the needle tip after it has been retracted. When analyzing the needs and constraints during a design activity, it can be advantageous to meet not only the direct users but also other stakeholders such as sales personnel, repair and maintenance personnel, and other persons who will come in contact with the product. Face-to- face interviews, questionnaires requiring both qualitative and quantitative answers, and personal observations provide insights. Personal experience of the product can also beneﬁt similarly, but it also carries the risk of introducing bias. The observations and experiences of a designer are not necessarily the same as those of users. Observations are valuable since they reveal the true behavior of a user. When interviewed, users tend to give more favorable descriptions of their use patterns. SkinA1BVein23The results obtained from the analysis of user needs and existing products are described in a user-need document. This document can include information on the actual use (and misuse) of the existing products and the context of use. Sometimes, the context is explained using personas which are descriptions of typical users and their use patterns. 2.4. DESIGN PROCESS 13 2.4.2 FUNCTION ANALYSIS A way to stimulate creativity and generate new and better ways of solving problems is to for- mulate an abstract description of how a product functions. Instead of describing a product as an assemblage of its components, it can be described as a set of abstract functions. Another advan- tage is to avoid product ﬁxation which is a risk when the names of previously used components are used. If a product is described in terms directly coupled to a speciﬁc action or form, the designer may become ﬁxated on a speciﬁc solution and ﬁnd it diﬃcult to imagine alternatives. For example, a concrete functional description such as “drive a person from point A to point B” will ﬁxate the designer in thinking of vehicles, whereas the abstract functional description “transport a person from point A to point B” will foster more open thinking so that a wider palette of solutions can emerge, e.g., conveyer belts and horseback riding. A product function is normally formulated using a verb/noun combination, such as “con- taining a liquid” or “cutting a piece of paper.” A complete description of the functions of and within a product can be made using a functions-means tree diagram [1, 9]. The sole trapezoid at the top of the diagram describes the main function that justiﬁes the reason why the product exists or should exist, whereas sub-functions describe what the constituent elements do. Means are physical manifestations that carry out a function. Both functions and means are explained in general terms without considering details such as shape or dimension. Figure 2.6 is a functions- means tree diagram in which the main function and sub-functions pertinent to drug delivery are identiﬁed along with the various means to accomplish each function. Note a diﬀerence in the way functions and means are described. All of the associated sub-functions are required for the realization of the main function. The more means that are recorded under a function, the more numerous are the ways of realizing that function. A functional surface identiﬁes where a speciﬁc function resides within the product [9]. A functional surface is typically marked on a sketch of the design object using hatched lines, as illustrated in Fig. 2.7. The ﬁgure shows that the two knife edges in a pair of scissors can be marked with hatched lines to indicate where the cutting function resides. Similarly, the holding function resides in a handle. The hatched lines do not invoke speciﬁc shapes, thus leaving the design assignment more open to innovation. A functional surface indicates the existence of an interface from the product to something else. Another notion used to describe the functionality of a product in an abstract way is that of an organ [11]. Like functional surfaces, an organ does not include information about shape and materials, but it does describe in abstract terms how a function is carried out. Two or more 14 2. WHAT IS DESIGN? Figure 2.6: A functions-means tree diagram for ways of delivering medicine inside a patient. Each trapezoidal block contains a function, each rectangular block a means. Figure 2.7: Examples of functional surfaces and organs for a pair of scissors. functional surfaces can be combined into an organ. For example, the two cutting surfaces in a pair of scissors form a cutting organ. Another example of an organ is the sealing organ in a container such as a bottle or a jar. A sealing organ can be realized as a lid with sealing surfaces in the lid and on the container. Using the term “lid” will automatically bring up mental pictures of existing solutions for bottles and jars. But referring to a “sealing organ” instead will make it easier to think freely of conceptually Using vacuumWith pressureTearing processCutting processUse impulseOralintakeInjectionthrough the skinAbsorptionthrough the skinStretch skinTopositionToﬁxate skinTopenetrate skinReduceresistancePreventbucklingInitiatefracturePropagatefractureTo delivermedicineTo transferliquidConnectingorganHoldingsurface2 cutting surfaces=cutting organdiﬀerent solutions. The designer could then propose a ﬂexible bottle where the opening is closed like a bag or the sealing organ could be a valve. 2.4. DESIGN PROCESS 15 2.4.3 DESIGN BRIEF AND PRODUCT SPECIFICATION A design assignment is typically speciﬁed using two diﬀerent documents: the design brief and the product specification. The design brief is a visionary document that explains the context of the intended product and how future users will beneﬁt, without going into details of the speciﬁcation. The design brief is targeted toward the conceptual-design phase discussed in Section 2.4.4. The product speciﬁcation includes more detailed descriptions and is targeted toward the design phases that follow the conceptual-design phase. The product speciﬁcation can be formu- lated in various ways. In the performance-speciﬁcation approach [1], several requirements are formulated, e.g., the performance metrics that the product must satisfy and the performance characteristics that it must exhibit. For instance, the product must be manufactured in a certain range of colors and/or that it must be small enough to be stored in a standard storage space. The performance-speciﬁcation approach is useful as it delivers a checklist to ensure that a design proposal is within acceptable limits. However, this approach is less helpful when comparing diﬀerent design proposals and existing solutions. The product-speciﬁcation approach [10] overcomes that problem. In this approach, both requirements and criteria are stated. The requirements are ﬁxed and must be met by the design proposal; otherwise, the design proposal is unviable. The criteria are used to compare diﬀerent design proposals using evaluation matrixes (Section 2.4.5) and need to be formulated to indicate a desirable direction but not set limits. For a new toothbrush as an example, the requirements could include maximum dimensions and color; the criteria could specify that the toothbrush should be pleasant to the mouth, be easy to clean, and have a low weight. 2.4.4 CONCEPTUAL DESIGN Conceptual design is the creative process of generating ideas for solving the overall design problem and ﬁnding partial solutions to each of the functional challenges identiﬁed in the functions-means tree diagram. A typical way to come up with ideas is to form a brainstorming team. There are many prac- tical approaches [1] for brainstorming, but all have in common that as large a number of ideas be generated as possible and that criticism of ideas be avoided during brainstorming sessions. Diﬀerent brainstorming approaches introduce diﬀerent ways of viewing the design problem; hence, using several diﬀerent approaches increases the number of ideas. Brainstorming can be done by single persons on their own, but doing it together with other people will drastically increase the chance of ﬁnding new ideas because participants will inspire each other. Also, the brainstorming session can have many diﬀerent formats. One format involves a whiteboard on which a moderator writes up all the ideas that the participants propose. 16 2. WHAT IS DESIGN? In this way, a participant needs to articulate each of his/her ideas so that it is intelligible to the moderator, which also facilitates the uptake of that idea by other participants to generate additional as well as downstream ideas. Another brainstorming format lets each participant write down their ideas on colored post-it notes that are then stuck on a whiteboard. The advantage of this format is the delivery of multiple ideas by each participant, but there is a risk that the participants do not see the ideas of others and do not use those ideas to generate more ideas. Brainstorming is a creative idea-generation method whereby the participants are not re- quired to follow rigid rules or constraints. In contrast, systematic idea-generation methods set rigid rules for the participants, those rules possibly stimulating the participants to examine is- sues that they would not have otherwise thought of. Examples of systematic idea-generation methods include analysis of existing or competing solutions, TRIZ, and biologically inspired design. Analysis of existing or competing solutions requires identiﬁcation of their weaknesses and strengths so that a comparative assessment may be made of the opportunities oﬀered by each. TRIZ is the Russian acronym for the Theory of Inventive Problem Solving which is a method for developing innovative solutions [12]. It is based on a large (39 39) matrix of con- tradictory features (e.g., larger in volume but lighter in weight). Each ﬁeld in the matrix contains a list of possible solutions developed from analyses of very large number of patents. (cid:2) Biologically inspired design emerges from the thought that the bioworld oﬀers a palette of solutions to numerous technological problems. A function analysis must be made of a candidate structure or process in the bioworld, the relevant principles must be extracted from that analysis, and ﬁnally those principles must be applied to the problem being addressed in the design activity. It is important to diﬀerentiate between ideas and concepts. An idea in creative design work is basically just a principle for how to solve a problem. Application of that principle in a speciﬁc context transforms the idea into a concept that satisﬁes the context-speciﬁc constraints and conditions. For example, the idea of using a lid to seal a container becomes a concept in the context of closing a beer bottle, a context-speciﬁc constraint being that the lid must be able to withstand the pressure within the bottle. Conceptual design normally starts by an examination of partial solutions to each of the functions required in the product. It is assumed that the superposition principle applies so the partial solutions can be combined to form the overall solution. One way of combining partial solutions into an overall solution is by using a morphology chart [1]. This chart is a table con- taining lists of possible partial solutions for each of the functions required in the product. The partial solutions can be described in words but even better with small icons for easier communi- cation within the design team. A candidate overall solution can be formulated by selecting one partial solution for each function. 2.4. DESIGN PROCESS 17 2.4.5 CONCEPT EVALUATION The diverse concepts gathered for a given design activity can be comparatively assessed in dif- ferent ways. Often, the concepts in the form of prototypes can be ranked by major stakehold- ers including prospective users, who can also provide feedback in the form of written and oral comments. A risk in this type of assessment is that the evaluation may be based on parame- ters other than what is important for the product. For example, a poorly produced prototype could be ranked poorly even though the underlying concept could lead to superior performance. To avoid such biased evaluations, the major criteria must be clearly formulated in the product speciﬁcation and used for structuring the interviews with stakeholders and users. A good tool for concept evaluation is the evaluation matrix which can be one of two types [1]: (i) the comparison matrix also referred to as the Pugh matrix and (ii) the rating matrix also called the weighted-objective-method matrix. 1), worse ( The comparison matrix compares each concept with a reference product which is typically an existing product. For every criterion in the product speciﬁcation, each concept is rated better 1), or similar (0) to the reference product and the ratings are added to produce ( C the overall rating for the concept. The major advantage of the comparison matrix is its simplicity which makes it easy to understand and discuss its results. A limitation is that all criteria need to be of equal importance since they are weighted equally. (cid:0) That limitation is taken care of in the rating matrix. Each criterion is given a weight w de- pending on its importance. For every criterion in the product speciﬁcation, each concept is given a numerical score. The overall rating for the concept is found by multiplying the score numbers with the weight for each criterion and adding the numbers together. The rating matrix should produce a better comparison of the diverse concepts than the comparison matrix. However, the rating matrix is more complicated than the comparison matrix, and stakeholders and users may ﬁnd it harder to understand and accept the outcomes of a comparison. 2.4.6 TOWARD DETAILED DESIGN What has been described so far in this chapter is normally referred to as conceptual design. The results are design concepts describing the product at a general level without going into detail about materials, shapes, and dimensions. Conceptual-design proposals are often made as hand drawings to signal that they are not ﬁnished and many details can still be altered. The more detailed design work is done thereafter: the product embodiment is carefully planned, typically using software for computer-aided design; precise dimensions are determined; tolerances are added; materials are selected; and manufacturing techniques are speciﬁed. Besides drawings by hand and the more detailed drawings produced using computer-aided design tools, physical models are often made. Depending on their ﬁdelity and purpose, physical models are referred to using diﬀerent terms. A rudimentary model using rough materials such as 18 2. WHAT IS DESIGN? cardboard, clay, and paper is typically called a mock-up. It serves to demonstrate only a few rele- vant aspects of the product such as physical size and how it interfaces to other products. When a physical model appears close to the ﬁnal product, it is referred to as a visual model. Another type of physical model is a functional model, which only serves to demonstrate that a given principle and embodiment will actually fulﬁll the requirements. Finally, prototypes are traditionally used to denote models that comes very close to the ﬁnal product but are typically made as one-oﬀs. However, the terminology is drifting and many designers use the term prototype as a synonym for a mock-up or a functional model. While all of these more detailed design activities are important elements in the overall design process, we will not go into more detail with them in this book. Biologically inspired design is typically incorporated in the conceptual-design phase. 2.5 REFERENCES [1] N. Cross, Engineering Design Methods—Strategies for Product Design, Wiley, Chichester, UK, 2008. 5, 6, 7, 9, 13, 15, 16, 17 [2] B. R. Lawson, Cognitive strategies in architectural design, Ergonomics, 22:59–68, 1979. DOI: 10.1080/00140137908924589. 6 [3] N. Cross, Design Thinking: Understanding how Designers Think and Work, Berg, Oxford, UK, 2011. DOI: 10.5040/9781474293884. 6 [4] D. Adriaens, Evomimetics: The biomimetic design thinking 2.0, Proceedings of SPIE, 10965:1096509, 2019. DOI: 10.1117/12.2514049. 7 [5] N. Eldredge and S. J. Gould, Punctuated equilibria: An alternative to phyletic gradual- ism, Models in Paleobiology, T. J. M. Schopf, Ed., pages 82–115, Freeman Cooper, San Francisco, CA, 1972. 7 [6] M. J. Benton and P. N. Pearson, Speciation in the fossil record, Trends in Ecology and Evolution, 16:405–411, 2001. DOI: 10.1016/s0169-5347(01)02149-8. 7 [7] C. M. Christensen, M. Raynor, and R. McDonald, What is disruptive innovation?, Har- vard Business Review, 93(12):44–53, 2015. 7 [8] G. Pahl, W. Beitz, J. Feldhusen, and K.-H. Grote, Engineering Design: A Systematic Ap- proach, 3rd ed., Springer, London, UK, 2007. DOI: 10.1007/978-1-84628-319-2. 7, 8 [9] E. Tjalve, A Short Course in Industrial Design, Butterworth, London, UK, 1979. DOI: 10.1016/C2013-0-00824-9. 9, 10, 13 [10] M. M. Andreasen and L. Hein, Integrated Product Development, IFS (Publications) Ltd., Kempston, UK, 1987. 10, 11, 15 2.5. REFERENCES 19 [11] M. M. Andreasen, C. T. Hansen, and P. Cash, Conceptual Design: Interpretations, Mindset and Models, Springer, Cham, Switzerland, 2015. DOI: 10.1007/978-3-319-19839-2. 11, 13 [12] J. F. V. Vincent, O. A. Bogatyreva, N. R. Bogatyrev, A. Bowyer, and A.-K. Pahl, Biomimetics: Its practice and theory, Journal of the Royal Society Interface, 3:471–482, 2006. 16 C H A P T E R 3 21 Engineered Biomimicry: Solutions from the Bioworld If a group of engineers, mindful of our need to tap natural energy sources, were to embark on designing a machine that would pump water out of the ground over an area of 100 square meters continuously, and would boil oﬀ the water into steam, using only the energy directly from the sun for the whole process, it is possible that they might do it. But their ﬁnished machine would certainly never resemble a tree! Eric R. Laithwaite (1988)1 Although we humans have long been envious of feats of performance displayed by a variety of an- imal species [1], and we have been creative in emulating and even surpassing some of those feats, biomimicry began to acquire an organizational framework only during the 1990s. Coinage of the term biomimetics is usually attributed to Otto Schmitt during the late 1950s [2]. The simi- lar term biomimesis coined during the next decade [3] does not have much currency nowadays. The term bionics, once synonymous with biomimetics [4], is nowadays employed in English exclusively to the science and practice of replacing an organ in a living being by a prosthesis. The umbrella term biomimicry has come to subsume its precedents, although one (namely, bionics) survives as bionik in German. Biomimicry opens “the possibility of a new industrialism that is more attuned to nature’s needs” [5] and therefore intersects with the discipline of sustainable design. As discussed in Chapter 1, engineered biomimicry does not require consideration of sustainability. In this chapter, we ﬁrst lay out the case for engineered biomimicry, then present a few representative ex- amples, identify some characteristics of the solutions available in the bioworld for technological problems, and ﬁnally discuss the importance of having biologists on design teams for bioworld solutions. 3.1 THE CASE FOR ENGINEERED BIOMIMICRY Charles Darwin used the word evolve only once in the ﬁrst edition [6] and just 16 times in the sixth edition [7] of his most famous book On The Origin of Species. Instead, he used the term 1E. R. Laithwaite, Gaze in wonder: an engineer looks at biology, Speculations in Science and Technology, 11:341–345, 1988. 22 3. ENGINEERED BIOMIMICRY descent with modification to describe the origin of new species. Most traits of a child are derived from those of its parents, but some modiﬁcations may occur. Later scientists realized that genes are the vehicles for heritability or descent and that imperfect replication of parental DNA results in random modiﬁcations called mutations. Most mutations are either inconsequential or harmful, but a certain mutation may confer reproductive success in the prevailing environment. That mutation becomes more prevalent in succeeding generations, the process being called natural selection. Whereas mutations are random, natural selection is not. Only those mutations that lead to better adaptation to altering or altered environments are successful. A continuum of mor- phological varieties thus arises in a species. A series of successful mutations, genetic transfer from one population to another as a result of migration, and random changes in the frequencies of certain genes are mechanisms which eventually result in a new species that does not have morphological intermediates between it and the older species. As of now, about 1.3 million species have been identiﬁed, but some 86% of terrestrial species and 91% of marine species are estimated to still await description [8]. Add the 4 billion species that are estimated to have gone extinct [9] since life began on our planet some 4 billion years ago [10]. Each of those species can be considered as being successful for a certain period, dying out only when the environmental conditions were no longer conducive enough to sustain it. The success of any mutation cannot be predicted and there is no prescient agency for nat- ural selection. Still, looking at the history of the bioworld, both recent and in the prehistoric past, we may regard all species as data points in a multidimensional space. The mutually orthog- onal axes of this space are physical variables (such as ambient temperature, ambient pressure, and mass density) and performance characteristics (such as speed of locomotion, longevity, and fecundity). Each species as a data point represents a successful experiment. Since the laws of physics hold sway over every biological process just as completely as over every technological operation, we should then consider the bioworld as a repository of answers to billions of technological questions [11]. Some of those answers may not be optimal for our technological requirements but can still illuminate possible research directions. Other answers may be used by us without much fuss. Furthermore, the bioworld contains a plethora of processes some of whom can be replicated either partially or wholly in industrial operations. No wonder, humans have long been inspired by attractive outcomes and functionalities evident in plants and animals. 3.2 ENGINEERED BIOMIMICRY Engineered biomimicry encompasses both basic research on outcomes and mechanisms of di- verse phenomena displayed by living organisms and the application of fundamental principles uncovered by that basic research to devise useful processes and products. Engineered biomimicry is classiﬁed into bioinspiration, biomimetics, and bioreplication, as shown in Fig. 3.1 [12], based 3.2. ENGINEERED BIOMIMICRY 23 Figure 3.1: Classiﬁcation of engineered biomimicry into bioinspiration, biomimetics, and bioreplication. on whether outcomes, mechanisms, or structures in the bioworld are aimed for reproduction in technoscientiﬁc settings. 3.2.1 BIOINSPIRATION Ancient stories provide numerous examples of the human desire to ﬂy. After rescuing two chil- dren from a sacriﬁcial altar, a ﬂying ram became the constellation Aries in Greek mythology. Zeus, the king of Greek gods, had a winged steed named Pegasus. Quetzalcoatl, the Aztec god of wind and learning, was a winged serpent. Hindu mythology is replete with ﬂying chariots and palaces. Mohammad, the prophet of Islam, was ﬂown to heaven by a white mule-donkey hybrid named Bur Some 500 years ago, Leonardo Da Vinci (1452–1519) studied birds to conceptualize sev- eral ﬂying contraptions which evidently never took oﬀ. Sir George Cayley (1773–1857) made a pilotless glider that did ﬂy in 1804. Orville and Wilbur Wright were to ﬁrst to successfully ﬂy a heavier-than-air machine with a person onboard, on December 17, 1903. The emergence of aeroplanes inspired by birds in self-powered ﬂight is an excellent example of bioinspiration, but birds and aeroplanes have diﬀerent ﬂying mechanisms. The goal in bioinspiration is to reproduce a biological outcome but not the underlying biological mechanism(s) and structure(s). aq. N 3.2.2 BIOMIMETICS Biomimetics is the reproduction of a physical mechanism responsible for a speciﬁc outcome or functionality exhibited by a biological structure. Greek mythology furnishes the classical exam- ple of biomimetics through Icarus, a ﬂying human who escaped from a Cretan prison using wings made of feathers and wax. Sadly, he perished after the wax melted when he ﬂew too close to the sun. A modern example is that of insulin, a hormone produced naturally in mammalian pan- creas but nowadays modiﬁed and synthesized in either yeasts or Escherichia coli bacteria [13, 14]. Yet another example of biomimetics is Velcro™ that comprises dense assemblies of hooks and loops, the former emulating the hooked barbs on a burdock seed and the latter, the fur of a furry animal. The commercialization of this biomimetic analog of a natural mechanism of adhesion is a fascinating story of determination [15]. BioinspirationBioworldOutcomeBiomimeticsMechanismBioreplicationStructure24 3. ENGINEERED BIOMIMICRY 3.2.3 BIOREPLICATION Bioreplication is the direct replication of a structure found in a biological organism in order to reproduce one or more functionalities exhibited by the biological structure copied. During the last ten years, diverse physical techniques have been harnessed to replicate several biological structures such as the eyes and wings of several types of insects [16]. The techniques include the sol-gel method; atomic layer deposition; physical vapor deposition; and some combination of imprint lithography, casting, and stamping [17]. Some of these techniques are more suitable for reproducing surface features, others for bulk three-dimensional structures. 3.3 EXAMPLES OF ENGINEERED BIOMIMICRY 3.3.1 BIOINSPIRED COMPUTATIONAL TECHNIQUES Every multicellular organism contains one or more networks in which information is sensed, transmitted, processed, transmitted again, and then acted upon. Relying on physical and chem- ical phenomena, all of these processes are quantitative and therefore may be mathematically modeled by us, albeit not always easily. Mathematical models of many biological processes employ diﬀerential equations to re- late spatial and temporal gradients of physical quantities, such as the concentrations of some chemicals, partial pressure of various ﬂuids, and the electric charge density transported by ions. Initial and boundary conditions therefore must be concurrently considered [18, 19]. Successful examples include models of oxygen-deﬁcient dermal wounds [20] and cancer growth [21]. Often, the data gathered about a biological process is both discrete and huge, as exem- pliﬁed by tumor growths [22] and neuronal activity [23]. To analyze these data, mathematical methods commonly used for time series [24] and dynamical systems [25] are pressed into service. The two foregoing paragraphs provide examples of mathematical methods applied to un- derstand biological processes. Are some mathematical methods to analyze non-biological phe- nomena inspired by the bioworld? An aﬃrmative answer to that question has emerged in modern times [26]. Inspired by the structure of animal brains, artificial neural networks (ANNs) are being used for pattern recognition tasks, including speech recognition, machine translation, video games, and traﬃc control; fuzzy logic seeks to emulate human cognition for automated decision making; swarm intelligence guides mathematical investigations of emergent phe- nomena; genetic algorithms are often used for optimization; and so on. Let us focus on two of these bioinspired computational techniques. Artiﬁcial Neural Networks ANNs have been inspired by animal brains which are networks of neurons connected to other neurons through synapses [27, 28]. In an ANN, neurons are replaced by nodes and synapses by connections, as depicted schematically in the top panel of Fig. 3.2. 3.3. EXAMPLES OF ENGINEERED BIOMIMICRY 25 Figure 3.2: Top: Schematics for artiﬁcial neural networks. The middle panel of Fig. 3.2 shows two nodes providing inputs I1 and I2 to a node whose output is denoted by O. The output is related to the inputs by a nonlinear function f .x/ such that ( O D 0 ; w1I1 w2I2 < b ; f .w1I1 C w2I2/ ; w1I1 w2I2 b : (cid:21) C C (3.1) The on/oﬀ characteristic of real neurons is simulated by the conditionality on the right side of Eq. (3.1), with b as the bias or the threshold value of the argument x of f .x/, and the relative importance of the inputs coded through the weights w1 and w2. An ANN can have several input nodes arranged in a layer and several output nodes ar- ranged in a diﬀerent layer. In between is at least one layer of hidden nodes, called thus because these nodes have no direct connection to: (i) the sensors providing data to the input layer and HiddenlayerOutputlayerOWeightConnection(synapse)Node(neuron)Node(neuron)I1I2w2I2w1I1Inputlayer26 3. ENGINEERED BIOMIMICRY (ii) the actuators implementing actions controlled by the output layer. The bottom panel of Fig. 3.2 shows an ANN in which information moves in the forward direction, i.e., from the input nodes, through the hidden nodes, to the output nodes. ANNs of other types can have backward connections and even loops. Known sets of input-output data are used to train an ANN, i.e., determine the weights. More training data will determine the weights better (usually but not always), the assumption being that the ANN learns just like a biological brain. After the ANN is deemed to have learned enough, it can be fed data to predict the output with conﬁdence. Genetic Algorithms Genetic algorithms are commonly used to design a device or structure to meet a numerical cri- terion for performance [29]. The device performance depends on the values of a certain number (say N ) of characteristic variables. The algorithm begins by randomly selecting M1 > 1 sets of the N characteristic variables. A performance function denoted by p is calculated for every one b1 for a speciﬁc set, where b1 is a threshold value, then that particular set of the M1 sets. If p M1 sets survive to reproduce is retained; if not, that set is eliminated. The result is that the next generation comprising M2 new sets. M1 N (cid:20) (cid:21) D The simplest reproduction method is mutation, whereby each new set is based on a single surviving set of the previous generation. If the population is being doubled by mutation (i.e., M1), each set of the old generation is reproduced twice, once as itself and once by multi- 2 M2 N plying its characteristic variables by a random factor. A more complex method of reproduction is crossover, whereby each set of the new generation is based on some combination of the surviving sets of the previous generation. The performance function p is calculated for each one of the M2 b2 for a speciﬁc set, where b2 > b1 is a new threshold value, then that particular set sets. If p is retained; if not, that set is eliminated. (cid:21) This process of creating new generations continues until a criterion for terminating it is satisﬁed. At that stage, several devices satisfying the performance criterion p b1; b2; : : : g f could have been identiﬁed. Then comes the task of selecting and making at least one of those devices. max (cid:21) 3.3.2 BIOMIMETIC PRODUCTION OF HUMAN INSULIN The peptide hormone insulin began to be used in 1922 to treat diabetic patients. In a normal person, insulin is produced in the pancreas where it is stored well in excess of daily needs. A series of biochemical reactions in response to elevated concentration of glucose in blood triggers the release of insulin from the pancreas. Its half-life ranging between four and six minutes, it lasts outside the pancreas for about an hour, and is eventually cleared by the liver and the kidneys. The human insulin molecule has 51 amino acids, its molecular formula being C257H383N65O77S6. Insulin is produced and stored in the pancreas as a hexamer, i.e., an ag- 3.3. EXAMPLES OF ENGINEERED BIOMIMICRY 27 gregate of six molecules. The hexamer is very stable. Insulin is released from the pancreas as a monomer, which acts very rapidly. Until about three decades ago, virtually all insulin injected into patients was derived from the glands of either cows or pigs obtained as waste products from abattoirs. Bovine insulin diﬀers from human insulin in only three amino acids, porcine insulin in just one. Fourteen cattle or 70 pigs had to be slaughtered to harvest enough insulin to last a patient for a year. However, the responses of some patients were unpredictable and some patients had severe reactions. Research began in the 1970s for a biomimetic route to synthesize human insulin itself [13]. That research has been wildly successful [14]. The sequence of biochemical reactions in mam- malian pancreas is replicated in yeasts and bacteria. The reproduction of yeasts and bacteria can be regulated fairly easily, which then eliminates the need for continually harvesting mammalian pancreas. Moreover, as the production process is initiated with human insulin, the biomanufac- tured insulin is maximally compatible with human patients. Pancreatic Production The production of a molecule called preproinsulin is encoded in a gene found in chromosome 11 in the nuclei of human cells. A chromosome is a DNA molecule comprising nucleotides of four diﬀerent types arranged into two strands that are coupled to each other by hydrogen- hydrogen bonds. There are also packing proteins in the chromosome to keep the DNA molecule untangled. Every nucleotide contains a nitrogenous base. There are four types of nitrogenous bases: adenine, thymine, guanine, and cytosine. Whereas adenine can form a hydrogen-hydrogen bond only with thymine, guanine can form a hydrogen-hydrogen bond only with cytosine. Thus, ade- nine and thymine are mutually complementary, and so are guanine and cytosine. The sequence of bases in one strand of a DNA molecule is matched by the sequence of complementary bases on the accompanying strand. Three consecutive bases form a codon. A codon contains the instructions to produce a protein-creating amino acid. There are 22 protein-creating amino acids. Of the 64 codons pos- sible, 61 provide instructions for producing 20 of those amino acids. Some amino acids can be produced by more than one codon. The ﬁnal two protein-creating amino acids are synthesized through complex reactions. A short sequence of amino acids is called a peptide. A long sequence of amino acids is called a polypeptide or a protein. Three codons are used to indicate the end of an amino-acid sequence, the start of that sequence being signaled in a more complex way. Thus, the DNA molecule in a chromosome comprises two complementary chains of codons. A gene is a sequence of codons that contains instructions to produce a molecule that performs a function. Some genes contain instructions to produce proteins, others to produce diﬀerent types of RNA molecules. An RNA molecule is a single strand of nucleotides of four 28 3. ENGINEERED BIOMIMICRY types, each containing either adenine, thymine, guanine, or uracil (diﬀerent from cytosine found in DNA molecules). The DNA molecule can then be considered as two chains of identical genes, but it also contains codon sequences that may either have no purpose or whose purpose has yet not been discovered. The process of insulin production in pancreatic cells begins when an enzyme called RNA polymerase, accompanied by molecules called transcription factors, attaches to a region in the DNA molecule just before the start of the preproinsulin-producing gene. Then the two DNA strands separate, and RNA nucleotides attach via hydrogen-hydrogen bonds to the nucleotides in one of the two strands of the DNA molecule until the stop codon is encountered. At that stage, the RNA molecule dissociates from the DNA strand, and the two strands of the DNA molecule couple again. The RNA molecule thus synthesized is called a messenger RNA (mRNA). It has the in- structions to produce preproinsulin. That process begins when a transfer RNA (tRNA) molecule and a ribosome attach themselves to the start codon of the mRNA molecule. Depending on the next codon, the appropriate amino acid attaches itself to the end of the tRNA molecule. The ribosome then translocates to the next codon, and the next appropriate amino acid attaches itself to the previous amino acid. This elongation of the tRNA molecule continues until the stop codon is reached. At that stage, the single-chain preproinsulin molecule is attached to the original tRNA molecule. The two then dissociate. A chemical reaction in the endoplasmic reticulum in the pancreas causes the removal of 12 amino acids from the preproinsulin molecule, which then folds into two linear chains connected by a peptide. The resulting molecule is called proinsulin. Removal of the connecting peptide turns the proinsulin molecule into the insulin molecule. Biomimetic Production of Insulin This complex process had to be reproduced biomimetically. Researchers chose E. coli, a bac- terium that contains a circular chromosome [13]. Some strains of E. coli also contain a circular plasmid, which is a genetic structure that is not a chromosome. The gene INS is responsible for producing preproinsulin in humans. This gene is inserted in the plasmids of some bacteria, as shown schematically in Fig. 3.3. As the bacteria with the altered plasmids reproduce in a fermen- tation chamber, the number of the altered plasmids increases. Biochemical reactions are then used to harvest proinsulin molecules, which are then converted chemically to insulin molecules. Some manufacturers use yeasts in place of E. coli. The dominant mode of reproduction in both types of single-celled organisms is asexual. In a process named mitosis, a cell elongates and then divides once to form two identical cells. Both of these cells are genetically identical to the cell that underwent mitosis. 3.3. EXAMPLES OF ENGINEERED BIOMIMICRY 29 Figure 3.3: Schematic for biomimetic production of insulin. The entire biomimetic process is initiated by some copies of INS, but no more are needed after production begins. The proclivity of single-cell organisms to reproduce rapidly via mitosis makes the biomimetic production of insulin economically viable. Fast-acting insulins are produced by slight interchanges of codons in the initiating copies of the human genes to minimize the tendency to form hexamers. The type of interchange se- lected regulates the ratio of monomers to hexamers. Intermediate-acting insulins are produced by adding chemicals that help maintain hexamers. Long-acting insulins are produced by slight modiﬁcations of an amino acid. Thus, a therapeutically signiﬁcant functionality is imparted to biomanufactured insulin in comparison to insulin produced in the pancreas. 3.3.3 BIOREPLICATED VISUAL DECOYS OF INSECTS An industrially scalable bioreplication process with nanoscale ﬁdelity has been devised to pro- duce visual decoys of females of the buprestid insect species Agrilus planipennis, commonly called the emerald ash borer (EAB). The decoys are more successful than freshly sacriﬁced females in luring males of the species toward attempted copulation followed by electrocution [30, 31], thereby providing forestry managers a tool to limit the spread of the invasive species. The emerald ash borer is a native of northeast Asia. Its shipborne arrival in North America was detected in 2002. That very year, it was identiﬁed as devastating ash trees. EAB females deposit eggs in the bark of ash trees; the EAB larvae chew long meandering tunnels in the Human DNAINS geneFermentation chamberNuclear DNAE. coliRecombinant E. coliRecombinantDNA insulinExtractionandpuriﬁcationstepsPlasmid DNAHuman pancreas cell30 3. ENGINEERED BIOMIMICRY Figure 3.4: Top: Female of the species Agrilus planipennis. Middle: Three types of bioreplicated decoys produced with an industrially scalable process [30]. Bottom: 3D-printed decoy [35]. trunks as they feed, thereby disrupting the transport of nutrients and water to the leaves; and adults chew their way back to the bark and exit the trunk [32]. EAB are thriving in North America in the absence of natural predators and parasitoids. Although their populations spread about 20 km per year, long-distance transport of wood products allows them to colonize far- ﬂung areas. Ash wood being used for numerous purposes, the destruction of ash trees is having a severe economic impact. Furthermore, as other invasive species move into the aﬀected areas, native species suﬀer from habitat reduction and the soil chemistry changes [32]. EAB do not have sex pheromones to attract mates, relying instead on visual communica- tion. Adult EAB are conspicuous by their bright metallic green elytra (hardened forewings), as shown in the top panel of Fig. 3.4. Adult EAB males patrol tree canopies for adult EAB females resting and feeding on ash leaves. After seeing a female from as high as 100 cm, a male drops like a paratrooper toward her and makes vigorous attempts to copulate [33]. 3.3. EXAMPLES OF ENGINEERED BIOMIMICRY 31 A visual decoy looking very similar to an EAB female with its elytra folded over its body would be necessary to lure EAB males. The decoy’s color must be iridescent green to contrast 10-(cid:22)m surface features present on the against the the background of ash foliage. Additionally, elytra must be reproduced on the decoy. (cid:24) An industrially scalable bioreplication process was therefore devised [30]. This process involved two major stages. In the ﬁrst stage, a pair of matching positive epoxy and negative nickel dies were bioreplicated from an euthanized female EAB. The negative die was made by the deposition of a 500-nm-thick conformal ﬁlm of nickel on the upper surface of the euthanized female EAB in a low-pressure chamber. The nickel thin ﬁlm was then thickened by electroforming to about 100 (cid:22)m. The female EAB was then plucked out, leaving behind a negative die with ﬁne-scale features, the conformal ﬁlm comprising 22-nm-diameter nickel grains. A positive die of epoxy was made from the negative die of nickel using several casting steps and the deposition of a conformal thin ﬁlm of chalcogenide glass. (cid:24) (cid:24) In the second stage, a sheet of poly(ethylene terephthalate) (PET) was hot stamped be- tween the pair of matching dies. The PET sheet had been previously coated on the upper side with a quarter-wave-stack Bragg ﬁlter [34] made of two distinct polymers to reﬂect normally incident green light and on the lower side by black paint to absorb visible light of all other colors. Light stamping between the pair of matching dies kept the Bragg ﬁlter intact. How- ever, heavy stamping for better reproduction of the ﬁne-scale features of the elytra pulverized the Bragg ﬁlter, for which reason the lower side of the decoy was spray-painted metallic green, again to mimic the actual color of the EAB elytra. The middle panel of Fig. 3.4 is a photograph of bioreplicated decoys of three diﬀerent types. In a preliminary ﬁeld experiment, males of the related species A. bigutattus were targeted, the inter-species attraction having been previously recorded by entomologists. The bioreplicated decoys were 40% more eﬀective in luring males than dead EAB females [30]. The lower eﬀective- ness of the dead EAB females is indicative of the suboptimality of many biological phenomena, as discussed in Section 4.5. The eﬀectiveness of the bioreplicated decoys was evaluated against that of 3D-printed decoys, an example of which is shown in the bottom panel of Fig. 3.4. Although EAB males were almost equally attracted to decoys of both types, they would ﬂy toward and alight on the bioreplicated decoys for a couple of seconds, but they would break oﬀ midway toward the 3D- 10-(cid:22)m surface features on the 3D-printed printed decoys and veer away. The absence of the decoys rendered them insuﬃciently authentic on closer inspection by the EAB males. (cid:24) In the third ﬁeld experiment [31], the bioreplicated decoys were oﬀered to EAB males. These decoys evoked complete attraction, paratrooper ﬂight, and attempted copulation from EAB males. Some decoys were electrically wired for alighting males to be electrocuted. The electrocuting decoys could assist forestry managers in slowing the spread of the pest species. The bioreplication process for industrial-scale production of these decoys was sped up [36] by making the negative nickel die from an array of several female EABs instead of only one. 32 3. ENGINEERED BIOMIMICRY Also, the positive die was eliminated by a decision to ﬁll up the multiple cavities of the negative die with the thermally curable liquid polymer poly(dimethyl siloxane). Multiple decoys made simultaneously were painted metallic green. The tale of EAB decoys is one in which a biological structure is directly replicated by technoscientists in order to fulﬁll a societal goal: to eliminate a pest species, or at least reduce its proliferation. Can this nanoscale bioreplication process also assist biologists in answering certain questions that cannot be answered otherwise? The answer is a guarded “yes.” For instance, the spectral ranges of buprestid vision systems could be determined by coloring the decoys red, blue, or yellow, or even ultraviolet. Of course, humans cannot see ultraviolet, but many insect species can [37]. The same bioreplication technique could be applied to determine the spectral ranges of the vision systems of their predator species. Even evolutionary scenarios could be investigated by determining the aversion or aﬃnity of a predator species to color mutations in a prey species. 3.4 DESIGN TEAMS FOR BIOWORLD SOLUTIONS The examples of engineered biomimicry presented in some detail in this chapter strongly in- dicate that this topic transcends the boundary between science and engineering. Until perhaps the middle of the 19th century, there was no distinction between engineers and scientists. The explanation of natural phenomena, today considered the domain of scientists, and the commer- cially viable exploitation of those phenomena for the betterment of the human condition, today considered the domain of engineers, were conjoint goals of a person who functioned either as a scientist or as an engineer in diﬀerent phases of professional life. Sometimes, that person even functioned concurrently as an engineer and a scientist. The English word scientist was coined in 1834 for someone dedicated to the pursuit of new knowledge in any branch of science [38, 39]. In the ensuing decades, scientists were dif- ferentiated from engineers, the former as the discoverers of new facts in nature and formulators of potentially veriﬁable theories to explain those facts, the latter as those who apply scientiﬁc knowledge to solve practical problems at a cost that society can bear. This diﬀerentiation is less pronounced nowadays, especially when multidisciplinary teams are formed to undertake complex research projects, whether at universities or in industries or in university-industry consortia. Teams comprise physicists, chemists, materials scientists, me- chanical engineers, chemical engineers, electrical engineers, medical scientists, etc., as dictated by project requirements. The scope of biologically inspired design is the formulation of design strategies to re- produce desirable outcomes, mechanisms, and structures from the bioworld. The practice of biologically inspired design requires both scientists and engineers to work collaboratively, just as for other types of complex research projects with an industrial focus. There is, however, a crucial issue. Such a team must have biologists each of whom who specializes in a particular species that exhibits a desirable outcome, mechanism, or structures. But the expertises of these biologists may 3.5. 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Graeﬀ, N. Maranzana, and A. Aoussat, Engineers’ and biologists’ roles during biomimetic design processes, towards a methodological symbiosis, Proceedings of the 22nd International Conference on Engineering Design (ICED19), pages 319–328, Delft, The Netherlands, Aug. 5–8, 2019. DOI: 10.1017/dsi.2019.35. 33 C H A P T E R 4 37 Rationale for Biologically Inspired Design Wilful waste makes woeful want. James Kelly, A Complete Collection of Scottish Proverbs (1721) Since the laws of physics hold sway over every biological process just as completely as over every technological operation, the bioworld should be considered as a repository of answers to billions of technological questions [1]. Some of these answers have already been implemented by humans. Some answers may not be optimal for our technological requirements but can still illuminate possible research directions. The fact is that the bioworld oﬀers a palette of solutions that may be otherwise unavail- able to humans. An example is furnished by three-dimensional photonic crystals with diamond crystal structure, which reﬂect incident electromagnetic waves in a speciﬁc spectral regime, re- gardless of the direction of incidence [2]. These photonic crystals have been made for operation in the microwave and infrared spectral regimes, but no technique has been successful to fabricate them for operation in the visible spectral regime [3]. Yet the exocuticle of the Brazilian weevil Lamprocyphus augustus displays the desired response characteristics in the yellow-green portion of the visible spectral regime [4], as shown in Fig. 4.1. Clearly, then a fabrication route exists in the bioworld that is not known yet to humans. A review of relevant characteristics of bioworld solutions is undertaken in this chapter to oﬀer the rationale for biologically inspired design. ENERGY EFFICIENCY 4.1 Neither biological processes nor industrial processes can overcome the fundamental limitations encoded in the laws of physics. Nevertheless, the contrast between the two types of processes is remarkable. Chemical routes are commonplace for material transformations in biological pro- cesses, whereas physical routes are routinely employed in industrial processes. This diﬀerence is quite succinctly captured by just one environmental variable: temperature. Consider the temperature diﬀerences between biological and industrial processes. Al- though a few animals live in extreme conditions, the range of temperature in the majority of the bioworld is quite restricted. Deep-sea creatures at 1000 m below sea level have to live at 70(cid:14)C and desert foxes with 50(cid:14)C. But the tem- about 5(cid:14)C, polar bears have to contend with (cid:0) 38 4. RATIONALE FOR BIOLOGICALLY INSPIRED DESIGN Figure 4.1: Exocuticle fragment from the Brazilian weevil Lamprocyphus augustus. peratures of internal tissue vary in a much smaller range, because biological cells are mostly water. Accordingly, numerous biological processes occur between, say, 5(cid:14)C and 45(cid:14)C. In con- trast, very high temperatures are routinely employed in industrial processes. Wood combusts at about 300(cid:14)C, clay bakes at about 760(cid:14)C, and iron melts at higher than 1500(cid:14)C. The metal zirconium is produced on reducing zirconium chloride by liquid magnesium at about 825(cid:14)C [5]. The hardness of zirconium on the Mohs scale is 5, the scale ranging from 1 (talc) to 10 (diamond). Tooth enamel, which has the same hardness as zirconium, is formed at a much lower temperature of about 37(cid:14)C. The production of high temperatures requires considerable expenditure of energy, imply- ing that biological processes are energy eﬃcient in comparison to industrial processes [6]. This energy efficiency is a persuasive argument for mimicking biological processes when designing an industrial production line, especially during the time of climate emergency we are presently living in [7]. Indeed, one can justiﬁably argue that an embrace of biologically inspired design is essential to the survival of the human species as well as numerous other species, in the 21st century on Earth. 4.2 CIRCULAR ECONOMY OF MATERIALS About 40,000 metric tons of cosmic dust fall on our planet every year [8], but about 50,000 metric tons of hydrogen and helium escape every year too [9]. These changes to the mass of Earth are so tiny that it can be regarded as a closed system wherein materials cycle between the lithosphere, atmosphere, and hydrosphere. The biosphere comprises parts of each of these three regions of Earth. Biomass, i.e., the mass of living organisms, varies greatly with time [10]. For example, it reduces signiﬁcantly during the autumn season in the northern hemisphere. Despite such variations, the main out- puts, byproducts, and wastes of every living organism become inputs to living organisms of other 4.3. MULTIFUNCTIONALITY 39 species. Herbivores eat plants, carnivores eat herbivores, numerous organisms sustain themselves on the excretions and secretions of other species, and the bodies of dead organisms return nutri- ents to the ground in which plants grow. Leaving aside the sequestration of materials through geological processes, materials thus circulate in the bioworld. In other words, the bioworld exhibits circular economy [11] of materials, especially when annually averaged over ecologically distinct parts of the biosphere. This circular economy becomes easily evident when an island subspecies are compared to its continental counterpart in average size. Adjustment to serious restrictions on the availability of edible matter on islands is commonly shown by increases and decreases of average sizes of diverse species in relation to their continental cousins [12]. The circular economy of materials evinced by various swathes of the bioworld is not ac- companied by the circular economy of energy. This is because our planet is a closed but not an isolated system thermodynamically. A closed system can exchange energy but not mass with its surroundings. An isolated system can exchange neither energy nor mass with its surround- ings. The sun supplies energy to Earth, which is in addition to the energy made available to the biosphere by the planetary core. In the bioworld, every organ is functional over a certain period of time that is, on average, not less than the time needed to reproduce at least once. Many organs are repairable and some organs are not totally necessary for the survival of the individual. The byproducts and waste products of bioworld processes are used as inputs to other bioworld processes, not necessarily in the same organism. Materials in a dead organism provide sustenance to other organisms, either directly or indirectly. Biologically inspired design can inﬂuence the manufacture, use, and disposal of speciﬁc products with minimal depletion of materials and with minimal impact on the rest of the biosphere; furthermore, energy could be harvested from whatever remains that cannot be cannibalized after use. 4.3 MULTIFUNCTIONALITY Multifunctionality is commonplace in living organisms [13–15]. Thus, limbs are used for moving, signaling, gathering and preparing food, wielding weapons, and initiating as well as warding oﬀ physical assaults, among other things. Mouths are used for ingesting food and ﬂuids, releasing sounds, breathing, and kissing. As certain organs can perform two or more distinct functions that are not highly related to each other, fewer organs need to be formed and housed in the organism and fewer structures need to be coordinated by the organism’s brain. This economy of multifunctionality is an attractive feature of biologically inspired de- sign [16, 17]. A multifunctional module can be incorporated in a variety of products, thereby reducing inventory costs, enhancing repairability and product lifetimes, and promoting stan- dardization. A multifunctional product may designed and fabricated as an assembly of mono- functional components. A simple example is a Swiss Army knife. A multifunctional product could also be made from multifunctional materials, whether natural or composite. The costs of 40 4. RATIONALE FOR BIOLOGICALLY INSPIRED DESIGN eventual disposal may be higher when composite materials are used, and designers will have to make choices based on lifecycle audits [18]. 4.4 MULTICONTROLLABILITY The concept of multicontrollability [19] is closely allied to multifunctionality. Multicon- trollability is also exhibited commonly in the bioworld. Thus, multiple modes of locomotion can be used by an organism to propel itself from one location to another, and often the same sound can be uttered using two or three diﬀerent placements of the tongue in the buccal cavity. We get alarmed by hearing the sound of an approaching car and/or by seeing it. Reliance on mul- tiple mechanisms thus builds resilience via redundancy. That’s why multiple control modalities are used to ensure speciﬁc actions in critical facilities such as nuclear power plants and missile guidance centers. 4.5 SUBOPTIMALITY When mimicking a bioworld product or process, it is important to remember that biological phenomena are adapted to a speciﬁc context with a given set of constraints. This means that the solutions derived from a biological phenomenon may not be suitable in contexts with diﬀerent constraints. For instance, the wings of an owl are silent but are unsuitable for rapid ﬂight, the wings of a swan are noisy but can lift a heavy body, and the wings of a swift allow for very high speed but make it very diﬃcult for the bird to take oﬀ from the ground. A bioworld solution is also constrained by evolutionary history since it arises from succes- sive mutations of several species [20]. Each mutation could be suboptimal that performs just well enough in a particular niche. A succession of such mutations will deﬁnitely produce a solution that too is viable in its niche, but that solution could be suboptimal even in that niche. Suboptimality in the bioworld has long been exempliﬁed by the plethora of visual prob- lems that plague humans [21], not to mention other mammals. Aberrations, astigmatism, and blindspots are structural deﬁciencies that have kept generations of ophthalmologists gainfully employed. Although all of their patients would like to keep using their eyes for as long as pos- sible, the human eye can hardly be regarded as the product of a well-designed instrument [22]. As a bioworld solution is not necessarily optimal even in the bioworld, it is likely to re- quire some modiﬁcation to optimize it for a speciﬁc technoscientiﬁc application. This should be viewed as a welcome opportunity, all the more so as the need for modiﬁcation may allow the incorporation of functionalities not associated with the bioworld solution in the bioworld. Thus, the rapidity of action of biomimetic insulin can be controlled by the alteration of the codon se- quence, as mentioned in Section 3.3.2. Similarly, bioreplicated decoys can be colored diﬀerently from the the species being replicated, as discussed in Section 3.3.3. Further opportunities may arise after realizing that several bioworld solutions can be com- bined for a speciﬁc technoscientiﬁc application. This is exempliﬁed by the tennis racquets in 4.6. CONTRAINDICATED PERFORMANCE 41 the Dunlop Biomimetic 200™ series. The racquet beam is made of Dunlop HM6 carbon sand- wiched between aerogel-enhanced carbon sheets. Dunlop HM6 carbon mimics the morphology of honeycombs which are extraordinarily strong and lightweight structures [23]. The surface of the racquet frame is covered by a fabric with overlapping scale-like protrusions to reduce aero- dynamic drag. These protrusions mimic denticles that reduce hydrodynamic drag and prevent fouling of shark skins [24, 25]. The surface of the racquet grip mimics the setae on the feet of a gecko that enable it to walk upside down on smooth surfaces [26, 27]. 4.6 CONTRAINDICATED PERFORMANCE For over two millennia, humans have known that an object denser than water sinks in a bathtub but an object of lesser density than water ﬂoats. Well, boats ﬂoat in rivers and seas, but that is because the volume-averaged density of a boat’s hull and superstructures as well as of air below the waterline is the same as of water. Air is a liquid and a rigorous scientiﬁc study [28] is not needed to prove that a bird is deﬁnitely heavier than air on a unit-volume basis. Although avian ﬂight is thus contraindicated, birds of most species can ﬂy well, some even at altitudes higher than 10 km [29]. The secret lies in the arrangement of ﬂight feathers arranged on concave wings that can be ﬂapped to raise the underwing pressure and provide lift. Mushrooms and their mycelium roots are well known to be very fragile. But a fungus growing in a ﬁbrous material functions as a glue that provides the resulting composite material with surprisingly high stiﬀness and strength. This can be seen in the forest ﬂoor where the soil in places with fungus can become harder and stiﬀer, provided the soil is a good mixture of organic material of various sizes. The same phenomenon can be utilized for making building components and plates from straw by letting a fungus grow in the humidiﬁed material. The mycelium roots will bind the straw ﬁbers together and form a stiﬀ composite material, as depicted in Fig. 4.2. Both foams and structural composites are being made of mushrooms [30, 31]. Mollusk shells are calcareous, created by the secretion of calcium carbonate mixed in a broth of polysaccharides and glycoproteins which controls the position and elongation of calcium-carbonate crystals [32]. As talc, calcium carbonate is among the softest natural ma- terials known. As aragonite, the material’s hardness does not exceed 4 on the Mohs scale. Yet, mollusk shells comprising interlaced plates of aragonite are extremely durable, with a modulus of elasticity similar to wood’s, tensile strength similar to copper’s, and compressive strength higher than porcelain’s [33]. The secret lies in the arrangement of aragonite plates that prevents crack propagation and thereby provides the toughness needed to protect the enclosed body. The same arrangement of plates of Norwegian slate has been used in the retaining walls constructed on the undulating terrain of the Lyngby campus of Danmarks Tekniske Universitet (DTU) as shown in Fig. 4.3. 42 4. RATIONALE FOR BIOLOGICALLY INSPIRED DESIGN Figure 4.2: Mycelium bio-composite made from straw and other agricultural byproducts. Figure 4.3: (a) Retaining wall on the Lyngby campus of DTU. (b) The inter-plate regions of the wall provide habitat for terrestrial mollusks of the species Cepaea nemoralis. 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Barthelat, Nacre from mollusk shells: A model for high-performance struc- tural materials, Bioinspiration and Biomimetics, 5:035001, 2010. DOI: 10.1088/1748- 3182/5/3/035001. 41 C H A P T E R 5 47 Problem-Driven Biologically Inspired Design It is, that as existing human inventions have been anticipated by Nature, so it will surely be found that in Nature lie the proto- types of inventions not yet revealed to man. The great discoverers of the future will, therefore, be those who will look to Nature for Art, Science, or Mechanics, instead of taking pride in some new invention, and then ﬁnding that it has existed in Nature for countless centuries. Rev. John G. Wood, Nature’s Teachings, Human Invention Anticipated by Nature () INTRODUCTION 5.1 Biologically inspired design (BID) can be approached from two diﬀerent directions [1–3]. The approach from the engineering side is referred to as problem-driven BID, whereas the ap- proach from the biology side leads to solution-driven BID. The former is treated in this chapter, the latter in Chapter 6. As the name implies, problem-driven BID is initiated by an engineering problem whose solutions are sought; hence, it is very similar to traditional engineering design. The major diﬀer- ence is that the solution principles are searched in the bioworld. As engineering designers will be familiar with the design-oriented parts of the process but are likely to be less knowledgable and experienced in the tasks that relate to biology, problem-driven BID should be carried out in a collaboration between engineers and biologists. However, there are strong limitations for problem-driven BID in such a collaboration, as explained in Sections 5.2.2–5.2.4. Problem-driven BID is the term used by researchers at the Georgia Institute of Tech- nology [1], Arts et Métiers ParisTech [4, 5], and Danmarks Tekniske Universitet (DTU) [2]. The International Standards Organization calls it technology-pull biomimetics because a technological need initiates it and drives the work [6]. The term top-down bionik has been used by researchers at the Technische Universität München for many years [7]. It is also this type of BID that is handled with the design spiral from the Biomimicry Institute [8]. There are other ways than problem-driven BID to generate new ideas for how to design products and other artifacts. One can look at already existing products or even search patents. Or 48 5. PROBLEM-DRIVEN BID Figure 5.1: The ﬁve phases of problem-driven BID implemented using the DTU biocard method. one could turn to a range of diﬀerent creativity techniques such as brainstorming, 635-method or the Scamper method [9, 10]. Two questions naturally arise. First, how well does BID perform as an idea-generation technique? Second, are its outcomes worth the eﬀort? Answers to these questions have been sought by comparing the BID methodology to traditional brainstorming [11]. Several design students were given an assignment to generate ideas to a given problem, with half of the students asked to use brainstorming and the other half to use the BID methodology. The novelty of each resulting design proposal was identiﬁed by comparing it with other solutions found on the internet. The comparison was made using the SAPPhIRE model for causality [12] where the similarity between new and existing design proposals was compared at seven levels of abstraction. The use of BID methodology resulted in fewer design proposals, but the ones that were found were more novel (and, therefore, presum- ably of higher quality). This is a key argument for using the BID methodology. Brainstorming is easy to learn and requires little preparation or skills, thereby producing many design proposals. On the contrary, the BID methodology requires a stricter procedure to be followed as well as some interest in and some knowledge of biology, but results in novel proposals. 5.2 PHASES OF PROBLEM-DRIVEN BID Implementation of problem-driven BID is done in ﬁve phases, beginning with an initial analysis of the design problem, followed by a search for biological analogies, then distilling an under- standing of biological phenomena to extract key principles, followed by a reformulation of design principles, and ending with the actual design of new objects after validating the principles in the context of the design problem. The ﬂow chart in Fig. 5.1 illustrates these ﬁve phases using the biocard method developed at DTU. Abstraction is done at least twice during the problem-driven BID process, as is clear from Fig. 5.2. First, the technical problem is abstracted from the initial analysis of the design Formulate problem (context- speciﬁcFunctional keywordgenerationSelectAbstractionExtractionRedeﬁne problemRedeﬁne problemLearn moreReﬁne principlesBiological keywordsAbstractionContextualizationValidationProblem analysisUnderstandDesignTransferSearchFormulate challenge (generalized) Make search termsSketch conceptual solutionsValidate principles in contextUnderstand biological phenomenaSearch databasesMake biocards describe generalized principlesExtract key principles5.2. PHASES OF PROBLEM-DRIVEN BID 49 Figure 5.2: Interaction of technology and biology in problem-driven BID [5]. problem. Second, key biological principles or strategies are abstracted from the understanding of a biological phenomenon and brought into a form useful for design work. 5.2.1 FIRST PHASE: PROBLEM ANALYSIS The ﬁrst phase in problem-driven BID is no diﬀerent from those in numerous other goal- oriented projects, since a thorough understanding of the problem being tackled is required. Asking the right question(s) is halfway to ﬁnding good solutions. The problem-analysis phase can involve just a single person but is often better carried out as a collaboration of several peo- ple. Discussions among team members force clarity in the description of the problem so that every member can get a clear and complete picture. The following tasks have to be undertaken in the problem-analysis phase: problem description, function analysis, and engineering-biology translation. Problem-Description Task Describing the design problem adequately is among the most important activities in BID, just as it is in design work in general. Adequate understanding of the core issues and the short- comings of existing products determines the form and the substance of the remainder of the design process. Understanding the design problem and describing it clearly for others can be diﬃcult enough for a single person, but it becomes even more complicated when many persons 3. Transposetobiology1. Problemanalysis5. Selectbiological model(s)of interest2. Abstracttechnicalproblem6. Abstractbiologicalstrategies4. Identifypotentialbiological models8. Implementand test in theinitial context7. TransposetotechnologyInputOutput50 5. PROBLEM-DRIVEN BID Figure 5.3: A hand-drawn sketch describing the window problem. The window must allow an external view but prevent the solar infrared radiation from entering the room. collaborate in a design team. Therefore, the problem must be described and communicated in a way that it is easily and uniformly understood by many persons. A sequence of illustrations, whether drawn by hand or on computers, accompanied by bulleted points in text can docu- ment the problem reasonably well. Illustrations can be rapidly made and transcend barriers of language, terminology, and expertise. The technical problem can then be abstracted quite easily. But, care must be taken that the illustrations focus on the desired functionality but not on the manner in which the problem is to be solved. As an example, consider the window problem that architects often encounter when designing buildings in normally sunny locales. People inside a building are interested both in having sunlight enter rooms through windows and in being able to view the outside. However, solar radiation contains not only visible light but also infrared waves that heat the room and may necessitate the increased use of air-conditioning systems. The design problem is that of a window that allows the occupants of a room to enjoy the external view but (partially) prevents solar infrared radiation from entering the room. This design problem can be described by the simple sketch shown in Fig. 5.3. The window pane is represented by two parallel lines, the external view is illustrated by a dashed straight line that begins at one eye of a stickperson and crosses the window pane to the exterior, and the infrared restriction is represented by bouncing arrows. Such an abstract description will stimulate an open-minded approach to identify the core functionality and allow for a broader and goal-oriented search for biological organisms displaying that functionality. Another method that is useful for problem analysis and description is the four-box method [13]. This method requires the design team to specify 5.2. PHASES OF PROBLEM-DRIVEN BID 51 Figure 5.4: The four-box method for problem analysis and description [13]. (i) the operational environment for the product (i.e., the context), (ii) the core functions delivered by the product, (iii) the main speciﬁcations of the product, and (iv) the performance criteria that the product must satisfy. The responses are entered as bulleted lines of text in the table shown in Fig. 5.4. For the win- dow example, the operational environment includes the type of room in which the window is to placed (i.e., oﬃce, school room, bed room, etc.) as well as the geographical location and cli- matic conditions (e.g., dry/humid, sandy/salty, hot/cold, etc.). Functions could include “provide transparency,” “prevent solar infrared radiation to pass through,” and “allow cleaning;” see also Section 5.2.1. Speciﬁcations include linear and areal dimensions and orientation toward the sun in summer. Performance criteria could include the fraction of visible light that is allowed to pass through the window, the color tint that is acceptable, and the minimum acceptable viewing angle. Function-Analysis Task A problem is typically speciﬁed using a terminology which is closely related to the context of the problem. For instance, will a car driver explain a puncture in a tire as “having a ﬂat tire”? However, as described in Section 2.4.1, it is important to provide an abstract functional description rather than a concrete one, in order to prevent ﬁxation. The puncture problem can, of course, be solved by changing the tire; but if the goal is to prevent punctures, it is advantageous to describe the function in more abstract terms. The tire is a solution to the functions “provide road grip” and OperationalenvironmentFunctionsSpeciﬁcationsPerformance criteria52 5. PROBLEM-DRIVEN BID Figure 5.5: Functions-means tree diagram for a window. Each trapezoidal block contains a func- tion, each rectangular block a means. “provide driving comfort.” By broadening the problem description using such abstract terms, it is more likely that a completely diﬀerent solution will be found. The road grip could be provided by spiked solid wheels and the comfort could be supplied by a sturdy mechanism for wheel suspension. Such a wheel solution will not suﬀer from punctures. More generally, an engineering problem can be analyzed by describing an artifact that solves the problem. The artifact can be decomposed into functional units each of which is de- scribed in terms appropriate for the context. The next step is then to formulate the function(s) of each artifact with a more abstract terminology that allows for a broader search for alternative means to solve the problem. The overall problem is decomposed into sub-functions, each de- scribing speciﬁc aspects of what the artifact does and deﬁning a set of metrics for the required performance. Function analysis for the window problem of Fig. 5.3 can be performed as follows. The main function of a window is to provide a view. This can be done with glass panes, but an open hole in the wall will also deliver this function. A functions-means tree diagram, as described in Section 2.4.2, helps to deﬁne which functionalities are required and thus support a search for alternative solutions. Figure 5.5 shows a functions-means tree diagram for the window problem with each trapezoidal box containing a function or sub-function and each square box containing a means to provide the needed functionality. The search for solutions is thus broken down into identiﬁcation of various means, each of which solves a speciﬁc aspect of the overall problem. The top-level functionality in the functions-means tree diagram is “to provide a view.” The main function can be broken down into ﬁve sub-functions: “to allow light to enter,” “to prevent ex- cess heat from entering,” “to prevent heat loss,” “to keep out insects,” and “to prevent sound Glass paneFinely meshed netDouble layerglazingBlindsWindowGlass paneTo allow light to enterTo prevent excessheat from enteringTo preventheat lossTo keepout insectsTo providea viewTo preventtransport of sound5.2. PHASES OF PROBLEM-DRIVEN BID 53 transport.” The sub-function involving insects can be solved by using a ﬁnely meshed net as an alternative to a glass pane. The last sub-function rules out a hole as a window and also the ﬁnely meshed net. The functions-means tree diagram therefore is a tool for qualifying the search for solutions and it is also very helpful in the search for analogous solutions from the bioworld. A challenge in describing functionalities for the functions-means tree diagram is to select the right phrases that will be helpful in the search phase. Assistance can be taken from on-line thesauri wherein synonyms and antonyms can be found [14]. Another helpful resource is the WordNet database from Princeton University [15]. Engineering-Biology Translation Task After a designer (or a design team) has described the problem and identiﬁed the desired func- tionalities, the formulation is often very technical. This is a good starting point, since the designer should be familiar with the engineering terminology and therefore should be able to formulate the problem precisely enough to ﬁnd good technical terms for searching the literature. In Fig. 5.1, this task is referred to as the context-speciﬁc formulation of the design prob- lem. However, it is not very likely that exactly the same terms are used to describe similar func- tions in the engineering and biology literatures. Before searching in the biology literature, it is therefore beneﬁcial to translate the engineering terms to biology terms. This task can be ap- proached by looking at synonyms in a thesaurus as well as by looking in those segments of the biology literature wherein similar phenomena are likely to be found. If, for instance, a new type of cleaning mechanism is to be designed, then one could consult the literature on how domesti- cated animals as well as animals housed in diverse research institutions (such as zoological parks) keep themselves tidy. In that literature, terms such as “washing,” “licking,” and “removing hair and dirt” are used instead of “cleaning.” The terms from biology literature could be more useful in ﬁnding similar phenomena among other animals. The abstraction activity of ﬁnding good biological search terms is referred to as the formulation of generalized challenges in Fig. 5.1. For the window example, technical search terms could be “semi-transparent,” “sun block- ing,” and “shield light.” These would only ﬁnd a few biological analogies but that is a good starting point. Once the ﬁrst biological analogy has been identiﬁed, the biology literature could be consulted to ﬁnd out what terms are used to describe protection from high-intensity light. As animal eyes are likely to possess features for such protection, literature on veterinary oph- thalmology would be appropriate. Animals protect their eyes from high-intensity light by con- tracting the iris, closing eye lids, moving the eyelashes, and using skin folds that shade. Another search could be for plants growing in sunny deserts, because those plants somehow avoid being overheated, e.g., how cacti utilize corrugated surfaces and spines for cooling by convection. The insight gained could then be used to deﬁne search terms more likely to be found in the biology literature. Examples of search terms could be “eye protection” and “temperature regulation.” Another helpful approach is to translate the terms used for biological phenomena into Latin. Latin words are universally used in the scientiﬁc literature, especially in the biology lit- 54 5. PROBLEM-DRIVEN BID erature. Taxonomists use Latin terms for kingdoms, phyla, classes, orders, suborders, families, genera, and species, each term usually referring to a speciﬁc biological attribute. After a Latin term is found in taxonomy, it is straightforward to move up, down, or sideways in the hierarchy to ﬁnd other organisms and then explore other bioworld solutions to the design problem. Researchers at the University of Toronto have developed a natural search approach for BID and a method for identifying good biological search terms. They have proposed a set of techniques for abstraction and identiﬁcation of relevant search terms to be used for the bio- logical search [3]. Verbs are recommended instead of nouns since it is more likely that nouns will lead to pre-conceived analogies. Furthermore, verbs describe actions and hence are better for ﬁnding a greater variety of biological forms. As an example, the verb “protect” helps ﬁnd a greater variety of phenomena than the noun “cuticle” does. If certain verbs that can be consid- ered as biologically meaningful (signiﬁcant or connotative) occur more commonly than others, they can be considered as bridge words that are more likely to be helpful in the biological search. 5.2.2 SECOND PHASE: SEARCH Searches can be done in many diﬀerent ways. Most straightforwardly today, internet search en- gines such as Yahoo, Google, and Bing should be used. The challenge is that, as no search engine is restricted to biology, a large number of hits will result that can be diﬃcult to navigate through. It is therefore important to identify a good starting point when using an internet engine. One way is to apply a bio-brainstorm where the person or groups of persons formulate a question of following kind: “How would this particular problem be overcome in the bioworld?” Based on the biological knowledge already available in the design team, animals and plants can be identiﬁed. For instance, many people would readily propose mammalian eyes as biological solutions to the window problem. This ﬁrst hit will be a good starting point for a wider search. Another approach is to use dedicated biology databases that will be more likely to propose relevant biological organisms. Among the better known databases is AskNature developed by the Biomimicry Institute [16]. AskNature contains a large number of examples of biomimicry, with biological organisms described alongside how a biological strategy has been transferred into technical applications. AskNature provides at least two ways to initiate a search. One is a simple free-text search very similar to the use of internet search engines. Another is to use a biomimicry taxonomy [17] which describes functions on three hierarchical levels: group, sub- group, and function. Relevant for the window example could be to focus on the group “protect from physical harm,” the subgroup “protect from non-living threats,” or the function “(protect from) light.” The terms from the biomimicry taxonomy can be used not only for a focused search in AskNature but also when searching more broadly in other databases or on the internet. As additional search terms are needed to limit an internet search to biological phenomena, terms such as “biology,” “animal,” and “plant” or other biology-related terms should be added. The 5.2. PHASES OF PROBLEM-DRIVEN BID 55 right terms must be found through an iterative approach where relevant hits can be used to identify relevant biological terms that will guide the search in a fruitful direction. Yet another approach is to use library search engines to search scientiﬁc books and papers. The library databases are prepared to oﬀer goal-directed searchs where the focus is on recognized and quality-tested scientiﬁc knowledge. What is found using library search engines therefore has a high degree of trustworthiness. The diﬃculty in using scientiﬁc literature is that is written in the language of a sub-culture, i.e., it can be diﬃcult for a layperson to understand a paper written for a specialist journal or book. There are also other ways to search for biological organisms with relevant mechanisms and functionalities. An obvious one is to consult a professional biologist. They have broad insights about the bioworld, they know how many biological organisms function, and they can easily peruse scientiﬁc literature to gather further information. However, as they may require payment for their services, the value of conducting a biological search must be higher than the cost of hiring a biologist. Besides, a limitation is the growing specialization within the broad discipline of biology. Many biologists today have deep knowledge of only a narrow sub-discipline and therefore are less suited for the broad search for biological phenomena that could help solve a speciﬁc design problem. Finally, there is the option to visit some parts of the bioworld. Once a mind is tuned to looking for a functionality, it is natural to wonder about the things that we see in a forrest, a zoological park, a botanical garden, or a protected area set aside as a nature reserve [18]. For instance, if one is searching for new strategies for bearing structural loads (e.g., columns for holding motorway signs, large tents, or bridges), it is natural to wonder about how trees are structured and anchored in the ground so they can resist high wind pressure in storms. Or, if one is look for self-cleaning strategies, one will ﬁnd many plants that stay clean despite dirty surroundings. A possible pitfall when searching for biological phenomena is that only well-known ones are explored. Experiences from teaching BID courses show that many students limit their searches to the larger animals, i.e., mammals, birds, and insects [19]. By limiting the search to the more familiar fauna and ﬂora, the probability of ﬁnding really novel ideas decreases. If the search is forced to be broader to cover items such as marine life, microbiology, and single-cell organisms, more and novel ideas emerge [19]. 5.2.3 THIRD PHASE: UNDERSTAND Once a list of promising biological phenomena has been created, the next step is to understand the underlying mechanisms. The mechanism is straightforward to understand in some cases, but not for all. See, for example, Section 3.3.2 for the complexity of insulin production in the human pancreas. It can also be that the overall functionality is easy to understand but becomes more complex after additional detail is required for implementation. For the window example, it is easy to understand that the iris in a mammalian eye functions like a camera aperture with the 56 5. PROBLEM-DRIVEN BID size of the hole determining how much light is allowed through, but the activation of muscles causing the contraction and widening of the iris is more complicated for a non-specialist to understand. Better understanding normally requires access to trustworthy literature which can inform about a particular biological phenomenon and explain the underlying mechanism(s) in adequate but not overwhelming detail. Whereas internet searches will supply the needed insight in some cases, a proper library search is necessary more often than not. Relevant keywords and descriptive names of the biological phenomenon combined with boolean operators (and, or, not) will help identify relevant books and journal papers that can retrieved though the library facilities. Latin terms will be especially useful in library searches since they precisely deﬁne the type of biological phenomenon that is described, thereby oﬀering the opportunity to select a more general level in biological taxonomy and ﬁnd literature for a wider group of organisms. It can be advantageous to use a dedicated database such as BIOSIS Previews [20] at the li- brary. Another useful tool is the Encyclopedia of Life [21], a community-driven resource to which many biologists worldwide supply information about animals and plants. A supplementary valu- able resource are the biologists themselves. If approached correctly and politely, they will often help with basic explanations and guide toward the relevant literature for deeper understanding. 5.2.4 FOURTH PHASE: TRANSFER In the next phase of BID, the ﬁndings must be transferred to the design problem by describing the underlying functional principle of each biological phenomenon found. This is important to facilitate precise and accurate communication among the members of the design team. If the ﬁndings are communicated too loosely, much is left to interpretation and the ﬁnal design may be inspired by something other than what was intended by the person(s) who found a relevant biological phenomenon. One way to document the ﬁndings is to use biocards [22], an example of which is presented in Fig. 5.6. The ﬁgure shows two similar yet diﬀerent biocards on the mechanism that keeps equine eyes clean: a concrete description using biological terminology and graphics in the left biocard but an abstract description using neutral non-biological terms and graphics in the right biocard. The biocard on the left mentions a tear ﬁlm to which dust particles adhere, that is removed periodically removed by the eyelid, and which is replenished periodically by tears. This description is suitable for designers to generate ideas, but its scope is limited compared to the abstract description in the biocard on the right. Terms such “tears” and “liquid” will ﬁxate the designer in thinking only of solutions that rely on a liquid to collect and clean. The abstract description replaces both of those terms by the more neutral “substance.” This will make it more likely for the designer to think freely and consider both liquid and solid substances for collecting dirt particles. The same argument applies to the graphics in the biocard. Drawings of bioworld solution should be eschewed in favor of more symbolic drawings. 5.2. PHASES OF PROBLEM-DRIVEN BID 57 Figure 5.6: (left) Concrete and (right) abstract descriptions in a biocard. The biocard on the right is better suited for problem-driven BID. 5.2.5 FIFTH PHASE: DESIGN The biocards can be used in diﬀerent ways in the ﬁfth phase of BID. One way is to make a collection of biocards describing diﬀerent functional principles based on diﬀerent biological phenomena. The designer or design team can then take one card at a time and sketch solutions based on the functional principle in that biocard. It is important not to evaluate the quality of that principle but wait until a design proposal utilizing it has emerged. In that way, it will be the physical embodiment in a given context that will be evaluated. For each promising design proposal, a physical model should be constructed for demon- stration in order to convince decision makers about investing resources needed to better investi- gate the proposal. Students taking a BID course at DTU routinely build such proof-of-principle models [23]. Figure 5.7 shows an example. The design problem is that of reducing drag on a ship and thereby lower energy consumption. The model ship in the ﬁgure is inspired by emperor pen- guins [24]. When threatened, an emperor penguin releases air from underneath its feathers. The resulting air bubbles form a thin layer that encapsulate its body to drastically reduce friction. The penguin then increases its speed several times and escapes its enemies by rocketing out of the water to the ice ﬂakes where it will be safer. To prove the air-bubble principle for drag reduction, ,,58 5. PROBLEM-DRIVEN BID Figure 5.7: Inspired by the use of air bubbles by emperor penguins to reduce friction in water, this toy ship as a physical model demonstrated that the same functional principle will reduce drag on a full-size ship. Courtesy: David Maage, Enzo Hacquin, and Anders Lui Soerensen. a student team made a toy ship and equipped it with two aquarium pumps. On pumping air in tubes with tiny holes underneath the toy ship, its bottom and sides were surrounded by a layer of air bubbles. Measurements of the drag resistance conﬁrmed that a reduced force was needed to propel the toy ship. 5.3 ENGINEERS AND BIOLOGISTS Since BID is basically about transferring biological knowledge to the engineering domain, it seems obvious to carry out the design work as a collaboration of people with the two compe- tences. There are good examples of successful and sustained collaborations. For instance, Julian Vincent is a biologist who has worked for many years at an engineering college. Biologists employed at agricultural universities are oriented toward developing more eﬃ- cient techniques for agriculture and forestry. Although endowed by their education with deep insights into biology, they are oriented toward development work in institutions where the re- sults are solutions that keep the citizenry well fed. Furthermore, their orientation must be suf- ﬁciently broad to encompass both botany and zoology. In contrast, typical faculty members in a biology department are highly specialized, be- cause they achieve professional rewards by focusing on narrow topics within sub-disciplines such as entomology, mycology, and molecular biology. Although beneﬁcial for conducting novel re- search on narrow topics, that outlook poses a challenge to engineering-biology collaborations. When an engineering designer searches the bioworld to ﬁnd applicable biological strategies, 5.4. REFERENCES 59 those strategies may have to be searched through the length and breadth of available biolog- ical knowledge. If the biologist in the collaboration is a marine biologist, they will have little knowledge about strategies involving insects or mountain plants. A research group in Paris examined the role of biologists in biologically inspired de- sign [25]. They found that mixed teams are more eﬀective in coming up with more ideas and make fewer mistakes. They also found that there is an increase in the diversity of biological strategies identiﬁed as potentially useful in design work. 5.4 REFERENCES [1] M. Helms, S. S. Vattam, and A. K. Goel, Biologically inspired design: Process and prod- ucts, Design Studies, 30:606–622, 2009. DOI: 10.1016/j.destud.2009.04.003. 47 [2] T. A. Lenau, A.-L. Metze, and T. Hesselberg, Paradigms for biologically inspired design, Proceedings of SPIE, 10593:1059302, 2018. DOI: 10.1117/12.2296560. 47 [3] L. H. Shu, K. Ueda, I. Chiu, and H. Cheong, Biologically inspired design, CIRP Annals— Manufacturing Technology, 60:673–693, 2011. DOI: 10.1016/j.cirp.2011.06.001. 47, 54 [4] P.-E. Fayemi, N. Maranzana, A. Aoussat, and G. Bersano, Bio-inspired design character- isation and its links with problem solving tools, Proceedings of DESIGN: 13th International Design Conference, pages 173–182, Dubrovinik, Croatia, May 19–22, 2014. 47 [5] P. E. Fayemi, K. Wanieck, C. Zollfrank, N. Maranzana, and A. Aoussat, Biomimet- ics: Process, tools and practice, Bioinspiration and Biomimetics, 12:011002, 2017. DOI: 10.1088/1748-3190/12/1/011002. 47, 49 [6] ISO 18458:2015, Biomimetics—Terminology, Concepts and Methodology, International Standards Organization, Geneva, Switzerland, 2015. https://www.iso.org/standard/ 62500.html DOI: 10.3403/30274979. 47 [7] T. Lenau, K. Helten, C. Hepperle, S. Schenkl, and U. Lindemann, Reducing consequences of car collision using inspiration from nature, Proceedings of IASDR: 4th World Conference on Design Research, Delft, The Netherlands, Oct. 31–Nov. 4, 2011. 47 [8] D. DeLuca, The Power of the Biomimicry Design Spiral, Biomimicry Institute, Missoula, MT, 2017. https://biomimicry.org/biomimicry-design-spiral/ 47 [9] N. Cross, Engineering Design Methods—Strategies for Product Design, Wiley, Chichester, UK, 2008. 48 [10] G. Pahl, W. Beitz, J. Feldhusen, and K.-H. Grote, Engineering Design: A Systematic Ap- proach, 3rd ed., Springer, London, UK, 2007. DOI: 10.1007/978-1-84628-319-2. 48 60 5. PROBLEM-DRIVEN BID [11] S. Keshwani, T. A. Lenau, S. Ahmed-Kristensen, and A. Chakrabarti, Comparing novelty of designs from biological-inspiration with those from brainstorming, Journal of Engineer- ing Design, 28:654–680, 2017. DOI: 10.1080/09544828.2017.1393504. 48 [12] V. Srinivasan and A. Chakrabarti, Investigating novelty–outcome relationships in engi- neering design, Artiﬁcial Intelligence for Engineering Design, Analysis and Manufacturing, 24:161–178, 2010. DOI: 10.1017/s089006041000003x. 48 [13] M. Helms and A. K. Goel, The four-box method: Problem formulation and analogy evalu- ation in biologically inspired design, Journal of Mechanical Design, 136:111106, 2014. DOI: 10.1115/1.4028172. 50, 51 [14] Merriam-Webster, Thesaurus, Springﬁeld, MA. https://www.merriam-webster.com/ thesaurus 53 [15] Princeton University, WordNet: A Lexical Database for English, Princeton, NJ. https:// wordnet.princeton.edu/ 53 [16] The Biomimicry Institute, AskNature: Innovation Inspired by Nature, Missoula, MT. https: //asknature.org/ 54 [17] The Biomimicry Institute, The Biomimicry Taxonomy, Missoula, MT. https://asknature.org/ resource/biomimicry-taxonomy/ 54 [18] Protected Planet, https://www.protectedplanet.net/en 55 [19] T. A. Lenau, Do biomimetic students think outside the box? Proceedings of the 21st In- ternational Conference on Engineering Design (ICED17), Vol. 4: Design Methods and Tools, 4:543–551, Vancouver, Canada, Aug. 21–25, 2017. 55 [20] BIOSIS Previews®. https://www.ebsco.com/products/research-databases/biosis-previews 56 [21] Encyclopedia of Life. https://eol.org/ 56 [22] T. A. Lenau, S. Keshwani, A. Chakrabarti and S. Ahmed-Kristensen, Biocards and level of abstraction, Proceedings of the 20th International Conference on Engineering Design (ICED15), pages 177–186, Milan, Italy, July 27–30, 2015. 56 [23] Posters from DTU-BID course. http://polynet.dk/BID/ 57 [24] J. Davenport, R. N. Hughes, M. Shorten, and P. S. Larsen, Drag reduction by air release promotes fast ascent in jumping emperor penguins—a novel hypothesis, Marine Ecology Progress Series, 430:171–182, 2011. DOI: 10.3354/meps08868. 57 [25] E. Graeﬀ, N. Maranzana, and A. Aoussat, Biomimetics, where are the biologists?, Journal of Engineering Design, 30:289–310, 2019. DOI: 10.1080/09544828.2019.1642462. 59 C H A P T E R 6 61 Solution-Driven Biologically Inspired Design I think the biggest innovations of the 21st century will be at the intersection of biology and technology. A new era is beginning. Steven P. Jobs (2011)1 6.1 INTRODUCTION Biologically inspired design (BID) can be approached from two distinctly diﬀerent direc- tions [1–3], leading to problem-driven BID and solution-driven BID. Whereas the former was described in Chapter 5, this chapter explains the latter approach which is called biology- push biomimetics by the International Standards Organization because it is the experience from biology that initiates and drives industrial application [4]. Although the term bottom-up bionik was initially used by researchers at the Technische Universität München [5], solution- driven BID is now referred to as solution-based biomimetics by them [6]. The challenge in solution-driven BID is to identify technical applications that will bene- ﬁt from a set of solution principles identiﬁed from the bioworld. Solution-driven BID is often initiated by biologists with deep insights into biological functionalities but, typically, only lit- tle knowledge of technical applications and design methodologies. The search for applications followed by design work can therefore be quite arduous tasks for many biologists. Nevertheless, several examples of solution-driven BID exist in the literature, two of the most well-known ex- amples originating from burdock seeds that inspired Velcro™ [7] and the self-cleaning leaves of the lotus plant [8] that inspired superhydrophobic surfaces [9, 10]. A few examples are described in this chapter to illustrate how observations of and inspirations from bioworld phenomena have been transformed into technical applications, followed by a description of the eight steps of an approach to implement solution-driven BID [11]. 1Walter Isaacson, Steve Jobs, Simon & Schuster, New York, 2011. 62 6. SOLUTION-DRIVEN BIDS 6.2 EXAMPLES OF SOLUTION-DRIVEN BID 6.2.1 MYCELIUM BIO-COMPOSITES Mycelium is the root system of mushrooms and other types of fungus. It is typically a ﬁne mesh of tiny white strands referred to as hyphae [12]. The root system grows very rapidly through soil where it degrades dead lignocellulosic material such as straw and wood into nutrients used by the fungus. Other organisms also beneﬁt from this process, since many fungi form symbiotic relationships with plants. The fungus lives at the base of many plants, the mycelium spreading along the plant’s roots. In a symbiotic relationship, the plant supplies the fungus with carbon in the form of sugars made via photosynthesis in exchange for water and minerals such as phospho- rus [13]. The exchange is actually more complex since the mycelium also serves as a connector between larger plants such as trees and small seedlings for exchange of water and nutrients. The fungi, especially due to the mycelium, act as important waste-treatment actors in the bioworld, ﬁrst degrading organic material and then transforming it into other types of organic material. This process can be technologically adapted for the production of mycelium bio- composites that can be used for insulation, packaging material, and other lightweight struc- tural products [12, 14, 15]. Agricultural waste streams comprise straw and husk which can be transformed into porous solids using fungi [16]. The left panel of Fig. 6.1 illustrates a corrugated panel made of a mycelium bio-composite. The surface is similar to that of plastics but is a bit rougher in texture and appearance. The natural origin of the bio-composite is evident to both eyes and ﬁngers, promoting its use as a natural and biodegradable alternative to foamed plastics. The American company Ecovative has commercialized the manufacturing process for a range of foamy products [17, 18]. The ﬁrst products were insulation and packaging items to replace foamed polystyrene. In these products, sometimes referred to as mycocomposites, the mycelium functions as a self-assembling biological binder for agricultural byproducts. Ecovative has also used the mycelium-based technology to produce a reﬁned material for clothing fabrics and foamy skincare products. As the mycelium is edible, mycelium bio-composites can be consumed as food. It is pos- sible to achieve a texture and ﬂavor similar to meat and in that way oﬀer a vegetarian alternative. No animal products are used at all, which makes mycelium bio-composites attractive as food for vegans. A limitation of the currently available mycelium bio-composites is their relatively high weight; hence, these materials cannot compete with the very lightweight foamed plastics. This has to do with the manufacturing method in which the ﬁnely chopped agricultural wastes are kept in shape by loading them into the cavity of a mold, thereby limiting the growth of the hyphae to the void regions between the ﬁbers of the agricultural material. This was the experi- ence of a design team at Danmarks Tekniske Universitet (DTU) when making the foam core of a 2-m-long surfboard of a mycelium bio-composite, shown in the right panel of Fig. 6.1. Although such a large object could be made with the required strength, it was still too heavy for the intended purpose. 6.2. EXAMPLES OF SOLUTION-DRIVEN BID 63 Figure 6.1: (Left) Corrugated panel made of a mycelium bio-composite with a similar but more natural appearance compared to foamed plastics. (Right) Foam core of a 2-m-long surfboard made from hemp ﬁbers bound together by mycelium. Courtesy: Dan Skovgaard Jensen, Kristian Ullum Kristensen, and Lasse Koefoed Sudergaard. To improve the mycelium bio-composite, DTU researchers are working to combine the mycelium growing process with 3D printing [16]. One approach is to 3D print a porous matrix material in which the fungus grows much the same way as it does in the bioworld when degrading dead lignocellulosic material. Another approach is to use a 3D-printing technique in which the printing nozzle is maneuvered by a robotic arm to place the matrix material in space in the same way as spiders make their webs. After the hyphae spread in the 3D web, the resulting foamy material is very light and highly suitable for high-performance sandwich composites. 6.2.2 BOMBARDIER-BEETLE SPRAY Ground beetles of many species such as Stenaptinus insignis [19] and Brachinus crepitans [20] are commonly called bombardier beetles because they exhibit an extraordinary self-protecting behavior. When approached by a predator such as an ant, a bombardier beetle sprays a boiling liquid toward the approaching predator, as depicted in Fig. 6.2. The liquid is ejected through a nozzle at the abdomen which can be directed to point toward the desired target. The amaz- ing feature is that it is possible for the beetle to generate and handle a boiling liquid without harming itself. Another remarkable feature is the way in which the very hot aerosol is made. A gland containing hydrogen peroxide and another gland containing hydroquinone shoot their respective contents through the anus. When the two liquids mix with the enzymes catalase and peroxidase, hydrogen peroxide decomposes into water and oxygen and hydroquinone oxidizes 64 6. SOLUTION-DRIVEN BIDS Figure 6.2: Hot spray is used by Stenaptinus insignis as a defense against predators [19]. Copy- right (1999) National Academy of Sciences, U.S.A. into p-quinones. Both reactions are exothermic, bringing the mixture to the boiling point and vaporizing it partially before expulsion along with free oxygen. At the University of Leeds, the entire defense mechanism of the bombardier beetle species was found relevant to gas turbine igniters [20, 21]. The initial part of a research project under- taken at Leeds can be considered to be problem driven, as the desire to improve the combustion process in a gas turbine led to interest in a biological phenomenon. After studying the spray mechanism in the beetle, researchers constructed a scaled-up replica of the combustion chamber to demonstrate a similar spray formation. It was soon realized that the fascinating and remark- able properties of the bombardier spray mechanism could be useful for pharmaceutical sprays, ﬁre extinguishers, and fuel injectors in combustion engines. That realization moved the work from problem-driven BID toward solution-driven BID. This can be seen as a deﬁnition of the attractive characteristics of a biological phenomenon (which is the ﬁrst step in solution-driven (a)(b)6.2. EXAMPLES OF SOLUTION-DRIVEN BID 65 Figure 6.3: Tubercles on the leading edges of the ﬂippers of a humpback whale improve lift and reduce drag as well as the risk of stalling. Courtesy: Whit Welles (Wwelles14) https://commons. wikimedia.org/w/index.php?curid=2821387. BID, as explained in Section 6.3.2) for a spray technology that can reduce the environmental impact typical of existing spray technologies [21]. That understanding led to the identiﬁcation of spray applications, such pharmaceutical sprays and ﬁre extinguishers, that release polluting gases such as propane into the atmosphere. The biomimetic spray technology is being applied in other scenarios too. For example, exhaust from internal combustion engines contains nitrogen oxides (NOx), which contribute to smog and acid rain [22]. The release of NOx is normally regulated by ﬂow-restricting mixers. However, the principles for vapor formation in the bombardier beetles can be exploited to inject small droplets of a solution of urea into the exhaust and thereby inhibit NOx release [23]. Swedish Biomimetics 3000 is commercializing the bombardier-beetle spray technol- ogy [24, 25]. This industrial company realized the potential of this biomimetic technology and began to explore applications in diverse industrial sectors, e.g., for air humidiﬁers in supermar- kets. 6.2.3 TUBERCLES FOR FLOW CONTROL Serendipity can play a big role in solution-driven BID. Frank Fish, a biology professor at West Chester University, happened to notice a curious feature in a ﬁgurine of three humpback whales (Megaptera novaeangliae) displayed at an antiques store [26]. The leading edges of the large ﬂippers of the whales in the ﬁgurine were not straight but had tubercles. A little research showed that the artist had not made an error; indeed, the ﬂippers of humpback whales have turbercles, as illustrated in Fig. 6.3. Why do whale ﬂippers have this strange geometry? Flippers are adaptations of hands. The biologist Fish found that the tubercles closely follow the joints in the phalanges of the 66 6. SOLUTION-DRIVEN BIDS “ﬁngers” in each ﬂipper. The ﬂippers of a fully grown whale are about 3.60 m long, relatively long for an animal that is four times longer. The natural assumption for the biologist was that the tubercles serve a special purpose. This turned out to be true because humpback whales are very agile swimmers and can quickly change direction when swimming at a high speed. Unlike whales of other species, a group of humpback whales forms a circle when hunting a shoal of ﬁsh. The whales release bubbles from their blowholes to collectively form a cylindrical curtain to conﬁne the shoal. The curtain is tightened as the radius of the circular formation decreases, delivering the prey in densely packed mouthfuls to the predators. Computer models using the equations of ﬂuid dynamics as well as experiments conﬁrmed that the tubercles aﬀect motion in a ﬂuid signiﬁcantly: lift is increased and drag is reduced [27]. These features explain the agility of humpback whales. The tubercles also reduce the risk of stalling which can happen when the lift of the ﬂipper suddenly drops. Having uncovered the physical principles underlying the fascinating capability of an ani- mal arising from its anatomy, Fish wondered which technical applications could beneﬁt from the enhanced ﬂow characteristics when using a ﬂipper or a ﬁn with tubercles on the leading edge. This is the classic initiation of solution-driven BID, which justiﬁes the appellation biology- push biomimetics. Many applications were investigated [28]. One is on the ﬁn of a short surfboard which would enable a surfer to make a more sudden cutback, i.e., change direction when riding a wave. Another is on the keel of a sailing boat which can allow the boat to make tighter turns. Like water, air is a ﬂuid. Could applications in air also beneﬁt from tubercles? Truck mir- rors can be ﬁtted with tubercles to reduce the drag and thereby improve fuel economy. The same eﬀect can be achieved by adding tubercles to ﬁns on racing cars. Helicopter rotors can deliver more lift with a reduced risk of stalling. Fans in stables can save energy while also becoming quieter. Windmills can generate more energy because of reduced drag. Many good proposals for possible applications of the tubercles on the ﬂippers of hump- back whale emerged. Which of those proposals becomes commercial depends on the trade-oﬀ between achievable technical beneﬁts and possible drawbacks as well as on the ease of produc- tion. 6.2.4 ABALONE-SHELL ARMOR Abalone is the common name for marine mollusks belonging to the family Haliotidae. An abalone shell is shown in Fig. 6.4. The inner layer of the shell is made of nacre which is extremely tough, considering that most of it is aragonite which is very brittle because it is essentially chalk. 2 for aragonite The toughness can be measured as the speciﬁc work of fracture which is 0.2 J m(cid:0) 2 for nacre [29]. The explanation for nacre being 2,000 times tougher than aragonite but 400 J m(cid:0) is found in the layered “brick-and-mortar” micromorphology also shown in Fig. 6.4 [30, 31]. The bricks are plates of aragonite and the mortar is a ductile proteinaceous material [32]. 6.2. EXAMPLES OF SOLUTION-DRIVEN BID 67 Figure 6.4: (Left) Nacre in an abalone shell. (Right) Schematic of the crack-resistant brick-and- mortar micromorphology of the abalone shell. Toughness is often explained as prevention of crack propagation. A propagating crack is arrested when it encounters the proteinaceous mortar. When the shell experiences an impact from a crab or another predator, the impact energy causes the formation of microcracks in the aragonite plates. In a more homogeneous material, the microcracks would propagate and cause a failure, but the proteinaceous mortar absorbs the impact energy by deforming elastically and distributing part of the energy for microcrack formation in many other aragonite plates. Shell failure is thereby averted, the abalone shell thus providing an example of contraindicated per- formance. The abalone shell happens to provide a documented example of a misapplication of solution-driven BID [1]. Fascinated by the impact resistance of the abalone shell, a group of engineering students at the Georgia Institute of Technology exploited the brick-and-mortar micromorphology for a bullet-proof vest. It was clearly a solution-driven approach where the inspiration came from a biological solution and was applied to a technical problem. However, the design team did not approach the exercise with suﬃcient rigor, going directly from a de- scription of a fascinating functionality of a biological structure to a detailed speciﬁcation of a solution to an appealing technical problem. They did not spend time on a closer analysis of what the properties of the abalone shell actually are and what type of impact it is best suited for. The abalone shell is very good at resisting the force from the jaws of a predator which typically applies the force at a slow speed. This is very diﬀerent from the very sudden impact of a bullet ﬂying at a high speed. Furthermore, the team designed the vest mimicking not only the micromorphology but also the chemical constituents (small ﬂakes of chalk and elastic matrix) of the shell. Not only was the vest incapable of resisting bullets, it was much too heavy as well. “Brick” = Aragonite chalk“Mortar” = protein68 6. SOLUTION-DRIVEN BIDS 6.3 STEPS FOR SOLUTION-DRIVEN BID Section 5.2 provides a ﬁve-phase implementation scheme along with several ways to adopt in each phase. In contrast, literature contains much less information on formal implementation of solution-driven BID. Researchers at the Georgia Institute of Technology have formulated a seven-step implementation plan as follows [1]: (i) become aware of a biological phenomenon, (ii) deﬁne the functionalities that brought attention to that biological phenomenon, (iii) extract the key principles underlying the attractive functionalities, (iv) specify the usefulness of the biological functionalities for human activities, (v) search for technical problems that can be solved using the identiﬁed functionalities, (vi) select a technical problem from the ones identiﬁed, and (vii) apply the key principles to that technical problem. However, the instructions available in the design literature for some of these steps are scant. DTU researchers therefore developed an eight-step procedure to implement solution-driven BID, with inspiration from the way application search is done for conventional technology [11]. 6.3.1 APPLICATION SEARCH Application search is routinely carried out in any company that is focused on using a speciﬁc production technology. In order to ensure future sales, the company will regularly evaluate its present portfolio of products and search for new areas that will beneﬁt from its production tech- nology. The company will encounter challenges when seeking expansion into industrial sectors that it has no experience in. Due to this limitation, the company will serve as a subcontractor to companies that have both the required experience and contacts with end users. Another limiting factor for such a company is that its principals are not trained in design thinking and are less experienced in working with open problems and large spaces of solutions. Instead, their forte is a deep knowledge of the speciﬁc production technology which enables their company to mass produce at a competitive price. The company will also be good at improving the technology to incorporate new features. But unlike companies with end-user contact (such as manufacturers of furniture or household appliances), it does not have a well-deﬁned user group that can be explored to identify expansion potential. Identiﬁcation of industrial sectors for expansion can therefore be a challenge. Application search is a way to meet this challenge. As an example, consider application search carried out by a company that specializes in re- action molding of polyurethane, which is used to make toilet seats, panels for interior decoration, and dashboards of cars. A design-oriented approach to application search for this company is to 6.3. STEPS FOR SOLUTION-DRIVEN BID 69 Figure 6.5: Pinart toy for children. ﬁrst identify the attractive characteristics of the reaction-molding technology and then search for end-user applications in order to identify candidate companies that will beneﬁt from its tech- nology. The low tooling price for manufacturing polyurethane objects enables: (i) the production of small batches of custom-designed objects, (ii) a high degree of freedom for free-form geom- etry, and (iii) the production of lightweight components with foamed core that can be inserted in metal, wood, and textile items. For each of these three enabling attributes, an open search for applications can be made, in brainstorming sessions and/or on internet search engines. Another example is a project carried out by two engineering students to develop a new type of production technology based on the pinart toy shown in Fig. 6.5 [11]. The production technology is based on a mold that can change shape on demand and hence be useful for casting individually shaped items. An application search to justify the development of the mold iden- tiﬁed 136 quite diﬀerent applications encompassing prosthetics, contact lenses, hearing aids, chocolates, compact-disk covers, jewelry, propellers for sailing boats, and concrete bridges. A speciﬁc application must be selected in the development phase, since many parameters for the production tool (in this case, the mold), such as dimensions, accuracy, resolution, and through- put rate depend on the application. Based on an analysis of the applications and dialogue with possible collaborators for each of the application areas, two applications were selected: (i) a tool to fabricate individually shaped curved concrete facade elements and (ii) a tool for inscribing marks on casts to enable subsequent traceability during manufacture. The two resulting tools are shown in Fig. 6.6. Both applications are very diﬀerent and addressed very diﬀerent business areas. 70 6. SOLUTION-DRIVEN BIDS Figure 6.6: (Left) A tool for the fabrication of individually shaped curved concrete facade ele- ments [33] and (right) a tool for inscribing marks on casts [34], both developed based on the pinart toy shown in Fig. 6.5. Figure 6.7: Lotus leaves repel water and stay clean thereby. 6.3.2 EIGHT-STEP PROCEDURE With the knowledge that application searches are routinely carried out in some industrial sectors, DTU researchers devised an eight-step procedure that has some overlap with the seven-step implementation plan from the Georgia Institute of Technology. The eight steps of the DTU approach for solution-driven BID are provided in Table 6.1. The eight-step procedure is exempliﬁed in Table 6.1 by the leaves of the lotus (Nelumbo nucifera), a plant native to many tropical countries. Considered sacred by Hindus, Buddhists, and Jains, lotus grow in wetlands, ponds, and lakes. The remarkable characteristic of this plant is that the ventral surfaces of its leaves stay clean even in dirty surroundings because those surfaces are superhydrophobic [9], as may be noticed in Fig. 6.7. Table 6.1: The eight steps of the DTU approach for solution-driven BID along with the lotus- leaf example of self-cleaning surfaces in the bioworld 6.3. STEPS FOR SOLUTION-DRIVEN BID 71 Step 1. Solution-driven BID begins with the awareness of a biological phenomenon that could either constitute or provide a solution to a technical problem that has not been identiﬁed. Thus, solution-driven BID can be initiated by merely an interest in an animal or a plant with a fascinating behavior or capability. It can also be initiated by a biologist who has studied biological organisms of a certain species or genus for many years and begins to wonder which engineering applications could beneﬁt from the biological insight. Deﬁning the biological solution then requires a description of its characteristics that may be relevant to some applications. Biological organs are typically multifunctional, so it may be arduous to describe all of its characteristics. Fortunately, a complete description is not called for, since it was a speciﬁc characteristic that drew attention. In the ﬁrst step, that attractive characteristic of the biological phenomenon must be deﬁned. The persistent clean condition of lotus leaves can be explained by its water-repellence char- acteristic which prevents dust particles and other detritus from attaching to its ventral surface. The superhydrophobicity is responsible for the formation of water beads that roll oﬀ the surface, thereby removing foreign matter. In turn, this superhydrophobicity arises from surface topol- ogy at the 10-(cid:22)m length scale [35]. However, as the matte appearance of lotus leaves is quite No.StepLotus-Leaf Example1biological phenomenonCharacteristic: Water repellence2Make an open search for applicationsSelf-cleaning vehicles3Formulate constraints to limit the scope of the searchConstraint: Only applications for which 4Apply constraints one by one to eliminate some results of Step 2Inside the shield of a lawn mower5Create a concept for each result of Step 4Coat the inside of the shield of the lawn mower for cleaning with a garden water hose6Consult selected stakeholdersTalk to a few gardeners7Repeat Step 5 for new application Wheelbarrows8Assess every concept against Criteria: (i) Longer life time for lawn mower and (ii) lower risk of spreading pests72 6. SOLUTION-DRIVEN BIDS diﬀerent from the glossy appearance of clean and hygienic surfaces, the superhydrophicity due to surface topology may not be attractive enough for certain applications. Step 2. Next, an open search is made for applications that will beneﬁt from the attractive characteristic deﬁned in the ﬁrst step. This can be done in diﬀerent ways, but a simple one is for the design team to brainstorm in order to answer the following question: “In what situations can the described characteristic be advantageous?” The question for the lotus-leaf example is: “Where can self cleaning be advantageous?” A more general question is: “In which situations do surfaces become dirty?” The unwanted con- sequence of having a matte surface could lead to the following question: “Where are clean but non-glossy surfaces required?” Step 3. The characteristic deﬁned in the ﬁrst step will most likely result in ﬁnding a large number of possible applications in the second step. Therefore, the third step requires the for- mulation of constraints that will not only limit the scope of the search but also force deeper explorations of the fewer possible applications. A constraint can require focus on items of speciﬁc types—e.g., household items, leisure and sports equipment, hospital articles, professional tools, etc. Another constraint can be on the type of materials deemed acceptable. A third way to approach setting up constraints could be to analyze daily or professional routines while looking for activities that beneﬁt from the deﬁned characteristic. Such a routine could be what a person does while working in an oﬃce or while traveling every week to meet clients on site. Professional routines can also be incorporated by choosing a professional activity such as gardening, hospital sanitation, painting houses, and graf- ﬁti removal. The framing of a context makes it easier to imagine where the deﬁned characteristic of the biological solution may be beneﬁcial. A simple constraint for the lotus-leaf example is to focus on situations in which particle accumulation is undesirable and the particles are diﬃcult to remove. Step 4. Application of the constraints formulated in the third step will eliminate many of the possible applications identiﬁed in the second step. The constraints can be applied either sequentially or concurrently. Brainstorming by the design team will deliver context-speciﬁc ap- plications. For the lotus-leaf example, application may be sought for lawn mowers in which the oper- ator is protected from the cutting blade by a shield. The cut grass often sticks to the inside surface of the shield and is not easy to remove. Another possible application is for a house painter’s tools to have non-stick surfaces. Likewise, exterior walls of oﬃce buildings require treatment to pre- vent becoming canvases for graﬃti artists. Step 5. For each of the results of the constrained search undertaken in the fourth step, a concept has to be created. As explained in Section 2.4.4, whereas an idea is merely a principle for how to solve a problem, the application of that principle in a speciﬁc context leads to a concept 6.3. STEPS FOR SOLUTION-DRIVEN BID 73 because it satisﬁes the context-speciﬁc constraints. The intended performance of each concept must be described in concrete terms in the ﬁfth step. For the lotus-leaf example, a concept for the lawnmower is to endow the internal surface of the shield with topology at the 10-(cid:22)m length scale to prevent wet cut grass from attaching to that surface. Likewise, a concept for the house painter’s tools is have the exposed surface of every tool with a similar topology to prevent paint from adhering to the exposed surface. Finally, providing the surfaces of walls with a similar topology will deter graﬃti artists. Step 6. Each concept for every application has to be discussed with knowledgeable stake- holders in the sixth step. The stakeholders should be presented with the relevant concept(s) instead of being asked about possible applications. Some stakeholders are very likely to have reservations about why a concept may not work well in the real world, but the main point is to stimulate their creativity so they may come up with their own application proposals. Often it is easier to be creative when criticizing a concept. For the lotus-leaf example, the stakeholders to be consulted should be gardeners for the lawn-mower concept, house painters for the painting-tools concept, and janitors for the graﬃti- prevention concept. In the case of the production technology based on the pinart toy shown in Fig. 6.5 [11], a concept was of a ﬂexible mold for use by sandcasting companies. When sandcasting personnel were consulted on this concept, they informed the design team that the need for ﬂexible molds is insigniﬁcant but a major need exists for traceability during the manufacturing process. If an individual code or number could be inscribed on each cast by the mold, then it would be possible to trace each cast subsequently. The quality of representative casts from a batch could be assessed and related to the personnel who produced that batch as well as to the speciﬁc material composition used. The company could in this way get a better quality-assurance system. The design team had not been aware of the need for traceability, but consultation with knowledgeable stakeholders led to a new application of their technology. Step 7. The penultimate step is a repetition of the ﬁfth step for the new applications iden- tiﬁed by knowledgeable stakeholders during the sixth step. For the lotus-leaf example, gardeners could suggest superhydrophobic surfaces for wheel- barrows, house painters could suggest similar surfaces for lunchboxes, and janitors for walls in children’s bedrooms and school rooms. Step 8. 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Gandhi1 7.1 SUSTAINABILITY AND THE ENVIRONMENT Concern about sustainable development is mounting as the number of people on our planet in- creases. In 1987 the Brundtland Commission of the United Nations [1, 2] deﬁned sustainable development as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs.” The commission considered three ar- eas of concern for sustainable development: (i) the environment, (ii) social organization, and (iii) economy. Technological development as well the global organization of human society cur- rently require the imposition of serious curbs on consumption, especially considering the limited ability of the biosphere to absorb diverse types of waste excreted by human activities. However, both technological development and social organization can be managed and improved to make way for enhanced economic growth and poverty removal. Sustainable development requires that the more aﬄuent humans adopt lifestyles that are consistent with the planet’s ecological well being—for instance, in their consumption of energy. Also, population increase needs to be in harmony with the changing productive potential of the ecosystem. The quest for sustainable development was taken further in the 2030 Agenda for Sustain- able Development which, in 2015, resulted in the United Nations General Assembly adopting 17 sustainable development goals (SDGs) [3]. The SDGs are operational goals focused on con- crete actions. Figure 7.1 classiﬁes all 17 SDGs in relation to the previously mentioned three areas of concern: the environment (also referred to as the biosphere), social organization, and economy [4]. 1https://bestquotes.wordpress.com/2007/03/24/hello-world/ 78 7. BID FOR ENVIRONMENT Figure 7.1: The 17 sustainable development goals classiﬁed for relevance to the biosphere, social organization, and economy. Credit: Azote Images for Stockholm Resilience Center, Stockholm University. Biomimicry can help in addressing current actions and proposing new actions within all three areas, with focus on using inspiration from the bioworld to solve problems relating to the biosphere. The following SDGs can be impacted by biomimicry: SDG 6: clean water and sanitation, SDG 7: aﬀordable and clean energy, SDG 13: climate action, SDG 14: life below water, and SDG 15: life on land. Both economy and social organization are human constructs and, even though inspirations for their improvement can be found in the bioworld, the dominant application of biomimicry is for technological solutions in line with SDGs 6, 7, 13, 14, and 15. The bioworld presents many avenues that can be adapted for circular economy, resource eﬃciency, and ecosystem balances. 7.2. MATTER OF SCALE 79 7.2 MATTER OF SCALE A crucial challenge to sustainable development is posed by the growing number of people on the planet. More people share the limited resources available, more people produce waste, and more people pollute. Equal opportunities for everyone being a human right, countries should aim at providing the highest standard of living consistent with the overall health of the biosphere that includes not only all humans but all other living organisms too. An activity that seems to be only a small problem when carried out by a few people can turn out to be a huge problem when carried out by many people. Numerous examples show how small problems grow out of proportion when scaled to larger populations. In Jakarta, Indonesia, it is common practice for landowners to pump water from aquifers deep underground since piped water is not reliably available. However, with 10 million inhabitants this practice has caused land subsidence of as much as 4 m in the coastal areas of the city, thereby making it highly vulnerable to ﬂooding [5]. Another example is eutrophication of lakes and rivers [6]. The use of fertilizers is desirable to increase agricultural yields, but the right amounts may not be applied at the correct times. Excess fertilizer will run oﬀ during rain and/or irrigation to cause increased growth of algae in rivers and lakes, leading to oxygen depletion and ﬁsh deaths on a large scale. This would not be a problem if conﬁned to a few locations. However, widespread use of excess fertilizers impacts not only water bodies in landmasses but also causes dead zones in seas and oceans. Thus, a supposedly harmless action when undertaken by an individual can have grave repercussions on a large population in a large area when that same action is simultaneously implemented by more than a few individuals. The global environmental impact (GEI) can be quantiﬁed as the product of three factors [7]: the number N of people on our planet, the per-capita economic activity E, and the eco-eﬃciency F deﬁned as the environmental impact per economic activity. That is, GEI N F (cid:2) (cid:2) D E: The global population N in 2019 is around 7.5 billion, rising from 4 billion in 1974 and projected to rise to 10 billion in 2057 [8]. Concurrently, living standards (i.e., E) have improved for many people. In 1990, 36% of the global population was living in extreme poverty [9], deﬁned by the World Bank as an income of US$ 1.9 a day [10]. Extreme poverty was reduced to 8% of the world population in 2018, which illustrates the fast pace at which the standard of life is being enhanced globally. To maintain an unchanged GEI, the eco-eﬃciency F must be decreased, i.e., the environmental impact for the economic activity must be lowered. 80 7. BID FOR ENVIRONMENT U.S., Canada, most European countries, Japan, Taiwan, South Korea, Saudi Arabia, Qatar, Bahrain, and, increasingly, parts of China and India have an opportunity in being role models for sustainable life-styles of desirable quality. These regions can demonstrate that it is possible to maintain a high standard of living that is consistent with sustainable development— a win-win situation. Sustainable development does not overburden planetary resources, and a high quality of life allows the citizen to reap the beneﬁts of techoscientiﬁc advances. A major requirement to engender this win-win situation is the low-cost production of energy from nonpolluting sources for millions of years to come. These sources include the sun, winds, tides, and reservoirs. Another major requirement is the minimization of the extraction of ores, minerals, and petroleum from the planetary crust by industrywide recycling of ma- terials that have already been extracted. Improved quality of life for a growing population is possible only if both resource consumption and waste production are greatly reduced, resulting in improved eco-eﬃciency. Highly eﬃcient systems in the bioworld can inspire technological developments for an eﬀective transition toward sustainable development. 7.3 SUSTAINABLE PRACTICES FROM NATURE The biosphere and the sun together can act as an ecosystem to sustain our species and countless others for very long periods of time compared to the human lifespan. Photosynthesis transforms solar energy into organic matter that is the basis of the food chain for other living organisms. The organic matter consists mainly of a few elements—carbon, oxygen, hydrogen, nitrogen, phosphorus, and sulfur—which can be combined into a large number of materials that later can be decomposed to form new materials. All materials are synthesized by self assembly into living organisms at ambient temperatures, and those organisms either excrete or decompose into materials that can be re-synthesized into living organisms. There is no external agent following some masterplan that determines the sequence and method of assembly. Instead, the entire process is embedded within the organisms so they can self replicate. A good example of how nature produces materials with remarkable properties at ambient temperatures is the iridescent nacre found in mollusks. The material is very stiﬀ and its hardness equals that of manufactured materials such as ceramics which require very high production tem- peratures. Located on the inside of the shell, nacre is a composite layered structure consisting of aragonite crystals (calcium carbonate) separated by very thin layers of a cross-linked protein. The structure is often referred to as brick-and-mortar structure due to its visual similarity to building materials [11]. The material-shaping mechanism is not completely understood but a good model has been described by Addadi et al. [12]. The layered structure is made through a long sequence of steps. The epithelial cells in the mollusk’s mantle secrete the highly cross-linked periostracum protein layer under which a gel-like matrix is formed. The matrix includes both hydrophobic and hydrophilic proteins as well as colloidal particles of the chemically unstable amorphous calcium carbonate. Aragonite crystals form at nucleation sites and grow until the periostracum layer 7.4. CIRCULAR ECONOMY OF MATERIALS 81 is reached. In between the crystals, chitin molecules are trapped so that the brick-and-mortar structure is formed. An example from nature, but not the bioworld, is the way sediments are transported by sea currents along coasts. Soil is removed from places along coastlines, thereby causing land to disappear while cliﬀs are formed. The soil is moved by the sea currents and deposited at other places, typically forming headlands. Amazingly thus, water breaks down solid material and carries it over long distances simply through the persistent application of fairly small forces over long periods of time. A similar mechanism is applied by humans to convert seabed into agricultural land. In Denmark, Germany, and the Netherlands, the tides are fairly large and the coastal areas are usually wide and ﬂat. By deliberately placing obstacles to delay water brought over by the tides, the deposition of sediments is promoted causing the land to form above the sea level. This approach of using many repeated actions to create a shape abounds in nature. Each individual action is in itself not very powerful. In contrast, humans typically apply a lot of force for a short while to create similar formations—e.g., when an excavator is used to move soil. The bioworld thus presents a very diﬀerent approach for manufacturing materials com- pared to the approaches humans take. When considering length scales of up to 1 m, humans manufacture objects primarily by using high levels of energy and through a planned selection of materials [13]. For instance, polymers are typically processed by pressing the melted poly- mer into a mould while applying large forces. The bonding energies for polymerization are quite similar in magnitude for a large variety of polymers, whether manufactured in a factory or in the bioworld. But, biological systems do not use elevated temperatures and rely instead on chemical reactions when building blocks of the right basic materials are brought into position. Biological polymers are mainly proteins and polysaccharides in ﬁbrous form, found in collagen, silk, mus- cles, and arthropod exoskeletons. Hard tissue in biology is mostly made from calcium and silicon with smaller fractions of iron, zinc, and manganese—all processed at ambient temperature [14]. 7.4 CIRCULAR ECONOMY OF MATERIALS Most biological materials can be used directly or indirectly by other organisms. Many mammals, for instance, eat the placenta after the birth of an oﬀspring. All spiders produce silk but not all spiders spin webs. Webmaking saves a spider the energy-consuming eﬀort of hunting by rapid locomotion, but it requires a sizable investment of proteins that the web is made of [15]. Many spiders eat their old webs so that the proteins are recycled to make new webs [16, 17]. Less directly, biological materials are broken down to simpler molecules by bacteria, mak- ing them useful for other organisms. Biodegradation is a well-known process whereby bacteria in the ground decompose dead organic material into carbon dioxide, nitrogenous compounds, and other materials [18]. Mycelia from fungi break down lignin and cellulose from plants. Fungi grow on dead trees on the forest ﬂoor after the wood has been moisturized, and the same can be 82 7. BID FOR ENVIRONMENT seen in buildings with wooden structures. Thus, moisturized wood provides a good environment for fungi to grow and eventually break down the lignin and cellulose in the wood [18]. Colors in plants are usually produced using pigments [19] though sometimes structural colors are also found [20]. A structural color arises due to spectrally selective scattering of visible light in response to the morphology of a physical structure [21, 22]. Usually, the morphology has a repeat pattern that is tuned to a certain color. Whether dull or brilliant, a structural color is not produced by pigments, which is immensely important for biologically inspired design for environment in that material diversity is not enhanced by incorporating a structurally colored object. Multifunctionality is commonplace in living organisms [23, 24], because fewer organs need to be formed, housed, and coordinated if those organs are multifunctional. As an example, a mouth is used for ingesting nutrients, releasing sounds, breathing, and showing aﬀection. A multifunctional module can be incorporated in a variety of products, thereby reducing inven- tory costs, enhancing repairability, extending product lifetimes, and promoting standardization. Lifetime extension slows down the depletion of raw materials, reduces the consumption of en- ergy for manufacturing, and reduces the volume of waste for disposal. 7.5 MUTUALLY BENEFICIAL COEXISTENCE No organism in the bioworld exists on its own but is dependent on interactions with other organisms, whether of the same species or not. Within a species, wolves and dingoes hunt in coordinated groups for greater success, starlings ﬂy in coordinated murmurations to confuse predators such as falcons, and ﬁsh similarly form schools (not to be confused with the much less coordinated shoals) to elude predators. Mammal mothers rely on kin to bring food and even look after infant oﬀsprings. Mammals rely heavily on symbiosis with microorganisms in their digestive tract. On aver- age, a human has 0.2 kg of bacteria primarily in the intestines [25], not only to help break down food into substances that can be adsorbed through the intestine wall but also to supply signaling compounds essential to the mental health of the person [26]. Transplants of fecal matter can improve the health of humans suﬀering from a range of diseases [27]. Plants can produce carbohydrate building blocks through photosynthesis by extracting carbon from the air and water from the ground. However, they cannot extract minerals such as phosphorus from the soil and therefore beneﬁt from a symbiotic relationship called mycor- rhiza between their roots and mushrooms [18]. In exchange, the mushrooms get carbohydrates. Similarly, some bacteria extract nitrogen from air and supply it to plants as ammonia [18]. Ni- trogen ﬁxation is essential for the biosynthesis of amino acids, proteins, nucleic acids, and other nirogenous compounds. Many animal species rely on social relationships to thrive and even exist. These relation- ships are very pronounced in social insects such as bees, ants, and termites. They are characterized by a division of labor whereby some individuals provide food, others nurture the eggs and lar- 7.6. ENERGY EFFICIENCY 83 vae, and still others build and maintain the physical living facility. The individuals communicate using a range of signals including visual (e.g., color in ﬂowers and waggle dance among bees), olfactory (e.g., pheromone trails made by ants) and acoustic (e.g., bees buzz with their wings). The role of the individual appears to be centrally controlled only to a limited degree, with guards allowing entry only to the inhabitants of the hive or pit. So, how do individuals know their roles and how to perform tasks without feedback from a central authority? A very subtle type of communication to control ﬂock behavior involves pheromones. A pheromone is an olfactory agent that, unlike many fragrances that animals consciously recognize, makes a short cut to the brain and produces almost instantaneous recognition. Pheromones assist in a range of diﬀerent activities such as initiating alarms, attracting mates, and marking trails to be followed by others [28]. Inter-species communication is also commonplace. The approach of a fearsome predator leads to a single alarm signal that warns birds and mammals of diverse species to take evasive action [29]. Not only animals but plants also communicate. The roots of grasses and cereals of many types excrete chemical compounds that are processed by other plants to determine if the secreting plants belong to their family. This phenomenon has been deduced from the way in which the growth of roots of a certain plant is inﬂuenced by the roots of neighboring plants [30]. Human society too can beneﬁt from symbiosis whereby the residual energy and materials from one company become resources for another company. Industrial symbiosis is an element in the circular economy which, apart from better utilization of resources, beneﬁts society by increasing the number of jobs and boosting the Gross Domestic Product [31]. In the city of Kalundborg in Denmark, 11 public and private companies have formed a partnership facilitating a circular approach for the reﬁnement of crude oil; production of insulin, fertilizers, and gypsum wallboards; and heating residences and oﬃce buildings [32]. The symbiotic activities direct waste energy, water, and materials from one company to another. For example, the insulin factory uses fermented sugars resulting in residual yeast biomass which is directed to a factory for producing fertilizers and biogas, the biogas is used in the gypsum factory for heating, and the residual thermal energy is transferred to a central heating plant. The result is better utilization of resources and materials combined with enhanced economy and employment. Another example is the Danish Pig-City project that aims at combining diﬀerent types of agri-businesses [33]. The project combines the husbandry of pigs and production of tomatoes with a slaughter house, an energy generation plant, and a bio-reﬁnery. Heat from the piggery on the ground level is used for growing tomatoes in a greenhouse on the ﬂoor over the piggery. Organic waste from both the piggery and the greenhouse is treated in the bio-reﬁnery to produce biogas for heating and fertilizers for the greenhouse. 7.6 ENERGY EFFICIENCY Access to enough energy is a limiting factor for all physical and chemical processes in the bioworld. Just as for aeroplanes and helicopters, the range and duration of avian ﬂight depend 84 7. BID FOR ENVIRONMENT on how much energy does a bird have when it takes oﬀ into the air. Avian bodies have therefore evolved to have lightweight structures. Many large birds such as albatrosses, condors, and eagles exploit the warmer air currents for lift and thus minimize energy consumption by their pec- toral and supracoracoideus muscles [34, 35]. Mammals regain energy cyclically when running. On the downstroke of a leg, the tendons, ligaments, and muscles stretch to store energy that is released on the oﬀset. This is true for most animals, but a surprising phenomenon is seen for kangaroos which are very eﬃcient energy regainers. At moderate speeds they are more energy eﬃcient in terms of oxygen consumption compared to running bipeds and quadrupeds of similar size [36]. The force that impedes forward motion in a ﬂuid is called drag. Several species have intri- cate mechanisms for reducing drag. Sharks are covered with tiny corrugated scales which intro- duce microturbulence close to the body surface. The microturbulence allows for a more laminar ﬂow of seawater, thereby reducing the overall drag. The phenomenon has been mimicked in polymer ﬁlms applied on aircraft to reduce drag [37]. The sharkskin scales are multifunctional since their corrugated shape also prevents fouling [38], because barnacles are not able to get a good grip and therefore fail to attach. Penguins reduce drag by releasing microbubbles of air trapped under their feathers. If necessary, a penguin can thus increase its speed several times over short distances, e.g., when chased by a predator [39]. 7.7 DESIGN APPROACHES Several approaches have been devised to support the designer toward the goal of sustainability enhancement. Formal guidelines help keep a tight focus toward that goal. The system-oriented approach of circular design orients the designer not solely toward the manufacture of a spe- ciﬁc product, but on its entire lifecycle to encompass raw materials, the use phase, and the utilization of waste products. A third approach is to assess the environmental footprint of the product. 7.7.1 ENVIRONMENTAL GUIDELINES An approach suitable for the early-design stages when many product details are yet unknown is to use Green Design Guidelines (GDG) [40]. The widely used GDGs may have either very concrete forms such as the speciﬁcation of acceptable materials, or be abstract by exhorting the embrace of techniques that produce less waste than those techniques that require remedial cleanup of the produced waste. Another approach involves a systematic methodology to aim for eﬃciency in the use of energy and materials [41]. This approach comprises diﬀerent types of eﬃciency (such as me- chanical, material, and thermal eﬃciencies) and a framework to use bioinspiration. Once a type of eﬃciency is selected, analogies from the bioworld can help the designer by providing insight into functioning and eﬃcient solutions. 7.7. DESIGN APPROACHES 85 The International Standards Organization deﬁnes biomimicry as “philosophy and inter- disciplinary design approaches taking nature as a model to meet the challenges of sustainable development (social, environmental, and economic)” [42]. A distinction has been made in Chap- ter 1 between biomimicry and engineered biomimicry, the former being contained in the latter. Whereas engineered biomimicry does not need to be focused on reaching for sustainabil- ity goals, the term biomimicry—often associated with the Biomimicry Institute, an American non-proﬁt organization—is focused on using inspiration from the bioworld to design solutions that contribute to sustainable development. The Biomimicry Institute has a sister organization called Biomimicry 3.8 which is a con- sultancy working together with companies to solve design problems. One of the founding mem- bers of both organizations is Janine Benyus. The two organizations have developed a basic frame- work for design work [43] and the database Asknature [44] which allow searches for biological strategies to solve speciﬁc functional challenges. To support sustainable development, the orga- nizations have formulated the following six lessons from the bioworld: • • evolve to survive, adapt to changing conditions, • be locally attuned and responsive, • use life-friendly chemistry, • be resource eﬃcient, and • integrate development with growth. Each lesson leads to speciﬁc guidelines, such as incorporate diversity and use low-energy pro- cesses, that are mainly concerned with the environmental part of sustainable development. These guidelines function in the same way as the criteria for evaluation of design proposals described in Chapter 2. When two proposed solutions are compared, the preferred one has to satisfy more guidelines in the best way. Thus, these guidelines are not absolute but indicate desirable out- comes. In a study of biomimicry practices in the Nordic countries, it was found that only a few companies have combined biologically inspired design and environmentally conscious de- sign [45]. But there are many examples of companies adopting either biologically inspired design or environmentally conscious design, so that their amalgamation is a realistic goal. In another study, designers were found to use several diﬀerent sustainability frameworks when working with bio-inspiration, but without an established system of accountability [46]. 7.7.2 CIRCULAR DESIGN Designing a product with circularity in mind entails an insurance that recycled materials are used for production and that the product at the end of its life can be reused or recycled. 86 7. BID FOR ENVIRONMENT Circular economy is an approach to promote sustainable development with parallels to how resources are circulated in the bioworld. The Ellen MacArthur Foundation deﬁnes circular economy as an industrial economy that is restorative by intention [47]. Motivated by lessons learned from studies of living nonlinear systems, circularity is premised on the use of renewable energy, minimum consumption of chemicals, and eradication of waste. Circularity aims to op- timize systems rather than their components. This is done by managing the ﬂows of materials of two types: (i) biological nutrients that re-enter the biosphere safely and (ii) technical nutrients designed to circulate without diminishing in quality and without entering the biosphere. Consequently, circular economy distinguishes between consumption and use of materi- als. It promotes a functional service model whereby the ownership of a product is retained with the manufacturer who acts as a service provider rather than as a product seller. The manufac- turer therefore does not promote one-way consumption but ensures that the product will be reabsorbed in the economy after the end of its life. Circularity can be applied to all types of industrial production. An example is the cloth- ing industry. The current system is regarded as extremely wasteful and polluting from the initial production of textile ﬁbers, through the production of fabrics and a wearable followed by re- peated washes during use to the ﬁnal after-use destiny of the wearable [48]. Typically, an item of clothing is discarded after the wearer is no longer interested in wearing it, although sometimes it can be passed on to another person. A cotton wearable may be collected by rag pickers as a raw material for producing paper and industrial wiping rags, there is hope that blended poly- mer/cotton wearables could be reprocessed after recovering and separating ﬁbers of diﬀerent materials, wool extracted from woolen wearables can be used for insulation panels for housing, acrylics and nylons can be reprocessed into blankets, but polyester wearables are mostly inciner- ated [49]. Circular economy in the clothing industry would be greatly facilitated by ﬁber-to-ﬁber recycling. Cradle-to-cradle is an approach to maximize the positive eﬀect of human activities on the environment as opposed to eco-eﬃciency that focuses on reducing damage to the environ- ment [50, 51]. It is based on three key principles: • waste equals food, • use only energy provided currently by the sun, and • celebrate diversity. The ﬁrst principle is inspired by the nutrient cycles seen in the bioworld. Instead of reducing waste, only that waste should be produced which another process can use as an input. The sec- ond principle dictates that all energy should come from the sun, i.e., from photovoltaic solar cells, solar thermal heaters, wind turbines, hydroelectric generators, and biomass incinerators. The third principle encourages design that respects local cultures and environments and also recognizes that nonhuman species have the right to thrive in their own ecosystems. A criticism 7.8. BIOLOGICALLY INSPIRED DESIGN FOR ENVIRONMENT 87 of the cradle-to-cradle approach is that is does not address trade-oﬀs between energy use and resource conservation, because even healthy emissions can adversely aﬀect the ecosystem [50]. 7.7.3 IMPACT ASSESSMENT Life-cycle analysis is an approach to assess the eco-eﬃciency of a design. A comprehensive inventory is made of materials, energy, and chemicals used to make, distribute, use, and dispose of the product. The impacts of the materials, energy, and chemicals on the environment are also cataloged. In order to compare the eco-eﬃciencies of two diﬀerent designs, a functional unit is deﬁned to represent the desired functional performance. As an example, the functional unit can be used to facilitate the comparison of the eco-eﬃciencies of diﬀerent ways of maintaining a golf course. A functional unit could be deﬁned as the acreage of a certain terrain in which the height of grass must be maintained, which makes it possible to compare diﬀerent methods to maintain grass height—e.g., using lawn mowers or letting a ruminant species such as goats or sheep graze. Assessing the environmental impact is a fairly complex task since a design can have envi- ronmental eﬀects through several mechanisms such as the emission of greenhouse gases leading to global warming, the emission of chloroﬂuorocarbons and halons leading to ozone-hole for- mation, and the acidiﬁcation of lakes and rivers. When designing products, a simpler and less precise method is often used—namely, the use of indicators such as CO2-equivalents. The in- dicators make it possible to compare quite diﬀerent designs. For example, they can be used to compare the production of vegetables in heated greenhouses in a cold region with the production of vegetables produced in a warm region followed by transportation to the same cold region. The use of life-cycle analyses has been criticized for not including the full potential of approaches such as biomimicry and cradle-to-cradle [50, 52]. Instead, a life-cycle analysis can become so easily focused on the function of a speciﬁc product that its goal can be best charac- terized as the reduction of unsustainability. Formulation of the functional unit can in some cases lead to ignoring ancillary issues whose consideration could have enhanced sustainability. Thus, a life-cycle analysis can lessen the use of energy and materials in a factory, but it will not address the improvement of air quality which could be very important for public health. The life-cycle analysis of a product can be supplemented with clear criteria of when a product can be considered sustainable and when not. This is not an easy task, but attempts are in progress to deﬁne green products as having zero waste, producing zero emissions, and being environmentally safe. 7.8 GRAFTING “BIOLOGICALLY INSPIRED DESIGN” ONTO “DESIGN FOR ENVIRONMENT” Design for environment aims at developing products to enhance sustainability without com- promising functionality, cost, quality, etc. The bioworld presents many approaches that can be 88 7. BID FOR ENVIRONMENT adapted for circular economy, resource eﬃciency, and ecosystem balance. As an example, micro- scopic scales on sharkskin swimsuits indeed reduce drag; likewise, sharkskin polymer ﬁlms on aircraft and ships lower energy consumption [37]. But care must be exercised when transferring solution principles from the bioworld to industrial activities [53]. A bioworld phenomenon may appear simple at ﬁrst glance but it may actually involve many intricate mechanisms to assure a desirable outcome. Its complexity may be inimical for adoption by designers. Additionally, a bioinspired solution may not comply with our ethics; for instance, the predator-prey relation- ship [54] is highly undesirable as a model for controlling the human population. Finally, an attractive solution principle may simply be impractical for adoption. As an example, a penguin can increase its speed several times over short distances underwater by releasing microbubbles of air trapped under its feathers [39], but the application of the same mechanism to reduce drag on a regular ship appears practically unimplementable. The grafting of biologically inspired design onto design for environment requires a careful delineation of the design object. Design for environment is often focused on reducing the overall environmental impact of a speciﬁc product. An automobile engine that consumes less gasoline than its competitors delivering the same performance and driver satisfaction will comply with the objectives of design for environment. In other cases, a system involving many products and processes has to be considered. An example is the introduction of electric vehicles or hydrogen- powered vehicles that will necessitate the development of a comprehensive new infrastructure. In the bioworld, any organism relies on being part of a larger system comprising organisms of the same and diﬀerent species. Environmental sustainability must therefore be addressed at both the product level and the system level, when a bioinspired solution principle has to be considered for adoption. The mutualistic relationship between plants, rhizobial bacteria, and mycorrhizal fungi which beneﬁt from an exchange of nutrients and energy [18] illustrates how it can be insuﬃcient only to consider an isolated object as the design object. The design of a product or system typically involves the following four phases [55] de- scribed in detail in Chapter 2: • deﬁnition and clariﬁcation of the need for the product or system (Sections 2.4.1–2.4.3), • conceptualization of the product or system and the production/realization process (Sec- tions 2.4.4–2.4.5), • preparation of its embodiment to focus the attentions of all stakeholders (Sec- tion 2.4.6), and • creation of the necessary detail for production and realization (Section 2.4.6). Of these four phases, the conceptualization phase oﬀers the most opportunities for implement- ing strategies associated with design for environment. These strategies include: reduction of material diversity, ease of disassembly and repairability for longer useful life, use of recyclable 7.9. REFERENCES 89 and recycled components, reduced use of toxic materials and nonrenewable resources, and ease of disassembly for circularity and recyclability. An ever-growing compendium of bioinspired solution principles needs to be established for each of these strategies. This compendium could lead to the identiﬁcation of new generic design principles for disruptive innovation. For example, egg shells and sea shells illustrate how chalk, a soft material, can be microstructured to bear huge static and dynamic loads. Thus, in- ferior materials can be biomimetically reformulated to deliver superior performance. The com- pendium would also promote multifunctionality, as exempliﬁed by avian plumage being used for ﬂight without signiﬁcant increase of weight, water repellency, and conservation of body heat. Design for environment brings additional constraints for biologically inspired design, which may considerably minimize the solution space. However, a clear environmental goal will facilitate a more focused search in the compendium and would stimulate creativity in ﬁnding new solutions. As an example, the nests of most birds are made from waste materials held to- gether with friction and thus exemplify temporary structures that require very low investment but fulﬁll short-term needs for temporary housing. The grafting of biologically inspired design onto design for environment will bring certain challenges. The evaluation of a radical solution from the bioworld may be diﬃcult not only due to lack of data but also because of uncertainty in how it will aﬀect use patterns and impact associated products. For example: inspired by the way spiders eat their own web every second day in order to regenerate the proteins [16, 17], a solution could be the local reuse of building materials. However, this will impact the business system for building materials and the working procedures of the construction industry. The uncertainty may be especially high when the context and the expected-use scenario for a product or system are not yet deﬁned. 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Braungart, Cradle to Cradle: Remaking the Way We Make Things, North Point Press, New York, 2002. 86 [52] I. C. de Pauw, P. Kandachar, and E. Karana, Assessing sustainability in nature- inspired design, International Journal of Sustainable Engineering, 8:5–13, 2015. DOI: 10.1080/19397038.2014.977373. 87 94 7. BID FOR ENVIRONMENT [53] T. A. Lenau, D. C. A. Pigosso, T. C. McAloone, and A. Lakhtakia, Biologically inspired design for environment, Proceedings of SPIE, 11374:113740E, 2020. DOI: 10.1117/12.2558498. 88 [54] A. A. Berryman, The origins and evolution of predator-prey theory, Ecology, 73:1530– 1535, 1992. DOI: 10.2307/1940005. 88 [55] G. Pahl, W. Beitz, J. Feldhusen, and K.-H. Grote, Engineering Design: A Systematic Ap- proach, 3rd ed., Springer, London, UK, 2007. DOI: 10.1007/978-1-84628-319-2. 88 Authors’ Biographies 95 TORBEN A. LENAU Torben A. Lenau is an Associate Professor in design method- ology, material selection, and biomimetics at the Department of Mechanical Engineering, Danmarks Tekniske Universitet. His research interests are creative methods in product design with focus on materials, manufacturing, and biomimetics (in- spiration from nature). He has conducted a number of indus- trial case studies on how to integrate biomimetics in product development and has developed the biocards used to commu- nicate design principles found in nature. Furthermore, he stud- ies natural occurring photonic structures in order to develop new surface coatings based on structural colors. AKHLESH LAKHTAKIA Akhlesh Lakhtakia is Evan Pugh University Professor and the Charles Godfrey Binder (Endowed) Professor of Engineering Science and Mechanics at The Pennsylvania State University. He received his B.Tech. (1979) and D.Sc. (2006) degrees in Electronics Engineering from the Institute of Technology, Ba- naras Hindu University, and his M.S. (1981) and Ph.D. (1983) degrees in Electrical Engineering from the University of Utah. He was the Editor-in-Chief of the Journal of Nanophotonics from its inception in 2007–2013. He has been elected a Fel- low of the American Association for the Advancement of Sci- ences, American Physical Society, Institute of Physics (UK), Optical Society of America, SPIE–The International Society for Optics and Photonics, Insti- tute of Electrical and Electronics Engineers, Royal Society of Chemistry, and Royal Society of Arts. His current research interests include: electromagnetic ﬁelds in complex mediums, sculp- tured thin ﬁlms, mimumes, surface multiplasmonics and electromagnetic surface waves, forensic science, and engineered biomimicry.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6812753.pdf&bkn=6812752&pdfType=book	Style and Ethics of Communication in Science and Engineering Copyright © 2009 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes www.morganclaypool.com ISBN: 9781598292985 paperback ISBN: 9781598292992 ebook DOI: 10.2200/S00128ED1V01Y200809ENG009 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING #9 Lecture #9 Series ISSN ISSN 1939-5221 print ISSN 1939-523X electronic Style and Ethics of Communication in Science and Engineering Jay D. Humphrey Texas A&M University Jeffrey W. Holmes University of Virginia SYNTHESIS LECTURES ON ENGINEERING #9 iv ABSTRACT Scientists and engineers seek to discover and disseminate knowledge so that it can be used to im- prove the human condition. Style and Ethics of Communication in Science and Engineering serves as a valuable aid in this pursuit—it can be used as a textbook for undergraduate or graduate courses on technical communication and ethics, a reference book for senior design courses, or a handbook for young investigators and beginning faculty members. In addition to presenting methods for writing clearly and concisely and improving oral presentations, this compact book provides practical guide- lines for preparing theses, dissertations, journal papers for publication, and proposals for research funding. Issues of authorship, peer review, plagiarism, recordkeeping, and copyright are addressed in detail, and case studies of research misconduct are presented to highlight the need for proactive attention to scientific integrity. Ample exercises cause the reader to stop and think. Style and Ethics of Communication in Science and Engineering thus motivates the reader to develop an effective, indi- vidual style of communication and a personal commitment to integrity, each of which are essential to success in the workplace. KEyWoRDS journal publication, theses, grant writing, peer review, oral presentations, authorship, record keeping, research misconduct v Preface How to write well. How to publish your results. How to secure funding. How to speak well. How to ensure integrity. This book was written to help address these important aspects of beginning a career in science and engineering. In essence, scientists and engineers seek to discover and disseminate knowledge so that it can be used to improve the human condition. Effective communication thus plays an essential role in promoting technical advances. Simply put, communication is the ability to express oneself in a way that is understood readily and clearly. There will be no impact of scientific or engineering discoveries without effective written and oral communication. In sections on writing well, we focus primarily on style — that is, rules of usage as well as principles of composition and form — and draw heavily from Strunk and White (1979), Berry (1971), and Brogan (1973). Indeed, many illustrative phrases and sentences were inspired by or modified from these works. We thus note here our indebtedness to these outstanding works and the examples therein. We encourage the reader to consult these excellent resources as well. Although written communication, particularly the archival journal article, is most important to the widespread and long-term advancement of science and engineering, oral communication plays a vital role. From didactic lectures by an instructor to entertaining presentations for a lay audience, oral communication has the potential to capture the imagination and promote the ad- vancement of science and its applications. Similar to theater, oral communication requires one to “tell a story” well, that is, to package information in a way that is assimilated quickly and retained. Technical advances in audiovisual capability can aid tremendously in stimulating and capturing an audience and thus should be integrated thoughtfully within the oral presentation. It takes a lifetime to establish a good reputation, but only a moment to destroy it. Integrity in the workplace is just as important as understanding well the basic principles of science and en- gineering or the basic operation of a scientific instrument. Yet, even within the narrow context of technical communication, it is impossible to articulate a prescriptive set of rules or procedures for vi STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg acting ethically. Despite the increasing prevalence of courses in research ethics, surveys suggest that most students learn the ethics of research and communication primarily “on the job,” principally from their research mentor. Good training in the ethics of research thus begins with selecting a mentor who values such training and seeks to develop integrity through regular discussion and introspection. One goal herein is to stimulate this process of interaction around major issues most likely to face scientists and engineers in documenting and reporting their research. The overall goal of this short book is not to be a standalone source on matters of style (which is left to professors of English or communication) or ethics (which is left for professors of philoso- phy or law). Rather, it is meant to motivate the reader to develop an effective, individual style of communicating and a personal commitment to integrity simply because it matters. Hence, this book is written based on personal experiences of the authors in research and training in the biomedical sciences and engineering, including the development and delivery of related graduate courses at Texas A&M University, Columbia University, and University of Virginia. Nevertheless, one of the best ways to learn to write well is to read extensively the works of good writers; one of the best ways to learn to speak well is to listen carefully to good speakers; one of the best ways to ensure integrity in the workplace is to learn from reputable professionals. The reader is thus strongly encouraged in this regard and, indeed, to keep a notebook wherein personal experiences and helpful observations can be recorded and reviewed periodically. Best wishes. vii Acknowledgments We thank Jodi Eyhorn, from the Department of Communication of Texas A&M University, for expert assistance in correcting early portions of the manuscript. We also thank Joel Claypool, of Morgan & Claypool, for patience and support during the writing process. Portions of this work began via a Special Opportunity Award from the Whitaker Founda- tion. Finally, J.D.H. thanks Carolyn S. and Tommie E. Lohman for their continued support of many different educational initiatives at Texas A&M University, including composition of portions of this work. ix Contents 1. motivation .........................................................................................................1 2.4 2. Writing Well ......................................................................................................5 2.1 Overall Approach ............................................................................................... 5 2.1.1 Outline ................................................................................................... 5 2.1.2 Write Freely ............................................................................................ 7 2.1.3 Edit Critically ......................................................................................... 8 2.1.4 Read Out Loud ...................................................................................... 8 2.1.5 Have a Colleague Proofread ................................................................... 9 2.2 Removing Redundancies and Unnecessary Words ........................................... 10 2.3 Active Voice, First Person, and Different Tenses .............................................. 15 2.3.1 Voice ..................................................................................................... 15 2.3.2 Person ................................................................................................... 19 2.3.3 Tense .................................................................................................... 21 Infinitives and Modifiers .................................................................................. 22 2.4.1 Infinitive ............................................................................................... 22 2.4.2 Modifiers .............................................................................................. 23 2.5 Additional Issues of Word Choice .................................................................... 26 2.6 Punctuation, Abbreviations, and Foreign Languages ....................................... 30 2.6.1 Exploit Methods of Punctuation .......................................................... 30 2.6.2 Abbreviations ........................................................................................ 32 2.6.3 Foreign Languages ................................................................................ 33 2.7 Footnotes, Quotations, and Proper Citation ..................................................... 35 2.7.1 Footnotes .............................................................................................. 35 2.7.2 Quotations ............................................................................................ 35 2.7.3 Proper Citation ..................................................................................... 36 2.8 Vocabulary ........................................................................................................ 36 2.9 Closure ............................................................................................................. 40 x STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 3. 4. Scientific Publications ...................................................................................... 41 3.1 Basic Content ................................................................................................... 41 3.1.1 Cover Page and Letter to Editor .......................................................... 42 3.1.2 Results .................................................................................................. 44 3.1.3 Methods (or Materials and Methods) .................................................. 45 3.1.4 Discussion and Conclusion ................................................................... 47 3.1.5 Introduction .......................................................................................... 48 3.1.6 Abstract ................................................................................................ 49 3.1.7 Acknowledgments ................................................................................ 49 3.1.8 Appendices ........................................................................................... 50 3.1.9 References ............................................................................................. 50 3.1.10 Figures and Tables ................................................................................ 52 3.2 Publishing an Archival Journal Paper ............................................................... 53 3.2.1 Origin ................................................................................................... 53 3.2.2 Composition and Authorship ............................................................... 54 3.2.3 Submission and Review ........................................................................ 54 3.2.4 Revision ................................................................................................ 56 3.2.5 Typesetting, Galley Proofs, and Proofreader Marks ............................. 57 3.2.6 Copyright, Permissions, and Page Charges .......................................... 58 3.3 Thesis or Dissertation ....................................................................................... 59 3.4 Technical Reports ............................................................................................. 61 Proposals and grant Applications ..................................................................... 63 Introduction ...................................................................................................... 63 4.1 4.2 Types of Grants ................................................................................................ 63 4.3 The Review Process .......................................................................................... 64 4.4 The NIH R01 Grant ........................................................................................ 67 4.4.1 Specific Aims ........................................................................................ 68 4.4.2 Background and Significance ............................................................... 68 4.4.3 Preliminary Results ............................................................................... 69 4.4.4 Research Plan ....................................................................................... 70 4.4.5 References ............................................................................................. 72 4.5 The Preproposal ............................................................................................... 73 4.6 Summary .......................................................................................................... 74 Appendix .................................................................................................................... 76 5. oral Communication ....................................................................................... 77 5.1 Effective Styles ................................................................................................. 77 5.2 The 15-Minute Presentation ............................................................................ 82 5.3 Summary .......................................................................................................... 84 CoNTENTS xi 6. Authorship ....................................................................................................... 85 6.1 The Slutsky Case .............................................................................................. 85 6.2 Basic Conventions ............................................................................................ 86 6.2.1 Order of Authors .................................................................................. 86 6.2.2 Submission Agreement ......................................................................... 87 6.2.3 Publication Impact ............................................................................... 87 6.3 Common Problems ........................................................................................... 88 6.3.1 Expectations ......................................................................................... 88 6.3.2 Gift, Guest, and Ghost Authorship ...................................................... 89 6.3.3 Financial Support ................................................................................. 91 6.3.4 Quid Pro Quo ...................................................................................... 91 6.3.5 Students and Technicians ..................................................................... 92 6.4 Current Standards and Emerging Ideas ........................................................... 93 6.4.1 International Committee of Medical Journal Editors Standards ................................................................................. 93 6.4.2 Author Notification .............................................................................. 94 6.4.3 Specifying Contributions ...................................................................... 95 6.4.4 Quantifying Contributions ................................................................... 96 6.5 Our Approach .................................................................................................. 96 6.5.1 Authorship Criteria .............................................................................. 97 6.5.2 Predraft Group Meeting ....................................................................... 97 6.5.3 Final Review and Approval .................................................................. 97 6.5.4 Default Position for Abstracts .............................................................. 98 7. Recordkeeping ................................................................................................. 99 7.1 The Slutsky Case Revisited .............................................................................. 99 7.2 Why Keep Records? ....................................................................................... 102 7.2.1 Medical Records ................................................................................. 103 7.2.2 Industry Research Records ................................................................. 104 7.2.3 Academic Research Records ............................................................... 104 xii STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 7.3 Electronic Data ............................................................................................... 105 7.3.1 Date-Stamps, Time-Stamps, and Backup Systems ............................ 106 7.3.2 Images ................................................................................................ 106 7.3.3 Software Development ....................................................................... 106 7.4 Fraud: Fabrication and Falsification ............................................................... 107 7.4.1 Retaining or Discarding Data ............................................................. 108 7.4.2 Image Manipulation ........................................................................... 109 7.4.3 Statistical and Image Forensics ........................................................... 110 8. ownership of Ideas, Data, and Publications ..................................................... 111 8.1 Data and Resource Sharing ............................................................................ 112 8.1.1 Research Data ..................................................................................... 112 8.1.2 Model Organisms ............................................................................... 113 8.1.3 Other Research Products .................................................................... 113 8.2 Copyright ....................................................................................................... 114 8.2.1 Online Publishing .............................................................................. 115 8.2.2 Public Access to NIH-Funded Journal Articles ................................. 115 8.3 Patents ............................................................................................................ 118 8.3.1 Patents and Publicly Funded Research ............................................... 119 8.3.2 Patents and Publication ...................................................................... 120 8.4 Plagiarism ....................................................................................................... 121 8.4.1 Attribution Within a Research Group ............................................... 122 8.4.2 Citation .............................................................................................. 123 8.5 Peer Review .................................................................................................... 124 8.5.1 Archival Journal Articles .................................................................... 124 8.5.2 Grants ................................................................................................. 126 References .............................................................................................................. 129 Author Biography .................................................................................................... 131 Index ...................................................................................................................... 133 1 C H A P T E R 1 motivation The first part of this book is about communicating well, which is just as important to success in the workplace in science and engineering as it is in professions such as business, law, politics, and theol- ogy. Although there are useful guidelines for communicating well, there are no unique formulas. In- deed, individual differences can bring a freshness and vitality to a field; individual personalities can generate excitement and interest. Each person should thus develop a style that is most effective for him or her. The second part of this book addresses the need for professional responsibility, that is, integrity in the workplace. It has been correctly said that it takes a lifetime to establish a good reputation, but only a moment to destroy it. There is, therefore, a need for consistent and concerted atten- tion to ethical conduct and the appropriate communication of research findings. This, too, requires thoughtful, personal commitment — it is more than simply trying to follow the rules, for rules may change, it is doing the right things for the right reasons. Consequently, this book is different from most textbooks in science and engineering. We seek to cause one to stop, contemplate, and adopt a personal course of action. In some sections, therefore, the style is more like a workbook. Indeed, as a point of departure, let us consider the following. Exercise 1.1 List five of the most important inventions of all time. 1. 2. 3. 4. 5. Exercise 1.2 of all time. 1. 2. 3. 4. 5. List five of the most important scientists, mathematicians, or natural philosophers 2 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg If you are like many of our previous students, you listed among your selections of the most impor- tant inventions of all time the airplane, automobile, computer, electric motor, refrigeration, steam engine, telephone, and so forth. Each of these inventions is truly great, and so too many others, but did you consider the invention of the printing press with movable type? If not, you are not alone. Yet, take a few minutes and imagine what the world would be like without books or scientific periodicals. Indeed, think about how the development of science, medicine, and engineering may have differed over the past five centuries had the printing press not been invented. For this reason, Time-Life magazine selected the printing press as the most important invention of the second millennium. The rapid growth of printing with movable type reveals its overall importance. Invention of movable type is generally attributed to Johann Gutenberg (ca. 1397–1468), and the first book so printed is the famous Gutenberg Bible, which was completed in 1454/1455 at Mainz. By 1480, 111 towns throughout Europe boasted printing presses, and by 1500, this number grew to more than 238 (Boorstin, 1983, p. 270). In addition to the printing of the Bible, which had a significant influ- ence on the development of science and Western culture (Dillenberger, 1961; van Doren, 1991), these presses allowed the printing and widespread distribution of classics by Aristotle, Cicero, Euclid, Plutarch, Ptolemy, and many others. It is thus thought that Gutenberg’s invention played a singularly important role in the European Renaissance. Recalling Exercise 1.2, many scientists, mathematicians, and philosophers deserve recogni- tion as great. Among them, you may have listed Socrates, Plato, Aristotle, Archimedes, Copernicus, Galileo, Newton, Euler, Lavoisier, Gauss, Darwin, Maxwell, Planck, Einstein, or Pauling. How is it that we know about these great investigators? How is it that we know what they accomplished? Consider Sir Isaac Newton (1642–1727), for example, who is universally listed as one of the greatest natural philosophers of all time. Many know of Newton based on comments in courses on physics related to his law of gravitation, his laws of motion, or perhaps his experiment with a glass prism that revealed a spectrum of colors in sunlight. Fewer people know about Newton through in depth study, for example, by reading books such as The Life of Isaac Newton by Westfall (1993). Still fewer yet know of Newton because they have read his great works, his Principia of 1687 or his Opticks of 1704. Regardless of the particular path, we all know of Newton primarily through the written word, not oral tradition and certainly not first-hand interaction. When reading about Newton, it is interesting to learn that he abhorred criticism of any kind and, in particular, interpersonal conflicts. Indeed, it appears that he was so concerned about criti- cism, especially from R. Hooke (1635–1703), then secretary of the Royal Society of London, that for many years he had little interest in publishing his greatest ideas. Apparently, the Principia was published only because of the persistent encouragement and personal financial sacrifice by Edmund Halley (1656–1742). This is remarkable! Similarly, it seems that Newton withheld publication of his Opticks until just after the death of Hooke. What if Newton had died first? Can we imagine moTIvATIoN 3 how the development of science may have differed had Newton not revealed his brilliant thoughts through these two books? Likewise, it is interesting to contemplate the development of Western society, which de- pended so strongly on Greek thought, had it not been for Plato (ca. 427–347 bc). It seems that Plato’s mentor, the great Socrates, was content to lecture or discuss rather than to write or dictate. Although it is not clear how much of Plato’s writings truly reflect Socrates, the importance of works such as The Republic is without question. The written word and its widespread distribution has im- pacted the world like few other things — it is fundamental to communication among scientists and engineers as well as the general public. Communication is defined as follows: To make known; impart. To transmit; have an interchange, as of ideas. To express oneself in such a way that one is readily and clearly understood. American Heritage Dictionary Whether to have a long-lasting impact on human history or simply to contribute to success in the workplace, communicating well is a vitally important skill for the scientist or engineer. Indeed, not only must one communicate well with colleagues or a technical boss, there is often a need to com- municate with diverse scientists, engineers, clinicians, venture capitalists, or the general public. For example, the National Institutes of Health (NIH) is currently promoting the importance of “team science” in biomedical research, which depends strongly on effective communication among indi- viduals having diverse backgrounds, and many universities in the United States are promoting the importance of translational research, which requires interactions among clinicians, scientists, engi- neers, and those in business. Hence, we cannot overemphasize the importance of effective written and oral communication in research and development. Because our focus is on technical communication, note that March 6, 1665, marks a begin- ning of the scientific periodical, based on the proceedings of the Royal Society of London entitled Philosophical Transactions. In the preface to the first issue, Henry Oldenburg (ca. 1617–1677) wrote (see Boorstin, 1983, p. 393): Whereas there is nothing more necessary for promoting the improvement of philo- sophical Matters, than the communicating of such, . . . ; It is therefore thought fit to employ the Press, as the most proper way to gratifie those, whose engagement in such Studies, and delight in the advancement of Learning and profitable Discoveries, doth entitle them to the knowledge of what this Kingdom, or other parts of the World, so, 4 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg from time to time afford. . . . All for the Glory of God, the Honor and Advantage of these Kingdoms, and the Universal Good of Mankind. A careful editor would likely revise this Preface in the interest of conciseness and clarity, yet the message would remain apparent and the motivation to improve our communication skills certain. Indeed, from its beginning, the Royal Society of London sought clear communication in both writ- ten proceedings and oral presentations, not an “Artifice of Words.” We are well advised to pursue the same today. In conclusion, recall from the Preface that a good way to learn to write well is to read widely. The student having an interest in engineering, mathematics, medicine, philosophy, or science can learn much from the many books on the historical development of these fields. See Shamos (1959), for example, who provides brief background information on great physicists from Galileo to Ein- stein and includes excerpts from their original publications. Lightman (2005) provides a similar resource for scientists of the 20th century, and Clendening (1960) reprints portions of the early great publications in medicine. Other books of interest include Bell (1986), Mason (1962), Motz and Weaver (1989), Tarnas (1991), and van Doren (1991). It is interesting to conclude, consistent with aforementioned comments by Boorstin (1983), that Shamos (1959) observed: “The exchange of knowledge, facilitated by the publication of scientific journals, became — and remains — one of the most significant factors in the growth of physical science.” Write and submit a three-page (double-spaced, 1-inch margins, 12-point font) es- Exercise 1.3 say on the role of printed books and scientific periodicals during the Age of Enlightenment. Write and submit a three-page (double-spaced, 1-inch margins, 12-point font) es- Exercise 1.4 say on the development of the Royal Society of London and its role in the advancement of science. Write and submit a three-page (double-spaced, 1-inch margins, 12-point font) Exercise 1.5 report on the origins of the university and how it differed from the scientific academies of the 17th and 18th centuries. • • • • 5 C H A P T E R 2 Writing Well Vigorous writing is concise. A sentence should contain no unnecessary words, a para- graph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subject only in out- line, but that every word tell. W. Strunk Jr. and E.B. White, (1979, p. xiv) 2.1 ovERAll APPRoACH Two of the most difficult aspects of writing are “getting started” and “finishing well.” In other words, once we truly get started, it is usually easy to continue our line of thinking and to produce a first draft. Revising and polishing the first draft often takes longer than the initial writing, yet this is time well spent. Consider, therefore, some general guidelines for writing well, including a simple five-step recipe for completing a technical document: 1. 2. 3. 4. 5. Outline in detail. Write freely. Edit critically. Read out loud. Have a colleague proofread. Although these steps may seem obvious, even trivial, they serve as important reminders and aid greatly in the composition of each new work no matter the level of one’s experience. 2.1.1 outline Most writers agree that it is useful to begin with a detailed outline. Such an outline should contain the major headings that guide the flow of the work, but perhaps more importantly, it should also 6 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg contain subheadings with bullets that highlight and order the major points within each section.1 Each document is different, thus we should not feel compelled to force our presentation to fit within the confines of a particular outline. Nonetheless, most technical works adhere to the following basic outlines: The technical proposal Project summary Specific aims Background and significance Preliminary results Research plan References The technical paper or report Abstract Introduction Methods Results Discussion References The M.S. thesis or Ph.D. dissertation2 Abstract Introduction Background Methods Results Discussion Conclusions and recommendations • • • • • • • • • • • • • • • • • • • 1 Some encourage full sentences rather than bullets to document the main ideas in each subsection or paragraph, sentences that may later be used directly in the document. This, however, is a matter of personal style. 2 Many European dissertations are very different. They consist of a sequence of individual chapters, each similar to a technical paper, all of which are tied together via short introductory and concluding chapters. • • References Appendices WRITINg WEll 7 Because of their importance, we discuss these different forms of technical communication in detail in Chapters 3 and 4. Here, we simply emphasize that a basic outline is the first step toward success- ful writing; it organizes the flow of the presentation and reminds us to address particularly impor- tant issues. Additional bulleting within each subsection further directs the writing. Indeed, with the use of word processors, one may easily use the final outline as a beginning document. In summary, as in any activity, we increase our chances of “reaching the destination” when we have a map or detailed instructions to show the way. Note, therefore, that an outline will tend to be most useful and focused when it is constructed against the background of two questions (Gibaldi, 1995): What is the overall goal that you wish to achieve with the document? Who is the intended audience? Toward this end, it is useful to critique the final outline with regard to both consistency and con- ciseness. For example, do points made in the introduction set up well the key points made in the discussion? Moreover, we tend to allow space in our outline for all of the information that we have collected during our research; we should, however, delete information that unnecessarily duplicates other documents or simply is irrelevant or unnecessary. Once done, it is then time to begin the actual writing. 2.1.2 Write freely One of the biggest impediments to writing efficiently and effectively is untimely self-criticism. How many of us have labored over that first sentence or first paragraph, rewriting and editing to the point of fatigue or frustration? Such editing is essential, but it is productive only if addressed at the right time and in the right way. By writing freely, we mean the unencumbered recording of a logical thought process. Indeed, it is often useful to disable the spell- and grammar-checking capabilities of word processors during the initial writing, for they contribute to the distractions of worrying about the initial spelling of words, ordering of phrases, and even punctuation. These and similar issues are addressed easily once we complete the initial draft. Indeed, we likewise should not initially worry about emphasizing active voice, ensuring sufficient variety in our word choice, focusing on concise- ness, and so forth. Rather, at this early stage of composition, the most important thing is to get the major ideas onto paper (or the screen) and organized roughly in the right order. 8 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 2.1.3 Edit Critically Once the first draft is finished, it is usually best (if time permits) to put it aside for at least a few days before beginning to edit critically. The reason for this is that we often see “what should be there” rather than “what is there” when we proofread our documents. Most of the remainder of this chapter addresses specific aspects of editing critically, which typically includes adding, deleting, and rearranging text. The fundamental components of any technical document are sentences and paragraphs. A sentence is a grammatical unit typically consisting of a subject and a predicate (which tells something about the subject). A simple example is — I am. R. Descartes (1596–1650) expanded this to read — I think, therefore I am. Clearly, important sentences need not be complex. A paragraph is a gram- matical unit typically consisting of multiple sentences that together express a complete thought. Many suggest that the lead sentence of each paragraph should introduce the main idea of that para- graph and the final sentence of each paragraph should summarize the main thought. This simple guideline helps to minimize unnecessary generality, that is, it helps to keep the writer focused. A stepwise approach to editing critically exploits these two fundamental units of compo- sition. For example, many suggest that the first step should consist of reading the first and last paragraphs of the document to ensure a consistent introduction and conclusion. The second step should consist of reading the first sentence of each successive paragraph to ensure that the work flows logically. Indeed, some go further to suggest that one should be able to glean the salient points of a document by reading only the first sentence of each paragraph. Although we do not wish to suggest such a dogmatic approach, casual guidance can certainly come from such an exercise. The third step of critical editing is a careful evaluation sentence by sentence. In other words, while read- ing each sentence within context, we should ask if it is necessary, if it is consistent in tense, and if it as concise and clear as possible. This brings us to the fourth and last step of critical editing, an evaluation word by word. We should ask, for example, if we have avoided the use of jargon as well as redundant or unnecessary words and if the intended meaning of each word actually reflects its definition. Word choice is critical. From a pragmatic perspective, we can simultaneously evaluate sentence by sentence and word by word. As noted previously, the importance of critical editing cannot be overemphasized, hence we return to this issue in detail in Sections 2.2 to 2.8. Here, however, let us finish our discussion of an overall approach to writing well. After we have outlined our work, written freely, and edited care- fully, our next step should be to read the document out loud. 2.1.4 Read out loud Although this step may seem trivial or perhaps uncomfortable, it is amazing how sensitive the ear is to effective writing — different tenses, logical sequencing, unintentional rhymes, the overuse of certain words, and so forth. We strongly recommend, therefore, that one read the document out loud before going to the final step, asking a colleague to provide constructive criticism. WRITINg WEll 9 2.1.5 Have a Colleague Proofread Technical advances in science and engineering have been spectacular, and continued promises of important discoveries make these professions intellectually attractive. Because of the trend toward multidisciplinary teams, one of the most enjoyable aspects of these professions is the opportunity to work with colleagues from many allied fields. Consequently, there is not only a need to write concisely, but also to write clearly. Although it is common to have colleagues from these allied fields coauthor many of our works, it is essential to have others proofread our work. That is, even though we may know best what needs to be said, the definition of an effective paper, proposal, report, or book is one that is understood and valued by others — this is the goal of effective communication. Classmates and colleagues tend to be busy, thus we sometimes hesitate to ask them to proof- read our work. Yet, they too would appreciate having someone provide feedback on their work and consequently will many times agree to do so for you. Consider establishing reciprocal agreements, whereby you exchange documents to be proofread. This will not only help the author by provid- ing specific feedback, chances are it will help the reader both directly and indirectly. One not only learns by reading, oftentimes going through a document carefully and looking for ways to improve its clarity and conciseness teaches us much more. This is similar to the adage, “the best way to learn something is to teach it to others.” If you ask someone to proofread your work, make sure to tell them that you want them to be “brutally honest” rather than overly concerned about being critical. Moreover, once you receive the feedback, be careful to avoid the two most common responses: either to ignore the comments because you “know” that you were correct in the first place or to incorporate the suggested changes without questioning. These two responses are equally inappropriate. If a colleague questions the way something is stated, particularly if based on deep knowledge of the technical area, this at least sug- gests that the text could be written more clearly. In other words, if they do not understand what you are trying to say, chances are others will likewise not understand. Consider revising the text along the lines they suggest or in another way; the important thing is to give the suggested revision careful consideration. Conversely, incorporating suggested changes without questioning is dangerous. The primary goal is to communicate most effectively that which you are trying to say. If your col- league’s suggestion does that, great; if not, work to improve clarity and conciseness and perhaps have your colleague read it again. Often, it is helpful to ask them what was confusing or what they thought you meant to say. Sometimes an explanation reveals how best to say it in the written word. Finally, remember that it is good to keep marked manuscripts to evaluate them for possible consistent errors or patterns. In this way, we can become proactive in avoiding problems, whether 10 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg it is an overuse of passive voice or an inappropriate use of modifiers. Being conscious of potential errors is the first step to avoiding them. Recover from your files at least three documents you have written and that were Exercise 2.1 evaluated/graded on writing style. Compile a list of errors that occurred repeatedly and write brief examples of how to correct these problems. Read a journal paper in your area of expertise and record at least 10 sentences that Exercise 2.2 could be improved for conciseness or clarity. Next, reread the paper out loud and record another five sentences that you could improve; note the types of concerns that are identified more easily when heard. Finally, suggest possible improvements for each of the 15 sentences. 2.2 REmovINg REDuNDANCIES AND uNNECESSARy WoRDS Now that we have a feel for an overall approach to writing well, let us begin to address specific aspects of “critical editing.” Recall that effective technical writing is first and foremost clear and con- cise, which for obvious reasons is better written “Recall that effective technical writing is clear and concise.” One way to ensure such characteristics in our writing is to remove redundancies and unneces- sary words, sentence by sentence. Let us consider a few specific examples below (note: the original version is on the left and the corrected version is on the right, hence it is best to cover the right side first and consider how you might improve each example before looking at the suggested change): The cells were cultured for a period of three weeks. The temperature of the chamber remained between 35 and 39°C. The cells were cultured for three weeks. The chamber remained between 35 and 39°C. The associated mechanisms are not known at this time. The associated mechanisms are not known. (or, . . .remain unknown.) The experiments were performed over a period of 10 hours. The experiments were performed for 10 hours. The new transducer is much smaller in size, which simplifies the design. The new transducer is smaller, which simplifies the design. The temperature increased at a rate of 3°/min. The temperature increased at 3°/min. The signal is lost below a threshold level of 10 Hz. The signal is lost below a threshold of 10 Hz. WRITINg WEll 11 This thesis reports work done during the period from January 1998 to December 2000. This thesis reports work accomplished from January 1998 to December 2000. The algorithm searches outward from the center location. The algorithm searches outward from the center. The A/D converter allows a maximum of eight input signals. The range of the output signal was from a minimum of 2 to a maximum of 5 volts. The A/D converter allows eight input signals. The output signal ranged from 2 to 5 volts. The results of our experiments support the established theory. Our experiments support the established theory. Turn the potentiometer in the clockwise direction to increase the gain. Turn the potentiometer clockwise to increase the gain. Use the lenses that are convex in shape. Use lenses that are convex. The problem should first be formulated and then solved. The problem should be formulated, then solved. The amount of noise will be excessive if the signal is not filtered. The noise will be excessive if the signal is not filtered. There is no known analytical solution to this equation at this time. No analytical solution exists for this equation. The biopsy should be redesigned in the future to minimize the amount of tissue needed. The biopsy should be redesigned to minimize the tissue needed. The reason for this difference can be attributed to. . . This difference can be attributed to. . . Remember to remove the specimen during the calibration procedure. Remember to remove the specimen during calibration (or, when calibrating). There is a growing body of evidence that the hypothesis is indeed true. There is growing evidence that the hypothesis is true. After one test, there should be a sufficient quantity of culture media for a second test. After one test, there should be sufficient culture media for a second test. 12 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg In the first example, the use of the word weeks implies a period or duration, which is therefore not needed. In the second example, the use of the unit °C specifies that the numerical value refers to a temperature, which thereby becomes redundant. Similarly, in the third example, we see that if something is not known, it is implied that it is not known at this time, which is thereby unneces- sary. In hindsight, the other examples are likewise clear. Indeed, because these specific examples highlight a redundancy or unnecessary words, they may seem so obvious that we would be surprised if we ever wrote such sentences. Upon close examination of our previous works, however, we often find similar or even more flagrant examples. It is for this reason that we must be conditioned to look for redundancies and unnecessary words, which is often best learned via examples; see Brogan (1973) for additional examples. Find a technical research paper that you have written and scan it specifically for ex- Exercise 2.3 amples of redundancies or unnecessary words. Record five examples below with possible revisions. If we read a number of published technical papers for style, we quickly realize that we could make many commonly used phrases more concise or even omit them without a loss of clarity. For example, how many times have we read the phrase “The purpose of this paper is to present. . . ,” which we could write more concisely as “This paper presents. . . .” Consider the following phrases (left side) that occur frequently but can often be rendered better or omitted (right side) as follows (cf. Brogan, 1973; Valiela, 2001): WRITINg WEll 13 is used to develop is dependent on develops depends on We propose to use the combination of We propose to combine results in the simplification of simplifies It is interesting to note that Note that (or, omit) due to the fact that in order to in spite of the fact that as a result of appears to be experienced a peak at in the event that was found to be a number of may be a mechanism responsible for It is well-known that because to despite Omit seems peaked at if was many (or, various) may cause Omit for a long period of time for a long period is described in detail in in the absence of is detailed in without It is not uncommon that It is common that The finding is not inconsistent with The finding is consistent with 14 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Note, in particular, that the last two entries in this table emphasize that double negatives should be avoided. Moreover, see Appendix 2 in Day and Gastel (2006) for an expanded list of words and expressions to avoid. In addition to removing redundancies and unnecessary words, there are many opportunities to introduce conciseness via word choice and sentence structure. For example, consider the following examples: Because the structure is assumed to remain circular, . . . This will enable us to develop a better understanding of. . . This finding is the opposite of that reported by. . . Assuming the structure remains circular, . . . This will enable us to understand better. . . This finding is opposite that reported by. . . The model is capable of describing. . . The model can describe. . . Table 1 is a list of all findings. . . Table 1 lists all findings. . . The next section is a brief description of the experimental methods. The next section briefly describes the experimental methods. The faculty advisor was the supervisor of both the undergraduate and the graduate students. The faculty advisor supervised both the undergraduate and the graduate students. The temperature readings will be dependent upon the contact stress. . . The temperature readings will depend upon the contact stress. . . Our laboratory technician also serves as the budget manager. Our laboratory technician also manages the budgets. The following example is an illustration of the basic concepts of. . . The following example illustrates the basic concepts of. . . Before continuing, note that some of the suggested changes in the right-hand column assume a particular style not accepted by all technical writers. Some suggest that a table cannot list, a figure cannot show, a model cannot describe, a paper cannot present, and so forth. That is, some argue that only people can list, show, describe, or present; results are simply listed in a table, shown in a figure, WRITINg WEll 15 described by a model, or presented in a paper. Because this is a matter of style, one must decide what approach to take, then be consistent. As we shall see in Chapters 3 and 4, removing redundancies and unnecessary words not only results in writing that is clearer and more concise, it enables us to meet stringent limitations on words or pages in published works or proposals. Consider two instructive exercises: Write a three-page (double-spaced, 1-inch margins, 12-point font) biography of a Exercise 2.4 leading scientist. Work hard to write clearly and concisely. Two days after finishing your essay, edit it further to reduce it to a single page without losing significant content. You will be surprised how easy and yet how powerful this exercise is. Finally, note that a one-page “white paper” is often all that is used to render important decisions in many professions; thus, it is important be able to write an effective short report. Use the “Word Count” tool in your word processor to determine the number of Exercise 2.5 words in a short document (e.g., abstract) that you recently composed. Once done, set out to reduce the length of the document by 50% without compromising the content. ACTIvE voICE, fIRST PERSoN, AND DIffERENT TENSES 2.3 2.3.1 voice In active voice, the subject of the sentence performs the action indicated by the verb. Conversely, in passive voice, the subject of the sentence receives the action of the verb. The simple example below distinguishes between passive and active voice: Passive voice: The data were analyzed by him using an ANOVA.3 Active voice: He analyzed the data using an ANOVA. Although passive voice is acceptable, indeed sometimes more appropriate, most writers agree to prefer active voice, for it engenders conciseness and directness. In the example given, we see that seven words suffice rather than nine — this reduction represents a savings of approximately 20%. Given a 10-page paper, a 20% reduction in the number of words would yield an eight-page paper or else would provide an extra two pages to include more information; such savings can be significant. Moreover, comparing the two sentences in this example reveals the increased directness of the active voice, which promotes clarity and conciseness. Albeit preferred, active voice is less common than passive voice in scientific writing. A simple change in the preceding example illustrates one reason for this: 3 ANOVA is a common acronym for analysis of variance in statistics. 16 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Passive voice: The data were analyzed using an ANOVA. Active voice: We analyzed the data using an ANOVA. In this case, each sentence contains seven words, thus the active voice does not increase conciseness. Moreover, the context can imply the “we” in the case of the passive voice, thus there need not be a difference in clarity (e.g., who did what). In many cases, authors prefer not to write in the first or the third person and revert to passive voice. The issue of person is addressed in the next section (or should we say, we address the issue of person in the next section). Here, however, consider examples of passive voice (left) and easy ways of changing them to active voice (right). First, changes primar- ily in verb form can be effective: The specimen is connected to the device through a custom cannula. The specimen connects to the device through a custom cannula. The output signal is fed into a signal conditioner. The output signal feeds into a signal conditioner. In the next section, the underlying theory is given. The next section gives the underlying theory. In our current research, attention is directed to finding the mechanism. Our current research directs attention to finding the mechanism. The theory is dependent on five basic postulates. The theory depends on five basic postulates. X was used to create a surface-confined computational mesh. X created a surface-confined computational mesh. Increasing evidence has implicated the importance of. . . Increasing evidence implicates the importance of. . . Three different sectioning planes were used to form. . . Three different sectioning planes formed. . . Experimental noise is increased when unshielded cables are used. Experimental noise increases with the use of unshielded cables. A reader’s attention is increased by the liberal use of figures and schematic drawings. A reader’s attention increases with the liberal use of figures and schematic drawings. Second, changing the subject, which often necessitates changing the order of the words in the sen- tence, is often equally effective: WRITINg WEll 17 The specimen is connected to the device through a custom cannula. A custom cannula connects the specimen to the device. The results of the study are listed in Table 1. Table 1 lists the results of the study. The control is simplified by using commercial software. Commercial software simplifies the control. An improved result is obtained by refining the computational grid. A refined computational grid improves the result. The proper use of the equipment is described in Chapter 2 of the manual. Chapter 2 of the manual describes the proper use of the equipment. Ensure that all specimens are tested under the same conditions. Use the same conditions to test all specimens. The temperature is measured by a thermocouple. A thermocouple measures the temperature. These empirical findings are used as inputs into the theoretical model. The theoretical model uses the empirical find- ings as inputs. A detailed derivation of this equation is given in the appendix. The appendix details the derivation of this equation. The culture system is optimized by maintain- ing body temperature. Maintaining body temperature optimizes the culture system. A common excuse for (over)using passive voice is that it is natural because we often discuss past events, as, for example, “it was reported that” or “it was found that.” Tense need not be the deciding factor, however, as revealed by the following simple example: The pressure was measured by a mercury manometer. The pressure is measured by a mercury manometer. A mercury manometer measured the pressure. A mercury manometer measures the pressure. 18 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Finally, as noted previously, writing in the first or third person often allows us to avoid passive voice. Whereas the next section discusses the issue of person, as appropriate in scientific writing, consider the following, which revisit previous examples with alternate changes: The specimen is connected to the device through a custom cannula. We connected the specimen to the device us- ing a custom cannula. The results of the study are listed in Table 1. We list the results of the study in Table 1. These empirical findings are used as inputs into the theoretical model. We used the empirical findings as inputs into our theoretical model. The temperature is measured by a thermocouple. We measured the temperature using a thermocouple. A detailed derivation of this equation is given in the Appendix. I derive this equation in detail in the Appendix. Experiments were performed in triplicate for each set of. . . We performed three experiments for each set of. . . The culture system is optimized by maintain- ing body temperature. We optimized the culture system by maintain- ing body temperature. In summary, we do not have to avoid passive voice at all costs; indeed, passive voice is preferred in many cases. We also do not need to invoke first person to avoid passive voice. Nevertheless, our general guideline is to prefer active voice when editing critically. Exercise 2.6 examples of passive voice. Record five examples below with possible revisions. Select a journal paper in your field that interests you and scan it specifically for WRITINg WEll 19 2.3.2 Person Students of the history of science know that scientific writing used to be much more personal. As a simple example, consider the following excerpt from one of the works of W. Harvey (1578–1657) on the motion of the heart, (Clendening, 1960, p. 159): Besides the motions already spoken of, we have still to consider those that appertain to the auricles. Casper Bauhin and John Riolan, most learned men and skillful anatomists, inform us from their observations, that if we carefully watch the movements of the heart in the vivisection of an animal, we shall perceive four motions distinct in time and in place, two of which are proper to the auricles, two to the ventricles. With all deference to authority I say, that there are four motions distinct in point of place, but not of time. . . . If written today, we may well have read (with little other editing): Besides the motions already noted, there is a need to consider those concerning the auricles. Bauhin (16xx) and Riolan (16xx) report that careful monitoring of the heart in an open-chest animal reveals four motions distinct in time and place, two of the auricles and two of the ventricles. Nevertheless, it is suggested here that these four motions are distinct in place but not time. . . . Why has scientific writing become so impersonal today? Certainly, there has been an appropriate move away from the verbose, from patronizing prose, and from self-aggrandizement. Nevertheless, science and engineering are personal — they are advanced by people, usually for the good of people — and it is not only acceptable, in many cases it is more honest, direct, and effective to write in first person. For example, in Chapter 4 on writing research proposals, we will see that an important part of the NIH-R01 grant is a section called Preliminary Results. Imagine that you review such a sec- tion and read, “It has recently been shown that . . . (12).” Noting that (12) denotes reference number 12 in the list of references, the reviewer would not know if it was the applicant or another investiga- tor who showed this important finding unless he/she looked at the reference list. Conversely, there 20 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg would be no ambiguity if the applicant wrote “We recently showed that . . . (12).” In the case of a research proposal, clearly demonstrating one’s previous work may increase tremendously the chances of funding, thus employing first person may be both effective and advantageous. As a reminder that first person can yield effective and memorable prose, recall the following sentences from the seminal paper by James Watson and Francis Crick on the structure of DNA: We wish to suggest a structure for the salt of deoxyribose nucleic acid (D.N.A.). . . . It has not escaped our notice that the specific pairing we have postulated immediately sug- gests a possible copying mechanism for the genetic material. There are three persons in typical grammatical structure: first person refers to the person or persons who are speaking or writing; second person refers to the person or persons spoken or written to; and third person refers to person(s) spoken or written about. For example, consider the common pronouns, singular and plural, in the three persons and three common cases (Vivian and Jackson, 1961): SINgulAR fIRST PERSoN SECoND PERSoN THIRD PERSoN Nominative I Possessive Objective My, Mine Me You Your, Yours You He, She, It His, Hers, Its Him, Her, It PluRAl fIRST PERSoN SECoND PERSoN THIRD PERSoN Nominative We You They Possessive Objective Our, Ours Us Your, Yours Their, Theirs You Them Whereas the words he or him were used generically in the past to denote males or females, modern writers tend to be much more sensitive to issues of gender. Thus, there has been a move to use neutral pronouns. For example, the famous imperative from Star Trek fame, “To boldly go where no man has gone before,” can be written as “To boldly go where no one has gone before.” It is also acceptable to write he/she or him/her when desired, but we should prefer neutral constructions. WRITINg WEll 21 Finally, numerous terms such as department chairman or layman can be written as department chair or layperson to avoid this issue. Albeit largely a matter of style, we suggest that it is acceptable and many times preferable to use a personal style in scientific writing. For example, it is acceptable to write: “Although they were the first to exploit their novel empirical observations by identifying quantitative correlations, we were the first to develop a theoretical basis to explain the observations.” As food for thought, consider the following simple examples as you decide on a particular style: The authors recommend, therefore, that. . . We recommend, therefore, that Hence, it is suggested that. . . Hence, I suggest that. . . It will be seen that. . . You will see that. . . Based on these results, it was decided that. . . Based on these results, we decided that. . . It has been shown previously that. . . We previously showed that. . . One important warning, however, is that when “I” is used, be careful not to give the impres- sion that it serves an egotistical end. 2.3.3 Tense Tense is a property of time; it signifies when events occur or when conditions exist (Vivian and Jackson, 1961). There are six tenses: past, present, future, past perfect, present perfect, and future perfect. The perfect tenses typically involve the use of the words “have” or “had.” Consider the following simple examples: Past: I completed the experiment. Present: I am completing the experiment. Future: I will complete the experiment. Past perfect: I had completed the experiment. Present perfect: I have completed the experiment. Future perfect: I will have completed the experiment. 22 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Two of the key questions in scientific writing are, “What tense should I use when reviewing what others reported previously?” and “What tense should I use when reporting what I did?” Al- though it is of little comfort, the answer to these questions is that there is no set answer. Some authors suggest, however, that if concepts or findings reported in a previous peer- reviewed work remain true, one should refer to them in the present tense. As a simple example, consider Newton’s second law of motion, which was put forth in the 17th century. One could write “As Newton showed in the Principia, force equals mass times acceleration.” Alternatively, one could write “As Newton showed in the Principia, force equaled mass times acceleration.” All should agree that if it is still believed that force equals mass times acceleration, then present tense should be used. A more modern example could be, “Smith et al. (1999) show that . . .” versus “Smith et al. (1999) showed that. . . .” Again, the choice is largely a matter of personal style; the most important thing is to be consistent within a given paper. Most authors agree that we should use past tense when reporting our own new findings, for they have not yet been verified or accepted widely. Hence, when writing the results section of a paper, it is appropriate to use “we measured” and “we found” or similar constructs. INfINITIvES AND moDIfIERS 2.4 2.4.1 Infinitive An infinitive is a verb form, a characteristic sign of which is the word to, for example, “to measure,” “to quantify,” or “to report” (Vivian and Jackson, 1961). A split infinitive occurs when a word or phrase separates the “to” and its complement. A famous split infinitive in recent years comes from the aforementioned quote from Star Trek: “To boldly go where no man has gone before,” which we could rewrite as “to go boldly where no man has gone before.” The issue is how we wish to go, boldly or fearfully. Although it is best not to split infinitives, grammarians are now less dogmatic with regard to this rule. Indeed, a purposefully split infinitive may be preferred in some cases. For example, consider the phrase “to promote exercise vigorously” (Iverson et al., 1998). There could be confusion by some as to whether vigorously relates to promote or exercise, hence writing “to vigorously promote exercise” could be clearer, unless of course the intent was “to promote vigorous exercise.” Strunk and White (1979) also note that the sentence “I cannot bring myself to really like the fellow” is clear, concise, and relaxed. Nevertheless, the general rule should be: Do not split infini- tives unless the sentence is less awkward when doing so. Let us consider a few examples of split infinitives and how to correct them easily. The goal of this project is to better understand. . . The goal of this project is to understand better. . . We plan to quickly initiate the funded study. We plan to initiate the funded study quickly. WRITINg WEll 23 It is difficult to separately control X and Y. . . It is difficult to control X and Y separately. . . . , they failed to correctly diagnose . . . , they failed to diagnose It is bad practice in the laboratory to arbitrarily stop an experiment. It is bad practice in the laboratory to stop an experiment arbitrarily. To effectively study the source of the error, . . . To study the source of the error effectively, . . . The sponsor requested us to, with all possible haste, complete the final report. The sponsor requested us to complete the final report with all possible haste. The last example in this table is a particularly flagrant abuse of the infinitive. Other examples of split infinitives occur when a single “to” serves multiple infinitives. Whereas it is generally acceptable to write, “There is a need to assemble and test the device,” rather than “There is a need to assemble and to test the device,” it is also better to write “There is a need to assemble the device according the sponsor’s specification, then to test it . . .” rather than “There is a need to assemble the device according the sponsor’s specification, then test it. . . .” Finally, note that infinitives can occur in active or passive voice and in past or present tense. In these cases, the infinitives may take different forms, such as: Present active: to tell Present passive: to be told Past active: to have told Past passive: to have been told Hence, that a word or phrase appears between the “to” and its complement need not signal that an infinitive has been split. 2.4.2 modifiers Another mistake common in technical writing is the use of nouns as modifiers. A modifier is a word, phrase, or clause that renders another word or group of words more specific; two common kinds of modifiers are adjectives and adverbs. In contrast, a noun is a person, place, or thing. Perhaps it has been in the spirit of trying to write concisely that nouns have been misused frequently as modi- fiers. In a syndicated column, J.J. Kilpatrick noted a few examples from the New York Times: “their court victory,” which is better written “their victory in court,” and “close-knit classical music world,” which is better written “close-knit world of classical music.” Common examples in the technical literature include “material science” rather than “the science of materials” and “fluid mechanics” 24 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg rather than “the mechanics of fluids.” Yet, such constructions need not be considered problematic, which reminds us that certain cases are acceptable. More flagrant examples of noun modifiers exist in many scientific papers and should be minimized. Tabulated below are a few examples found in recently published works (which we do not cite so as not to criticize particular authors, for many, including us, are equally guilty): The primary extracellular matrix components include. . . The primary components of the extracellular matrix include. . . When tissue temperature reached. . . When the temperature of the tissue reached. . . Force and length data were used to compute stresses. Stresses were computed from data on forces and lengths. An increased wall stiffness of the aorta. . . Minimum residual microfibrillar function. . . An increased stiffness of the wall of the aorta. . . Minimum residual function of the microfibrils. . . Ultrastructural analysis has begun to. . . Analysis of ultrastructure has begun to. . . . . .could detect molecular level changes. . . . . .could detect changes at the molecular level. . . . . .will use gene expression measurements to. . . . . .will use measurements of gene expression to. . . Changes in cell structure and function reveal. . . Changes in the structure and function of cells reveal. . . The resulting surface stress appears. . . . The resulting stress at the surface appears. . . . . .the ability of the cells to move into the wound area. . . . . .the ability of the cells to move into the area of the wound. . . . . .to undergo changes in contractile protein expression. . . . . .to undergo changes in the expression of contractile proteins. . . . . .organ development becomes highly sensitive to. . . . . . .development of the organ becomes highly sensitive to. . . . . .of the neonatal fibroblast. . . . . .of the fibroblast in neonates to. . . WRITINg WEll 25 In contrast to previous tables of examples on redundancies, the “corrected” right-hand side here often resulted in a longer sentence or phrase. Again, it may have been in the interest of concise- ness that nouns have come to be misused (left side). Nevertheless, one is well advised to use nouns properly. Next, consider a few simple suggestions to promote the proper use of appropriate modifiers (adjectives and adverbs). Recall, that adjectives modify nouns, whereas adverbs can modify a verb, an adjective, or another adverb. Adverbs may come before, after, or between the words that they modify. When possible, a sequence of modifiers should be listed according to length or logical order. For example, Berry (1971) suggests that “tired, bored, and exhausted” is written better as “bored, tired, and exhausted” because it is likely that one becomes bored before tired. He likewise suggests that the modifiers “dry, withered, and flaky” should be ordered in the sequence in which they occur: “withered, dry, and flaky.” Finally, note that “a,” “an,” and “the” are called articles. The definite article “the” refers to something or someone in particular. Hence, when we read “A significant finding was…” versus “The significant finding was . . . ,” we see that the former refers to one of many significant find- ings, whereas the latter refers to one finding that was significant. This simple distinction must be respected. Although many modifiers are effective in different forms of writing, their overuse in scientific writing may suggest that one’s results are not quantitative, that they need embellishing. For example, instead of saying that data “are very noisy,” we need only say they “are noisy,” then provide specific measures such as a signal-to-noise ratio to quantify the degree of the noise. Similarly, a numerical method may be “very robust,” but if it is robust, that is all that needs to be said. In other words, the modifier “very” often adds very little (as in this case). Similarly, “quite” is quite unnecessary in most cases, including this one, and although the word “rather” is considered by some to be rather impor- tant, it often is not. A general rule, therefore, is: Do not use modifiers unless the meaning is clarified by doing so. Review a technical paper that you wrote previously and eschew all unnecessary or Exercise 2.7 inappropriate modifiers. If you are somewhat puzzled why you used words such as “somewhat,” take comfort that you are not alone. As examples, record five illustrative sentences below and possible corrections. 26 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg ADDITIoNAl ISSuES of WoRD CHoICE 2.5 The best advice related to word choice is to keep a dictionary within easy reach and to consult it frequently. With regard to the five-step recipe for composition given in Section 2.1, however, we should remember that this should be done during the phase, “edit critically.” Indeed, if you are struggling for just the right word while “writing freely,” it is often best to put an “xx” in the text so that you are reminded to search for an appropriate word later and not interrupt the flow of your thoughts and composition. Here, however, we briefly identify and discuss some words that are often used interchangeably but should not be so used. Consider, for example: Alternative/alternation: An alternative is a choice between two mutually exclusive possibili- ties. An alternation is a successive change from one thing to another and back again. Amount/number: Amount refers to a quantity that is not countable, whereas number is used when it is possible to count. It is thus correct to say “The amount of information available was not sufficient for . . .” or “The data suggest a number of conclusions.” Because/since: Strictly speaking, because refers to a cause–effect relationship and since refers to a past event. It is appropriate to write “Because the results suggested . . .” and “Since the last conference . . .” Between/among: In general, use the word between when considering two things and use the words among or amongst when dealing with more than two things. Can/may: The word can has to do with ability, whereas the word may has to do with having permission. Compare with/compare to: Use compare with when examining or discussing similarities or differences. In general, only use compare to when representing a metaphorical similarity. Complement/compliment: A complement is something that completes or brings to a whole. A compliment is an expression of congratulations or praise. WRITINg WEll 27 Comprise/compose: Comprise means to consist of or to include. Compose means to make up the constituent parts of, to constitute or form. Good examples are “The Union comprises 50 states” and “Fifty states compose (or constitute) the Union.” Continual/continuous: Continual means with occasional interruption, whereas continuous means without interruption. Data/datum: Data are plural, typically representing facts or information. Datum is the sin- gular form of data, often used in the context of a point from which to measure. Due to/because of: Due to means attributable to. Because of relates to a cause or reason for occurring. A helpful hint is that a sentence should not start with due to. Effect/affect: An effect is a noun; it implies a result, something that is caused. Affect is a verb; it brings about a change. To affect is thus to influence or impress. Either/neither: It is correct to write “either A or B” and likewise “neither A nor B,” but we do not use “neither A or B.” Moreover, in each case, these words imply only two options, hence we cannot say “either A, B, or C.” Essential/important: Essential implies indispensable, fundamental, or absolute. Important merely implies significant or noteworthy. Farther/further: Farther should be used when the context is distance. Further implies some- thing in addition, such as the need for further experiments. Hence, one does not move a fixture further toward the center. Good/well: In most cases, good is used to modify a noun (e.g., she is a good writer), whereas well is used to modify a verb (e.g., she writes well). However/nevertheless: Strunk and White (1979) suggest that we should avoid beginning a sentence with the word however when the meaning is nevertheless or yet. This is easily corrected via replacement with these more acceptable beginning words or by moving the however to the middle or end of the sentence. When used at the beginning of a sentence, however should be thought of as “in whatever way” or “to whatever extent.” A good example is given by Strunk and White, (1979, p. 49): “However discouraging the prospect, he never lost heart.” In contrast, it would be better to write “Nevertheless, he never lost heart despite the discouraging prospects” rather than to write “However, he never lost heart despite the discouraging prospects.” Imply/infer: Imply means to suggest or indicate by logical necessity, whereas infer means to deduce based on available evidence. Precede/proceed: Precede means to come before in time, to occur prior to. Proceed means to go forward, especially after an interruption, or to move on in an orderly fashion. Principal/principle: A researcher may be the principal investigator on the project but not the principle investigator. One may use a scientific principle but not a scientific principal. 28 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Another usage that is often confused is that the solution to an eigenvalue problem yields a principal value and in mechanics one may compute a principal stress or strain. Shall/will: It is suggested by some that shall should be used for future expectations in first person and will should be used in second and third person. This distinction between shall and will occurs only in formal writing, however, and the word will often suffices. A good example is that will is appropriate in grant proposals, for example, “We will test the hy- pothesis that. . . .” That/which: In general, use that to lead into a defining or essential clause and use which to lead into an inessential or nonrestrictive clause. Kilpatrick (1984) suggests an easy way to decide usage in most cases: use which whenever the clause is set apart by commas and use that otherwise. The key point, however, is the word that is used with essential clauses. For example, note the difference between the following sentences. “The transducer that is broken is on the shelf.” “The transducer, which is broken, is on the self.” In the first case, only the transducer that is broken is on the shelf. In the second case, the transducer is on the shelf and it happens to be broken. That/who: That refers to things and who refers to people. While/whereas: Strictly speaking, while should be used to convey a sense of time, for ex- ample, “The computer acquired data while the device subjected the cells to increasing me- chanical loads.” Nonetheless, many accept while as a substitute for although. In contrast, whereas means “it being the fact that” or “inasmuch as.” Next, consider a few words that are useful in technical writing but sometimes misused. Aforementioned: This word is an adjective; it must be combined with a previously used noun. For example, it is correct to write “The aforementioned finding suggests. . . ,” but it is incorrect to write, “As aforementioned, . . . .” And/or: This is a construction used by some, but often best avoided. Use either the word and or the word or as appropriate. Correlate: To put into a complementary, parallel, or reciprocal relationship, not implying causality. Dilemma: Either a situation that requires one to choose between two equally viable alterna- tives or a predicament that seemingly defies a satisfactory solution. Former: The first mentioned of two things. Latter: Like former, this word implies two choices. If one has a list of three or more items, then to refer to the last one in the list, simply say “the last one,” not “the latter one.” Per: “Pursuant to” This: For clarity, follow the word this with a noun. For example, do not write, “This is to be expected,” but rather write, “This nonlinearity is to be expected” or “This finding is to be expected.” WRITINg WEll 29 Finally, some words have specific meanings in science and mathematics even though they are often used loosely in everyday speech. Because our interest is scientific writing, however, we must respect the specific meanings. Three prime examples of such words are significant, necessary, and sufficient. It would be natural, for example, to write: “The response of Group A differed significantly from that of Group B.” Yet, we must ask whether this is what we really mean. The word significant in science usually carries a statistical meaning, that is, it usually implies that based on a standard statistical test, there is a significant difference between two metrics (e.g., as indicated by a p < 0.05 associated with a specific statistical analysis). If such a test was performed and passed, then we could write our illustrative sen- tence as given; if not, it would be better to use a different word or to delete the modifier altogether. In the absence of a statistical test, it would be better to write: “The response of Group A differed mark- edly from that of Group B” or simply “The response of Group A differed from that of Group B.” The words necessary and sufficient similarly have precise meaning in mathematics and they are often used together. In this context, necessary means required and sufficient means adequate. For example, a neces- sary and sufficient condition for a solution to hold is much stronger than a sufficient condition alone. In concluding this section, it is interesting to consider a comment ascribed to the famous ancient philosopher Socrates: The wise man knows that he knows not; the fool knows not that he knows not. Similarly, consider a comment by the famous modern philosopher Bertrand Russell: Although this may seem a paradox, all exact science is dominated by the idea of approxi- mation….When a man tells you he knows the exact truth about anything, you are safe in inferring that he is an inexact man. If we accept that science represents relative, not absolute, truth, then should we be careful not to use strong phrases such as “the data demonstrate” or “the data prove.” For example, should we use phrases such as “the data suggest” or “the data imply.” Similarly, should we avoid saying that some- thing “is,” but instead say that “it appears that.” Here, again, we simply suggest that one should think carefully about this issue, make a purposeful decision within the context of common usage, and be consistent. 30 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Read three technical papers in your field and generate a list of phrases that reflect Exercise 2.8 either a “certainty” or a “possibility” with regard to important findings or conclusions. Write a one- page summary and indicate the approach to communicating such results that you find to be the best. 2.6 PuNCTuATIoN, ABBREvIATIoNS, AND foREIgN lANguAgES 2.6.1 Exploit methods of Punctuation Punctuation is a system of devices or marks (e.g., commas, semicolons, colons, dashes, and paren- theses) that clarify relationships between words and groups of words (Vivian and Jackson, 1961). Aside from the standard use of the period, many writers of science and engineering tend to use commas sparingly and to avoid using semicolons, colons, and dashes. Although we should not over- use such devices, variety in punctuation can be as effective in written communication as variety in tone can be in oral communication. We list here a few rules of punctuation, but we encourage the reader to give particularly careful thought to the effective use of semicolons, dashes, and parenthe- ses. As a start, consider Rules 2 to 4 of Strunk and White (1979): One should use a comma after each entry, except the last, in a list of three or more entries that share a common conjunction such as and or or. For example, we should write “this finding was unexpected, repeatable, and important.” To appreciate this usage, recall from Section 2.1 that the fourth step in writing well is “read out loud.” Doing so here, the ear reveals a difference between “this finding was unexpected, repeatable, and important” (with a verbal pause after each comma) and “this finding was unexpected, repeatable and important.” In other words, the latter case sounds like the finding was “unexpected” as well as “repeatable and important.” When paired, commas are useful devices to set off a nonessential clause, for example, “The transducer, which is broken, is on the shelf.” When used with a conjunction to introduce an indepen- dent clause, the comma should be omitted before the and when the clauses relate closely. In contrast, the comma should almost always precede conjunctions such as but, for, and or. Commas are also useful to set off an introductory phrase, such as “In this paper, we show. . . .” Finally, a comma can be used to separate three or more modifiers, such as in the case of a “randomized, double-blind, clinical trial.” Use the semicolon instead of a period when independent clauses relate closely and it is ef- fective to highlight this similarity. The only exception to this rule is the case of short independent clauses. Consider, therefore, the following examples from Strunk and White (1979): Stevenson’s romances are entertaining. They are full of exciting adventures. Stevenson’s romances are entertaining; they are full of exciting adventures. WRITINg WEll 31 It is nearly half past five. We cannot reach town before dark. It is nearly half past five; we cannot reach town before dark. Man proposes, God disposes. Here today, gone tomorrow. — — The semicolon is also useful to separate main clauses that are joined by conjunctive adverbs such as the following: indeed, yet, however, moreover, or hence. For example, we might write (Iverson et al., 1998): “This consideration is important in any research; yet it is often overlooked, if not denied.” Use the colon before a long in-line quotation (see Section 2.7), to introduce a list, or to sepa- rate independent clauses when the first clause introduces the second one. For example, if we wish to specify the composition of a physiological solution used in an experiment, we might write the following. The specimens were immersed in a physiological solution consisting of, in mM: 116.5 NaCl, 22.5 Na2HCO3, 1.2 NaH2PO4, 2.4 Na2SO4, 4.5 KCl, 1.2 MgCl2, 2.5 CaCl2, and 5.6 dextrose. Like the comma, one can use short dashes (or em dashes) and parentheses to set off nonessential, but clarifying, clauses or entries. The decision to use the em dash or parenthesis (more common) is again a matter of style, with the em dash typically reserved for the longer, sometimes tangential, breaks in thought. Consider the following two cases: Of the many risk factors for coronary artery disease — high cholesterol, high salt intake, cigarette smoking, lack of exercise, diabetes, and hypertension — some can be avoided by simple changes in lifestyle. Many risk factors for coronary artery disease can be controlled by simple changes in lifestyle (e.g., cholesterol, high salt, and smoking). Parenthetical setoffs are also useful in providing supplementary information or identifications. For example, it is common to read: “of the 10 tests, only 5 (50%) were successful,” “the differences were not significant ( p > 0.05),” or “a consistent volume of fluid (10 ml) was injected.” As noted below, it is common to include clarifiers within parenthetical set offs such as (for example, . . .) or (that is, . . .), abbreviations for which are given below. 32 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg The hyphen has many uses as well; see Brogan (1973) for a good discussion of this device. Commonly misunderstood uses are numerical or multiword modifiers. For example, we should write “The diameter of the device is 5 mm,” but we should use the hyphen to write “The 5-mm- diameter device. . . .” We should also use the hyphen to write out numbers such as thirty-seven or two-thirds. Another use of a hyphen is in the pairing of words that, via the natural evolution of grammar, often become single words. A simple example is mechanical transduction, which became mechano-transduction and now is mechanotransduction. Finally, multiword modifiers are often hy- phenated, for example, “the signal-to-noise ratio” or “one-way Student t-test.” Uses such as “pre- and post-surgical” are also common. With regard to numbers, it is common to write out in words those numbers less than 10 (e.g., zero, one, two) but to write out numerically those numbers 10 or greater (e.g., 11, 100, 1000). There are exceptions, however (Blake and Bly, 1993). For example, if data are collected at days 0, 3, 7, and 14, we would not write “at days zero, three, seven, and 14.” In other words, one of the best rules of thumb is consistency and clarity. Moreover, always write large numbers in a way that is most easily understood. For example, the number 30,000,000 may be best understood as 30 million if referring to dollars or population; in contrast, it may be best understood as 3 × 107 if referring to a quantity in physics or chemistry or 30 MPa if referring to stress in mechanics. The example of 30 MPa reminds us to use, when appropriate, accepted prefixes: giga (G), mega (M), kilo (k), milli (m), nano (n), and so forth. The best rule of thumb, therefore, is always write for clarity. Finally, it should be noted that decimal values less than unity should be written with a leading zero, for example, 0.15 rather than .15. Whether one uses decimal values or not, also remember to include only significant digits, that is, information that is reliable. For example, although a calculator or computer may provide an answer of 4.1248432, if only three of the digits are reliable then we should write this as 4.12. Refer to elementary textbooks on physics or chemistry for good discussions on the appropriate use of significant digits. As last reminders, do not use the apostrophe in special cases of decades or centuries, rather one should write 1970s or 1700s. Words such as its and it’s and whose and who’s are often confused. This is simple to remember: it’s and who’s are contractions of “it is” and “who is,” whereas its and whose show possession. Contractions should be avoided in formal writing, however. Finally, it is im- portant to emphasize that most publishers use a single space after a period, not two spaces. Not only is the single space typically more pleasing to the eye, it is also an effective means to reduce the number of pages and hence cost of publication because those extra spaces add up. 2.6.2 Abbreviations Many writers suggest that abbreviations should be avoided in formal writing. In technical writing, however, we should merely minimize the use of abbreviations, using them only when they improve WRITINg WEll 33 conciseness or are common within the intended context. One of the easiest ways to decide whether to use a particular abbreviation is to ask if it will improve or impede the reader’s understanding. For example, many readers of technical papers go directly to the figures or results to see what was found, or they go directly to the discussion to see what was deemed to be important. They can be frus- trated, therefore, if the figure legends, results, or discussion contain uncommon abbreviations that require them to search the introduction or methods to find the associated meanings. This should be avoided. Nevertheless, many abbreviations are so common that it would be surprising if they were used with explanation. Examples include ANOVA (analysis of variance), DNA (deoxyribonucleic acid), ECG (electrocardiogram), MRI (magnetic resonance imaging), and mRNA (messenger ri- bonucleic acid). There are, of course, many similarly common abbreviations. Scientific units should also be abbreviated without definition, for example, kPa (kilopascal), MHz (megahertz), ml (mil- liliters) mmHg (millimeters of mercury), and mM (millimolar). Many other abbreviations, such as LV (left ventricle) or MAP (mean arterial pressure), are used widely and so too for abbreviations of many biologically important molecules and chemical compounds. For example, one would be expected to use the following abbreviations: NO (nitric ox- ide), transforming growth factor (TGF), and (poly)methyl methacrylate (PMMA). In these cases, however, common practice is to introduce the abbreviation only if it is used three or more times in subsequent text and to define the abbreviation at its first occurrence in the body of the paper, not the abstract. It is best not to construct new abbreviations, however, just because a descriptor is used repeatedly. For example, we would not introduce NM for noun modifier even if used extensively. Similarly, we would not use SI for split infinitive. Indeed, this example reveals that one should be careful not to define new abbreviations that are identical to commonly accepted abbreviations (e.g., SI is French for Systeme Internationale, the common units of measurement in most of science and engineering). Iverson et al. (1998) provides an extensive list of accepted abbreviations in medicine. 2.6.3 foreign languages Many publishers seek to reduce the length of a publication because additional pages translate into additional costs. For this reason, some well-accepted abbreviations are encouraged and thus are common. Four of the most common abbreviations come from Latin, namely: 1. et al., which means “and others,” is commonly used when referring to a publication by three or more authors. In such cases, it is customary to cite the last name of the first author fol- lowed by “and others,” for example, Smith et al. (1999) or (Smith et al., 1999). Whether one italicizes the Latin et al. depends on the publisher, but in most cases, a period should follow the al. 34 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 2. 3. 4. e.g., which means “for example,” is often used in parenthetical situations (e.g., in this way). Remember, too, that an example is just that, one of many possible illustrations; it is not a unique clarifier. i.e., which means “that is,” is also often used in parenthetical situations (i.e., it often appears in this type of context). In contrast to e.g., using i.e. is similar to using the phrase “in other words” and thus is meant to clarify a meaning, not to provide an illustrative example. cf., which means “compare with,” is often used to draw attention to a similar or related il- lustration, equation, or other scholarly work, for example, (cf. Figure 1). Another common abbreviation from the Latin is, 5. etc., which means “and other unspecified things of the same class” or simply “and so forth.” Albeit commonly used, most grammarians agree that etc. should not be used in formal writing or, if so, only sparingly for good purpose. If one does not wish to provide an exhaus- tive list, using “for example” is an appropriate way to indicate the listing of some, but not all, of the members of that class. One would thus never use e.g. and etc. within the same parenthetical statement. Although scientific and engineering documents should be scholarly, they should not be pretentious. An attempt to impress the reader by using phrases or words from Latin, Greek, or other “foreign” languages is not advised in general unless their meaning is well-known and they engender concise- ness or clarity. For example, some words and phrases are common in the biomedical literature and should be used, for they are well understood. In addition to the aforementioned et al., i.e., e.g., and cf., consider for example: de novo: anew in situ: in its natural place in vitro: “in glass” or generally in an artificial environment in vivo: within a living organism ex vivo: outside of a living organism, but still living Other acceptable, but less common, examples are: ad infinitum: without end or limit in toto: totally, altogether, entirely reductio ad absurdum: reduction to the absurd status quo: as it is now WRITINg WEll 35 fooTNoTES, QuoTATIoNS, AND PRoPER CITATIoN 2.7 2.7.1 footnotes Footnotes are brief notes placed at the bottom of a page that provide a citation (older use) or a comment on a specific part of the main text. Although scientists and engineers used footnotes extensively in the past, such usage is generally discouraged today. We do not advocate eliminating footnotes, but we do encourage sparse usage. For example, footnotes can provide brief examples or clarifications that do not otherwise fit within the text using parenthetical devices such as commas, parentheses, or em dashes. Footnotes should not be used to solve problems in organizing material or sentence structure, however. 2.7.2 Quotations Quotations must be denoted in one of two ways: if integrated within the text, they must be enclosed within quotation (“ ”) marks; if longer, and singled out, they should be indented but appear without quotation marks. Some publishers also use a smaller font for indented quotations although we do not advocate this policy. For example, let us recall the quotation from W. Strunk Jr. that is given at the beginning of this chapter: Vigorous writing is concise. A sentence should contain no unnecessary words, a para- graph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subject only in out- line, but that every word tell. In general, use longer block quotations sparingly, if at all, in a technical document. Many times, the reader will skip such quotations to get to the meaning or importance of the quotation that follows. Another rule of thumb is to ask whether the quotation is necessary or if it is simply an easier alterna- tive. If the latter, a brief reference to the original source with original commentary would be better. Ellipses, that is, three dots in sequence (. . .), indicate that words are omitted, usually from a quotation. Four such dots in sequence usually indicate that words are omitted at the end of a sen- tence, hence the last dot can be thought of as the period at the end of that sentence. Beginning a quotation with a lowercase letter indicates that the author has omitted the initial part of the quote; beginning with a capital letter indicates that one is beginning the quotation at the beginning of the sentence. Thus, ellipses are not needed at the beginning of a quotation. When information is missing or incorrect in a quotation, it is acceptable to provide complete and accurate information. The information that is added should be enclosed by brackets [ ]. For example, given the quote “Newton postulated…,” one may write “[Isaac] Newton postulated. . . .” 36 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg It is acceptable, however, to provide a quotation exactly as it appears without correcting obvious or subtle errors provided this does not mislead the reader. Finally, one may find or insert [sic] in a quotation. The form [sic] comes from the Latin and indicates that a seemingly paradoxical word, phrase, or fact is not a mistake; it should be read as given. 2.7.3 Proper Citation Although we discuss issues of ethics in Chapters 6 to 8, including plagiarism, we briefly mention it here for convenience. Simply put, plagiarism is the passing off as one’s own the ideas and words of another. Actually, “pass off ” is too soft of a word; plagiarism is intellectual theft. Most universities have writing centers and associated Web pages, hence one can find formal definitions and excellent examples of plagiarism. The best way to avoid plagiarism is through proper citation. Although we tend to learn in English classes that there is a particular way to cite works in a bibliography, in scientific writing, the citation format varies considerably from publisher to publisher. Hence, the best advice is to read the “instructions to authors,” which can be found on the Web page for the journal or publisher or often within the journal itself. We give examples of different styles of citation in Section 3.1.9. “The Double Helix” by J.D. Watson is a wonderful account of the events that sur- Exercise 2.9 rounded the discovery of the double-helix structure of DNA. Read this book and write a three-page summary that highlights issues of ethical interest. voCABulARy 2.8 Vigorous writing should be clear and concise; nevertheless, it should also be provocative and en- gaging. The reader is thus encouraged to read Chapter 5 in Strunk and White’s The Elements of Style. There is a need to employ words of power (i.e., having strong meaning) without becoming verbose or haughty. One way to accomplish this is to expand our vocabulary, which is perhaps best accomplished by keeping a diary of words as we read technical papers and books. When we come upon a forceful, precise, or attractive word, we should take note of it. Knowing that the author may have misused the word, however, we should always consult a reliable dictionary when recording the associated definition. A good dictionary can be found online at www.m-w.com. Here, we list a few words that one can use advantageously in technical writing, which may or may not be used on a daily basis by the reader.4 4 These definitions are taken largely from the American Heritage Dictionary. WRITINg WEll 37 Abate: To reduce in amount, degree, or intensity; lessen. Adverse: Antagonistic in design or effect; hostile; opposed. Ancillary: Subordinate. Assume: To take for granted; suppose. Attenuate: To make slender, fine, or small. Augment: To make greater, as in size, extent, or quantity; enlarge. Causal: Pertaining to or involving a cause. Caveat: A warning or caution. Cogent: Forcibly convincing. Copious: Yielding or containing plenty; affording ample supply. Corroborate: To strengthen or support; attest the truth or accuracy of. Cull: To pick out from others; select. Cursory: Hasty and superficial; not thorough. Delve: To search deeply and laboriously. Didactic: Intended to instruct; expository. Disparate: Completely distinct or different in kind; entirely dissimilar. Dubious: Fraught with uncertainty or doubt; uncertain. Egregious: Outstandingly bad; blatant; outrageous. Eminent: Towering above others; projecting; prominent. Enigma: An obscure riddle; puzzling, ambiguous, or inexplicable. Equivocal: Capable of two interpretations; cryptic; evasive; ambiguous. Erudite: Deeply learned. Exacerbate: To increase the severity of; aggravate. Extant: Still in existence; not destroyed, lost, or extinct. Extenuate: To lessen or attempt to lessen the magnitude or strength of. Fortuitous: Happening by accident or chance; unplanned. Fraught: Attended; accompanied. Glean: To collect bit by bit. Hypothesize: To assert a hypothesis (i.e., an assertion subject to proof ). Inadvertent: Accidental; unintentional. Inchoate: In an initial or early stage; just beginning; incipient. Inexplicable: Not possible to explain. Inordinate: Exceeding reasonable limits; immoderate; unrestrained. Integral: Essential for completion; necessary to the whole. Intrinsic: Pertaining to the essential nature of a thing; inherent. Lucid: Easily understood; clear. 38 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Manifold: Of many kinds; varied; multiple. Marked: Having a noticeable character or trait; distinctive; clearly defined. Myriad: A vast number; a great multitude. Nadir: The place or time of deepest depression; lowest point. Nullify: To make ineffective or useless. Obviate: To prevent or dispose of effectively; to render unnecessary. Ostensible: Given or appearing as such; seeming; professed. Ought: Indicates obligation or duty, prudence, or desirability. Use with to. Paucity: Smallness of number; fewness. Permeate: To spread or flow throughout; pervade. Peruse: To read or examine, especially with great care. Posit: To put forward as a fact or truth; to postulate. Postulate: Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument. Premise: A proposition upon which an argument is based or from which a conclusion is drawn. Proliferate: To reproduce or produce new growth rapidly and repeatedly. Promulgate: To make known by public declaration; announce officially. Propensity: An innate inclination; tendency; bent. Purview: The extent or range of function, power, or competence; scope. Quiescent: Inactive or still; dormant. Recant: A formal retraction of a previously held belief or statement. Recondite: Not easily understood by the average person. Reiterate: To say over again. Replete: Plentifully supplied; abounding. Requisite: Required; absolutely needed; essential. Retrospect: A review, survey, or contemplation of things in the past. Salient: Striking; conspicuous. Spurious: Lacking authenticity or validity; counterfeit; false. Substantiate: To support with proof or evidence; verify. Succinct: Clearly expressed in few words; concise; terse. Sundry: Various; several; miscellaneous. Surmise: To infer without sufficiently conclusive evidence. Tacit: Not spoken. Tantamount: Equivalent in effect or value. Used with to. Tractable: Easily managed or controlled; governable. Ubiquitous: Seeming to be everywhere at the same time; omnipresent. WRITINg WEll 39 The space below allows you to record additional words, with their definitions, that you would like to add to your technical vocabulary. 40 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg CloSuRE 2.9 Recalling that one of the best ways to improve one’s writing is to read widely, we should not only read for pure enjoyment or the gaining of new technical information, we should also read with the intent of learning how to write well. In other words, take note of the infinitives, the effective use of punctuation marks, and so forth; record and use particularly forceful words and phrases. Aside from scientific publications, works of history, philosophy, and theology (one of the four original academic disciplines, with law, medicine, and natural philosophy) often represent good examples of writing well. As a specific example, consider the book On Growth and Form by D’Arcy Thompson (1917). In the foreword of the 1961 abridged edition, it is noted that P.B. Medawar wrote that Thompson’s work was “beyond comparison the finest work of literature in all the annals of science that have been recorded in the English tongue.” What gave rise to such a claim? Thompson was a true scholar, with expertise in the classics, mathematics, and zoology; moreover, he purposed both to document good science and to write well. Although we should not expect to achieve such success in writing well, we should remain committed to producing the best work possible. • • • • 41 C H A P T E R 3 Scientific Publications BASIC CoNTENT 3.1 There are many different types of publications in science and engineering, including abstracts, con- ference proceedings, journal articles, books, theses, dissertations, and technical reports. We focus on that which is generally regarded as most important, however, the archival journal article. There are also different types of journal articles, including original articles, technical notes (sometimes called brief communications), and review articles. We focus on the original article, which is both most common and most important to the advancement of science and engineering, for it documents significant, novel findings. Some journals impose stringent guidelines on the organization of such an article, including particular subheadings, yet considerable flexibility often allows the author(s) to present the material in the best way possible. For purposes of illustration, however, we follow an outline recommended by the majority of scientific journals, namely Abstract Introduction Methods (or Materials and Methods) Results Discussion Acknowledgments References Indeed, because most papers have the same basic structure, it is expedient to use a custom, generic file (e.g., called PaperTemplate.doc) to begin writing each paper. This file not only can remind us of the basic outline, it can ensure the proper formatting (often 1-inch margins, double-spaced, and 12-point font unless the particular journal states otherwise or provides its own template), including the place- ment of tables and then figures at the end of the manuscript. Having such an electronic outline in place can be a brief time saver, but perhaps, more importantly, it serves as a mental aid to begin writing. Recall from Chapter 2 that there are five basic steps of writing well: formulating a detailed outline, writing freely, editing critically, reading out loud, and having a colleague critique the final draft. Moreover, a detailed outline not only includes major headings, as noted above for the original journal article, it also includes potential subheadings and either bullets that highlight key ideas or in 42 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg some cases leading sentences. Although different authors employ different approaches in crafting the original detailed outline, a good place to start is to call all authors together and to lay out on a table the primary findings: figures, images, tables, equations, and so forth. These key findings can then be discussed and ordered logically, which will define the key bullets in the results and serve to remind us what methods were essential in obtaining the results. Once we have outlined the methods and results sections, it is then easy to outline the introduction and discussion. We discuss each of these key sections in detail below. First, however, let us consider a few items. Submission of a paper for consideration for publication in a technical journal usually requires a cover letter to the editor, a list of potential reviewers, and a cover page. Let us begin with the cover page, an important part of the submitted paper. 3.1.1 Cover Page and letter to Editor The cover page serves to communicate to the editor and publisher a number of important pieces of information: the title (and thus subject) of the work, those who performed the work (i.e., the author list in a specific order) and their professional affiliations, keywords that classify further the area of study, and finally the full address of the corresponding author. The title is extremely important; it will determine to a large extent who reads the paper. A good title captures the essence of a paper without being overly long. Indeed, general rules of thumb are that the title should not exceed 120 characters and it typically should not contain verbs. Consider, for example, well-known titles from two of the most important and widely cited papers from the 20th century: On the Electrodynamics of Moving Bodies Molecular Structure for Nucleic Acids: A Structure for Deoxyribose Nucleic Acid The first example is from Einstein’s famous paper of 1905 that introduced his special theory of rela- tivity; the second example is from Watson and Crick’s famous paper of 1953 that introduced their concept of the double-helix structure of DNA. The American Medical Association Manual of Style (1998) recommends further that titles should not contain phrases such as “The Role of . . .” or “The Effects of . . .” or “The Treatment of . . .” and so forth. Although there is no need to be dogmatic when crafting a title, simple guidelines are useful reminders nonetheless. Select keywords that are distinct from words used in the title and based on general, but not generic, aspects of the paper to ensure broader distribution. It is both much easier and more impor- tant today to identify appropriate keywords. One can log onto a standard computer-based search engine, such as PubMed, and compare results for different keywords to identify those that highlight papers most closely related to your work; such words would be good candidates for keywords. Be- cause most investigators now search for technical papers using computer-based search engines, we SCIENTIfIC PuBlICATIoNS 43 cannot overemphasize the importance of appropriate keywords. In other words, writing well is not enough — if the work does not reach the intended audience, it will not have an impact. Significant attention must be given to the title, keywords, and, as noted below, the abstract. Most journals require a cover letter even if the submission is completed online. This letter serves as the official “intent to submit” the paper and thereby to agree to all policies and procedures of review adopted by the selected journal. Among the many points that can be addressed in this let- ter, it is customary to confirm that the work is original, that the paper is not simultaneously under consideration for publication elsewhere, and that all authors contributed to the work and agree to its submission. One may also wish to note why the work will be of interest to the readership of the journal or to identify potential reviewers who either should or should not be selected and why. Like the paper itself, however, the cover letter to the editor should be concise. Here, we provide a simple example; letters will vary depending on individual circumstances. Date Dr. J. Smith Editor, Journal Name Address Dear Dr. Smith: Enclosed please find the manuscript entitled, “Title,” which is submitted for consideration for publication in Journal Name. This paper represents original research that has not been, nor will it be, considered for publication elsewhere until a decision is reached by you or your staff. All authors contributed to the work and its preparation and agree to its submission. With very best wishes, I am Sincerely, Name Title In some cases, the letter to the editor should also contain statements that, if applicable, all re- search involving human subjects or animals conformed to accepted standards and was approved by the appropriate institutional committee. Similarly, if applicable, this letter can communicate that permissions have been obtained from the appropriate parties to republish previously published work and it can offer suggestions of possible reviewers. In all cases, however, it is important, indeed often 44 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg required, to include a statement that the paper has been submitted to only one journal for evalu- ation. That is, just as with submissions of grant applications to most agencies, there is a standing agreement among scientists and engineers that it is improper to submit the same work for simul- taneous evaluation by two or more journals because of the significant effort required of others to provide proper and timely reviews. Let us now turn our attention to the technical sections of a journal article. Rather than dis- cussing them in the order in which they appear in a paper, however, we discuss them in the usual order of composition. Hence, we end with a discussion of the abstract rather than beginning with such a discussion. 3.1.2 Results The section on results is the heart of the technical paper; it reports the primary findings, which often represent the most important information contained in the paper. The results should be easy to write, thus many authors prefer to write this section first. Indeed, in cases of multiple authors working on a single document, the first author often drafts the results and methods first, then the senior author drafts the discussion and introduction. All authors then revise the completed first draft. Regardless of approach, one of the best ways to write the section on results is to lay out all of the figures, tables, equations, or other major findings that you may include, then to prioritize and order them in the most logical fashion. It is important to emphasize in this regard that we need not order the results chronologically; in some cases, authors order results by importance. Once done, it is then easy to write freely. This approach is particularly effective when a paper is coauthored by two or more investigators, for laying the results out on a table facilitates discussion of the relative merits of each finding. Note, too, that although some journals require subheadings within the results, they are often omitted, and the lead sentence of each paragraph serves to introduce the different key findings. Indeed, some recommend that the lead sentence of each paragraph in the results should state the most notable finding in that paragraph. One of the most frequently asked, and often most difficult to answer, questions is: How much interpretation of the findings should be in the results versus discussion? The reason that this is dif- ficult to address is that it depends in part on the style of the author and recommendations by the specific journal. In general, however, most technical writers agree that the results section should be objective; it should focus solely on presenting the findings. Hence, although it is common to point out within results any interesting or important features within specific figures, images, equations, or tables, it is best to reserve for the discussion any interpretation of the significance of the finding as well as any comparison to findings by others. Another question that arises often is how best to refer to a figure or table. For example, should we write SCIENTIfIC PuBlICATIoNS 45 A and B were found to be related linearly (Figure 1), or is it better to write Figure 1 reveals a linear relationship between A and B. In other words, is it best to state the key finding and refer parenthetically to the associated figure, image, equation, or table, or is it best to cite directly the particular evidence that reveals (shows, il- lustrates, or so forth) the key finding? Notwithstanding some exceptions (e.g., specific instructions to authors for some journals), the answer to this question is often that it is a matter of personal style. Note from our illustrative example, however, that the first approach involves passive voice, whereas the second approach involves active voice but further requires the figure, image, equation, or table to “do something” — reveal, show, illustrate, confirm, or so forth. Some editors suggest that inani- mate devices such as figures cannot “reveal” or “show” such things, thus they prefer parenthetical references over the direct approach. Conversely, others prefer the crisp, active voice in the second example, which helps to minimize the use of passive voice as desired in general. We encourage the reader to consider these and similar options carefully and to adopt a consistent, but not rigid, per- sonal style. Such a decision should affect other aspects of writing a technical paper, for example, the introduction wherein one often reads “This paper presents.” Again, some would argue that only the investigators can present, not the paper, yet many prefer this crisp, active style of introduction. 3.1.3 methods (or materials and methods) The methods section is usually the easiest to write. Indeed, if one has trouble getting started in the “write freely” phase, it is often best to go to the methods. Simply put, the methods section is where we document how we accomplished the work. In principle, this section should contain enough detail to allow the reader to repeat the study in the same way — this alone allows one to test and confirm the basic tenet of science, reproducibility. Given the increasingly sophisticated methods and procedures used in science and engineering, however, writing an effective section on methods demands significant planning. Moreover, given that one can use many commercially available kits or software packages, there is a need for balance between detail and proper citation. Two effective devices in writing the methods section are to use ample subheadings and paral- lelism. Here we emphasize that we should not write scientific papers to be read, we should write them to be studied. Subheadings thus aid the student in organizing information or locating quickly particular aspects of the methods when needed. Typical subheadings in a paper on cell biology could be: Immunohistochemistry 46 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg In Situ Hybridization Statistics Subheadings in a paper on mathematical modeling could include: Theoretical Framework Constitutive Models Numerical Methods In either case, subheadings should proceed logically and thereby reveal to the reader the thought process followed by the investigators. The format for the subheadings, for example, numbering or italicizing, is dictated by the particular journal and thus is provided in the specific instructions to authors. Because many scientific findings result from or imply a mathematical statement, it is impor- tant to address the treatment of equations within a paper, often within methods or results. Simply put, write an equation as a normal part of a sentence. For example, Newton’s famous second law of motion is usually written simply as f = ma, where f denotes force, m denotes mass, and a denotes ac- celeration. Consistent with the presentation here, mathematical symbols usually appear in a distinct font, which may include italics (e.g., scalars) or boldface (e.g., vectors). In many cases, however, either for emphasis or simply because of complexity, equations are set off as a separate line within the text. In this case, the equation is still part of the sentence and thus should include commas and periods as appropriate. For example, we could write the following. It is important to remember that Newton’s second law of motion, namely f = ma, holds only with respect to an inertial reference frame. Similarly, we could write the following. The governing equation in this case is Newton’s second law of motion, which can be written as f = ma. An easy way to remember that equations are part of the normal grammatical structure is to recall step 4 from Chapter 2 on how to write well — reading out loud forces us to include equations as natural parts of the text. A final reminder is that most journals do not allow a nomenclature for symbols used within equations. Hence, one should always state the meaning of a symbol just before or just after the equation in which it is introduced, just as we did above for Newton’s second law (e.g., noting that f denotes force). For those symbols that are universally accepted or familiar to readers of a particular journal, there is no need to define them explicitly. Examples of well-recognized symbols are +, −, =, and also SCIENTIfIC PuBlICATIoNS 47 those for summation, derivatives, integrals, and so forth. Given the increasing complexity of sci- ence and engineering, commonly used symbols may represent multiple quantities within the same paper, hence there is a need for care. For example, R is often used for radius, but it is also used for the universal gas constant [R = 8.314 J/(g mol) K]. The most important suggestion in this regard is to be clear and self-consistent. Finally, a frequently asked question relates to the level of detail needed in cases where one re- ports results obtained using methods reported previously in other journal articles. Although there is no rigid answer, the best practice is to document the essential, new methods and to refer the reader to previously established methods, where appropriate. For example, if your group established the previous methods, simply state that the details can be found in a previous publication, then briefly outline the methods; if others established the previous methods, cite the key paper(s) and provide a brief, but slightly more detailed summary of the methods. Conversely, one must provide significant detail when reporting a new method or procedure. Such detail can include specific instruments and vendors, chemicals and their sources and concentrations, specific versions of software, and so forth. In cases of human or animal research, one must first note that the appropriate institutional oversight committee (e.g., the Institutional Review Board, or IRB, for human research and the Institutional Animal Care and Use Committee, or IACUC, for animal research) approved the work. 3.1.4 Discussion and Conclusion Most journals recommend against using a separate section for conclusions, which would typically be brief, hence the discussion often serves a dual role. One should address at least three specific points in the discussion: Interpret the specific results and emphasize the significance. Compare the current with past results. Identify limitations and potential needs for further research. Whereas the introduction normally addresses the significance of the overall research topic or area, the discussion should address the potential significance of the particular findings. For example, an introduction may note the importance of cardiovascular consequences of hypertension, which affects more than 50 million Americans, but the discussion may note the significance of the new finding that blocking a particular receptor in vascular smooth muscle cells reduces hypertension in an experimental cohort. Like the introduction, therefore, the discussion should cite appropriate references, albeit often with greater discussion of the relevant details. It is important in this regard to cite only the most relevant literature. In other words, the goal is to place the current findings within the most appropriate context, not to provide an exhaustive collection of all previous work 48 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg that is remotely related to the overall topic or specific findings. Because of the explosion of scientific and engineering knowledge, citing good review papers can often serve to cover general information without concern that some important papers may be missed. Related to issues of ethics, of course, one should not purposely fail to cite a relevant paper for personal gain. A frequent question with regard to the discussion is how much information should be in- cluded on the inherent limitations or future needs. In some ways, this addresses both the style and the ethics of written communication. It is both prudent and useful to others to point out many of the limitations of the study, with justifications, for this will both put the current study in perspective and guide future work. Nevertheless, one must be careful not to focus on the negatives in a way that it distracts from the significant accomplishments or advancements of the study. The key, therefore, is to maintain an appropriate and candid balance. Similarly, it is useful to point the reader toward important, useful directions for future research. Yet, many investigators do this in a guarded fashion to allow themselves the opportunity to exploit their present findings and achieve further advances. The key point, therefore, is to maintain a proper balance — provide guidance so that others can advance the field while protecting intellectual property. In summary, the primary goals of the discussion section of a paper are to reemphasize the significance or innovation of the study, interpret and discuss implications of the specific findings, compare the current findings with similar work by others, discuss limitations of the methods or findings, and summarize the major finding(s) while giving direction for future work. 3.1.5 Introduction As with any introduction, the primary goal of this section is to capture the reader’s interest and “set the stage.” Toward this end, it is generally recommended that the introduction answer three basic questions: Why is the general topic or particular study important? What is currently known and what remains unknown? What does the current paper address or accomplish? One should be able to answer these questions easily after having written the results. Consistent with answering these questions, the typical introduction consists of three to four paragraphs even though there is considerable variety in the number and especially the lengths of these paragraphs. Experienced writers may write the introduction first, but most writers write the introduction after completing the methods and results and sometimes even the discussion. Regardless, it is important to provide sufficient references in the introduction to justify both the need for the study and the general approach adopted. SCIENTIfIC PuBlICATIoNS 49 An important issue with regard to writing a journal article, including the introduction, is the appropriate use of abbreviations. Good rules of thumb are to use only commonly known abbrevia- tions (e.g., DNA), to use them only if the word or phrase is repeated three or more times throughout the document, and to introduce them at the first occurrence in the body of the paper (cf. Section 2.6.2). Some journals require the author to collect abbreviations together, for example, in a footnote on the first page of the paper or in a table. Regardless, it is best to use abbreviations sparingly. 3.1.6 Abstract The technical abstract has always served an important role — it provides a brief summary of a paper and thereby helps a reader decide whether to read or study the paper. With the advent of computer- based search engines, however, the abstract has become a particularly important means of captur- ing the attention of the intended audience. Hence, albeit a short section, often not more than 250 words, the abstract deserves great attention. Most writers compose the abstract last. It must reflect briefly the overall paper, including the basic motivation, significance, general approach, and key discoveries or final solution; it must be written clearly, without jargon, acronyms, or uncommon abbreviations, and must stand alone, generally without references. As with the introduction, the first sentence of the abstract should be engaging. In contrast with the introduction, the last sentence of the abstract generally summarizes the most important finding or points to pressing needs for future research. Whereas most journals allow the authors to write the abstract as they see fit, a few journals require the authors to follow a uniform outline, including specific subheadings. As in all cases of technical writing, it is thus im- portant to read the “instructions to authors” for the particular journal. 3.1.7 Acknowledgments It is customary, indeed required in most circumstances, to acknowledge the financial support that enabled the work. As an example, one might read: This research was supported, in part, by grants from the National Institutes of Health (R01 HL-10000 and R21 HL-01000). Because of the increasing move in science and engineering toward translational research, investiga- tors cite industrial support more frequently. In such cases, the journal may require the authors to disclose conflicts of interest related to potential financial gain related to the results. If there are no disclosures, this should be noted. In addition to financial support, it is often appropriate to acknowledge technical support as well as intellectual or editorial contributions by individuals who were not involved extensively enough to merit coauthorship but who contributed nonetheless. Such acknowledgment should be merited, 50 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg however, and those noted must be informed. Indeed, some journals now require individuals ac- knowledged in this section to stipulate in writing that they are both aware of and deserving of such recognition. 3.1.8 Appendices Appendices are not found in all scientific papers; indeed, they appear in the minority of papers. Nevertheless, when used well, appendices can serve a very important role. In general, appendices contain important information that either does not fit well within the flow of the body of the pa- per or is simply best stated separately for those few readers who will be interested in such details. A good example of appendix material would be the step-by-step derivation of key equations, the final result of which can be found in the body of the paper. In this way, the author fulfills his/her responsibility of providing methods that are sufficiently detailed to enable the reader to reproduce a result while not distracting the reader from the key points presented in methods. Similarly, detailed “recipes” for molecular or cellular assays may fit well in an appendix. 3.1.9 References It is interesting that we are often taught “proper methods of citation” in courses and books despite different journals and publishers requiring very different citation formats. In some cases, references must be arranged according to the order of appearance within the work and numbered sequentially beginning at 1; in other cases, references must be arranged alphabetically by the last name of the first author, then numbered beginning at 1; in yet other cases, references must be arranged alphabetically and not numbered. This basic scheme dictates how to cite any reference within the text — by num- ber or by author. Similarly, the format for the references that details the authors, year of publication, title, volume, and inclusive pages also varies from journal to journal. The best advice, therefore, is to follow the specific instructions to authors. As specific examples, however, consider multiple ways to cite the same article within the text: Watson and Crick (1953) proposed the double helix . . . Watson and Crick [20] proposed the double helix . . . Watson and Crick20 proposed the double helix . . . or similarly, The double-helix structure of DNA was . . .(Watson and Crick, 1953). The double-helix structure of DNA was . . .[20]. The double-helix structure of DNA was . . . .20 SCIENTIfIC PuBlICATIoNS 51 As seen, the third approach in both cases results in some savings with regard to printing, which is important to some publishers given that most journal articles cite ~35 papers and most re- view articles cite over 100 papers. When these simple savings are multiplied 30-fold or more, one can appreciate the potential savings in page costs. It is noted, however, that numerical citation has the disadvantage that the reader must constantly refer to the reference list to determine who was responsible for the cited finding. Informed readers often know who has done what in a field, which is to say who has produced reliable or important findings. Citation by author names (e.g., Smith et al., 1999) thus has the advantage of increasing the flow of the paper. Nevertheless, one must follow the format prescribed by the journals and publishers. Usually the only case wherein one can pick a format is while writing proposals, which is discussed in Chapter 4. Citation is similar to that discussed above when there is but a single author. For example, we might find the following: Einstein (1905) proposed . . ., Einstein [15] proposed . . ., or Einstein15 proposed . . ., and similarly we might find . . .the special theory of relativity (Einstein, 1905), . . .the special theory of relativity [15], or . . .the special theory of relativity15. In the case of three or more authors, however, the format differs slightly. Recall from Chapter 2 that “and colleagues” is ab- breviated in the Latin as “et al.” Hence, we might find the following: Smith et al. (2008) proposed . . .or . . .(Smith et al., 2008). Whereas some journals use (Smith et al. 2008), that is, they omit the comma after the et al., it is a mistake to add a comma after the first author’s last name (i.e., Smith, et al., 2008 is not an accepted format). Again, the best advice is to refer the specific instructions to authors for the journal of interest. Finally, note that the citation within the reference list can also appear in various forms. For example, we can cite the same paper as: Watson JD, Crick FHC (1953) Molecular structure of nucleic acids: A structure for deoxyri- bose nucleic acid. Nature 171: 737–738. Watson JD, Crick FHC. Molecular structure of nucleic acids: A structure for deoxyribose nucleic acid. Nature. 1953;171:737–738. Watson, J.D., and Crick, F.H.C., 1953, “Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid,” Nature, 171 pp. 737–738. Other formats exist, which is why one must consult the instructions to authors for each journal. A final, and important, reminder is to cite only those papers that you have actually read. Per- haps surprisingly, many investigators will cite papers that someone else has cited simply because it is easier. Such a practice can be dangerous. In science and engineering, one should always check and double-check everything, including interpretations of other work used in citations. 52 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 3.1.10 figures and Tables It has been said that a picture is worth a thousand words. Actually, a well-prepared and appropriately selected picture (e.g., figure or image) can be worth a thousand words if done well. As an example, consider the following figure, a standard x–y scatter plot, which is the most common type of figure found in a technical paper. Although this example contains the basic ingredients of an effective fig- ure (e.g., clear data points and labeled axes, with the unit of measurement denoted parenthetically on the x-axis), we can improve it considerably with little effort. Compare the following version of this figure (reprinted with permission, CISM) to the pre- vious one. It is easy to see that a reduced number of tick marks along each axis as well as larger numbers and lettering improve the readability considerably. Indeed, one of the most important considerations is that typesetters will reduce the size of many submitted figures before placement within the final version of the paper. This is particularly important when placing a figure within a single column in a dual-column layout, which most technical journals use. Albeit a small point, note that the solid curve in these figures represents a best-fit to data obtained using a formal regression method. Whereas solid lines are appropriate for showing such “theoretical” or “model” fits, it is best to use lightly dashed lines when the goal is to connect the data points for emphasis. It should be remembered, however, that simply connecting the dots may be misleading if data sampling missed key points. SCIENTIfIC PuBlICATIoNS 53 Finally, realizing that many readers go to the results after having only read the title and per- haps the abstract, it is important to write complete legends so that the reader can understand the importance of the figure easily. In summary, the original journal article should be both well written and well illustrated; it should address the following primary questions: Introduction: What was done and why? Methods: How was the work accomplished? Results: What was found? Discussion: Why are the results important, how do they compare to previous work, and what remains to be investigated? Seeing one’s name in print for the first time on an archival paper can bring a sense of excite- ment and pride. Seeing one’s name on a paper that contains errors or fundamental flaws can bring a sense of regret. There is, therefore, a need to give such work our most careful attention from start to finish. Interview someone who serves on an editorial board of a technical journal and ask Exercise 3.1 how reviewers are selected, what are good reasons for excluding reviewers in particular cases, and what is done when different reviewers have diametrically opposing views. Write a one-page sum- mary of the results of the interview. All journals limit the number of words or pages allowed for papers within par- Exercise 3.2 ticular categories. For example, it is common for an original article to be limited to 6000 words inclusive. Noting that an abstract typically is ~250 words, each one-column table and a single panel figure is equivalent to ~250 words, and a standard full-citation reference is typically equivalent to 20 to 30 words (some up to 40 words), estimate the number of words for an abstract, 6 figures, 1 table, and 35 references, which is typical for a standard original paper. Next, calculate the number of words available and estimate reasonable lengths for remaining sections: introduction, methods, results, and discussion. PuBlISHINg AN ARCHIvAl JouRNAl PAPER 3.2 3.2.1 origin According to Boorstin, (1983, pp. 390–394), The printed scientific ‘paper’ or ‘article’, which was simply a later version of the letter, would be the typical format in which modern science was accumulated and communi- cated. . . .The letter was an ideal vehicle for the increasing numbers of men dispersed over Europe who no longer expected to storm the citadel of truth, but hoped to advance 54 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg knowledge piece by piece. . . . A letter had obvious advantages over a book. While works of science were often large tomes easy to stop for censorship, the novel observations in a letter could slip unnoticed or be delivered with the ‘ordinary post’. In contrast to early European investigators such as Galileo (1564–1642), few modern investigators need be concerned about potential censorship of their work. Rather, the primary concern today is to ensure that a paper receives broad distribution to the intended audience. Toward this end, electronic publishing and the Internet have revolutionized the availability of scientific papers, yet the methods of composition, presentation, and submission have not changed. 3.2.2 Composition and Authorship It is difficult, if not impossible, to write by committee. Indeed, one of the most important documents in American history, the Declaration of Independence, was assigned to a committee of five for com- position but was drafted in seclusion by a single author, Thomas Jefferson. As it should have done, the committee evaluated and revised the final draft penned by Jefferson before forwarding the final version for consideration by the Continental Congress of 1776. Although there has been a significant increase in the number of authors on scientific papers, particularly in biomedical science and engineering, the primary responsibility of writing a paper must similarly fall to one author or in some cases two authors (e.g., the first and senior authors). As noted above, however, the best way to ensure that the first draft represents the ideas and expecta- tions of all authors is to meet together to define the initial outline and to discuss what findings to report in the results. We address the issue of joint authorship further in Chapter 6, hence we merely note here that it is essential that all authors agree on the contents and presentation of a paper before submission for consideration of publication. 3.2.3 Submission and Review As noted earlier, the essential first step when preparing a paper for consideration for publication is to read the instructions to authors for the intended journal. Only in this way will one be able to fulfill the requirements of each journal. In general, however, the two primary items needed for sub- mission are the aforementioned cover letter to the editor (cf. Section 3.1) and the complete paper, including the cover page, body of the paper, tables, and figures. A few journals allow authors to submit a paper for consideration directly to a Exercise 3.3 member of the editorial board or the sponsoring society. In these cases, that member can assume the sole responsibility for review and may then “communicate” the paper to the editor for publication. Identify two different journals that allow such a procedure and write a two-page summary discuss- ing the history of this approach and the associated advantages and disadvantages. SCIENTIfIC PuBlICATIoNS 55 An editor or associate editor will usually solicit two or three experts to provide a recommen- dation on the potential suitability of a paper submitted for publication. These reviewers are asked to provide objective assessments and thus to decline to review a paper if there is either a real or a possi- bly perceived conflict of interest. The period allowed for review varies considerably among different journals, with some biological and clinical journals allowing only 2 weeks and some mathematical journals allowing up to 3 months for review. Differences also exist between journals with regard to the possible categories of recommendations available to the reviewer, but general categories are: Accept (i.e., accept as submitted) Accept pending minor revision (not requiring rereview) Major revision (with required rereview for further consideration) Reject (i.e., not suitable for publication) Inappropriate for this journal. In cases where the topic, type, or length of a paper is deemed to be inappropriate for a journal, an editor can communicate this to the author(s) without a formal review, even though reviewers are also allowed to make such a recommendation independently. A recommendation to reject a paper may be rendered for any of a number of reasons: the paper does not contain original or novel find- ings, it contains serious flaws in design or analysis of the data, it does not address a relevant prob- lem, results contradict previously published findings without addressing adequately the associated reasons, there is insufficient new information (i.e., it is only an incremental advance at best), and so forth. In the case of a recommendation to reject, the editor should ask the reviewer(s) to state this case diplomatically, although this does not always happen. It is common for a journal to reject 50% or more of all submissions. The recommendation to request major revisions generally implies that there is a need for ad- ditional experiments, analysis of data, or computations. Such a recommendation can also reflect the need to correct a major, but not fatal flaw, to reduce the length of the paper if it is overly long, or to improve significantly the presentation, including improved figures, tables, and writing. In contrast, minor revisions (not requiring further review) can reflect a need to expand the methods or discussion or conversely to eliminate information that is available in other publications. There may also be a need to add some key references or reduce the overall number of references. Minor improvements in writing or the need to eliminate results that are duplicated in tables and figures may also lead to a recommendation of the need for minor revisions. Finally, albeit very uncommon, the recommendation to accept (as is) suggests that the study is important, novel, and well presented. All authors should strive to submit such work, but should be prepared to revise a paper as needed. As one might expect, unanimous recommendations by two to three reviewers are uncommon, hence the editor or associate editor usually must make a decision based on the information received. 56 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg For example, if two reviewers recommend major revisions and a third reviewer recommends rejec- tion, the editor is justified in recommending either major revision or rejection. In cases where the editor rejects a paper, the authors can try to rebut the reviews and request either the privilege to sub- mit a revised paper or that additional reviewers are asked to review the paper further. In most cases, however, editors tend to stand by the initial, carefully weighed decision, and it is best to consider other options. For example, some authors will simply resubmit the same paper to another journal for consideration for publication; in such cases, they are usually not required to reveal that the paper has been rejected previously, which enables the second assessment to be objective. Authors must realize, however, that reviewers are often picked carefully for their expertise, and it is possible that different editors from different journals will select the same reviewers. For this reason, and simply because one should always use any opportunity to improve a paper based on any feedback obtained, it is best to revise a paper that has been rejected before submitting it to another journal. Finally, it is useful to know how editors select reviewers and what instructions are given to the reviewers. Ideally, the editor, associate editors, or editorial consultants are familiar enough with the topic of the submitted paper that they know the experts personally or at least know of them. In cases wherein such experts either decline to review a paper (because of conflicts or simply because they are not able to provide a timely review) or cannot be identified easily, editors will often peruse the references cited in the paper. In other words, frequently cited authors are good potential review- ers because their work is related closely to that which was submitted and has passed previous peer review. Alternatively, editors may also use computerized search engines to identify potential review- ers based on the publication of similar work in reputable journals. 3.2.4 Revision As noted earlier, only a small percentage of technical papers are accepted upon the first submission, hence authors should expect to revise a submitted paper. Indeed, in most cases, revision along the lines suggested by the reviewers improves the paper significantly, thus revision should be seen as an opportunity not a failure. Nevertheless, it is human nature to be disappointed or, in some cases, upset by a negative review. Toward this end, we recommend two things. First, read the review carefully but do not take any action until at least a few days later. In other words, neither a rash response to the editor nor a hasty attempt to revise a paper is likely to be productive. Second, avoid both of the two most natural responses to a negative review — to adopt all of the reviewer’s recommendations be- cause “they must be the expert” or to ignore all of the comments because you “know better.” Rather, it is best to take comments and concerns by reviewers at face value. For example, if a reviewer states that a particular section is hard to understand even though you think it is clear, chances are that at least some other readers will also find the section hard to understand. The best response in this SCIENTIfIC PuBlICATIoNS 57 case, therefore, is to take advantage of the opportunity to improve its clarity and to ask a colleague to assess the changes. In other words, because it is your name on the paper, take every opportunity to make the paper the best it can be. When a journal allows or requests a revision, the author(s) usually must submit the revision within a certain period (often 3 to 6 months, but highly variable) and provide evidence of the revi- sions. In some cases, the author(s) can meet this requirement simply by summarizing the revisions on a separate page or in a letter to the editor. In other cases, the journal may either require separate detailed responses to each of the reviewer’s concerns or marks within the submitted manuscript that identify the revisions. The latter requirement is now met easily using features such as “track changes” in MS Word. Once the authors decide to revise a paper, they should ask how to do this most efficiently. For major revisions, it is best to identity the requisite experiments, calculations, analyses, and so forth and to generate the additional results. Next, one can follow the same approach used in writing an initial draft — lay out all results, new and old, on a table and determine which to include and in which order. Once done, revise the results, methods, discussion, introduction, and abstract accord- ingly and document the revisions appropriately. For minor revisions, it can be efficient to begin by writing the required “response to reviewers” or “summary of revisions.” After knowing how one wants to address the concerns, the paper can then be revised accordingly. Although policies differ among journals, it is uncommon to allow authors to submit more than one revision because of the time invested by both the editors and the reviewers. In other words, one should work very hard to satisfy reviewer’s concerns and to make a revised manuscript acceptable. 3.2.5 Typesetting, galley Proofs, and Proofreader marks Years ago, a typewritten copy of a manuscript was copyedited, then typeset from scratch. Today, nearly all journals require electronic versions of accepted papers, which are then copyedited and formatted for publication. Briefly, copyediting is an important step wherein a manuscript is checked carefully by the editorial staff of the journal, or a third-party associate, for format, style, spelling, complete and consistent citations, and so forth. In some but not all cases, the copyedited version is sent to the authors along with the galley proof to show the changes that were made. A galley proof is the final draft of the paper formatted exactly as it will appear in print. The authors are asked to check the galley proof carefully to ensure accuracy, yet it is expected that only minor changes or corrections will be made at this stage of publication. In the case of major changes due to author errors, the publisher may charge extra to make the requested changes. For this rea- son, authors should ensure that the final version of a manuscript is correct as submitted. Although 58 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg the advent of electronic publishing decreased tremendously the number of necessary corrections, authors should be diligent to check the galley proof carefully, including the layout of tables, figures, and equations. If errors are discovered after approval of the galley proof and publication of the paper, the authors’ only recourse is to publish an erratum (or errata, which is the plural form of erratum and used in the sense of correcting simultaneously multiple errors). Because of the importance of the galley-proof step, publishers developed a nearly universal set of symbols and directives to communicate changes that were needed in the paper. Again, however, because of the increasing capabilities of word processors, it is now common for such corrections to be made electronically — for example, using the “comment” function in PDFs or the track-changes function in word files. If needed, however, one can find proofreader marks in standard dictionaries (e.g., American Heritage Dictionary) or online. Find a 10- to 20-page paper that you have written previously and scan it for minor Exercise 3.4 errors. Use standard proofreader marks to note the appropriate changes just as you would do for a galley proof. 3.2.6 Copyright, Permissions, and Page Charges Copyright is a legal procedure that grants exclusive rights to the production, publication, sale, or distribution of a work by the owner of the copyright. Because this deals with the ownership of ideas, it is addressed in Chapter 8. Here, therefore, we simply note that upon acceptance of a paper for publication, the publisher will usually request that the authors transfer copyright to the publisher. Although copyright agreements tend to be standard for the publishing of scientific papers, one should read such agreements carefully before signing. If there are questions regarding anything within the agreement, one should either consult a more experienced author or contact the copy- rights division of the publisher. Transfer of copyright requires that the material to be transferred is original and, when ap- propriate, that special permissions have been obtained to republish any previously published ma- terial. In the latter case, the most common situation is the desire to republish a figure or image from another work. One may obtain permissions to do so by writing the copyrights division of the publisher that holds the copyright and requesting permission to republish the work in a specific way. In most cases, a publisher will grant such permission provided that a simple statement is associated with the republished material [e.g., “From Smith (2001), with permission from Publisher Name.”]. In some cases, however, such permission is granted only after receipt of a fee, which could be hundreds of dollars for a single figure. In cases of financial constraints, it is best to contact the publisher early to identify potential fees. Although one only needs to contact the holder of the copyright, which is SCIENTIfIC PuBlICATIoNS 59 often the publisher, not the original author(s), requesting permission from the author, if he/she can be located easily, is a good gesture. In some cases, one step remains before the publication of your paper — payment of “page charges” or fees to cover the publication of color figures. In many cases, journals charge standard fees, according to the length of a paper, to offset portions of the cost of publication. Such page charges are mandatory in some cases but voluntary in other cases. The rationale behind voluntary page charges is that many agencies that financially support research also desire that the associated findings be published, and consequently, they provide researchers with funds to support publication. Payment of page charges often entitles the author(s) to free hardcopy reprints or PDF versions of the paper. Independent of page charges, some journals assess mandatory fees for the publication of color figures in print (but not electronic) versions. Because fees for color figures can be hundreds to thousands of dollars, it is prudent to minimize the use of color figures or images to those that are best understood in color. With the continued growth of online publishing, however, one can also consider using color figures in the online version that are equally clear if printed in black and white by the reader or by the publisher of the print version. Regardless, it is also good to determine before submission if such fees will be charged. Like all submitted figures and images, color versions must have the required resolution and must be submitted in the proper file format. Again, the author is referred to the instructions for authors for each journal for requirements vary with journal. Read the article “Structural Outline of an Archival Paper for the Journal of Biome- Exercise 3.5 chanics” [Brand RA, Huiskes R (2001) J Biomech 34: 1371–1374]. Construct a two-column table to record hints therein that reinforce or contradict that which was presented in this section (3.2). Provide a summary, not to exceed one page, that articulates your preferences in cases where there is disagreement. 3.3 THESIS oR DISSERTATIoN Most universities require the completion of a thesis as part of the requirements for a master of science (M.S.) degree or a dissertation for the completion of a doctor of philosophy (Ph.D.) or a doctor of science (D.Sc.) degree. It is common for an M.S. thesis to range from 50 to 150 pages and for a Ph.D. or D.Sc. dissertation to range from 100 to 250 pages (each double spaced with ample margins). Although it may seem a formidable task to write such a long document, it is actu- ally not difficult if one formulates a good outline and simply writes chapter by chapter. One should obtain specific guidelines for formatting such documents from the local Office of Graduate Studies, however, for requirements differ from institution to institution. Here we note briefly the two most common styles for organizing a thesis or dissertation. 60 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg First, a thesis or dissertation can be organized along traditional lines and thus consist of the following: Abstract Chapter 1: Introduction Chapter 2: Background Chapter 3: Methods Chapter 4: Results Chapter 5: Discussion Chapter 6: Conclusions and Recommendations References Appendices Note the strong similarity between this outline and that for the archival journal paper, with two notable exceptions. To encourage students to understand the literature well, most institutions require a separate chapter, entitled background, which highlights past work on the topic of graduate study and identifies areas of need for further study. Because a dissertation must represent original work, review of the background literature is a particularly important part of the doctoral student’s early work. To encourage students to recognize the limitations of their own work and thereby to identify areas of further study, most theses and dissertations end with a chapter entitled “conclusions and recommendations.” A simple way of thinking about recommendations is to ask the question, “What should the next graduate student in the laboratory do to push the current work forward?” In contrast to the traditional outline, it is becoming increasingly common to organize theses and particularly dissertations around individual papers that are based on the student’s work and either have been or will be submitted for publication in archival journals. For example, consider the following outline: Abstract Chapter 1: Introduction Chapter 2: Paper 1 Chapter 3: Paper 2 Chapter 4: Paper 3 Chapter 5: Conclusions Appendices Packaging the multiple papers (often one for a thesis and three to seven for a dissertation) between general introductory and concluding chapters allows the student to focus on writing the individual journal papers. In this case, each chapter contains its own introduction, methods, results, discus- SCIENTIfIC PuBlICATIoNS 61 sion, and references. It is clear that the individual papers should be written first, as described above, and the introduction and conclusions written last. In the traditional case, it is common to write the background first, then methods and results, and finally discussion, introduction, and conclusions and recommendations. If one adopts this second style of organization and papers are published be- fore submitting the final dissertation, it is important to consider issues of copyright; the best advice in this case is to check with your local office of graduate studies. 3.4 TECHNICAl REPoRTS Whether a technical report will be published or not, it is a formal document and thus requires careful attention. In contrast with the aforementioned types of technical documents, however, the technical report does not demand a particular outline. Indeed, such reports can range from a one- page summary to a thousand-page document. The best advice, therefore, is to discuss in detail the expectations before beginning the outline, then use, as appropriate, the aforementioned guidelines for writing an archival journal paper. Exercise 3.6 tion. Write a one-page bulleted summary of the key stylistic requirements. Find and read carefully the instructions for a thesis or dissertation at your institu- • • • • 63 C H A P T E R 4 Proposals and grant Applications INTRoDuCTIoN 4.1 Whether it be a proposal to undertake a particular senior design project, a graduate student’s pro- posal to a committee to pursue a particular area of research for his/her thesis or dissertation, an employee’s request of management to support a new area of R&D, an organization’s application for state or federal support, or a professor’s request for support of basic research, the technical proposal is fundamental to securing the resources needed to advance science and engineering. Notwithstand- ing the many different types of proposals, most are similar in basic structure and preparation. Hence, for illustrative purposes, we focus on the NIH individual investigator grant application known as the R01, the primary mechanism for funding health-related research in the United States. 4.2 TyPES of gRANTS The R01 mechanism supports two general types of grant applications: investigator-initiated and those in response to a request for proposals (RFP) or program announcement (PAR). By investigator- initiated, we mean a scientist or engineer identifies a fundamental question or important problem, conceives of an approach to address this issue, and takes the initiative to request the funding needed to complete the project. In contrast, an RFP or PAR is a “call for proposals” that addresses a particu- lar need or area of investigation that a working group, committee, or administrator has deemed im- portant. In the latter case, the scientist or engineer must first learn of the opportunity, then respond according to the stated instructions. Indeed, one of the most important aspects of a successful grant submitted in response to a call for proposals is that it is responsive to the announcement. Go to the NIH Web site, www.nih.gov, and search for current PARs. Pick a PAR Exercise 4.1 of interest and read the instructions carefully. Write a three-page summary of the PAR that would be sufficient as an overview of the motivation, scope, and requirements for submission. Exercise 4.2 The National Science Foundation (NSF) funds basic research and training in the sciences and engineering. Go to the NSF Web site, www.nsf.gov, and search for current PARs. Pick an announcement of interest and read the instructions carefully. Write a three-page summary that would be sufficient as an overview of the motivation, scope, and requirements for submission. 64 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg There are three general classes of motivations for any proposal: hypothesis-driven, curios- ity-driven, and technology-driven. No one motivation is more important or more scholarly than another; they are simply different. Hypothesis-driven: The NIH defines a hypothesis as “an educated prediction about the outcome of your study.” Under some programs, the omission of a hypothesis is a major oversight, one that can result in the reviewers suggesting that the proposal is merely a “fish- ing expedition,” that is, a project without clear direction. Curiosity-driven: We have all heard the saying that when asked why he/she climbed the mountain, the climber simply stated “Because it was there.” Curiosity-driven research is the desire to answer a new and intriguing question. Curiosity has been, and will remain, the primary driver of scientific inquiry. Technology-driven: In our increasingly technology-based society, there are many cases wherein the ability to design and build a new instrument is motivation enough to pursue such research. Indeed, in many cases there are excellent opportunities to modify previous designs to address new applications. Regardless of the motivation — hypothesis, curiosity, or technical need — the approach to apply for and secure funding for research is similar. 4.3 THE REvIEW PRoCESS Proposals undergo a two-step review process at the NIH. First, proposals are evaluated for technical merit and feasibility. Second, they are evaluated administratively for funding potential. A committee called a study section, under the direction of a scientific review administrator (SRA), accomplishes the first step; a council accomplishes the second step while attempting to balance the desire to fund the best science and the need to accomplish the fundamental mission of the NIH — to improve the health of people in the United States. Just as we should identify the intended audience before writing a journal article or giving an oral presentation, we should also understand the audience that will read and review a particular proposal. In contrast to many funding agencies, the NIH publishes the names of those constituting most study sections, which enables the applicant to know the audience. In this case, it is prudent to read recent publications by members of the study section to get a feel for their scientific interests and basic perspectives. Although each member of the committee will be asked to score all grant ap- plications for which they do not have a conflict of interest, only three to five individuals generally read each application in detail. These individuals are referred to as the primary reviewer, secondary reviewer, and discussant(s); they are selected based on the closeness of their technical expertise to PRoPoSAlS AND gRANT APPlICATIoNS 65 that of the proposal, as revealed primarily by its title and project summary. Recalling that we use the NIH R01 herein mainly to illustrate issues that are important in preparing a proposal, a graduate student would similarly be well advised to know the composition of his/her committee and to read recent papers by these individuals to anticipate what types of questions might arise. Whether or not one knows the composition of a review panel, perhaps the most important things to know are the criteria that the panel will use to evaluate the proposal. Again, we use the NIH criteria, but the need to be familiar with such criteria would even apply to a master’s or doc- toral research proposal, which a faculty committee would evaluate during a proposal defense. At the NIH, the evaluation criteria include1: Significance: Does the study address an important health problem? Approach: Are the design and methods appropriate to address the aims? Innovation: Does the project employ novel concepts or methods? Investigators: Are the investigators appropriately trained? Environment: Will the scientific environment contribute to success? Overall evaluation: Will the study advance health care or medical science? Additional considerations of importance during a review include whether a proposed human or animal research protocol respects current guidelines; before beginning any such study, a local insti- tutional committee (e.g., IRB or IACUC) must evaluate and approve such protocols, but this need not be completed before submission. Similarly, reviewers will address whether the proposed budget is justified. We focus here, however, on the scientific aspects of the review enumerated above. In- deed, because reviewers are asked to comment specifically on how well an applicant addresses these criteria, it can be helpful to the reviewer, and thus the applicant, to include succinct, highlighted statements that address significance and innovation in particular. Because each reviewer can interpret what is meant by significant, innovative, or appropriate, it should not be surprising that different reviewers often have very different opinions with regard to the value of the same proposed research. Hence, the applicant should try to write in a way that engages different people, noting in particular that not all reviewers are experts in the specific area proposed. Rather, it is expected that good scientists and engineers can recognize good work when they see it; a key challenge, therefore, is to help the reviewer appreciate the overall objective, sig- nificance, logic of the methodology, and innovation of the proposed work from both a general and a problem-specific perspective. This may be even more important in cases where the reviewer has 1 Portions of this discussion are based on Proposal Writing: The Business of Science by Wendy Sanders, then at NIH (www.wm.edu/grants/PROP/sanders.pdf ). 66 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg expertise in the proposed area but a different scientific opinion. In this case, the need is even greater for convincing, objective arguments. There are, however, a number of things that all reviewers appreciate. For example, because reviewers are often asked to review multiple proposals (e.g., 8 to 12), it is important to make the proposal easy to read and understand. Rather than using a small font or small figures to fit more infor- mation into the same space, use larger fonts and ample figures to aid the reader and write clearly and concisely to increase the value of what is provided. Indeed, this brings us back to the importance of Chapter 2. Note, therefore, that in a 1987 publication of the NIH, entitled Helpful Hints on Prepar- ing a Research Grant Application to the National Institutes of Health, one reads Try to develop a clear, concise, coherent scientific writing style. A few guidelines that may prove useful include: (1) using the active voice, which is more direct, less wordy, and less confusing than the passive voice; (2) keeping together related ideas and in- formation, for example putting clauses and phrases in sentences as close as possible to the words that they modify; (3) simplifying and shortening overly long and involved sentences and paragraphs; and (4) eliminating redundant and awkward words, phrases, and sentences. Additional, subtle things can likewise make it easier for the reviewer. For example, although citing the many references numerically (often 100 or more) can save space and thus enable the applicant to include additional information, this forces an educated reviewer to refer back continually to the references to determine what work has been cited. It can be constructive, therefore, to cite refer- ences by name, for example, Smith et al. (1999) or (Smith et al., 1999) rather than [20], for the reviewer may know of and respect the work of Smith and colleagues. Similarly, recall that schematic drawings, images, figures, and tables can each be worth a thousand words if done well. Indeed, many reviewers will first skim through an application by paying particular attention to these visual aids. For this reason, it is useful to provide descriptive legends so that the reviewer does not have to search the text to find the meaning and importance. Because of the importance of the accompany- ing text, however, it is also good practice to cite the schematic drawings, images, figures, and tables using boldface type to enable the reviewer to locate easily that part of the text that discusses each figure (e.g., boldface figure 1 and Table 1 are much easier to identify quickly in the text than are Figure 1 and Table 1). Although they should be kept to a minimum, introducing key abbreviations in boldface also enables a reviewer to find them much more quickly in the text, for example, nitric oxide (No) versus nitric oxide (NO). The key, therefore, is to keep the reviewer’s perspective in mind at all times and not to compromise the use of effective devices and strategy because of stated limitations on the number of pages allowed – concise writing will generally provide the extra space needed to include all the necessary information. PRoPoSAlS AND gRANT APPlICATIoNS 67 The NIH Web site, www.nih.gov, has specific instructions for writing a K-series Exercise 4.3 grant application. Write a three-page summary that would be sufficient as an overview of the moti- vation, scope, and requirements for submission of such a grant application to the NIH. 4.4 THE NIH R01 gRANT As noted previously, the R01 grant is but one of many funding mechanisms administered by the NIH. One can obtain information about the other types of grants from the NIH Web site (www. nih.gov), but we consider here the format for the R01 because it represents well how to design an effective application. The R01, or single investigator grant, consists of a cover page, brief description (project sum- mary) and list of primary personnel, table of contents, budget and budget justification, a biosketch for each of the primary personnel, information on resources (i.e., the research infrastructure) that are available to the investigator(s), the main body of the application, and further administrative information. With the exception of the main body of the application, all other information must be provided within appropriate NIH-supplied form pages. Again, see the NIH Web site for instruc- tions and details on the overall grant application package, including form pages. Here, we focus on the main body of the application, that is, the five basic sections that detail the scientific need and proposed method of approach. These sections are: specific aims, background and significance, preliminary results, research plan, and references. Whereas the R01 application currently allows 25 pages, single-spaced, for the main body of the application, other types of NIH applications have different requirements. One of the most important aspects of successful grant writing is to follow the instructions, which includes respecting page limitations and using approved fonts and margins. For example, the current NIH R21 mechanism allows 15 pages, single-spaced, for the main body of the application, whereas the NIH BRP (Bioengineering Research Partnership) mechanism allows 40 pages, single-spaced. Whether 15, 25, or 40 pages, a key to successful grant writing is to write with clarity and conciseness. Indeed, after having written numerous 25-page ap- plications, we have found that trying to provide the same level of detail in a 15-page application is a very good exercise — it forces one to write more concisely. Before discussing in detail each of the five primary sections of the main body of the grant, note that each section should answer a specific question: Specific Aims: What are you going to do? Background and Significance: Why is it important? Preliminary Results: Are you capable of being successful? Research Plan: How are you going to accomplish the work? References: What are the key findings on which you will build? 68 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg As in any good technical document, the writing should flow logically from section to sec- tion and the applicant should reinforce the main ideas throughout. Similar to the situation of multiple authors writing a paper, when multiple investigators write different parts of a proposal, it is important for the principal investigator to ensure a consistent style throughout, including tense. 4.4.1 Specific Aims (1 Page Required) The specific aims section is particularly important; it must capture the reader’s interest, show the need for the proposed research, and detail specific results that will be sought — all in one page. Different applicants use different formats, but a general approach to constructing the specific aims is to begin with two or three short paragraphs that identify the overall problem or long-term goal of the applicant(s) as well as the specific problem that needs to be addressed and why, then list the individual specific aims, and conclude with a brief paragraph that highlights the innovation and overall significance of the work. There is no limitation on the number of specific aims that one can propose, but most R01 applications focus on three to four aims, which sometimes include multiple sub-aims. Just as it can be efficient to begin writing a technical paper by identifying the primary findings, so too it can be efficient to begin writing a proposal by first identifying the specific aims. Indeed, it is often useful to draft the specific aims page and have multiple colleagues provide feedback on the overall plan before beginning to write the remainder of the proposal Specific aims should be just that, specific. Moreover, construct these aims in a forceful way — to quantify, to determine, to design, to prove, to develop, and so forth. Many applicants con- struct each specific aim to test a specific hypothesis; the key objective, therefore, is that the aim is testable. Although one can provide some indication in this first section as to how the aims will be accomplished (e.g., using a particular animal model or data from a particular clinical trial), it is best to focus on methods and approaches in the section on Research Plan. 4.4.2 Background and Significance (3 Pages Recommended) In some ways, the background and significance section can be the hardest section to write well. Whereas one may think of this section simply as a brief literature review and statement of the obvi- ous (e.g., that the problem is significant because a particular number of Americans experience the highlighted disease or problem), it actually must be much more. Within the context of answering the question, “Why is this research important?,” the applicant should critically assess the literature to show convincingly what is unknown and why this lack of understanding is impeding scientific PRoPoSAlS AND gRANT APPlICATIoNS 69 advances, improvements in health care delivery, the development of better medical devices, and so forth. In the words of the NIH, there is “a need to identify the gaps” in our knowledge. For example, we may know that a genetic mutation is responsible for a particular disease, but we may not under- stand how this mutation affects the activity of a particular type of cell. Similarly, we may know that hemodynamic factors give rise to a particular vascular pathology, but we may not know how the associated forces induce the changes in gene expression that ultimately cause the disease. Although identifying gaps will often require one to point out shortcomings in previous investigations of oth- ers, we should do this diplomatically. When identifying key gaps in the literature within the background section, one should show convincingly the need for the proposed specific aims. In other words, background should “set the stage” for the research plan. In addition, however, we must remember that not all reviewers will be intimately familiar with the specific area of research, hence also use this section to educate the re- viewer so the he or she can appreciate better the importance of the identified gaps and the proposed method for research. For example, if the study seeks to identify the relative effects of particular cytokines in a disease process, some background on cytokines — their discovery, general activity, half-lives, receptor affinity, and so forth — may help the reviewer appreciate the motivation for the underlying hypothesis. Well-illustrated schematic drawings, flowcharts, figures, and images often add considerably to this section. Finally, remember that this section is entitled background and significance. If one commits three pages to this section, only half of one page will typically be devoted to significance. Never- theless, significance is one of the criteria that the reviewers must address, and the council increas- ingly bases funding decisions on significance. It is useful, therefore, to address in this section the potential impact of the overall project, that is, the importance of filling the identified gaps. To aid the reviewers, the applicant should highlight key points in this section, for example, by italicizing, underlining, or boldfacing the text. Given the overall importance of significance, but limited space in this section, successful applicants are generally very good at weaving the significance throughout the proposal: the last paragraph of specific aims, the significance portion of background and signifi- cance, and the rationale sections in research plan. The challenge, therefore, is to reinforce key points throughout without redundancy. 4.4.3 Preliminary Results (6 Pages Recommended, But Not more Than 9) The primary goal of the preliminary results section is to demonstrate the capability of the principal investigator(s) and assembled team to accomplish that which is proposed in research plan. In many ways, this is the easiest section to write; indeed, if you are having difficulty getting started, it is often good to focus first on the preliminary results. 70 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg This section is best written in the style of a results section in an archival journal paper, but with abundant subheadings. Proceed logically by documenting your previous successes on closely related problems (with citations to previous journal publications) or your new results that show explicitly that you can successfully complete the proposed aims. It is beneficial, therefore, to remind the reviewers when such results demonstrate that a specific aim can be achieved or that hypotheses on which they are built are tenable. Like a good results section in a journal paper, this section should contain copious figures, images, equations, and tables that highlight key findings. One of the key challenges can be the decision on how much information to include from past publications because the reviewers have access to such information if so directed. The best advice is to provide sufficient detail on critical methods or findings — that is, make it easy on the reviewer by not forcing him or her to find and read the previous paper — but to refer the reader to original papers for nonessential information that nevertheless may strengthen the argument. Indeed, whereas the NIH used to al- low the applicant to deposit up to 10 key previous papers in an appendix, this is no longer possible if the paper can be found on the Web. Just because a paper can be found on the Web does not mean that a busy reviewer will take the extra time to do so, however; again, it is critical to make the most important information readily accessible within the grant application itself. Because of the importance of team science in biomedical research, most grant applications to the NIH rely on a team of collaborators. Hence, it is also important to demonstrate the capability of the different investigators to work well together just as they will need to do during the proposed project. The best way to demonstrate this is via joint publications, or at least joint abstracts for pa- pers presented at technical meetings. In the absence of such evidence, it is important to show that materials, data, and so forth have already been shared as will be required by the proposed research. 4.4.4 Research Plan (15 Pages Recommended, But Not fewer Than 12) Recall that the primary question that needs to be answered in this section is, “How are you going to accomplish the proposed work?” In conjunction with the specific aims, this section is the most important and thus demands careful attention. Perhaps the best word to remember when writing this section is “detail.” There is no required format for research plan, yet an effective strategy has evolved over the years. Many applicants begin this section with a paragraph that highlights the overall research plan and its importance, sometimes including a schematic drawing to show how the different aims complement one another. Next, they describe the rationale, methods, and expected results/potential limitations for each aim in sequence. Finally, they conclude with a brief summary of the overall proj- ect and an expected timeline to accomplish the project. One small variation on this strategy has also arisen in recent years, due in large part to the extensive but common procedures used in molecular PRoPoSAlS AND gRANT APPlICATIoNS 71 and cell biology. Similar to the format of some technical journals, one can collect detailed methods (often common to multiple aims) at the end of this section, almost like an appendix, so as not to interrupt the flow of the main portion of the section; this allows the interested reader to evaluate the appropriateness of the details nonetheless. Indeed, in some cases, these detailed methods are set apart by the use of a smaller font, which saves some space while emphasizing the importance of the preceding text. If one adopts the most common strategy, then the basic outline for the main portion of this section becomes2: Aim 1. Restate the specific aim exactly from the first page. Rationale. Methods. Expected Results and Limitations. Aim 2. Restate the specific aim exactly from the first page. Rationale. Methods. Expected Results and Limitations. Aim 3. Restate the specific aim exactly from the first page. Rationale. Methods. Expected Results and Limitations. Restating each aim in its entirety reminds the reviewer of the specific goal — to quantify, to determine, to design, to prove, and so forth. Restating the aim in boldface serves as a natural and effective visual cue for organizing this long section; this approach is much less distracting than needless section numbers such as 4.1, 4.1.1, and so forth. Whereas the significance section discussed previously should focus primarily on the importance of accomplishing the overall project, the ra- tionale should focus on the fundamental reason(s) for each specific aim. For example, the applicant should note what important gap in our understanding this specific aim will address and why the adopted approach is innovative. The methods section for each aim is similar to a methods section in an archival paper — it should provide methodological details sufficient to enable the reviewer to repeat the study. For 2 There are many slight variations, however. For example, one could replace the generic methods section with sepa- rate sections on experimental design and data analysis, or one could separate the expected results and limitations section and rename the latter potential difficulties and alternate approaches. 72 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg example, one should not write “the cells will be cultured in an appropriate media.” Rather, one should document the specific media to be used (including vendor), any supplements with appro- priate concentrations, and the temperature and CO2 level. Similarly, one should not write “the governing differential equation will be solved numerically” or “the data will be analyzed for possible statistical significance.” Rather, one should provide details on the specific numerical method and why it is appropriate for the expected class of differential equation, and similarly one should provide details on the specific statistical tests, including post hoc testing, why they are appropriate, and the levels of desired significance. Again, the operative word in this section is detail, assuming of course that the methods are both appropriate and proven. Although NIH-funded research does not need to be hypothesis-driven, one should always anticipate the results. It is thus prudent to discuss why you expect such results, which actually al- lows one to justify further the importance of the aim. Although results should be new, it is always good to cite related studies that provide further confidence that the aim will prove successful and important. Similarly, although methods should be chosen and justified carefully, it is always possible in science and engineering for difficulties to arise that prevent one from conducting the experiments or analyses as originally planned. There is also a need, therefore, to anticipate such difficulties and to have reasonable contingency plans. Just as in the discussion of an archival journal paper, however, one must achieve the proper balance in identifying potential pitfalls while not implying that the aim will be very difficult to achieve as planned. It is wise to discuss the presentation of this balance with a valued colleague. Finally, it is useful to conclude the research plan with a detailed timeline showing the antici- pated duration of each part of the project and how the different parts will progress together, per- haps in different laboratories. It is also good to provide a single paragraph that concludes the grant — remind the reviewer what the key gaps are in the literature and how the present study will fill these gaps using innovative approaches that promise significant findings. 4.4.5 References The reference section was limited to four pages in the past, but there is currently no such page limitation. Nevertheless, one should not seek to compile an exhaustive list of references; it is more important to be selective, focusing on the key papers that support the need for the research and the methods used to address this need. Similarly, there is no required format for references except that each must include the list of authors, year of publication, title of the work, the publisher, or journal title, volume, and inclusive pages. Because reviewers are typically familiar with the proposed research area, and thus the key authors in the field, it can be helpful to list the references alphabeti- cally. Indeed, this is consistent with the aforementioned recommendation to cite by author (e.g., PRoPoSAlS AND gRANT APPlICATIoNS 73 Smith et al., 1999) rather than by number (e.g., [20]), for this eliminates the frustration felt by knowledgeable reviewers who do not want to go back and forth to the references to see who did what. Because of the availability of research papers through the Web, some applicants also provide links to enable the reviewers to download key references easily. 4.5 THE PREPRoPoSAl Perhaps the best example of the need to write concisely with clarity is the preproposal. Because of the greater numbers of applicants applying for limited financial resources, many agencies have instituted a two-stage review process. The applicant must first submit a brief preproposal, which an expert panel will review. Based on the findings by this panel, only a subset of full proposals is invited for consideration for funding. The state of Texas, for example, has a competition called the Advanced Research Program (ARP) that is open to any full-time member of the faculty of a Texas institution of higher learning. Preproposals for ARP grants have been limited to 4000 characters (use the word/character counting feature of your word processor to count); this is essentially 11/3 pages, double-spaced, in 12-point font — not a lot of information. Yet, a panel will decide whether to invite the applicant to submit a full proposal, the next important step toward possible funding, based solely on these 4000 char- acters. Again, the need for clarity and conciseness is clear. The format for the ARP preproposal is simple: • • • • Project goals and methods Staff Facilities and resources Education and training Although such preproposals are very short, one clearly wants to communicate information similar to that contained in the much longer R01 application: What are you going to do? Why is it important? Are you capable of being successful? How are you going to accomplish the work? Recalling these simple questions, and noting four sections required for the proposal, it is prudent to think carefully how to partition the essential information within the required format. For example, whereas one uses the preliminary results in a NIH application to demonstrate capability, it may be better to use the section entitled staff in the ARP application. Similarly, whereas it may be appro- priate to highlight the available equipment in preliminary results or research plan in an NIH ap- plication, it may be more appropriate to list these in facilities and resources in the ARP application. Again, the key thing to consider when beginning a grant application is what information you feel 74 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg will best represent you and your ideas. Only then will you be able to decide best how to package this information within the format for the particular agency. SummARy 4.6 The Whitaker Foundation recently closed, but it provided millions of dollars of funding over de- cades to support new investigators in biomedical engineering and to develop new academic pro- grams. They provided reviewers of individual investigator grants with a checklist to ensure that applicants covered a number of critical aspects of research in biomedical engineering. Reasons for scoring a Whitaker application poorly included: No clear hypothesis Mundane/uninteresting Little engineering Little biology Not enough detail Unrealistic/faulty approach Needed collaboration missing Other reasons commonly cited for scoring NIH applications poorly include: Not significant; not innovative; not exciting Unjustified hypotheses Unaware of previous related work Insufficient pilot data Poorly designed research plan; unorganized Overly ambitious One or more aims are poor The success of one or more aims depends on the success of a previous aim Although we should focus on the positives, it is prudent to appreciate causes for failure. In summary, some of the most important reminders for grant writing are: Know the mission of the agency and target the proposal accordingly. For example, you would not think of sending a proposal on cancer research to the American Heart Association. Read a recently funded proposal to the agency to which you are applying. Read the instructions and follow them carefully when preparing your application. PRoPoSAlS AND gRANT APPlICATIoNS 75 Ensure that the proposal addresses an important issue and offers the potential for significant advancement. Remember that your proposal must generally address simultaneously two technical audi- ences: those who are very familiar with the field and those who are less so. Finally, finish early so that colleagues can review the application and provide constructive criticisms that you have time to employ. Only in this way can we avoid the common pitfalls that plague so many proposals. Write a 4000-character preproposal using the Texas ARP format. Select a topic of Exercise 4.4 interest to you, assume you are the only investigator, and describe resources available in your labora- tory or department that would be sufficient to conduct the work. The NIH Web site (www.nih.gov) provides useful guidelines on “How to Write a Exercise 4.5 NIH Grant.” Go to the site, review the material, and prepare a 25-slide PowerPoint presentation that could be used as an introduction to writing and submitting NIH grants. 76 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg APPENDIX (Copy and use this as a quick reference) Specific Aims (What you are going to do?) • • • • The first sentence or two should engage the reader and motivate the need for the work. Briefly note long-term goals/overall hypotheses, then draw focus to the work. State your specific aims (three to four) and how you will achieve/test them. Conclude by emphasizing the novelty and innovation of the proposed work. Background and Significance (Why it is important?) • • • • Review the literature critically, that is, identify foundations and gaps. Do not simply state that A did this, B did that, and C did that. Gaps are important areas that your work will address and fill. Being unaware of important findings in the field does not engender confidence; conversely, citing work from recent meetings or personal communication with leaders in the field suggests that you are on the cutting edge (do not overdo though). Only a few of the reviewers will have expertise in the specific area, yet many will read the proposal. Back- ground should educate the general reader. Significance refers to overall importance and long-term potential rather than the significance of each of the aims — address the latter as rationale in research plan. Preliminary Results (Are you are capable of being successful?) • • This section should do two things: demonstrate capability in the area and demonstrate feasibility with respect to the specific aims. In other words, convince the reader that you are capable of successfully com- pleting the aims as stated. A picture can be worth a thousand words, and so too a table, flowchart, figure, or equation — illustrate the proposal well, taking note that an aesthetically pleasing document that is easy on the eyes is much appreci- ated. Use many subheadings while avoiding the use of numbering sections (e.g., C.1.1, C.1.2) that simply forces the reader to think about a nonessential. Research Plan (How you are going to accomplish the work?) • • • • • One of the most effective strategies is to address each aim separately, but to do so in a consistent, well- ordered manner. For example, for each aim, cover in subsections (a) rationale, (b) methods, (c) expected results and limitations. The rationale of each aim should address the importance of this part of the project and how it fits into the overall/long-term goal. This is also a good time to remind the reader of novelty or innovation. One short paragraph should suffice. Methods for each aim may include materials, equipment, theoretical frameworks, assays, statistical meth- ods, and so forth, all given in sufficient detail. For example, do not merely say that a physiological solution will be used — give the specific composition. Similarly, do not just say that a particular device will be used — give the resolution of the device and any unique capabilities. Whether hypothesis- or curiosity-driven, one should know what to expect with regard to findings. Discuss this and note its potential importance. Likewise, one should know what limitations or pitfalls may arise. Noting and addressing them is much better than hoping a reviewer will not think of them; someone al- ways does and this could relegate an otherwise outstanding proposal to a lower score. Finally, remember that detail is the operative word in research plan and that the aims should form a logi- cal, supporting sequence. Tell them what you are going to do, how you are going to do it, and briefly why it is important. • • • • 77 C H A P T E R 5 oral Communication Just as we must write well, so too we must speak well — a belief that is not new to modern science or engineering. According to Boorstin, (1983, p. 395), Bishop Sprat suggested that the goal of the Royal Society of London (founded ~1660) was “not the Artifice of Words, but a bare knowledge of things.” Hence, they extracted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathemati- cal plainness, as they can: and preferring the language of Artizans, Countryman, and Merchants, before that, of Wits, or Scholars. In other words, as Boorstin concluded, “It was not enough that the language of science be simple. It had to be precise — and, if possible, international.” Although audiovisual aids available today are very different from those of the 17th century, the need for simple, clear, and informative presenta- tions remains. Written documents and oral presentations both reflect one’s professional reputation. Yet, the oral presentation is unique in that it can serve as the all-important “first impression.” If a talk is lucid and enjoyable, those in the audience will likely seek out the speaker again; if a talk is poorly organized and boring, it may be the last time that they seek to hear the speaker. The need for excellence in oral presentations is not unique to science and engi- Exercise 5.1 neering. Hence, find a good book on public speaking and read two chapters that are particularly appealing. Write and submit a three-page summary of the main points. Among the many books available, consider the timeless work, How to Develop Self-Confidence and Influence People by Public Speaking, by Dale Carnegie. 5.1 EffECTIvE STylES Carnegie (1956) suggests that four things are essential in one’s pursuit of becoming an effective public speaker: 78 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 1. 2. 3. 4. Start with a strong and persistent drive. Know thoroughly what you are going to talk about. Act confident. Practice, practice, practice. Although these four essentials should not surprise anyone, they should cause some reflection. In particular, just as in writing well and ensuring integrity in the workplace, effective oral presenta- tions do not just occur, even with experience — one must resolve to learn to present well and to continue to improve. Moreover, because of the importance of self-confidence when speaking to either small or large audiences, it is essential to know the subject so well that you could give the talk even if the audiovisual equipment failed or if you forgot your typewritten notes. Finally, the old adage “practice makes perfect” is certainly true, but there is one caveat. One can practice a bad talk over and over, but it need not improve. Rather, one’s practice should include peers constructively criticizing both the technical material and the method of presentation; it is better to make mistakes among friends and to receive helpful suggestions or corrections before the actual presentation. Attend three professional seminars and record seven specific personal habits and Exercise 5.2 seven audiovisual techniques used by the speakers that were particularly effective (four each) or inef- fective (three each). Summarize your findings in a table and submit a two-page report. Many suggest that much of communication is nonverbal during discussions between individ- uals. Do we look the other person in the eye and reveal our interest or do we look at other people or things while they are talking? Do we change our facial expressions appropriately to reveal sympathy or understanding or do we remain stoic? So too in public speaking, nonverbal communication can help make a talk engaging or it can render the attempt boring or, even worse, annoying. By defini- tion, habits are natural and repetitive; they usually arise unconsciously and can manifest nonverbally or verbally. For this reason, it is essential to have peers provide feedback on potentially distracting habits that arise while we speak. For example, if one tends to jingle keys in his pocket when ner- vous, recognizing this problem allows him to remove the keys before speaking, thus removing the potential distraction. Similarly, if one uses a lot of aaahs or uumhs, there is a need to identify these problems and remove them from both formal and informal speech, for we develop new habits through consistency. Indeed, note that we have found that paying careful attention to composing well-written documents also serves to help us speak well. Finally, if one’s hands shake badly during a talk, it is best not to use a laser pointer, which will project exaggerated motions onto the screen. Instead, one whose hands always shake should practice using verbal cues such as “as seen in the first term of Equation 1” or “as illustrated well in the top curve in the left panel.” A laser pointer can be an effective aid if used well, but it can also be very distracting. Indeed, even if held by a steady hand, oRAl CommuNICATIoN 79 a rapidly moving or constantly circling laser pointer can be a significant distraction. Finally, be care- ful not to keep the laser on if you “talk with your hands,” for the audience gets both distracted and concerned when the laser shines across someone’s face or constantly goes from floor to ceiling. Valiela (2001) correctly suggests that effective technical presentations share some common- alities with successful theater. Two prerequisites for good theater are a good story and actors who “connect with” or “relate well to” the audience. A good story in science or engineering requires an in- teresting or important problem to be formulated, then solved in a novel and logical manner. Below, however, we focus on relating the story well to an audience, first by tabulating reminders related to basic techniques and habits of effective presentations. Indeed, although it is essential in science and engineering to have something important to say, as you compare the suggestions below, consider the suggestion of Carnegie (1956) that “It is not so much what you say as how you say it.” Do Do NoT Be confident, appear confident Be arrogant or prideful Be enthusiastic — it is contagious Pace too much Speak loudly, clearly, slowly Speak in a monotone voice Be respectful of questions Ask rhetorical questions Finish early enough for questions Go over the allotted time Maintain balanced eye contact Look only at screen or at a distance Dress appropriately Apologize for dress Use (laser) pointer effectively Circle everything with laser pointer Know your audience Discourage interactions Define terms, use analogies Use jargon, try to impress Minimize nervous habits Assume every talk begins with a joke Why is it important to be or at least appear confident? Why is it important not to Exercise 5.3 be prideful or arrogant? What message will we convey to an audience if we finish early and allow questions? What message will we convey if we go over the allotted time and ignore calls to stop? 80 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg What is the appropriate dress for different audiences? Ask yourself these and similar questions re- garding this tabulated list of things to “do” and “not do,” and write a two-page summary. If possible, conclude the summary with a few overarching statements. Experienced actors tend to be nervous on opening night, and so too experienced speakers tend to be nervous before walking up to the podium. Yet, recognizing that nervousness is natural, indeed expected, allows us to identify ways to minimize its effects and to settle into a comfortable rhythm quickly. For example, an early visit to the room where you will speak will help you to feel more at ease — the environment will not be foreign. If you need to use a microphone and have not done so before, ask the A/V technician if you can test the system before your talk. If you expect to be nervous nonetheless, eat sparingly before the talk to avoid further complications of the nervousness. Having complete command of the technical material will also engender self-confidence, which is the best way to negate nervousness. Remembering the first sentence or two will ensure a good start, which is essential in transitioning from nervousness to confidence. Beginning with an engaging slide will capture the audience’s attention, which will reinforce your confidence (provided you make eye contact with the now engaged audience). Conversely, memorizing a talk word for word can pro- mote nervousness; you may become concerned that you will forget something and lose track of your message. Below we tabulate some reminders related to basic techniques that promote confidence as well as contribute to telling the story well. Do Do NoT Visit the room before speaking Show up late or just before your talk Remember the first sentence Memorize the talk or read it directly Use an engaging first slide Start with a bulleted outline Use slides as your reminders Require audience to read a lot on own Maximize good figures/images Use lots of words and small fonts Be consistent in slide format Mix slides with different backgrounds Use slides to capture attention Use slides to communicate most info Remember the concluding remarks End by saying, “Well that is all I have” Reflecting on these suggestions, it should be clear that we recommend that one use audio- visual aids to support a talk, not to carry it. In other words, the speaker should strive to capture the oRAl CommuNICATIoN 81 audience’s attention so that they look at him/her and only look to the slides when so directed for clarification. Hence, the speaker should use comments like “and thus x is important, as illustrated well in this figure” or “x . . . as can be seen in this image,” noting that a well-used pointer can remind the audience when and where to look. Conversely, detailed text on a slide will usually entice the audience to read on their own and not to look at or listen to the speaker; this situation should be avoided. Use slides primarily to show clear black and white or color images and figures, schematic drawings and flowcharts, equations, and to a lesser degree, tables, each of which should support what is said. Providing a short heading on each slide can indicate the focus of that slide; beginners may also put bullets on the slides as further reminders to themselves, particularly to prompt appro- priate transitions. When referring to figures, start by defining the variables of interest and the axes; when referring to equations, start by defining the meaning of important variables or terms; when using color images, use the different colors as indicators of important features or points. Remember, too, that less information explained well is always better than more information explained poorly. Software programs such as PowerPoint can be tremendous tools when used well. Resist the temptation, however, to use all the “bells and whistles.” For example, having figures fly in from the edges of a slide or animating molecules that come to screeching stops generally distract from the technical content. Similarly, using complex backgrounds, particularly ones with gradients in color, can be less effective overall — some words show up well, while others do not. Remember, too, that some members of the audience may be color blind; appropriate choice of color, particularly when delineating curves in figures, must be given careful consideration. Depending on the fixed lighting in the room, slides having dark backgrounds can excessively darken a room and thereby create a more conducive sleeping environment. For these and other reasons, black print on a white back- ground and color images on a white background continue to be effective for they generally project well, maintain modest lighting in the room, do not discriminate unnecessarily against color blind- ness, and even allow one to use information directly from print versions of abstracts, proceedings, or papers that often appear in primarily in black and white because of considerations of cost. The first slide is traditionally a title slide — it should give a brief (60 to 120 characters) but informative title and list the authors and their affiliations. Many try to add a touch of color by showing the university or business logo or perhaps a picture of a building or scenic area in which the group works. The last slide is traditionally an acknowledgment slide — it should list others who contributed to the work, financial support, and relevant disclosures. Some prefer to read the names and the funding agencies, but it is sufficient simply to list them in most cases. The last slide often remains projected the longest, that is, during the question and answer period, thus it is also a good place to list key references to your work and to provide contact information (e.g., an e-mail address). Consider adopting a common format/master slide, which enables you to use these slides for different talks with minor modifications; having a common format (including font sizes for headings versus text) enables you to insert any slide from a different talk into the present talk with no modification. 82 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Finally, the next to the last slide usually provides a summary of the work or the “take home” mes- sage. It is best to end on a high note, emphasizing the major findings, rather than listing all of the limitations or future needs. Address such needs in response to appropriate questions. Prepare a 15-minute PowerPoint presentation on effective grant writing. Practice Exercise 5.4 the talk, paying particular attention to the time limit. Have two or three peers critique the presenta- tion, then make corrections and repeat the presentation. Prepare a 15-minute PowerPoint presentation on a technical topic of your Exercise 5.5 choice, but do so in a way that that highlights bad presentation skills and personal habits. For ex- ample, use different backgrounds from slide to slide, use small fonts, use long detailed quotes, read directly from the slides, and so forth. Exaggeration often provides an important reminder of what not to do. Prepare a 15-minute PowerPoint presentation on a topic of your choice that ad- Exercise 5.6 dresses an issue having potential ethical consequences. For example, previous students in our classes have discussed embryonic stem cell research, cloning, the use of human subjects in clinical trials, animal research, issues of science and religion, patents, and copyright. 5.2 THE 15-mINuTE PRESENTATIoN Seeing your name appear in print on a journal article generally produces a sense of accomplishment and pride. So too, learning that your abstract or paper has been accepted for a podium presentation at a national meeting produces a sense of excitement. After the initial euphoria, however, you realize that you have to find a way to describe in a short period, often 12 to 20 minutes, a project that you may have worked on for months or years. One is tempted, therefore, to pack as much information into the talk as possible. Surely the audience will be impressed by how much you did, right? As noted above, however, you will generally make a much more positive impression if you present less information well. There is, therefore, a critical need to identify the most important information and to ensure a logical sequence from identifying the problem to interpreting the results and appreciat- ing the significance. Similar to writing a technical paper, a good way to start this process is to collect together all of the figures, images, equations, tables, or other major findings that you may include, then to prioritize and order them in the most logical fashion. This ordering need not be chronologi- cal; in many cases it is best to order the talk in the way that makes the most sense in hindsight. A good rule of thumb is to prepare approximately one slide per allowed minute of presentation, in- cluding the first (title) and last (acknowledgment) slides, which need not be discussed. Moreover, each slide should generally highlight one main idea. Again, we emphasize that the first slide after the title slide should capture the audience’s attention. It is much more effective, for example, to oRAl CommuNICATIoN 83 show a picture or image that motivates the work than to show a bulleted outline noting that you will introduce the overall problem, describe some of the methods, discuss the results, then draw conclusions — one expects such an approach. Carnegie (1956) suggests multiple ways to capture the audience’s attention immediately: “arousing curiosity, relating a human interest story, begin- ning with a specific illustration, using an exhibit, asking a question, opening with a striking quota- tion, showing how the topic affects the vital interest of the audience, or starting with a shocking fact.” A brief anecdote highlights the importance of the second slide (or first slide when one does not use a title slide) in a PowerPoint presentation. One of the authors was asked to give the second technical talk at an anniversary celebration for the college of engineering. The first technical talk followed directly some brief comments by the president of the university. Out of courtesy, the presi- dent remained for the first talk because it began immediately following his comments. During the subsequent question and answer period, however, the president discretely moved toward the rear of the auditorium. Yet, as he approached the door, it was evident from the podium that the first slide of the second talk had captured his attention — the talk began with “This electron micrograph shows the fine structure of the heart and in particular. . . .” The president remained standing at the door and listened to the entire 10-minute talk. It is very important to capture the audience’s atten- tion quickly. Finishing well is equally important to effective presentations. The conclusion is often that which the audience remembers best. Although Carnegie (1956) wrote on public speaking in gen- eral, not technical communication, it is interesting nonetheless to consider his suggestions for end- ing a talk: “summarizing, restating, outlining briefly the main points you have covered; appealing for action; paying the audience a sincere compliment; raising a laugh; quoting a fitting verse of poetry; using a biblical quotation; building up to a climax.” Regardless of approach, ensure consistency be- tween the opening and closing and try to memorize the ending so that it is thoughtful and forceful. Remember, too, that two of the best words to end with are “thank you.” It is important to embrace the question and answer period. Although many speakers tend to abhor criticism and do not want to be questioned, one can obtain valuable suggestions and guidance during this exchange. Indeed, many times, one will learn something that will improve the quality of a subsequent paper that will be written on the topic of the presentation. Three useful guidelines are: first, repeat the question both to ensure that you address what was really asked and to help the audience hear both question and answer; second, be respectful even if the questioner is antagonistic or if the question is truly a “dumb” question; and third, if you do not know the answer to the ques- tion, say that you do not know. It is best, however, not to answer all questions by stating that you do not know, hence the need for complete command of your subject. Finally, if a questioner tends to be unrelenting, suggest that you would enjoy discussing the issue at the next break. Remember, 84 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg too, that because the question and answer period can be illuminating to both the speaker and the audience, finish the presentation early to allow sufficient time for this important exchange. Although we addressed only the typical 15-minute talk, presentations of other durations should be treated similarly. Indeed, if you become proficient at “telling your story” concisely, it is easy to do so for any specified duration. The one caveat, however, is to remember that you should always present concisely — a longer duration simply means that you should communicate more information, not that you should communicate the same information less well. Remember, too, that it is always good to think ahead about which slides to skip if time is running out or if there is an unavoidable delay or slowdown. In other words, be prepared and be flexible. Prepare a 30-minute technical presentation, on a topic of your choice, using ap- Exercise 5.7 proximately 30 slides. After having given the presentation to your peers, reduce the presentation to 15 minutes without losing any significant technical content. SummARy 5.3 It has been said that “Everyone has but one story to tell, they merely tell it in different ways to dif- ferent people.” We reemphasize, therefore, that one must know the intended audience. Rather than trying to sound scholarly, it is most important to be clear and effective. Avoid jargon; define terms carefully; read faces in the audience to obtain a sense of their understanding and engagement. Recall from Chapter 1 that individual differences can bring a freshness and vitality to a field; individual personalities can generate excitement and interest. Each person should develop a style that is most effective and natural for him or her. The guidelines presented in this chapter are sim- ply that, guidelines. We encourage the reader to consider or try the ideas presented here, but more importantly, to pay close attention to styles and techniques used by different speakers in different settings. You will be well served to take note of what is most effective and what is most ineffective, and to adjust your style accordingly. • • • • 85 C H A P T E R 6 Authorship Seeing your name on your first published paper may be one of the most exciting moments in your career. Many students thus enter a discussion on authorship focusing on the question, “How do I get my name on a paper?” In our experience, the more important and difficult questions include when and how to keep your name off a particular paper and how to negotiate questions of authorship among your collaborators in a multi-investigator project. If you have authored a journal article, answer the following questions about your Exercise 6.1 experience before proceeding. If not, interview someone who has authored a journal article and report their answers. 1. 2. 3. 4. 5. How did you become an author on your first paper? What was your contribution to that paper? Who decided whose names would appear and in what order? At what point during the research did you first discuss authorship? Did you sign a legal agreement as an author, and if so, to what did you agree? 6.1 THE SluTSKy CASE Many widely publicized cases of research fraud, plagiarism, and other forms of misconduct exist in science and engineering. Discussing these cases often sheds light on important aspects of ethics in science and engineering. We will take as an example the case of Dr. Robert Slutsky, a member of the faculty at the University of California–San Diego School of Medicine in the 1980s. While in many ways similar to other cases of plagiarism or data fabrication, the Slutsky case is unusual for two reasons: the university committee, formed to investigate allegations of research fraud against Dr. Slutsky, included a philosopher as well as medical school faculty, and the committee attempted to draw broader conclusions about this type of fraud. The committee ultimately published its find- ings in an article in The New England Journal of Medicine (Engler et al., 1987). We briefly review details of the case below, but this excellent article is so integral to our discussion that it should be read before proceeding. 86 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Read the journal article regarding the Slutsky case [Engler RL, Covell JW, Fried- Exercise 6.2 man PJ, Kitcher PS, Peters RM (1987) Misrepresentation and responsibility in medical research. N Engl J Med 317: 1383–1389] and list the five aspects of the case you find most surprising: 1. 2. 3. 4. 5. Dr. Slutsky, then associate professor of radiology at the University of California-San Diego, was being evaluated for tenure when a member of the tenure committee noticed an apparent dupli- cation of data in two published research papers. The ensuing investigation by a faculty committee revealed a number of striking facts of interest for our discussion. First, the committee found clear evidence that Dr. Slutsky reported fictitious experiments and statistical analyses, reported incorrect procedures and statistical analyses, and listed colleagues as coauthors who did not contribute to the work and in some cases did not know about the publications. Second, the normal peer review pro- cess did not detect any of these concerns in the fraudulent papers, and some of the journals refused to retract the fraudulent papers upon notification of the committee’s findings unless Dr. Slutsky agreed to the retractions. Third, at one point during the period under investigation, Dr. Slutsky was publishing a paper every 10 days, including many in prestigious journals. Fourth, much of this work was apparently sound; the committee established the validity of 77 of the 137 publications they reviewed and classified only 12 publications as fraudulent. Finally, the investigation revealed missed warning signs over the course of Dr. Slutsky’s early career: several of his colleagues and at least one journal editor questioned the validity of manuscripts they read, and some recommendation letters for his original appointment to the faculty expressed concerns about the validity or quality of his research. 6.2 BASIC CoNvENTIoNS Before discussing common problems regarding authorship, it is helpful to review current conventions. These conventions will be familiar to practicing scientists and engineers but not necessarily to under- graduate and graduate students, particularly those who have not yet authored a journal paper. 6.2.1 order of Authors The order of authors on an archival journal paper usually has special significance, but conventions vary by field and occasionally by journal. In most biomedical science and engineering journals, the AuTHoRSHIP 87 first author is usually the one who performed most of the work; this person is often a graduate stu- dent or postdoctoral fellow who worked on the project described in the publication. Designation as first author is so important that footnotes are sometimes used to indicate equal contribution by two or more “first” authors. The last author is typically the senior investigator who conceived, guided, and financially supported the project. The ordering of all other authors is generally of less signifi- cance, as we assume that their contributions were less but otherwise important. In stark contrast, some fields encourage an alphabetical listing of authors. Notwithstanding customary variations by field and journal, surveys of scientists and engineers reveal widespread disagreement and confusion regarding conventions for authorship (Bhopal et al., 1997; Tarnow, 1999). 6.2.2 Submission Agreement Most journals ask the author(s) to sign a submission agreement. Typically, this agreement transfers copyright to the publisher and asserts that the author(s) will pay any page charges levied by the journal as part of the publication process. In addition, this agreement usually asks the author(s) to verify the accuracy of the submitted manuscript and that it has not been published by or submitted to another journal. Much more variable are policies regarding who must sign the agreement. In many cases, the corresponding author (i.e., the person who submits the manuscript and lists his/her con- tact information in the final version) can sign on behalf of all coauthors. This explains, in part, how Dr. Slutsky submitted some papers without the knowledge of some people he listed as coauthors. Conversely, some journals require all coauthors to sign the submission agreement; it appears that Dr. Slutsky subverted this requirement by forging the signature of some coauthors (Engler et al., 1987). 6.2.3 Publication Impact One’s record of publication is critically important when applying for jobs, grants, awards, or pro- motion and tenure. In any discussion of authorship, it helps to understand how reviewers evaluate your published works. Obviously, one important factor is the number of publications, but this is far from the only consideration. For example, some journals are more selective and more widely read than others; publications in these journals are typically valued more in an evaluation. Such assess- ments are subjective, however, because investigators in the same field may have different opinions on the relative quality of the relevant journals or their ability to assess the quality of a particular work. For example, a complex mathematical model of a biological process will likely receive a more rigorous review by a mathematics journal than by a biology journal even though the latter may have a larger readership. In an attempt to weigh the quality of a journal more objectively, one can define quantitative metrics. One such metric is the “impact factor,” a measure based on the idea that more frequent citations of a journal’s articles implies a greater impact by that journal on its field. Scientific information service companies, such as Thomson Scientific, compute and report impact factors 88 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg for a wide range of journals (to obtain links, search for “Journal Citation Reports” or “ISI Web of Knowledge”). These services also track the number of citations of particular publications, and some reviewers use the number of citations as a surrogate measure of the impact of a publication. Even if one relies on a metric such as impact factor to value a publication, most publications have multiple authors. The question then becomes, “How much credit should each author receive for a given publication?” For example, consistent with conventions discussed above regarding the order of authors, the first and last authors typically receive most of the credit for any biomedical publication. When someone evaluates your publication record, they will notice not only the number of publications and the quality of the journals but also how often you appeared first or last in the au- thor list. Note, however, that even if your name appears last on a publication, implying that you were the senior author most responsible for the ideas, if a well-recognized senior colleague also appears on the paper, other scientists may assume that your senior colleague deserves much of the credit for the ideas. This issue becomes especially relevant in multi-investigator collaborations, which are more common in today’s research. 6.3 CommoN PRoBlEmS In June 2005, an article in the journal Nature, titled “Scientists Behaving Badly,” reported results from a survey of more than 3000 NIH-funded scientists regarding the frequency with which they engaged in a range of questionable research practices (Martinson et al., 2005). While only 0.3% admitted to falsifying research data within the previous 3 years, many more admitted to some of the other problems highlighted by the Slutsky case, such as publishing the same data in two or more publications (4.7%). Particularly relevant to our discussion is that 10% admitted inappropriate as- signment of authorship within the past 3 years. Strikingly, such misbehavior was more common among mid-career scientists (12.3%) than early-career scientists (7.4%). Read the article “Scientists Behaving Badly” [Martinson BC, Anderson MS, de Exercise 6.3 Vries R (2005) Nature 435(9): 737–738] and formulate three hypotheses why mid-career scientists are more likely to engage in admittedly inappropriate behavior than early-career scientists. Com- pare and discuss your hypotheses with a colleague. 6.3.1 Expectations The importance placed on publications as a measure of career progress can create substantial pres- sure to publish, particularly for tenure-track junior faculty. Managing this pressure begins by devel- oping clear and reasonable expectations. AuTHoRSHIP 89 For Ph.D. students and postdoctoral fellows. Answer the following questions re- Exercise 6.4 garding the number of publications you expect a junior faculty member to produce in your field. First, estimate the number of publications one might produce (or you did produce) during doctoral study. Next, estimate the number of publications one might produce (or you did produce) during 3 years of postdoctoral research. Finally, estimate the number of publications a successful junior faculty member in your field should produce during the first 5 years of his/her career. Now, perform two different “reality checks” on your estimates: 1. 2. First translate your estimates of productivity into rates (number of papers per year, which may be < 1), noting that most papers tend to be produced near the end, not beginning, of one’s study. Then, use these rates to compute how many graduate students and/or post- doctoral fellows your model junior faculty member would need to employ if each paper was coauthored by only one student or fellow. Do you think these numbers are reasonable? Which of your estimates would you adjust based on this check? As a second check, ask a senior faculty member in your department to give the same three estimates. How do they compare to your estimates? If possible, discuss any discrepancies with a senior colleague. One thing that seems apparent in the case of Dr. Slutsky is an unrealistic expectation (or perception of external expectations) regarding productivity. No reasonable person expects a junior faculty member in any field to produce a paper every 10 days. Yet, Dr. Slutsky apparently felt pres- sure to improve upon the number of valid publications (at least 77 in 7 years according to the au- thors of the report in the New England Journal of Medicine) through various types of research fraud. Clearly, there is a need for open discussion of authorship and productivity with everyone involved, from students to advisers to department chairs. Only in this way can we develop and clearly express realistic expectations regarding the number and quality of publications. 6.3.2 gift, guest, and ghost Authorship Gift authorship entails granting authorship to a person who did not contribute directly to the work (Davidoff, 2000). As an example, a new trainee discovered upon her arrival in Dr. Slutsky’s labora- tory that she was an author on a paper she knew nothing about (Engler et al., 1987). Why would someone do this? Misplaced generosity could be one motivation — colleagues may believe they are doing you a favor by listing you as an author on a publication. Another possible reason could be the pressure to show productivity by trainees who are supported by certain types of grants. Regardless, gift authorship could associate your name with a fraudulent paper, as in the Slutsky case. Cases of 90 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg research fraud are rare, however; embarrassment is a more likely concern if you consider the paper to be of poor quality, you disagree with its conclusions, or you are forced to admit (e.g., during the question and answer period after a scientific talk or during a discussion with a colleague you respect) that you did not contribute to the work. One of the most difficult situations related to authorship is receiving an unwanted gift au- thorship, especially if you are a junior colleague of the person conferring it. What choices did the trainee in Dr. Slutsky’s laboratory have when she was told about the gift authorship? The paper was already published, thus any change of authorship would have involved admitting the situation to the journal. Asking your new boss to admit publicly to conferring gift authorship may not be a good way to begin your research career, nor is contacting the journal directly and triggering an in- vestigation. Few would suggest driving a scientist from his faculty position for an isolated incident of gift authorship. Yet, some early action might avert subsequent, more serious problems. Two points can be made here. First, there exists an anonymous procedure at most universi- ties and companies for seeking advice if you encounter a situation such as gift authorship; typically, an officially designated ombudsman will help you resolve conflicts and difficult situations. Second, an adviser who puts you in a precarious situation is likely not the right adviser for you. The conse- quences of confronting a situation like this early are not likely as bad as they seem, while the conse- quences of avoiding confrontation are likely much worse. Studies of scientific authorship often define guest authorship separately as listing a colleague who did not contribute directly to a paper in the hope that his or her reputation will enhance the odds of acceptance for publication (Davidoff, 2000). Combining gift and guest authorship into a single category, termed honorary authorship, Flanagin et al. (1998) surveyed the authors of papers in six major biomedical research journals (including Annals of Internal Medicine, JAMA, and the New England Journal of Medicine) and found that 19% of those publications had evidence of honorary authorship. They also found that 11% had evidence of ghost authorship, defined as the omission of an author who contributed significantly to the publication. Ghost authors may be junior colleagues who simply did not receive the credit they deserved, but they may also be professional medical writers hired to write articles anonymously or even representatives from companies with a financial interest in the findings who wish to hide their involvement. A 1993 survey of postdoctoral research fellows at the University of California–San Francisco suggests even higher rates of inappropriate practices: 38% of the respondents thought that at least one coauthor on their papers was undeserving, while 20% thought they were excluded on at least one paper for which they deserved authorship (Eastwood et al., 1996). One of the most telling results of this particular survey was evidence that trainees who have unfavorable initial experiences with authorship lose faith or interest in the integrity of the system. Overall, 32% of the fellows surveyed said they would be willing to list an undeserving author on a paper if it would enhance the probability of publication or otherwise benefit their career; that number jumped to 72% among those who reported a previous adverse experience with authorship. AuTHoRSHIP 91 6.3.3 financial Support Accepted practice regarding authorship varies by field and by culture. While relatively rare, some strongly hierarchical departments expect that the chair of the department should be listed as an au- thor (possibly even senior author) on every paper, regardless of contribution. Such an environment may pose a challenge for younger investigators who disagree with the policy, especially if following the expected procedure weakens their own publication records by preventing them from assuming senior authorship on their own work. It is important to recognize and discuss cultural variations when working in a group composed of colleagues who trained under different systems and when collaborating internationally. 6.3.4 Quid Pro Quo Nearly everyone agrees that gift authorship is wrong, yet there are many related cases where a col- league who has contributed to a study in some way requests or expects authorship in return. The most common situation involves valuable resources such as antibodies or transgenic mice. Consider a situation where an investigator devotes significant time and energy developing such a resource, then publishes a paper describing it. Colleagues then ask for access to the resource for studies they wish to conduct. It is not uncommon for the investigator to offer to provide access in exchange for authorship on the resulting paper(s). This basic situation has unlimited variations. At one extreme, a request for a resource can lead to a genuine collaboration on a new study that is reflected accurately in coauthored papers de- scribing the results. At the other extreme, however, the situation can approach scientific extortion, with the original developer of the resource demanding authorship in exchange for access, knowing few colleagues will deny the request due to the substantial time and effort required to replicate the resource. While many who disagree with such arrangements accept them as a fact of life, some de- fend the practice, regarding authorship on related papers as appropriate reward for developing the resource. Most believe that the appropriate reward for any innovation, whether a new equation, method, antibody, or transgenic mouse, is citation, not authorship. Colleagues who employ the innovation cite the original publication, giving appropriate credit to its originator. In the case of an equation or its solution, the original paper contains everything colleagues need. In the case of a transgenic mouse, the original paper contains only a description of how to generate such a mouse. Is it reason- able to expect the scientist who first generates the mouse to send mice to any colleague who requests 92 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg them? Does the answer change if federal or state resources funded the original development of the mouse, as with most biomedical research? These and related questions about access to resources and data from publicly funded science are currently a topic of vigorous discussion in the scientific com- munity; they are explored again in Chapter 8. 6.3.5 Students and Technicians We have highlighted some common problems related to authorship beginning with the simplest and least controversial and proceeding to the more complex and controversial (and therefore inter- esting). Next, we consider the key question of who should or should not be an author on a particular paper or, to generalize the problem, of exactly what qualifies someone to be an author. Before pro- ceeding, use the following exercise to define better what you think should be considered in making decisions about authorship. List up to five minimum criteria needed to justify authorship on a scientific or Exercise 6.5 engineering paper. According to your criteria, would a laboratory technician or an undergraduate student who orders supplies and prepares samples qualify as an author on papers produced by the laboratory? What about a technician or student who runs tests according to instructions and turns over the data for analysis? What about one who runs tests, analyzes data, and makes a figure for the paper but does not write any of the text? 1. 2. 3. 4. 5. As this exercise illustrates, it is remarkably difficult to articulate general guidelines for author- ship that provide practical guidance. Common responses to this exercise are that each author should make a “significant” contribution to the work, that each author should make an “essential” contribu- tion to the work, or that each author should make an “intellectual” contribution to the work. This last point illustrates general agreement that a student or technician who simply prepares samples or collects data without a true understanding of the project should be acknowledged, not listed as an author. Nevertheless, none of these statements provides practical guidance. To increase our appreciation of this situation, it is useful to consider the contribution of a potential author against the backdrop of what is required to produce a paper. First, one must gener- ate an idea or identify a problem, then plan an approach to address the problem. Next, one must AuTHoRSHIP 93 perform the study and collect the data or solve the equations. Analysis and interpretation of the data or results then precedes writing the paper, which typically requires a comparison to previous related findings. The example of a student or technician who only collects data or runs a computer code as instructed suggests that an author should be involved in more than one aspect of the study; if that person also analyzes data and summarizes the results for the paper, the claim to authorship would be stronger. Requiring involvement in multiple aspects of a study would limit the quid pro quo arrangements discussed above to cases where involvement went beyond providing a particular resource. It seems reasonable to stop short of requiring every author to participate in every phase, however. For example, most investigators would support authorship for a person who joined a group after the study was conceived and planned but otherwise was involved deeply in all aspects of a study. The concept that all authors should be involved in multiple aspects of a study (e.g., design, experiment, analysis, interpretation, or writing) seems reasonable. Nevertheless, your list from Ex- ercise 6.5 likely includes additional criteria. Must every author understand everything in the paper? Must every author read the final version before submission? Recalling that some of Dr. Slutsky’s coauthors experienced the stigma of being authors on fraudulent papers, should every author review the original data that form the basis for the conclusions? Each investigator must wrestle with these questions over the course of a career; your answers to these questions may well evolve with experi- ence. It is important to think carefully about these issues early in your career so that you can develop practices consistent with the ethical standards you set for yourself. 6.4 CuRRENT STANDARDS AND EmERgINg IDEAS Many people have thought about ways to improve upon practices used to define authorship in the archival literature. In particular, some professional societies and journals have introduced simple practices that reflect more accurately the contributions of those involved in a publication. These practices also have the beneficial effect of forcing increased discussion among coauthors on issues related to authorship. 6.4.1 International Committee of medical Journal Editors Standards The International Committee of Medical Journal Editors (ICMJE) evolved from meetings that be- gan in 1978 to establish guidelines for the format of manuscripts submitted to medical journals. This group regularly revises and disseminates the document “Uniform Requirements for Manuscripts Submitted to Biomedical Journals: Writing and Editing for Biomedical Publication,” available at their Web site, www.ICMJE.org. This Web site also lists journals that adopted these standards. The uniform requirements continue to provide guidelines on style and format for articles in biomedical journals and also guidelines on ethical aspects of writing and reviewing journal articles. 94 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg The uniform guidelines provide criteria for deciding who should be an author on an archival paper. Although these guidelines are similar to principles discussed in the previous section, they have provoked objections from many scientists who believe them to be too strict (Bhopal et al., 1997); they are also rarely enforced, even by journals that claim to have adopted them (Davidoff, 2000). Under the ICMJE guidelines, all authors must meet the following three criteria: 1. 2. 3. Substantial contributions to conception and design OR acquisition of data OR analysis and interpretation of data. Drafting the article OR revising it critically for important intellectual content. Final approval of the version to be published. In general, it is difficult to assess whether authors follow (or are even aware of ) these criteria when submitting articles to journals that have formally adopted them. As discussed in Section 6.4.3, one study that attempted to test compliance with these guidelines found that only 56% of authors of articles in a prestigious journal that subscribes to the guidelines actually fulfilled them (Yank and Rennie, 1999). Finally, as another example, the American Heart Association (AHA) publishes multiple out- standing scientific journals dealing with cardiovascular health and disease. Among other things, the AHA form entitled “Authorship Responsibility and Copyright Transfer Agreement” stipulates that to qualify for authorship, one must have participated in one or more of the following: conceived and designed the research acquired the data analyzed and interpreted the data performed statistical analyses handled funding and supervision drafted the manuscript made critical revisions of the manuscript for important intellectual content Other journals continue to require a simple statement that all authors contributed to the work and agree to its submission for consideration for publication (recall Section 3.1.1). 6.4.2 Author Notification One of the simplest recent innovations is that many conferences and journals now require the submitting author to provide e-mail addresses for all authors, who are notified electronically of the submission of an abstract or manuscript. While no coauthor should ever learn of a submission for AuTHoRSHIP 95 the first time through such an e-mail, this is not an infrequent occurrence. Notification allows an investigator who was unaware of a submission to raise objections while the abstract or manuscript is under review, rather than being forced into the much more difficult position of addressing the issue after acceptance or publication. Notification may also increase the odds that the submitting author will discuss the submission with all coauthors in advance to avoid surprising colleagues. Electronic notification is not a foolproof defense against those who are willing to forge the names of coauthors on a submission agreement. Those intending to deceive could easily construct false e-mail accounts for coauthors, but at least this would require more effort than simply forging a signature. 6.4.3 Specifying Contributions A more radical approach is to discard the traditional premise that all authors bear equal responsi- bility for the content of an archival paper. Instead, some journals now ask authors to specify their contributions to an article at the time of submission. In theory, responsibility for integrity of the research partitions accordingly, with authors only responsible for ensuring the validity of their work. In addition, most journals require at least one author to declare responsibility for oversight of the entire article. Specifying individual contributions simplifies attribution of responsibility or blame. It could also allow societies or journals to impose more uniform standards for authorship. For example, a journal could refuse authorship to anyone unwilling to take responsibility for more than one aspect of a publication. Partitioning responsibility may prove the only practical solution for large multi-investigator projects. Nevertheless, this approach changes the traditional understanding of an archival publication and meaning of authorship. It could have the disadvantage of weakening scientific collaborations, as papers increasingly become a compendium of individual miniprojects. Such a weakening is certainly contrary to what most of us envision when we discuss the need to foster more and better multidisciplinary collaboration on today’s increasingly complex scientific and engineering problems. One of the first journals to ask authors to specify their contributions as part of the submis- sion process was the medical journal The Lancet, a signatory to the ICMJE Uniform Requirements for Manuscripts Submitted to Biomedical Journals discussed in Section 6.4.1. During the first 6 months after authors began specifying contributions, Yank and Rennie (1999) studied the reported contributions with three goals: to determine how author contributions related to position in the author list; to determine whether self-reported author contributions fulfilled the ICMJE guidelines; and to determine the degree of overlap between the contributions of those listed as authors and those listed in acknowledgments. They made the generous assumption that all authors read and ap- proved the final version (ICMJE criterion 3), but they found that only 56% of authors fulfilled the 96 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg other two criteria. Specifically, 78% of authors reported participating in conception, design, analysis, or interpretation (ICMJE criterion 1), a finding that was consistent for those who were listed first, second, third, or last in the author list. By contrast, 65% reported participating in writing or revis- ing the paper (ICMJE criterion 2), with a range from 84% for the first author to 54% for the third author. The Yank and Rennie study contains other interesting findings, hence we recommend this study as a basis for a journal club or group discussion on authorship. 6.4.4 Quantifying Contributions A natural response to uncertainty, especially among scientists and engineers, is to introduce quan- titative measures. In addition to specifying what each author did, some have advocated specifying each author’s percent contribution to the overall work. This is probably most common during tenure evaluation, when a junior professor under consideration for tenure estimates his/her percent con- tribution to each published paper. This is a difficult question to answer, especially during a tenure evaluation, because the desire to report strong contributions for yourself may tempt you to devalue the contributions by your coauthors. Typically, a group of collaborators who estimate the contribu- tion of each group member produce percentages greater than 100% unless some mechanism (such as an interactive form or pie chart) constrains the total. Another quantitative approach appeared in the biostatistics literature, reflecting the unique role played by many statisticians in research. Statisticians may be involved in design and analysis for many different studies but not directly involved in collecting data, performing experiments, or writing papers for any of those studies. This “specialist” role makes it difficult to apply typical criteria for authorship. As a possible solution to this problem, Parker and Berman (1998) proposed a scoring system to help decide when statisticians should or should not be listed as authors. Their system divides the statistician’s role into three phases of a research project (design, implementa- tion, and analysis) and requires for authorship either a deep involvement in two of the phases or a deep involvement in one and moderate in the other two. They also propose that it is unreasonable to hold a statistician who is listed as an author responsible for the integrity of the entire published article. 6.5 ouR APPRoACH As is common when discussing interesting ethical issues, we raised many more questions than we answered in this chapter. What is most important is that each person utilizes cases and questions such as those presented herein, as well as discussions with advisers and senior colleagues, to establish individual principles about authorship early in a career. It is impossible to do what you think is right if you do not know what you think is right. Once you establish your principles, the question remains of how best to put them into practice. In this section, we offer some of our own experiences as ex- amples of how to apply a set of principles to the everyday practice of science and engineering. AuTHoRSHIP 97 6.5.1 Authorship Criteria In our own groups, we expect that all authors on a paper should be involved in more than one aspect of a study, should agree to be listed as an author, and should be given a chance to contribute directly to the final version of the manuscript before submission. Ideally, each new group member and each new collaborator should discuss these criteria at the outset. At the very least, all members of the group working on a particular project must discuss issues of authorship before submitting the first abstract or publication related to that work. This is easiest to accomplish when all authors work at a single location and most difficult when the publication involves collaborators from different depart- ments or institutions. Fortunately, the Internet and track-changes features in most word process- ing applications enable all coauthors to contribute directly to developing manuscripts regardless of physical location. 6.5.2 Predraft group meeting In our experience, one of the simplest and most useful ideas is to convene a meeting of all poten- tial authors to review findings and interpretations as well as to agree on authorship before writing an abstract or manuscript. The senior investigator who is funding or driving the project calls the meeting, inviting all contributors who potentially satisfy the criteria for authorship. In cases of coauthors from multiple locations, Web conferencing or teleconferencing becomes a vital resource. At the meeting, each contributor presents results to the group and answers questions. Then, the group discusses proposed figures, the proposed author list, and the choice of journal for submission. Notwithstanding the effort required to bring everyone together for an hour or two, this approach allows all potential authors to gain confidence in the validity of the studies, to ask questions and comment on the results and their importance, and to voice any concerns about the content of the paper, interpretation of the results, or author list before the bulk of the writing begins. This ap- proach also helps improve the paper by subjecting the results to a round of “internal review,” helps graduate students and fellows practice oral presentation skills, and helps strengthen relationships among collaborators. 6.5.3 final Review and Approval Once a manuscript has become a final draft, it is essential for all authors to review and approve the draft before submission. This is also an appropriate time to settle final questions of authorship, 98 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg especially if no previous discussion has taken place. One reasonable approach is to list as authors on the draft those colleagues you believe merit authorship, but to include in the distribution list other people who have made some contribution and may feel they should be authors. Ask each recipient whether they feel they deserve to be an author on the paper (or whether they agree with the pro- posed author list) and whether they have any comments or suggestions for the manuscript before submission; follow up with those who do not reply. Like the predraft group meetings, this step en- sures that all authors are aware of the content of any publication bearing their names and provides a round of internal review to improve the manuscript before external peer review. Most investigators basically agree on the rules of authorship and are willing to follow them. Inappropriate attribution of authorship usually reflects someone succumbing to real or perceived external pressures or simply not giving the matter sufficient attention, rather than attempting to deceive. In general, our experience with regard to questions of authorship has been heartening. In most cases where a claim to authorship appeared marginal to us, our colleagues have responded to our question of whether they want to be an author, as we would have hoped, by stating that their contribution merits an acknowledgment rather than authorship. Many have provided help- ful comments on a draft even after stating that they did not wish to be listed as authors. Perhaps surprisingly, our most difficult experiences have typically involved refusing authorship offered by a colleague rather than denying authorship to a colleague. 6.5.4 Default Position for Abstracts The process described above is time-intensive. A confounding situation that can arise, therefore, is the last-minute abstract for consideration for presentation at a technical meeting. Such abstracts are short and typically have a fixed deadline for submission, thus they are often written just before the deadline. On such short notice, the collaborators involved in a particular study may not be available to meet to discuss the abstract or even to read, revise, and approve the final submission. In such cases, it is best to agree ahead of time on a “default” position for last-minute abstracts — if contributors cannot be reached to review an abstract on short notice, do they prefer to be listed as an author and review the abstract after submission or do they prefer to be left off the author list? We recommend the latter approach, for it is dangerous practice to include authors who have not read, revised, and approved the abstract before submission. We also note that it is appropriate to delay submission when a coauthor cannot be reached; there will always be other meetings and thus other opportunities. • • • • 99 C H A P T E R 7 Recordkeeping Scientists and engineers must keep records of their work, using a combination of laboratory note- books, images, file folders, and electronic data. Similarly, clinicians must record each step of di- agnosis and treatment in a patient’s medical records. Although keeping precise records may seem mundane, those records are central to many important decisions in science, engineering, medicine, and public policy. Exercise 7.1 not yet worked in a research laboratory, answer the following questions before continuing: Based on your experience in a research laboratory, or a laboratory course if you have 1. 2. 3. 4. 5. Did you maintain a laboratory notebook? If yes, what instructions were you given about what to record? If no, where did you record information related to the work? Did your supervisor review your notebook or records? If yes, how often? If someone tried to reconstruct your work from these records, what percentage could they reconstruct without your help? If possible, compare your answers to those of a colleague who has worked in the pharmaceutical or medical device industry. It is likely that your answers will differ substantially; discuss the most likely reasons for this. 7.1 THE SluTSKy CASE REvISITED In Chapter 6, we considered the case of research fraud by Dr. Robert Slutsky, as described in a 1987 article in the New England Journal of Medicine (Engler et al., 1987), and we asked what aspects of this case were most surprising. In response to this question, many cite the following paragraph from the section entitled “What is Fraud?” After due consideration of what requirements and standards applied, the . . . commit- tee adopted the position that the ethos of scientific research requires that hypotheses be validated before they can be accepted and that claims to observation be open to 100 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg scrutiny by peers. The legal principle of “innocent until proved guilty,” which might be rephrased as “assume correct until proved wrong,” does not apply to scientific work; the burden of proof remains with those claiming new findings. Thus, the authors of a scientific publication that is reasonably alleged to be fraudulent bear the responsibility for establishing the accuracy of their results. Engler et al. (1987) This excerpt should be sobering to anyone involved in research or development. Most of us have lost records to a computer crash, accidentally overwritten a file, lost a notebook, discarded old data, or at times kept less than complete records. If the supporting data are missing and the burden of proof against an allegation of fraud lies with the researcher, an anonymous accusation of fraud from a disgruntled colleague, employee, or student could be enough to support a finding of research fraud and end a career. The proposition that the burden of proof lies with the researcher raises two questions. First, do you agree with the argument that the nature of science and engineering should place the burden of proof on the investigator, or should it rest (as in criminal law) with the accuser? Second, is the burden of proof actually placed on the researcher in current practice? While the first question pro- vokes interesting discussions in any room of scientists or engineers, most are surprised to learn that the answer to the second question is a resounding yes. The Office of Research Integrity (ORI) of the U.S. Department of Health and Human Ser- vices (http://ori.hhs.gov/) performs a range of functions designed to maintain the scientific integrity of biomedical and behavioral research funded by the U.S. Public Health Service (PHS). One of these functions is investigating and issuing reports on scientific fraud or misconduct involving PHS grants. Moreover, to heighten awareness of the importance of scientific integrity, the ORI publishes Findings of Scientific Misconduct (i.e., brief reports summarizing each case and its outcome) on their Web site and within weekly electronic mailings on funding opportunities distributed by the NIH. A review of past cases demonstrates that the burden of proof against an allegation of research fraud does indeed rest with the researcher. As an example, we reproduce below, in its entirety, a Finding of Scientific Misconduct issued in 2000. Particularly relevant to our discussion is that the ORI found that “Dr. Duan . . . engaged in scientific misconduct by reporting research that was inconsistent with original data or could not be supported because original data were not retained,” even though “Dr. Duan de- nies all allegations of scientific misconduct and contends that some of his original data is missing.” Read and discuss with a colleague the following Finding of Scientific Misconduct. Exercise 7.2 What aspects of this report do you find surprising? What impact did the sanctions likely have on Dr. Duan’s career? Do you agree with the practice of publicly distributing these findings and naming the researcher involved? What impact might the fraud in this case have had on other researchers, doctors, or patients? Given the impact of the fraud, was the severity of the imposed sanctions appropriate? RECoRDKEEPINg 101 FINDINGS OF SCIENTIFIC MISCONDUCT Release Date: June 27, 2000 NOTICE: OD-00-043 Department of Health and Human Services Notice is hereby given that based on oversight by the Office of Research Integrity (ORI) and decision by the Assistant Secretary for Health, the U.S. Public Health Ser- vice has taken final action in the following case: Lingxun Duan, M.D., Thomas Jeffer- son University: The U.S. Public Health Service (PHS) alleges that Dr. Duan, former Research Assistant Professor of Medicine, Division of Infectious Diseases, Depart- ment of Medicine, Jefferson Medical College, Thomas Jefferson University, engaged in scientific misconduct by reporting research that was inconsistent with original data or could not be supported because original data were not retained. The research in question was supported by a National Institute of Allergy and Infec- tious Diseases (NIAID), National Institutes of Health (NIH), grant, R01 AI36552, entitled “Intracellular antibodies and HIV 1.” Specifically, the research in question was reported in an NIAID, NIH, grant application; in an FDA-approved phase I gene therapy investigational new drug (IND) application entitled “Intracellular immuniza- tion against HIV-1 infection using an anti-rev single chain variable fragment (SFV);” and in two publications: (1) Duan, L., Bagasra, O., Laughlin, M.A., Oakes, J.W., & Pomerantz, R.J., Potent inhibition of human immunodeficiency virus type I replica- tion by an intracellular anti-Rev single chain antibody, Proc. Natl. Acad. Sci. USA 91:5075–5079, 1994; and (2) Levy-Mintz, P., Duan, L., Zhang, H., Hu, B., Dorna- dula, G., Zhu, M., Kulkosky, J., Bizub-Bender, D., Skalka, A.M., and Pomerantz, R.J., Intracellular expression of single-chain variable fragments to inhibit early stages of the viral life cycle by targeting human immunodeficiency virus type 1 integrase, J. Virol. 70:8821–8823, 1996. Dr. Duan denies all allegations of scientific misconduct and contends that some of his original data is missing. Both Dr. Duan and PHS are desirous of concluding this mat- ter without further expense of time and other resources. Thus, Dr. Duan has entered into a Voluntary Exclusion Agreement (Agreement) with PHS, in which Dr. Duan has voluntarily agreed: 102 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg (1) to exclude himself from any contracting or subcontracting with any agency of the United States government and from eligibility for, or involvement in, nonprocurement transactions (e.g., grants and cooperative agreements) of the United States Government as defined in 45 C.F.R. Part 76 for a period of two (2) years, beginning on June 7, 2000; (2) that for a period of one (1) year after the conclusion of the voluntary exclusion pe- riod, any institution that submits an application for PHS support for a research project on which his participation is proposed or that uses him in any capacity on PHS sup- ported research, or that submits a report of PHS funded research in which Dr. Duan is involved, must concurrently submit a plan for supervision of his duties to the funding agency for approval; the supervisory plan must be designed to ensure the scientific in- tegrity of Dr. Duan’s research contribution, and the institution must also submit a copy of the supervisory plan to ORI; (3) to exclude himself from serving in any advisory capacity to PHS, including, but not limited to, service on any PHS advisory committee, board, and/or peer review commit- tee, or as a consultant for a period of two (2) years, beginning on June 7, 2000; (4) that he will not oppose the submission to journals of a statement summarizing the current state of the science with respect to the scientific matters at issue relating to grant R01 AI36552, which has been jointly agreed to by Thomas Jefferson University and the United States of America. FOR FURTHER INFORMATION CONTACT: Acting Director, Division of Investigative Oversight Office of Research Integrity 5515 Security Lane, Suite 700 Rockville, MD 20852 (301) 443-5330 7.2 WHy KEEP RECoRDS? Accurate records are central to any investigation of scientific misconduct, yet such investigations are rare. Not surprisingly then, defense against an accusation of misconduct is not the primary reason researchers keep records, and this potential concern should not dominate our discussion of record- keeping. A discussion of what records to keep and how best to do so begins with a consideration of what information will be needed in the future and why. First, list reasons why physicians write information in a medical chart. Compare Exercise 7.3 your list with one or more colleagues and add to your list as needed until you believe it is complete. Second, make a similar list of reasons that researchers at a medical device company record infor- mation in laboratory notebooks. Compare this list with your list for medical charts; how many of the reasons for keeping records appear on both lists? Third, list reasons why a researcher work- ing in academia records research methods or findings. Are there any reasons unique to this third list? RECoRDKEEPINg 103 7.2.1 medical Records Although your list may differ, commonly cited reasons for writing in a medical chart are immediate transfer of information, long-term transfer of information, training medical students and residents, and legal documentation. Examples of immediate information transfer include a physician writing an order in a chart that another member of the hospital staff must execute later in the day, or a resi- dent who is called in the middle of the night to examine a patient deciding an appropriate course of action based in part on his or her review of the patient’s chart. Because many different people come in contact with each patient during a typical day in a hospital, a smooth transfer of information can literally be the difference between life and death. Availability of an accurate longer-term medical history can be equally important to a patient’s health. Diagnosing and treating a patient often depends critically on details of that person’s medical history: previous illnesses and surgeries, current medical problems and medications, allergies, and so forth. Few patients will remember, or even know, all the details of their own medical history, and few physicians can remember the complete histories of patients under their care. Consequently, a written record of each patient’s medical history is not only essential to the accurate exchange of information between physicians, it is also critical as an accurate, detailed substitute for each physician’s memory. Perhaps less obvious, good recordkeeping can be useful in training medical students, nurses, and other health care professionals. Most entries in medical records have very specific formats. Learning and using these specific formats is integral to learning the thought process associated with medicine. One usually records a detailed medical history and results from a physical examination on a form that lists standard questions and aspects of the examination. Recording the same informa- tion for each patient helps students learn the essential components of a good examination; they soon begin to ask the questions and perform the examination in the same order each time, which helps ensure that they do not miss anything. Another common entry in hospital charts is the SOAP note, an acronym for “subjective, objective, assessment, and plan.” Organizing daily updates under these four headings encourages a particular thought process: gather the information, think about what it means, then decide what to do. Finally, it is no surprise that medical charts serve as an important legal record of what hap- pened to a particular patient and why. In fact, most respondents to Exercise 7.3 place this first in their list. Unfortunately, many increasingly view this legal function as conflicting with the training function discussed above. Many hospitals no longer allow medical students to write in a patient’s chart for fear that an erroneous assessment or plan, even if corrected later by the supervising physi- cian, could increase vulnerability in a lawsuit. 104 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 7.2.2 Industry Research Records Your second list from Exercise 7.3 may not differ much from the first list. Laboratory notebooks kept by employees of a medical device company serve many of the same functions as a medical chart. Multiple technicians might record results from a series of tests for review and compilation by their supervisor the next day (short-term transfer of information); technicians may consult their records when performing the same tests a month later to make sure they set them up exactly the same way (long-term transfer of information). Asking new employees to follow a specific structure for re- cording data from a particular test can help them learn how to perform that test (training). Finally, approval of new drugs or devices by the U.S. Food and Drug Administration requires stringent recordkeeping (legal documentation); such records are thus essential for the survival of pharmaceu- tical and device companies. If you or a colleague with whom you discussed Exercise 7.3 has worked in industry, the topic of cosigning likely surfaced in your list. Most industrial research facilities require a supervisor to re- view and cosign laboratory notebooks at the end of each day. This requirement can assist many of the functions of recordkeeping discussed above. If a test result is surprising, a supervisor can learn about the result and take appropriate action immediately: check the equipment, schedule a repeat test, or discuss the findings with his or her boss (information transfer, quality control). Daily review also provides an excellent opportunity for feedback on how best to perform the test or record the results. Finally, for companies that depend critically on regulatory approval of their products, cosigning not only helps ensure proper performance, it also properly documents all tests and procedures (legal). 7.2.3 Academic Research Records By now, the pattern should be apparent; recordkeeping serves similar functions in diverse disciplines and settings. Academic researchers use records to transfer information between members of a group, as a long-term record of what was done and how it was done, to help train students to perform and record their work, and as a legal record. Because most academic researchers are more interested in publishing journal articles than protecting themselves against product liability suits, the need for long-term documentation tends to dominate in academic practice. Nevertheless, answers to Exer- cise 7.1 usually reveal that many research groups do not keep adequate records, even to meet the basic goal of documenting what research was performed, when, and by whom. One of many inter- esting findings that emerged from a 1993 survey of postdoctoral research fellows at the University of California–San Francisco was that fellows with an M.D. degree were significantly more likely to keep laboratory records in ink in a permanently bound research notebook than were those with a Ph.D. degree (Eastwood et al., 1996). RECoRDKEEPINg 105 Design a recordkeeping policy for your research group. What should be recorded and Exercise 7.4 where? Should cosignatures be required? If yes, who should cosign and how often? Should cosign- ing or other rules of recordkeeping differ for different members of the group (e.g., undergraduates, graduate students, postdoctoral fellows)? How should new members who join the group be instructed in keeping records? Who should be responsible for ensuring that rules are followed? What should be the consequences for a group member who fails to keep appropriate records? What should happen to a member’s records when they graduate or leave the group? Finally, are any special rules needed for electronic data? How does your policy compare to your own current practices in your research? 7.3 ElECTRoNIC DATA Consider a spreadsheet or data file containing results from a dozen experiments performed over a 6-month period. If you had produced this data file and were asked to verify that you actually performed the experiments, what proof could you offer? The data file itself is of little use; one can numerically generate data and save the results in the desired format. The operating system will likely display the date you created the file and the date you last modified it, but these dates can be manipulated by changing the computer’s clock. If you had kept every version of the file as you entered data from each new experiment, paging through these versions would be more convincing, but this trail of different versions of the file could also be fabricated. Having different versions of the file plus a laboratory notebook showing data acquisition on dates that match those for the files would be better, especially if the notebook had been cosigned by a supervisor at intervals over the period in question. That most research today relies either entirely or in large part on storing results electronically presents enormous challenges for ensuring integrity of the science and engineering. While research- ers rarely need to prove that they performed specific experiments, they often need to revert to an older version of software or refer to computer files that have been deleted or altered. Consider this fairly common dilemma from the perspective of the director of a research laboratory at a university. A new student begins working for you, taking over a project from a previous student who graduated. Her project involves imaging cells and analyzing the images with custom-written software that is still under development in your group, and her early results appear to contradict findings by her pre- decessor. To differentiate between possible changes in experimental protocol, methods of collect- ing the images, misusing the current version of the software for analysis, and consequences due to recent changes in the software, you will need a trail of previous images, versions of the software, and well-annotated analyses. Few laboratories proactively anticipate such situations in their recordkeep- ing or established procedures for data backup, but most will experience them. 106 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 7.3.1 Date-Stamps, Time-Stamps, and Backup Systems The most rudimentary form of information about a digital file is its date- and time-stamp. These stamps have little weight in an investigation of potential fraud because of their ease of manipulation, but they can be very helpful in typical situations wherein everyone acts in good faith. In the example just discussed, trying to reconstruct the version of a particular program used for a particular analysis could be aided greatly by comparing the date-stamp of the file containing the results with dates as- sociated with successive versions of the software. The major problem with date- and time-stamps is that they can be changed easily, even inadvertently. Simply opening, printing, or resaving an old file may result in a new date- and time-stamp, depending on the setup for autosaves. A cumbersome solution is to lock each data file when creating it, thus forcing subsequent changes to be made on copies of the original. A more common approach is to create periodic tape or hard-drive backups of data files. This approach stores both the current versions of the files and their current date- and time-stamps, thus enabling one to recover deleted or altered information and to reconstruct the his- tory of modifications to a particular file. Given the low cost of disk space, systematic routine backup of all electronic data is a prudent and affordable safeguard. 7.3.2 Images Digital images raise many of the same questions as other electronic data files. Because image files are often large, there is a temptation to delete an image following analysis, thus retaining only final results that occupy less storage space. In general, however, it is more effective to do exactly the op- posite: store copies of the original images on recordable media such as CD-R and force group mem- bers to manipulate only copies of the original image. Indeed, in cases where an analysis subsequently becomes suspect, one can always return to the original image and reinterpret the findings. Most medical images contain information that identifies the patient, which raises another important concern with regard to image handling. Recent efforts to protect a patient’s privacy have led to important new regulations and training for everyone who views, analyzes, or handles medical images. Similarly, concerns about potential attacks on researchers and facilities has led many univer- sities to formulate policies for handling and storing images that show research with animals. Given the imperfect nature of computer security, many policies prohibit the storage of sensitive images involving patients or animals on any computer connected to the Internet. 7.3.3 Software Development When seeking solutions to a problem, it is often useful to consider who has the best incentive to solve that problem; they will often have the best solution. Developing software often requires many people to work on different aspects of a single code, integrating changes made by different group members in an orderly way while tracking previous versions so that problematic changes can be undone. It is RECoRDKEEPINg 107 not surprising, therefore, that the software industry has developed excellent systems for controlling revisions. A number of these systems are now available as open-source software, making such solu- tions accessible even to research groups whose main business is not software development. Now that we have discussed electronic data in more detail, return to the recordkeep- Exercise 7.5 ing policy you designed for your research group in Exercise 7.4. Provide more specific instructions for the primary types of electronic data in use within your group. What would your group need to change to implement your plan? If you would need additional servers or individual external hard drives for routine backups, estimate the amount of storage space you would need and determine how much this would cost. If you believe your group should implement software revision control, identify open-source and commercial products that might meet your needs. If you feel strongly that changes are needed, consider discussing potential changes and options with your colleagues at a group meeting. fRAuD: fABRICATIoN AND fAlSIfICATIoN 7.4 Even in a book dealing with the ethics of communication in science and engineering, it seems futile to admonish readers not to falsify or fabricate data. Very few would willingly do so, and the remaining few will not be stopped by our disapproval. We focus, therefore, on the need to clarify the boundary between ethical and unethical behavior, not on why one should behave ethically — we assume that the latter is clear. Most universities provide extensive information related to issues of academic Exercise 7.6 dishonesty and misconduct. For example, undergraduate students at Texas A&M University are referred to http://ugr.tamu.edu/resources/. Search three university Web sites and record their defi- nitions of academic dishonesty as well as specific actions that constitute such dishonesty. Compare results and submit a three-page summary. Before continuing, consider some widely accepted definitions related to academic or research misconduct, which in this case are found on the aforementioned Web site at Texas A&M University: Misconduct in research or scholarship includes fabrication, falsification, or plagiarism in proposing, performing, reviewing or reporting research. It does not include honest error or honest differences in interpretations of data. Fabrication: Making up data or results and recording or reporting them. Falsification: Manipulating materials, equipment, or processes, or changing or omitting data or results such that the findings are not represented accurately in the research record. 108 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Plagiarism: The appropriation of another person’s ideas, processes, results, or words without giving appropriate credit. Recall, too, the following definition: Fraud: A deception deliberately practiced in order to secure unfair or unlawful gain; a misrepre- sentation of material fact consisting of a false representation, concealment, or nondisclosure. 7.4.1 Retaining or Discarding Data Consider a student who has carefully collected and plotted a dozen data points on an x–y graph, then fitted a line through the data. Fabricating extra data that lie near the best-fit line would improve the r2 value typically reported to indicate how well the line fits the data; classifying a few points far from the best-fit line as outliers and discarding them would similarly improve the reported fit. Why is it that every scientist or engineer would consider fabricating extra data points to be fraudulent, while many would at least consider discarding outliers? The Nature article titled “Scientists Behaving Badly” reported findings from a survey of more than 3000 NIH-funded scientists regarding the self-reported frequency of behaviors identified as concerning by focus groups of researchers (Martinson et al., 2005). While only 0.3% admitted to falsifying research data within the previous 3 years, 15.3% admitted to “dropping observations or data points from analyses based on a gut feeling that they were inaccurate.” The only more frequent offense (27.5%) was “inadequate record keeping related to research projects.” Unfortunately, the high incidence of self-reported manipulation of data in the 2005 report in Nature agrees well with earlier surveys that asked research trainees about their willingness to commit various types of research fraud. In a 1993 survey of postdoctoral fellows at the University of Cali- fornia–San Francisco, 12% of respondents reported first-hand knowledge of a scientist intentionally altering data for a presentation, while 4% reported first-hand knowledge of data fabrication. The numbers were slightly lower, but substantial, for grant applications (8% alteration, 2.5% fabrication) and publications (8% alteration, 2.5% fabrication). Despite the respondents constituting a self- selected group of fellows interested enough in research ethics to return the survey, 15.4% indicated they would be willing to select or omit data to improve their results “if it would make publication of [their] work more likely or benefit [their] career,” rising to 27.2% “if it would increase the chances of [their] grant application being funded.” Formulate criteria for appropriately discarding a data point, observation, or study. Exercise 7.7 Compare your draft policy with that of one or more colleagues and revise until you believe that your policy could be implemented in your group. Next, find a data set collected in your group that you know contains noise or errors and test your policy by applying it to the data set. How many points would you discard, if any, and what justification would you give? As a final step, discuss your analysis with col- leagues, then with a senior colleague or mentor. Submit a three-page summary of your conclusions. RECoRDKEEPINg 109 An Internet search will return many different criteria and algorithms for identifying “outliers” in a data set, yet such statistical analyses are rarely sufficient for excluding data. Exclusions must combine good experimental and statistical practices with an understanding of the overall study and potential impact of those exclusions. In general, exclusion criteria should be established before performing the study and should depend on something other than the values obtained. Excluding data points collected on a single day that appear to be outliers, based on the rationalization that the equipment must have been miscalibrated, is a dangerous practice. In contrast, performing a cali- bration at the end of each day and excluding from analysis all measurements taken on days where the calibration fell outside a preset tolerance is good technique. Discussing criteria for excluding data before performing a study can help ensure that you have enough information to make good decisions later. Other good practices include disclosing exclusions and the associated justifications within publications, discussing exclusions with your mentor before making them, and remembering that “if something does not feel right it probably is not.” 7.4.2 Image manipulation The importance of digital images in many types of research raises additional questions about the degree of processing or manipulation that is appropriate in a given situation. Consider a gel such as a Western blot, where a series of stained bands indicate relative amounts of certain proteins (rows) in different samples (columns or lanes). Is there anything unethical about cutting and pasting from several images of gels run on different days to create a composite image showing results from certain samples side by side? What if one or more of those gels was underexposed? The resulting image would then be lighter than expected and this problem could be corrected in one of two ways: reimage the gel with a longer exposure time or adjust the image contrast and brightness using an image pro- cessing program. Are these two options really the same, or is manipulating the image fraudulent? It turns out that your answer to this question may change if you learn more about how im- age processing programs adjust contrast and brightness and how densitometry programs quantify bands on a gel. Commercial densitometers often output optical density, which relates directly to concentration. Other devices (CCD cameras, scanners) commonly used to image gels produce im- ages in which pixel intensity has a nonlinear (logarithmic) relationship to optical density; in such cases, manipulating images before analysis may have important consequences. When deciding how to interpret findings, it is not enough to want to make good decisions; it is critical to gather enough information to make good decisions. 110 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg 7.4.3 Statistical and Image forensics After reading case summaries on the Web site of the ORI (http://ori.hhs.gov/misconduct/cases/), it is easy to become concerned. There are cases of undergraduates, graduate students, postdoctoral fellows, and principal investigators fabricating data, scientists manipulating images in applications for funding, and even a laboratory member altering another’s experiments to ensure that attempts to repeat his earlier (fraudulent) experiments would not expose him. As you move forward in your career, you will begin to get more of your data secondhand from employees or students whom you supervise. You will also spend more time reviewing technical reports, manuscripts, or grant applica- tions from other researchers. At some point, it is natural to wonder how best to check the validity of the data and images that you encounter. Within your own group, good training, good recordkeeping, and replication of randomly se- lected experiments remain important. Even in an environment that emphasizes integrity, replication of selected experiments can help guard against error and ensure continuity of methods as members join or leave the group. When you have less information about the source of data in a figure or table, however, or when you have reasons to suspect that data or images have been altered, emerging tools for statistical and image forensics may help. The ORI Web site is a good resource for such tools. Statistical forensics generally relies on the observation that those who fabricate data rarely do so with much statistical sophistication. Dr. Slutsky (discussed in Chapter 6) published two papers that contained data sets having different sample sizes but identical means and standard deviations. Other cases have identified fabrication via nonrandom distributions of the rightmost digit in a series of numbers, including a case wherein the rightmost digit was either 5 or 0, thus suggesting that the sample size had been inflated by averaging pairs of samples to fabricate points for additional, nonexistent samples. Image forensics relies on software tools that detect the manipulation of images. One fre- quently used set of tools is called Forensic Droplets; it is available on the ORI Web site (http://ori. hhs.gov/tools/droplets.shtml). These droplets run in Photoshop and help the user detect common methods of manipulation. The Web site also provides illustrative uses of these droplets in actual cases of misconduct (http://ori.hhs.gov/tools/principles.shtml). Download and read the article, “What’s in a Picture? The temptation of image Exercise 7.8 manipulation” [Rossner M, Yamada KM (2000) J Cell Biol 166: 11–15]. This article summarizes conventions adopted by several top journals regarding accepted types of image manipulation and how they should be identified. This article is also interesting because it presents several images that were altered intentionally. Download the appropriate Forensic Droplets from the ORI (http://ori. hhs.gov/tools/droplets.shtml) and use them to see whether you can detect the manipulation of the images presented in Rossner and Yamada’s paper. • • • • 111 C H A P T E R 8 ownership of Ideas, Data, and Publications Imagine sitting down 20 years into a successful career to write a book on your area of expertise. Everyone would agree that it would be wrong to copy verbatim a paragraph from another scientist’s paper without attribution; we call that plagiarism. On the other hand, most would find it reasonable to include in your book a figure from one of your earlier journal papers. You may be surprised that to do so would be illegal in most cases. The publisher of the journal probably holds the copyright on that figure, and either you or the publisher of your book must secure permission from the journal to reprint the figure; such permission may involve paying a substantial fee. One of the many interesting questions in science is who owns the results. Recent trends, such as the drive to commercialize products of university research and to increase public access to data from federally funded research, highlight this question of ownership. Debates about ownership of and access to the results of scientific and engineering research have important consequences for individuals, universities, companies, publishers, the government, and the public at large. In Chapter 7, we compared medical charts to laboratory notebooks when considering why we should keep records. This comparison also provides an interesting entry into the question of owner- ship of information. Who owns your medical record and what conceptual tests for ownership does your answer suggest? The information is about you and you can request a copy of the records, which suggests some level of ownership. Nevertheless, you typically cannot alter or destroy the original medical record, which suggests that someone else shares ownership. The physicians, nurses, and other medical personnel who produced the record can write in it and read it, but they cannot obtain a personal copy to take home. What about the insurance company who paid for your care? Does paying for the associated diagnostic tests and office visits give the company any stake in ownership of the information? Based on your experience in research and the analogy to a medical chart outlined Exercise 8.1 above, discuss why each of the following parties should or should not be considered owners of 112 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg scientific data (not the resulting publications or patents) that result from a research project funded by the federal government using tax dollars and performed at a private university: 1. 2. 3. 4. 5. The principal investigator of the study The students, technicians, and fellows who performed the experiments The university The federal government The public/taxpayers Now, for each of the people, groups, or institutions listed above, specify appropriate levels of access to the original data. In other words, who should be able to acquire copies of all the data, to alter those data, or to use them to write papers or submit patents? Are there people who should not be considered co-owners but who should still be granted some access? Explain. 8.1 DATA AND RESouRCE SHARINg In 1999, Congress amended the FY 1999 Omnibus Spending Bill to require federal agencies that fund research to ensure that all resulting data be made available to the public under provisions of the Freedom of Information Act. This new requirement prompted an outcry from the scientific com- munity (Frankel, 1999). Concerns ranged from how researchers could disclose data from clinical studies without violating the privacy of human subjects to whether colleagues, companies, or even political activists might use data obtained under the new policy to compete with or disrupt the work of individual scientists. Such concerns are not unique to biomedical science, but because the NIH funds so much science in the United States, we focus below on NIH policies regarding the sharing of data, model organisms, and publications resulting from federally funded research. 8.1.1 Research Data Ultimately, the NIH adopted limited requirements for sharing data. The Final Statement on Shar- ing Research Data reads, in part, as: NIH reaffirms its support for the concept of data sharing. We believe that data sharing is essential for expedited translation of research results into knowledge, products, and procedures to improve human health. The NIH endorses the sharing of final research data to support these and other important scientific goals. The NIH expects and sup- ports the timely release and sharing of final research data from NIH-supported studies for use by other researchers. See http://grants.nih.gov/grants/policy/data_sharing/index.htm for more on the NIH state- ment. Note, however, that provisions outlined later in the statement exempt most researchers from oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 113 this policy. Most importantly, only applicants requesting over $500,000 of direct costs in any year must file a data sharing plan. Because the most common type of NIH grant (the R01, which is discussed in Chapter 4) typically has annual direct costs of $250,000 or less, this provision exempts most NIH-funded researchers. In addition, the NIH defines “timely release and sharing” to be “no later than the acceptance for publication of the main findings from the final data set.” It is not un- common for a successful researcher to renew the same grant repeatedly over 20 or more years while studying a particular disease; in such situations, it is unclear what constitutes “the final data set.” Other critical issues, such as how long an investigator must continue to share data after completing a study, are not addressed by the NIH policy. Finally, note that the wording refers to sharing of data for use by other researchers, possibly circumventing scientists’ original objections to sharing data with companies and the general public. Community practice in some fields has overtaken the debate on data sharing. For example, researchers studying gene expression using DNA microarrays have established open databases and standards for submitting data (http://www.mged.org/). Top journals in this field also typically re- quire authors to deposit their microarray data in a database as a condition of publication. Interest- ingly, although arguments for data sharing typically focus on benefits to the scientific community or public, Piwowar et al. (2007) recently reported a direct benefit to researchers: papers associated with publicly available microarray data are cited more frequently. 8.1.2 model organisms In contrast to its data sharing policy, the NIH’s policy on model organisms is clear, demanding, and relatively uncontroversial. All grant applicants who plan to develop a model organism such as a transgenic mouse must provide a plan for sharing that model organism with other researchers. Peer reviewers evaluate sharing plans as part of the grant review process and NIH staff may require “ad- equate progress in model organism sharing as well as a demonstrated willingness to make research resources developed during the project widely available to the research community . . .” to continue funding an existing grant (see http://grants.nih.gov/grants/policy/model_organism/index.htm). 8.1.3 other Research Products Any researcher can quickly and easily share data in a computer spreadsheet by posting the file to a public Web site. Even those who do not wish to maintain a Web site can usually deposit tables of supplemental data with a journal at the time of publication. Annotating the data with clear head- ings, comments, and notes about exclusions, then answering occasional questions from colleagues about the posted data, requires a little more time, but not much. By contrast, maintaining a colony of transgenic mice and providing breeding pairs to any interested colleague can be time consuming and expensive. Should we require researchers to continue to breed and supply mice to colleagues 114 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg even after the NIH grant that funded development of that mouse expires? What alternatives are available to the scientist who wishes to share a transgenic mouse without the expense of maintaining a mouse colony indefinitely? Sharing of computational models and custom software presents similar difficulties. Devel- opers of computational models typically publish a description of the model and its results, not the actual code. As with transgenic mice, another researcher who attempts to reproduce the model from the published description could easily invest significant time and effort and still generate a slightly different model. Requiring researchers to post raw code for models developed with public funding would help, but this raises questions about how much support the developer should provide to those who download and attempt to use the code and for how long. Software companies have a financial incentive to provide user-friendly interfaces and technical support, but individual researchers do not. Research-grade models and software may be difficult for someone other than the developer to understand and operate, but as long as the software performs its intended task, the developer may have little interest in making it more user-friendly or in writing a supporting manual. The incomplete nature of published descriptions of models, uneven practices regarding shar- ing, and the variety of operating systems and programming languages worldwide all combine to limit the effective sharing of computational models. Fortunately, several organizations are focused on improved sharing and interfacing of computational models across groups. One such effort is the Physiome Project (http://www.physiome.org/), organized by the International Union of Physi- ological Sciences. One component of this effort is to use markup languages to standardize coding of models and handshaking between them. A visit to the CellML Web site (http://www.cellml .org/models) provides more information on this effort as well as an idea of the difficulty of imple- menting, documenting, and debugging computational models of biological systems based only on their published descriptions. 8.2 CoPyRIgHT We noted in the introduction to this chapter that technical journals typically hold the copyright to any articles they publish. As an author, you transfer copyright to the journal as a condition of publi- cation, even if the journal assesses page charges and labels your paper an advertisement. You are writing a review article and wish to include several figures from your earlier Exercise 8.2 papers. Most publishers of those articles agree that you can use the figures as long as you state that they are used with permission of the publisher and include the appropriate citation. One publisher demands several thousand dollars in fees to reprint your figures, however. List all the options you can think of, including paying the fees, and discuss the relative merits and ethics of each approach. Based on that discussion, what would you do? oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 115 8.2.1 online Publishing The past few years have brought forth the most dramatic shift in the history of scientific publishing since the printing press. Like newspapers, scientific journals have experienced a drop in individual print subscriptions and a shift to online delivery of content. The critical question for journals, as for newspapers, is how to remain solvent selling content to an online audience that is used to getting in- formation free. Not surprisingly, different journals have taken different approaches. Most publishers continue to sell print copies of their journals to libraries, at least for now; some restrict online access to print subscribers to encourage print subscriptions; others offer online-only access at a lower price than print subscriptions; still others provide full, free access to anyone. Regardless, most journals partially defray costs of publication by assessing substantial fees for publication. Increasingly, pub- lishers and third-party services sell universities and other large institutions bundled access to groups of journals. Students and faculty at a typical research university can now access most major scientific and engineering journals through the university library’s portfolio of electronic subscriptions. These subscriptions often include extensive collections of scanned back issues, virtually obviating the need to visit the library when studying the literature. One of the consequences of the shift of journal content to electronic format is that it is often unclear to the typical academic user in the United States which journals charge for content and which distribute it freely. If you access a paper through your library’s electronic journals portal, it is equally easy to obtain a PDF of an article whether or not the journal normally charges an individual for the download. If you access the same paper from outside your library’s portal, however, the download fees are often $20 to $30 per article. This charge explains why you, as an author, are likely to receive occasional e-mails requesting a PDF reprint of one of your articles; the request usually comes from someone who does not have free access to the article. As an author, should you send a PDF when you receive such an e-mail? Sending the requested PDF deprives the journal of the fee it would normally charge for a download; on the other hand, what if the request comes from a colleague in a country where the download fee represents an exorbitant sum? What about the fairly common practice of posting PDFs of recently published articles on your laboratory or group Web site? Is this unethical? Illegal? 8.2.2 Public Access to NIH-funded Journal Articles If the NIH funds your research, recent policy changes rendered moot the problem of whether to share PDFs of your article. Nevertheless, the NIH may have also placed you in an uncomfortable position between the people who fund your studies and those (often your main professional societ- ies) who publish them. The NIH began by asking grantees to deposit a copy of any accepted manu- script resulting from NIH funding into a publicly accessible database, PubMed Central. The policy was initially voluntary, although many NIH investigators felt pressured to deposit manuscripts 116 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg because they thought that applications for renewing grants would be judged in part on productivity and that the number of deposited papers would be used as a measure of productivity. Many journals considered the NIH database a violation of their copyright on the accepted articles, and some that depended heavily on selling access to their content claimed the NIH require- ment would put them out of business. The American Physiological Society (APS), which publishes a portfolio of journals on physiology, genomics, and physiology education, was one of the most vo- cal critics. Among other actions, the chair of the APS Publications Committee sent the following e-mail in November 2005: Dear APS Author, On February 3, 2005, the NIH announced a new policy (NOT-OD-05-022) to en- hance public access to publications resulting from NIH-funded research. The policy itself and information about it are available at http://www.nih.gov/about/publicaccess/ index.htm. As the Publications Committee Chair of the American Physiological Soci- ety (APS), I am writing because some confusion has arisen about the NIH Policy. The NIH Public Access Policy is a voluntary program that applies to NIH-funded investigators. Such authors are asked to submit electronic copies of articles accepted by peer-reviewed journals that report research funded by the NIH to the National Library of Medicine’s PubMed Central (PMC). The NIH will then make the journal-accepted manuscript free to the public at an interval (ranging from immediately to 12 months) after publication that is chosen by the author. This Policy goes into effect on May 2, 2005. Since the policy was announced, questions have arisen about whether or not participa- tion is truly voluntary. On the day the policy was published, NIH Director Elias Zer- houni sent a letter to all extramural scientists and their research institutions describing the policy and urging them to participate. Although Dr. Zerhouni stated that the policy is a request, many researchers, university officials, and even some NIH program officers have interpreted it as a mandate for grantees. However, in public statements, Zerhouni and other NIH officials have repeatedly underscored that it is voluntary and there will be no repercussions for those who choose not to participate. Funded inves- tigators can still fulfill their progress report requirements by providing print copies of their publications with their annual progress reports. While the APS does not support the NIH Plan, we do recognize that it does put you, our authors, in a difficult position. Do you abide by a request issued by the granting oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 117 agency or do you abide by the copyright statement that you signed when you submit- ted your manuscript to the journal? The APS does not want to see you placed in that position. Therefore, we are modifying our copyright statement to help you fulfill the voluntary request of the NIH Plan. In doing so, we ask that you recognize that the Society has been at the forefront of online publishing, putting content online as early as 1994, providing authors with one of the first online manuscript submission and review systems, and underwriting the scanning of APS journal content back to 1898. We were one of the first publishers to change our access policies so that all content is free to all 12 months after publication. These efforts have cost the Society millions of dollars and subscriptions are one of the few ways available for us to recover those costs. With over 50% of articles published in our journals funded by NIH, free release of manuscripts by PMC sooner than the Society’s access policies allow could lead to losses of subscription revenues that would interfere with the journals’ ability to meet the needs of the Society and its members. Moreover, NIH is seen as a leader among biomedical funding agencies. If others including NSF, NASA, or funding agencies in other countries such as the Wellcome Trust follow suit, we may end up in a situation where the vast majority of content is subject to mandates requiring public release be- fore the journal release date. Should this occur, the APS and other scholarly publishers may be forced to increase author fees to compensate. Ultimately it would be detrimen- tal to science if the APS had to charge authors the full cost of publication, which is currently about $3,000 an article. Given the importance of subscription revenue to the Society’s ability to provide our members with high quality and innovative publications, the APS asks that if you choose to deposit your manuscript into PMC, you will specify that it should not be made avail- able to the public until 12 months after publication in the Society’s journals. The Soci- ety intends to modify its copyright agreement so that NIH-funded authors are granted permission to deposit their accepted manuscript into PMC for release to the public 12 months after publication. By abiding by the Society’s modified copyright agreement, you will be able to participate in the NIH public access program while still protecting the ability of the APS to recover the costs associated with its publication program. Thank you for your past and future support of the Society’s journals. We will be able to continue to publish these respected journals with your recognition that the NIH Public Access Plan is a voluntary plan that seeks release at 12 months, a time consis- tent with the Society’s current access period. Please do not hesitate to contact me, or 118 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg [the] APS Director of Publications, if you have any questions about this important issue. Recently, the NIH made it mandatory to deposit accepted manuscripts to PubMed Central for all NIH-funded investigators. The APS has maintained its stance that it will accept deposit as long as public access is delayed for 12 months; in fact, APS journals now automatically deposit ar- ticles and specify the 12-month delay rather than leaving this decision to authors. As of this writing, however, many journals and societies have not adjusted their copyright statements to account for the NIH policy, and some universities now urge authors to amend, or refuse to sign, journal copyright transfer agreements to avoiding placing themselves in a legally untenable situation. PATENTS 8.3 In 1970, only three major research universities devoted at least one half-time staff position to tech- nology transfer and research universities as a group secured only ~150 patents (Sampat, 2006). Most universities consciously confined their activities to the generation and free exchange of knowledge; they avoided the business aspects of translating that knowledge into profitable products for fear that it would taint their academic missions. Among others, Columbia University, Harvard University, Johns Hopkins University, The University of Chicago, and Yale University specifically prohibited the patenting of results from biomedical research. At that time, private companies performed most federally funded research and development, and patents derived from that research belonged to the federal government. University owned patents typically resulted from industry funded research and were designed primarily to protect against misuse of the technology. Licensing was assigned via independent foundations or corporations (Sampat, 2006). Today’s landscape for technology transfer differs dramatically. Most research universities op- erate substantial technology transfer offices, securing and licensing patents covering a range of ideas and products derived largely from federally funded research. A network of consulting, research, and technology transfer agreements links universities to companies, and ownership of intellectual property is frequently the critical concern during the negotiation of such agreements. Professors routinely form “spin-off ” companies to translate their discoveries into products. Every practicing scientist and engineer, whether in industry or academia, must now learn the basics of intellectual property law and technology transfer. In fact, if you accept a faculty position at a research university tomorrow, it is likely that the second piece of paper you will sign (after your offer letter) will be a patent agreement. Economists consider a strong university system to be a major driver of innovation Exercise 8.3 and economic growth. Make a list of the ways that universities transfer information and technol- oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 119 ogy to companies. Next, order your list starting from the mechanism you consider most important. Finally, compare your list to one based on surveys of managers of industrial research and develop- ment [see Table 4 in Cohen WM, Nelson RR, Walsh JP (2002) Links and impacts: The influence of public research on industrial R&D. Management Sci 48: 1–23]. Discuss with a colleague possible reasons for the main discrepancies between your list and the one compiled by Cohen et al. (2002). Maintaining our focus on communication in science and engineering, we restrict the remain- der of our discussion of patents and technology transfer to two small aspects of this very broad topic: private ownership of patents derived from publicly funded research and the impact of university technology transfer efforts on scientific communication. 8.3.1 Patents and Publicly funded Research Before 1980, the federal government owned patent rights to any discovery made with federal fund- ing. The simple rationale for this policy was that inventions generated with public funds should belong to the public. As we discussed for data and models in Section 8.1 and for publications in Sec- tion 8.2, however, the general question of ownership is not simple. As with data and publications, generating patents not only requires funding but also knowledge, ingenuity, hard work, equipment, space, and other resources. Hence, faculty, students, the university, and the government might all credibly claim at least partial ownership of a patent based on publicly funded research performed in a university laboratory. In 1980, the U.S. Congress passed the Bayh–Dole Act, which granted universities and small businesses the rights to patents arising from their federally funded research. From an ownership perspective, this policy was balanced better than the one it replaced — it granted patent rights to universities, required universities to share royalties with the inventors, and retained limited rights for the government. Yet, proponents of the change cited the need to stimulate innovation rather than the need to attribute ownership properly. At that time, federal funding agencies often trans- ferred their patent rights to universities and companies, but each agency had a different policy. The Bayh–Dole Act aimed to replace the array of existing policies with a single, uniform policy. Sup- porters argued that the government failed to promote licensing and use of the patents it owned, and transferring ownership to companies and universities would promote greater dissemination and utilization of innovations generated from federal funding. Read “Patenting and U.S. Academic Research in the 20th Century: The World Exercise 8.4 Before and After Bayh–Dole” [Sampat BN (2006) Res Policy 35: 772–789], then research the impact of the Bayh–Dole Act. Write a one-page position paper arguing that Bayh–Dole either has 120 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg or has not enhanced commercialization and utilization of the results of federally funded research in your field. 8.3.2 Patents and Publication We discuss here a typical process for technology transfer at a research university, but please note that each university and company has its own patent policies. If you have a new idea that you think might merit a patent, you begin by filing an invention report with your university’s office of technology transfer. A member of that office will review your report, discuss the idea with you, help research whether existing patents already cover your idea, and make a decision about whether to proceed. If positive, the next step is usually to file a provisional patent application. Filing a provisional patent is relatively inexpensive and protects your idea for 12 months while the university decides whether to proceed with a full patent application. Subsequent actions differ widely depending on the university and the nature of the invention. Because it can be expensive to file a full patent application, some universities spend the 12 months shopping your idea to potential corporate partners and proceed only if a partner is willing to license the patent once awarded. This approach works well when your invention is developed fully, a prototype has been tested, or the new idea has such obvious value that an investor will commit based on the idea alone. University-based research commonly produces ideas at a much earlier stage of development, however. In these cases, it is often difficult to decide whether to invest in a full patent application based on the limited information at hand. After reviewing your invention report, the office of technology transfer may recommend that you delay initiating the patent process until you have developed and tested your idea further. This approach is where the patent process can begin to conflict with the normal practice of academic research. Because any public disclosure of the idea impacts the patent process, it is critical that you discuss your ideas with your office of technology transfer before submitting them for publication or presentation at professional meetings. Without publications, however, it may be difficult to obtain additional funding to mature your idea, and even a grant application might constitute a public dis- closure in some circumstances. There is also the risk that someone else will advance a similar idea while you wait. No one, including those in your office of technology transfer, can tell you how best to bal- ance such concerns. In general, we recommend entering any discussion of technology transfer with a clear vision of your research and career goals, communicating those goals to your technology transfer officer, and doing your best to make decisions consistent with those goals. If, for example, your ultimate goal is to make a significant impact on the treatment of cancer, patenting a new drug or method of drug delivery and marketing it to companies may be an integral part of achieving your goal. In contrast, if your goal is to design a simple and effective water filter that can be assembled oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 121 cheaply and easily in the developing world, posting your design on a Web site and publicizing it through the press or nonprofit agencies might be a more effective approach. Concerns of intellectual property also impact scientific communication when industry funds academic research. Universities negotiate the terms of research contracts and agreements with spon- soring agencies and companies. Large federal agencies such as the NIH can essentially dictate terms to universities, but individual research agreements with companies vary widely. Intellectual property rights are often the major focus of negotiations, and restrictions on publication and other dissemi- nation of the results of the research are common. Companies often demand the right to prereview and block any planned public disclosure, including abstracts, conference presentations, journal pub- lications, and grant applications. Few universities agree to such stringent limits, but many agree to a waiting period to give the sponsor adequate time to review any planned disclosure and file appro- priate patent applications. As a principal investigator of an industrial sponsored project, it is critical to work closely with the contract negotiating team at your university to make sure you understand and are willing to accept any proposed limits on publication. As a student or postdoctoral fellow considering whether to work on an industrial sponsored project, it is essential to ask whether the project includes restrictions on publication, for your ability to publish is critical to building your track record and thus your career. PlAgIARISm 8.4 Most scientists and engineers would tell you that they know what constitutes plagiarism, that they consider it a serious offense, and that they would never do it, suggesting that plagiarism is not a major problem among working scientists and engineers. Many faculty members would admit that there is more of a problem with plagiarism among university students, but they would attribute this primarily to two factors: the Internet, which provides easy access to text written by others, and students from cultures that have different conventions regarding how and when to incorporate or cite ideas from published work. Yet, data from recent surveys contradict these common percep- tions. Undergraduates in the United States are frequently confused over what constitutes plagia- rism, they do not consider it a serious form of cheating, and they do it with shocking frequency. Although scientists self-report much lower rates of plagiarism, they report frequent observations of plagiarism by colleagues, suggesting that plagiarism is a significant problem, and not just among students. Studies on undergraduate cheating by McCabe and colleagues, in association with the Center for Academic Integrity, provide an interesting introduction to student attitudes about plagiarism (McCabe et al., 2001; McCabe, 2005). This group conducted a series of surveys of undergraduates at universities within the United States and Canada and reported that more than 75% of students admit to some type of cheating. In particular, one study revealed that 26% of students admitted to 122 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg committing “plagiarism” in the past year, while twice as many (54%) admitted that they “copied one or two sentences without footnoting.” A more recent survey found no evidence that the Internet is to blame: 38% admitted to “paraphrasing/copying a few sentences . . . without footnoting” from a written source, whereas 36% admitted to copying from an Internet source. Apparently many under- graduates simply do not feel that this as a serious offense; only 56% rated plagiarism as moderate or serious cheating (versus trivial or not cheating; McCabe, 2005). It may be surprising that graduate students took plagiarism only slightly more seriously: 32% considered paraphrasing or copying a few sentences without footnoting to be trivial or not cheating and 25% admitting to doing it in the past year. Even more concerning than the high rates of self-reported plagiarism in these studies is that the students surveyed appeared to have a narrow understanding of plagiarism as direct word- for-word copying, believing that it was acceptable to use someone else’s ideas without attribution as long as they expressed those ideas in their own words (McCabe et al., 2001). Whether it is called plagiarism or simply misconduct, “Using another’s ideas without obtain- ing permission or giving due credit” is a pretty good working definition of a key problem that arises often in science and engineering. De Vries et al. (2006) found that although only 1.4% of NIH- funded scientists admitted to using another’s ideas within the past 3 years without giving credit, 45.7% reported observing this behavior among their colleagues over the same period. “Using another’s ideas without obtaining permission or giving due credit” covers a Exercise 8.5 wide range of potential behaviors beyond direct word-for-word copying of published text. Perhaps a colleague suggested an interesting experiment during a conversation at a conference, prompting you to perform that experiment and publish the results without further discussion with your colleague. Is this misconduct? What about testing a hypothesis suggested in the discussion section of a paper you read, then publishing your findings without citing the paper that suggested the hypothesis? To- gether with a colleague, list 10 examples of using another’s ideas without permission or credit, then decide which you consider to be appropriate or inappropriate. Compare your list with colleagues to determine the most frequently listed examples. Include within your discussion the concept of com- mon knowledge versus personal intellectual property. Problems that arise commonly in a discussion of using another’s ideas involve interactions with group members, citation, and peer review. We discuss the first two categories briefly below and peer review in the following section. 8.4.1 Attribution Within a Research group Many issues regarding attribution within a group are addressed by the discussion of authorship in Chapter 6. Ideally, every group member should receive proper credit on publications through ap- oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 123 propriate authorship or acknowledgment. Yet, ideas conceived within a group are often presented in other venues. Must a professor giving an academic seminar explicitly list the names of all students and fellows who gathered the data presented? Is it sufficient to acknowledge the entire group on a slide at the end, as is common, or should the advisor specifically attribute each graph and figure, as with figures taken from published work by other groups? Such questions become particularly deli- cate as postdoctoral fellows approach the transition to an independent academic career. Fellows may view the use of their ideas in their adviser’s grant applications as appropriation, while their adviser may see these ideas as belonging to him or her as principal investigator of the group. 8.4.2 Citation It is clearly unethical to omit citations of relevant work intentionally, whether to claim undue credit for previously published ideas or to slight the work of a rival. Omission of an important reference is more commonly an honest mistake — the author simply misses an important paper in the expo- nentially expanding sea of archival literature. That a mistake is honest does not lessen its impact, however. Omission of a key reference deprives deserving colleagues of credit for their ideas and misleads readers interested in the topic. In medical malpractice cases, actions are judged accord- ing to the “standard of care,” that is, what most physicians would do in a given situation. If most researchers diligently review the relevant literature and find key references before writing an article, should missing an important reference be considered research misconduct? All of us have experienced another problem related to citation: while reading an article, we encounter an interesting statement referenced to an earlier publication, retrieve the original refer- ence, and find that it says something very different than was claimed. In some cases, this may be an honest difference of opinion; two researchers reading the same article may interpret its key findings differently. Frequently, however, discrepancy between attributed content and actual content arises through a scientific version of the “telephone game” — a chain of citation, where each author de- pends on a previous citation rather than retrieving and reading the original paper, propagates an error in describing the content of that paper. As with omitted references, inaccurate citation mis- leads the reader and misrepresents the work of colleagues. Such errors are not considered actionable misconduct by universities or funding agencies, yet their impact on the archival literature and on your reputation can be significant. High-profile plagiarism cases occur regularly in science and engineering as well as Exercise 8.6 in history, literature, and other fields. Find and evaluate one recent case in science or engineering and one case outside science and engineering. For each case, write a one-page summary, including what the author plagiarized, how the plagiarism was detected, any explanations offered by the au- thor, and the impact of the plagiarism on the author’s career. 124 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg PEER REvIEW 8.5 Science and engineering rely heavily on peer review, the evaluation of your work by your peers. Peer review is central to deciding which papers a journal will publish, which grants agencies will fund, which patents will be issued, and which drugs and devices will be approved. Any system of peer review must balance the fact that colleagues who work in your field are best qualified to review your work against the possibility that those colleagues include former students or mentors as well as cur- rent collaborators or competitors. Evaluating and avoiding conflict of interest is integral to effective peer review. Imagine you have been named editor of a new journal in your field. Formulate a Exercise 8.7 policy stating how your journal will handle potential conflicts of interest when assigning review- ers. What constitutes a conflict of interest? Are all conflicts equal? How will conflicts be handled? Must any reviewer with a potential conflict decline to review, or are there some situations where declaring the conflict will suffice? Will you hire staff to search for potential conflicts or will you rely on reviewers to disclose conflicts? Will you allow authors to name reviewers they consider to be in conflict? What other measures will you take? Summarize your thoughts in a two-page paper. 8.5.1 Archival Journal Articles A journal editor who receives a manuscript for review usually begins by reading the abstract and scanning the paper to verify that it is appropriate for the journal. The next step is to assign review- ers. Editors typically identify reviewers from a variety of sources, including personal knowledge of investigators in the field, databases maintained by the journal, literature searches using keywords or title words from the manuscript, and the references cited within the manuscript. Some journals allow authors to suggest reviewers at the time of submission. Selection of appropriate reviewers helps to ensure a fair and thorough review. Typically, edi- tors try to assign several reviewers who are experts in the field but not associated closely with the authors or one another. Achieving this goal is not as easy as it sounds; it assumes that the editor knows professional relationships among those working in the field — who trained in which labora- tories, who has collaborated with whom, who has published with whom. Most of this information can be found with enough research, but such research would be too time-consuming for every sub- mitted manuscript. Hence, journals rely on multiple safeguards against conflict of interest. Securing multiple reviewers provides one such safeguard, for it is less likely that multiple reviewers will have a conflict of interest or the same personal bias for or against a particular author. Some journals divide the task of assigning reviewers among multiple associate editors or members of an editorial board to help ensure that assignments are based on detailed scientific and professional knowledge about oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 125 subfields within a broader discipline. Many journals ask authors to list those whom they feel have a conflict of interest and will often exclude those reviewers. Allowing authors to name potential reviewers for exclusion raises many interesting ques- tions. As an author, you may have genuine concerns whether a particular competitor will judge your work more harshly than normal. Yet, are you willing to assert to the editor, often a senior colleague in your field, that this rival is incapable of judging your work fairly? Does having the potential to exclude particular reviewers tempt authors to try to avoid valid criticism that ultimately could help improve the research and the paper? Ultimately, much relies on the judgment of the editor. Ideally, an editor who receives two very positive reviews and one negative, but unfair, review will read the reviews, recognize the lack of substance in the negative comments, and discount the unfair review when making a decision. If a journal receives a large number of submissions and is highly selective, however, an editor may simply average scores from all reviewers without resolving potential discrep- ancies; in such cases, one negative review may be enough to prevent acceptance. Fortunately, there are many journals in each field, so there are always other opportunities to publish a high-quality paper. Recall from Chapter 3, however, that one should always take advantage of any opportunity to improve a paper via revision. Assigning reviewers and integrating their feedback can be demanding, but it is usually straightforward from an ethical point of view. In contrast, reviewing an unpublished manuscript frequently raises difficult ethical questions. First, you must decide whether to accept the request to review. Generally, you should not agree to review the work of colleagues from your institution, of former students or mentors, or of current or recent collaborators. What if your former student graduated 20 years ago, however, and you have not collaborated since? What if one of the authors is a former collaborator whom you have not published with or spoken to in 5 years? Few journals provide potential reviewers with specific instructions on exactly what constitutes a conflict of inter- est. Most rely on the judgment of the reviewers and ask them to err on the side of caution. Main- taining the integrity of peer review thus requires individuals to avoid not only actual conflicts of interest but also apparent conflicts of interest. In other words, if the author of a manuscript might believe you are biased, you should not review the paper, even if you are confident you can provide an objective review. You may find it difficult to evaluate objectively the work of a colleague you dislike; most would agree that this constitutes a bias. A more interesting question is whether you should review a manuscript written by a colleague whose work you consider to be generally of poor quality. On one hand, your responsibility as a reviewer is to help the editor evaluate the quality of work submitted for publication and to ensure the publication of only high quality research; if you know the work of a particular group well, you may be uniquely qualified to explain why a particular manuscript does not merit publication. Yet, if you consider a particular group’s work to be poor, it is likely that the 126 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg authors will consider you misinformed or even biased against them. Fortunately, this is another situation where multiple reviewers provide a safeguard. If you explain carefully why you believe the work is flawed, the editor can balance your evaluation against those of other reviewers in making a final decision. This discussion raises an issue that is critical to consider, especially by novice reviewers. The primary responsibility of the reviewer is to recommend whether to accept or reject a particular manuscript; in most cases, however, an intermediate step is to recommend potential revisions that would improve the work. By explaining carefully the strengths and weaknesses of a manuscript, you not only help the authors improve the manuscript, you also help advance their research and the field in general. Few things are more frustrating to an author than receiving a review that rates the paper poorly without providing specific criticisms. By contrast, few things are more helpful than a critique that suggests a critical new experiment or an alternative interpretation of your data that you had not considered previously. Again, however, we see that the reviewer is faced with an ethical decision. What if you, the reviewer, realize that the authors have missed the most important experiment or calculation? You could argue that the paper should be rejected because the authors have not proved their hypothesis or provided convincing results, then pursue the correct approach on your own and publish it later. Alternatively, you could provide significant guidance to the authors so that they can pursue the correct approach and publish what would be an important result that they would be congratulated for without any recognition of your anonymous contribution. Who would you ask for advice in this situation? Imagine that you are a third-year Ph.D. student and your faculty advisor asks you Exercise 8.8 to review a paper that he or she was asked to review by a top journal. If you have never reviewed a paper before and have not yet published a paper, how should you proceed? What information would you expect your advisor to provide? If you complete the review and it is to be submitted to the jour- nal based solely on your evaluation, should the editor be so notified? Should you get the “credit” for the review? How do you think the authors would feel if they disagreed with the conclusions of the review, which were very negative, and they learned that it was conducted by a student? 8.5.2 grants De Vries et al. (2006) met with a number of focus groups consisting of researchers and formulated a survey that they eventually conducted and reported in the Nature article “Scientists Behaving Badly” (Martinson et al., 2005), which was discussed earlier in this book. In the focus groups, they found researchers to be less worried about frank plagiarism or fabrication of data than about handling the “fuzzier” situations that arise in science and engineering, such as excluding data or properly appor- tioning credit for ideas and discoveries. We have focused much of our discussion in this chapter on oWNERSHIP of IDEAS, DATA, AND PuBlICATIoNS 127 these gray areas, where each of us must rely on our values and judgment in the absence of universally accepted rules. Regarding peer review, the primary concern of the researchers interviewed by De Vries and colleagues was potential theft of their ideas during grant review. One commented (De Vries et al., 2006). I’m always wary of submitting grants to [NIH] study sections, because those people who sit on the study sections, it’s not unknown for them to take your ideas, kill your grant, and then take and do it. And I think all of us have either had that happen to them or know somebody who had that happen to them. Determining whether to excuse yourself from reviewing a particular grant is often simpler than for a particular journal article because funding agencies usually issue more specific guidelines than journals. At the NIH, for example, you may not participate in the review of any grant applica- tion from your institution; if you are on the panel, you must leave the room during the discussion of these applications. You must also excuse yourself from the review of applications involving any colleague with whom you have published during the past 3 years. Furthermore, the review panel on which you sit may not review any application involving you; these grants must be sent to a different panel for consideration. NIH reviewers and staff also work to identify and avoid other conflicts, whether real or apparent, not governed by specific guidelines. The more challenging issue with regard to reviewing grants is deciding how to handle infor- mation contained within the applications. Although each application is confidential and must be destroyed following review, you will remember many of the things that you read (and heard during a panel review). Indeed, in addition to the importance of fulfilling a professional responsibility, reviewing grant applications often benefits a reviewer in three ways: you see the difference between well-prepared and poorly prepared applications, which can help you prepare more competitive ap- plications, you learn more about the overall process and what other reviewers value, and you are exposed to things that you may not have been aware of, including important references, new instru- mentation or materials, useful experimental methods or computational tools, and so forth. Indeed, you may even learn of individuals who would be good potential collaborators. Yet, because applica- tions are confidential, what information can you use and when? A good rule of thumb is that any information available in the public domain can be used in good conscience, including published papers, commercially available instruments, materials, software, and contacts listed on the Web for indi- viduals in academia and industry. In other words, if you can obtain the same information elsewhere, it can be used. In contrast, novel ideas (e.g., new experimental protocols or methods to solve a complex equation) that are not available in the public domain should not be used. Some might ask in this regard if it would be acceptable to contact the investigators and ask for permission to use their ideas. 128 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Albeit perhaps surprising, the answer is that you are not supposed to discuss any aspect of the grant application or its review with the applicant(s), hence it is not appropriate to seek such permissions. Rather, one should wait for the ideas to be made public by the investigators, often via a conference presentation, published paper, or posting on the Web. Once such disclosure has been made, it is then acceptable to use the available information or to contact the investigators for further clarifica- tion or possible collaboration. If the disclosure appears via a patent rather than via free information, however, one must then respect the conditions of the patent. That it is appropriate to use information in the public domain should be obvious, but this does not resolve all potential issues. What if the applicants did not get funded and they were unable to pursue their ideas? What if they were funded but decided to pursue a different approach? In other words, is it good for science and engineering in general to let an excellent idea die simply because those who conceived the idea could not bring it to fruition? Is there a statute of limitations on such ideas or should there be? What if you wish to apply their idea to a completely different problem, one they are most likely not interested in and would never pursue? What if you were already planning to do the same experiment or one related closely — do you need to forego your experiment to avoid what may appear to be misconduct? Who should you approach to find answers to such questions? We identified some situations regarding “intellectual property” that may arise when Exercise 8.9 a person reviews, in confidence, a grant application. Another situation could arise if you submitted a grant application to the NIH that needed to be revised two times (which generally means a two or more year delay in starting the research). What could you do if you suspected that someone on the review panel was purposely trying to delay your research so that they could pursue the same idea? List five other potential situations that could arise in grant reviews and discuss potential ethical issues. In conclusion, recall from the Preface that it was not the goal of this book to be a standalone source on matters of style or ethics in communication. Rather, our goal was to motivate the reader to develop an effective, individual style of communicating and a personal commitment to integrity because it matters. We sought to raise questions, not answer them. Our best advice is simply to seek advice from good role models whose writing and ethics you respect — learn from others, so- licit constructive feedback on oral presentations as well as drafts of manuscripts and proposals, and discuss potential concerns on ethical matters with peers, advisors, supervisors, and administrators. Work hard to ensure that, when you look back over your career upon retirement, you are proud of a job well done. • • • • 129 References Bell ET (1986) Men of Mathematics. Simon & Schuster, New York, NY. Berry TE (1971) The Most Common Mistakes in English Usage. McGraw-Hill, New York, NY. 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Ballantine Books, New York, NY. Tarnow E (1999) The authorship list in science: Junior physicists’ perceptions of who appears and why. Sci Eng Ethics 5: 73–88. doi:10.1007/s11948-999-0061-2 Valiela I (2001) Doing Science: Design, Analysis, and Communication of Scientific Research. Oxford University Press, New York, NY. Van Doren C (1991) A History of Knowledge. Ballantine Books, New York, NY. Vivian CH, Jackson BM (1961) English Composition. Barnes & Noble, New York, NY. Walters R, Kern TH (1991) How to eschew weasel words. Johns Hopkins Magazine, December 1991. Westfall RS (1993) The Life of Isaac Newton. Cambridge University Press, Cambridge, UK. Yank V, Rennie D (1999) Disclosure of researcher contributions: A study of original research ar- ticles in The Lancet. Ann Intern Med 130: 661–670. 131 Author Biography Jay D. Humphrey is Regents Professor and Carolyn S. and Tommie E. Lohman Professor of bio- medical engineering at Texas A&M University. He has authored a graduate textbook (Cardiovascu- lar Solid Mechanics), coauthored an undergraduate textbook with a former student (An Introduction to Biomechanics), published more than 150 archival papers and chapters in other books and ency- clopedias, and serves as coeditor in chief for the international journal Biomechanics and Modeling in Mechanobiology. He has served as a reviewer for 50 technical journals and 20 funding agencies in the United States and abroad. He is a fellow of the American Institute for Medical and Biological Engineering. Jeffrey W. Holmes is Associate Professor of biomedical engineering and medicine at the University of Virginia. He has published more than 40 archival papers and book chapters and has reviewed for 15 technical journals and several funding agencies, including the American Heart Association and the National Institutes of Health. Before moving to Virginia, he developed and taught the course “Ethics for Biomedical Engineers” at Columbia University, where he won the Distinguished Fac- ulty Teaching Award. Other awards include an Alexander von Humboldt Research Fellowship, the Y.C. Fung Young Investigator Award, and an Established Investigator Award from the American Heart Association. 133 Index A Abbreviations, 32-33, 49 Abstract, 49, 98 Academic research records, 104-105 Acknowledgments, 49-50 Active voice, 15-17 Adjectives, 25 Advanced Research Program, 73 Adverbs, 25 Affect/effect, 27 Aforementioned, 28 Alternative/alternation, 26 American Heart Association, 94 American Physiological Society, 116-118 Among/between, 26 Amount/number, 26 And/or, 28 Apostrophe, 32 Appendices, 50 Archival journal paper authorship of, 54, 86-87 composition of, 54 copyright, 58 galley proofs, 57-58 order of authors in, 86-87 origin of, 53-54 page charges, 59 peer reviews, 124-126 permissions, 58-59 revisions, 55-57 submission and review of, 54-56, 124-125 typesetting of, 57 Attribution within a research group, 122-123 Audience for grant, 64 for oral presentation, 81, 83 Audiovisual aids, 78-80 Authors/authorship abstracts, 98 attribution within a research group, 122-123 citation vs., 91-92 copyright transfer to journal, 114 criteria for, 97 expectations for, 88-89 final review and approval by, 97-98 financial support issues, 91 ghost, 90 gift, 89-90 guest, 90 guidelines for, 92-93 honorary, 90 impact of, 87-88 inappropriate practices involving, 90-91, 98 International Committee of Medical Journal Editors standards, 93-95 134 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Authors/authorship (cont.) notification of, 94-95 order of, in publication, 86-87 predraft group meeting with, 97 problems associated with, 88-93 quantifying of contributions, 96 quid pro quo issues, 91-92 requesting reviewers by, 125 Slutsky case, 85-86 specifying of contributions, 95-96 standards for, 93-96 students, 92-93 submission agreement, 87 technicians, 92-93 B Background and significance section, of grants, 68-69, 75-76 Bayh–Dole Act, 119 Because of/due to, 27 Because/since, 26 Between/among, 26 Brackets, 35 Brief communications, 41 C Can/may, 26 cf., 33 Cheating, 122-123 Citations, 36, 50-51, 91, 123 Colleagues. See also Authorship communicating with, 3 proofreading of writing by, 9-10 Colon, 31 Comma, 30 Communication with colleagues, 3 definition of, 3 individual differences in, 1 nonverbal, 78 oral, 77-84 Compare with/compare to, 26 Complement/compliment, 27 Comprise/compose, 27 Computational models, 114 Conciseness, 14 Conclusion section, 47-48 Confidence, 79 Continual/continuous, 27 Copyediting, 57 Copyright, 58, 114-118 Correlate, 28 Cover page, 42-44 Critical editing, 8 Curiosity-driven research, 64 D Dash, 31 Data annotating of, 113-114 datum vs., 27 electronic, 105-107 fabrication and falsification of, 108, 110 manipulation of, 108 retaining or discarding of, 108-109 sharing of, 112-114 Date-stamps, 106 Digital images, 106, 109 Dilemma, 28 Discussion section, 47-48 Dissertation, 59-61 DNA microarrays, 113 Due to/because of, 27 E Editing, 8 Editors, 54-56 Effect/affect, 27 e.g., 33 Either/neither, 27 Electronic data, 105-107 Electronic publishing, 58 Ellipses, 35 Em dash, 31 Essential/important, 27 et al., 33 etc., 33 Expectations, for publication, 88-89 Expert reviewers, 54-55 F Fabrication of data, 108, 110 Falsification, 108 Farther/further, 27 15-minute presentation, 82-84 Figures, 52-53, 66, 81 Financial support, 91 Financial support disclosures, 49 First person, 20 Footnotes, 35 Foreign languages, 33-34 Former, 28 Fraud authorship, 99, 101-102 INDEX 135 data, 108-109 images, 109 recordkeeping, 107-110 Free writing, 7 Future perfect tense, 21 Future tense, 21 G Galley proofs, 57-58 Gender, 20 Ghost authorship, 90 Gift authorship, 89-90 Good/well, 27 Grants background and significance section of, 68-69 instructions for, 67 methods section of, 71-72 NIH R01. See NIH R01 grant peer review of, 126-128 preliminary results section of, 69-70 references section of, 72-73 renewing of, 113 review of, 126-128 revising of, 128 specific aims section of, 68 summary of, 74-75 types of, 63-64 Guest authorship, 90 Gutenberg, Johann, 2 H Habits, 78 Halley, Edmund, 2 Harvey, W., 19 136 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Honorary authorship, 90 Hooke, R., 2 However/nevertheless, 27 Hyphen, 32 Hypothesis-driven research, 64, 72 I i.e., 33 Image(s), 106, 109 Image forensics, 110 Impact factor, 87-88 Imply/infer, 27 Important/essential, 27 Industry research records, 104 Infinitives, 22-23 Intellectual property, 121, 128 International Committee of Medical Journal Editors, 93-95 Interpretation of findings, 44 Introduction section, 48-49 L Laboratory notebooks, 104, 111 Laser pointer, 78-79 Latter, 28 Letter to editor, 42-44 M Manipulation of data, 108 Markup language, 114 May/can, 26 Medical history, 103 Medical images, 106 Medical records, 103-104, 111 Methods section of grants, 71-72 of scientific publications, 45-47 Microarrays, 113 Misconduct, 101-102 Model organisms, 113 Models, 114 Modifiers, 23-25 Motivations, for proposals, 64 M.S. thesis, 6-7, 59-61 N National Institutes of Health. See NIH National Science Foundation, 63 Neither/either, 27 Nervousness, 80 Neutral pronouns, 20 Nevertheless/however, 27 Newton, Isaac, 2-3 NIH data sharing limitations, 112-113 description of, 3 model organisms, 113 proposal review at, 64-67 public access to journal articles funded by, 115-118 R01 grant. See NIH R01 grant NIH R01 grant annual costs of, 113 background and significance section of, 68-69, 75-76 methods section of, 71-72 overview of, 67-68 preliminary results section of, 69-70, 76 references section of, 72-73 specific aims section of, 68, 75 Nonverbal communication, 78 Noun, 23 Number/amount, 26 Numbers, 32 INDEX 137 O Office of Research Integrity, 100 Oldenburg, Henry, 3-4 Omitted citations, 123 Omnibus Spending Bill, 112 Online publishing, 59, 115 Oral communication, 77-84 Outliers, 109 Outline, 5-7 Ownership copyright, 114-118 issues involving, 111 patents, 118-121 P Page charges, 59 Paragraph, 8 Parentheses, 31 Passive voice, 15-19 Past perfect tense, 21 Past tense, 21-22 Patents, 118-121 Peer review. See also Reviewers archival journal articles, 124-126 description of, 124 grants, 126-128 Per, 29 Permissions, 58-59 Person, 19-21 Ph.D. dissertation, 6-7, 59-61 Physiome Project, 114 Plagiarism, 36, 108, 111, 121-123 Plato, 3 Precede/proceed, 27 Preliminary results section, of grants, 69-70, 76 Preproposal, 73-74 Presentation, oral, 77-84 Present perfect tense, 21 Present tense, 21 Principal/principle, 28 Principia, 2-3, 22 Printing press, 2 Professional responsibility, 1 Program announcement, 63 Pronouns, 20 Proofreader marks, 57-58 Proofreading, 9-10 Proposals motivations for, 64 preproposal, 73-74 review process for, 64-67 Provisional patent, 120 Publications. See Scientific publications Public Health Service, 100 Publicly funded research NIH-funded journal articles, 115-118 patent issues regarding, 119-120 Public speaking, 77-84 PubMed Central, 116, 118 Punctuation, 30-32 Q Question and answer period, of oral presentation, 83 Quid pro quo, 91-92 Quotations, 35-36 R Reading, 4 Reading aloud, 8-9 Recommendations, 54-55 Records academic research, 104-105 138 STylE AND ETHICS of CommuNICATIoN IN SCIENCE AND ENgINEERINg Records (cont.) backup systems for, 106 electronic data, 105-107 fraud involving, 107-110 industry research, 104 loss of, 100 medical, 103-104, 111 reasons for keeping, 102-105 Slutsky case, 99-102 training purposes of, 103 Redundancies, 10-15 References, 50-51 Reprint requests, 115 Request for proposals, 63 Research plan, 70-72, 76 Resource sharing, 112-114 Results section, 44-45 Reviewers, 54-55, 65-66, 124-126. See also Peer review Reviewing of archival journal paper, 54-56, 124-125 of grants, 126-128 Revisions, 55-57 R01 grant. See NIH R01 grant Russell, Bertrand, 29 S Scientific information service companies, 87-88 Scientific publications abbreviations in, 49 abstract, 49 acknowledgments, 49-50 appendices, 50 citations, 50-51 conclusion section of, 47-48 content of, 41-53 cover page, 42-44 discussion section of, 47-48 expectations on, 88-89 figures, 52-53 financial support disclosures, 49 findings, 44, 46 format of, 41 impact factor for, 87-88 interpretation of findings, 44 introduction section of, 48-49 keywords, 42 letter to editor, 42-44 methods section of, 45-47 patent issues, 120-121 references, 50-51 results section of, 44-45 subheadings in, 46 symbols used in, 46-47 tables, 52-53 types of, 41 writing of, 41-42 Second person, 20 Self-confidence, 79 Self-criticism, 7 Semicolon, 30-31 Sentence, 8 Shall/will, 28 [sic], 36 Since/because, 26 Slides, 81-83 Slutsky case authorship issues, 85-86, 89-90 recordkeeping issues, 99-102 SOAP note, 103 Socrates, 3 Software, 81-82, 107 INDEX 139 Specific aims section, of grants, 68, 75 Statistical forensics, 110 Statisticians, 96 Students authorship by, 92-93 plagiarism by, 121-122 Submission, of archival journal paper, 54-56 Submission agreement, 87 Symbols, 46-47 T Tables, 52-53, 66 Team science, 3 Technical paper, 6 Technical presentations, 79 Technical proposal, 6 Technical reports, 61 Technical writing. See Writing Technician authorship, 92-93 Technology-driven research, 64 Technology transfer, 118, 120 Teleconferencing, 97 Tense, 21-22 That/which, 28 That/who, 28 Thesis, 6-7, 59-61 Third person, 20 This, 29 Thompson, D’Arcy, 40 Time-stamps, 106 Transgenic mice, 114 U Universities, 120-121 Unnecessary words, 10-15 U.S. Public Health Service, 100 V Verbs, 25 Vocabulary, 36-39 Voice, 15-19 W Web conferencing, 97 Well/good, 27 Which/that, 28 While/whereas, 28 Whitaker Foundation, 74 Who/that, 28 Will/shall, 28 Word choice, 26-30 Workplace integrity, 1 Writing abbreviations, 32-33 approach to, 5-10 editing, 8 footnotes, 35 free, 7 infinitives, 22-23 modifiers, 23-25 outline for, 5-7 person, 19-21 punctuation, 30-32 quotations, 35-36 reading aloud during, 8-9 redundancies, 10-15 tense, 21-22 unnecessary words, 10-15 vocabulary, 36-39 voice, 15-19
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813532.pdf&bkn=6813531&pdfType=book	Series ISSN: 1946-7680 Series ISSN: 1946-7680 Series ISSN: 1946-7680 SyntheSiS LectureS On engineering SyntheSiS LectureS On engineering SyntheSiS LectureS On engineering The Engineering Design Challenge: A Creative Process The Engineering Design Challenge: A Creative Process The Engineering Design Challenge: A Creative Process Charles W. Dolan, P.E., University of Wyoming Charles W. Dolan, P.E., University of Wyoming Charles W. Dolan, P.E., University of Wyoming The Engineering Design Challenge addresses teaching engineering design and presents design The Engineering Design Challenge addresses teaching engineering design and presents design The Engineering Design Challenge addresses teaching engineering design and presents design projects for first-year students and interdisciplinary design ventures. A short philosophy and back- projects for first-year students and interdisciplinary design ventures. A short philosophy and back- projects for first-year students and interdisciplinary design ventures. A short philosophy and back- ground of engineering design is discussed. The organization of the University of Wyoming first-year ground of engineering design is discussed. The organization of the University of Wyoming first-year ground of engineering design is discussed. The organization of the University of Wyoming first-year Introduction to Engineering program is presented with an emphasis on the first-year design chal- Introduction to Engineering program is presented with an emphasis on the first-year design chal- Introduction to Engineering program is presented with an emphasis on the first-year design chal- lenges. These challenges are presented in a format readily incorporated in other first-year programs. lenges. These challenges are presented in a format readily incorporated in other first-year programs. lenges. These challenges are presented in a format readily incorporated in other first-year programs. The interdisciplinary design courses address the institutional constraints and present organizational The interdisciplinary design courses address the institutional constraints and present organizational The interdisciplinary design courses address the institutional constraints and present organizational approaches that resolve these issues. Student results are summarized and briefly assessed. A series approaches that resolve these issues. Student results are summarized and briefly assessed. A series approaches that resolve these issues. Student results are summarized and briefly assessed. A series of short intellectual problems are included to initiate discussion and understanding of design issues. of short intellectual problems are included to initiate discussion and understanding of design issues. of short intellectual problems are included to initiate discussion and understanding of design issues. Sample syllabi, research paper requirements, and oral presentation evaluation sheets are included. Sample syllabi, research paper requirements, and oral presentation evaluation sheets are included. Sample syllabi, research paper requirements, and oral presentation evaluation sheets are included. “The H. T. Person Endowment at the University of Wyoming was established in 1990 to focus “The H. T. Person Endowment at the University of Wyoming was established in 1990 to focus “The H. T. Person Endowment at the University of Wyoming was established in 1990 to focus on undergraduate education. Introducing and teaching design to undergraduate students on undergraduate education. Introducing and teaching design to undergraduate students on undergraduate education. Introducing and teaching design to undergraduate students has been the focus of the H. T. Person Chair for over a decade. It is my pleasure to share has been the focus of the H. T. Person Chair for over a decade. It is my pleasure to share has been the focus of the H. T. Person Chair for over a decade. It is my pleasure to share some of the chair’s experiences with you in the hope that they may be of assistance to your some of the chair’s experiences with you in the hope that they may be of assistance to your some of the chair’s experiences with you in the hope that they may be of assistance to your program. This book focuses on both first-year projects and interdisciplinary senior design program. This book focuses on both first-year projects and interdisciplinary senior design program. This book focuses on both first-year projects and interdisciplinary senior design project. In addition to the description of the projects, the methodology for organizing and project. In addition to the description of the projects, the methodology for organizing and project. In addition to the description of the projects, the methodology for organizing and executing the projects is presented.” executing the projects is presented.” executing the projects is presented.” — Robert Ettema, Dean, College of Engineering and Applied Science, — Robert Ettema, Dean, College of Engineering and Applied Science, — Robert Ettema, Dean, College of Engineering and Applied Science, University of Wyoming. University of Wyoming. University of Wyoming. d d d o o o l l l a a a n n n T T T h h h e e e i i i i i i e e e n n n g g g n n n e e e e e e r r r n n n g g g D D D e e e s s s i i i g g g n n n C C C h h h a a a l l l l l l e e e n n n g g g e e e About SYNtHESIS About SYNtHESIS About SYNtHESIS This volume is a printed version of a work that appears in the Synthesis Digital This volume is a printed version of a work that appears in the Synthesis Digital This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide Library of Engineering and Computer Science. Synthesis Lectures provide Library of Engineering and Computer Science. Synthesis Lectures provide concise, original presentations of important research and development topics, concise, original presentations of important research and development topics, concise, original presentations of important research and development topics, published quickly, in digital and print formats. For more information visit published quickly, in digital and print formats. For more information visit published quickly, in digital and print formats. For more information visit www.morganclaypool.com www.morganclaypool.com www.morganclaypool.com w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m w w w . m o r g a n c l a y p o o l . c o m 9 781627 051767 9 781627 051767 9 781627 051767 ISBN: 978-1-62705-176-7 ISBN: 978-1-62705-176-7 ISBN: 978-1-62705-176-7 90000 90000 90000 m m m o o o r r r g g g a a a n n n & & & c c c l l l a a a y y y p p p o o o o o o l l l The Engineering Design Challenge: A Unique Opportunity Synthesis Lectures on Engineering The Engineering Design Challenge: A Unique Opportunity Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 iv Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeffrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 v Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2013 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. The Engineering Design Challenge: A Unique Opportunity Charles W. Dolan www.morganclaypool.com ISBN: 9781627051767 paperback ISBN: 9781627051774 ebook DOI 10.2200/S00487ED1V01Y201303ENG021 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #21 Series ISSN Synthesis Lectures on Engineering Print 1939-5221 Electronic 1939-523X The Engineering Design Challenge: A Unique Opportunity Charles W. Dolan University of Wyoming SYNTHESIS LECTURES ON ENGINEERING #21 CM& Morgan & cLaypool publishers ABSTRACT The Engineering Design Challenge addresses teaching engineering design and presents design projects for ﬁrst-year students and interdisciplinary design ventures. A short philosophy and background of engineering design is discussed. The organization of the University of Wyoming ﬁrst-year Intro- duction to Engineering program is presented with an emphasis on the ﬁrst-year design challenges. These challenges are presented in a format readily incorporated in other ﬁrst-year programs. The interdisciplinary design courses address the institutional constraints and present organizational ap- proaches that resolve these issues. Student results are summarized and brieﬂy assessed. A series of short intellectual problems are included to initiate discussion and understanding of design issues. Sample syllabi, research paper requirements, and oral presentation evaluation sheets are included. KEYWORDS engineering, design, challenges, ﬁrst-year, interdisciplinary, multidisciplinary, assess- ment, outcomes, organization, evaluation ix To M for years of understanding, help, and support Contents xi 1 2 3 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix The World of Engineering Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Design Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 What is Engineering Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Why Teaching Design is Difﬁcult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 The Engineering Design Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Introduction to Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 2.2 2.3 ES 1000 Introduction to Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Introduction to University Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Intellectual Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Information Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Role of H. T. Person Chair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Closing Comments on ES 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Student Engagement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 The Course Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 First-year Design Challenge Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 Overall Challenge Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 3.3 3.4 3.5 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Cost and Time Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Awards and Prizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 xii 4 The First-year Design Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Fleet Efﬁciency and the Auto Design Dilemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.2 The Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2.4 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2.5 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.6 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3 Dunebuggy Dash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3.4 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3.5 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4 First Flight: Fly a Foam Airplane 100 Yards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4.4 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4.5 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4.6 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.5 Hackysack Flip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5.4 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.5.5 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.5.6 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.6 Mousetrap Powered Car Slalom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.6.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.6.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.6.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.6.4 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.6.5 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.6.6 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 xiii 4.7 4.8 The Great Wall of Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.7.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.7.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.7.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.7.4 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.7.5 Some References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.7.6 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.7.7 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.7.8 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Underwater Recovery Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.8.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.8.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.8.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.8.4 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.8.5 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.8.6 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.9 Wind Turbines and Wind Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.9.1 Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.9.2 Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.9.3 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.9.4 Developing a Test Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.9.5 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.9.6 Challenge Day Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.9.7 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.9.8 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.9.9 Challenge Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.9.10 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5 Interdisciplinary Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Administrative Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2 Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3 5.3.1 NASA Zero Gravity Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3.2 Automated Transit System for Campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3.3 Disappearing Roads and Gas Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3.4 University Energy Plant Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3.5 Medieval Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 xiv 6 5.4 5.5 5.6 Student Recruitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Project Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Interdisciplinary Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.3 6.1 6.2 Interdisciplinary Design Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 NASA Zero Gravity I: Construction in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.3 Class Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.4 Student Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2.5 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 NASA Zero Gravity II: Exercise Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.3.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.3.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.3 Class Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.4 Student Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3.5 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.4 Design of an Automated Transit System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.4.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.4.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.4.3 Class Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.4.4 Student Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.4.5 Assessment Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.5 Disappearing Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.5.3 Class Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.5.4 Student Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.5.5 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.5.6 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.5.7 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Beetle Kill and Biomass Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.6.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.6.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.6.3 Class Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.6.4 Student Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.6 6.6.5 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.7 Gothic Cathedrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.7.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.7.2 Class Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.7.3 Student Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.7.4 Assessment Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 xv 7 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.1 H. T. Person Design Challenge for Primary and Secondary Schools in Wyoming 103 7.1.1 Engineering Background and History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.1.2 What an Equation Tells you About Design . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.2 Meteor Collision Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Tire Particle Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.3 7.4 What Happened? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.4.1 Windmill Collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.4.2 Bridge Accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.4.3 Development of Stress and Strain Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Notes for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.5.1 Paper Column Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.5.2 Meteor Collision Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.5.3 Tire Particle Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.5.4 What Happened . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.5.5 Stress-Strain Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.5 A H.T. Person Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 B Sample Course Syllabus and Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 C Information Literacy Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 D Sample Oral Presentation Evaluation Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Author’s Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Foreword xvii If you were to teach engineering design to ﬁrst-year undergraduate students, how should you proceed? This question is at the heart of the present book by Professor Charles Dolan, an accomplished designer and adept educator. The question may seem daunting, as engineering design entails the interplay of creativity and specialist expertise gained from a rigorous path of engineering study. First-year undergraduate students may be naturally creative, but they are just starting down the path and thus unlikely to have the know-how needed for meaningful engineering design. Yet as Professor Dolan shows, the design process essentially entails a series of basic considerations that ﬁrst-year students can readily grasp. Professor Dolan’s design challenge requires that students organize themselves into teams to pursue a given design objective subject to a set of prescribed design constraints (rules, as he calls them).To attain the design objective, each team must prepare a simple plan, coordinate and record its activities, performance test the resulting design, and write a concise technical report. The challenge provides students with a substantial foretaste of the design process, and enables them to better anticipate the knowledge needed for successfully undertaking more complex engineering designs. Not satisﬁed with tackling one major question about teaching design, Professor Dolan then shifts gears to take on another: How to teach interdisciplinary design to a team of undergraduate students drawn from different engineering disciplines? Addressing this question can be complicated by non-trivial curricular and administrative issues, as he explains. Additionally, it can be complicated by the issue of conceiving design projects that meaningfully involve students from different engineering disciplines over a single semester. Nevertheless, Professor Dolan successfully addresses all of these issues, to the extent that one of his interdisciplinary projects, Disappearing Roads, received national recognition and was implemented at sites requiring a minimal construction footprint. Professor Dolan’s design expertise draws on his vast experience as a consulting engineer work- ing with teams to design a broad range of concrete structures, including a remarkable series of concrete monorail structures where design requirements were subject to comprehensive sets of constraints pertaining to sound structural performance, transportation efﬁciency, convenience, economics, and aesthetics. He has coauthored a leading book on the design of concrete buildings, engaged in nu- merous research projects, and for many years has been a member of the country’s (and arguably the world’s) principal committee prescribing the design rules for concrete buildings. He teaches in an engaging and anecdote-rich manner, and occasionally enjoys pointing out less common factors that sometimes enliven the design process. For example, I recall him recounting with some humor the challenge he once faced as a member of an international design team whose xviii FOREWORD members spoke four languages including Norwegian and Japanese. Great care was needed to ensure clarity of communication, a point he often emphasizes to students. Professor Dolan is a “designer par excellence.” The University of Wyoming has been fortunate to have him as its founding H. T. Person Chair of Engineering Education, which was established for the express purpose of attracting world-class engineers and engineering educators to help teach the design process to undergraduate engineering students. Professor H. T. Person himself was an ac- complished teacher extensively recognized for his contributions to engineering practice in Wyoming and surrounding regions. This book is Professor Dolan’s leave-taking contribution to engineering education. It offers a useful, brief digest of his experience teaching design and introducing engineering to ﬁrst-year students. In late 2012 he retired from the H. T. Person Chair, and now works at his own pace on a variety of very interesting engineering design and research activities. Robert Ettema Dean and Professor College of Engineering and Applied Science Laramie, Wyoming March 2013 xix Preface Hjalmar Thorval (H. T.) Person was Professor, Department Head, Dean, and President of the University of Wyoming in the period from 1929 to 1968. Known as “Prof,” he was an accomplished teacher, sometimes teaching 20 credit hours per semester. As dean he was instrumental in moving the College of Engineering and Applied Science from its infancy to a nationally recognized program. As president, he is credited with quelling faculty dissention on campus and returning the university to a sense of progress. A Fellow of the American Society of Civil Engineers, he served as a director, on the executive committee, and on technical committees including Drainage and Irrigation, and Registration of Engineers. H. T. worked summers as a prac- ticing engineer for American Bridge Company and the Missouri High- way Department in order to bring state-of-the-art design to his classes. In Wyoming he served variously as the director for the U.S. Coast and Geodetic Survey and the State the Control Survey. Person was state’s chief negotiator on the Upper Colorado, Yellowstone, Cheyenne, Snake, Niobrara, and Columbia River Compact Commissions. He was appointed to the President’s Mis- souri River Basin Survey Commission and in 1965 was named to the Upper Colorado River Com- mission. In a region of the country where “whiskey is for drinking and water is for ﬁghting” the commitments to and importance of these commissions were both time consuming and essential to the State of Wyoming. He was recognized for his service by the National Council of State Board of Engineering Examiners, and the Four-State Irrigation Council. H. T. Person received the ﬁrst Wyoming Society of Professional Engineers’ “Engineer of the Year” award and the University of Wyoming’s “Medallion of Service.” In the early 1990s, several alumni joined to create an endowment to establish a chair to honor the vision of H. T. Person and the “Prof ’s” dedication to undergraduate education. Over 200 individuals, groups, and foundations supported the endowment. I had the distinct pleasure to discuss H. T. Person’s legacy with several of the leaders of this effort including Gus Albert, “Tut” Ellis, Harold Kester, Albert “Boots” Nelson, Frosty Kepler, and Ken Kennedy. To a person, they all xx PREFACE expressed admiration for the contribution that H. T. made to their careers and the support he offered to the multitude of students studying at the university. As the endowment was being initiated a series of lectures in H. T. Person’s honor was estab- lished. Each fall the college invites a noted individual to be the H. T. Person Distinguished Lecturer to address our alumni, students, and faculty as part of the university’s homecoming weekend. The selection of the speakers is an opportunity to present timely topics and, in many cases, to high- light the accomplishments of our alumni. For example, when the movie Apollo 13 was released, Mr. David Reid, a graduate of the University of Wyoming Mechanical Engineering program and ﬂight controller for the Apollo 10, 11, 12, 13, and 14 missions, spoke on the real issues of bringing Apollo 13 back to earth. Mr. Larry Novak of the design ﬁrm Skidmore, Owens and Merrill, spoke on the rescue efforts at the World Trade Center in 2002. In 2010 Mr. Joe Leimkuhler, Manager of Offshore Well Delivery for Shell Oil, spoke on oil drilling operations following the Deepwater Horizon oil spill. Complementing these lectures, speakers meet with classes to discuss the projects in detail and to provide insight on the value of engineering education. Even though H. T. Person was a civil engineer, a conscious effort is made to select speakers from all engineering disciplines. Thus, students and faculty have an opportunity to explore new ideas and concepts. A complete list of the H. T. Person distinguished speakers is found in Appendix I. In 2000, Mr. John Clark, noted bridge engineer, spent a semester on campus as the H. T. Person professor in residence. He supplemented the H. T. Person Homecoming Lecture with a presentation on the collapse of the Quebec River Bridge. Mr. Clark brought the background of the bridge design and construction and the Order of the Engineers ceremony together for the students. He challenged and exposed the students to the high level of responsibility that is expected of them as practicing engineers. The successful completion of Mr. Clark’s professorship suggested that a permanent chair would best suit the vision for improved undergraduate education. In 2002 a national search was conducted for the ﬁrst permanent H. T. Person Chair. I received the appointment and have had the privilege to focus on undergraduate education and engineering design. It has been a true pleasure to be able to share this endeavor for others to use. My years of professional practice have been essential to my ability to provide meaningful and relevant experiences. The challenges presented here are the culmination of over a decade of development. When they began, the college had an embryonic ﬁrst-year engineering experience focusing on the student transition from high school to the university. Therefore, initial efforts of the H. T. Person Chair focused on the ﬁrst-year Engineering Design Challenge. After three years, the Introduction to En- gineering course was well established and was being managed by Dr. Thomas V. Edgar. The design and preparation of the annual ﬁrst-year Design Challenge remained in the purview of the H. T. Person Chair. Dr. Edgar prepared many of the common lectures for the course and his collaboration on this course provided me opportunity to initiate interdisciplinary design courses. His keen insight and ability to involve students was a particular asset. The Interdisciplinary Senior Design program courses were created to be truly broad in scope. The completed projects are discussed in detail as is the philosophy and organization to make them PREFACE xxi work. In 2010, Dean Robert Ettema and I discussed the possibility of creating this volume to transfer the experience of developing undergraduate design programs to others who are interested in similar ventures. While this effort focuses on the work of the undergraduate students at the University of Wyoming, the concepts are transferrable. As is the case in most educational situations, motivated students and faculty rise to the challenge. More than anything, this book is a testament to the ability of the students to accept the challenges. As John Donne’s poem reads, “No man is an island entire of itself …” such is also true of this volume. As with any venture, there are many colleagues contributing to these projects. Dean O. A. Plumb and Dean Robert Ettema have supported the sometimes non-conventional approaches to developing design efforts. Associate Deans for undergraduate education, David Whitman, Richard J. Schmidt, and Steven F. Barrett were always available for consultation on methods to assess progress and to issue the semester-end student evaluation surveys. Dr. David Mukai and Dr. Jennifer Tanner have been valuable colleagues and co-PIs for research endeavors. Most important is the concept of a chair devoted to undergraduate teaching. The ﬁnancial and moral support of the original donors to the H. T. Person Endowment is deeply appreciated. Four people in particular have served on the H. T. Person Advisory Board and have been sounding boards for some of the ideas developed in this program. Albert “Boots” Nelson has been a constant source of inspiration and support of these efforts. Tom Lockhart, Floyd Bishop and, Bill Bellamy have also provided ideas and insight for these efforts. In addition to their support of undergraduate education, it is a tribute to their professional careers and foresight that several of the original donors are members of the College of Engineering and Applied Science Hall of Fame. I thank them all for their active interest in engineering education even as they pursued other interests in their careers and retirement. Charles W. Dolan H.T. Person Chair of Engineering Laramie, Wyoming March 2013 C H A P T E R 1 1 The World of Engineering Design When Jacob Boorstin, formerly head of the Library of Congress, released his book The Discoverers,1 there was no mention of any engineering feat. The Discoverers examines the intense and often individual pursuits of people driven to understand the world around them. Beginning with the ancient Greeks and progressing through Newton to Watson and Crick, The Discovers presents a personal quest to understand science and the natural world. As such, science requires the intellectual capacity to examine a multitude of data and assimilate that information into a coherent theory. When successful, each theory can be replicated and validated by others. It wasn’t until Boorstin’s publication of The Creators2 that engineering was acknowledged. In The Creators, art, music and sculpture appear alongside works in stone, concrete, and steel as testament to human creativity. Michelangelo, Monet, and Mozart share space with DaVinci, Brunelleschi, and Eads. While engineers do not typically see themselves in the same venue as the great artists, composers, and playwrights, they share a common trait. They create something where nothing existed. Engineering design is a unique activity with a single problem statement and multiple solutions. Often only a small number of the solutions come close to meeting all of the project requirements. In Path Between the Seas,3 David McCullough describes the extraordinary difﬁculties of working in the mud and landslides during excavation of the Panama Canal. When John Stevens, J. J. Hill’s chief engineer of the Great Northern Railroad, was put in charge of the construction, he immediately saw a railroad problem not an excavation problem. By employing the steel rails instead of working in the constantly changing mud, Stevens was able to stabilize the construction and move the project toward a successful conclusion. Path Between the Seas additionally places engineering design into the larger context of societal needs. Less than 10 percent of the book deals exclusively with the technical problems while the remainder deals with the politics, organization, and personalities engaged in this world class project. 1.1 DESIGN RECOGNITION If engineering design is such a creative process, why are so few engineers recognized for their endeavors? This question evokes two different and somewhat diametric responses.The ﬁrst argument is that engineering practice has not engendered the cult of personality evident in the arts, architecture, and scientiﬁc communities.The second argument is far more germane to the development of the craft. 2 1. THE WORLD OF ENGINEERING DESIGN Engineers work in teams with more emphasis on the end result than on the individual contribution. Simply put, individuals are easier to recognize than teams. The word Science derives from the Latin scientia, meaning “knowledge.” Using the Wikipedia description, science “is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.” Scientiﬁc theories and discoveries, unlike design projects, are often named for the discoverer not the principle involved. Newton’s laws of motion and Boyle’s law for gas pressure are examples of named scientiﬁc principles. An examination of the development of the atomic bomb at Los Alamos, New Mexico, illustrates the counter practice. Everything from the uranium separation to the development of the explosive detonation devices are engineering endeavors. That is, scientiﬁc principles are used to develop practical applications to meet project criteria. Yet, by deﬁnition, there were no engineers at Los Alamos, only scientists and “research scientists.”5 While Henry Petrosky, in Remaking the World: Adventures in Engineering,4 decries the lack of engineering recognition, the profession identiﬁes the larger issue as the need to be able to com- municate with each other and with the public at large. Engineering education places a premium on teamwork and oral and written communication. Articulation of complex issues, solutions, and the impact on society fall to the engineer. History has proven there is no place for hubris in the engineering design profession. One needs only to read the impact on Robert Mulholland after the collapse of the St. Francis Dam in California, to fully appreciate the impact on the individual and society resulting from neglect or oversight on design.6 1.2 WHAT IS ENGINEERING DESIGN Design is a creative process. As such, the deﬁnition of design changes with its associate profession. Art, engineering, music and all creative enterprises have design components. For example, civil engineering design may include creation of contract documents, calculations, or studies that describe how to assemble materials in new or novel ways. Similarly, computer designers may create a new generation core chip just as a musician drafts a score or an artist sketches the start of a painting. An example of the creative symbiosis of technology, design, and the arts is Wikipedia, which is why it is used in this context. The platform allows all to assemble information and at the same time contains a series of checks and balances to assure validity of the work. More formally, Wikipedia deﬁnes design as follows: (noun) a speciﬁcation of an object, manifested by an agent, intended to accomplish goals, in a particular environment, using a set of primitive components, satisfying a set of requirements, subject to constraints; (verb, transitive) to create a design, in an environment (where the designer operates) This formal deﬁnition provides a framework for the development of engineering design chal- lenges presented in this book. Speciﬁcally, the design must satisfy a set of criteria or requirements and is constrained by external factors such as available materials or cost. 1.3 WHY TEACHING DESIGN IS DIFFICULT 1.3. WHY TEACHING DESIGN IS DIFFICULT 3 The idea that design creates something where nothing previously existed is a source of anxiety when teaching design. In the university environment, courses are offered by individual topic and subject area, which are often aligned with the professor’s personal and professional interest. In most cases, the subject material is further structured to be narrow and analytic in nature. “Analytic” implies the student assesses the information provided, prepares the necessary calculations, and presents a unique solution.This is especially true in the developmental years of engineering education. In these courses, the student is assembling the building blocks needed for the rest of his or her career. At the same time, coordination between these core courses is minimal or non-existent. In consequence, students have several years of experience and practice generating a single solution to a well constrained problem, which is then graded by the faculty member as right or wrong. Throughout this process, thinking that integrates coursework from multiple subjects is generally absent or not developed. Somewhere late in the junior year, or certainly in the senior year, the engineering or computer science student runs into the “design project.” Depending on the resources available, faculty members often simplify the design practice questions. Simpliﬁcation is for self-survival. In a class of 30 to 100 students there will be a wide array of acceptable solutions. Grading this multitude of solutions engages a substantial amount of the faculty member’s time and is often not suitable for delegation to a “teaching assistant.” Even if a teaching assistant is available to aid with the grading, the faculty member is responsible for deﬁning the range of acceptable solutions and needs to provide insight on the “correctness” of the solution domain. Developing engineering design problems that require substantial interaction with a student group is even more challenging. These challenges range from introductory ﬁrst-year courses to interdisciplinary senior design courses. In each case the logic, organization, and assessment of the design courses are presented. 1.4 THE ENGINEERING DESIGN CHALLENGE The “Engineering Design Challenge” is then a paradox. To the educator, the challenge is to impart concepts of design to students steeped in a tradition of solving analysis problems. To the student design is an uncomfortable step from known to unknown conditions, often with apparently sketchy deﬁnitions of the problem requirements.The following is an examination of both sides of the paradox. Each section discusses the design challenge presented to the students and the objectives and trials of managing the design challenge effort. Complementing the Engineering Design Challenge is an overview of the University of Wyoming ﬁrst-year Introduction to Engineering course. This course is required of all ﬁrst-year engi- neering students and includes the ﬁrst-year design challenge.The success, failure, and lessons learned from this course are discussed. 4 1. THE WORLD OF ENGINEERING DESIGN REFERENCES [1] Boorstin, D. J., The Discovers, First Vintage Books, New York 1983. [2] Boorstin, D. J., The Creators: A History of Heroes of the Imagination, First Vintage Books, New York 1993. [3] McCullough, David G., Path Between the Seas: The Creation of the Panama Canal, 1870–1914, New York, Simon and Schuster, 1977. [4] Rhodes, Richard, The Making of the Atomic Bomb, Simon & Schuster, New York, 1986. [5] Petroski, Henry, Remaking the World: Adventures in Engineering, First Vintage Books Edition, New York 1997 [6] Reisner, Marc. Cadillac Desert: The American West and its Disappearing Water, New York, Penguin Books, 1993. C H A P T E R 2 5 Introduction to Engineering 2.1 ES 1000 INTRODUCTION TO ENGINEERING Each fall semester, the University of Wyoming College of Engineering and Applied Science offers 13 sections of ES 1000 - Introduction to Engineering. With 22 to 30 students per section, this is the largest common course in the university. Instructors are typically tenured faculty or extended term lecturers who volunteer to lead the course. The professor is assisted by an undergraduate engineering peer assistant. A common course syllabus is developed and a set of prepared lecture notes accompanies the syllabus to assist each professor. A sample course syllabus is included in Appendix II. Each fall a design challenge is developed and presented to the ﬁrst-year students. The University of Wyoming Introduction to Engineering course is one credit hour and is intended to cover a variety of topics that are required by the University Studies Program (USP) as well as introducing the students to a design exercise. Embedded within the ES 1000 course are the university requirements for information literacy and intellectual community. Both of these requirements are somewhat loosely deﬁned. For example, the University Studies Program deﬁnes an intellectual community: Intellectual Community Deﬁnition: Courses that fulﬁll the Intellectual Community requirement of University Studies provide stu- dents with an introduction to the purpose and philosophy of higher education. These academic, content-based courses, designed for ﬁrst-year students, focus on the critical-thinking skills nec- essary to understand, analyze, and produce knowledge within the framework of the discipline or area of inquiry in which the course is offered. In attempting to address all areas of study within the university, this deﬁnition is more of a description than a deﬁnition and offers only marginal guidance for the organization of the course. Similarly, the University Studies Program deﬁned information literacy from the American Library Association. Information Literacy Deﬁnition: Information Literacy, as deﬁned by the American Library Association, is the ability to “rec- ognize when information is needed and to locate, evaluate and use effectively the needed information.” These two requirements are complementary to the design process. Even so, combining all of these actions into a single course, let alone a single credit hour, is challenging. Considering the above, the university catalog description of the ES 1000 course is as follows: 6 2. INTRODUCTION TO ENGINEERING ES 1000. Orientation to Engineering Study. 1. Skills and professional development related to engineering. Involves problem solving, critical thinking and ethics, as well as activities to help transition to university environment. Required of all freshmen entering engineering curricula. Students with credit in UNST (University Studies) 1000 may not receive credit for this course. (Normally offered both semesters) The I and L designation in the catalog description indicate that the course meets the intel- lectual community and information literacy requirements and are approved for such by the USP Committee. With only a single credit hour to accomplish the objectives of this myriad set of re- quirements, the course content is relatively packed. Over the years, the course has evolved from an effort to assist engineering students transitioning from high school to college life to a course with substantial engineering and design content. The current content primarily addresses the philosophy of engineering while engaging the student in the engineering profession. Approximately 10 years ago the course was modiﬁed to meet both the 2003 USP criteria listed above; it also added a design challenge to the curriculum. In addition to the course professor, each section is assigned a peer assis- tant, who receives a small stipend. The peer assistant assists the faculty member in the presentation of the course and becomes a contact for the ﬁrst-year students. The peer assistant concept has proven to be exceptionally valuable. The peer assistant is able to answer a number of transitional questions that faculty members are, by and large, unaware of or unable to address. These questions deal with issues such as campus food, dating, roommate problems, selection of faculty members for courses during advising, and related topics. When broken down to its fundamentals, ES 1000 has three important components. The ﬁrst component introduces the students to campus life. The second component requires students to become active in collaborative work, primarily by establishing groups engaged in the design challenge. The third component, information literacy, is an individual effort that requires the students to prepare a paper on a topic related to the design challenge and a second paper assessing the sources used in the research paper. 2.1.1 INTRODUCTION TO UNIVERSITY LIFE The introduction to university life component engages students in the College of Engineering and Applied Science and the campus at large. There are a required number of activities that each student must attend. These include professional society meetings within the college and events external to the college. Each student is asked to attend the senior design symposium presentations at the end of the semester. Participation is recorded by a self-reporting system structured to foster responsibility and communication. A critical piece of this component is encouraging students to participate in professional society activities. An underlying philosophy for this requirement is to retain students. Retention is improved if the student is engaged in their areas of interest. Undeclared students visit professional societies in areas of interest. In addition to the regular professional societies, the students may also select from the Society of Women Engineers, the Minority Engineering Program, and Engineers without Borders. Through this effort students meet upper-class students and become comfortable both in the college and their area of study. 2.1. ES 1000 INTRODUCTION TO ENGINEERING 7 2.1.2 INTELLECTUAL COMMUNITY The intellectual community requirement engages the students through the design challenge. While the students work in small groups, the challenge is organized to reward collective efforts. In the detailed challenges that follow, the entire section is taken as a team. This structure supports the exchange of ideas and concepts within the class rather than developing an attitude of secrecy and exclusion. To encourage cooperative endeavors, students are required to present oral summaries on the progress of their design efforts. Typically, two presentations occur during the semester. The ﬁrst presentation is during the preliminary design phase. This presentation opens the array of potential solutions to the design challenge or focuses on the development of one aspect of the design. The second presentation either follows the research paper or the design challenge. If the presentation is on the design challenge, then the students must explain why their designs worked and what aspects of the design could be improved. If the oral presentation is on the research paper, the students correlate their research to the solution they developed for the design challenge. The selection of the design challenge or the research topic for the challenge is at the discretion of the section professor. The selection of an option in any given semester depends upon the scheduling of the design challenge. Because the design challenge often requires the use of particular buildings or facilities on campus, the presentation date often has to be coordinated with other academic units. When the challenge occurs at the very end of the term, the research topic is selected for oral presentation. To engender building an intellectual community, each group is required to develop a design notebook. As motivation for developing and maintaining a notebook, the work of College Hall of Fame member Thomas Osborne is used as a case study. Osborne worked for Hewlett Packard and was involved in the design of handheld calculators. Osborne’s notebooks at HP were instrumental in HP winning a lawsuit and receiving the patent for the ﬁrst fully functional engineering calculator. A thought-provoking interview with Osborne can be found on the web.1,2,3 The Design Notebook To assess student engagement, each group is required to maintain a design notebook. Bound note- books, e.g., spiral or similar volumes, are preferred, however, loose leaf notebooks are allowed to accommodate the students’ conﬂicting schedules. The notebook is started early in the semester to record ideas, thoughts, and designs. The notebook must contain the following information: (cid:129) A title page containing the design group name and the name and email of each group member. (cid:129) A summary page, following the title page, with the following critical information: – Page numbers for the testing and evaluation program. – A brief summary of the test data results. 8 2. INTRODUCTION TO ENGINEERING – The total expenditure to construct the project including a statement that the budget restrictions were met. (cid:129) Pages must be numbered and dated. (cid:129) Pages should include components of the design work including: sketches, references, notes, calculations, list of materials, costs, alternate materials considered, summaries of group dis- cussions, conclusions and decisions, and any other activities relevant to the design challenge. Comments on ideas that work, things that didn’t work, and changes to initial design concepts are appropriate. (cid:129) The design notebook is turned in at the design challenge. (cid:129) The design notebook is source material for the oral presentation. (cid:129) The ﬁnal entries should include comments on how to improve the design. Notebooks are reviewed by the peer assistants at the registration for the design challenge.They are graded on a three-part scale. Zero points are assigned for no notebook, 5 points for a fair to poor compilation, 7 points for an average submittal, and 10 points for a thorough effort. All members of the group receive the same grade. 2.1.3 INFORMATION LITERACY The information literacy component of ES 1000 requires the students to prepare a brief paper and to acquire the skills to critically assess information sources. Students examine a number of different information sources and evaluate the quality of those sources. The paper requires the students to evaluate relevant sources and limits the number of references allowed. The limitation of references forces students to concentrate on those references most valuable to presenting their topic. Each student is asked to locate one reference from a peer-reviewed journal, one reference from popular literature, one reference from the Internet, and one reference in opposition to the position they are presenting. A critical part of the information literacy paper is explaining to the students how to differentiate between Internet sources and peer-reviewed articles since both appear on the Internet. With the availability of search engines in the University Library, and the accessibility of Google Scholar, the students must be able to differentiate between general Internet-based sources and peer reviewed material. A second paper asks the students to assess their sources. Restricted to two–three pages in length, the exercise forces students to critically examine the material they were presenting and create a rationale for the validity of their source material. The students submit a portfolio of the articles that they used for their paper. The portfolio accomplishes two objectives. The ﬁrst objective demonstrates to the student that resource material should be archived for their own use.The second objective allows the professor to verify that the source requirements are satisﬁed. A full description of the information literacy requirements and the assessment paper requirements is provided in the Appendix III. 2.2. ROLE OF H. T. PERSON CHAIR 9 Perhaps one of the more interesting outcomes of this exercise occurs when students comment on how difﬁcult the journal papers are to read. Comments like this provide an opportunity to reinforce the value of the education, why the curriculum is structured to build the fundamentals of and engineering education, and promote an awareness of the value of professional papers compared to news sources. 2.2 ROLE OF H. T. PERSON CHAIR The H. T. Person Chair of Engineering position was made possible by University of Wyoming Alumni who recognized the value of a strong emphasis on engineering fundamentals and desired to make a serious contribution to undergraduate education. An annual task of the H. T. Person Chair is to establish the ﬁrst-year design challenge. The endowment also provides a small amount of discretionary funds to support these challenges. The H. T. Person Chair job description is 60 percent teaching, 5 percent advising, 5 percent service, and 30 percent research and creative endeavors. Historically, two–three credit courses and one section of ES 1000 are taught in the fall and 2-three credit courses are taught in the spring. Honors courses are often taught as a voluntary overload. Two to four graduate students are directed each year. In retrospect, managing the interdisciplinary senior design courses require considerable effort. In addition to the course organization, these courses require coordination with faculty in related ﬁelds so expertise is available when needed. A reasonable work load would be to teach only the interdisciplinary course in a given semester. 2.3 CLOSING COMMENTS ON ES 1000 2.3.1 STUDENT ENGAGEMENT Prior to 2003 the student response to ES 1000 had been relatively lackluster. To reinforce the importance of the course and to emphasize its place in the University Studies Program, in 2003 the college instituted a Freshman Convocation. The Convocation is held on the Monday of the ﬁrst day of class with ES 1000 classes beginning on Tuesday. At the Convocation, the Dean welcomes the students and presents the importance of the class, the faculty members and peer assistants are introduced, and the design challenge for the semester is unveiled. The convocation improved student engagement signiﬁcantly. 2.3.2 THE COURSE STRUCTURE After the ﬁrst cycle of teaching ES 1000, it was apparent that a typical one-hour schedule had to be restructured to meet the demands of the program. The course dragged on and students lost interest toward the end of the semester. Consequently, the course was modiﬁed to meet twice a week for half a semester. The modiﬁed schedule enhanced student engagement and eliminated conﬂicts between the design challenge and ﬁnal term projects in other classes. 10 2. INTRODUCTION TO ENGINEERING 2.4 ASSESSMENT ES 1000 is successfully engaging students in the college. The course provides the students with critical tools needed to advance their education and a myriad of topics and activities to explore. The expanse and complexity of an engineering education is presented and enables students to assess early in their career if this course of study is appropriate for them. The grading structure of ES 1000 balances class attendance, the design challenge, and outside activities. Adoption of a similar program can adjust where the emphasis is placed in the grading system. REFERENCES [1] www.hp9825.com/html/osborne_s_story.html [2] www.viddler.com/explore/sleibson/videos/4/ [3] www.edn.com/electronics-blogs/4306814/how-hp-got-its-first- calculators-video-interview-with-tom-osborne C H A P T E R 3 11 First-year Design Challenge Development 3.1 OVERALL CHALLENGE PHILOSOPHY An overriding concern in engineering educations is engineering and applied science students do not see design until their junior or senior years.This is a long time to wait and an opportunity for students to lose interest. The ﬁrst-year design experience is to motivate students to realize engineering can be fun as well as complex. The details of ﬁrst-year engineering challenges are provided in the following chapter. The philosophy and underlying assumptions of the challenges are presented here. A review of some design challenges began to show the difﬁculty in designing challenges for large groups of students. The MIT “King of the Hill” challenge and the University of Oklahoma “Pumpkin Toss” demonstrate excitement and student engagement. At the same time, they are a competition, complex for ﬁrst-year students, and involve a substantial ﬁnancial outlay. While life itself is a competition, engineering generally requires collaboration. Therefore, challenges, not com- petitions, are developed to promote a cooperative endeavor. The challenges are sensitive to the fact that college and students’ budgets are severely constrained.This leads to a second goal of these design challenges: limit the budget for the project. In several of the following challenges, parts are identiﬁed and supplied to the students. Funding for these parts comes from the H. T. Person endowment. These parts were supplied to balance the playing ﬁeld by requiring all groups to work with a common set of components. The motors are typically underpowered or have a high a RPM in their native mode. Thus, each group has to adjust their design to the materials available. One global objective of the challenge is to minimize the rules. This makes the challenge a true outcome-based activity where creativity and innovation are rewarded. For each challenge, questions arise that require clariﬁcation.These questions are classiﬁed as “proprietary” or “public” by the faculty member in charge or by the student request. Public questions request general clariﬁcation of the rules and are answered on a FAQ site set up on the ES 1000 class website. For example, a public question might be: “Can I change the batteries after each run?” Proprietary questions deal with groups wanting to know if an aspect of the design is allowed. An example of a proprietary question that is used in class is the keel design of the Australian America’s Cup yacht several years ago. The winged keel design was approved but kept secret until the race and the Australian yacht ended up with a signiﬁcant competitive advantage. Students identify their request as public or proprietary and, if private, they are responded to individually. An example of a proprietary question might be: “Can 12 3. FIRST-YEAR DESIGN CHALLENGE DEVELOPMENT we use CO2 cartridges for power?” In the case of the CO2 cartridge, the response may also ask for a safety plan on the cartridge use. The challenge envisions designs that can be completed in the student dorm room. The college machine shop has space available for the ﬁrst-year students. The area contains a number of hand tools and drill presses. Students must attend a shop safety video before gaining permission to use shop facilities. Shop times are scheduled when shop staff supervision is available. 3.2 SAFETY The ﬁrst challenge assumed that the students would behave in a safe, responsible manner, especially following the lectures on ethics and holding public safety paramount in professional engineering efforts. On the day of the challenge, one group launched a vehicle powered by 16 bottle rockets on the ballroom ﬂoor of the Student Union! Therefore, the following safety clause became part of every challenge. The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your professor. The safety statement is general and intended to remind the students of their obligations. Occasionally, designs come forward that are on the margin of safe operation. In these cases, the group is required to prepare a safety program that must be approved before their design is allowed to participate. Requiring a safety plan has two outcomes. Either the design is modiﬁed so a plan is not needed or the students prepare a plan and learn another important aspect of design development. 3.3 COST AND TIME CONSTRAINTS Engineering design is driven by cost effectiveness. To maintain this philosophy in the challenge, students’ budgets were initially set at $10–$15 per group. “Free” materials could be used; however, the deﬁnition of “free” needed explanation. The deﬁnition of “free” is that it has no commercial value. In short, the professor can elect to keep it or throw it in the trash following the competition. “Rented” or “borrowed” materials are not allowed. The “free” aspect of the challenge is to encourage the students to use materials that may be commonly available or otherwise scrap. Plastic drink containers, cardboard, and similar materials are readily available and have successfully incorporated into many student designs. 3.4. AWARDS AND PRIZES 13 The “borrowed or rented” clause is added because students are very skilled in “gaming the system.” In one design challenge, a group showed up with a $20,000 piece of robotic equipment “borrowed” from a parent’s company. While the design was certainly creative, it was not in the spirit of economical design or the design challenge. The design challenge has students working in groups of two or three. Experience with these challenges suggests that providing kits is not needed when parts are readily available locally. Challenge budgets increased to $30–$50 per group when no parts were provided. This is incorporated into the class structure as appropriate. The class schedule also constrains the budget. With only seven to eight weeks from start to ﬁnish, there is not sufﬁcient time for students to execute a full set of design plans, prototypes, and ﬁnished products. The quality of the student designs improves when trial runs are required. Time to repair or upgrade the designs is built into the schedule. The ideal schedule has one to two weeks between trial testing and the ﬁnal challenge. In cases where trial runs can be completed and initial data recorded in a continuous manner, less time is needed between the trial and the challenge. An important parameter in determining the schedule for trial runs and the challenge is the possibility of damage to the design from the challenge testing. Thus, the car side impact and the Styrofoam airplane ﬂight require a longer period between testing and the challenge as the design may be damaged in testing. Awareness of these limitations allows the schedule to provide ample time for modiﬁcation or replacement. 3.4 AWARDS AND PRIZES To minimize the competition aspect of the challenge and to reinforce collaboration, individual prizes are not generally offered. Pizza parties for the section with the best overall performance are often provided. The latter is consistent with encouraging cooperation among the groups in each section. To assess whether prizes were an effective inducement to improve the design, on two occasions, the author provided cash prizes for the best design performance. In one case, the carpet climb, this was extremely effective inducement. In another case, the underwater recovery vehicle, it led to a chaotic situation with less than professional behavior. Keeping awards at the section level was most effective. 3.5 ASSESSMENT The design challenge is very popular and is often cited as the most interesting and memorable part of the ﬁrst-year experience. At the end of each semester, the professors and peer assistants gather and critique the challenge, and a semester-end survey is issued to each student. These closing comments are based on student reviews and faculty and peer assistant debrieﬁngs. (cid:129) The low-cost, open-ended design challenges are very popular. (cid:129) The design challenges are an effective introduction to the engineering program. 14 3. FIRST-YEAR DESIGN CHALLENGE DEVELOPMENT (cid:129) On a typical challenge, approximately 20 to 30 percent of the groups will successfully complete the challenge. The toughest challenge, the carpet climb, had 2 of 134 groups succeeded. (cid:129) Requiring trial runs as part of the challenge improves the overall design by effectively requiring the groups to complete their design prior to the actual challenge. (cid:129) The budgets listed on each challenge are typically sufﬁcient. (cid:129) Access to the shop or to basic hand tools is a beneﬁt but not absolutely necessary. (cid:129) Challenges can be used by individual sections or by an entire class. The one minor deﬁciency in the ES 1000 program is the lack of time spent working with the students on formal design development. There are two reasons for this. First, the total number of topics to be covered diminishes the time available for design. Second, with 13 sections and typically 10 different professors, a lack of consistency on the design effort between sections is possible. A pre- semester brieﬁng helps assure all faculty and peer assistants understand the objectives of the challenge. Faculty members have considerable freedom to then adjust the course, but not the challenge rules, to suit their own goals. The syllabus in Appendix II illustrates the overall course and design-directed activities. C H A P T E R 4 15 The First-year Design Challenges 4.1 INTRODUCTION This chapter presents the design challenges developed at the University of Wyoming. The chal- lenges are updated to describe the facilities needed for the design challenge, to incorporate relevant “Frequently Asked Questions,” and to incorporate results from running the challenges. The issue of facilities is not trivial.The University of Wyoming is fortunate to have widespread cooperation among various facilities within the university community. At the same time, gaining access to the indoor football practice ﬁeld requires coordination between the College of Engineering and Applied Science and the Athletic Department. One consequence of this cooperation is that the design challenge is typically held in October during an away football game. This timing provides the challenge with wider access to campus facilities and less competition for attention but also means that the syllabus is modiﬁed each year to synchronize with the facilities needed for the challenge. Consideration of the facilities is additionally tied to visibility of the engineering program. When possible, the challenges are held in highly public areas. The atrium of the campus library was an ideal setting for the carpet climb. The Student Union ballroom served for the slalom challenge. Having an audience augments the experience. If the challenge is held in a public area, a poster or other description of the challenge assists the public in understanding the activity. Each challenge describes the challenge objective, the rules for the challenge, the safety state- ment, the challenge organization, and concluding comments. The challenge and rules statements vary depending on the constraints placed on the challenge and available facilities. The organiza- tional discussion addresses preparation, evaluation, and peer assistant activities required prior to the semester, during the semester, and on the challenge day. If the challenge is subsidized, the subsidy is discussed in the challenge description. Subsidies often take the format of providing common components that must be used in the challenge and are funded by the H. T. Person Endowment. The source of these components is identiﬁed, although some caution is offered because the individual parts are not uniformly available from year to year. Subsidies are typically less than $1,000 spread over the 13 sections of ﬁrst-year students. The challenge is typically completed on Saturday morning, although one challenge was suc- cessful on a Thursday evening. The challenge is conducted outside of class hours so some allowance is needed for students who cannot attend. The rules require at least one person from each group to 16 4. THE FIRST-YEAR DESIGN CHALLENGES be present. This has been successful. In addition, all groups are allowed to request a preferred time if there is a personal conﬂict. This option has been rarely exercised. The challenge requires about 15–20 minutes per section and is dependent on the number of test sites available. With 13 sections, the University of Wyoming typically schedules an entire morning to complete the challenge. Faculty and peer assistant participation during the challenge is needed. Typically, the course coordinator and the H. T. Person Chair are present for the entire challenge and serve as the adjudi- cators for safety and rule violations. The peer assistants handle the administrative tasks. Professors are encouraged to attend when their sections participate. Each challenge describes the peer assistant assignments. The peer assistant assignments are provided assuming 10–15 sections are participating in the challenge. A single section can be conducted with a faculty member and peer assistant. 4.2 FLEET EFFICIENCY AND THE AUTO DESIGN DILEMMA Figure 4.1: Side impact safety test. 4.2.1 FACILITIES This challenge requires a test track. Buildings with a concourse around the perimeter of the building work as does an indoor running track. The challenge is designed for a smooth ﬂoor. If the challenge 4.2. FLEET EFFICIENCY AND THE AUTO DESIGN DILEMMA 17 is conducted on a running track with a composite surface, the qualifying distances may have to be adjusted to account for the higher ground friction. A side impact test area needs to be established. Typically, this is an area about 12 feet square with a heavy plastic sheet placed on the ﬂoor. The impact hammer is placed in the center and the plastic collects the egg splatter. The challenge has been run in a smaller area with the impact hammer in a cardboard enclosure to capture the egg splash, but the visual impact of the test is greatly diminished. 4.2.2 THE CHALLENGE This challenge calls for each section to form its own automobile company and to manufacture a ﬂeet of electric motor powered automobiles that are both efﬁcient and safe. The EPA CAFE (Corporate Average Fuel Economy) rules require an increase in the average fuel efﬁciency for automobiles and trucks. Meeting these economy goals generally leads to a design solution favoring smaller engines and lighter weight cars. This creates a conﬂict between vehicle fuel efﬁciency and safety. Many lighter cars perform less well in collisions than heavier cars. Safety rules require side impact resistance and side airbags to help mitigate this problem. In order to gain an insight into the design tradeoff between fuel efﬁciency and safety, each section will: a) construct a ﬂeet of vehicles to meet fuel efﬁciency requirements and b) conduct side impact tests on vehicles that the team constructs. Fuel efﬁciency will be determined by a test of the distance traveled by your vehicles. The distance test begins with fresh batteries and runs until the vehicle stops. The impact test consists of a sledgehammer mounted on a frame that will deliver the side impact. The sledgehammer will be raised through a 90-degree angle. The vehicle will be placed against the side impact frame. An egg is placed in the driver/passenger compartment. The hammer is released to strike the car. The raw egg must survive. The ﬂeet consists of three sizes of vehicles: economy, standard, and SUV. All are powered by a 4.5 volt electric motor. Economy cars will use one AAA battery, standard cars use two AAA batteries, and SUVs use three AAA batteries, provided by the students. At least one vehicle of each size must be built and tested as described below. In that regard, the company (section) must decide what constitutes its best overall ﬂeet composition. The objective of each company is to earn the most points. The section with the highest point total gets the admiration of the entire freshman class and a pizza party on the last day of class. Bonuses and Penalties will be assigned to each company as follows: (cid:129) Each vehicle meeting the minimum distance standard: 5 points. (cid:129) Bonus for ﬂeet vehicles exceeding distance standards: 2 times the qualifying standard—10 points, 4 times—15 points, 8 times—20 points, etc. Each additional doubling of the qualifying standard gains 5 points. (cid:129) Companies not having at least one vehicle from each category will be penalized 50 points. 18 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Vehicles that fail to meet the minimum distance target: zero points. (cid:129) Each vehicle with an intact egg: 20 points. (cid:129) Each vehicle with a cracked egg: 5 points. (cid:129) Failure to pass the side impact test: zero points. (cid:129) All vehicles must be operated in a safe manner. Explosive, pyrotechnic, or similar devices are disqualiﬁed, and a 40 point deduction will be assessed to the team if they are brought to the challenge. On the challenge day, vehicles will be weighed, measured, classiﬁed, and logged in prior to the test program. Heat times will be assigned in advance so each group knows when their ﬂeet will run. 4.2.3 THE RULES Companies consist of a complete section. Individual corporate divisions (groups) consist of two or three students. Single-person entries and teams greater than three students are not allowed. Remember, you are working as a company so internal communication is encouraged. The sole source of power for the vehicle is a 4.5 volt electric motor provided in a kit to your group. Each kit includes the motor, gear set, and battery box (Figure 4.2). Figure 4.2: Motor, battery box, and gears provided. (Note: Jameco http://www.Jameco.com has motors and gears, pictured above, and provides torque/speed curves for the motors. Electric motors and gears are available from a number of web sites including Edmunds Scientiﬁc.) Each team must maintain a design notebook (see Chapter 2). No team shall spend more than $15.00 for supplies and equipment to manufacture the vehicle. It is OK to use free stuff. The deﬁnition of “free” is that it has no commercial value. In short, 4.2. FLEET EFFICIENCY AND THE AUTO DESIGN DILEMMA 19 the instructor can elect to keep it or throw it in the trash following the competition. Modiﬁed prefabricated cars are automatically disqualiﬁed. “Rented” or “borrowed” materials are not allowed. This budget can be adjusted if motors and gears are not provided. Vehicles will be weighed, measured, and logged in prior to the test program. At your appointed time, take your vehicle to the distance trial station. Upon completion of the distance trials, remove the batteries and place them in the recycling box. Take your vehicle to the Safety Test station. Vehicle fabrication: (cid:129) The vehicle is to be constructed using only 1/4-inch-thick foamcore board, engineering cal- culation paper, and white (Elmer’s) or thermo plastic (hot-melt) glue. The vehicle must ﬁt within an envelope that is 10 inches long, 4 inches wide, and 3 inches tall. Place a mark on the centerline of the driver location on your vehicle. This corresponds to approximately 1:18 scale of an actual car. (cid:129) A box having these inside dimensions will serve as a template to verify compliance of the vehicle size. The ﬂoor of the vehicle must be at least 1/2 inch above the ground level (Figure 4.3) under impact criteria. A 1/2-inch-thick block must pass freely beneath the vehicle. (cid:129) Wheels, motor mounts, axles, and gear shafts may be metal or plastic as appropriate. The vehicle must be hollow; however, you can consider the use of transverse elements for the ﬁrewall and ﬂoor bracing. (cid:129) You may consider stiffening elements at the ﬂoor, doors, and doorposts, and strategic placement of the battery box. No seats or other accoutrements are required; however the “sheet metal” parts of the cars should not be so ﬂimsy that the aesthetics of the car suffers. (cid:129) The car body should be shaped to include the passenger compartment, hood, and trunk area. Front and rear windshield areas must be open. Doors need not open, but there must be a way to replace batteries without damaging the vehicle. (cid:129) There must be a hole 1 3/4 inches in diameter on one side or the roof for the insertion of the egg. You must decide what portions of the car may be fabricated from sheet paper and where the foamcore may be used as strengthening elements. Vehicle weights with batteries but without the egg are as follows: (cid:129) Compact car (1 battery): less than 225 grams (cid:129) Standard car (2 batteries): 225 to 300 grams (cid:129) SUV (3 batteries): greater than 300 grams The distance criteria: 20 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) The vehicle and driver (the egg) will be placed at the starting line. The vehicle is started by turning on the power. No push starts are allowed. The total distance traveled around the track will be measured. Teams may redirect the cars to keep them in their lanes. (cid:129) To qualify, a vehicle must travel a minimum of 100 yards. (cid:129) Masking tape lines on the ﬂoor will indicate the qualifying distance and bonus point locations. The vehicle safety criteria test: (cid:129) Side impact safety tests are conducted with the apparatus shown in Figure 4.3. Figure 4.3: Side impact safety test apparatus and vehicle envelope. Once each car has completed its distance trial, the batteries are removed, placed in the recycle bin, and the vehicle is taken to the impact test machine. (cid:129) The egg is reinstalled and the car placed in the impact testing machine with the centerline aligned with the hammer. The egg is placed loosely in the vehicle. “Seatbelts” and “airbags” are permitted if they are in the car during the distance trial. The hammer handle is moved to the horizontal position and then released. (cid:129) An egg is deemed to have survived if there are no cracks in the shell. Therefore, careful removal of the egg after the impact test is important. 4.2.4 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or 4.2. FLEET EFFICIENCY AND THE AUTO DESIGN DILEMMA 21 (a) Test setup (b) Results Figure 4.4: Side impact test execution. suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. 4.2.5 CHALLENGE ORGANIZATION Early organization: (cid:129) Identify a test facility track and schedule the design challenge day (cid:129) Identify a practice area and setup. Preparation for challenge day: (cid:129) Prepare an overall summary score spreadsheet (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet (cid:129) Prepare compliance box (cid:129) Build the impact test hammer (cid:129) Prepare a recycling box for used batteries (cid:129) Draw lots for the section challenge times (cid:129) Prepare a press release if appropriate 22 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Prepare a descriptive poster if the challenge is in a public area Challenge day: Peer assistant assignments: (cid:129) Set up a registration table: log in each group, weigh and measure the vehicle, score the design notebooks, and provide the individual data sheet: Typically, four assistants (cid:129) Distance qualiﬁcations: Typically, two assistants. The assistants lay out the qualiﬁcation and bonus lines and conﬁrm the distance traveled. (cid:129) Side impact test: Typically, two assistants. The assistants conﬁrm the outcome, sign off on the data sheet, and assure each group complete their cleanup. (cid:129) Data recording: Students turn in data sheets and one or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee the site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party for the best section. 4.2.6 CONCLUDING COMMENTS This challenge has been very successful. About 80 percent of the vehicles make the distance require- ment and approximately 25 percent of the vehicles pass the entire challenge. One vehicle traveled nearly 1,000 yards. As seen in the photos, the side impact test is extremely popular. Aligning the hammer to the level position, so there is no excess energy and no “cutting corners,” is a valuable experience, especially with the competitors watching to keep everything fair. 4.3 DUNEBUGGY DASH 4.3.1 FACILITIES This challenge requires an obstacle course. As seen below, the challenge was completed in the Civil Engineering Sediment Transport facility lab. A dirt road, grassy strip, gravel pile, or similar terrain is acceptable. The challenge should require the students to consider the effects of foreign materials getting into critical parts of the vehicle and affecting performance. The challenge is modeled after the Mars Rover, so lightweight motors are emphasized. 4.3.2 CHALLENGE This challenge requires construction of an electric motor powered dune buggy that can drive across the sediment transportation laboratory “sandbox” shown below in Figure 4.5. 4.3. DUNEBUGGY DASH 23 (a) Spring (b) Fall Figure 4.5: Challenge course. 4.3.3 THE RULES (cid:129) Teams consist of three or four students. Single and two-person entries are not allowed. This size limitation is partially based on the size of the lab where the challenge will take place. If space is available, two- and three-person teams are preferred. (cid:129) The sole source of power for the vehicle is a 4.5 volt electric motor available from a kit in the Dean’s ofﬁce. The price is $5.00 and includes the motor, gear set, and battery box (Figure 4.2). (Note: The motors provided in the kit are underpowered and require the students to adjust the gear ratios for successful results. The kits cost more than $5.00 so the project is partially subsidized. The motors are required otherwise students will use commercial toy dune buggy motors, which are far more effective.) (cid:129) Each team must maintain a design notebook (see Chapter 2). (cid:129) No team shall spend more than $20.00 for supplies and equipment to manufacture the dune buggy. This includes the $5.00 for the motor so each group has a $15.00 operating budget for other materials. It is OK to use free stuff. The deﬁnition of “free” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the competition. “Rented” or “borrowed” materials are not allowed. (cid:129) The vehicle will be placed on the sand with the back of the buggy touching the south wall. The vehicle is started by turning on the power. No push starts are allowed. (cid:129) No one is allowed on the sand. A peer assistant is on a movable walkway to collect stalled or stranded vehicles. 24 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) All vehicles must be operated in a safe manner. Recognition will be given for the following categories: (cid:129) Rube Goldberg Award–most complicated design that actually works. (cid:129) Students’ Choice Award. (cid:129) Instructor and Peer Assistant Award in each section. (cid:129) The section with the highest average distance travelled by all vehicles in the section receives a pizza party. 4.3.4 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a test facility and schedule the design challenge day. (cid:129) Identify a practice area and setup. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Prepare a recycling box for used batteries. (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments (cid:129) Set up a registration table: log in each group, verify the motors, and provide the individual data sheet: Typically, two assistants. (cid:129) Distance qualiﬁcations: Typically, two assistants. The assistants conﬁrm the distance traversed. (cid:129) Recovery team: Typically, two assistants. The assistants recover stalled or damaged vehicles. (cid:129) Data recording: One or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee the site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party or gift certiﬁcates for best categories. 4.4. FIRST FLIGHT: FLY A FOAM AIRPLANE 100 YARDS 25 4.3.5 CONCLUDING COMMENTS An underlying assumption in this challenge was for the students to experience the difﬁculty of working in “dirty” environments. The sand in the sediment basin was ideal for this. Background for this challenge included discussion of the Mars Rovers. About half the vehicles bogged down before moving ﬁve feet. Gearing was also critical since the motors were high rpm and low torque. Some groups elected to use balloons to lift the vehicle and the motor for a propeller to move it across the test area. Thus, the challenge was changed from “traverse” the facility to “drive across” the facility. One group built a catapult to propel the vehicle across. After almost hitting a student on the opposite side, the design was judged “unsafe.” Lastly, recognition took the form of in-class awards for the different categories. The instructors and peer assistants made comments on the evaluation sheets and these formed the basis of the selections. 4.4 FIRST FLIGHT: FLY A FOAM AIRPLANE 100 YARDS Figure 4.6: Foam airplane ﬂight preparation. 4.4.1 FACILITIES This project requires a large open ﬁeld. We selected the indoor football practice facility for two reasons. First, by October, Wyoming weather conditions can be snowy and an outside activity may be compromised. Second, the average wind in Laramie in October is in the 10–30 mph range and is highly variable.This creates a potentially unfair comparison condition. By moving inside we provided a stable environment that comes with a very nice graduated scale on the ﬂoor. 26 4. THE FIRST-YEAR DESIGN CHALLENGES 4.4.2 CHALLENGE This challenge is to modify a foam plane to ﬂy 100 yards—the length of a football ﬁeld.The challenge will be held in the football indoor practice facility. From Wikipedia: the deﬁnition of an airplane: A ﬁxed wing aircraft is an aircraft capable of ﬂight using wings that generate lift due to the vehicle’s forward airspeed and the shape of the wings. Each section will function as a team. A team consists of groups of two to three students. Each group will receive one foam model plane. The basic plane is to be redesigned, modiﬁed, and tested to optimize the number of planes in the team to make the required distance. In that regard, the team must decide what constitutes its best selection of power and ﬂight strategies. Individual groups present their ideas in class and receive input from the team. (cid:129) Each group works to design a plane to optimize the team response in the challenge. (cid:129) A successful plane will ﬂy 100 yards from end zone to end zone. (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) One plane is supplied to each group and is classiﬁed as “free.” (cid:129) No group shall spend more than $30.00 for supplies to equipment to modify the plane. It is OK to use “free stuff.” The deﬁnition of “free stuff ” is that it has no commercial value. In short, the instructor can elect to keep it or throw it away following the challenge. “Rented” or “borrowed” materials are not allowed. Only the cost of the ﬁnal plane need be included in the budget. If a plane is destroyed in testing, the cost of a new plane must be included in the budget. (cid:129) All planes must be designed, fabricated, and tested prior to submittal. 4.4.3 THE RULES (cid:129) The plane may be powered by any safe device including elastic bands, launchers, electric motors, or other mechanical contraptions. For safety reasons, no gasoline or model airplane engines or rocket engines (e.g., Estes) are allowed. Part of the challenge is for the team to optimize ﬂight selection and design. (cid:129) The plane must be launched behind the goal line and attempt to cross the opposite goal line. As in football, if just the nose crosses the line, it is a success. Length is measured to the ﬁnal position of the nose of the aircraft. (Bounces on the ground count.) (cid:129) All components of the original plane must be used in the challenge; however, decals and tickers are optional. (cid:129) Following initial testing, the group may elect to construct a new plane based on the performance 4.4. FIRST FLIGHT: FLY A FOAM AIRPLANE 100 YARDS 27 of the trial runs. (cid:129) By deﬁnition, planes ﬂy by lift. They are not dragged, towed, pulled, fastened to a wire, or suspended from balloons. (cid:129) On the challenge day, the team will have ten minutes to ﬂy the length of the ﬁeld. Scoring Each team may ﬂy as many planes as there are groups.The team score is the average distance traversed by the best ﬂight of each group. At least three groups must ﬂy to qualify. Thus, if six planes ﬂy the full length of the ﬁeld and two ﬂy 20 yards, the score is 80 points (6 ﬂights x 100 yards + 2 x 20)/8. In addition, each team receives and additional points based on the design notebook grade. Awards The team with the highest overall score will receive a pizza party during the ﬁnal class session. 4.4.4 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. 4.4.5 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a test facility track and schedule the design challenge day. (cid:129) Identify a practice area and setup. This is often the same facility and scheduling the facility for two activities is a critical endeavor. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Prepare a recycling box for used batteries. (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. 28 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments: (cid:129) Set up a registration table: log in each group, inspect for safety issues, grade notebooks, and provide the individual data sheet: Typically, two assistants. (cid:129) Distance qualiﬁcations: Typically, two assistants. The assistants conﬁrm the distance ﬂown. (cid:129) Data recording: Two or three assistants verify the data on the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange award, e.g., pizza party or gift certiﬁcates for best categories. 4.4.6 CONCLUDING COMMENTS Figure 4.7: Plane launch. 4.5. HACKYSACK FLIP 29 Class lectures addressed power, lift, speed, drag, and launch options. The longest ﬂight was just over 60 yards. The principle difﬁculty was a high speed launch raised the nose of the plane to a stall position followed by the plane crashing. There were three weeks between the trial and the ﬁnal design. Most students used this time to improve their designs. Some of the planes crashed during testing and students did not rebuild them for the ﬁnal challenge. This again is a function of the scoring and emphasis on participation not success. At least one group used CO2 cartridges for propulsion. The group was required to present a safety plan to assure that the cartridges were secured and controlled when ﬁred. Two groups tried to tow their planes across the ﬁeld. They were disqualiﬁed. Several groups tried using balloons to lift the plane. The drag from the balloons generally resulted in the plane ﬂying in circles. The deﬁnition of an airplane and the requirement for the plan to ﬂy by its own lift should limit balloons in the challenge. This challenge included the value of the design notebooks in the overall scoring.The inclusion was to place additional emphasis on the value of recording progress. 4.5 HACKYSACK FLIP 4.5.1 FACILITIES The number of available tracks is a limiting feature for planning the amount of time needed to complete the challenge. Three tracks were constructed for this challenge. The challenge was held on the stage of one of the auditoriums on campus. This provided a waiting and viewing area for students and guests. This challenge is well suited for public viewing. 4.5.2 CHALLENGE This challenge requires each section to form its own company to manufacture a ﬂeet of electric motor powered vehicles that runs on a prefabricated track and can perform the tasks listed below. Each section will enter 8–10 vehicles. Scoring will be completed by averaging the total number of points from each vehicle’s best run. Each section will function as a team. A team consists of groups of two to three students. Vehicles are to be designed, built, and tested to optimize the team’s point score. In that regard, the team must decide what constitutes its best composition of vehicles. Individual groups present their ideas and receive input from the team. Each group designs and constructs a vehicle capable of performing the following tasks: 1. Pass through the start gate (S), 2. ascend a 20-degree hill, 3. propel a “hackysack” bean bag through the hole in a vertical wall (W) at the top of the hill, 4. knock down a ﬂag or ﬂags located at the top of the hill, and 30 4. THE FIRST-YEAR DESIGN CHALLENGES Figure 4.8: Challenge day setup. 5. descend the hill and round the exit run-out to the ﬁnish line. The points scored on the best run will be recorded. The Hackysacks Details of the Hackysacks are given in Figure 4.9.They weigh 37 to 39.8 grams and are approximately 2 1/2 in. in diameter. The Track Figure 4.10 shows the approximate dimensions of the track. The drawing is not to scale. The track width dimension may vary by ± 0.5 inches at any point. The side rails are made from 2.5-inch tall pressboard. The carpet is a standard, commercial grade. Contestants will approach the right-hand side of the ramp as seen from the side view (see S below). The “top of the hill” zone is deﬁned by the two lines (T). A dowel extends 1” into the track opposite the “Hackysack” wall (W). The Hackysack must be launched through the hole in the wall. The diameter of the hacky sack hole is 5.” The ﬂags, each consisting of a dowel extending 4.5. HACKYSACK FLIP 31 Figure 4.9: Hackysack details. approximately 1.4 inches above the track wall (see illustration), are mounted on either side of the track at the centerline. You may lower either or both ﬂags as you exit the top of the hill. A vehicle’s ﬂag will pivot only in the direction of the forward motion of the vehicle. Design should include consideration of “high centering” at the start and top of the hill climb. One track is available for testing cars prior to the challenge. 4.5.3 THE RULES Vehicle Design Speciﬁcations 1. The complete vehicle must be designed to ﬁt inside a 6-inch cube. The complete vehicle is deﬁned by all its parts. Appendages, such as an arm, may extend beyond this limit once activated by passing through the vehicle portal, P, but cannot be activated before the start of the run. 2. The vehicle must remain intact throughout the competition, that is, it may not jettison any unattached part, and may not divide into two or more separate sections or pieces. All parts must remain attached to the vehicle. For the purpose of this rule, the deﬁnition of “attached” is meant to exclude attachment by string, wire, or other ﬂexible tether. 3. The weight of the vehicle, including batteries, must not exceed 1.0 kg (2.2 pounds). 4. Peer assistants will supply competition “Hackysacks” at each ramp. “Hackysack” speciﬁcations are attached in Figure 2. 5. The vehicle must be stationary prior to the start, and it cannot be pushed by a group member as part of the start. After the start signal, the vehicle’s propulsion system may be activated using the switch on the battery box, but cannot be activated prior to the start. 32 4. THE FIRST-YEAR DESIGN CHALLENGES Figure 4.10: Schematic test track. 6. In the execution of its tasks, the vehicle may not damage the track, its walls, or the roadway carpet. 4.5. HACKYSACK FLIP 33 7. Onboard computing devices, such as microcontrollers, are not permitted. Power Power to propel the vehicle and to run any onboard activation or electronic devices is derived using two AAA 1.5 V batteries and one 1.5–4.5 volt DC motor supplied in the parts kit (Figure 4.2). Batteries may be connected to the vehicle in any conﬁguration. Supplemental mechanical power may be derived from such devices as springs, mousetraps, balloons, and rubber bands. Compressed gas cylinders, chemical reactions, or combustion of any type are not allowed. Mercury switches of any type are not allowed. Challenge Day Procedures Team members will have two minutes to reach the starting position after being called for a round. At the judges’ discretion, any vehicle not ready after the two minute countdown will forfeit the round and may be allowed to compete after all other teams have completed their rounds. A timer will count down the ﬁve minutes for each round. Groups can have as many runs as possible within the ﬁve minutes.The run will last until the vehicle crosses the ﬁnish line. Contestants may maintain contact with vehicles prior to “go” but may not touch vehicles during the run interval. If a group member touches its vehicle before run has been completed, the run will be considered incomplete, and the accumulated score to that point will be reduced by two points. All vehicle wheels must remain within the side rails of the track. Deployed appendages may extend beyond the side rails after the start, but the tops of the side rails may not be used to support the vehicle. Groups may provide a fresh set of batteries at the initiation of their round. The round must be completed on the fresh batteries. If the batteries die, points accumulated up to stop of the vehicle will be counted. Groups may modify vehicles between runs; however, the time limit for the round will be maintained. Only the called groups may enter the stage competition area and the vehicle repair area. Similarly, only team members may request veriﬁcation of opposing vehicles for compliance with contest rules and design limits. Spectators are not permitted to make such requests. Any vehicle compliance challenge must be made to the judges prior to the awarding of points for a particular round. If a vehicle is challenged and found to violate context requirements, it may be disqualiﬁed. Scoring challenges for a particular round must be made by the end of that round of the competition and may only be made by team members. Resolution of point challenges will be made at the sole discretion of the judges. Vehicle modiﬁcation and rerun following disqualiﬁcation is at the sole discretion of the professor. 34 4. THE FIRST-YEAR DESIGN CHALLENGES Scoring For each run of the round, a maximum of 9 points will be awarded for each run as follows: Ascending Points: One point will be awarded to each vehicle that successfully ascends to the “top of the hill” of the ramp. To earn “top of the hill” points, the vehicle, and all its parts, must reside between points (T). Hackysack Points: One point will be awarded to each vehicle that successfully propels its hackysack through the hole in the wall. An additional point will be awarded to each vehicle that propels the entire diameter of its hackysack beyond the (L1) line and two points for the hackysack completely passing the L2 line. Descending Points: One point will be awarded to each vehicle that passes, including all its parts, the bottom of the descending ramp (D). To receive descending points, a vehicle must ﬁrst earn ascending points. Flag Points: One point will be awarded to each ﬂag knocked down during the run. Run-out Points: Two points will be awarded to any vehicle that completely exits the run-out curve. Completely exit means that a ruler may be placed between the end of the track and the end of the vehicle. Penalty Deductions: Two points will be deducted from the run for a vehicle not completing the course. The minimum score for a run is zero; penalty points cannot yield negative scores. Vehicle Mishap: If a vehicle falls off the ramp for any reason or the batteries die, it will retain points earned for the run prior to the mishap. Points for the best run are recorded. General Rules (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) No group shall spend more than $15.00 for supplies and equipment to manufacture its vehicle. It is OK to use “free stuff.” The deﬁnition of “free stuff ” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the competition. Modiﬁed prefabricated cars are automatically disqualiﬁed. “Rented” or “borrowed” materials are not allowed. (cid:129) Vehicles will be weighed, measured, and logged in prior to the test program. (cid:129) Vehicle fabrication: The vehicles must be constructed from scratch, that is, no premade plas- tic bodies can be used. While the choice of materials is left to each group, 1/2 inch thick foamcore board, white (Elmer’s) or thermo plastic (hot-melt) glue have proven to be a suitable construction material, except for axles and wheels, and are available at the campus store. Prior to the start of the challenge, groups must conduct a “calibration round” on the test track and record the results in the design notebook. No tools will be supplied on the competition day. teams are expected to bring all necessary items to repair or modify vehicles during the competition, including spare parts. After the ofﬁcial start of the competition, only registered student contestants will be allowed in the competition and work areas. Spectators are welcome to view the competition from the seating area in the auditorium. After each run, and prior to leaving the ramp area, groups are responsible for verifying that point totals have been correctly recorded by the ramp judge and that the challenge area is clean. Judges are instructed to oversee these checks. One group member will sign each score sheet. 4.5. HACKYSACK FLIP 35 4.5.4 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. Students have access to the College of Engineering and Applied Science shops. Sign up for shop time is required and students must have watched the safety practices video presented in class. 4.5.5 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a challenge facility area and schedule the design challenge day. (cid:129) Fabricate the test tracks. (cid:129) Identify a practice area and set up one track for trial runs. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Prepare a recycling box for used batteries. (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments: (cid:129) Move the challenge tracks into place before students arrive. 36 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Set up a registration table: log in each group, measure vehicles, grade notebooks, and provide the individual data sheet: Typically, two assistants. (cid:129) Run qualiﬁcations: Typically, three assistants, one per track. The assistants conﬁrm the points earned. (cid:129) Data recording: One or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party. 4.5.6 CONCLUDING COMMENTS Figure 4.11: Vehicle testing. This was the most complex challenge we attempted because of limits imposed by the test track. The college shop fabricated the tracks. One track was set up in a lab space for students to test their designs. The few days prior to the challenge the room was full. 4.6. MOUSETRAP POWERED CAR SLALOM 37 About 10% of the vehicles completed the challenge. The original challenge has a 30o ramp and many vehicles had great difﬁculty making the climb. This challenge has been reduced to 20o to improve the opportunity for success. Several cars rolled over on the descending ramp. The lower grade should alleviate this problem. The end runout also proved to be a stumbling block as cars were getting stuck. An 18 in. radius runout would resolve this issue. 4.6 MOUSETRAP POWERED CAR SLALOM 4.6.1 FACILITIES A hard ﬂoor 25 feet x 25 feet works best and allows the slalom course to be set up and the width allows 6 to 8 lanes to be laid out side by side. Tight carpet also works but the decision should be made prior to initiation of the challenge as it will affect both distance and steering. A meeting room in the student union or equivalent provides high visibility and public access. 4.6.2 CHALLENGE This challenge requires each group to construct a mousetrap-powered car that can negotiate a slalom course consisting of four 3 3/4 in square pylons placed in a straight line 4 foot on centers. 4.6.3 THE RULES Each section will function as a team. A team consists of groups of two to three students. Cars are to be designed, built, and tested to optimize the team’s point score. In that regard, the team must decide what constitutes its best composition of cars. Individual groups present their ideas in class and receive input from the team. (cid:129) The team works to design vehicles to optimize the team response in the challenge. (cid:129) Each group must design and fabricate at least one car. (cid:129) Mousetraps will be supplied in class. (cid:129) In addition to the two mousetraps supplied, no group shall spend more than $20.00 for supplies and equipment to manufacture its car. It is OK to use “free stuff.” The deﬁnition of “free stuff ” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the challenge. “Rented” or “borrowed” materials are not allowed. (cid:129) All cars must be designed, fabricated, and tested prior to submittal. (cid:129) Groups will consist of two or three students. Single-person entries are not allowed. (cid:129) The sole source of power for the vehicle is a mousetrap; rattraps are not allowed. (cid:129) The vehicle may use one or two mousetraps in any combination for power and/or steering. 38 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) The vehicle will be placed at the start line and released by the group members. Each vehicle must be placed with its longitudinal axis parallel to the course. Wheels may be aligned at the group’s discretion (see layout in Figure 4.12). Once released, the car cannot be touched by any group member. The vehicle must cross the centerline before passing the ﬁrst pylon (see Figure 4.12). (cid:129) Prior to the actual challenge, each car should complete a successful trial run and distances of each run should be recorded in the design notebook. (cid:129) On the challenge day, the group will have ﬁve minutes to make a successful run. (cid:129) Vehicle fabrication: The car must be constructed from scratch, that is, no premade units, e.g., premade steering mechanisms. The choice of materials is left to each group. Figure 4.12: Challenge course and starting conﬁguration. Scoring Each group receives 0 to 4 points based on the number of pylons successfully passed. The group earns an additional 2 points for completing the run and crossing the ﬁnish line. The team score is the average of the group scores. Developing a Test Program Engineering design and development requires validation and testing. Your notebook must clearly identify a development schedule, test dates, and test results. Modiﬁcation to the design after each test must be documented. The best run and points must be clearly recorded and dated in the notebook. 4.6.4 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design groups are responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to suitably modify the design before continuing in the challenge. Offending vehicles may be disqualiﬁed at the discretion of the professor. Use of pyrotechnic or similar devices is strictly prohibited. 4.6. MOUSETRAP POWERED CAR SLALOM 39 4.6.5 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a challenge facility track and schedule the design challenge day. (cid:129) Identify a practice area and setup. The initial practice area can be a single track in a classroom. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Fabricate pylons. (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments: (cid:129) Set up pylons, start and ﬁnish lines prior to the students arriving. (cid:129) Set up a registration table: log in each group, verify the power source, grade notebooks, and provide the individual data sheet: Typically, two assistants (cid:129) Run qualiﬁcations: Typically, four assistants. The assistants conﬁrm the course was successfully traversed. (cid:129) Data recording: One or two assistants enter the number of points into the summary spread- sheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party or gift certiﬁcates for best categories. 40 4. THE FIRST-YEAR DESIGN CHALLENGES 4.6.6 CONCLUDING COMMENTS This challenge is deceptive. Many students have participated in mousetrap cars in high school. The autonomous steering, however, requires closer coordination of forward progress and sinusoidal action. At least two groups in the challenge used mousetrap-powered cars and radio-controlled steering. One student group brought in a RC controller with the comment that sabotage is not disallowed! The rule eliminating prefabricated steering is intended to exclude the most egregious use of RC controls. This challenge needed a gross of mousetraps. No one in town stocked that many so they were special ordered and provided to the teams. This can be a professional student group fund raiser. 4.7 THE GREAT WALL OF CARPET Figure 4.13: Carpet climb challenge. 4.7. THE GREAT WALL OF CARPET 41 4.7.1 FACILITIES This challenge works best with a two-story atrium and carpet hung from the upper ﬂoor. The particular challenge was held in the atrium of the campus library. Two similar types of carpet were used. The carpet strips were approximately 2 feet wide. The carpets are hung so only the fabric side is available for the challenge. 4.7.2 CHALLENGE This challenge requires construction of an autonomous robotic device that can climb a carpet draped in the atrium of a two-story building. Each group will design and construct a robot according to the rules laid out below. To qualify, a robot must climb at least two vertical feet. 4.7.3 THE RULES Each section will function as a team. A team consists of groups of two to three students. Robots are to be designed, built, and tested to optimize the team’s point score. In that regard, the team must decide what constitutes its best composition of robots. Individual groups present their ideas in class and receive input from the team. (cid:129) The team works to design vehicles to optimize the team response in the challenge. (cid:129) Each group must design and fabricate one robot. (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) No group shall spend more than $40.00 for supplies and equipment to manufacture its robot. It is OK to use “free stuff.” The deﬁnition of “free” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the competition. “Rented” or “borrowed” materials are not allowed. (cid:129) All robots must be designed, fabricated, and tested prior to submittal. (cid:129) The robot must be constructed from scratch, that is, no premade units can be used. The choice of materials is left to each group. (cid:129) Groups will consist of two or three students. Single person entries and groups of more than three students are not allowed. (cid:129) The robot may be powered by any device, elastic bands, electric motors, or other mechanical contraptions. Part of the challenge is for the team to optimize very small lightweight climbers with heavier and more powerful alternatives. (cid:129) The entire robot must make the climb; however the robot may work in discrete elements if needed and the robot must grip the carpet to climb. 42 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) The robot will be placed at the start line and released by the group members. Each robot must function autonomously, that is, it cannot be touched by a group member while operating. If touched, it must be restarted. (cid:129) Prior to the actual challenge, each robot should complete a successful qualifying run. A survey rod will be provided and the height for each run recorded. (cid:129) On the challenge day, the robot will have ﬁve minutes to make a successful run. (cid:129) Special note: there may be two different carpet types. You are not assured which one you will get on the challenge day. Ceiling Carpet Wall Floor Start line 1’ 2’+- Figure 4.14: Approximate challenge course and starting conﬁguration. 4.7. THE GREAT WALL OF CARPET 43 Developing a Test Program Engineering design and development requires validation and testing. Your notebook must clearly identify a development schedule, test dates, and test results. Modiﬁcation to the design after each test must be documented. The runs and climb height must be clearly recorded and dated in the design notebook. 4.7.4 SCORING The best height of the challenge run will be recorded. If the robot does not climb in the challenge, a challenge height of zero will be recorded. The team with the highest average climb height divided by the average cost will be recognized as the highest climbing/most efﬁcient team on campus! To start each run, the judge will indicate start, and the timing clock will begin. The test will last until the run is complete or time expires. Groups may maintain contact with robots prior to the robot start but may not touch the robot during the run. A group member may touch the robot to prevent damage but the run must then be restarted. The run record must be completed without manual assistance or the run will be disqualiﬁed. Only team members may request veriﬁcation of opposing robots for compliance with contest rules and design limits. Spectators are not permitted to make such requests. Any challenge must be made to the judges prior to the awarding of points for a particular test. If a robot is challenged and found to violate context requirements, it will be disqualiﬁed and a height of zero recorded. 4.7.5 SOME REFERENCES If you have never seen a climbing robot, consider looking on Bing or Google. There are a number of good sites, many of which are far more complex than needed for this challenge. The description of these robots will give you an idea of some of the design considerations to be included in your project. 4.7.6 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. 4.7.7 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a challenge facility track and schedule the design challenge day. 44 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) Identify a practice area and setup one of each type of carpet. Preparation for challenge day: (cid:129) Procure the challenge carpet. As the rules note, we had two different types of carpet so the students did not know which carpet they will climb until the challenge. (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments: (cid:129) Hang carpet and arrange survey rods. (cid:129) Set up a registration table: log in each group, grade notebooks, and provide the individual data sheet: Typically, two assistants. (cid:129) Distance qualiﬁcations: four assistants. The assistants conﬁrm the distance was climbed. We set up four climbing stations and brought over survey rods to assist with measuring the height climbed. Place masking tape at the challenge ﬁnish. (cid:129) Data recording: One or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party. 4.7.8 CONCLUDING COMMENTS Only two of 131 climbers made it to the top and one design used helium ﬁlled balloons to lift the robot. These results made this the most difﬁcult challenge in terms of success. Nothing in the rules precluded using the edge of the carpet, and several groups used this option. One group made a catapult with a three-pronged ﬁshing hook. The design launched the hook then used a winch to pull itself up. It performed poorly and required a safety plan for throwing the hook. About 30 years ago the University of Utah had a similar challenge using small elastic band-powered paperclip climbers. 4.8. UNDERWATER RECOVERY VEHICLE 45 Figure 4.15: Edge climber. 4.8 UNDERWATER RECOVERY VEHICLE 4.8.1 FACILITIES The challenge requires use of the university swimming pool. In addition to gaining access to the pool, life guards are hired to assure safety. No students are allowed in the pool, hence the requirement for the robots to be tethered. Local pool rules and depths must be incorporated in the rules. 4.8.2 CHALLENGE This challenge is to construct a tethered robotic device that can retrieve a marker from the bottom of the swimming pool according to the rules laid out below. The ﬁnal challenge will be in the shallow end of the pool and the pool will not available for practice prior to the challenge. A stock watering tank will be set up and available for practice. 46 4. THE FIRST-YEAR DESIGN CHALLENGES Figure 4.16: The beginning of the underwater challenge. 4.8.3 THE RULES Each section will function as a team. A team consists of groups of two to three students. Robots are to be designed, built, and tested to optimize the number of retrieved weights. In that regard, the team must decide what constitutes its best selection of robots; however, each team must have at least two underwater robots (submarines) and two surface robots. Individual groups present their ideas in class and receive input from the team. (cid:129) The team works to design vehicles to optimize the team response in the challenge. (cid:129) Each group must design and fabricate one robot. (cid:129) A successful robot will retrieve a designated small weight from the bottom of the campus pool by picking up the hook on the weight (Figure 4.13). A steel washer will be placed on the magnet for the challenge. (Note: the washer prevents the magnetic base from attaching to a pool drain.) 4.8. UNDERWATER RECOVERY VEHICLE 47 Weight approximately 30 grams Figure 4.17: Marker to be retrieved from pool. (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) No group shall spend more than $50.00 for supplies and equipment to manufacture its robot. It is OK to use “free stuff.” The deﬁnition of “free stuff ” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the challenge. “Rented” or “borrowed” materials are not allowed. (cid:129) All robots must be designed, fabricated, and tested prior to submittal (cid:129) Robot fabrication: The robot must be constructed from scratch, that is, no premade boats may be used, but premade components are allowed. A surface vehicle with a winch is permitted. The choice of materials is left to each group. (cid:129) The robot may be powered by any device, elastic bands, electric motors, or other mechanical contraptions. Part of the challenge is for the team to optimize robot selection and design. (cid:129) The robot must travel to the designated weight, connect to the hook on the weight, and bring the weight back to the surface at the pool edge. (cid:129) The robot must be tethered to the shore. A land controller, which may contain the power supply, navigation, and ballast equipment, can serve as the tether; however, the tether may not be used to pull or drag the robot or the marker string. Any power supply must be internal to the robot or the controller, i.e., not plug into a wall outlet, and no large external batteries are allowed. 48 4. THE FIRST-YEAR DESIGN CHALLENGES (cid:129) The robot will be placed at the edge of the pool and released by the group members. Each robot must function remotely, that is, it cannot be touched by a group member while operating other than from the control panel. If touched, pulled, or dragged, it must be recovered and restarted. (cid:129) Prior to the actual challenge, each robot must complete a successful run in the test tank. Each group should document the robotic performance: e.g., ballast and steering control, power, ability to lift the weight. (cid:129) On the challenge day, the robot will have ten minutes make a successful recovery. Developing a Test Program Engineering design and development requires validation and testing. Your notebook must clearly identify a development schedule, test dates, and test results. Modiﬁcation to the design after each test must be documented. The ﬁnal runs must be clearly recorded and dated in the notebook and the ﬁnal results reported on the summary page. For example, consider buoyancy design. This can be done with a ﬂotation device or by using downward propulsion. Several trials may be required to select and test a suitable design. 4.8.4 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. The pool deck is wet and slippery. No shoes are allowed to be worn on the deck. Because the deck is wet, plug in power is prohibited. 4.8.5 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify the pool, and schedule the design challenge day. (cid:129) Arrange for life guards. (cid:129) Identify a practice area and setup. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. 4.8. UNDERWATER RECOVERY VEHICLE 49 (cid:129) Draw lots for the section challenge times. (cid:129) Prepare a press release if appropriate. (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments (cid:129) Set up a registration table: log in each group, verify the power supply rules, assign a target number, and provide the individual data sheet: Typically, two assistants. (cid:129) Check design notebooks: Typically one or two assistants. (cid:129) Recovery targets:Typically, two assistants.The assistants conﬁrm the target numbers are visible and replace them in the pool after recovery distance was traversed. (cid:129) Data recording: One or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party. 4.8.6 CONCLUDING COMMENTS There is nothing like water to compromise the best design, and this challenge amply demonstrates that fact. Three strategies emerged. Submarines trawled the bottom. Surface ships trawled for the weights then tried to bring them to the surface, and, ﬁnally, surface ships with winches attempted to grapple the weights, pull them to the surface, and return them to the edge of the pool. Each weight had a string and a ping pong ball hot glued to the string. Ten weights were spread around the pool and each section had numbers 1–10 assigned to the group for retrieval. The distance from the edge of the pool to the weight was similar for all groups. The pool has a current. That current was sufﬁcient to keep underpowered boats from reaching the weights. Our fall guest speaker was the Manager for Gulf well delivery for Shell Oil, and this project was tied into the oil spill recovery efforts. 50 4. THE FIRST-YEAR DESIGN CHALLENGES Figure 4.18: Redesign consultation time. 4.9 WIND TURBINES AND WIND POWER GENERATION 4.9.1 FACILITIES This challenge requires a fairly large open space. Three test facilities were set up with large fans providing the wind. We used an auditorium for the challenge although a large conference room would work equally well. The fan was set up on a table and the distances marked on the table with masking tape. The Electrical Engineering Department fabricated a power meter to record the wind turbine output. This challenge is suitable for a public location. 4.9.2 CHALLENGE This challenge requires each section to form its own company to manufacture and test a series of prototype wind turbines to generate electrical energy. The national energy policy has a goal that 20 percent of all electric energy produced in the US should come from renewable sources by 2020. This has led to considerable development of wind farms across the country. Wyoming is one of the premier wind locations in the US and a substantial 4.9. WIND TURBINES AND WIND POWER GENERATION 51 Figure 4.19: Wind turbine testing. amount of research into wind energy is conducted at UW. Just how efﬁcient is wind energy? This design challenge is intended to let you examine the design issues associated with efﬁcient wind generation. Each group will design and construct a wind turbine to maximize the energy output and to determine the efﬁciency of the design. To complete the challenge, each group must complete the following tasks: 1. Design and fabricate the wind turbine, 2. Set up the wind turbine 4 feet in front of the industrial fan, 3. Measure the wind speed immediately in front of the wind turbine (instrumentation will be provided), 4. Compute the theoretical energy input of wind, 5. Attach the power meter and measure the energy output of the turbine, 6. Repeat steps 3–5 with the wind turbine 6 and 10 feet in front of the fan, 7. Compute the efﬁciency of the wind turbine for each wind velocity and plot the resulting data, 8. Enter all data and test results in your design notebook, and 9. At the design challenge, demonstrate that your turbine can generate the energy output reported from your development program at 6 ft. from the face of the fan. 52 4. THE FIRST-YEAR DESIGN CHALLENGES 4.9.3 THE RULES Each freshman Section will function as a team. A team consists of eight groups of two to three students. Wind turbines are to be designed, built, and tested to optimize the team’s point score. In that regard, the team must decide what constitutes its best composition of turbines. Scoring will compare the instantaneous energy output of all wind generators in the team. The highest average energy output receives the outstanding team award. Individual groups present their ideas in class and receive input from the team. (cid:129) Each team must design and fabricate at least one vertical axis and one horizontal axis turbine. The remaining turbines are at the discretion of the team (Figure 4.20). (cid:129) Each group will receive an electric generator and a gear set. This generator must be used; the gears are optional. Gears may be traded within a team to optimize performance. (cid:129) Each group must maintain a design notebook (see Chapter 2). (cid:129) In addition to the parts supplied, no group shall spend more than $20.00 for supplies and equipment to manufacture its wind turbine. It is OK to use “free stuff.” The deﬁnition of “free” is that it has no commercial value. In short, the instructor can elect to keep it or throw it in the trash following the competition. “Rented” or “borrowed” materials are not allowed. (cid:129) All wind turbines must be designed, fabricated, and tested prior to submittal. (cid:129) The turbine must be constructed from scratch, that is, no premade units can be used. The choice of materials is left to each group. Wind Turbine Design 1. The cross-sectional area of the turbine blades (perpendicular to the wind direction) must be less than 324 square inches (18 in square or 10.2 inch radius). 2. The center of the wind turbine should be about 27 in. above the table—roughly at the center of the fan axis. 3. Bricks will be available to anchor the wind turbine base. The bricks should not extend more than 3 in. above the table. 4. You may construct a gearbox out of plastic sheet available in the shop. 5. The College of Engineering and Applied Science shop is available for fabrication of your turbine. 4.9. WIND TURBINES AND WIND POWER GENERATION 53 (a) Horizontal Axes (b) Vertical and Horizontal Axes Figure 4.20: Sample wind turbines. Generator and Transmission The generator is a 6 volt DC motor supplied in the parts kit. The optimum drive speed is 2,180 rpm, so a step up from the turbine blade speed may be needed. Each generator must have a 4 ft. long 2-wire conductor (available in the shop) attached to the generator for connection to the power meter. Data for the generator is given in Table 4.1. Table 4.1: Generator Technical Data: Nichibo DC Motor—FE-260-18130 Available from Jameco Inc. Nichibo DC Motor – FE-260-18130 Available from Jameco Inc. Current @ Max. Efficiency (A) Efficiency Nominal Voltage (VDC) Shaft Diameter (inch) Shaft Length (inch) 0.08 50.6 6 0.078 0.385 Size (Dia) 1.259 x 0.767 Speed @ Max. Efficiency (RPM) 2180 Terminal Type Voltage Range (VDC) Solder 1.5-12 Torque @ Max. Efficiency (g-cm) 11.6 Each kit has a set of gears similar to those in Figure 4.2. The design may include assembling the gears into a gearbox with one axle to the turbine blade and an output axle to the generator. 54 4. THE FIRST-YEAR DESIGN CHALLENGES 4.9.4 DEVELOPING A TEST PROGRAM Figure 4.21 shows a schematic of the turbine test setup. One test setup is available for testing and measurement prior to the challenge. A schedule of lab availability times for testing will be posted. Figure 4.21: Schematic test setup. Each group must establish a test program for their turbine. The wind turbines are to be set and tested at 4, 6, and 10 feet from the fan. The vertical axis turbine is set with the axis at the 4, 6, and 10 ft. marks. The horizontal axis turbine is set with the face of the blades positioned at 4, 6, and 10 feet from the face of the fan. Turn on the fan and measure the wind speed and compute the theoretical wind energy. The fan will be positioned on a 12 in. high pedestal to make the centerline of the fan axis at an elevation of 27 inches and to reduce ground effects. A wind velocity meter and the power meter will be available for testing. 4.9.5 CALCULATIONS The average mass of air at 7,000 ft. (2130 m) is 0.0620 lbm/ft 3 (0.9920 kg/m3). The total kinetic energy from the wind is 1/2 mv 2, where the mass of the air is that swept by the turbine. The output energy of the wind turbine is measured with a power meter. Electrical energy, P, is computed by: Where P is energy in joules, V is voltage and I is current. P = V I 4.9. WIND TURBINES AND WIND POWER GENERATION 55 Efﬁciency is computed: η = 100% Energy−out Energy−in where the energy-in is the theoretical wind energy and the energy-out is from the power meter data. Be sure your units for the kinetic energy and electrical energy are compatible when you complete the efﬁciency calculation. Compute the energy-in and -out for the three turbine locations and then plot the efﬁciency versus wind velocity. 4.9.6 CHALLENGE DAY SETUP Prior to the start of the ofﬁcial challenge, groups must complete “calibration tests.” design notebooks must be submitted on the challenge day. Each group will have ﬁve minutes to set up the turbine and measure the output. On the challenge day, all tests will be run at 6 ft. from the face of the fan. At the judges’ discretion, any turbine not ready after the ﬁve minute countdown will forfeit and an energy output of zero will be recorded. The group may be allowed to retest after all other teams have completed their test. At the start each test, the judge will indicate start and the clock will begin. The test will last until the energy is recorded or time expires. Groups may maintain contact with turbines prior to “go” but may not touch the turbine during the test interval. Turbine blades must be stationary when the test begins and the fan is turned on. A group member may touch the turbine to adjust parts but the energy record must be completed without manual assistance or the test will be disqualiﬁed. Only the called group may enter the stage challenge area and the turbine repair area. Only team members may request veriﬁcation of opposing turbines for compliance with contest rules and design limits. Spectators are not permitted to make such requests. Any challenge must be made to the judges prior to the awarding of points for a particular test. If a turbine is challenged and found to violate context requirements, it will be disqualiﬁed and an energy output of zero recorded. Scoring challenges for a particular round must be made by the end of that round of the challenge, and may only be made by team members. Resolution to point challenges will be made at the discretion of the judges. No tools will be supplied on the challenge day. teams are expected to bring all necessary items to repair or modify turbines during the challenge, including spare parts. After the ofﬁcial start of the challenge, only registered groups will be allowed in the challenge and work areas. Spectators are welcome to view the challenge from the seating area in the auditorium. After each test and prior to leaving the test area, groups are responsible for verifying that point totals have been correctly recorded by the challenge judge. Judges will be instructed to oversee these checks. One group member will sign each score sheet. 4.9.7 SCORING Scoring for the project will be based on completing tasks on time. Table 4.2 indicates the task and timing.The challenge requires the model to be completed, calibrated, and operational.The maximum 56 4. THE FIRST-YEAR DESIGN CHALLENGES energy output will be recorded for each group. The team score is the average of the maximum energy output from all groups in the team. Table 4.2: Challenge scoring ksaT etaD Design Notebook progress Have a model prototype that is described in the design notebook Energy Generation Curve Functioning Corresponds to Design Notebook Energy Prediction within 25% Model which Design Day –Week 4 Design Day –Week 4 Challenge Day Challenge Day Challenge Day ksaT Points 10 10 20 10 10 Total Points 10 20 40 50 60 4.9.8 SAFETY The objective of the challenge is to foster engineering creativity and cooperation. The design group is responsible for ensuring safety of participants and spectators during the challenge. Groups using any feature deemed dangerous by the judges may be asked at any time to prepare a safety plan or suitably modify the design before continuing in the challenge. Offending designs may be disqualiﬁed at the discretion of the faculty member or peer assistants. Use of pyrotechnic or similar devices is strictly prohibited. Any questions regarding safety may be directed to your instructor. 4.9.9 CHALLENGE ORGANIZATION Early Organization: (cid:129) Identify a challenge facility track and schedule the design challenge day. (cid:129) Identify a practice area and setup. Preparation for challenge day: (cid:129) Prepare summary score spreadsheet. (cid:129) Prepare data sheets and coordinate individual score sheets with the summary spreadsheet. (cid:129) Procure an handheld anemometer. (cid:129) Procure a power meter and make sure it is calibrated for the generator speciﬁed in the challenge. (cid:129) Draw lots for the section challenge times (cid:129) Prepare a press release if appropriate. 4.9. WIND TURBINES AND WIND POWER GENERATION 57 (cid:129) Prepare a descriptive poster if the challenge is in a public area. Challenge day: Peer assistant assignments: (cid:129) Set up tables, fans, and distance marks prior to students arriving. (cid:129) Set up a registration table: log in each group, grade notebooks, and provide the individual data sheet: Typically, two assistants. (cid:129) Power output: Typically, two assistants. The assistants conﬁrm the power output of each group. (cid:129) Data recording: One or two assistants enter the data into the summary spreadsheet. One person may have to go back to the other activities to conﬁrm data, so two people are preferred. (cid:129) Oversee site clean-up: all. Following the challenge: (cid:129) Provide the summary data sheet to all instructors. (cid:129) Arrange any awards, e.g., pizza party. 4.9.10 CONCLUDING COMMENTS The fans provided a reasonable wind velocity for the test; however, the power meter was somewhat overdesigned so we were always reading the low end of the scale. For the ﬁnal challenge, we placed foamcore panels around the edge of the fan to better direct the wind toward the turbines. Virtually all the turbines measured some output. The gear box is essential to the success of this challenge. Scrap Plexiglas and Lexan sheet pieces, adhesive, and axle materials were available in the shop for “free.” C H A P T E R 5 59 Interdisciplinary Design 5.1 OBJECTIVES Goals of both ABET and the College of Engineering and Applied Science is to offer and evaluate comprehensive senior interdisciplinary design projects. Interdisciplinary in this instance means stu- dents from different departments are recruited to design a project as opposed to teams of students from within a single department. The following addresses how such projects are organized and executed. 5.2 ADMINISTRATIVE ISSUES The ﬁrst major administrative issue of a interdisciplinary project is addressing the individual de- partmental requirements for senior design. The University of Wyoming senior design requirements are summarized in Table 5.1. Initiation of an interdisciplinary team requires negotiation with each department to assure that the students receive proper credit, that workloads are commensurate with the credit hours, and that each department is satisﬁed that the project is commensurate with existing departmental protocols. Table 5.1: Departmental Senior Design Requirements Department Civil Engineering Civil Engineering- Transportation Electrical Engineering Energy Systems Mechanical Engineering Chemical Engineering Fall Term Credit Hours 3 hours 2 hours 2 hours 3 hours 3 hours 2 hours Spring Term Credit Hours 1 hour 2 hours 3 hours 3 hours 4 hours Further compounding the credit hour requirements are the departmental deliverable require- ments. Civil and Chemical Engineering students prepare project plans and require oral presentations of their projects. Electrical and mechanical students must go through a product development process, fabricate their project, and prepare poster presentations. 60 5. INTERDISCIPLINARY DESIGN Establishment of a separate section within each department for the interdisciplinary project resolved the departmental credit hours issue. The entire class meets as a group even though the students are all in “different” classes. While straightforward, the solution generated a second set of administrative issues. The university has a policy that undergraduate classes must have at least 10 students enrolled for the class to proceed. No department had that many students in one section. The college successfully petitioned an exemption on that basis that the entire project had sufﬁcient student population. 5.3 PROJECTS Six different interdisciplinary projects are presented. Two projects were tied to the NASA Zero Gravity research initiative, and the remaining four were local projects. The local projects required 1) design of an automated transit system for the campus, 2) develop more environmentally sustainable solutions for accessing gas ﬁelds in the state 3) converting the university energy plant from coal to wood, and 4) a non-engineering interdisciplinary course on medieval construction in conjunction with the History Department. The projects are summarized below and the projects are presented in the following chapter. 5.3.1 NASA ZERO GRAVITY PROJECTS The NASA Zero Gravity program allows students to propose projects that would assist NASA in space endeavors. Students prepare proposals, submit them to NASA, and if accepted, construct the prototypes. Students then take their projects to the NASA center in Houston, Texas. After review and training by the NASA staff, the projects are loaded into the NASA KC-135A, and the students conduct their experiments in a weightless environment. The ﬁrst Zero Gravity project challenged students to develop truss elements and connections for the construction of three-dimensional truss structures in space. The project consisted of design- ing carbon ﬁber truss elements and plastic connectors. The second Zero Gravity project involved developing a zero gravity exercise machine for use on the international space station. 5.3.2 AUTOMATED TRANSIT SYSTEM FOR CAMPUS The students were asked to design an automated transit system for campus that linked the remote parking lots with the main campus. Completion of the project involved trafﬁc studies for both parking and walking distances from stations, development of the vehicle concepts, vehicle design, guideway design, power supply, and operations. The project was conducted over a two-year timeframe. 5.3.3 DISAPPEARING ROADS AND GAS EXTRACTION Jonah Field in western Wyoming was one of the ﬁrst major gas ﬁelds developed by fracking processes. Aerial views show a spider web pattern of roads in a region that is highly sensitive to pronghorn migration and sage grouse habitat. The design project required the students to interact with energy companies and the Bureau of Land Management to develop alternative designs to reduce the site impact. 5.4. STUDENT RECRUITMENT 61 5.3.4 UNIVERSITY ENERGY PLANT CONVERSION The University of Wyoming Energy Plant provides steam heat to the campus. Originally constructed to burn anything from garbage to coal, it has functioned as a coal plant since its inception. Recent years have seen an extraordinary amount of beetle kill in the nearby national forest. The student project evaluated if the plant could be converted to wood chips fuel source, established that sufﬁcient wood was available to support the conversion, designed handling and transportation of the wood, developed plans for modiﬁcation of the energy plant, and participated in the ﬁrst pilot burn. 5.3.5 MEDIEVAL CONSTRUCTION This was a joint project with the History Department. Dr. Kristine Utterback of the History De- partment presented the life and times of Medieval Europe. The engineering aspect of this project focused on the design and construction of the ﬁrst Gothic Cathedral in St. Denis, France. 5.4 STUDENT RECRUITMENT The general concept of each design project is developed to the summary level indicated above. The project is open to all seniors needing to fulﬁll a senior design project. The projects are run for an academic year beginning in the fall term. To suit the departmental requirements, Civil Engineering students completed their work in the fall and a new group of civil engineering students joined in the spring. Other students enrolled for the full year. Critical to recruiting students is the selection of the project. Student engagement was highest when the project either directly addressed an issue the students recognized or had a clear envi- ronmental beneﬁt. One year several national competitions were suggested in addition to a local project. The local project was overwhelmingly the student choice. The professor in charge of an interdisciplinary project must be able and willing to adapt to the projects that will attract students. Consideration was given to using an Engineers without Borders project. Engineers without Borders was not selected because it was not clear that all of the interdisciplinary design criteria could be satisﬁed. In addition, Engineers without Borders has projects underway and the schedules did not mesh. Each spring, in the week prior to advising and two weeks prior to students signing up for fall courses, an announcement of the project is emailed to all seniors, and posters are placed in the college. A project open house for the project is held. A general overview of the project is presented at the open house and the students are invited to ask questions to explore their interest. It is only after the students sign up for fall courses that the composition of the class is known. Supplementing the general sign up for the course, certain “specialists” are recruited directly. For example, one junior student in the chemical engineering department was mobility impaired and 62 5. INTERDISCIPLINARY DESIGN served on the university committee for campus mobility. After discussions with the department head, she was allowed to take this class early and had the responsibility for addressing all ADA requirements for the campus transit system design in addition to her technical responsibilities. Similarly, for the disappearing roads project, an Environmental and Natural Resources student was recruited to be the in-house environmental specialist. In both cases, these students added immeasurably to the quality of the project. To further expand the class horizons, external classes are recruited to assist the design team. For example, on one project a senior class in Computer Graphics assisted in conducting focus group studies and preparing graphic imagery for the transit system alternatives. PROJECT ORGANIZATION 5.5 Two key elements determined how the interdisciplinary design class was organized. First, the com- position of the class had to be established. Because the class was open enrollment, the number of civil, mechanical, electrical, and chemical engineers is not known until the end of the spring term. Once the composition of the class is known, the actual project is modiﬁed to ﬁt the class composition. Second, during the ﬁrst week of class in the fall, each student is interviewed to establish the goals and aspirations the student has for the course. Prior to the interview, each student ﬁlls out a data card with their name, major, specialized skills like speciﬁc computer programming experience, GPA, and a statement on what they expect to gain from the course. From these interviews, the project is further adjusted to meet the skills and majors of the available students. A project manager and project engineers for each of the key components are selected. The class is structured similar to a design ofﬁce. The professor becomes the “principal in charge,” and the day-to-day work responsibilities are given to the students. The project manager is immediately charged with establishing a schedule and works with the professor to assign students to the individual tasks. During class periods, the professor meets with the project manager, each lead engineer, and individual students to review progress. Each team member is expected to provide written or oral weekly updates on progress, difﬁculties, and resources needed to complete the task. The transit system description in Chapter 6 contains a representative organization chart. All senior design projects require written ﬁnal reports and public presentations. The professor’s job is to assure that the project stays on schedule, redirect the project if it is going off track or the students propose solutions well outside their capabilities, and to arrange for supporting materials. The supporting materials include anything needed to design and fabricate the project, meetings with sponsors, ﬁeld trips, or access to key personnel on or off campus. These resources vary with the project. Classes have guest presenters ranging from U.S. senators, to the university president, to maintenance staff. Every project involved at least one ﬁeld trip. Each project required some level of funding. The funding came from corporate support, the dean’s ofﬁce, or the H. T. Person Endowment. Individual funding is discussed in the project descriptions. Securing funding support is the responsibility of the professor. 5.6. ASSESSMENT 63 5.6 ASSESSMENT Multiple assessments of the projects were conducted. The NASA Zero Gravity projects were as- sessed by whether NASA accepted the project, and the NASA critique of their ﬁnal report. Each project required the student teams to make a public presentation of their project. Members of the university, industry, professional engineers, and the press are invited. Everyone in the audience is given an assessment sheet and asked to critique the presentation. Professionals associated with the development of the project or the ﬁeld trips are invited to the presentation and are given copies of the written report in advance of the oral presentation and asked to critique the presentation. A sample critique summary is provided in Appendix IV. The work demands of these classes are one of the biggest challenges of their academic careers. The interdisciplinary designs have been well received by the students.They became the best advocates for the next year’s class and many used their ﬁnal design report as an example of their work in job interviews. C H A P T E R 6 65 Interdisciplinary Projects 6.1 INTERDISCIPLINARY DESIGN PROJECTS Each of the following interdisciplinary projects follows a parallel format. The objective of the design project is presented, the student composition is given, the course organization is presented, the student results summarized, and an assessment in the form of closing comments are provided. 6.2 NASA ZERO GRAVITY I: CONSTRUCTION IN SPACE 6.2.1 OBJECTIVE This Zero Gravity project challenges the students to develop techniques and connections for the construction of a truss structure for space applications. The project consists of designing carbon ﬁber truss elements and plastic connectors, practice assembling the truss, developing safety plans, and executing the design in the NASA KC-135 aircraft. 6.2.2 CLASS COMPOSITION This class consisted of seven undergraduate students ranging from sophomores to seniors. Two were civil engineers and four were mechanical engineers and one was a senior journalism major. The two engineering seniors promoted the project as an independent study program to meet their senior design requirements. Dr. David Walrath, of the Mechanical Engineering department, provided technical assistance and coordination with the ME department requirements. 6.2.3 CLASS ORGANIZATION The class was structured in a discussion format and given a single course number.The original concept of space construction came from the professor. The ﬁrst quarter of the semester explored the range of possible solutions. The project was organized into tasks commensurate with the NASA project requirements. These included design of the experiment, detailed component design and fabrication, safety plans, and storage and material retention devices for on board the aircraft. Connection of the truss elements at the nodes emerged as the critical element of the project. 6.2.4 STUDENT WORK The student design consisted of hollow carbon ﬁber truss elements and polyethylene connector units (Figure 6.1). The truss was to be assembled in the zero gravity environment onto base elements 66 6. INTERDISCIPLINARY PROJECTS Figure 6.1: Snap together truss design. fastened to the top of a container box. The container box was fastened to the aircraft ﬂoor in accordance with NASA guidelines. For comparative evaluation, two different truss concepts were developed. The ﬁrst truss con- cept consisted of snap together elements.The second concept had a cam mechanism on the connector so that the node could be opened, a ball from the truss end inserted, and the cam twisted shut to complete the connection. The zero gravity ﬂight consists of a series of parabolic curves. Weightlessness occurs while the plane is in the parabolic arc. The gravity free time to work is on the order of 20 seconds. In order to prepare for the ﬂight, the students practiced the truss assembly underwater in the campus swimming pool (Figure 6.2). This trial program worked out especially well because the amount of time available for holding their breath and working underwater was again approximately 20 seconds. The underwater fabrication occurred in a semi-weightless environment. The truss elements were close to neutral buoyancy and the students had no ﬁrm surface to grip. The project was accepted by NASA and scheduled to ﬂy in the spring semester. Each truss element and connection element had a Velcro strap attached to it and a corresponding Velcro tie 6.3. NASA ZERO GRAVITY II: EXERCISE MACHINE 67 Figure 6.2: Underwater trial fabrication. down on the container box. The Velcro prevented the pieces from ﬂoating free during the zero gravity portion of the ﬂight. Both truss concepts were capable of being constructed within the time constraints of the ﬂight. The ﬁnal report to NASA concluded that the cam device was superior to the snap together design. While the snap together design initially could be constructed faster, the cam system was much easier to disassemble or reconﬁgure. All components were designed and fabricated by the students. The aluminum storage box and the foundation of the truss were designed by the students and were common to both truss systems. The design included the safety padding along the edge of the truss container box (Figure 6.3). 6.2.5 ASSESSMENT The project required two semesters due to the NASA review and acceptance process. Students presented their results to both NASA and to their respective student professional societies on campus. There was sufﬁcient interest in the project that a second project was undertaken the following year. NASA was critical of the student ﬁnal report in not being detailed sufﬁciently for deployment. In addition to the construction write-up, NASA indicated they wanted a full weight and strength analysis. 6.3 NASA ZERO GRAVITY II: EXERCISE MACHINE 6.3.1 OBJECTIVE In zero gravity, astronauts need self-contained, self-reacting, light weight exercise equipment for transport to space and it needs to be compact enough for easy storage on the space station. The NASA ﬂight must demonstrate the suitability of the equipment in zero gravity. Students designed a “Bowﬂex ®” based exercise platform that allowed upper and lower body exercises. The ﬁnal device 68 6. INTERDISCIPLINARY PROJECTS Figure 6.3: Snap together truss construction in zero gravity. (Photo courtesy of NASA) 6.4. DESIGN OF AN AUTOMATED TRANSIT SYSTEM 69 was designed to be collapsible and ﬁt in a minimum volume for both transport to and storage on board the space station.The project organization and executions were similar to the truss construction project. 6.3.2 CLASS COMPOSITION The class consisted of ten students, four civil engineers and six mechanical engineers. Four of the team were female students. Dr. David Walrath assisted with the mechanical engineering components. 6.3.3 CLASS ORGANIZATION The class was structured in a discussion format and given a single course number. The original concept of space construction came from the professor. The class worked in a colloquium setting and was responsible for fabrication of all components and preparation of reports. STUDENT RESULTS 6.3.4 The students examined a range of exercise equipment and eventually selected on modifying Bowﬂex® system components to provide a force resistance system. The Bowﬂex® rods were lightweight, and could be procured in varying stiffness. They could be conﬁgured to provide upper and lower body strength exercises (Figure 6.4). Elastic band solutions provided similar exercise options, but the rigidity of the student design allowed easier mounting and dismounting exercise positions. 6.3.5 ASSESSMENT The project ended up being only partially successful. While the student design functioned as planned, one of the project sponsors did not want to continue due to potential liabilities of elements breaking in space. Breakage was never an issue in the trials, but the inability to potentially replace a part remained a concern to the team. Complementing the student effort, the college supported the travel expenses for a reporter from the local TV station to accompany the students to Houston. This resulted in a ﬁve-day TV documentary featuring the students, their project, and their ﬂight. 6.4 DESIGN OF AN AUTOMATED TRANSIT SYSTEM 6.4.1 OBJECTIVE The main campus of the University of Wyoming is growing, and parking is being relocated to the campus perimeter. An interdisciplinary senior design class was recruited to design an automated transit system for the campus. This was a two-year project. The ﬁrst year involved planning and preliminary design of the system. The second year involved constructing a prototype model transit system and alternative guideway designs. 70 6. INTERDISCIPLINARY PROJECTS (a) Demonstrating leg strength (b) Changing exercise setup Figure 6.4: Flight team on board the NASA KC-135A test ﬂight (Photos courtesy of NASA). 6.4.2 CLASS COMPOSITION The class composition consisted of ﬁve to eight civil engineers, two chemical engineers, one electrical engineer and four mechanical engineers. One of the mechanical engineering students was a dual major in ME and EE. The number of students varied from semester to semester due to the civil engineering departmental requirements. 6.4.3 CLASS ORGANIZATION This was the ﬁrst fully interdisciplinary senior design project. The course was divided into ﬁve components.The ﬁrst component required about half a semester and dealt with project planning.The second component reﬁned initial concepts and selected the overall transit system. This component included ﬁeld trips to assist in understanding the magnitude and complexity of the undertaking. The third component began in the second semester and included detailed design of the system elements including vehicle, guideway, geometric layout, stations, maintenance facility, and control 6.4. DESIGN OF AN AUTOMATED TRANSIT SYSTEM 71 center. This activity additionally incorporated graphic art consultants. The last two components occurred in the second year and included design of an alternative guideway and fabrication of an operational prototype. The class was organized similar to a design ofﬁce. Figure 6.5 provides the second semester organization chart for the class including the various project assignments. The graphics design portion of the project was provided by the senior Computer Graphics II class. Figure 6.5: Class organization chart. 6.4.4 STUDENT RESULTS First semester established the design parameters for the project. Five tasks were completed. First, the students reviewed material on automated transit systems found in the literature and lectures prepared by the professor. Second, they conducted trafﬁc studies to determine the demand to be placed on the system, stations, and vehicles. Third, they examined the Americans with Disability Act requirements. Fourth, they developed the technical design guidelines. Fifth, they developed the preliminary design concept. Augmenting the literature review was a ﬁeld trip to Denver, Colorado, 72 6. INTERDISCIPLINARY PROJECTS where the team visited Rocky Mountain Prestress, Six Flags–Elitch Gardens, and the Denver In- ternational Airport Transit system. Rocky Mountain Prestress provided the team with insight to understand how construction could be prefabricated to minimize on site construction time and dis- ruption. Six Flags–Elitch Gardens engineers discussed switching, safety, and operation of rides with small vehicles (Figure 6.6). Figure 6.6: Discussing switches at Six Flags–Elitch Gardens and conducting bus trafﬁc studies. The Denver International Airport automated transit system requires very high reliability and has a sophisticated maintenance area. Students were introduced to transit operation reliability concepts. The second task developed the overall load criteria and transit layout. This study included the size of the transit vehicles, frequency they would run, and the route they would take. To complete this task the students conducted extensive surveys of the shuttle bus. The university runs buses on 10–15 minute headways from about 7:30 in the morning until 8 in the evening. The student ﬁndings were enlightening. First, the only times the buses were heavily used were in the 20-minute period prior to 8 AM and 9 AM morning classes. Many times during the day the buses ran empty. Supplementing the trafﬁc study, the students met with the president of the university to review the long range planning and capital construction plans. In addition to determining where the campus trafﬁc would likely locate, they also examined athletic events on campus to evaluate if the transit 6.4. DESIGN OF AN AUTOMATED TRANSIT SYSTEM 73 system could assist access to football and basketball games. The study determined that the transit system would be elevated to eliminate conﬂict with street trafﬁc. As part of the trafﬁc study, the students conducted an assessment of how far patrons would walk. From a series of transit studies in Canadian cities, they determined that transit users would walk about 1,000 feet before considering alternative mobility options (Figure 6.7). The present and future station locations provide access to 100 percent of the present and future campus. Figure 6.7: Aerial plan showing station locations and walking distances. The third task determined how the Americans with Disabilities Act (ADA) would impact their design. In addition to reviewing the ADA requirements, the students laid out a mockup of the interior of the vehicle, then used wheelchairs to enter, exit, and position themselves in the vehicle. This study led to four major conclusions. First, all stations would require elevator service. Second, the vehicle must be able to accommodate one and preferably two wheelchairs. Third, wheelchair access 74 6. INTERDISCIPLINARY PROJECTS must not require supplemental assistance or restraints. Fourth, the team must develop appropriate emergency egress solutions. The fourth task established the design guidelines for the system. These were divided into two parts. The ﬁrst part examined ASCE-7 Loads on Structures1 for external loads on the structure and stations. ASCE-7 does not provide wind loads for guideways or vehicles, so the students had to extrapolate the speciﬁcation data to suit their conditions. The second part addressed the vehicle requirements and consisted of two components. The ﬁrst component was the overall frequency of vehicles, travel times, and interface requirements with the guideway to assure fatigue performance and ride comfort. The latter item leads to maximum horizontal accelerations and corresponding minimum curve radii. The second component was the size of the vehicle and its orientation on the guideway. The conclusion resulting from the ﬁrst semester was that the vehicle would be suspended under the guideway to mitigate the effects of weather in the Laramie area. An overhead support system assures that the bogie supporting the vehicle is within an enclosed area and out of the weather. While Laramie is semi-arid, the winter snowstorms and associated winds were a concern that an exposed guideway surface could become iced and result in the vehicle being stuck on inclined areas. To further assure all weather operations, a linear induction motor drive was selected. A linear induction motor not only provides the power climbing hills but also works to control downhill speed without having to resort to a mechanical braking system. The mechanical braking system for the vehicle served as a backup. Safety and emergency egress solutions were developed and included in the recommendations. The trafﬁc analysis suggested that vehicles with a capacity of six seats were adequate for the majority of the travel. The ﬂoor space was then designed to accommodate two wheelchairs. This provided a vehicle with a total capacity of approximately 20 students if wheelchairs were not present. That would be six students sitting and 14 standing. While this would be a relatively tight conﬁguration, it was satisfactory to carry the peak load occurring just before the 8 AM and 9 AM classes. The students concluded that a small vehicle operating at a four-minute headway would be optimal for the peak hours. Vehicles would automatically be removed from the system and headways increased to 5- to 10-minute headways off peak. The students further decided that the transit system should offer two-way operation. That is, one side of the track would carry vehicles in a clockwise direction while the opposite side would carry them in a counterclockwise direction. The guideway would split at a station so the station would be between the two tracks and therefore only require one set of stairs and elevators. The two-directional operation assured that the minimum transit time would result and provide redundant operation. A rider could go counter ﬂow to get to a station immediately across campus instead of having to ride the entire route to get to the same location. During the second semester, the engineers “hired” the ART 4110 Computer Graphics II design class to assist in developing the system graphics. Three teams from this group presented graphic concepts to the engineers. Stagecoach emerged as the system theme. The graphics classes presented marketing concepts for advertising on the side of the vehicles to assist in defraying operational costs. 6.4. DESIGN OF AN AUTOMATED TRANSIT SYSTEM 75 To publically assess the overall concept, the two classes conducted a focus group study. The study was conducted in the lobby of the student union (Figure 6.8). Students visiting the booth were requested to vote on a name, ﬁnal graphic themes, and provide opinions on travel times and station locations. Figure 6.8: Focus group booth and one schematic of a vehicle. The guideway design was a steel truss spanning between precast concrete columns. The columns were designed to have a sandstone ﬁnish to match the buildings on campus. The ﬁnal guideway design layout was selected to minimize the number of parking spaces taken and trees impacted. The suspended vehicle system had a secondary beneﬁt that should one of the large cot- tonwood trees surrounding the campus lose a branch, that branch would hit the guideway but would not cross the guideway in a manner to disrupt or dislodge a vehicle. The stations were designed in precast concrete and galvanized steel. The architectural ﬁnish was selected to match the buildings on campus and to be in accordance with the university trustees’ guidance for overall campus architecture. The stations were intended to be modular to facilitate ease of construction. Where possible, it was also anticipated that the stations might be integrated into any new building construction to provide even more efﬁcient access to campus facilities. The mechanical engineering component of the project was satisﬁed by using the rapid pro- totype modeling equipment at the university. Students designed the overall cab for the vehicle and the bogie system. Each of the components was “printed” on the rapid prototype machine. They were manufactured to approximately 1/10 scale and were available for inspection during the public presentations. Chemical engineering students were charged with developing a fuel cell component for each car to allow a vehicle to return to a station in the event of a power outage. Following their initial research, the students concluded that such power supplies were available commercially. They un- dertook a study for an alternative power supply for the project. The students developed a concept 76 6. INTERDISCIPLINARY PROJECTS for using a solid oxide fuel cell currently under development by Siemens in Germany. The fuel cell operated on natural gas at a temperature of approximately 900 F. The fuel-cell generated sufﬁcient electric energy to completely operate the transit system and have a 20 to 30% excess capacity to provide base load and off peak transit power to the university. The student analysis concluded that the heat from the fuel cell would be sufﬁcient to replace the heat generated by the coal burning furnaces at the university energy plant and thereby reduce the university carbon footprint. ◦ The projected construction schedule for the project was 700 working days from bidding until ﬁnal construction. The project budget was estimated to be $64.3 million and a 15% contingency for future design cost increases. The design was presented at a public meeting and included invited judges. Adjudicators in- cluded the president of the university, the vice presidents of Research and Facilities, the dean of Engineering, ﬁve faculty members, and three professional engineers. In preparation for the presen- tation, one of the students suggested that an animated graphic of the systems would be impressive. The class provided aerial views of the campus and graphics of the transit system to Mr. Brendan Dolan, who in turn generated a complete campus model in the computer game Roller Coaster Tycoon. The model was used in the presentation and included aerial views of the system and a comprehensive passenger’s view from inside the vehicle as it circumnavigated the campus. The third semester broke the project into two parts. The ﬁrst part occurred in the civil engi- neering course for design of prestressed concrete. That class used the design guidelines developed the previous year to develop design an alternative guideway in precast-prestressed concrete. In the execution of the precast concrete design, the students were introduced to signiﬁcant geometric de- sign constraints due to the centrifugal force on the vehicles and the corresponding torsional effects in an inverted C shaped structure. Mechanical engineers undertook the task of constructing a prototype transit system. During the ﬁeld trip to the Denver International Airport, Logplan LLC offered to provide the university with a small section of the original Denver baggage handling system. The students used the bogie and guide rails from the baggage handling system as the basis for the demonstration system. They modiﬁed the bogie to support a Plexiglas cabin complete with operational doors. The students modiﬁed the LIM rail and LIM motor to correspond to the overall design criteria. The ﬁnal project demonstrated the operation of the automated vehicle system. The vehicle pulled into the ﬁrst station and cycled the doors automatically. Optical sensors checked for obstructions and recycled the doors if an obstacle was present. The vehicle traversed to the next station, cycled the doors, then shut down (Figure 6.9). 6.4.5 ASSESSMENT COMMENTS The project was complex, difﬁcult, and highly engaging for the students. It was assessed in two different environments. The ﬁrst assessment was a public presentation of the project at the end of the ﬁrst year. The presentation team included the engineering students and the Computer Graphics students. Evaluation sheets were given to everyone in the audience and speciﬁc sheets were given to 6.4. DESIGN OF AN AUTOMATED TRANSIT SYSTEM 77 Figure 6.9: Students programming the model transit system. individuals asked to adjudicate the project. Each critique sheet asked the reviewers to evaluate the project on the basis of the written report, the technical merits, and the oral presentation. On a scale of 1 to 4 with 4 being outstanding, the technical review team score was 3.6. Non-engineers rated the team somewhat higher, 3.8, than the technical reviewers. A sample evaluation sheet is provided in Appendix IV. A press announcement was compiled by the graphics class, and press releases were prepared. The project received coverage in most newspapers in the state. Copies of the ﬁnal report were sent to the board of trustees and several state legislators. UW TV conducted the second semester interview and presentation and the tapes were release within the state. One of the interesting facets of the mechanical engineers design was the fact that the students were able to make the Denver Airport baggage handling system work. 78 6. INTERDISCIPLINARY PROJECTS Figure 6.10: Final project graphics (Courtesy ART 4110). The second level of review occurred when the ﬁnal report was distributed to the various ﬁeld trip sponsors. Several comments were received; however, a most interesting critique came from a ﬁrm that conducts planning of specialty transit systems. They had acquired a copy of the report from the Denver International Airport. Their comment was that the students had not followed all of the relevant speciﬁcations for transit design. At the same time, the ﬁrm understood that working from ﬁrst principles not just following speciﬁcations was a class objective. They then requested the names and contact information for every member in the class as they wanted to hire as many as they could. 6.5 DISAPPEARING ROADS 6.5.1 OBJECTIVE Jonah Field in western Wyoming was one of the ﬁrst major gas ﬁelds developed by fracking. The tight sandstone led to wells being placed in close proximity to each other. Consequently, a spider web pattern of access roads developed. The class was charged with designing methods to reduce the surface impact of drilling. In the process of the course, the class also elected to enter the “Disappearing Roads” competition sponsored by Halliburton Corporation and run by Texas A&M University. 6.5. DISAPPEARING ROADS 79 6.5.2 CLASS COMPOSITION The class consisted of seven civil engineers, 12 mechanical engineers, and one Environmental and Natural Resources student. The second semester introduced a new group of civil engineers. Two civil engineers elected to take the second semester as an elective credit to complete the project design. 6.5.3 CLASS ORGANIZATION The Disappearing Roads competition was presented to the class as a model but not a requirement for the project. The ﬁrst two weeks discussed the environmental and engineering issues to be addressed. The class then traveled to Pinedale, WY, for a three-day ﬁeld trip. The trip included stops at the Halliburton facility in Green River, WY, and a brieﬁng of environmental and regulatory constraints by the Bureau of Land Management in Pinedale, WY. EnCana Corporation arranged a full day tour of Jonah Field including brieﬁngs on fracking operations, gas recovery, disposal of drilling materials, and overall operations. Following the ﬁeld trip the class elected to enter the Disappearing Roads competition. The class was interviewed by Mr. Richard Haut, of the Houston Area Research Consortium, and, based on their interview, were allowed to compete. The second semester included a ﬁeld trip to the Questar Productions, virtual drilling facility in Denver, CO. The tour included a 3D visualization of the Pinedale Anticline Production Area and the difﬁculties of hitting the small gas formations. Near the beginning of the class, a request came from U.S. Senator John Barrasso’s ofﬁce for a student panel discussion of energy policy based on the book Beyond Oil.1 Six students from the class participated with one student serving as moderator. At the conclusion of the course the group that was representing the university at the Disappearing Roads competition presented their ﬁndings to Senator Barrasso. The senator met with the students for well over an hour and quizzed them closely on their work. This brieﬁng was exceptionally helpful in preparing the students for their Disappearing Roads presentation. 6.5.4 STUDENT RESULTS The following student results focus on the environmental considerations leading to development of a mat road system. The work included research, development, testing of concepts, and concluded with the class participating in the Disappearing Road competition. The Pinedale Anticline Production Area (PAPA) and Jonah Field are in West Central Wyoming west of the town Pinedale. Though these two ﬁelds share many of the same charac- teristics, there are a few key differences. First and foremost is the size of the drilling ﬁeld. PAPA encompasses 198,000 acres. This is over eight-and-a-half times the size of Jonah Field. The PAPA is a long narrow swath of land that stretches from Pinedale to 70 miles north of Rock Springs. The 80 6. INTERDISCIPLINARY PROJECTS Figure 6.11: Class brieﬁng U.S. Senator John Barrasso. terrain at the PAPA is generally not as level as the terrain at Jonah Field. The PAPA does have a very similar dry climate to Jonah Field. The ﬁelds contain over 3 billion cubic feet of natural gas. Common environmental concerns in PAPA and Jonah Fields include: impacts on sage grouse, pronghorn antelope, big game animals, top soil disturbance, air pollution, preserving view sheds, soil chemical composition, and addressing archaeological issues. While the two sites share many of the same environmental concerns, the PAPA has far more habitat concerns. The PAPA is a vast area, and it is broken into nine separate management areas that are based on land ownership and environmental concerns. Each management area has a set number of wells that can be developed and its own set of environmental concerns. These concerns range from preserving historic wagon trails to protecting big game winter habitat. Because of these additional concerns different strategies will have to be applied to the two natural gas ﬁelds. 6.5. DISAPPEARING ROADS 81 Figure 6.12: Aerial view of Jonah Field (Photo copyright Jeff Vanuga, used with permission). The Pinedale Anticline Project Area and Jonah Field have many shared geological traits. In both ﬁelds the natural gas being recovered is contained in over-pressurized pockets in the Lance Formation. These pockets in the Lance Formation are described as a bowl of potato chips. Each chip contains the gas bearing formation. These pockets require hydraulic fracturing in order to recover the gas. Hydraulic fracturing sites require a larger and heavier footprint than a conventional natural gas well site. A key to reducing reclamation time is to reduce the disturbance of the topsoil. When the topsoil is torn up, and stored in piles for several years, the soil loses vital microbes and nutrients. The root structure of the sage brush is also heavily damaged in this process. Sagebrush can take 10 to 30 years to reestablish but if the root structure is preserved, the recovery can be as little as two years. Implementing strategies that would lessen the disturbance of the topsoil and sagebrush would lead to a reduced recovery time which would be beneﬁcial both to the environment and to the energy companies as the regulations will only allow more drilling when an equal area is recovered. Both Jonah Field and the PAPA are on land once inhabited by indigenous cultures and still maintain very important archeological sites scattered throughout the ﬁelds. Damage to these sites should be avoided, and strategies to account for these sites implemented. Additional regulations that affect PAPA and Jonah Field include: 82 6. INTERDISCIPLINARY PROJECTS (cid:129) In order to preserve air quality in limiting NOx emissions, all drill rigs shall use natural gas powered engines with low NOx emissions. (cid:129) Mat roads and pads cannot be in the same location for two years or more. If a mat is in place for two years at one location, it must be removed and cannot be placed in that location for another year. (cid:129) All compressing and condensate facilities must produce no more than 49 decibels of noise pollution. (cid:129) The owner of the land reserves the right to have any main road removed. If it is desired to have the main road removed, it shall be done by the energy company who must remove all foreign soil from the road system. A two track access road must remain for maintenance purposes throughout the service life of the well. (cid:129) If heavy equipment is required to access any site after development, a mat road must be deployed for access. (cid:129) All reclamation criteria will be according to the current BLM mandated reclamation criteria. (cid:129) In management areas with big game winter range there will be no development occurring from November 15 through April 30. The Pinedale Anticline and Jonah Field have enough differences that they warrant two dif- ferent strategies for drilling. This summary of the student work addresses the PAPA ﬁeld. The recommendations for the Jonah Field are in their full report. The PAPA is slated to have about 2,000 wells drilled in the next 20 years and will be operating through the foreseeable future, whereas production at Jonah Field is on the decline, and suggested strategies may not be as applicable. The PAPA has to account for additional time constraints due to winter range of big game and breeding season of the sage grouse population. Therefore, the solution in the PAPA is to limit the development footprint using temporary roads for ﬁeld delineation. This research suggests a temporary mat road system would improve access and reduce recovery time. The timeline for an individual well pad at the Pinedale Anticline is constrained as follows: no surface activity is allowed from November 15 to April 30 in management areas with big game winter range concerns. This leaves 198 days for development to take place. It is estimated that a well will be completed in approximately 72 days; at this pace ﬁve wells can be drilled in areas where operation can be year-round and three wells in areas where drilling operations must shut down in the winter. In order to complete one well pad with 32 wells it would take 11 years in areas with winter range concerns and seven years in other areas. Due to these constraints, the timeline for a pad in an area with big game winter range concerns is as follows: on May 1, the mat road would be deployed. A temporary mobile modular frame would then be setup, with all equipment and material needed to complete three wells. Once all the equipment is in place, the mat road would be picked up, and a two-track road would serve as access 6.5. DISAPPEARING ROADS 83 for the workers. Once the ﬁnal well is completed for the season, the mat road is redeployed and all the equipment that is required to leave the pad site would leave at that time. The mat road is then picked up and the site is vacated until the next year. A main paved road would be designed for the spine of the PAPA ﬁeld and should meet the following criteria: provide an adequate base, sub grade, and pavement type with a thickness capable of withstanding a repeated 80,000 lb truck load. A preliminary design indicates that the paved road would reduce dust, noise, and maintenance. It would be 6 in. thick consisting of a 3 3/4 in. nominal hot plant mix. The paved road would be at least 24 feet wide to allow for the larger turning radius of trucks and equipment. This scenario requires mat roads of up to one mile and would therefore need a complex mat road system. The mat roads would be at least 12 feet wide and as much as 24 feet where turns are required. Advantages of this scenario include not having to spray chemicals on a dirt/gravel road for dust suppression along with a smoother, faster, dust-free access to well and hydro fracking sites. The disadvantages of this system include a higher initial cost, and the requirement of a more complex mat system and maintenance access to the site. The gravel roads that spur from the paved road would be placed when a mat road is unable to connect a desired well pad site to the paved road because of safety or terrain reasons. Due to topsoil concerns, the maximum deployment for a mat road would be two years with a minimum of one year before redeployment in the same location. A roll-out road concept is suggested for short access roads. The roll-out road incorporates hinged board segments linked with cables that can be rolled out into 50-foot road sections. These sections can be rolled out to construct a temporary road and then rolled up when ﬁnished. This concept will reduce the time required for setup and removal and enhance the ability to conform to uneven ground surfaces (Figure 6.13). Figure 6.13: Roll-out road segment. The key beneﬁt of the roll-out road concept, compared to other alternatives, is the ease of placement and removal on site by incorporating a continuous roll rather than individual mat segments 84 6. INTERDISCIPLINARY PROJECTS in a grid/matrix format. Parallel 10-foot-wide lanes allowing for a complete 20-foot-wide two-lane road to be rolled out. The four main components in the initial design included board selection, hinge design, segment connection design, and road dimensions. During the class ﬁeld trip to Jonah Field, representatives stated that the main problem with currently available mat designs was the longevity of the oak. The design team found a solution with Heartland Bio-composites, a Wyoming-based company that specializes in manufacturing natural ﬁber-reinforced/polymer-based lumber products (bio-composite). Some advantages in using bio- composite lumber are long-term durability, enhanced weather resistance, and their ability to be recycled. In following the “low impact/environmentally friendly” theme of the project, the design team felt that bio-composite lumber was an ideal solution. To enhance strength and minimize the number of segments required for the roll-out road, the team decided to base the initial design on a 2 x 8 in. board cross section. With board selection completed, the next task was to maximize the ability of the boards to conform to uneven ground surfaces. The plan for the roll-out road called for individual board segments to be chained together in the longitudinal direction. Transverse hinges, centered in each board, hold the connection together in the direction of travel while still allowing individual segments to conform to changing terrain (Figure 6.14). with hinge without hinge Figure 6.14: Lateral ﬂexibility with and without hinge assembly. Two conceptual hinge designs were developed for the roll-out road. The ﬁrst hinge design incorporates a ﬂexible elastomer/rubber hinge.The elastomer/rubber hinge is afﬁxed to slotted board segments and held together with lag screws. The second hinge concept utilizes U-bolt fasteners and fabricated with ASTM A1018 steel endplates. Before ﬁnalizing the roll-out road design, testing was performed on both an individual com- ponent basis and as a scaled prototype in the ﬁeld. Testing can be broken down into “sandbox” board tests, hinge tests, and ﬁeld tests. Preliminary tests were run to assess the durability of the bio-composite boards by subjecting them to cyclic loading, which represents a continuous series of heavy duty vehicles driving over the road. To replicate ﬁeld conditions, a “sandbox” was constructed and ﬁlled with a sand/soil mixture and placed under the hydraulic ram of a MTS machine. Oak and bio-composite test boards were continuously loaded with 4,500 lbs at a cyclic frequency of 1 Hz. Each material was tested for one hour (3,600 cycles) and the corresponding maximum deﬂections were recorded as 3.78 in. for bio-composite, and 3.28 in. for oak. 6.5. DISAPPEARING ROADS 85 The second test administered in the laboratory was designed to test the tensile strength of the reinforced rubber and U-bolt hinge connections. Two types of reinforced rubber (Capralon® and Masticord®) provided by JVI Industries were used to assemble two separate hinges, both of which underwent tensile loading until failure. The U-bolt hinge was tested using the same procedure. The tensile loads at the point of failure for the Capralon®, Masticord®, and U-bolt hinge assemblies were recorded as 2,200 lbs, 1,450 lbs, and 4,800 lbs respectively. With a predicted maximum tensile load for the hinges of 780 lbs under ﬁeld conditions, all three hinge designs performed reasonably well (Figure 6.15). Figure 6.15: Hinge assembly testing. The ﬁnal testing application involved placing the prototype road section utilizing the Capralon® elastomer hinges in the ﬁeld. The prototype was taken to Mountain Cement Com- pany in Laramie, WY, where 80,000 lb twin side-dump trucks were continually driven over the road system on their way from the gravel/limestone quarry to the cement plant. The results of the ﬁeld testing revealed some serious problems with the elastomer hinge design. After approximately four days and 153 truck passes in the ﬁeld, two of the boards failed at the middle hinge connection. The failure was determined to be caused by stress concentrations in the notched cuts on the board ends, which encase the rubber hinge components. The design team feels that cold temperatures (nearing 0 F) also contributed to the brittle fracture that resulted in failure. Even with the elastomer/rubber hinge failure, the design received praise from the cement company as well as several drivers who thought the concept would be excellent if a better hinge connection could be implemented. The initial rubber hinge connection was abandoned and the U-bolt hinge design was chosen as a ﬁnal design. ◦ For the roll-out road system to function as intended, the following guidelines need to be fol- lowed. First, all large obstacles should be removed from the path of travel and the route brush-hogged. While the road should be able to conform to most terrain, not following the above recommendations will lead to premature failure of the road. For the placement and removal process of the road, a simple solution rolling and unrolling the road from around a forklift attachment was selected. 86 6. INTERDISCIPLINARY PROJECTS The process will allow the road to be rolled up and rolled out without ever having to drive directly on the terrain. When rolling out the road, the forklift will drive directly over the road section as it is unrolling. When rolling up the road, the forklift will be driven in reverse down the road section, allowing the forklift to remain on the roll-out road at all times. The weight of the forks, beam attachment, and beam is thought to be enough weight to compel the road to roll up. This process will become easier once an initial wrap is completed. A replicate mat was designed similar to the wood mats currently in use but used a bio- composite material. The bio-composites were attractive for their potential lifetime over the oak mats used today and their ability to be recycled. The extra cost of using bio-composites is a concern. Therefore, these mats are designed to have a life cycle cost that is substantially less and have a longer lifetime than the wood mats that are currently in use today. The complete layout of these bio-composite mats incorporated some ideas from the current wood mats with a few layout changes. The mats are 8 x 8 foot squares in order to be used both on drilling pad sites along with roads leading into these sites. The 8-foot width of the mat allows for a 24-foot road leading into the well sites, which is compatible with any size vehicle in Jonah Field. 6.5.5 TESTING Various tests were completed for the bio-composite material and the prototype mat. The goal was to determine if the bio-composite material would be more conducive to the environmental constraints and more cost effective to the consumer. The tests were completed to assess how well the bio- composite material performed. The standard of comparison for the tests was oak, the material currently used in the ﬁeld. The tests performed were for: friction, fatigue, abrasion, shear, deﬂections under loading, and a ﬁeld test. Concurrent with these lab tests, a ﬁeld test was performed. Four quarter-scale mat prototypes (4 foot x 4 foot x 4 1/2 in.) were built and placed in a rock quarry road owned by Mountain Cement Company outside of Laramie, Wyoming, for ﬁeld testing. Two mats were replicates of the oak mats currently in use and two were built with a 0˚/45˚/0˚ conﬁguration to test for strength and durability for either conﬁguration. These mats withstood an average of 2,400 tons per day for 18 days (Figure 6.15). After testing, both conﬁgurations came out looking exactly the same. There were no broken boards, the mats did not warp and they showed very little wear. The only problem that arose was when the mats were being removed, the interlocking boards ended up breaking because they were frozen to the ground and improper removal techniques were used. Because all mats were removed the same way, it is felt that the 0˚/90˚/0˚ composite prototypes should be pursued over the 0˚/45˚/0˚ conﬁguration simply because they are easier and cheaper to manufacture. Students recommended additional tests including an Izod test at extreme temperatures, a creep test on the prototype, the tests already performed with wider temperature variant conditions, longer ﬁeld testing, properties testing to compare the theoretical properties to the actual properties, a screw withdraw test with various screws, and a shear test with various screws. They also recommended that 6.5. DISAPPEARING ROADS 87 Figure 6.16: Field test. a demonstration installation should be performed on Jonah Field to further test the bio-composite mats in the ﬁeld. The bio-composite mats are beneﬁcial to use in the ﬁeld over the oak mats.The bio-composite material is more environmentally friendly because it does not absorb signiﬁcant amounts of moisture, it does not leach into the soil, and it can withstand varying temperatures. The bio-composite mats are also more cost effective because, even though there is a higher initial cost, the life of the bio- composite mat exceeds the oak mats and that the composite materials can be recycled by melting and reforming. After the mat/rollup road is removed, there will be emergency ﬁeld situations. Efﬁcient ways of responding to these situations were addressed. Finding an efﬁcient solution to an emergency situation requires weighing the effects of the emergency against the environmental effects. In the situation where a worker is hurt, the ﬁrst option is to drive out to the site of the accident. When there is a serious injury to a worker, there is always the option of driving off-road because at that point, the risk of injury or death greatly outweighs the environmental effects of driving off road. The second option is to use a helicopter from Flight for Life. In ﬁre or other such emergencies at one of the well sites, there are multiple options for handling the situation. If you need large equipment at the site, such as a crane, tracked vehicles can be available. These tracked vehicles are large enough to haul the necessary equipment to the site of the accident. An advantage of these tracked vehicles is that they will produce a minimal footprint, even while hauling other large equipment. When the ﬁre needs to be contained very quickly, the only option is to drive ﬁre equipment to the site, even if this means driving off-road. 88 6. INTERDISCIPLINARY PROJECTS 6.5.6 ASSESSMENT The above description addresses the design, fabrication, and testing of roll-out and mat road portion of the design. The students also designed at portable drilling pad structures to reduce the footprint. Presentations at the University of Wyoming were provocative with varying opinions being offered by the students, oil and gas industry, and BLM. The students defended their design well. The learning experience was enhanced by the differing opinions and positions of the reviews. External assessment of this project included taking ﬁrst place at the Disappearing Roads competition. The same year we received a request from Grand Teton national park on the project. The National Park incorporated wooden mats into their park improvement project using some of the recommendations in the student report. The mat road concept, using composite mats, has been incorporated into projects in Texas in part because of the Disappearing Roads report. 6.5.7 ACKNOWLEDGMENTS The research team acknowledges the materials supplied by Heartland Biocomposites, Torrington, WY, and JVI Inc., Lincolnwood, IL.Technical support was provided by EnCana U.S.A. Inc. Pinedale, WY; Questar Production Inc., Denver, CO; Bureau of Land Management, Pinedale, WY; Mountain Cement, Laramie, WY; the University of Wyoming School of Energy Resources; the H.T. Person Endowment; and the College of Engineering and Applied Science shop and staff. BEETLE KILL AND BIOMASS ENERGY 6.6 6.6.1 OBJECTIVES The massive beetle kill of Lodgepole Pine in the nearby National Forest creates a hazard for ﬁre, trafﬁc, hikers, and power lines running through the forest. Roads and power line rights of way were to be cleared to 75-foot setback to prevent trees from falling on the roads or the lines. This design project assessed whether the timber that was being removed was sufﬁcient to be an alternative energy supply for the University of Wyoming Central energy plant and the modiﬁcations to the Energy Plant to accommodate wood fuel. 6.6.2 CLASS COMPOSITION The class consisted of nine students; six civil engineers, two energy system engineers, and one mechanical engineer. In the second semester only the energy system and mechanical engineers continued. 6.6.3 CLASS ORGANIZATION The project was reﬁned to match the available student skills. The University of Wyoming Central Energy Plant uses coal as the main fuel source for providing the energy needed to heat the University of Wyoming campus. The stoker-grate boiler employed at the Central Energy Plant has the ability to burn a variety fuels to produce the required energy needed. This project explores options for 6.6. BEETLE KILL AND BIOMASS ENERGY 89 biomass use at the Central Energy Plant, reduction in emissions in relation to the University of Wyoming’s emission goals, acquisition of beetle kill wood as a biomass energy source, the facilities required to store the wood, site design and layout for the energy plant modiﬁcations and additions, the environmental advantages of the project, a risk assessment, and the cost analysis of implementing such a project. The project focuses on the implementation of the coﬁring solutions at the central energy plant including the following areas of interest: veriﬁcation of the fuel mixture ratio entering the boiler, energy and economic forecasting for coﬁring at the Central Energy Plant, and biomass coﬁring combustion effects. 6.6.4 STUDENT RESULTS This project was viewed as an economic opportunity for the University of Wyoming as well as an environmental opportunity. Currently the University of Wyoming campus is heated by a network pipes that deliver steam to individual buildings. The steam is produced at the Central Energy Plant where coal is burned in stoker boilers to produce the delivered steam.The University receives roughly 25,000 tons coal annually from the Grass Creek Mine of Thermopolis, Wyoming (Table 6.1). The University of Wyoming set a goal to reduce CO2 emissions 15% by the year 2015 and of 25% by 2025. The University of Wyoming is striving to be carbon neutral by 2050. The Medicine Bow and Routt National Forests are particularly susceptible to beetle infestation due to the morphology of the forest and mature trees that have had to withstand years of drought. These forests combined consist of approximately 2.7 million acres of which over 1 million acres, or nearly 40% of the forests, have been affected by the beetle epidemic. Table 6.1: University of Wyoming Annual Coal Consumption at the Central Energy Plant from FY04- FY08 Fiscal Year Amount of Coal Burned (tons) CO2 Emissions from On- Campus Coal (tons) 2004 2005 2006 2007 2008 24,097 24,059 24,297 25,864 24,510 57,926 57,446 58,221 61,248 58,165 Coal that is burned to heat the University of Wyoming campus contributes signiﬁcantly to the overall carbon dioxide, CO2, output of the University of Wyoming. The total carbon emissions of the university are 147,452 tons of CO2, and on-campus coal use makes up 39% or 58,165 tons CO2. These emissions have remained relatively constant from 1997-2009. By adding biomass as a 90 6. INTERDISCIPLINARY PROJECTS fuel source at the energy plant there is a potential to move the university well on its way to meeting or even exceeding its emissions goals (Figure 6.17). Transporta(cid:2)on & Other 15% Biomass/CO2 Oﬀset 8% On-Campus Sta(cid:2)onary 31% Purchased Electricity 46% Total UW CO Emissions: 147,452 Tons Oﬀset CO Emissions: 11,796 Tons Figure 6.17: Estimated FY11 CO2 Emissions Contributions by Source for the University of Wyoming with Coﬁring 20% Biomass Replacement. There are several environmental beneﬁts to burning biomass in place of coal. In the case of emissions there are three clear beneﬁts. They include: reduced sulfur dioxide emissions, reduced nitrogen oxides emissions, and reduced net carbon dioxide emissions. In this case, the sulfur and nitrogen oxides emission, reductions are minimal due to the low sulfur coal and the relatively small volume of coal being consumed. Therefore, the focus is on carbon dioxide emission reductions. Burning biomass still produces CO2 just as with any combustion reaction; in fact burning biomass produces almost the same amount of CO2 as burning fossil fuels. Therefore, it is not intuitive that the biomass energy production is carbon neutral. To understand the emissions tradeoff for fossil fuels (coal) to biomass (wood) it is necessary to understand coal source. Coal is formed by plant matter from swamps that existed hundreds of millions of years ago that became buried; the plant remains became coal due to long-term exposure to heat and pressure. During its life, the plant absorbs CO2, and CO2 is stored in the plant matter as carbon. Therefore, when coal is burned it is releasing carbon dioxide captured by photosynthesis millions of years ago and is considered “new” 6.6. BEETLE KILL AND BIOMASS ENERGY 91 carbon emissions. Biomass, on the other hand, releases CO2 that was stored over the life of the plant, in our case several recent decades. The trees killed by the pine beetle are no longer growing and thus no longer acting as a carbon sink through the process of photosynthesis. Over time these dead trees will naturally release the carbon that they have stored through the decay process or from a forest ﬁre. If this carbon can be released during energy production and reduce the amount of coal that is burned, any CO2 that is offset by the burning of biomass is considered a reduction. A variety of solutions were considered for the use of biomass at the Central Energy Plant including: multiple offsite storage locations, four possible on-site storage areas, site modiﬁcations options, and boiler modiﬁcations for biomass-only fuel versus a biomass and coal coﬁring solution. The team’s ﬁnal recommendations included the development of two offsite storage sites for long term biomass storage and processing at Centennial, WY, and Foxpark, WY; modiﬁcations to the north side of the current Central Energy Plant site to allow for biomass transportation and storage; and implementation of coﬁring rather than boiler modiﬁcation. The decision to implement coﬁring rather than converting a boiler to burn only biomass affected a variety of other aspects of the project and was therefore one of the ﬁrst decisions required. A coﬁre solution evolved after reviewing the following decision matrix (Table 6.2). Boiler modiﬁcation allows for the displacement of a larger volume of coal; however, this option has signiﬁcantly more risk. By implementing coﬁring the Central Energy Plant maintains ﬂexibility to adjust for biomass fuel supply disruptions or price inﬂations, and a lower capital investment is required to begin the process. Based on GIS studies, two remote storage sites were selected in the Centennial and Fox Park locations. The sites total 18 acres, 14.5 acres dedicated to storage of wood and wood chips, 3.5 acres for contractor use to sort and load wood. The two-site solution provides ﬂexibility for forest access and reduces transportation requirements as compared to a single site solution. One of the concerns with introducing biomass to the current operations at the Central Energy Plant is the ability for the plant to store and handle the additional fuel while still maintaining the current coal storage and handling capacity. Maintaining the current coal capacity is important because it allows the facility to retain ﬂexible operations and having enough coal reserve should a disruption in fuel supply occur during a period of high demand. The addition of a separate biomass storage and handling system allows the plant to maintain current coal and biomass capacity for greater ﬂexibility to adjust fuel mixture ratios. Given the need to mix fuels, several modiﬁcations to the Central Energy Plant site were proposed. The requirements for the biomass storage and handling system included: the ability to store up 100 tons of biomass, an unloading area for biomass that did not interfere with the current coal delivery system or other components of the site, and a tie-in with the current plant design. Option 4 on the north side of the site was selected as it provided the least amount of disruption to the existing operations while providing signiﬁcant storage space (Figure 6.18 and 6.19). The recommendation for the Central Energy Plant is to implement coﬁring with the mountain pine beetle killed trees takes advantage of the environmental crisis and turns it into an opportunity. 92 6. INTERDISCIPLINARY PROJECTS Table 6.2: Risk Assessment Decision Matrix Comparing Boiler Modiﬁcation to Coﬁring at the Uni- versity of Wyoming Central Energy Plant Legend • √ O Option 1 Wood Boiler O O • O O √ √ √ O • √ • √ 5 - O 5 - √ 3 - • minimal risk moderate risk high risk Option 2 Cofiring • √ • • √ • • • √ • • • • 0 - O 3 - √ 10 - • Risk Wood availability or delay Not enough wood supply Must have carbon offset Coal price highly fluctuates Wood price fluctuates Regular boiler maintenance Boiler out of service Storage area Transport double handle Variation in wood moisture content Ash removal Environmental disadvantages Sustainability of project Total= Detailed design issues include: the ability to verify the fuel mixture ratio entering the boiler; the ability to predict the energy input into the boiler to account for any necessary control modiﬁcations, understanding how the addition of biomass will affect the burn chemistry within the boiler and how it relates to ash content and grate integrity as well as potential deposits on heat exchangers. There are alternative ways to mix biomass with coal for the purpose of coﬁring. At some plants coal and biomass fuels have been injected separately, while at smaller utilities they were mixed prior to injection. Premixing is done either on site or prior to delivery. At the Central Energy Plant, the pilot study determined that fuel mixing solution would store the woodchips to one of the three existing storage silos and then deposit them onto the conveyor ﬂow with the coal. This wood/coal 6.6. BEETLE KILL AND BIOMASS ENERGY 93 Figure 6.18: Aerial view of the central energy plant with the four proposed site modiﬁcations to accom- modate for biomass storage and delivery. mix will then be loaded into one of the three bunkers, which feeds directly into the boiler. The mixture ratio can be modulated by means of a guillotine valve at the base of the wood chip silo. Moisture content is a limiting characteristic when implementing a biomass fuel source, for a particular biomass to be a viable fuel source. Three different samples of Lodgepole Pine wood chips were obtained from the Medicine Bow forest and tested for water content in the UW Civil Engineering soils lab. These samples included wood chips from a tree with no needles, a tree with red needles (dying), and one with green needles. The results from these tests are shown in Table 6.3. These results are signiﬁcant because the water content of beetle kill trees is sufﬁciently low that an expensive and cumbersome drying process would not be required. Low water content also contributes to the recoverable heating value and greater boiler efﬁciency. If green trees are harvested, they must be allowed to dry to reduce the moisture content below 20 percent. The heat value of wood varies between species due to different chemical makeup. Most often the heating value is reported in units of energy per oven dry weight. When water is present, it 94 6. INTERDISCIPLINARY PROJECTS Figure 6.19: Rendering of biomass delivery and storage system. Table 6.3: Water content of different samples of Lodgepole Pine Sample Water Content (by mass) No Needles Red Needles Green Needles 8.83% 10.01% 57.91% contributes a signiﬁcant amount of weight to the sample, but not to its heat content. Also, when water is present in a sample that is to be combusted, there is a decrease in boiler efﬁciency because vaporizing water uses some of the heat that is liberated in the boiler. It was found that the water content of wood is the most signiﬁcant factor in determining the heat content of it. In fact, the per unit weight heat content of the wood decreases proportionally to the amount of water that is present. Although the heat content varies from species to species, 8,500 btu/oven dry pounds is an average for local wood fuels. The reported heat value for beetle kill trees was found by averaging the water content of the red needle and no needle trees and is approximately 7,600 btu/lb. Completion of a successful test burn of biomass and coal coﬁring at the Central Energy Plant required accurate determination of the mixture ratio of biomass and coal. An experimental program was developed to verify the mixture ratio of biomass and coal entering the boiler. The veriﬁcation 6.6. BEETLE KILL AND BIOMASS ENERGY 95 method needed to be simple and repeatable so that it could be performed by personnel at the Central Energy Plant at the time of the test burn and when the project goes forward. The procedure had to ﬁrst be calibrated for the coal and wood chips used at the plant. A “Mix Calculator” is a tool developed to process the basic information collected at the Central Energy Plant during the test burn and provide information about the mixture ratio (by volume and by mass), the estimated energy density of the fuel mixture, fuel cost estimates, estimated annual savings, and estimated annual carbon dioxide (CO2) emission reductions. The embedded assumptions for the “Mix Calculator” can be found in Table 6.4. Table 6.4: Assumptions embedded in the “Mix Calculator” Assumption Bulk Density of coal Bulk Density of wood Energy density of coal Energy density of wood Value 9.55 2.35 10500 7600 Units Source [lbs/gal] Experimental data [lbs/gal] Experimental data [btu/lbs] Central Energy Plant [btu/lbs] Theoretical results verified by an Cost Coal 56.00 [$/ton] independent lab Central Energy Plant In order to calibrate the “mix calculator” the following supplies are needed: a four-gallon sampling bucket, a scale capable of measuring weights up to 50 lbs, 300 lbs of coal from the Central Energy Plant, 35 lbs of dry wood chips from beetle kill trees, and two measuring buckets that can accurately measure samples as small as one half gallon. The procedure is: 1. Measure four gallons of coal, weigh the sample, and record the results. 2. Measure four gallons of wood, weigh the sample, and record the results. 3. Measure two gallons of coal and two gallons of wood; mix the components in the sampling bucket. Be sure that the mixture is homogeneous. Weight the sample and record the results. 4. Measure three gallons of coal and one gallon of wood; mix the components in the sampling bucket. Be sure that the mixture is homogeneous. Weight the sample and record the results. 5. Measure three and one half-gallons of coal and one half-gallon of wood; mix the components in the sampling bucket. Be sure that the mixture is homogeneous. Weight the sample and record the results. 6. Repeat steps 1-5 two more times to gather additional data points. 7. Calculate the bulk density of coal and wood for the different mix ratios. This actual mix validation requires a four-gallon bucket and a scale capable of weighing up to 50 lbs. The following process should be repeated every three minutes upon changing the fuel mixture ratio until steady state is achieved. 96 6. INTERDISCIPLINARY PROJECTS 1. Identify boiler which will be burning biomass-coal mixture and locate the sampling port. 2. Measure and record tare weight of the sampling bucket. 3. Gather a four-gallon sample from the sampling port into the sampling bucket. 4. Lightly shake the sample to allow for moderate settling and reﬁll the sample to the four-gallon level if necessary. 5. Weigh the sample. 6. Subtract the tare weight of the sampling bucket. 7. Enter the result into the “Mix Calculator.” 8. The output of the “Mix Calculator” will provide: volumetric mixture ratio, mass mixture ratio, the expected energy density of the fuel mixture entering the boiler as well as cost estimates for coﬁring. In order to use the “Mix Calculator” only three inputs are needed: 1. Cost of the biomass [$/ton] (Mountain Pine Beetle killed wood). 2. Current annual coal usage [tons/year]. 3. Weight of fuel sample taken at the Central Energy Plant. The above calibration and sampling method provides the Central Energy Plant a simple, quick, and effective method of measuring the mixing ratio and predicting the energy density of the fuel entering the boiler. A review of the literature concerning coﬁring coal with biomass revealed the technical issues related to the combustion process of these fuels. Table 6.5 is a summary of key differences of biomass compared with coal that should be considered when implementing a coﬁring project. Coal and biomass ash differ in terms of both their chemical and physical properties, as well relative amounts of ash produced during combustion. Further complicating matters is that interaction of these two fuels inside the boiler will have different effects on the predicted ash formation than if the two fuels were ﬁred separately. Typically, biomass has smaller ash content than coal with a different chemical composition. Coal ash is mainly composed of aluminum and silica, with clay and quartz, while biomass contains a high level of calcium and alkali metals such as sodium and potassium. It is the increased quantities of alkali metals that cause problems inside the boiler. These volatile compounds can act as ﬂuxing agents, which, when combined with other mineral elements, cause them to melt. One example of this reaction is when potassium from the biomass combines with silicon from the coal and forms low melting silicates. These low melting compounds can bind ﬂy ash materials onto the boiler tubes Table 6.5: Comparison of Key Differences between Biomass and Coal 6.6. BEETLE KILL AND BIOMASS ENERGY 97 Characteristic Carbon Content Moisture Volatile Matter Reactivity Heating Value Ash Content Ash Composition How Biomass Compares with Coal Lower carbon content than coal Higher moisture content than coal Biomass contains a much higher percent of volatile matter and will de-volatilize independently of coal Due to higher volatile content, biomass is more reactive and has a lower ignition temperature Lower heating value Lower ash content Higher volatile alkali metal content, especially in the form of potassium(K) and fuel grates in a process known as slagging, the consequences of which include efﬁciency losses due to decreased heat transfer and air ﬂow. Alkali metals are much more prevalent in “rapidly growing” biomass such as wheat straw and switchgrass, while “old-growth” biomass, such as wood from pine trees, tends to have much lower alkali quantities. Accordingly, the use of Lodgepole Pine as a coﬁring fuel will tend to cause less deposition problems than other biomass materials. Interestingly, the literature notes that one solution to the ash-related issues in biomass boilers is to coﬁre coal with the biomass. Some studies further suggest that the mineral elements in coal might have a “buffering effect” on the volatilization of alkali metals, which could further reduce the problem of ﬂy ash deposition. One other concern related to coﬁring combustion is the chlorine (Cl) content of the biomass. This concern is due in part to the potential for Cl in the ﬂy ash to corrode metal components of the boiler. Again, this is typically of greater concern for high Cl content herbaceous materials such as switchgrass and straw. Mitigation techniques for problems related to slagging and corrosion include increased soot blowing, the use of commercial chemical additives, ash deposition models, and attentive monitoring of the internal boiler conditions. A thorough chemical analysis should be performed on any type of biomass that will be combusted in order to understand the mineral composition of the resulting ﬂy ash. The ﬁnal design included development of the off loading facilities, screw drives for wood chips, storage bins, and fuel mixing details. The calibration of the coﬁring operation was completed. Fol- lowing the conclusion of this project the Central Energy Plant continued pilot studies for including wood fuel and had dedicated one of the three coal storage bins to wood. 98 6. INTERDISCIPLINARY PROJECTS 6.6.5 ASSESSMENT The small class size limited the scope of the project. Energy systems engineers deﬁned the quantity of wood needed annually for a 20-year coﬁring conversion and designed the boiler modiﬁcations. Civil engineers conducted the timber availability and designed the staging areas and plant site modiﬁcations. Managers of the Central Energy Plant were judges on the ﬁnal presentations. The student design work was used by the Central Energy Plant, and the plant has continued to convert one boiler to a coﬁring operation. The project served as the culminating senior design project for the ﬁrst two students to graduate from the college’s new Energy Systems Engineering program. 6.7 GOTHIC CATHEDRALS 6.7.1 OBJECTIVES The course was jointly developed with Dr. Kristine Utterback of the History Department. Dr. Utterback focused on the life, times, and society of medieval Europe at the time of the ﬁrst gothic cathedrals. The engineering effort focused on the state of knowledge at the same time of gothic cathedral construction. From an engineering perspective, this project presented engineering history to non-engineering students and introduced many engineering concepts used today. 6.7.2 CLASS COMPOSITION The class was advertised on the university website, and a notice was sent to the local papers. The class consisted of 15 students, none engineering majors. Four students were non-traditional students. One criterion for the class was that only the math known in the Middle Ages was required. The lack of math requirements was a draw for non-technical students to any class dealing with engineering. The class composition included regular undergraduate students and a number of non-traditional students interested in the topic. 6.7.3 STUDENT RESULTS A special summer course explored the development of medieval gothic cathedrals, which were built between about 1150 and 1400 in Europe. Bringing the vastly dissimilar areas of expertise, medieval studies and civil engineering, to bear on the subject gave the students very different perspectives on the life and times of the turn of the last millennium. The students explored the history of cathedrals as they developed in medieval society, examining the social, ecclesiastical, artistic, economic, and political elements. At the same time students planned and built a 1/8 scale model of a portion of a gothic cathedral, based on many of the same techniques medieval builders used. They began by conducting experiments on how arch and truss structures functioned.They continued by constructing their measurement tools, particularly the square and the level, using only a straight edge, a string, and a piece of chalk. The ﬂoor of the Kester Structural Research Laboratory became a “tracing room” as the students laid out the arches for the cathedral walls and vaulted ceiling. The engineering instruction began by asking the students to build an arch. Wooden blocks were precut and the students had to assemble the arch. Many hands substituted for falsework. The frustration was high until one group “discovered” that an abutment was needed to support the horizontal thrust. Suddenly, construction progressed at a rapid pace (Figure 6.20). 6.7. GOTHIC CATHEDRALS 99 (a) Attempted arch construction (b) “Discovery” of abutements Figure 6.20: Discovery of arch statics. The next task fabricated tools. A line was struck on the ﬂoor of the structures lab. Using a piece of chalk and a string, the line was bisected. The perpendicular lines were used to lay out a square. A triangular element was laid out on the ﬂoor with the perpendicular locations marked. Addition of a plumb weight through the perpendicular line provided a level. Division of a circle around the original intersection provided a rough protractor (Figure 6.21). These tools were used to lay out the model apse of the cathedral. The string and chalk exercise continued to develop the layout of the stones that would be used to create the pointed Gothic arch. The width of the cathedral would be laid out and circular segment drawn to intersect at the apex of the arch. This layout procedure demonstrated how blocks could be rough cut at the quarry. Rough cutting at the quarry reduced handling and shipping costs while ﬁne ﬁnishing was completed at the cathedral site. The base of one buttress was fabricated out of foam blocks. The ﬂying buttresses were laid out on foam boards and were representative of six of the major Gothic cathedrals. The project culminated with a “dedication” of the cathedral. The model and descriptive placards remained in place for approximately two months. 6.7.4 ASSESSMENT COMMENTS The course was successful in generating interest in medieval construction. The coordination between the History Department and Engineering was effective and the two elements of the course meshed 100 6. INTERDISCIPLINARY PROJECTS Figure 6.21: Design and fabrication of a working level. Figure 6.22: Cathedral dedication. well. Leading the students to “discover” how arches work and how tools could be made accurately with nothing more than a straightedge, string, and chalk was revealing to many. The project attracted a good deal of interest due to its location on the main campus quadrangle and remained up for the entire summer tour and freshman orientation period. REFERENCES 101 REFERENCES [1] ASCE/SEI 7–10 Minimum Design Loads of Buildings and Other Structures, ASCE, Reston, VA, 2010. [2] Kenneth S. Deffeyes, Beyond oil: the view from Hubbert’s peak, New York, Hill and Wang, 2005 198 pg. C H A P T E R 7 Getting Started 103 The previous design challenges require a substantial time commitment. Motivating the students to think about design problems often requires a small effort to initiate their thinking. The following are physical and thought problems to lead into thinking about design and design issues. The Column Design Challenge can be used for all ages. The maximum load recorded was a freshman engineering student and it exceeded 12,500 pounds using these rules with no limit on the amount of glue. The Column Design Challenge is coordinated with the state science fair and is an opportunity for the students throughout the state to be introduced to the College of Engineering and Applied Science. The satellite and rubber tire problems introduce students to problems requiring very large and very small numbers. They are ideal to instigate discussion on a problem with no conventional solution and to assign follow up discussion or papers to explore the consequences of their ﬁndings. It is not unusual to have solutions to these two problems varying by many orders of magnitude. 7.1 H. T. PERSON DESIGN CHALLENGE FOR PRIMARY AND SECONDARY SCHOOLS IN WYOMING The Challenge: Using a single sheet of copier paper and up to 4 oz. of white (Elmer’s) glue, construct a column that has a minimum height of four inches. The column carrying the largest load will be declared the winner. When: Testing will be conducted during the State Science Fair. [Students can submit entries in person, by their teachers, or by mail with their name, address, and school. Students need not be present to win.] Testing: Column load tests will be conducted in a structural testing machine or a frame similar to the photo to the right. Students add one brick at a time up to 15 bricks. Any column carrying 10 bricks will be unloaded and retested in a structural testing machine. 7.1.1 ENGINEERING BACKGROUND AND HISTORY (15 April 1707– 18 September 1783) was a pioneering Swiss mathematician Leonhard Euler and physicist. He made important discoveries in ﬁelds as diverse as inﬁnitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for 104 7. GETTING STARTED his work in mechanics, ﬂuid dynamics, optics, and astronomy. He is credited with the Euler buckling equation for the strength of columns (adapted from Wikipedia). 7.1.2 WHAT AN EQUATION TELLS YOU ABOUT DESIGN The Euler Bucking equation, Pcr = π 2EI/L2, indicates the load a column can carry before bucking. Pcr is the Euler bucking load and is proportional to its modulus of elasticity, E, the placement of the material away from the center of the column, I, and inversely proportional to the length squared, L. The modulus of elasticity is like a spring constant. Since everyone is using copier paper, the modulus is pretty much the same for everyone. So the challenge is to limit the length to just 4 inches and spread the paper out to improve performance. If the paper is spread too far, then it will buckle locally and not be as strong as a more compact design. Hint: Paper is made by a rolling process, so one direction of the paper has a higher modulus of elasticity than the other direction. 7.2 METEOR COLLISION PROBLEM This is an in-class problem that may be extended to homework with the solution due in the next class period. Students work in three- or four-person teams to develop an answer to the following problem. Each year the earth passes through the Perseus meteor shower. At the peak of the shower, meteorites hit the earth’s atmosphere at the rate of 100 per hour.The shower lasts approximately four days. You are working on a new geostationary satellite design team. The satellite is four feet in diameter and located 22,500 miles above the earth. Your supervisor is concerned that one of these pieces of space debris may damage the $2 billion dollar satellite. You are asked to evaluate two questions. First, what is the approximate probability of the satellite being hit by a particle from the Perseus meteor group? Second, is this a problem? For this problem, probability is not a formal calculation but an assessment, like one chance in a million, that there will be a hit. You will orally present your answer on the probability of being hit in class. Your presentation will include the approximate probability and your assessment of whether this is a problem. You should include a discussion of your logic, assumptions, and for any additional information needed to complete your assessment. 7.3 TIRE PARTICLE PROBLEM This is an in-class problem that leads to a short research follow-up activity. Students work in three- or four-person teams to develop an answer. The ﬁrst part is to be answered in class the day the problem is given. The second part is given in the next class period to allow the students to look up the impacts. 7.4. WHAT HAPPENED? 105 Firestone recently recalled over six million tires. The obvious ramiﬁcations of defective tires are the loss of control of the vehicle followed by the debris generated when the tread ﬂies off. In considering these impacts, the Environmental Protection Agency began to wonder about the health hazard of the particulate matter generated by normal tire wear. If you lived close to a freeway would this material cause respiratory or other problems? Your team is asked to investigate this problem. The ﬁrst question is: “What is the size of the particles generated by normal tire wear?” As a follow-up question, your team is asked to recommend whether the EPA should issue a warning about tire particulate matter or mandate new criteria for tire design. How does the size compare to other particles? How might these particles compare to known problems such as asbestos? Your team will orally present your answer on the size of the particles in class today with a discussion of your logic and your assumptions. For the follow-up question, identify other information that you may need to complete your recommendations. A one-page summary of your ﬁndings and a list of your team members will be handed in at the beginning of the next class period. 7.4 WHAT HAPPENED? 7.4.1 WINDMILL COLLAPSE An interesting discussion problem provides the class the picture below and asks them to work in groups of two to determine what happened. After about ﬁve minutes, ask each group to give one reason what caused the collapse and write it on the board. Continue around the class with each group adding one new possibility. When no further ideas come forward, ask each group to compare the total number of possible reasons they had developed with the total number of possibilities on the board. This leads to a discussion of why teamwork is better than individual effort. 7.4.2 BRIDGE ACCIDENT Using the four photographs, determine the sequence of the failure when the excavator hit the I-70 bridge. 7.4.3 DEVELOPMENT OF STRESS AND STRAIN CURVES Demonstrations in Mechanics of Materials classes typically test a steel, aluminum, or brass specimen to develop a stress-strain relationship. While instructive, the test requires specialty equipment and 106 7. GETTING STARTED Figure 7.1: Wind Turbine collapse (Photo Courtesy of Jason Shogren, University of Wyoming). “black boxes” that isolate the student from the mechanics. The following experiment requires some weights and a ruler to accomplish similar results.The experiment is set up in a room with the weights, platforms, and measuring devices available. There is no reason the experiment cannot be conducted by hanging the specimen from the ceiling. The specimen can extend several times its initial length, so a short specimen is preferred. Objective: In this experiment, you will determine the stress-strain characteristics of an un- deﬁned material and calculate the initial modulus of elasticity. Background: Read the entire memo before beginning. [All the necessary equipment for this experiment is available on the ﬁrst ﬂoor of the engineering building. The specimen materials, mass units, measuring tapes, and safety glasses are in a parts box on the shelf on the exterior wall. The test can be adapted to any lab that has weights and a tape measure.] 7.4. WHAT HAPPENED? 107 (a) (b) (c) (d) Figure 7.2: I-70 Bridge collision. You may work individually or in groups of no more than two. If you work in a group, only a single report is required but both names must be on it. Safety: Wear safety glasses (included in parts box) when conducting this experiment. Keep feet out from under weights. Prediction: Pick one of spools to use for your experiment. On the graph below, qualitatively predict what the stress-strain curve for the material will look like. 108 7. GETTING STARTED stress Specimen Color: ______________ Diameter: ___________________ strain Experiment: 1. Select a specimen (smaller diameters provide a greater range of response for the mass units provided). Record the color and diameter of the specimen labeled on the spool. 2. Cut off about 2.5 feet of the specimen from the spool. Tie an overhand loop around one end as shown below. (a) Grab one end and pull it against itself so that you form a loop. Take the loop you just formed and make an overhand loop back through, as you would if you were tying a knot. Keep the formed loop large enough to ﬁt over the post (Figure 7.3). Figure 7.3: Specimen termination. (b) Fix this loop securely around the post attached to the base, making sure that the strand is just underneath the washer. (c) Tie a small loop in the opposite end the same way. This end drapes over the pulley. Place the mass hanger through the loop you created. A picture of the set-up is shown in Figure 7.4. 3. Place one piece of tape around the material about an inch from the post. Place another piece of tape about ﬁve inches from the ﬁrst. Mark a line on each piece of tape, or on the specimen, to provide a consistent measuring location. Measure and record this initial distance between marks with only the mass hanger in place. 7.4. WHAT HAPPENED? 109 Figure 7.4: Test materials and test setup. 4. Add a mass to the mass hanger and measure the distance between the two pieces of tape. Record both the cumulative mass and distance. 5. Repeat step four, increasing the total mass until the hanger reaches the ground, you run out of weights, or the specimen breaks. 6. Repeat the experiment with a different sequence of mass placement and record the data. Mass Distance Mass Distance 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 10 11 12 13 14 15 16 17 18 19 20 110 7. GETTING STARTED 7. Calculate the stresses for each mass applied to the specimen and the corresponding strain. (a) Enter your data into Excel and perform the necessary calculations to obtain the stresses and corresponding strains. (b) Create stress-strain curves for the material using the Excel plot function. Stress should be plotted on the vertical axis and strain on the horizontal axis. Use a scatter plot function with straight lines between data points unless you trust Microsoft to properly interpret the curves between points. (c) Use the stress-strain plot to determine the initial modulus of elasticity, E. L , E = σ (Note: σ = P (cid:5) , and mass is not a force) A , (cid:5) = (cid:6)L Furthering the Experiment: Explain how your prediction compares to the actual stress-strain curve you created. How long did it take to complete the experiment and is this a concern? Does the sequence of loading make a difference? How would you further this experiment to collect more information about the unknown properties of this material? Format your response as a typed memo (no more than two pages plus the plot) to your professor and attach your worksheet along with your ﬁnal Excel sheet and plot, which may be embedded in the memo. This should be a professional quality report. 7.5 NOTES FOR CHAPTER 7 These notes are provided in a separate section so the problem statements may be copied directly. They are not “solutions” but are provided based on the classroom use of the problems. 7.5.1 PAPER COLUMN EXPERIMENT The paper column experiment typically ends up with loads less than 300 pounds. A simple test frame with about 15 bricks is both visually effective and exciting when the column crushes. We use a small hand-operated universal testing machine for ﬁeld testing. The hint about the orientation of the paper is to have students think about the consequences of paper alignment but alignment has little effect on the ﬁnal load carried. This project has worked well in the ES 1000 class as homework with the students bringing the completed columns to class for testing. The explanation of the moment of inertia I is necessarily vague as it is meant to be used by students without a mechanics of materials course. Euler originally deﬁned EI as a combination of material properties and geometry. Young’s modulus, E, was not deﬁned until after Euler’s death. 7.5.2 METEOR COLLISION PROBLEM The meteor collision solution requires a change in perspective. Since the meteor showers occur at the same time each year, it is not the meteors that are moving, rather the earth moving through the debris ﬁeld. One solution to this problem is taking the ratio of the earth’s diameter to the diameter 7.5. NOTES FOR CHAPTER 7 111 of the satellite and multiplying by the number of hits and the duration of the exposure. Because the satellite is in the earth’s shadow nearly half the time, a correction can made. This problem is an education when the student estimates are written on the board followed by each group explaining their methodology. Expect several orders of magnitude difference in the student solutions. Ask which solution is “right.” Sometimes the following hints are provided with the problem. Hints: What moves, the meteors or the satellite? What is the density of the meteor particles and what is the volume of the satellite orbit? 7.5.3 TIRE PARTICLE PROBLEM A solution to this problem requires a larger number of assumptions including the original and ﬁnal thickness of the tread, the number of miles of tire life and the outside diameter of the tire. From these assumptions an estimated thickness lost in each rotation can be calculated. Assuming each particle is a cube, the size of each piece of dust can be determined. This problem is a good introduction to nano-particles. The follow-up research requires students to look into the effects of nano-particles. The EPA website has guides for particulate matter size. Students should consider both the size of the particle and the chemical reactivity. 7.5.4 WHAT HAPPENED Wind Turbine Collapse The best estimate at the reason for the collapse is that the wind turbine over-sped and one of the blades fractured and hit the tower. No detailed failure mechanism was given. Be prepared for some pretty unusual possible causes. Possible causes ranging from mosquito swarm strikes to UFOs have been suggested. Bridge Accident One solution: From the lower left photo, the boom hit the bridge girder just below the parapet wall. Note that the parapet wall is intact. The force of the impact tore the trailer from the tractor, top left, forcing the cab of the equipment to rotate upward until the cab hit the bridge sofﬁt, upper right. The impact bent the boom and extended the hydraulic actuators, top right. When the cab settled, the boom extended well above the deck, lower right. 7.5.5 STRESS-STRAIN CURVES This experiment is intended to remove all “black boxes” from the determination of a stress-strain curve. The thread in the experiment is a polyurethane string used for kid’s snap-bracelets. It is available at Hobby Lobby, Michael’s or other craft stores. Larger quantities can be found online. In 112 7. GETTING STARTED several years of running this experiment, no student has broken the specimen because the weights hit the ﬂoor before the strand ruptures. Even at that, no student report has gone back and shortened the string to determine the breaking capacity. The snap-bracelet material is interesting because of its extremely high strain to failure. The same experiment can be done with a simple elastic band. A P P E N D I X A 113 H.T. Person Lectures raeY 1998 rekaepS Daniel P Welsh eltiT Project Manager for Main Street Parade at Walt Disney World cipoT Engineering at Walt Disney World – Making the Magic Happen 1999 Dr. Edward Anderson Professor, Texas Tech University Learning in the Digital Age 2000 Dr. Carl Mitchem Professor, University of Florida Technology and Ethics: From Expertise to Public Participation 2001 J. Howard Van Boerum Principal, Van Boerum and Frank Associated The Design and Construction of the Utah Olympic Park 2002 Lawrence C. Novak Senior Engineer, Skidmore Perspective from Ground Zero Owens and Merrill 2003 R. Paul Humberson Western Area Power Anatomy of a Blackout 2004 Michael K. Zyskowski Administration Program manager, Microsoft Flight Simulator project Microsoft Flight Simulator: The Engineering behind the Game 2005 Joseph A. Anselmi Mechanical Engineer GPS: How does it Work? Aerospace Corporation 2006 Neil Kelly National Renewable Energy Laboratory (NREL) in Golden, Colorado Engineering Challenges for Future Wind Energy Development 2007 Patrick Tyrell State Engineer, Cheyenne, Wyoming Defending our Borders – Protecting Wyoming’s Water 114 A. H.T. PERSON LECTURES 2008 Dr. Richard K. Miller President, Olin College, Needham, Mass. 2009 Lawrence C. Novak Portland Cement Association 2010 Joseph Leimkuhler Offshore Well Delivery 2011 Dr. Daniel Pack Manager Shell Exploration and Production – Americas Professor, United States Air Force Academy Education of Engineering Leaders for the 21st Century: Lessons Learned for Re- Invention at Olin College Philosophy of Engineering for the Burj Dubai, the World’s Tallest building Deepwater Well Design and Operations – Going Forward Post Moratorium Developing Cooperative, Autonomous, and Heterogeneous Unmanned Aerial Vehicles 2012 Governor Mike Sullivan Former Governor of Wyoming and Ambassador to Ireland Observations and Reflections on the Benefits and Importance of an Engineering Education A P P E N D I X B 115 Sample Course Syllabus and Policy ES 1000-1 Introduction to Engineering Study Course Syllabus and Policy – Fall 2012 Professor: Office: e-mail: Office Hours: M-W 2:30-4:00 PM Charles W. Dolan En 2082 [email protected] Catalog Description of Course: Peer Assistant: Jane Doe e-mail: [email protected] ES1000. Orientation to Engineering Study. 1. [F1<>I, L] Skills and professional development related to engineering. Involves problem solving, critical thinking and ethics, as well as activities to help transition to university environment. Required of all freshmen entering engineering curricula. Students with credit in UNST 1000 may not receive credit for this course. (Normally offered fall semester) Course Objectives To acquaint students with resources available at the University for their success To get to know some of the faculty and students To help students understand the fields of engineering and the engineering thought process Fulfills USP Requirements for I, L and a portion of the O components To help students to make a successful transition to the University and the College 116 B. SAMPLE COURSE SYLLABUS AND POLICY Week Topic-WED. Topic-FRI. Assignments 1 1 1 Wed. 2 1 In class 3 In class 4 ES-1000 Information Introduction/Project Professional courtesy and conduct International Engineering Information session Complete introductions and critique of presentations Information Literacy, Researc Topics Introduce classmate using Biographical Sketch; and first thoughts on research topic MON – Biographical sketch via email to Dolan and Peer Assistant Design Project: Teams and Design Process, "Deep Dive" video Provide feedback on oral presentations Critical Design Issues and schedule Design teams assigned over weekend Project Brainstorming Library Research Begin Advisor Interviews Shop Safety Video Meet in Library 216 Critical Issue 1 Critical Issue 2 Design Project: Methodology of Design Design Day/Shop time FRI – Research topic due Critical Issue 3 Sat Challenge trial run 9 AM-1 PM Indoor Practice Facility 22nd and Willett Drive 117 5 6 7 Student Success Brainstorming fixes Academic Policies Professional licensure Advising Critical fix 1 Critical fix 2 Preparing and Giving Oral Presentations Ethics for Engineers Research Project Oral Presentations Shop time Research Project Oral Presentations Advisor Interview FRI – complete TIP tutorial completed by midnight http://tip.uwyo.edu MON – Research Report Due by midnight, portfolio due in class Wednesday Friday College Open House Counts as an activity Shop time -Complete ES1000 8 Sat 9 Research Project Oral Presentations Career Services Knight Hall 222 ES-1000 Flight Competition Honors Advising Class evaluations 9 AM - 1 PM Indoor Practice Facility 22nd and Willett Drive 118 B. SAMPLE COURSE SYLLABUS AND POLICY INSTRUCTIONAL MATERIALS Additional Reference material on the web: http://wwweng.uwyo.edu/classes/es1000ref/home This is the “ofﬁcial” home page of the ES1000 class. It will have much of the information we cover. The “On-Line Textbook”—Changes, Challenges & Choices, Andrea Reeve & Diane LeBlanc (eds.) http://www.uwyo.edu/bettergrades/ on the right hand column. This webpage, though “old,” has a lot of great information with just a few broken links. Library Assignment: http://tip.uwyo.edu (Note: there is no www in the URL) Studying Engineering, 3rd edition, Landis, R.B., Discovery Press, L.A., 2007. If you would like a good, all around introduction to the ﬁrst year and more in engineering, Landis is a good start, cost is about $25. 119 CLASS REQUIREMENTS Prepare a Biographical sketch – FRI./Week 1 (Required for O component) (cid:1) Introduce Research topic – FRI./Week 1 (Required for O component) (cid:1) (cid:1) Achieve a 70 percent or better on the TIP exam by the end of week 5 o Note: Failure to complete the TIP exam with a 70% or better will result in an F for a term grade. (Required for L component.) (cid:1) Complete research topic and assessment papers by week 7 o Note: Failure to submit a research paper, an assessment paper, and a portfolio will result in an F for a term grade. (Required for L component.) (cid:1) Participate in a Team in the Design Challenge (cid:1) Participate in Final Oral presentation with group. Note: Failure to participate in Final Oral Presentation will result in an F for a term grade. (Required for O component.) (cid:1) Complete six outside activities and report by email o Required List - four activities 1. Advisor interview (by Sept. 18) 2. Two professional society meetings (one in Sept, one in Oct) 3. Senior Design Presentations (in December) o Elective List - two activities 1. One cultural activity (theater, symphony concert, lecture [not a rock concert]), one sports event (football, soccer, swimming, wrestling, etc; must attend the entire event), career fair, departmental presentation, resource fair, or one club activity (in addition to the required meetings, like Habitat, Field trip, etc.) Class meetings and Friday Night Fever don’t count. 120 B. SAMPLE COURSE SYLLABUS AND POLICY CLASS POLICY 1. Assignments are due when speciﬁed, Late = 0. 2. Class attendance is MANDATORY. University Regulation 6-713 explains how authorized class excuses may be obtained. Missing more than three classes will lower grade by one letter. GRADING CRITERIA GRADING CRITERIA The course grade will consist of the following points: Class attendance and Participation (15 @ 5 pt ea.) )stp 01 @ 6( seitivitcA 75 2 ,.coS 2 ,rosivdA ,.seD .rS( 06 hcteks lacihpargoiB egnellahC ngiseD )PIT( yrarbiL eniltuO hcraeseR tropeR hcraeseR tnemssessA ecruoS hcraeseR oiloftrop hcraeseR laro hcraeseR noitatneserp laro hcraeseR outline stnioP elbissoP latoT Elect.) 01 06 01 5 04 02 01 5 52 023 Grades A B C D = = = = 90 80 70 60 - - - - 100% 89% 79% 60 - 69% e.g. >= 288 points ASSIGNMENT FORMAT FOR REPORTING ACTIVITIES 1. Send a report of each activity you participated in by email to both the PA and to the instructor. 121 The “Send To:” line should read “[email protected]; [email protected]” 2. The “Subject:” line must start with: ES1000-XX and then indicate the purpose of the email, i.e., “ES1000-11 - Advisor Interview” 3. The report must be sent within three days of the event (i.e., Friday event, send by Monday). No late reports accepted. Only the Senior Design report will be accepted after Oct 19. 4. The report must be at least one coherent paragraph, using correct spelling and grammar (one or two lines do not make a coherent paragraph). 5. Content should contain: What you attended, who, when and where the event was held, and what you found to be of interest. Not knowing the name of the speaker or organization is not acceptable. Examples of two society meeting reports which would also be typical of an elective report: I attended the American Society of Civil Engineers meeting on Wednesday, February 4. The speaker was James Johnson, a civil engineer from Laramie. The topic was the development of a neighborhood and the various aspects that go into land development. He provided a detailed presentation on the project, addressing such issues as the layout of the neighborhood, plumbing, landscaping, and various legislative aspects of civil engineering. On Wednesday, February 25th at 5:00 p.m. in engineering building room number 3044, I attended an ITE (Institute of Transportation Engineers) meeting.The speaker was Tammy Reed from Trihedral Corporation which is an environmental and engineering ﬁrm located here in Laramie. Ms. Reed talked about a street project for the City of Laramie that will include a new sewer system and reconstruction of the street with medians. The most interesting part about this meeting was that they provided food, which was obviously a tactic to trigger people to come. Senior Design and advisor reports should be appropriately longer. (cid:129) “Disability Statement: If you have a physical, learning, or psychological disability and require accommodations, please let the instructor know as soon as possible. You must register with, and provide documentation of your disability to University Disability Support Services (UDSS) in SEO, room 330 Knight Hall.” (University Statement) Appropriate protocols will be developed after that time. (cid:129) “Academic Honesty: The University of Wyoming is built upon a strong foundation of integrity, respect and trust. All members of the university community have a responsibility to be honest and the right to expect honesty from others. Any form of academic dishonesty is unacceptable to our community and will not be tolerated” [from the UW General Bulletin]. Teachers and 122 B. SAMPLE COURSE SYLLABUS AND POLICY students should report suspected violations of standards of academic honesty to the instructor, department head, or dean. Other University regulations can be found at: http://www.uwyo. edu/generalcounsel/info.asp?p=3051 (University Statement) (cid:129) Academic Dishonesty is any use of any work other than your own or of using the same work in two classes. Any infraction of this nature will be pursued to the full extent allowed by University Regulation 6-802 or its successors. This does not disallow working together in groups. It does disallow copying homework within a group which you did not do. Example: Three people cannot do one problem each and share answers. Three people can work together to solve the problems and report them separately. It would be a good idea to read this regulation now. (cid:129) Team projects should be worked on jointly. Members of the teams will be required to report on how the team and its members functioned together. RESEARCH PAPER Find an application associated with the Design Challenge. Assess the state-of-the-art of that appli- cation and why the Challenge is relevant. For example, in robotics examine conditions that include working in hazardous environments, under sea, space, toxic or radioactive sites. You may address this problem from any angle of engineering or computer science including application, design, fabrica- tion, or artiﬁcial intelligence. A P P E N D I X C 123 Information Literacy Paper INFORMATION LITERACY (L) RESEARCH AND ASSESSMENT PAPERS Embedded in ES 1000 Fall 2012 DEFINITION: Information Literacy is the ability to “recognize when information is needed and to locate, evaluate, and use effectively the needed information.” (American Library Association and University Studies Literacy Document) OBJECTIVE: The objectives of the information literacy component in ES 1000 are several: to learn how to pose a research question, conduct a search on literature that will assist you in answering your question, present a written evaluation of your sources’ validity or usefulness, and prepare a written report on your ﬁndings. RESEARCH QUESTION REQUIREMENTS: You will pass the library TIP (Tutorial) quiz with a 70 or better. You will select a research question from the list of questions provided in class. A research question asks for validation of an idea or why or how something works or behaves in a particular manner. The objective is a statement of what is to be examined or demonstrated. For example: a research question may ask, “What is the longest span that a bridge can be constructed?” Answering this requires an understanding of engineering principles, loads, and materials. An objective may be that you will limit your research to suspension bridges as these have been the longest types of construction recorded. You may further reﬁne your objective, such as, “I plan to examine the main cables in a suspension bridge as they are the critical load carrying elements.” A question such as “How long is the longest bridge?” is simple fact ﬁnding and not a valid research question. By the same token, a report on the construction of the Great Wall of China does not ask a probing question, but rather asks for historical information. The research question and objective must be submitted to the ES instructor as indicated on the syllabus by the end of Week 2. The Instructor will assist in assuring that the research question and/or objective is not too broad, too complex, or so esoteric that references may be difﬁcult to ﬁnd. Each student must prepare a research paper independently. 124 C. INFORMATION LITERACY PAPER Your research paper will be based on four and only four sources: one each from a professional journal, a popular literature source, a web-based source, and one additional from any of these sources. You must select three sources that best support your position and one source that refutes it. Everything in your paper must be referenced to these four sources. Pick them carefully. You will prepare a written paper that answers your research question. The paper will be at least three full pages long (not two and one half ) and contain: A statement of the approved research question and objective. A discussion of your ﬁndings. This is the body of the paper and answers your research question within the limits set by your objectives. Proper identiﬁcation and citation of sources and quotations used to support your discussion. Conclusions regarding the outcome of your research. A reference list cited in the same format as the primary technical journal used for your paper. This reference list must be in the paper and properly cited in the text of your work. Academic Integrity: It’s your responsibility to be familiar with UW’s policies concerning academic dishonesty, both its deﬁnitions and its negative consequences. Details can be found under UW Reg 6-802. For more information, go here: http://www.uwyo.edu/generalcounsel/_files/docs/uw-reg-6-802.pdf RESEARCH ASSESSMENT PAPER You will prepare a second report at least two full pages long that critically assesses the material you used to select references to prepare your research question report. This critique will contain: A summary table of the number of sources found, the number read and the number used for your paper (1 or 2). The table will have three categories, journal papers, popular press, and Internet sources. You must identify at least three references read in each category. Literature Search Summary Journal Articles Popular Literature Website 125 Number of Sources Found Number of Sources Read Number of Sources Used The references for the source material used. Note that the sources selected for the research paper must be repeated in this and the research paper. An abstract, in your own words, of each source article read for the research report (four). The abstract is approximately one paragraph and restates the most important features of the article for your use. A critical assessment of the content of each source you read, including a comparison of common features and critical differences. The assessment must include why the ﬁnal reference used in your paper is selected. PAPER FORMAT Your papers will be typed, double spaced with 1” margins all around. Type font will be 12 point, Times Roman. Your name and section number will appear on the top right of the ﬁrst page. The entire project will be submitted in a paper, two pockets, folder, about 9”x12”. Grading: Each paper will receive a grade and comments. The intent of grading on this exercise is to assess your understanding of the research process.The comments provide you with an indication of how the writing meets expectations in college level courses. An A paper contains all of the required elements, the proper references, correct citation format, a clear response to the question, conclusions, and ﬁndings, and a critical assessment of the resources. A C paper typically shows a lack of focus on the research question and has a rambling response to the question, lacks conclusions, and has inadequate or improper references. The assessment is equally lacking in focus and comparison among articles. An F Paper is indicative of a student who did not bother to read the instructions, has a poorly formed research question, has not answered the question, and provided no logical references to support the answer to the question. The assessment totally misses the objectives. RESEARCH PORTFOLIO—OPTIONAL BY SECTION A research portfolio contains copies of the materials used to develop your papers. Several faculty members require that a research portfolio be included with the papers. Check your section syllabus. The portfolio need not be organized in any speciﬁc manner but it should include: 126 C. INFORMATION LITERACY PAPER Copies of the four articles cited in your paper. (Copy no more than four pages. The ﬁrst page should have the title and author of the article. If the journal or book name is not on that sheet, copy a ﬁfth page with the cover of the journal or the copyright page of the book.) Notes developed during your research sessions. Speciﬁc notes and references to sections in your paper. DEFINITIONS AND HELP SOURCES Journals: A journal is a record of transactions maintained by a deliberative body. Contents of a journal are typically peer reviewed and are archived by libraries. That means the articles in the journal are reviewed by two or more people familiar with the subject matter and a judgment is made that the content conforms to established practice. Electronic versions of journals are still considered as journals even if they are found on the Internet. They have the same content and review as the paper version. If the term “Journal” is not in the title, use the library resources to verify it has a journal format. Popular Literature: Articles in this category are typically authored by a single person and reviewed by an editor for grammar, for libel issues, and for consistency with the editorial objectives. These include newspapers and magazines like Popular Science. For this exercise, books are considered popular literature. (In fact, many books undergo a considerable peer review process. The objective is to have you use the search engines available for research work and to examine the content of shorter articles, not to use book as references. If you use a book, you must abstract each chapter that you review.) Internet Articles: Internet articles may be authored by anyone for any purpose. There is no requirement that they be factual, although many are very good, an equal number are truly bad or wrong. Assessing Internet sources requires some basic understanding of the subject material and often requires an exercise to see if the information on the site can be veriﬁed by a second source. Methods of assessing web based sources are located at http://www.pbs.org/teacherline/courses/tech340/docs/tech340_bull.pdf Writing resources: The Writing Center in Coe Library offers assistance in developing written materials for this and all University courses. The services and hours for the semester are found at the Writing Center website http://www.uwyo.edu/ctl/writing-center/ A P P E N D I X D 127 Sample Oral Presentation Evaluation Sheets If you want to add your name we would appreciate knowing who participates. If you would like to receive an electronic copy of the student work then add your email address and check the box. You are asked to provide a grade of the students’ presentation. The page on the reverse of this sheet has an eval- uation form and lists the speakers in the order of their appearance. Check the box to indicate your participation in the review and ﬁll out the sheet us- ing the criteria below and place your grade sheet in the box by the exit. Thank you. Grading Evaluation area Organization Clarity Verbal Response COMMENTS: Each item is graded on a 1-4 scale with 1 being poor, 2 fair, 3 good, and 4 excellent Expectation for a grade of 4 The concepts and designs are presented in a logical sequence with each point building on previous work Concepts and designs are presented in terms that are clear, well deﬁned, free of jargon, and easily understood The presenter had good verbal skill including eye con- tact, voice projection, posture, and poise The presenter was able to respond to questions in a clear, concise manner. 128 D. SAMPLE ORAL PRESENTATION EVALUATION SHEETS MULTIDISCIPLINARY ALL COLLEGE DESIGN PROJECT – EVALUATION SHEET Fall 2009 Order of Presentation Organization Clarity Verbal Response INTRODUCTION Leah BEETLE BACKGROUND Matt r WOOD AVAILABLITY Allysa Jonathan ENERGY PLANT SITE CHALLENGES Kolter ENERGY PLANT OPTIONS and CO-FIRING Jordan OPTIONS EVALUATION Leah WOOD QUALITY ENERGY and ENVIRONMENTAL CONSIDERATIONS Jordan Matt OFFSITE WOOD STORAGE AND HANDLING Jon ENERGY PLANT WOOD TRANSFER Sam ENERGY PLANT SITE DEVELOPMENT Kolter SILO DESIGN Allysa Dan WOOD CHIP HANDLING Shane COST ANALYSIS AND QUESTIONS Leah Author’s Biography 129 CHARLES W. DOLAN Dr. Charles W. Dolan is the ﬁrst permanent H. T. Person Chair of Engineering at the University of Wyoming. He received his BS in Civil Engineering from the University of Massachusetts and his Masters and Doctorate in Civil Engineering from Cornell University. Dr. Dolan has over 20 years of design experience as a consulting engineer and an additional 25 years of teaching experience. His design projects include the original people mover guideway at the Dallas–Fort Worth airport, the Detroit downtown people mover guideway, the Walt Disney World monorail, and the conceptual design of the Vancouver British Columbia Skytrain and the monorail running down the spine of the Palm Island in Dubai. He has taught at Cornell University, the University of Delaware, and has been involved in teaching classes at Seattle University and the University of Washington prior to joining the faculty at the University of Wyoming. The H. T. Person Chair is the ﬁrst endowed chair at the University of Wyoming College of Engineering and Applied Science and focuses on undergraduate education. For over a decade Dr. Dolan has developed the engineering design challenges for the ﬁrst-year Introduction to Engineering course and for a number of years he taught interdisciplinary senior design projects. In addition to conducting interdisciplinary senior design projects, Dr. Dolan is actively engaged in capstone design courses for civil and architectural engineers with a focus on concrete and prestressed concrete structures. He teaches courses on Society and Technology for the University Honors Program. He chaired the UW Read, ﬁrst-year common reading committee, and served as Department Head and on Tenure and Promotion committees. Dr. Dolan is co-author of the book Design of Concrete Structures with David Darwin and Arthur H. Nilson and serves on the American Concrete Institute Committee 318 Building Code for Concrete Structures. He conducts research on the innovative use of prestressed and precast concrete structures and the use of ﬁber reinforced polymers for strengthening concrete structures. In his research capacity he has served on National Science Foundation committees and edited and contributed to several volumes of work on FRP applications and the durability of FRP strengthening systems and authored numerous technical papers.
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=9050689.pdf&bkn=9050688&pdfType=book	The Search for the Absolute How Magic Became Science Jeffrey H. Williams, Formerly at Bureau International des Poids et Mesures History and archaeology tell us that when our far ancestors began to settle in localized groups, they codified their lives and experiences, and formed a collective for mutual support. This proto-civilization would have arisen from each individual’s questions about the world, and their attempt to understand themselves and their place in the world. These groups, or tribes, evolved rules of conduct to facilitate communal living, and made a calendar for the group’s celebration of harvests, and other events upon which the group was utterly dependent. This process of social evolution is the origin of religion, and of a magical way of looking at Nature. Eventually, this developing worldview was also the origin of science, which is our investigation of Nature to understand something of what is happening around us, and to use this knowledge to ensure our survival in a violent, indifferent Universe. After all, science and religion seek to answer the same question: Why and how is the natural world the way it is? This book seeks to show how science evolved from religion and magic, in response to a need to understand Nature. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis Lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool. store.morganclaypool.com W I L L I A M S T H E S E A R C H F O R T H E A B S O L U T E M O R G A N & C L A Y P O O L The Search for the Absolute How Magic Became Science iii Synthesis Lectures on Engineering, Science, and Technology Each book in the series is written by a well known expert in the field. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very specific topics not covered elsewhere in the Synthesis Digital Library. The Search for the Absolute: How Magic Became Science Jeffrey H. Williams March 2020 The Big Picture: The Universe in Five S.T.E.P.S. John Beaver January 2020 Relativistic Classical Mechanics and Electrodynamics Martin Land, Lawrence P. Horwitz December 2019 Copyright © 2020 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quota- tions in printed reviews, without the prior permission of the publisher. The Search for the Absolute: How Magic Became Science Jeffrey H. Williams www.morganclaypool.com ISBN: 9781681737775 print ISBN: 9781681737782 ebook ISBN: 9781681737799 hardcover DOI 10.2200/S00985ED1V01Y202001EST005 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY Lecture #5 Series ISSN 2690-0300 Print 2690-0327 Electronic The Search for the Absolute How Magic Became Science Jeffrey H. Williams Formerly at Bureau International des Poids et Mesures SYNTHESIS LECTURES ON ENGINEERING, SCIENCE, AND TECHNOLOGY #5 M&C MORGAN & CLAYPOOL PUBLISHERS vi ABSTRACT History and archaeology tell us that when our far ancestors began to settle in localized groups, they codified their lives and experiences, and formed a collective for mutual support. This proto-civi- lization would have arisen from each individual’s questions about the world, and their attempt to understand themselves and their place in the world. These groups, or tribes, evolved rules of conduct to facilitate communal living, and made a calendar for the group’s celebration of harvests, and other events upon which the group was utterly dependent. This process of social evolution is the origin of religion, and of a magical way of looking at Nature. Eventually, this developing worldview was also the origin of science, which is our investiga- tion of Nature to understand something of what is happening around us, and to use this knowledge to ensure our survival in a violent, indifferent Universe. After all, science and religion seek to answer the same question: Why and how is the natural world the way it is? This book seeks to show how science evolved from religion and magic, in response to a need to understand Nature. KEYWORDS origin of science For Mansel Morris Davies (1913–1995); a man blessed with the gift of friendship. He not only instructed the author in physical chemistry, but also taught him how to look at the world. ix Contents Introduction: Authority and the Collective Memory . . . . . . . . . . . . . . . . . . . . . . . . 1 1 In the Beginning Was the List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 The List as the Origin of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Ramón Llull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Details of the Ars Combinatoria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 The Origins of the Language of Power that Is Science . . . . . . . . . . . . . . . . . . . . . . 19 2.1 A Less Mythic Interpretation of the Babble after Babel . . . . . . . . . . . . . . . . 21 2.2 A Mystical Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 The Mixing of Physics and Metaphysics to Create a Language of Curiosity . . . . . 29 3.1 The Birth Pangs of Modern Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Gottfried Leibniz and the Nature of the Universe . . . . . . . . . . . . . . . . . . . . 34 3.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 The Transformation of Magic and Mysticism into Science . . . . . . . . . . . . . . . . . . 37 4.1 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5 The I Ching as a Model of the Cosmos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1 Details of the I Ching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.2 Divination with the I Ching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.3 Final Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6 Natural Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.1 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 The Laws of Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.1 The Complex Relationship Between Astrology and Astronomy . . . . . . . . . . 64 7.2 The Search for the Divine Lawgiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7.3 A Very Different Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.4 That Fearful Perfection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 x 7.5 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 8 Measuring the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Defining the Size of the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Other Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.1 8.2 8.3 9 Dividing Apples with Oranges to Make the Language of Science. . . . . . . . . . . . . 87 Creating Expressions in the Language of Science . . . . . . . . . . . . . . . . . . . . . 91 9.1 Derived Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 9.2 Location: The Surface of Mars, September 23, 1999 . . . . . . . . . . . . . . . . . . . 97 9.3 A Final Comment on the Value of a Quantity: Sacred Geometries . . . . . . . 98 9.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 9.5 10 What Powers Society? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 10.1 Social Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 10.2 International Regulation of Terms and Names: Dialects are Inevitable . . . 107 10.3 Science as a New Tower of Babel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 10.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 11 The Ghost of the Divine Language: The Theory of Everything . . . . . . . . . . . . . . . 113 11.1 Some Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 11.2 String Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 11.3 Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 11.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 12 Changing the Paradigm: From Long Lists to Short Explanations . . . . . . . . . . . . 127 12.1 The Great Paradigm Shift in Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 12.2 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 12.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 13 The Classification of the Living and the Dead . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 13.1 A Hierarchical System of Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 13.2 A Warning to the Unwary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 13.3 The Limits of Linnaean Classification: Two Unclassifiable Species Found off Australia . . . . . . . . . . . . . . . . . . . . . 144 13.4 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 14 Aspects of Chemical Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 14.1 The Problem of Naming Things in Contemporary Science . . . . . . . . . . . . . . 149 xi 14.2 The Transfermium War . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 14.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 15 The Evolving Science of History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 15.1 Social Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 15.2 Some Details of the Analysis of Personal Data on Social Media . . . . . . . . . . 162 15.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 16 Obfuscation: Why Are We Not Living in a New Golden Age? . . . . . . . . . . . . . . . 167 16.1 The Science Wars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 16.2 Anti-Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 16.3 The Limitations of the Enlightenment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Author Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 The world is like the impression left by the telling of a story (Yoga-Vāsis t ha 2.3.11) ̣ ̣ 1 Introduction: Authority and the Collective Memory History and archaeology tell us that when humans first began to congregate and settle, they codi- fied their lives and experiences, and formed a collective for mutual support. This proto-civilization arose inevitably from each individual’s questions about the world, and their attempt to understand themselves, each other, and their place in the world. These groups, or tribes, evolved rules of conduct to facilitate communal living, and they made a calendar for the celebration of important events— events such as planting the crops and when to go hunting and fishing upon which the group was utterly dependent for its survival. These early tribal societies also preserved their songs, their experiences or history, and their stories, fables, wisdom, and beliefs in the memories of the tribe’s Shaman or Bard. These collective memories led to myths and legends, which were extravagant and hence memorable, short-hand records of matters such as: invasions, migrations, conquests, dynastic changes, admission and adoption of foreign religious cults, and of social reforms. This inevitable process of social evolution is also the origin of religion, and of a magical way of looking at Nature; both of which are still with us today. Eventually, this evolutionary process was also the origin of science, which is essentially our investigation of Nature to understand something of what is happening around us, and to use this knowledge to ensure our survival, and the survival of our tribe or extended family in a violent, indifferent Universe. After all, science and religion seek to answer the same two questions: (1) Why and how is the natural world the way it is? (2) How best can we assure our survival? In addition, myths and science fulfill a similar function: they both provide man with a representation of the world, and of the forces that are supposed to govern it. Both myths and magic, together with science, fix the limits of what is possible. At first, the members of the tribe were easily cowed and controlled by the superstitious fear associated with mythology; such control cannot be generated in a group without myths and marvels. Thus magic, or proto-science, was at the heart of the social organization of early societies. But the essential part of this tribal codification of experiences was the recording of the information necessary for survival; that is, the tribal wisdom. For example, the recording for future generations of the hard-won collective experience that to sustain the life of the tribe, crops are best planted at a certain moment of the Solar Cycle, and harvested a certain number of Lunar Cycles later; that fish are best looked for at a high tide (again the relationship with the Moon), and that large animals are best hunted in early morning when they are rutting at certain times in the Solar Cycle. But how 2 does a non-literate society define those dates, and how did they determine when a particular date was approaching? The readily observed phases of the Moon formed man’s first chronometer, and by hard expe- rience the tribe would have learned the most appropriate time, relative to the phases of the Moon and the Solar Cycle to go hunting and gathering. Later, a combination of a Lunar Calendar and a Solar Calendar told agricultural man when was best for planting and harvesting. Our ancient ances- tors (who were probably no less insightful than we are today) would also have noted the similar and hence, perhaps, related time scales of Lunar Cycles and female fertility; hence, they evolved a Moon goddess, rather than a Moon god to represent this fertility and to whom supplications could be addressed, although the desired “responses” would only be forthcoming on a statistical basis, but this was evidently good enough. This tribal knowledge was so important that it needed to be preserved for the survival of future generations. Thus, a calendar based upon an understanding of astronomy and biology was one of the essentials for the survival of the earliest human communities, and, indeed, this remains the case for that shrinking part of humanity that does not live in towns and cities. This tribal wisdom or language of survival, which originally would have been passed down by the tribe’s Shaman or Bard, would have been articulated in the spoken language of the tribe. Other tribes would have learned the same essential things, but would have spoken about those same things in a different vernacular. Thus, as various spoken languages developed, they were incorporating, and permitting, the transmission of the same essential knowledge; that is, how to survive and prosper. This was the beginning of science, which was of necessity supra-tribal, and later became supra-na- tional. Consequently, common to all languages and cultures is a set of observations and facts; what today we call, in its most general form, science, but was in fact astronomy and biology. But back in the distant past, our ancestors would have considered all this magic, or perhaps religion. The question we shall investigate in this volume is: How did the modern form of the language of science arise from earlier tribal wisdom? Put another way: How did man develop a worldview which allows him to classify and understand all the phenomena and things observed in Nature? The modern, technical language of science is actually very simple as a language, but it has grown very far from the vernacular languages of literature. Yet, the clearly defined language of sci- ence, which is taught to students from a young age (although few realize that they are being taught a language different for the vernacular they use with each other) is the nearest thing that we have to a universal or perfect language; that is, a language that can be understood by all men cutting across the confusion and redundancy of vernacular languages. In these pages, we will see how it was that in attempting to construct a complete set of the observations needed by prehistoric man for his survival, and the survival and stability of his tribe or extended family, we were inevitably led to the development of a system of classification that best facilitated the transmission of this information. The earliest proto-scientists, or natural philosophers, or Shamans, or magicians realized that instead of learning long lists of natural phenomena, and INTRODUCTIONINTRODUCTION: A CALCULUS OF THOUGHT 3 of biological information and astronomical observations that would assist their society to survive the potentially fatal vagaries of Nature (e.g., climate change) it was more logical, and a lot simpler, to arrange the essential facts into different classes (which have today evolved to become different sciences) and then attempt to find a principle of coherence behind all these observed facts. Such a systematization would render the long lists irrelevant, thereby saving everyone’s limited and imper- fect memories. It also permitted the more insightful natural philosophers, or proto-scientists (and some of these early scientists also practiced magic) to begin making predictions about the working of Nature, thereby creating modern science and technology. But then, science like magic and religion was always interested in everything. It was the epistemological earthquake that was the French Rev- olution that gave us separate, non-communicating, independent disciplines and schools of thought. A CALCULUS OF THOUGHT First, we will explore how and why we record essential information. I am sure that I am not alone in that, when confronted by the complexity of daily life. I find it a great relief to make a list. The prepa- ration of the list allows me to put my thoughts in order by putting them down on paper. I am taking control of some aspects of my life, and instilling order into part of the chaos that surrounds me. This fetish with list-making probably stems from my student days, when my lists of things I had to learn were very long, but by the time I graduated they were considerably shorter and more concise. And in so doing, as we will see. I had not only earned a degree in natural science but I had also trained my memory in the manner of the Catalan mystic, the Blessed Ramón Llull (c.1232–c.1315) and his later follower, the Catholic heretic and savant Giordano Bruno (1548–1600)—two key figures in the early part of the search for the universal language of science (see Figure I.1). Figure I:1. Tree of Science (Arbor Scientiae) is one of the most extensive manuscripts of the 13th Century Ramón Llull, written in Rome between 1295 and 1296. It is a version of the author’s Ars magna written for a general readership (see Chapter 1). It is one of the first attempts in Europe to describe the holistic nature of science, that is, the oneness of Nature, and to try and commu- nicate this idea to a wide readership. As we can see, the work uses a familiar analogy: the organic comparison, in which science is represented by a tree with roots, trunk, branches, leaves, and fruits. The roots represent the basic principles of science; the trunk is the structure; the branches, the genres; the leaves, the species; and the fruits are the details. This vegetal allegory shows the influence of Aristotle. This image will serve as a metaphor for this work, and is taken from https://en.wikipedia.org/wiki/Tree_of_Sci- ence_(Ramon_Llull). 4 However, list making as a means of trying to order the overwhelming quantity of informa- tion we all come upon in our lives is not a new concept. At the dawn of literature, Homer presents us with the two possible ways in which information, or data, may be presented and stored for future reference. That is, either as a simple long list, or as a closed-system which contains all knowledge in microcosm and which shows us, the observers, how all things are interconnected in miniature—into which one must know how and where to look to find what it is one is seeking to understand, or to know. A list brings order, and through its use we can (at least) try to understand, influence, and per- haps control the world around us. We are able to exclude things; creating a list is a means of making choices. One might imagine that a list seeking to represent a complex set of information such as an entire discipline of science would produce a near infinity of possibilities and so be useless, but lists actually bring their own rules and orthodoxy. We will look at how it was that we moved from merely making and trying to memorize long lists of observations to a rationalization of such lists in terms of an underlying principle: the move from the qualitative to the quantitative. The I Ching of Ancient China is a good example of this evolutionary move from a magical worldview toward a truly empirical, science worldview. The earliest examples of a scientific or philosophical language, those from before the 17th century, were not quantitative. The language used by the proto-scientists when they communicated among themselves was purely qualitative. The early experimenters, or alchemists, were not overly keen to discuss in too much detail what it was they were doing and why they were doing it. Con- sequently, early manuscripts read more like a mystery story or a philosophical explanation than a description of an experiment and the resulting observation of the consequences of the experiment. But then, these proto-scientists were living a dangerous life; the Church would have condemned them and burned them if their actions were clearly described. There was safety in obfuscation and cloudy philosophical concepts. However, the baleful influence of the Church, and its own inability to effect any change in Nature (miracles) did eventually decrease in importance in society; the purely statistical success rates of prayer were finally deemed not to be good enough and eventually a quantitative language of science would be invented. Such a quantitative scientific language was naturally capable of extension, leading to explanation and prediction, able to support international communication and commerce. It was a new lingua franca, but a language devoid of metaphor and multiple, confusing meanings. This was, of course, not a new idea. The idea that there once existed a perfect language, which was spoken by all mankind, has occupied the minds of savants, mystics, Neo-Platonists, natural philosophers, and theologians for well over two millennia. This language was perfect in that it expressed without ambiguity the essence of all things and ideas—the quiddity of all things. It was a language in which there was only one possible way of describing, e.g., an animal, a natural phenomenon, or an explanation of why something happened. It was also accepted that if this perfect “language of Eden” could be recovered, men would again be able to comprehend INTRODUCTIONINTRODUCTION: A CALCULUS OF THOUGHT 5 each other fully and comprehend the functioning of Nature and thus the meaning of existence. Men would be able to abolish discord and strife, and return to a Golden Age. Even today, there are still physicists seeking to discover the perfect universal language in the form of the Theory of Everything (Chapter 11), although the majority of the physicists and math- ematicians researching this project do not appreciate the immensely old tradition within which they are laboring. The discovery of the Higgs’ boson, and of gravitational waves, are only the latest steps in man’s quest for the absolute, for the essence of the natural world, and for a single, unambiguous Theory of Everything. The development of modern science may, in large part, be considered as stages in this investigation; an attempt to understand the “make of all things.” Certainly, the cre- ation of the system of quantities and units, which today we call the International System of Units (SI from its French official name, Système International d’Unités), during the French Revolution was pivotal in allowing man to finally abandon magic and mysticism, and the memorizing of long, tedious, incomplete lists of properties and observations in his investigation of Nature, and to adopt a coherent, scientific worldview. CHAPTER 1 7 In the Beginning Was the List There must be a beginning in any great matter but the continuing unto the end, until it be thoroughly finished yields the true glory. Sir Francis Drake (c.1540–1596) Some may be surprised to read that there is a link between magic and modern science; that mod- ern science evolved out of magic. Indeed, one could go further and state that modern physics and chemistry would not exist had it not been for the ideas and “experiments” of the Neo-Platonists of the early-Christian world. The problem is that there is a spiritual aspect to Neo-Platonism; there is more metaphysics than physics in Neo-Platonism, and so many contemporary physical scientists would be aghast at a suggestion of the metaphysical origins of their subject. But you do not have to go too far into the quantum mechanical explanation of spin-entangle- ment and the mixing of quantum states, that is, the generation of qubits of quantum information, before you realize that what you are dealing with is more philosophical than physical. Today’s laser physicists attempting to teleport quantum information1 from a laboratory on one continent to a laboratory on another continent are having to revaluate what is actually meant by a “measurement,” to fully comprehend their results. These modern physicists are undergoing the same self-analysis that the Taoists recommended to all natural philosophers, and which the alchemists sought in their explorations of Nature (see Figure 1.1), although few contemporary physicists have ever thought about their sophisticated experiments in this way. History tells us that before there was science, and its most useful offshoot, technology, there was magic, and a magical way of looking at the world. In the evolution of a culture, the scientific worldview is always a late development. In the evolution of our culture, the 17th century supposedly marked the period when astrology, the burning of witches, and folk-magic yielded to Isaac New- ton’s rationalism, and the Laws of Nature were established as observation and experience explained 1 A pure qubit state is a coherent superposition of the states’ wave functions. This means that a single qubit can be , where α and β are proba- described by a linear combination of the wave functions \|0 bility amplitudes. When we measure this qubit in the standard basis, according to the Born rule, the probability of outcome \|0 . Because the absolute squares of the amplitudes equate to probabilities, it follows that α and β must be constrained by the equation + \|β\|2 = 1. Note that a qubit in this superposition state does not have a value between 0 and 1; rather, when 2 \|α\| 2 measured, the qubit has a probability \|α\| of the value 1. In other words, superposition means that there is no way, even in principle, to tell which of the two possible states forming the superposition state actually pertains. [1] 2 of the value 0 and a probability \|β\| ⟩ ⟩ with value 1 is \|β\| and the probability of outcome \|1 with value 0 is \|α\| and \|1: \|ψ = α\|0 + β\|1 2 2 ⟩ ⟩ ⟩ ⟩ 8 by reason. Yet before there was reproducible and reliable science, there was unreliable or “chancy” science. Even in the Renaissance, scientific work (what would then have been termed an “explo- ration of natural philosophy”) was a hit-and-miss affair, as few savants noted down the details of what it was they had done in their experiments. And as quantities of substances were not measured consistently, or measured at all (quantities of chemicals and materials could not even be defined precisely, as units of measurement were entirely parochial), and the materials used were of varying degrees of purity, experimental science was the affair of each individual practitioner. Consequently, at this time both science and magic were acceptable and interchangeable ways of interpreting Na- ture, as neither one nor the other was infallible or even reproducible; both appeared to work only on a statistical basis. And so the experimentalists would have believed they that had not been, for example, in the “right frame of mind,” or the stars were in the wrong alignment on the day their experiment did not yield the result it was supposed to yield. Indeed, the scientist or savant of that time dabbled in both natural philosophy and the occult. Isaac Newton (1643–1727) was himself something of a magus or, at least, a Neo-Platonist. At the tercentenary of Newton’s birth, John Maynard Keynes (Newton, The Man, lecture given as part of the Royal Society tercentenary celebration of the birth of Newton) described him as the last of the magicians, “Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.” Isaac Newton was a man with an immense, insatiable curiosity, for whom nothing could, or should, be taken at face value; he was above all a man interested in exploring everything, and spent much of his time in his laboratory doing experiments. Newton examined everything, including several stomach-turning experiments on his own eyes. Today we may consider ourselves as rational, coldly logical, non-superstitious, scientific beings with several degrees of separation from those who believe in magic and superstition. In the time of Newton, however, there were fewer degrees of separation between such individuals—if any at all. But by the end of Newton’s life, the European Enlightenment was underway and the triumph of science over hermeticism and religion was more or less assumed. But as it turned out, there was a huge revival of occultism and the hermetic arts in the late-19th century (Chapter 16). Before beginning our examination of the origins of science, let us consider the purpose of science, and the object of scientific investigation, that is, the understanding of Nature. Perhaps the most famous example of a magician in literature is Faust. In the earliest sections of Johann Wolf- gang von Goethe’s great poem (begun c.1772), the magician and his tempter correspond broadly to traditional mediaeval figure (the disillusioned old man manipulated by the Devil) and the plot gives a somewhat traditional, Christian version of the concepts of salvation and perdition. However, by the time that Goethe finished his poem (1831), Faust had evolved. He is no longer a magician excited and led astray by his desire for forbidden knowledge; Faust has been transformed into the 1. IN THE BEGINNING WAS THE LIST1. IN THE BEGINNING WAS THE LIST 9 Romantic figure of Everyman. Faust has become a seeker for oneness with all Nature. Between 1770 and 1830, our civilization had moved from the Classical world to the Romantic world, and today, we are all still lost in the late-Romantic world. The later, holistic Faust has abandoned a Manichaean dualism of good and evil, for a mystical sense of the unity of all things. This Romantic Faust would likely have been an early recruit to the politics of environmentalism. Faust no longer embodied heterodox magic, but acceded to a knowledge of the interconnectedness of all natural phenomena (which is the way modern science views Nature, see Chapter 9). In this way the char- acter of Faust follows the evolution of magical and scientific thinking; first there was magic, and then there was physics; first there was the sorcerer, and then there was the physicist. Figure 1.1: The Alchemist, a painting by Joseph Wright of Derby (1734–1797). An image of a man searching, both experimentally and mystically, to understand himself and his place in Nature. Image from: https://en.wikipedia.org/wiki/Joseph_Wright_of_Derby#/media/File:Joseph_Wright_of_Derby_ The_Alchemist.jpg. The magic that predates, and inevitably leads to, science is a force which follows processes and events that are inherent to consciousness, and is something implicitly connected to constructive and imaginative thought, therefore to the whole enterprise of artistic and scientific creation. Our imaginations, our dreams, our ability to use our consciousness to imagine and to describe, and then 10 to transfer theories and fantasies, are inherently bound up with our facilities for reasoning. And they are essential for making that great leap from observing and explaining a known phenomenon, to going beyond into the realms of prediction. The fabulous and the fantastic are all around us. Often, the more we examine a phenomenon that was once deemed to have been fully comprehended, the more we may learn, which allows us to speculate and then, perhaps, realize that the fantastic is not entirely separate from the natural. In the world before the 18th-century Enlightenment, magic and fantasy were inextricably linked with man’s attempt at understanding the forces of Nature, but nonetheless this pre-scientific worldview led to considerable advances in technology, and to many useful discoveries in engineer- ing, metallurgy, chemistry, and pharmaceuticals. When thinking about the world in a magical sense, one considers the phenomena of Nature to have arisen through the agency of certain secret forces of Nature; forces which may reside uniquely in certain objects (for example, the loadstone of the flying island of Laputa in Jonathan Swift’s Gulliver’s Travels of 1726, which would have relied upon repul- sive magnetic fields (see Figure 12.1), which were not fully explained until the late 19th century; see Chapter 12) or with certain inspired individuals, for example, Giordano Bruno, Leonardo Da Vinci, or Philippus Aureolus Theophrastus Bombastus von Hohenheim (Parcelsus). Such magical thinking structures the processes of imagination; and imagining something can, and sometimes does, precede the fact, or the act of discovery. This apparent breakdown in causality is something that we would today term intuition or instinct, and is something that a great many people experi- ence without thinking about it. Indeed, you do not have to investigate modern quantum mechanics and the quantum-view of nature very deeply before concepts such as causality and non-causality, of cause and effect, become much more confused than one would have ever supposed. Such concepts become, essentially, metaphysical. [2] 1.1 THE LIST AS THE ORIGIN OF SCIENCE But let us return to the very dawn of science. How was it that the earliest observers of Nature noted what it was they had observed? Not having a theory to explain their observations, it was likely that they merely made a list of what they had seen. Thus, the earliest stage of the evolution of science was the creation of long lists of things and events. Indeed, these long lists of observations and results would likely have been compiled of symbols (as there was no standard nomenclature of chemicals or phenomena), numbers, and words in a vernacular (see Figure 1.2). Of course, the natural philosopher may also have written his notes in a cypher; for example, the Angel Language of the Elizabethan alchemist John Dee. List making is a means of attempting to control and understand the complexity of life and of the world around us, and of trying to order the seemingly incomprehensible quantities of infor- mation we all come upon in our lives—not a new concept. It is simply a way of recording infor- 1. IN THE BEGINNING WAS THE LIST1.1 THE LIST AS THE ORIGIN OF SCIENCE 11 mation or data. But it is not the only way. At the dawn of literature, Homer presents us with the two possible ways in which information, or data, could be presented and stored for future reference. Either as a simple but long list, or as a closed system which contains all knowledge in microcosm and shows us, the observers, how all things are interconnected, but into which one must know how and where to look to find what it is one is seeking to know, or to remember; what today we would term a database. Figure 1.2: A table of alchemical symbols from Basil Valentine’s Last Will and Testament of 1670. (Image from: https://en.wikipedia.org/wiki/Alchemical_symbol#/media/File:Alchemytable.jpg). Basil Valentine, or Basilius Valentinus, was supposedly a 15th-century alchemist and Canon of the Benedic- tine Priory of Saint Peter, Erfurt, Germany. But this name could also have been an alias for a number of German chemists/alchemists. During the 18th century, it was suggested that the author of the works attributed to Basil Valentine was Johann Thölde, a salt manufacturer in Germany (1565–1624). Whoever he was, Basil Valentine had considerable ability and ingenuity as an experimental chemist. He showed that ammonia gas could be obtained by the action of alkali on sal-ammoniac (ammonium chloride), described the production of hydrochloric acid by acidifying brine (sodium chloride), and created oil of vitriol (concentrated sulfuric acid). Thus did modern chemistry grow out of alchemy; particularly, when the spiritual aspect of the alchemist’s craft lost its precedence. 12 In Book 2 of Homer’s Iliad, we encounter what is called The Catalogue of Ships. This catalogue is a long list of the various Greek forces who came together to attack Troy, and Homer uses it as a means of structuring information which the reader will need later in the story. However, in Book 18 of the Iliad, Homer presents us with a very different manner of presenting and storing infor- mation; he gives us a description of the shield the lame-god Hephaestus has made for swift-footed Achilles after the death of Patroclus. This shield was a microcosm within which all of Nature was to be found; the Sun, the Moon, the 12 Houses of the Zodiac, and the images of the world of men through the changing seasons of their year, all bound by the mighty river of Ocean running around the rim of the shield. This shield allowed the viewer, provided he knew where and how to look, to find whatever piece of information about the lives of men, or of astronomy and agriculture, he needed, or all the possible ways that these pieces of information could be coupled together. This shield was undoubtedly intended to promote the semi-divine nature of Achilles, and to protect him in battle. But even Hephaestus could not protect lion-hearted Achilles from his fate, not even with a database of all human knowledge on his arm. A list brings order, and through it we can understand and try to control the world around us. We are able to exclude things; creating a list is a means of making choices. One might imagine that a list seeking to represent a complex set of information such as the ephemerides of the Sun and Moon, or all the possible ways of reacting a number of the basic chemicals used in alchemy, would produce a near infinity of possibilities and so be useless, but lists actually bring rules and orthodoxy. Homer did not list all the petty kings of Bronze Age Greece, he only listed those relevant to the story he was about to relate of the Trojan War. The author had thought about these petty rulers and then placed them in the wider society and culture of the Ancient World. In a similar way, Homer had thought about Achilles’ shield, and designed it to represent the world in miniature. In other words, Homer had thought about the essential elements of Nature and how they interact, and was presenting this summary of the essential points to future generations as a database. Another example of this design, by an author of a detailed model of the world, which was then put on paper for future users is that greatest of all poems, the Divine Comedy by Dante Alighieri (1265–1321). In the 14,233 lines of this masterpiece, Dante gives us a complete repre- sentation of the medieval worldview; a concise summary of the Aristotelian-Thomist cosmogony of the late 13th century. The poem is a portable, readable summary of everything that a Christian needed to know to achieve salvation, and to understand the natural world in which he finds himself. But a list can also be a frightening thing. Our imperfect memories will always tell us that we have forgotten something, and that this something is hugely important. And the more we try desperately to remember that important something, the more it slips from our mental grasp. Lists can be troubling, even subversive. Our lives are limited; death is a particularly discouraging limit. This is why we all like subjects of investigation that have no limit, and therefore no end, for ex- ample, history, science, and philosophy. Long lists are a way of escaping from our thought about 1. IN THE BEGINNING WAS THE LIST1.2 RAMÓN LLULL 13 death. Even if a list makes us anxious about things we cannot remember we like it because we do not want to die. [3] Making lists, or pictorial or text-based summaries of a field of knowledge, may impose order, but what is really required to effectively use the contents of any long list is a means of manipulat- ing all the possible entries in the lists of all the various categories of all objects and all ideas. This could rapidly become a vast quantity of data. And what of the nature of science? Anyone who has ever attempted to study science knows that there is an awful lot of memory work to be done. Al- though all science students are told that the vast edifice of science rests on a few basic axioms and theories, it is unfortunately true that before one can get to study these foundation stones of science you have to spend years memorizing seemingly incomprehensible amounts of information, data, rules, and exceptions to the rules. Of course, the professors will tell the aspiring scientist that he or she must first be grounded in the factual matter of the subject before they can make an attempt at comprehending, and perhaps applying or even extending, the basic axioms. But then professors and teachers have always said that—in every discipline. What, of course, should be done is to explain and teach the axioms to the brightest of the eager students. Then the mountains of facts and gen- eralities could be derived by the students themselves. But, alas, that is not the way the teaching of science, or of any other subject, has evolved. This is the heart of the problem to be examined in this book; how do we construct a simple language of few words and few rules, and use this language to describe all the phenomena seen in Nature? How do we take endless lists of observations and facts and reduce, purify, and concentrate them, as the alchemists would have said, to a handful of base units that can be combined in various ways to describe everything we see around us, and everything we will ever see? 1.2 RAMÓN LLULL Perhaps the first person to attempt a method of systematizing and classifying information for the purpose of facilitating the compilation and generation of derived information systems was the Catalan mystic, the Blessed Ramón Llull, or Raymond Lull (c.1232–c.1315). He designed a teaching aid that was also a means of deriving or generating information from lists, which he called his Ars generalis ultima, or Ars magna (The Ultimate General Art, or Great Art), which appeared in 1305. This was an attempt to combine, or manipulate, the contents of long lists, in particular, to generate the theological and philosophical attributes of the Divine, selected from a number of lists of those attributes. Ramón Llull intended this technique of combining and manipulating lists of theological and philosophical information to be a debating tool for converting Muslims and Jews to Christianity using logic and reason. Through his detailed analytical efforts, Llull built a theological reference by which a reader, or proselytiser, could enter into a mediaeval calculating machine (it was called Llull’s 14 “thinking machine”) an argument or question which had been put to them about the Christian faith. The reader would then turn to the appropriate index and page in the Llullian calculator to find the correct answer to the question posed by the potential convert. The radical innovation of Llull was the introduction of logic into list making. In particu- lar, the construction and use of a “thinking machine” made of inscribed metal discs to combine elements of thought; for example, elements of language. With the help of connected geometrical figures, following a precisely defined framework of rules, Llull tried to produce all the possible statements of which the human mind could conceive on certain subjects. These declarations or statements were represented by a series of signs, or sequences, of letters derived from his pro- to-computer, or “thinking machine.” We will now briefly consider the hardware and software (see Table 1.1) of Llull’s “thinking machine.” Table 1.1: The alphabet of Llull’s thinking machine. This is the software of the device built by Ramón Llull to explore the logic of list making. It contains the theological and philosophical attributes of the Divine. The letters in the first column of the table (contain the “computer programme” of Llull’s device) correspond to the outer circle of the hardware, that is, to the engraved metal discs shown in Figures 1.3 and 1.4 Questions and Rules Figure T (given in Figure 1.5) Difference Whether? Figure A (given in Figure 1.4) B Goodness C Greatness Concordance What? D Eternity Power E F Wisdom G Contrariety Beginning Middle Will End H I K Virtue Truth Majority Equality Glory Minority Of what? Why? How much? Of what kind? When? Where? How and with what? Subjects Virtues Vices God Angel Heaven Man Imaginative Justice Prudence Fortitude Temperance Faith Avarice Gluttony Lust Pride Accidie (apathy) Sensitive Hope Vegetative Elementative Charity Patience Envy Ire Lying Instumentative Pity Inconstancy The software of Llull’s device, given in Table 1.1, is essentially an alphabetic list giving the meaning of nine letters, in which Llull (the programmer) says “B signifies goodness, difference, whether?, God, justice, and avarice. C signifies...,” and so on (there is no J in the mediaeval Latin alphabet). The components of the first column of Table 1.1 are set out in Llull’s Figure A (that is, Figure 1.3 here). The letters don’t represent variables, but constants. Here they’re connected by lines to show that in the Divine these attributes are mutually convertible. That is to say that God’s 1. IN THE BEGINNING WAS THE LIST1.2 RAMÓN LLULL 15 goodness is great, God’s greatness is good, etc. This, in turn, was one of Llull’s definitions of God, because in the created world people’s goodness is not always great, nor their greatness particularly good, etc. Such a system of vertices connected by lines is what mathematicians term a graph. This might seem to be of purely anecdotal interest, but as we shall see shortly, the relational nature of Llull’s system is fundamental to the idea of an Ars combinatoria. The components of the second column in Table 1.1 are set out in Llull’s Figure T (that is Figure 1.4 here). Here we have a series of geometrical principles related among themselves in three groups of three, hence the triangular links. The first triangle defines: difference, concordance, and contrariety; the second defines beginning, middle, and end; and the third triangle defines majority, equality, and minority. The concentric circles between the triangles and the outer letters show the areas in which these relations can be applied. For example, with the concept of difference, notice how it can be applied to sensual and sensual, sensual and intellectual, etc. “Sensual” here means perceivable by the senses, and Llull explains in the Ars brevis that: “There is a difference between sen- sual and sensual, as for instance between a stone and a tree. There is also a difference between the sensual and the intellectual, as for instance between body and soul. And there is furthermore a difference between intellectual and intellectual, as between soul and God.” This hardware consists of three inscribed metal disks fixed on a single axis on which they can be rotated independently. The disks contain a limited number of letters—a special lullistic alphabet. When the circles are turned, step-by-step, all possible combinations of these letters are produced. The metal-circle called the Prima Figura (Figure 1.3) gives the primary attributes. The next strictly defined table of words can be produced on the next circle, Secunda Figura (Figure 1.4), where we find categories and relations of thinking. Figure 1.3: A list of the attributes of God (see second column in Table 1.1). This is Llull’s Figure A or Prima Figura. Image from: http://www.ramonllull.net/sw_principal/l_br/home.php. Figure 1.4: A list of the categories and relations of thought (see third column in Table 1.1). This is Llull’s Figure T or Secunda Figura. Image from: http://www.ramonllull.net/sw_principal/l_br/ home.php. 16 Ramón Llull’s thinking machine allows all the words (attributes of the Divine) in the outer circle to be combined in different ways by turning the circles, relative to each other in a stepwise manner. It is therefore possible to connect every word with every other word placed in a position of a table—depending only on the construction of the individual tables. Ramón Llull created numer- ous devices for this manipulation, or combining of the contents of lists. One method is now called the Llullian Circle, which consisted of two or more solid circular discs, a disc of smaller diameter free to rotate inside a larger annular disc; both these independently rotating discs were inscribed with alphabetical letters or symbols that referred to, for example, components of lists of attributes of the Divine. A number of terms or symbols relating to those terms were laid around the circum- ference of the circle. The discs could be rotated individually, like a circular slide rule to generate an enormous number of combinations of ideas. Thus, the innermost disc could be inscribed with what Llull termed the “absolute characteristics” of God: goodness, eternity, power, volition, virtue, truth, glory, or wisdom, and it could be rotated to be next to attributes on the next outer disc, which was inscribed with “relative characteristics” such as greatness or extent or purpose. Llull conceived this combinatorial manner of generating ideas as a perfect logical language, which could be used to convert non-Christians to Christianity. The language was to be universal; it was to be articulated at the level of expression in rational mathematics, and its content was intended to consist of a network of universal ideas held by all people. Llull based this device on the notion that there were only a limited number of basic, undeniable truths in any field of knowledge, and that we could under- stand everything about these fields of knowledge by studying combinations of these elemental or fundamental truths. 1.3 DETAILS OF THE ARS COMBINATORIA Given a number of different elements n, the totality of the possible arrangements that can be made from them, in any order is expressed by their factorial n!, calculated as 1.2.3. .... n. This is the method for calculating the possible anagrams of a word of n letters (as in the art of Temurah in the Kabbalah). As n increases, the number of possible arrangements rises more rapidly: the possible arrangements for 26 letters of the alphabet would be a vast, incomprehensible number of combina- tions. If the strings of combinations admit repetitions, then the number of combinations rises even further. Consider the situation of four people. We want to arrange these four as couples on a train, where the seats are in rows that are two across; the order is relevant because we wish to know who will sit at the window. This is a problem of permutations; that is, of arranging n elements, taken t at a time, taking the order into account. The formula for finding all the possible permutations is n!/(n-t)! Suppose, however, that the order is irrelevant. This is a problem of combinations, and we solve it with: n!/t!(n-t)! 1. IN THE BEGINNING WAS THE LIST1.3 DETAILS OF THE ARS COMBINATORIA 17 This is an expression-system (represented both by the symbols and by the syntactic rules establishing how n elements can be arranged t at a time—and where t may coincide with n), so that the arrangement of the expression items can automatically reveal possible content-systems. In order to let this logic of combination or permutation work to its fullest extent, however, there should be no restrictions limiting the number of possible content-systems (or worlds) we can conceive of. As soon as we maintain that certain universes are not possible in respect of what is given in our own past experience, or that they do not correspond to what we hold to be the laws of reason, we are, at this point, invoking external criteria not only to discriminate the results of the ars combinatoria, but also to introduce restrictions within the art itself. This combinatorial method of Llull was an early attempt at using logic to retrieve knowl- edge, data, or information from a list; that is, to use mechanical means to generate concepts, which avoided the tedious necessity of memorizing vast numbers of combinations of ideas and thoughts. Of course, most of the combinations of ideas so generated would be redundant (in the definition of the Divine, what exactly is the difference between “glorious eternity” or “eternal glory”). Llull hoped to show that Christian doctrines and dogma could be arrived at from any starting point, from a fixed set of preliminary, arbitrary ideas. Llull knew that all believers in the monotheistic religions would agree with the absolute attributes of God, giving him a firm platform from which to argue that the Christian interpretation of the Divine was the most apposite interpretation, and so his lis- teners would be convinced of his logical vision and convert to Christianity. Whether or not Llull’s system of logical persuasion worked for its intended purpose we do not know; history tells us he was nearly killed at the age of 83 attempting to convert Muslims in North Africa. One can ask, what exactly is Ramón Llull’s place in the history of computers and computing? Llull is one of the first people who tried to make logical deductions in a mechanical, rather than a mental way; that is, based on the contents of his imperfect memory. His method was an early attempt to use logical means to generate and retrieve information. He demonstrated in an elemen- tary, but nevertheless workable way that human thought can be described and even imitated by a mechanical device. This was a small step toward the thinking machine of the contemporary world. The ideas of Ramón Llull about the systematisation or ordering, and the generation and retrieval of information and knowledge were developed further in a more esoteric manner by Giordano Bruno in the 16th century (but unfortunately for Bruno this was one of his undertakings that led him to be burned as a heretic by the Catholic Church in Rome, February 17, 1600), and subsequently by the great German savant Gottfried Leibniz (1646–1716) in the late 17th century for investigations into the philosophy of science. Leibniz gave Llull’s idea the name ars combina- toria (the art of combinations). Many consider Llull’s ideas on systems of logic, and their use in constructing new combinations of ideas as the beginning of the study of information science and semiotics. Although the combinatorial calculus of Ramón Llull was an extraordinary creation for the Middle Ages, giving us the earliest machine language and a perfect means of creating unbreak- 18 able encryption codes, Llull’s reputation was not always as high as it is today. The satirist Jonathan Swift ridiculed such Llullian devices in the third part of Gulliver’s Travels, where on the Island of Laputa Lemuel Gulliver is shown several large folio volumes of broken sentences generated by the ars combinatoria which he is told “.. [will] piece together; and out of those rich Materials to give the World a compleat Body of all Arts and Sciences...” Likewise, in François Rabelais’ exuberant, witty, and satiri- cal comment on his contemporary world, The Life of Gargantua and of Pantagruel the combinatorial arts of Llull are disparaged; Gargantua advices his son Pantagruel to master astronomy “but dismiss divinatory astrology and the art of Lullius as fraud and vanity.” 1.4 FURTHER READING 1 2 3 4 Two excellent, readable accounts of the difference between the real and the quantum worlds are: The Nature of the Physical World (1947); Sir Arthur Stanley Eddington; Lon- don, Dent & Sons Ltd., and QED: The Strange Theory of Light and Matter (1985); Richard P. Feynman; Princeton, Princeton University Press. The complex and close relationship between magic and science is touched upon in many places in Stranger Magic: Charmed States and the Arabian Nights (2011); Marina Warner; London, Chatto and Windus. Everything you have ever wanted to know about lists and list-making: The Infinity of Lists (2012); Umberto Eco; Maclehose Press (an imprint of Quercus). What is the definition of magic, and of a magical way of looking at the world? A Gen- eral Theory of Magic (1972); Marcel Mauss; London, Routledge; originally published in French in 1902. 1. IN THE BEGINNING WAS THE LISTCHAPTER 2 19 The Origins of the Language of Power that Is Science And God said, Let there be light: and there was light. Genesis 1: 3-4 Today, if you talk to a scientist about what it is that he/she believes science represents, you will likely be told that science is the only real source of truth; that the ideas of science are not culturally specific. That these scientific truths are as comprehensible for an American, as they are for a Russian or a Chinese savant. Of course, the American, Russian, and Chinese savants must be able to read their respective languages, and it is unlikely that anyone of them would be able to read the other two languages sufficiently well to comprehend what it was that the texts were describing. But the idea that science has an international, non-cultural character, not dependent upon particular elements of vocabulary, or particular rules of grammar, is certainly accepted by most scientists. About a thousand years ago it would still just have been possible for the majority of scholars and savants to have been able to discuss something through the medium of a true international language such as Latin, Arabic, or Greek. But such direct communication has not been possible since the end of the Middle Ages and was only ever possible in some parts of the European and Mediterranean worlds. Ancient Chinese scholars, like their Greek contemporaries, believed that their language was the only appropriate medium of communication, so they did not concern them- selves with the languages of barbarians. So, what exactly is the origin of this confusing association of science with a medium of universal communication? Indeed, can science be a universal medium of communication? This question is of particular interest, given the marked inability of the majority of scientists to explain to non-scientists, and even to scientists in areas of specialzation not their own, what it is they do and why it is that they do what they do. Therefore, what does it mean to say that science is a form of universal language, a culturally independent means of communication? Let us look at “the babble after Babel;” that is, the myth of the origin of the multitude of languages that we know today. The idea of an age when all men could converse with each other and could converse directly with their Creator, who had taught them this Ur-language, is a very wide- 20 spread myth.2 It is a myth about a Golden Age of innocence; a myth known to every culture—it is an idea deeply rooted in the Jungian collective consciousness. But for all its mythic qualities, the search for this ideal language, which according to monotheist beliefs had also been spoken by God to bring the Cosmos and humanity into existence (see the quote at the head of this chapter), obsessed European philosophers and savants right up until the Age of Enlightenment, when the Indo-European theory of the origin of modern languages was developed, and accepted. In Genesis 2:16-17, we are told that the Creator God spoke to man for the first time; telling our ancestor, Adam that everything in the earthly Paradise was his. God commanded him, how- ever, not to eat of the fruit of the tree of the knowledge of good and evil. We are not told in what language God spoke to Adam. Modern Biblical tradition has imagined it as a sort of language of interior illumination, rather than a communication of words, or of thunderclaps and lightning. After this command, we read that God “formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them.” Here we have a motif also common to most other religions and mythologies; that of the name-giver, the creator of language (nomothete). Figure 2.1 gives a late-mediaeval image of that naming process. Yet it is not at all clear on what basis Adam actually chose the names he gave to the animals. In the Latin Vulgate Bible, we are told that Adam called the various animals “nominibus suis” or “by their own names;” and in the King James Bible we have “Whatsoever Adam called every living creature, that was the name thereof.” But were the names given by Adam, the names by which each animal ought to have been known, or were they simply arbitrary names given by Adam? That is, did the given Adamic name refer to some fundamental or intrinsic property or characteristic of the animal, or was it purely a matter of what Adam was thinking at that moment. In Genesis 2:23 Adam speaks to his female companion, one again assumes that they are using the Divine Language of Creation as their means of communication, “This is now bone of my bones, and flesh of my flesh: she shall be called woman...” Eventually, Adam calls this female compan- ion Eve (which means life as she is to be the mother of humanity) so we see that Adam’s choice of name for those things he was charged by God to name was etymologically correct and not arbitrary. This would be a reasonable deduction given that the language in question was itself the language of Creation. The linguistic theme is taken up again in Genesis 11:1. We are told that after the Flood and the repopulation of the earth by Noah’s descendants, “the whole earth was of one language, and of one speech.” Yet, men in their vanity and arrogance conceived a desire to rival God, and thus erect a tower that would reach up to the heavens. To punish human pride, and to put a stop to the construction of their tower we are told that God devised a plan: “Go to, let us go down, and there confound their language, that they may not understand one another’s speech… Therefore is the name of it called Babel (as 2 In monotheist religions, the myth is given in the various sacred books. In Hindu culture, it is presented in the Mahabharata. 2. THE ORIGINS OF THE LANGUAGE OF POWER THAT IS SCIENCE2.1 A LESS MYTHIC INTERPRETATION OF THE BABBLE AFTER BABEL 21 represented in Figure 2.2); because the Lord did there confound the language of all the earth: and from thence did the Lord scatter them abroad upon the face of all the earth” (Genesis 11:7, 9). Figure 2.1: Image from the late-Byzantine, 14th-century Orthodox Holy Monastery of Saint Nicholas of Anapafsas, Greece. Adam, in his naked innocence, is seen naming the animals as they pass before him. The dragon-like creature, next to the lion(?) appears to be a remnant of a mediaeval bestiary. Image from: https://commons.wikimedia.org/wiki/File:Adam_naming_animals_-_Moni_Ayou_Niko- laou_(Meteora).jpg. 2.1 A LESS MYTHIC INTERPRETATION OF THE BABBLE AFTER BABEL Stories accounting for the multiplicity of human languages appear in nearly all mythologies and theogonies. But it is a major leap from knowing that many languages exist to deciding that this multiplicity is a fault or punishment that could be healed by a search for the imagined perfect original language. Indeed, how would you know you had discovered the Ur-language, the language of Eden? For Ancient Greek philosophers, Greek was the language of thinking and ratiocination. This was not a claim that the Greek language was a primary language: it was simply a case of the iden- tification of thought with its natural vehicle. About the speech of barbarians or non-Greeks, the Greeks knew little; hence, little was known about what it would be like to think in the language of barbarians. The Greeks admitted that the Egyptians and the Babylonians possessed wisdom, only because someone (Herodotus) had explained this to them in Greek. As Greek civilization expanded, the status of Greek as a language also evolved. In the period following the conquests of Alexander the Great (356–323 BCE), a common, universal form of 22 Greek spread rapidly—the koine. This was the language of Polybius, Strabo, Plutarch, Aristotle, and of the Eastern Roman Empire; it was the language taught in the schools of grammar. Gradually it became the official language of the Mediterranean world, and of the East of Alexander’s con- quests. Spoken by patricians and savants, Greek survived under Roman domination becoming the language of commerce and trade, of diplomacy, and of scientific and philosophical debate. It was finally the language in which the first Christian texts were transmitted (Septuagint translation of the Jewish Bible in the 3rd century BCE, and the Gospels in the first centuries AD), and it was the language of the early-Fathers of the Church. A civilization with an international language does not need to worry about the multiplicity of tongues. Nevertheless, such a civilization can, and did, worry about the rightness of its own tongue. While the Greek koine continued to dominate the intellectual life of the Mediterranean world, Latin was becoming the language of the administration of the empire, and thus the univer- sal language for those parts of Europe conquered by the Roman legions. Once again, a civilization with a common language is not troubled by the multiplicity of vulgar tongues. Learned Roman patricians would discourse in Greek, but the rest of the Latin-speaking world needed translators.3 Despite this Mediterranean civilization, by the 2nd century AD savants began to study lan- guages other than Latin and Greek, finding that human experience and wisdom could be expressed just as well in other languages. The Greco-Roman world was changing; new religions and beliefs were spreading from the East. Obscure revelations appeared—ome were attributed to Persian magi, others to an Egyptian divinity called Thoth-Hermes, to Chaldean oracles, and to Pythagorean and Orphic traditions which, though born in early-Greek civilization, had been buried by rationalist Greek philosophy. Today, we term these mystical beliefs Hermeticism, the product of the mythic Hermes Trismegistus (see Figure 6.1). The classical rationalism, elaborated and re-elaborated over centuries, began to show signs of age. With this loss of rationalism, the established religions entered a period of crisis. The Imperial Pagan religion had become a purely formal affair of the law courts; a simple expression of loyalty to the state. Each conquered people had been allowed to keep its own gods. And these new gods were, as in all conquering empires, accommodated to the Latin pantheon; no one bothering about contradictions, synonyms, or homonyms. A result of this widespread syncretism was the creation of modern monotheism, with its be- lief in a universal World Soul (an idea taken from Hinduism), a soul which subsisted in stars and in earthly objects alike. Our own, individual souls were but small particles of the great Universal Soul. However, as philosophers and savants proved unable to supply “truths” and detailed explanations about important matters (such as: What exactly happens after death?) men and women sought 3 This arrogance about one’s own language is one of the reasons for the political turmoil in the UK over Brexit. The British people have long been used to English being the universal language, or lingua franca; a situation that was certainly true for the century after the Battle of Waterloo, 1815. With the decline in the political status of the UK in the early 20th century and of the USA in the early 21st century, however, English is under threat as the lingua franca. 2. THE ORIGINS OF THE LANGUAGE OF POWER THAT IS SCIENCE2.1 A LESS MYTHIC INTERPRETATION OF THE BABBLE AFTER BABEL 23 revelations beyond reason, through visions, and through mystical communication with the God- head itself. This individual search for experience of the Divine led to mysticism being practiced by individuals, and the search for salvation of an individual soul, personal salvation, which was radically different from the basis of Pagan belief systems. Perhaps the syncretic religion that most blended physical and metaphysical concepts (that is blended matter and spirit, which the rationalist Greek philosophers had said could not be blended) was Pythagoreanism. The founder of this school was Pythagoras of Samos (c.570–c.495 BCE), whose political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato and Aristotle, and, through them, Western philosophy. Knowledge of the life of Pythagoras is clouded by legend. The teaching most securely identified with Pythagoras is metempsychosis, or the transmigration of souls, which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to strict mathematical rules (Isaac Newton would have agreed with this idea) and thus resonate to produce an inaudible (to us) symphony of music. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, in- cluding: Pythagoras’ theorem; Pythagorean tuning; the five regular solids; the theory of proportions; and the sphericity of the Earth. It was said that he was the first man to call himself a philosopher, that is, a “lover of wisdom,” and that he was the first to divide the globe into five climatic zones. Pythagoras influenced Plato, whose dialogues, especially his Timaeus, exhibit Pythagorean teach- ings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the 1st century BCE among Platonists, leading to the rise of Neo-Py- thagoreanism and Neo-Platonism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major influence on scientists, or natural philosophers, such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean sym- bolism led to early-modern European esotericism. From its beginnings, Pythagoreans had regarded themselves as the keepers of a mystic tradition of knowledge and practiced initiatory rites—something that always attracts attention and new adherents. Their understanding of the laws of music and mathematics, as being the basis for the physical world, was presented as the fruit of revelation obtained from the most ancient of civilizations of which they were aware, the Egyptians. By the time of Pythagoreanism’s second ap- pearance, however, Egyptian civilization had been eradicated by Greek civilization and then Latin conquerors. Ancient Egypt had become an enigma, a set of incomprehensible hieroglyphs. Yet there is nothing more fascinating than secret wisdom: one is sure that it exists and that it is hugely important, but one does not know what it is. In the imagination, therefore, it acquires exaggerated profundity. The language of Ancient Egypt, the hieroglyphs, naturally became the most ancient of languages—that of symbols. 24 For Saint Augustine of Hippo (354–430), as for nearly all the early fathers of the Church, Hebrew was the accepted primordial language. It was the language spoken before Babel, in the Garden between God and Adam. After the confusion induced by the fall of the Tower of Babel, Hebrew remained the tongue of the elected people. But Augustine was not interested in recovering its use. He was at home in Latin, by now the language of the empire, the church, and theology. Sev- eral centuries later, Isidore of Seville (560–636) found it easy to assume that, in any case, there were three sacred languages—Hebrew, Greek, and Latin. With this conclusion, the task of determining the language in which the God had said “Fiat lux,” which had brought forth the visible universe out of nothing, became more difficult. Figure 2.2: The Tower of Babel by Pieter Bruegel the Elder (1563). Image from: https://en.wikipe- dia.org/wiki/Tower_of_Babel#/media/File:Pieter_Bruegel_the_Elder_-_The_Tower_of_Babel_(Vi- enna)_-_Google_Art_Project.jpg. There is one sense in which Saint Augustine did have a clear idea of a perfect language, com- mon to all people. But this was not a language of words; it was, rather, a language made out of things themselves. He viewed the world as a book written by God’s own hand. Those who knew how to read this book were able to understand the allegories hidden in the scriptures, where beneath ref- erences to simple earthly things (plants, animals, stories, etc.) lay hidden symbolic meanings. This Language of the World, instituted by its Creator, could not be read, however, without a key; it was the need to provide such a key that provoked a rapid outflowing of bestiaries, lapidaries, encyclo- paedias, and imagines mundi throughout the Middle Ages. Many times in the last two millennia European culture has seized upon hieroglyphs and other esoteric ideograms, believing that funda- 2. THE ORIGINS OF THE LANGUAGE OF POWER THAT IS SCIENCE2.2 A MYSTIC LANGUAGE 25 mental truths are expressed in emblems or symbols,4 and all we need do to return to the Golden Age is comprehend those hieroglyphs [1]. Between the fall of the Roman Empire and the early Middle Ages, new languages came into being, but without the nationalism of individual nations. It is believed that, toward the end of the 5th century, people no longer spoke Latin, but rather Gallo-Romanic, Italico-Romanic, early-Welsh (with Latin additions), or Hispano-Romanic, while savants, less gifted than previous generations of savants, continued to write Latin, bastardizing it ever further. They heard around them local dialects in which survivals of languages spoken before Roman civilization were grafted onto, or crossed with new vernaculars arriving with the barbarian invaders. This age, characterized as Dark, seemed to witness a reoccurrence of the catastrophe of Babel: supposedly uncivilized and uneducated barbarians, peasants, artisans, the first Europeans—unlet- tered and unversed in official Latin-Greek culture—spoke a multitude of vulgar tongues of which official culture was unaware. It was the age that saw the birth of the languages which we speak today. European culture, and the cultures of those nations which started as European colonies, were all strongly influenced by these Dark age vulgar tongues. European critical culture begins with the reaction, often alarmed, to the explosive growth of the number of these tongues. Europe was forced at the moment of its birth to confront the drama of linguistic fragmentation, and European culture arose as a reflection on the perceived destiny of a multilingual civilization. Its prospects seemed uncertain; a remedy for linguistic confusion needed to be sought. Some savants looked backward, trying to rediscover the language spoken by Adam. Others looked ahead, seeking to create a rational language possessing the perfections of the lost language of power spoken in Eden. It was the latter that led to modern science, but the former path is still with us in the metaphysics of the search for the Theory of Everything (see Chapter 11). 2.2 A MYSTICAL LANGUAGE The mystical approach to seeking the secrets of sacred texts is the Jewish esoteric tradition, known as the Kabbalah. In the 12th and 13th centuries, the Jewish communities of northern Spain and the south of France developed a tool for the textural analysis of sacred texts. The Kabbalah is a mystical technique for interpreting the first five Books of the Hebrew Bible, the Torah, and which regarded creation itself as a purely linguistic phenomenon. Beneath the letters in which the Torah is written today, the Kabbalist sought to identify the shape of what is termed the “eternal Torah,” which had been created by God before He created the Universe, and which was believed by the Kabbalists to be the blueprint for Creation. 4 The best-selling Foucault’s Pendulum (1988) by Umberto Eco is all about the search for supposed hidden knowl- edge, or hidden truth; and explains how this endless search, for something that likely doesn’t exist has given rise to so many widely believed conspiracy theories. 26 The Kabbalist seeks to use the existing sacred text as an instrument. He knows that beneath the given text, beneath the familiar stories and events narrated in the Torah, there is another text which reveals a mystical and metaphysical reality. To uncover this mystical reality, and thus to come closer to the mind and intentions of the Divine, one must look beneath the literal narrative of the written text. Indeed, a Kabbalist would say that a sacred text can be read in four ways: (1) there is the simplistic or literal reading of the text; (2) there is an allegorical or philosophical manner in which to read the text; (3) the text may also be read hermeneutically (encompassing everything in the interpretative process including verbal and non-verbal forms of communication as well as prior aspects that affect communication, such as presuppositions, previous interpretations, the meaning and philosophy of language, and semiotics); and, finally, (4) the text may be read at the most pro- found level—at a mystical level. Just as the Kabbalists spoke of the four levels of meaning in a sacred text, the poet Dante, a near contemporary of the Occitan Kabbalists (certainly of the greatest of the Iberian Kabbalists, Abraham ben Samuel Abulafia, the founder of the school of Prophetic Kabbalah, who was born in Zaragoza in 1240, and died sometime after 1291) and who knew of their ideas, considered that there are also four levels of meaning in poetry. In the Divine Comedy (Inferno IX 61–63), Dante speaks to the reader and tells him of the meaning that is hidden within the verses, “O you whose intellects are sane and well,/ Look at the teaching which is here concealed/ Under the unfamiliar veil of verses.” The reader is then led to understand the four meanings of the poem, that is, the literal meaning, allegorical meaning, moral meaning, and finally anagogical meaning. Dante’s great poem is seen as a journey through and beyond life; an allegory about the stages of the soul’s redemption; a warning and guide, and a prophecy of Divine things to come. For the Kabbalist, language was a self-contained universe where the structure of the language represented the structure of physical reality. Thus, in contrast to the main schools of philosophy, in the Kabbalah, language does not represent the world merely by referring to it. If God created the world by uttering certain words or by combining certain letters, it follows that these elements were not representations of pre-existing things, but are the very forms by which the Universe was shaped and molded. The Divine Language was perfect not because it happened to reflect the structure of the Universe, but because it actually created the Universe. The Divine Language spoken by God, and used by Adam to name Creation, stands to the Universe in the same manner as the mold stands to the object cast from it. But, if there are secrets about how the Universe came into being hidden in well-known sacred texts, why then is man not able to fully comprehend all the mysteries of the Universe and to work prodigies by uttering similar combinations of letters from the Torah? The Kabbalists say that the reason God hid the true meaning of the Torah after the fall of Adam; that is, He did not give man the correct order of the letters which compose the Torah because if He had given man the true Torah then anyone who could read this version would have the power to perform miracles. 2. THE ORIGINS OF THE LANGUAGE OF POWER THAT IS SCIENCE2.2 A MYSTIC LANGUAGE 27 To this end, the letters which form the Torah we have today have been considered, over millennia by savants and linguists, as the basis-functions of other combinations which have been used in an attempt to find the words of power which will empower the speaker to control Nature and to work miracles. This is the reasoning behind the meditation techniques (on the Divine Name) of Abraham Abulafia. The Torah is interpreted as a mystical unity, whose primary purpose is not to convey a spe- cific, simple, and literal meaning or story, but rather to express the immensity of God’s power which is concentrated in His Name. The Kabbalists believe that the Name of God contains power, but at the same time it maintains and upholds the laws and harmonious order which pervade and govern the physical universe. Knowing the Name of God would enable man to penetrate the veil that sep- arates the visible created world from the numinous; and just as God created the Universe by His speech, the man who knows the Name of Power could also directly influence Creation. The Kabbalists, and those influenced by them also wished to read and fully comprehend the esoteric and apocalyptic books of the Bible, in particular, the Book of Daniel and the Revelations of Saint John. These Biblical texts were studied by Isaac Newton who was also searching for the Divine or mystical language. The Kabbalists and Newton (who possessed book on the Kabbalah) believed that Heaven and Earth were created by the uttering of the Name of God, and that the whole history and story of Creation were to be found in the gnomic utterances of the prophetic books of the Bible. The Torah was the source text in which to seek the power that had ordered Creation. Such concepts about names of power, and the power contained in such names, may seem more appropriate for the Classical or pre-Christian World, but names are very important, as we shall see in Chapters 13 and 14). Quintus Valerius Soranus (140–130 to 82 BCE) was a poet and Tribune of the Roman People at the end of the Roman Republic; he was crucified for revealing the secret arcane name of the Deity of Rome. To name something, or somebody is to know or under- stand that thing or that person, “to name is to know.” One did not reveal one’s name lightly as we read in all our myths, fairy tales, and legends. The mediaeval Kabbalists used combinatorial calculus (although they did not call it that) to combine various strings of letters in the established Torah as a means of seeking the Name of God. Intriguingly, at this same time and in exactly the same part of southern Europe, Ramón Llull was using very similar ideas to perfect his universal language of the philosophical and theological attributes of God. As we saw in Chapter 1, Llull was seeking a mechanical means of assisting the human memory and ingenuity in the association of combinations of characteristics and philosoph- ical attributes, which is precisely what the contemporary Kabbalists were doing in their prayers and spiritual exercises. The use of the Name of God to both affect and effect Creation is memorably expressed in the legends concerning the Golem, where a man could create a living but (importantly) an unthinking (that is, soulless) being from clay by use of the Ineffable Name of God. This story is beautifully 28 described in Gustav Meyrink’s novel, The Golem (published in serial form, 1913–1914), and in the magnificent silent movie, Der Golem, wie er in die Welt kam, based on this novel made by Paul We- gener in 1920. Of course, what investigations such as the above demonstrate is that man has long been searching for something he believes he lost long ago, and the retrieval of which will bring about a new Golden Age for humanity. It does not matter if you are a theologian, an Eastern mystic, or a particle physicist; we are all looking for that lost something. The perfect language of man’s inno- cence in the Garden. What was the language with which God conversed with Adam and in which God commanded Adam to name Creation? This perfect proto-language, (if it could be re-created) could be used to fully comprehend man’s place in the Cosmos, and perhaps allow man to manip- ulate Nature itself. A great deal of the history of science, and nearly all pseudo-science is really the record of man’s search for a simple language with which he could fully describe, comprehend, manipulate, and, perhaps, foretell or predict Nature, thereby allowing all men to comprehend all natural phenomena, whether known or as yet undiscovered. 2.3 FURTHER READING 1 A truly remarkable history of language; especially, the more esoteric aspects of that history: The Search for the Perfect Language (1995); Umberto Eco; Great Britain, Blackwell Publishers Ltd. 2. THE ORIGINS OF THE LANGUAGE OF POWER THAT IS SCIENCECHAPTER 3 29 The Mixing of Physics and Metaphysics to Create a Language of Curiosity It is astonishing how many foolish things one can temporarily believe if one thinks too long alone.’ J.M. Keynes (1883–1946) Languages are magical. They are the means of communicating to others our innermost secrets and thoughts, our desires and ideas. Such communication is not easy as we are not telepathic; we must construct sentences from the multitude of words in our memories. Such vocabulary is rendered into something that resembles our thoughts, via the rules of grammar, which are different for different languages but always serve the same purpose: to bring well-defined order out of chaos. But this process of verbal communication is rendered complex as no two people will describe something they both see in the same way; similarly, no two translators will render the same original text into exactly the same English text. Each of us brings to language, and to communication, our own ex- periences and limitations. There is, perhaps, no better way of exploring man’s abiding obsession with magic, with the occult, and with the hermetic arts than by looking at the ideas that have arisen about the creation of a single universal language. A language without ambiguity that would allow humanity to return to the Golden Age of simplicity, and the innocence of the Garden of Eden. 3.1 THE BIRTH PANGS OF MODERN SCIENCE The 17th century was full of the reciprocal influences of mysticism on science, and science on mys- ticism; all mixed together by the solvent of philosophy, and inexplicable observations of Nature. It is said to be the time when astrology, alchemy, and magic yielded to Sir Isaac Newton, to scientific rationalism and universal laws. But is this really true? It is not more a case that the astrology and popular folk magic were still present in society, and widely accepted by all levels of that society when Newton published, the most influential of all textbooks of physics, his Philosophiæ Naturalis Prin- cipia Mathematica in 1687 and 1713? Indeed, the magic, religion, and superstitions of that period merely blended into the Newtonian view of the Universe; magic and proto-science were not im- 30 miscible fluids in the 17th century. Newton himself was not adverse to experimental investigations of alchemy (he wrote a million words on the subject), nor of attempting to comprehend Biblical prophecies, and he was a respected caster of horoscopes. By the end of the 17th century, this mixture of popular and erudite beliefs had flowed to- gether, and then been overlaid by something else. Today, it is as pointless to say that one set of be- liefs gave way to, or was replaced by, another set of beliefs as it is to say that the Middle Ages ended in the mid-15th century, and were replaced by the Renaissance. No Age ever really ends, unless by the agency of a major catastrophe; the pre-existing Age is merely inundated by the succeeding Age. It is still there; just buried out of sight, and if some event causes the newer Age to be stripped away, the older Age will reappear as if nothing had happened in the intervening period. Today, belief in folk magic, superstition, and belief in the supernatural are still with us; many people today follow astrology, as did their ancestors in the time of Newton. What is true to say is that the 17th century in Europe was a period of intense spiritual awakening. The continent was a bubbling cauldron of ideas and beliefs, where savants were redis- covering the ideas of the Neo-Platonists and Hermeticists. The Rosicrucian manifestos exploded into a world waiting and wishing for something to happen; into a world shaking off much of the sterile baggage of mediaeval Christian Scholastic dogma, and seeking new spiritual directions and dimensions. The Rosicrucian manifestos were a potent stimulus in a period when men were seek- ing renewal; a new way of looking at the world, which the geographical discoveries of the previous century had been shown to be larger and more complex than had previously been imagined. Some 17th-century savants poured over magical texts; others labored at forges, melting and distilling metals; other thoughtful, wise men sought to understand the stars, and to comprehend their silent, slow, sacred dances; and still others invented secret alphabets and universal languages attempting to better understand the ordering of Creation. All such men were looking not only to understand Nature, but also to control Nature. In that period when magic and science mixed freely, everything was considered to be the hieroglyph of something else, and nothing was more lambent, more exciting, than a secret cypher. Galileo Galilee (1564–1642) was dropping weights from the Leaning Tower of Pisa and watching the isochronous oscillations of the chandeliers inside the nearby Cathedral of Pisa. In France, Car- dinal Armand de Richelieu (1585–1642) was seeking to create a new political and economic order in Europe. All had their eyes peeled for signs and portents. All were searching for the unusual, for the new. The attractive pull of Newton’s gravity and the oscillations of the pendulum became ob- sessions, and men not unnaturally reasoned that there must be something more; something quite different that lay behind, or perhaps above visible Nature. Another Italian savant, Evangelista Tor- ricelli (1608–1647), inverted a long, glass tube filled with Mercury with the open end of the tube in a bowl of Mercury and invented the barometer with a vacuum at the top of the sealed column of Mercury, showing that man could recreate the primal nothingness or void. Torricelli may not have 3. THE MIXING OF PHYSICS AND METAPHYSICS3.1 THE BIRTH PANGS OF MODERN SCIENCE 31 understood the physics of atmospheric pressure and how it changes from day to day, and from place to place; but he did know that he had captured a sample of the primordial nothingness from which the Cosmos had been created by God’s command. To Torricelli’s and Galileo’s contemporaries, such experiments were as much about magic as they were about science, because there was no clear way of distinguishing between these two ways of looking at Nature (see Figure 3.1). Figure 3.1: A table of symbols for celestial bodies, from the Berliner Astronomisches Jahrbuch of 1850. This list is from the mid 19th century, yet the symbols of the planets used date from Antiquity. A planet sym- bol is a graphical symbol used in astrology and astronomy to represent a planet, including the Sun (Sonne in Figure 3.1) and the Moon (Mond in Figure 3.1). The symbols are also used in alchemy to represent the metals that are associated with the planets. The use of these symbols is based in ancient Greco-Roman astronomy, although their current shapes are a development of the 16th century. The International Astronomical Union discourages the use of these symbols in modern publications, and their style manual proposes one- and two-letter abbreviations for the names of the planets: Mercury (Me), Venus (V), Earth (E), Mars (Ma), Jupiter ( J), Saturn (S), Uranus (U), and Neptune (N). The symbols of Venus and Mars are also used to represent the female and the male in biology and botany, following a convention introduced by Linnaeus (see Chapter X) in the 1750s. Even today, it is often difficult to separate the scientific and a more… magical description of Nature. (Image from: https://en.wikipedia.org/wiki/Planet_symbols#/media/File:Beze- ichnung_der_Himmelskörper_Encke_1850.png.) Indeed, at this time it is just about impossible to separate the world of magic and the world of science, where science is defined as the world of verifiable fact. Savants, who today are held up as paragons of rationalism, the standard-bearers of the scientific method, of rationalism, of mathemat- ical and physical enlightenment—such as Isaac Newton (1643–1727), Robert Hooke (1635–1703), Blaise Pascal (1623–1662), René Descartes (1596–1650), and Francis Bacon (1561–1626)—turn up in, what we might call, the fog of superstition which clung to their age. Many of these men worked with one foot in the laboratory, and the other foot in the Kabbalah.5 The savants of the 17th century may have sought to understand the workings of the natural world, but they also dabbled in alchemy, biblical prophec, and astrological cénacles. Perhaps Newton arrived at his Universal Law of Gravitational attraction because he believed in the existence of occult forces, which recalled his life-long investigation into astrology (the influence of the orien- tation of the stars and the planets on a man’s life) where he ended up proving that there is a force 5 But as Joseph Needham (1900–1995), one of the wisest of 20th-century savants commented, “Laboratorium est oratorium”—the place where we do our experiments is also a place of prayer and contemplation. 32 between the planets and the stars, and that this force is in the nature of an attraction, and would be differently experienced by each and every infant. Right up until his last days, Isaac Newton was working on a vast program that had obsessed him for half a century; to understand what he called the “mystic language” and to thereby fully understand the Divine Word as it came mysteriously from the mouths of the Prophets. A portion of his voluminous manuscripts on this work was published after his death in 1733, Observations Upon the Prophecies of Daniel and the Apocalypse of Saint John. Newton, who today is held up as the exemplar of rationality in a pre-scientific, barbarou,s and superstitious world, was not alone in this more mystical type of investigation. Many of Newton’s contemporaries worked on projects of this type, which they hoped would lead to a renewal of Christianity and the spiritual enlightenment of man, not based on the views and authority of the Pope, or of a small group of isolated theologians and churchmen, but instead based on reason which would be accessible to all. They were seeking an unchanging universal standard of spiritual awareness; one not tied to artifacts kept in the vaults in Rome or Canterbury. Today, many get embarrassed at the mention of magic, but even until the latter part of the 17th century practical magic was an accepted part of people’s lives. For the scientists or natural philosopher of that period, the possibility of magic and magical acts and interventions was a funda- mental presupposition. That the Bible contained fundamental truths about the place of man in the Cosmos was another presupposition, as was the possibility of identifying and using the Language of Creation. The prevailing cosmology of that time was of an inanimate Earth, or elemental world subject to the influence of the heavenly bodies or stars and planets. This in itself was sufficient to encourage speculation about the astral origins for earthly phenomena, and to give rise to much speculation and lore about the astrologically derived properties of plants and minerals, and to speculate as to whether magic could be used to gain power over Nature, hence the similitude between the astrolog- ical/astronomical and alchemical symbols seen in Figure 3.1. The chemical/alchemical experiments of the magician, or natural philosopher, were often devised to identify and expose divine harmonies and correspondences between metals and planets. It also suggested that the magician might be able to find some means of tapping into the influence of the stars and diverting it to other purposes. This is Neo-Platonism, which had for almost 2,000 years fostered a belief system which blurred the difference between matter and spirit, which had been the problem of philosophy in the West since it was first established in Ancient Greece; the Ancient Chinese were sensible enough never to have made such a separation. Instead of being regarded as an inanimate object, the Earth itself was deemed to be alive. (Today, we have returned to this essentially pantheistic view of Nature with the Gaia hypothesis of the self-regulating bio-sphere.) With its blurring of the boundaries between matter and spirit, Neo-Platonism also emphasized the influence of the human imagination upon the human body, of the mind upon matter and of words, incantations, and written charms 3. THE MIXING OF PHYSICS AND METAPHYSICS3.1 THE BIRTH PANGS OF MODERN SCIENCE 33 upon physical objects. By the exercise of his imagination, and the use of magic, symbols, and in- cantations, the operator or magician (the magus) could transform either himself or his subject. The invisible powers of Nature were believed to be analogous to the invisible powers of the magnet, which could be clearly seen to act at a distance and penetrate matter with its invisible rays (see Figure 12.1). Since the world was a pulsating mass of vital influences and invisible spirits, it was only necessary that the magician should devise the appropriate technique to tap into them, and then to be able to work wonders. Today, we would say the world is a complex field of interacting virtual particles as in the quantum field theory view of the vacuum. Perhaps a single seamless manifestation arising from the never-resting quantum flux of the universal vacuum, that is, at the quantum level the phenomena of Nature are more closely coupled than the savants of the 17th century could ever have imagined. In the 17th century, the Universe was believed to be peopled by a hierarchy of spirits thought to manifest all kinds of occult influences and sympathies, all linked together by invisible force fields through the Pythagorean Music or Harmony of the Spheres, and Newton’s gravity. The Cosmos was thought of as an organic unity in which every part, or manifestation bore a sympathetic re- lationship to every other part. Even colors, letters, and numbers were endowed with magical or mystical properties. The investigation of such phenomena was the primary task of the early scientist or natural philosopher. Modern science merely grew out of our magical and religious view of the world around us; it was able to correctly answer a few more of the questions that man kept asking. The project of finding the perfect, universal, divine or mystical language was something Newton followed all his life. It was a search for an unequivocal means of understanding the texts, which were the medium through which God communicated with man. First, Newton derived a mathematical language for formulating and predicting the dynamics of the heavens; then he would apply these techniques to the Bible and seek to tell us of the future. For Newton, numbers and equations were akin to those signs and clues by which the magicians or natural philosophers had first attempted to uncover the secrets of Nature. Newton regard Nature as a cryptogram created by God; as he put it, “Numero ponderi et mensura Deus omnia condidit” (God created everything by number, weight and measure). By pure reason, by hard work, by achieving wisdom through experimentation, this riddle could be solved by the dedicated savant. The question was one of discrimination; how do we tell the difference between the word of God and mere human words? The 17th-century search for a universal language was not new, but was a natural wish in light of the gradual decline of Latin. Literature in vernacular languages became more prominent in the Renaissance, and during the 17th century learned works written by savants for other savants largely ceased to be written in Latin; and the rise of printing spread these vernacular texts. But what these savants observed was that the vernacular languages were not as logical or coherent as they would like for a medium of communication, which they wished to use to truly describe the world they saw around them. This desire for a reformed language, a philosophical language where words would 34 perfectly describe objects, animals, and natural phenomena, and where the names of related objects, animals, and phenomena would be related to each other, led savants to consider again the Divine Language which Adam had used to name Nature (see Figure 2.1). The German savant, and competitor with Isaac Newton, Gottfried Leibniz conceived of a “characteristica universalis” or universal character of a language; that is, an algebra capable of ex- pressing all conceptual thought. This algebra would include rules for symbolic manipulation, what Leibniz called a calculus ratiocinator (a means of calculating the correct choice). His goal was to put debate, argument, and reasoning on a firmer basis by reducing much of it to a matter of calculation that men could grasp intuitively. This is, of course, what Ramón Llull had been seeking to achieve in the 13th century with his mechanical means of combining characteristics (see Chapter 1). There was no need to learn the endless lists of the current meanings of words, in the various vernacular languages; one could simply use algebra and mathematical manipulations on a small set of base concepts, or base units to describe everything in Nature. The characteristica would build an alphabet of human reasoning—a calculus of thought. It would be akin to throwing away the Catalogue of Ships found in Book 2 of Homer’s Illiad, and instead looking for what it was you wished to know in the shield of swift-footed Achilles (see Chapter 1). 3.2 GOTTFRIED LEIBNIZ AND THE NATURE OF THE UNIVERSE One of Leibniz’s most important developments was that of binary arithmetic. Although Leibniz was not the first to conceive of this arithmetic, he did formulate it coherently and believed that the Ancient Chinese must have known about it, on the grounds that it was implicit in the I Ching (see Chapter 5). The binary system is the simplest notation for numerals. Our decimal system has a choice of ten characters for each place (units, tens, hundreds, etc.). In the binary system, there are only two characters: one to designate an empty place, the other to indicate that the place is filled. Using the convention of 0 for empty, and 1 for filled, the system runs as follows: conventional decimal num- bers (binary equivalents): 0 (0), 1 (1), 2 (10), 3 (11), 4 (100), 5 (101), 6 (110), 7 (111), 8 (1000), 9 (1001), etc. Although Leibniz was proud of his discovery of binary arithmetic, he did little with it. This is a pity, because if the arithmetic used by machines had been developed in the 17th century we might have been able to develop calculating machines long before the 19th century. However, the binary system came into its own only with the advent of semiconducting electronics in the 1960s (an electron is either in a site, or it is not in that site—see footnote on Page 7). As far as Leibniz was concerned, the greatest significance of his work on binomial numbers was metaphysical, as showing how the Universe could be seen as constructed out of a number. 3. THE MIXING OF PHYSICS AND METAPHYSICS3.2 GOTTFRIED LEIBNIZ AND THE NATURE OF THE UNIVERSE 35 Gottfried Leibniz’s metaphysical account of the distinction between God and the visible uni- verse had both mystical and moral repercussions. Leibniz held that the visible, created universe was distinct from God by virtue of its passive, material, and mechanistic nature. This led him to construe that matter is unreal, which means that the materiality of the world consists in an admixture of un- reality, or not-being. God is a pure being: matter is a compound of being and nothingness. Leibniz elevated this idea into what he called a mystical theology, by developing the ideas of Pythagoras, who held that numbers (and the ratios of numbers; that is, proportions) were the ultimate realities, and that the Universe as a whole was harmonious. That is, it manifested simple mathematical ratios, like those of the basic intervals in music; the idea of the music of the spheres arose with Pythagoras back in the 6th century BCE. Leibniz’s contribution was to make these numbers binary. He was thus able to say that just as the whole of arithmetic could be derived from 1 and 0, so the Universe was generated out of pure Being (God) and Nothingness. God’s creative act was therefore at one and the same time a voluntary dilution of His own essence, and a mathematical computation of the most perfect number derivable from combinations of 1 and 0. Binary arithmetic was not merely a convenient notation for the hierarchy of all possible concepts, but it was the best way of repre- senting their very essence, with 1 and 0 themselves functioning as the only basic concepts. Thus, Creation becomes a dialectic between something and nothing; between 1 and 0. The 17th century produced many proposals for philosophical languages. The best known of these proposed philosophical languages, which we shall examine in Chapter 6, was that proposed by the Rev. John Wilkins in 1668 (An Essay toward a Real Character and a Philosophical Language), the classification scheme of which ultimately led to the Thesaurus. The search for the universal or perfect language originally concerned an attempt to redis- cover the primal matrix language. For many centuries, the leading candidate for this original or primordial language was Hebrew. Then in the 18th century, this search finally lost its utopian fer- vour, and its mystical component as the science of linguistics and the concepts of semiotics were born, and with them the Indo-European hypothesis of the origin of modern languages. For a long time, however, the idea of a primogenital language not only had a kind of historical validity—to rediscover the speech of all mankind before the confusion generated with the fall of the Tower of Babel—but it also entertained the minds of some of the greatest writers and thinkers of the Middle Ages and the Renaissance. This original language should incorporate a natural relationship between the words and the things we see around us in our world. Adam was told by God to name Creation, but how did he choose the names he used? The primordial language had a revelatory value, for in speaking it the speaker would automatically recognize the nature of the named reality, and it might even be possible for men to effect miraculous changes in Nature merely by speaking this original mother tongue. A lot has changed over the last two millennia, but today science is the only possible universal language that man can ever know. Science is the only endeavor which creates an absolute authority 36 to which we much all respond; science cannot be ignored, nor can it be defied, and the laws of phys- ics are absolute. It is only through science that we can hope to understand how the Universe came into existence, and why it is the way we observe and measure it to be. And the basic or semantic primes of the modern language of science are the base units or quantities, which we use to describe all known physical and chemical phenomena; indeed, these are also the base units and quantities we would use to try and understand any new phenomena as yet unobserved. This search for the perfect language, which is still ongoing in the physics community, could, perhaps, be considered ridiculous and pointless, but it could also be seen as arising from uneasiness, because people would like to find in the words we all use an expression of the way the world works and how history unfolds, and in this we have been regularly disappointed. 3.3 FURTHER READING For all aspects of the rise of science from an occult and magical background, the works of Frances Amelia Yates (1899–1981) are all worth reading. She was an English historian who focused on the study of the Renaissance, and also wrote books on the subject of the history of esotericism. In 1964, Yates published Giordano Bruno and the Hermetic Tradition, an examination of Bruno, which came to be seen as her most significant publication. In this book, she emphasised the role of Her- meticism in Bruno’s works, and the role that magic and mysticism played in Renaissance thinking. She wrote extensively on the occult or Neoplatonic philosophies of the Renaissance. Her books, The Occult Philosophy in the Elizabethan Age (1979), The Art of Memory (1966), and The Rosicrucian En- lightenment (1972), are major contributions, where the author deals with the supposed remoteness and inaccessibility of studies of magic and of the Hermetic arts. These volumes are available from Routledge Classics, Oxford, an imprint of Taylor and Francis. A truly remarkable history of languages; especially, the more esoteric aspects of that history: The Search for the Perfect Language (1995); Umberto Eco; Great Britain, Blackwell Publishers Ltd. 3. THE MIXING OF PHYSICS AND METAPHYSICSCHAPTER 4 37 The Transformation of Magic and Mysticism into Science So far as it goes, a small thing may give an analogy of great things, and show the tracks of knowledge. Lucretius (99–55 BCE) As mentioned in the Introduction, science, or rather the scientific worldview, was developed in early societies after the development of religion, and of a magical or mythological view of Nature. Men began to observe Nature with the desire to understand her better. They would have observed the progression of the Sun and the Moon: the ephemerides. This information would first have been memorized as literacy had yet to develop. As we have seen, eventually the long lists of observed phenomena and things would have been preserved, perhaps in painting, carvings, or the form of orally transmitted poetry or myth. And after many hundreds of generations, these myths, sculptures, and images would have formed the basis of a scientific interpretation of Nature; that is, first ob- servation, then hypothesis, and then further confirmatory observation and, perhaps, observational proof of hypothesis. Let us now consider how this transformation to a scientific view-point came about. Given that Chinese civilization is our oldest and best documented record of how societies developed, evolved, and became interconnected; it is in Ancient China that we must look for the origins of proto-science (see Further Reading). What was the main motive for the early natural philosophers, or Taoists of Ancient China, that compelled them to engage in the observation and study of Nature? The answer is straight- forward: to gain that peace of mind that comes from having formulated an hypothesis, however simple and provisional, about the most terrifying manifestations of Nature. Nature would have been seen as being all-powerful, and indifferent to the suffering of man. These ancient societies would have seen that when angered, Nature was able to easily perturb and destroy the fragile structure of human society. Nature still has this power, as the effects of global climate change upon our engi- neered structures gathers pace. Whether the natural phenomena studied by the Taoists were earthquakes, volcanic eruptions, floods, storms, or the various forms of plagues and disease, at the beginning of the adventure of science man felt himself to be stronger, more secure, once he had differentiated and classified the phenomena that assailed him. This security was particularly the case when he could name those 38 plagues and disasters. As we will see in many places in this work, “to name is to know”; if you can name something, you have power over it—or you think you do. The origin of the name given to the newly identified violent natural phenomenon, or plague would entail some character of the nature of that violent, destructive event. Thus, the men who observed Nature, and named and described the observed natural phenomena, would have formulated some naturalistic theory about the origin, and likely re-occurrence of those phenomena. This proto-scientific peace of mind was known to the Chinese as ching hsin (see Figure 4.1). The atomistic followers of Democritus and Epicurus in the West knew it as ataraxy (calmness, or peace of mind; emotional tranquillity). Figure 4.1: Early Spring (a hanging scroll painting) by Guo Xi. Completed in 1072, this is one of the most famous pieces of Chinese art from the Song Dynasty (960–1279). The painting is a meditation on Nature. The poem in the upper-right corner was added in 1759 by the Qianlong Emperor; it reads: The trees are just beginning to sprout leaves; the frozen brook begins to melt./ A building is placed on the highest ground, where the immortals reside. / There is nothing between the willow and peach trees to clutter up the scene. / Steam-like mist can be seen early in the morning on the springtime mountain. Image from: https:// en.wikipedia.org/wiki/Early_Spring_(painting)#/media/File:Guo_Xi_-_Early_Spring_(large).jpg. The Book of Master Chuang by Chuang Tzu, dating from the Warring States Period (476–221 BCE) tells us that “The true men of old had no anxiety when they awoke, forgot all fear of death and composedly went and came.” These ancient men knew from their studies of Nature that there was 4. THE TRANSFORMATION OF MAGIC AND MYSTICISM INTO SCIENCE 4 .THE TRANSFORMATION OF MAGIC AND MYSTICISM INTO SCIENCE 39 an order behind the apparent violent indifference of Nature. For his part, Chuang Tzu, and other Taoists speak of “Riding on the Normality of the Universe,” or on the “Infinity of Nature,” and thus de- scribe the sense of liberation which could be attained by those who could remove themselves from the petty squabbles of human society, and unify themselves with the great mystery of Nature; that is, to leave society and study Nature and become nature mystics (a beautiful term for a scientist). They had observed Nature, and had seen that it is possible for man to live in harmony with Nature, and not be the passive subject of Nature’s more violent manifestations. The same confidence in the power of, and the security that comes from observation is found in the West in Lucretius (c.99–c.55 BCE). The De Rerum Natura speaks of observation and deduction (that is, modern empirical sci- ence) as the only remedy for the numerous fears of mankind. The following lines are repeated three times in Lucretius’ poem: These terrors, then, this darkness of the mind Not sunrise with its flaring spokes of light Nor littering arrows of morning can disperse But only Nature’s aspect and her Law. (Translation by William Ellery Leonard) In modern science, the relationship between the rational and the empirical is seen to be so obvious as to require no explanation. However, this was not always the case. To emerge into the light in Europe, the modern scientific method had to struggle against the dead-hand of formal, mediaeval scholastic rationalism. Even up until the early-17th century, the proper marriage of rational thought to empirical observations had not been consummated. At this time, it was con- sidered in the ironic, but the Taoist words of Robert Boyle (1627–1691), the “father of chemistry” and author of the Sceptical Chymist of 1661, “much more high and Philosophical to discover things a priore than a postiore.” The origins of modern science are to be found in the interaction of four tendencies: two on one side of the argument, and two on the other side. On one side, theological philosophy allied itself with Aristotelian scholastic rationalism to oppose those natural philosophers who wished to more fully understand Nature by observation. On the other side of the argument, were those natural philosophers who wished to use experimental empiricism to explore Nature. This later group would be experimentalists who reacted against Thomist scholasticism, and who found a powerful ally in mysticism. In the European Middle Ages, Christian theology, given its universal domination was on both sides of the arguments about the rise of the modern scientific method; all those for and against the development of the scientific method would have been believers. But while rational theology was anti-scientific; mystical theology, or a mystical or spiritual view of the Divine, in all its aspects proved to be pro-scientific. The explanation for this apparent contradiction is to be found in the nature of magic; that essential pre-scientific element from which science evolved. Rational 40 theology was vehemently anti-magical (all those burnings of witches and heretics), but mystical theology tended to be more tolerant of magic and belief in magic; there was an affinity between mystical theology and Hermeticism in Europe, and that affinity arose from the study of Nature. But the fundamental cleavage here was not between those who were prepared to use reason to understand Nature, and those who felt reason to be insufficient to understand Nature, but be- tween those who were prepared to use their hands and those who refused to do so; between experi- mentalists and theoreticians. The Vatican theologians of the Inquisition who declined Galileo’s offer to look through his telescope and to see for themselves that the Ptolemaic System was incorrect, were Scholastics and so they believed they were already in possession of sufficient knowledge about the visible universe. If after looking through his telescope, Galileo’s findings agreed with Aristotle and with Saint Thomas Aquinas, there was no point in looking through the telescope; everything was already contained in the philosophy of the Angelic Doctor, Saint Thomas Aquinas. If the obser- vations from the telescope did not agree with established dogma, they would have been dismissed, and condemned by the churchmen as magical and Neo-Platonic. As it turned out, there was a fun- damental difference between Galileo’s observations and the philosophy of Saint Thomas Aquinas; a difference that the Church of Rome did not accept until 1992.6 Those Renaissance magicians, Nature mystics, and Neo-Platonists had discovered a new way of looking at Nature. This explanation of the origins of the modern scientific method explains so much about the “less rational” interests of those earliest scientists. Why it was that men such as Isaac Newton, Robert Boyle, and Sir Thomas Browne (1605–1682) were interested in the Kabbalah and astrology, believing that such ancient mystical doctrines, the Hermetica, contained ideas of value to them in their new empirical studies. Typical of the attitude of these 17th-century experimentalists (the key here is that they were all experimentalists who ‘got their hands dirty’ in the laboratory) was that of the Flemish chemist, Jan Baptist van Helmont (1580–1644). Van Helmont was one of the founders of biochemistry; he was among the first to use a balance in quantitative experiments, he devised an early-form of thermometer, and he demonstrated the acid in the stomach and the neutralizing alkali of the duodenum. Yet for all this detailed interest in the reproducibility of experiments, van Helmont was also deeply anti-rational, displaying an almost religious empiricism. He attacked the hair-splitting formal logic, scholastic logic, which he felt had little relation to observable reality, but 6 In 1633, the Inquisition of the Roman Catholic Church forced Galileo Galilei to recant his theory that the Earth moves around the Sun. Under threat of torture, Galileo recanted. But as he left the courtroom, he is said to have muttered, “all the same, it moves.” 359 years later, the Church finally agreed. At a ceremony in Rome, before the Pontifical Academy of Sciences, Saint Pope John Paul II officially declared that Galileo was right. The formal rehabilitation was based on the findings of a committee of the Academy the Pope set up in 1979, soon after taking office. The committee decided the Inquisition had acted in good faith, but was wrong. The Inquisition’s verdict was uncannily similar to cautious statements by modern officialdom on more recent scientific conclusions, such as predictions about greenhouse warming and climate change. The Inquisition ruled that Galileo could not prove “beyond doubt” that the Earth orbits the Sun, so they could not reinterpret scriptures implying otherwise. 4. THE TRANSFORMATION OF MAGIC AND MYSTICISM INTO SCIENCE4 .THE TRANSFORMATION OF MAGIC AND MYSTICISM INTO SCIENCE 41 merely trapped the mind in an endless circular argument. In truth, van Helmont was a European Taoist who believed in the need to observe Nature in order to understand Nature. It may be said, therefore, that at the early stages of modern science in Europe, the mystical (nature mysticism, see Figure 4.1) was often more helpful than the rationalist approach, when it came to finding an explanation or a cause of an observed phenomenon. This situation exactly mirrors the rise of a scientific-like worldview among the philosophical scholars of Ancient China. Resting on the value placed on manual operations, that is, doing experiments rather than merely attempting to think of an explanation, and not testing that theory by experiment, men such as van Helmond and Isaac Newton were active laboratory workers as well as thinkers and writers. The equipment they built to undertake their experiments is still with us today. The Confucian social scholastics of Ancient China, like the rationalist Aristotelians and Thomists of mediaeval Europe nearly two millennia later, had neither sympathy for, nor interest in manual operations. Hence, practical science and magic were together driven into mystical heterodoxy. It is the association of nature mysticism and empiricism that is the foundation of post-Renaissance scientific thought in the West. This same amalgam of empiricism and mystical theology, leading to a scientific worldview, can also be seen in Islam. The Brethren of Sincerity was an organization formed in Basra, Iraq, in about 950. Like the Chinese Taoists 1500 years earlier, and the Christian nature mystics of the 17th century, this semi-secret society had, at one and the same time, mystical, scientific, and political interests. The men who met in Basra acknowledged the existence of mysteries transcending reason, and believed in the efficacy of experimentation, particularly, manual laboratory experimentation in seeking to study those mysteries. All the savants involved in these early phases of the development of science recognized that effects may be brought about by specific manual operations without our being able to say exactly how or why; and they further believed that this unexplained data and in- formation ought to be recorded and accumulated for future generations of savants. Their opponents, and often persecutors (as with their Christian and Chinese colleagues), believed that the nature of the Universe could be apprehended by ratiocination alone, and that quite enough information had already been made available to scholars, and that in any case, the use of the hands to do work of any kind was unworthy of individuals claiming to be scholars. The early proto-scientists were thus in a dilemma, for they could either set up a ratiocination of their own consisting of obviously inadequate theories and models, or rest on the thesis that “there are more things in heaven and earth, Horatio, that are dreamed of in your philosophy,” and seek elucidation of the unexplained by further observation and study. Only cycles of experimentation and hypothesis would allow a resolution of this situation; thus, the modern scientific worldview was born. There is of course a great difference between the nature mysticism or mystical naturalism, which triggered the creation of modern science (but which did not lead to the scientific triumphal- ism of the late 19th century) and other forms of mysticism, which are focused in purely religious 42 contemplation, or meditation upon a God or gods. As is often said by theologians, religion is a belief in someone else’s experience of the Divine, while spirituality is having your own experience of the Divine. The Ancient Chinese Taoists and the first European scientists learned that by looking at the world, and thinking about what it was they were observing, a larger number of individuals could gain a first-hand experience of the Divine; that is a gnosis (a revelation of knowledge) as the Ancient Greeks and early Christians would have described this glimpse of the truth, or this discovery. All that nature mysticism asserts is that there is much in the Universe that transcends human reason, but since it required the empirical to the rational for comprehension it also implied that the sum total of incomprehensibility will diminish if men humbly (and without pre-conceived ideas) explore the occult properties and relations of things. Religious mysticism is very different; it dotes on an arbitrary uniqueness, and seeks to minimize or deny the value of investigations of the natural world. It is authority-denying mysticism, not rationalism, which at certain times in world history assists the growth of experimental science. And one may readily see why such upwelling of the sci- entific worldview often correspond with periods of social progress. As we read in the Tao Te Ching: “Everyone recognises good as good, and thus what is not good… is also known.” 4.1 FURTHER READING In the sections of this present work where I discuss Ancient China, I will be making use of the magisterial Science and Civilization in China (published 1956, re-published 1975), Joseph Need- ham; Cambridge, Cambridge University Press. In this chapter, I make reference to Volume II of this multi-volume work, The History of Scientific Thought. 4. THE TRANSFORMATION OF MAGIC AND MYSTICISM INTO SCIENCE43 CHAPTER 5 The I Ching as a Model of the Cosmos The situations depicted in the Book of Changes are the primary data of life—what happens to everybody, every day, and what is simple and easy to understand. Hellmut Wilhelm (1909–1990)7 The I Ching, also known as the Book of Changes, is an ancient Chinese divination text, and it is one of the oldest pieces of Chinese literature.8 The text has been used for well over two millennia as a cultural reference, and has inspired ideas in religion, psychoanalysis, literature, and art. Indeed, the text has had a profound influence on western culture, but it originated as a divination manual in the Western Zhou Period (1000–750 BCE) of Ancient China. Then during the Warring States Period (475–221 BCE) and early Imperial Period, the I Ching was transformed into a cosmological text with a series of philosophical commentaries known as the Ten Wings. After becoming part of the Five Classics in the 2nd century BCE, the I Ching was the subject of scholarly commentary, and the basis for divination practice for centuries across the Far East, and eventually took on an influential role in western understanding of eastern thought. Various modern scholars suggest dates for the original text ranging between the 10th and 4th centuries BCE. The form of divination involved in the I Ching is a type of cleromancy, which in the I Ching concerns the generation and interpretation of random numbers represented as figures termed hexagrams. The interpretation of the random readings, via the content of the I Ching is a matter of many centuries of debate, and many commentators have used the book symbolically, often to pro- vide guidance for moral decision making informed by Taoist and Confucian ideals. The hexagrams themselves have acquired cosmological significance and become associated with other processes of change such as the coupled forces Yin and Yang and the five Chinese elements, Wu Xing. Many believe that the I Ching is a book containing an explanation of all the laws of physics, an expla- 7 Hellmut Wilhelm was the son of Richard Wilhelm (1873–1930), the German sinologist, theologian, and mis- sionary, who is best remembered for his translations of philosophical works from Chinese into German, which in turn have been translated into other languages. His translation of the I Ching is still regarded as one of the finest, as is his translation of The Secret of the Golden Flower; both were provided with introductions by the Swiss psychoanalyst Carl Jung, who was a personal friend. 8 According to Google searches, the I Ching comes higher in the list of the most influential books than both the Old Testament and the New Testament. 44 nation of how everything is governed, and carries explicit directions on how men should conduct themselves in order to remain continually in harmony with these natural laws. Within both modern physics and Eastern philosophy, it is believed that all natural phenom- ena in this world of change and transformation are dynamically interrelated. Emphasizing move- ment and change, Chinese philosophy had long ago developed concepts of dynamic patterns which are continually formed and dissolved again in the cosmic flow of the Tao. The I Ching has elaborated these patterns into a system of archetypal symbols, the so-called trigrams and hexagrams. Ancient Chinese scholars contemplated the Cosmos in a way comparable to that of modern physicists, who with the advent of quantum mechanics introduced into their model of the Universe a psychophysical element. In the quantum view of Nature, the experimenter is an essential part of any experiment; as shown in the various interpretation of the (in)famous thought experiment by Schrödinger about a cat in a sealed box with a vial of poison. The observed microphysical event in an experiment necessarily includes the observer, just as much as the reality underlying the I Ching comprises subjective; that is, psychic conditions in the totality of momentary incidents and events. The 64 hexagrams of the I Ching become the instrument by which the meaning of the 64 different, yet typical, situations found in Nature can be determined. Therefore, for someone who regards the physical world in the same manner as the ancient Chinese scholars, the I Ching retains more than a slight attraction. In its original structure, the I Ching is made up of eight trigrams, consisting of eight com- binations of three lines of broken Yin-Hsiang (- -) lines and unbroken Yang-Hsiang (—) lines (see Figure 5.1). It is believed that these concepts have a cosmogonic significance. According to the Supreme Ultimate (Nothingness), a simple line symbolizing the positing of Oneness (—) produced the two modes Yin and Yang by splitting and filling of the lines. This creation ex-niho may seem strange, but as the Heart Sutra of Buddhism puts it: O Sariputra, Form does not differ from Emptiness And Emptiness does not differ from Form. Form is Emptiness and Emptiness is Form. The same is true for Feelings, Perceptions, Volitions and Consciousness. And monotheism is not without its own creation ex-nihlo. 5.1 DETAILS OF THE I CHING The Five Elements Theory (Wu Xing) has the same fundamental philosophy as the theory of the two coupled and inseparable forces Yin-Yang; that of continual evolution and balance. Each natural element (the five elements of Classical Chinese thought: wood, fire, earth, metal, and water com- pare with the four classical elements in the West: air, fire, water, and earth; see Table 7.1) has specific 5. THE I CHING AS A MODEL OF THE COSMOS5.1 DETAILS OF THE I CHING 45 attributes that vibrate with their own frequency or energy. These elements interact with each other to affect the flow of energy in an individual’s environment, in a positive or negative manner. Feng shui practitioners utilize the concepts of Yin-Yang and the Five Elements to balance competing energies in your environment. It is through the four hsiang that the eight trigrams are derived: each made up of combinations of three divided or undivided lines (see Figure 5.1). A summary of the properties and meanings of each of the eight trigrams is given in Table 5.1. Yang Yin Figure 5.1: The eight trigrams derived from the Nothingness that also gave rise to the Yin and the Yang. The origin of the eight trigrams is the two coupled forces, Yin and Yang, and it is from these eight tri- grams that the 64 hexagrams of the I Ching are derived. Table 5.1: The names and the attributes of the eight trigrams. We saw earlier how the German savant Leibniz read the sequence of the trigrams as a perfect representation of the progression of binary numbers (000, 001, 010, 110, 101, 011, 111 ...) Trigram Name (Chinese) Name ☷ Kun ☶ Gen ☵ Kan ☴ Xun ☳ Zhen ☲ Li ☱ Dui ☰ Qian The Keeping The The gentle The The The The receptive still abyssal arousing clinging joyous creative Attribute Devoted Standstill Danger Penetration Movement Pleasure Strong Light giving Image Earth Mountain Water, Wind, Thunder, Lightening, Lake Heaven Family Mother Youngest Middle Eldest Eldest son Middle Youngest Father clouds wood wood fire relationship Binary numeral equivalence Decimal equivalence 0 0 son 1 son 10 daughter daughter daughter 11 100 101 110 111 1 2 3 4 5 6 7 46 These eight trigrams are some of the most basic symbols of Eastern philosophy, representing transitional phases of Nature, and of human thought and psychology (see Table 5.1). They repre- sent the maximum number of Yin and Yang relationships in sets of three. Yin and Yang forces are combined as Yin/Yin, Yin/Yang, Yang/Yin, and Yang/Yang combinations. These four combinations of forces are again divided to form the eight trigrams, and are said to be linked to the forces of Nature: Heaven and Earth, fire and water, thunder and wind, mountain and lake (as given in Table 5.1). Figure 5.2: The 64 hexagrams of the I Ching (source: https://en.wikipedia.org/wiki/I_Ching#/media/ File:Diagram_of_I_Ching_hexagrams_owned_by_Gottfried_Wilhelm_Leibniz,_1701.jpg). 5. THE I CHING AS A MODEL OF THE COSMOS5.2 DIVINATION WITH THE I CHING 47 Each trigram has its own name and property, and the trigrams are considered to represent all possible cosmic, natural, and human situations. They are associated with the phenomena of Nature, and the various possible situations in our social lives. They were also associated with the cardinal directions, and with the seasons of the year. Thus, the eight trigrams are often grouped around a circle in the natural order in which they were generated, starting from the top (where people in Asia have always located the south) and placing the first four trigrams on the left-hand side of the circle, the second four on the right-hand side. The objects or attributes thus symbolized by the eight trigrams are made to represent the constituents of the Universe, which form the basis of a cosmological system elaborated by the scholars of the Han Dynasty (206 BCE–220 AD) using the Five Element Theory. By combining these trigrams as a symmetric matrix, a total of 64 combinations is obtained; known as the 64 hexagrams (shown in an ancient Chinese manuscript in Figure 5.2). The 64hexa- grams are traditionally arranged in 2 patterns: (i) a square of 8 x 8 hexagrams and (ii) a circular sequence showing the same symmetry as the circular arrangement of the trigrams; both are seen in Figure 5.2. The 64 hexagrams are the cosmic archetypes on which the use of the I Ching as an oracle book is based. For the interpretation of any hexagram that may arise in the initial selection or divination, the various meanings of its two trigrams have to be taken into account.9 In the I Ching, the trigrams and hexagrams represent all possible combinations generated by the dynamic interaction of the forces Yin and Yang, and are reflected in all cosmic and human in- teractions. All things and situations are in a state of continual transition: one changing into another, the solid lines pushing outward and breaking in two, the broken lines pushing inward and growing together. Therefore, the 8 trigrams, together with the 64 hexagrams are deemed to represent all the possible situations and temporal mutations of phenomena in the Universe. The I Ching is believed to describe a system of metaphysics relating the Universe and natural phenomena, as functions of the time of day, seasons, weather, family relations, personal relations, etc. 5.2 DIVINATION WITH THE I CHING To use the I Ching, an individual must first embark upon a process of divination; that is, they must allow themselves (in what they do) to be open to the influence of Nature. The person who has a question to ask of Nature must first invoke the forces of Nature; for example, by tossing a set of coins, or drawing lots to generate a set of results that may then be interpreted via the traditional text of the I Ching, which is the result of more than two millennia of interpretation of such divination experiments. The process of consulting the I Ching as an oracle involves determining the hexagram by a method of random number generation, and then reading the text associated with that hexa- 9 The Internet is full of sites detailing how these interpretations are made. 48 gram. Confucius said that one should not consult the Oracle for divination until one has passed the age of 40. Those studying the I Ching should also be free of compulsion; that is, repeatedly asking the same question in hope of either a different/better answer, or further enlightenment as to the meaning of the answers one first obtains. Hexagrams were traditionally generated by the casting of yarrow stalks (Achillea millefolium). The stalks must be cut and prepared, being plain, lacquered, or varnished. Fifty yarrow stalks are used, though one stalk is set aside at the beginning and takes no further part in the process of con- sultation, or divination; this is the Wu Chi—the unchanging ground of being. The remaining 49 stalks are roughly sorted into 2 piles, and then from each pile 1 stalk is initially removed, then the pile is “cast off ” in lots of 4; that is, groups of 4 stalks are removed. The remainders from each half are combined (traditionally placed between the fingers of one hand during the counting process) and set aside, with this process being repeated twice; that is, a total of three times. The total stalks in the remainder pile will necessarily (if the procedure has been followed correctly) be 9 or 5 in the first count and 8 or 4 in the second. Nine or 8 is assigned a value of 2; 5 or 4 assigned a value of 3. The total of the three passes will be one of only four possible values: 6 (2+2+2), 7 (2+2+3), 8 (2+3+3), or 9 (3+3+3); that count provides the number of the first line of the hexagram. When three successive changes produce the sum 3+3+3=9, this makes the old Yang, i.e., a firm line that moves. The sum 2+2+2=6 makes old Yin, a yielding line that moves. Seven is the young Yang, and eight the young Yin; they are not taken into account as individual lines. The 49 stalks are then gathered and the entire procedure repeated to generate each of the remaining 5 lines of the hexagram. (Each succeeding line is written above its predecessor; that is, the first line is at the bottom of the stack of lines, and the final, sixth line is at the top.) During the Eastern Han Dynasty (1st century AD), there were two schools of interpretation of the I Ching. The first school, known as New Text Criticism, was more egalitarian and eclectic, and sought to find symbolic and numerological parallels between the natural world and the hexagrams. With the fall of the Han Dynasty, I Ching scholarship was no longer organized into systematic schools. One of the most influential writer of this period was Wang Bi (226–249), who discarded the numerology of Han commentators and integrated the philosophy of the Ten Wings directly into the central text of the I Ching, creating such a persuasive narrative that earlier Han commentaries were no longer deemed important. By the 11th century, the I Ching was being read as a work of intricate philosophy, as a starting point for examining metaphysical questions and ethical issues. Cheng Yi (1033–1107), founder of the Neo-Confucian Cheng–Zhu school, read the I Ching as a guide to moral perfection. He described the text as a way for ministers to formulate honest political opinions, and so avoid factionalism, to root out corruption, and to solve problems in government. The contemporary scholar Shao Yong (1011–1077) rearranged the hexagrams in a format that resembles modern binary numbers, although he did not intend his arrangement to be used mathe- 5. THE I CHING AS A MODEL OF THE COSMOS5.3 FINAL COMMENTS 49 matically. This arrangement, sometimes called the binary sequence, is the format that later inspired Gottfried Leibnitz; when the text had been translated and published in Europe by the Jesuits. Gottfried Leibniz, who was corresponding with the Jesuit missionaries in China, wrote the first European commentary on the I Ching in 1703, arguing that it proved the universality of binary numbers and Theism, since the broken lines, the “0” or nothingness, cannot become solid lines, the “1” or oneness, without the intervention of God (see Page 35). This mystical interpretation was criticized by Georg Wilhelm Friedrich Hegel, who proclaimed that the binary system and Chinese characters were “empty forms” that could not articulate spoken words with the clarity of Western al- phabets. In their discussion, I Ching hexagrams and Chinese characters were conflated into a single foreign idea, sparking a dialogue on Eastern and Western philosophical approaches to questions such as universality, semiotics, and the nature of communication. Following the Xinhai Revolution of 1911, the I Ching was no longer part of mainstream Chinese political philosophy, but it maintained a huge cultural influence as China’s most ancient text. Borrowing back from Leibniz, modern Chinese writers offered parallels between the I Ching and subjects such as linear algebra and logic in computer science, seeking to demonstrate that ancient Chinese thought had anticipated Western discoveries. The Sinologist Joseph Needham (1900–1995) took the opposite viewpoint, arguing that the I Ching had actually impeded scientific development in China by incorporating physical knowledge into its metaphysics. The psychologist Carl Jung took a great interest in the possible universal nature of the imagery of the I Ching, and he introduced an influential German translation by Richard Wilhelm by discussing his theories of archetypes and synchronicity. The book had a notable impact on the 1960s counterculture, and on 20th Century writers and musicians such as Philip K. Dick, John Cage, Jorge Luis Borges, and Hermann Hesse. 5.3 FINAL COMMENTS In the initial phases of the transformation of magic into science in Europe, the mystical approach to Nature was often more helpful to savants and those seeking to comprehend what they saw around them than the theoretical or rationalist approach. After all, if one begins with a rationalist approach to the investigation of Nature, one will soon end up doing experiments to test and thus extent the- oretical models. And experiments are often difficult; they may not work for a whole host of reasons, and they may well be difficult and expensive. On the other hand, mystical interpretations of what one encounters in the natural world are cheap, and require no testing, only a vivid imagination and a knowledge of ancient history to provide the ancestral deities responsible for whichever natural phenomenon is being considered. However, experience tells us which of these two approaches yields the most useful, that is, reproducible results. In the British Isles, the Anglo-Irish alchemist and proto-scientist Robert Boyle paid considerable attention to this problem of resolving the use 50 of theory versus experiment (even mystical theories versus rationalist theories) in his publication of 1661, The Sceptical Chymist. Boyle came down on the side of practical experimentation as being the ultimate, the acid test, for all speculation about Nature.10 Since each of the 64 symbols, or hexagrams, of the I Ching came, in the course of the centu- ries, to have an abstract signification, such a reference was naturally alluring and saved all necessity for further thought and any experimental investigation. The technique of the I Ching resembled in many aspects the astrological pseudo-explanations of Nature and man’s destiny of pre-Renaissance Europe, but with the greater complexity (64 hexagrams as opposed to 12 Houses of the Zodiac); abstractness of symbolism gave it a deceptive sophistication. The 64 symbols, or hexagrams, in the system provided a set of abstract concepts capable of subsuming a large number of the events and processes, which any investigation is bound to find in the phenomena of the natural world. It has been said that the I Ching supposes a kind of translation of all natural phenomena into a mathematical language by means of a set of graphic symbols, the germs of what the German philosopher and mathematician Gottfried Leibniz would have called a universal language or a universal character, thus constituting a dictionary capable of permitting men to read Nature like a book whether with intellectual, or practices aims in view. This is, of course, as much about true science as it is about astrology. Furthermore, the I Ching brings us back to the illusory realms of numerology, where numbers are not the empirical and quantitative servants of science, but a straightjacket into which theories have to forced to fit our pre-conceived ideas. To paraphrase Jung, the I Ching has more to do with synchronicity than with physics. Yet for all its flummery and quackery, and lack of anything other than a statistical success rate, it is a technique which is still hugely followed (much like astrology). What seems to show through when one looks at the ideas of Taoism, and other similar thoughts about the origin and usefulness of the I Ching in early eastern natural science, is the effort made by the School of Naturalists and the Han Dynasty Confucians to use the figures made by the long and the short strokes; that is, the 64 hexagrams, as a comprehensive system of symbolism containing, in some way all the basic principles of all natural phenomena. That is, to construct a proto-language of science; even if it was a symbolic representation of this language. Like the Tao- ists, the naturalists who invoked the I Ching to comprehend the world were looking for peace of mind, as opposed to the worry of trying to learn long lists of things and phenomena, and forgetting some part of that list. It is likely that a similar argument can be made to account for the central importance of astrology in the Mesopotamian civilization. The Houses of the Zodiac and the Sun, Moon, and planets formed a sufficiently complex system that permitted a range of correspondences to be con- structed and maintained. If then one projects these theoretical, mystical interconnections onto ob- 10 Happily, experiment won out in the end, although theoretical physicists still have an exalted status in the physics community. 5. THE I CHING AS A MODEL OF THE COSMOSservations of Nature, one does have a system of sufficient flexibility to explain some part of Nature. But of course, this is a mystical theoretical model of Nature; one could say a mythological model. And this mystical model yielded to rational experimentation and evidence in the modern world, in both the East and the West. 5.4 FURTHER READING 51 5.4 FURTHER READING The Internet is crowded with sites providing information about the I Ching, and about the inter- pretation of results derived from divinations using the I Ching. As for recommendations for further reading, I suggest: 1 The American physicist and ecologist Fritjof Capra (born 1939) has explored the parallels between modern physics and Eastern Mysticism in The Tao of Physics (1975); Boston, Shambhala Publications, Inc. 2 forward by Carl Jung. I Ching translated by Richard Wilhelm (2003); London, Penguin Books. This book has a 53 CHAPTER 6 Natural Philosophy How many angels can dance on the head of a pin? (A standard question for students of Scholasticism in the 13th century) In our consideration of the concept of a perfect language, with which and through which man might truly appreciate and, perhaps, control Nature, we must now leave behind the fascinating but strangely exotic mixture of magic and science that had characterized the pre-scientific world, and examine the advent of the a priori philosophical language. The members of this new group of 17th-century seekers after a simpler, more perfect language were not magicians or Hermeticists, but savants and natural philosophers who sought a simple, but logical language which could eliminate the concepts and formalisms, which had previously clouded the judgment of men, and which had kept all men from fully and rapidly embracing the progress of science and technology. Jan Amos Komensky (1592–1670; he used the Latinized form of his name as Comenius) was a Protestant mystic from Bohemia. Although inspired by religious ideals, he is considered to be one of the first savants who as part of their investigation of Nature tried to formulate a more perfect language to describe his observations, and to allow him to transmit his observations to other savants. In his Pansophiae Christianae III (1639–1640), Comenius advocated a reform of the commonly used vernacular languages to eliminate the rhetorical and figurative use of words, which he regarded as a source of ambiguity and confusion. The meaning of the words that remained should then be fixed, with one name for each thing; this, he believed, would restore words to their original meaning. Although Comenius was never to construct his reformed, plain language, he had broached the idea of a universal language that attempted to overcome the political and structural limitations of Latin, which was still being used as a sort of universal language in Catholic countries. (Comenius came from the non-Catholic part of Central Europe, which from 1618–1648 was fighting for its existence in the Thirty Years War.) Comenius proclaimed that the lexicon of the new philosophical language would reflect the composition of reality, and every word in it should have a fixed, definite, and univocal meaning. Every idea should be represented by one and only one expression, and these definitions and expressions should not arise from an individual author’s fancy or imagination, but should represent only things that existed. Comenius wished to create a utopian language that would describe the fixed, unmoving connections of every element of Creation; but he recognized that it would not be a vehicle for the creation of great literature. 54 The utopian ideas of Comenius would have necessitated a prodigious ability at memorizing all the new words and the new meanings. But this was exactly the type of problem that had inspired Ramón Llull to invent his Ars combinatoria. The French philosopher René Descartes saw where the real problem lay with such new philosophical languages. In order to avoid having to memorize and learn how to use the new fundamental or primitive names Descartes conjectured it only would be necessary for these to correspond to an order of ideas or thoughts which had a logic of their own akin to that of numbers. That is, that it was through the medium of mathematics and mathematical logic that the new universal language would eventually come into being. Descartes pointed out that if we can count, we are able to generate an infinite series of numbers without needing to commit to memory the whole set of all possible numbers. But this problem coincided with that of discovering a philosophy capable of defining a system of clear and distinct ideas. If it were possible to enumerate the entire set of simple ideas from which we mentally generate all the complex ideas of which it is possible to conceive, and if it were further possible to assign to each idea a character, as we do with numbers, we might be in a position to manipulate them with a mathematics of thinking, or a calculus of thought, while the words of natural languages evoke only confusion. This was the idea that was pursued in Germany by Gottfried Leibniz. What we have here in the first half of the 17th century is a statement about the essential properties of a computer language, three centuries before the invention of the computer. In 1654, the English clergyman, alchemist, and astrologer John Webster (1610–1682) wrote his Academiarum examen, an investigation and attack on the academic world, which Webster felt had not given sufficient attention to the problems of creating a universal language. Like many En- glish contemporaries of Comenius, Webster was influenced by the Bohemian’s ideas. Webster fore- saw the birth of a “Hieroglyphical, Emblematical, Symbolical and Cryptographical learning.” Describing the general utility of algebraic and mathematical signs, numbers, and equations, Webster went on to say that “the numerical notes which we call ciphers, the Planetary Characters [the internationally known symbols for the planets, see Figure 3.1], the marks [the well-known alchemical emblems, see Figure 1.2, and Table 7.1] for minerals and many other things in Chymistry, though they be always the same and vary not, yet are understood by all nations, and when they are read, everyone pronounces them in their own Country’s language and dialect.” John Webster was attempting the synthesis of mathematics and alchemical and astrological symbolism (today we would rather say chemical and astronomical nomenclature). He went on to say that such a symbolic language would be the true philosophical or universal language. Webster was something of a controversial figure in his own life; an Anglican clergyman who supported the Parliamentary cause in the Civil War, who was openly an alchemist and astrologer and who was sceptical about witchcraft. Yet, in Puritan England, this chaplain to the Parliamentarian army produced a work that was at the center of the 17th century’s magico-scientific Hermetic tradition (see Figure 6.1), which also produced the astrology, mathematics, and Adamic language of Dr. John 6. NATURAL PHILOSOPHYDee, the eminent mathematician and astrologer to Queen Elizabeth I, and the Angel languages and alchemy of Robert Fludd. 6. NATURAL PHILOSOPHY 55 Figure 6.1: Hermes Trismegistus, a floor mosaic in the Cathedral of Siena (image from: https://en.wiki- pedia.org/wiki/Hermes_Trismegistus#/media/File:Hermes_mercurius_trismegistus_siena_cathedral. jpg). The mythic personality, Hermes Trismegistus, is associated with the Greek god Hermes and the Egyptian god Thoth. Greeks in the Ptolemaic Kingdom of Egypt recognized the equivalence of Hermes and Thoth, and the two gods were worshiped as one in what had been the Temple of Thoth in Khemenu, which was known in the Hellenistic period as Hermopolis. But the “personality” of this cultural mix of Ancient Egyptian and Greek gods became overlaid with something more. Hermes, the Greek god of interpretive communication, was combined with Thoth, the Egyptian god of wisdom. This multi-faceted deity thus became a god of wisdom. And it was as a source of all wisdom that he became known to the Neo-Platonists in the early centuries of the Christian era, particularly, in the Egyptian metropolis of Alexandria. As a divine source of wisdom, Hermes Trismegistus was credited with many writings, which were reputed to be of immense antiquity. Early Christians and Neo-Platonists were under the impression that the Egyptians had 42 sacred writings by Hermes, writings that detailed the training of Egyptian priests. These Hermetica are a collection of papyri containing spells and induction procedures for new adepts. The dialogue called the Asclepius (after the Greek-god of healing) describes the art of imprisoning the souls of demons, or of angels in statues with the help of herbs, gems, and odors, so that the statue could speak and engage in prophecy. This corpus of ancient wisdom was, however, merely a compilation of facts and a list of old observations. There was no underlying coherence, and all context had been lost. We are back with Homer’s Catalogue of the Ships, but the literary and historical context had been entirely lost. Yet not only did this list lead to science, but it also influenced Christian dogma. 56 Not surprisingly, Webster was attacked and his ideas were ridiculed by contemporaries, how- ever, his ideas were within the development of a universal, symbolic language based on mathematics and symbols, and not based upon phrases and the rules of grammar needed to try and keep order among the rapidly accumulating words of even a reformed language. The more mystical Hermetic ideas of Webster were denounced by John Wilkins (1614–1672), another Anglican clergyman and natural philosopher who was quite prepared to accept that a new language could be elaborated in which letters of the alphabet stood for mathematical quantities. But the critics of Webster argued that the only real character of which Webster spoke was actually the natural language of which the Kabbalists and Rosicrucians had sought for vainly in Hebrew. In spite of these mutual criticisms, the projects of the religious mystics did have something in common with those of the natural phi- losophers. The 17th century was full of reciprocal influences of mysticism on science and science on mysticism, all mixed together by the solvent of philosophy and observations of Nature that were at that time inexplicable. However, as we move toward the ideas of John Wilkins, we finally move away from the search for the lost language of Adam, and move to the secular world, which would centuries later lead to linguistics, semiotics, computer codes and modern science. The first serious attempt at producing a systematized universal language based on philo- sophic principles was due to John Wilkins. He was a polymath who became the Bishop of Chester and the brother-in-law of Oliver Cromwell; he was one of the pre-eminent scientific innovators of that period. Wilkins assisted in the founding of the Royal Society of London. He was one of the creators of a new natural theology which attempted to be compatible with the science of the time, attempting to synthesize natural philosophy with the theology and dogma of the Church of England. In 1668, Wilkins published his Essay toward a Real Character and a Philosophical Language, where he attempted to create a universal language to replace Latin as an unambiguous means of communication with which international scholars and philosophers could communicate. The Essay also proposed ideas on weights and measure which were similar to those which would later be found in the Metric System of 1795. In particular, Wilkins suggested that a more perfect system of weights and measures, a universal system of weights and measures could be generated by using the decimal metric system based upon a single universal measurement. In essence, Wilkins proposed that an entire system of units could be based on a single natural dimension, or universal measure (see Chapter 9). John Wilkins spoke of a single universal measure upon which all other measures could be based, and from which all other measures could be derived by mathematics. Wilkins’ Essay was translated into Italian in 1675 by Tito Livio Burattini (1617–1681), who translated Wilkins’ phrase universal measure as metro cattolico, thereby introducing the familiar modern word, meter, or “measure.” Tito Livio Burattini was a true Renaissance man, as interested in architecture and the designing of scenery for theatrical spectacles as in measurement science and mathematics. It was to- 6. NATURAL PHILOSOPHY6. NATURAL PHILOSOPHY 57 ward the end of his life in 1675 that he published his Misura universale (Universal Measurement) in Italian where he described the ideas of John Wilkins (whose essay had been published by the Royal Society of London in 1668). Burattini was one of the first European savants to make a detailed survey of the architecture of the Great Pyramid of Giza. Indeed, on his expedition to Egypt he was accompanied by the English mathematician John Greaves, who went on to become a professor of geometry at Gresham College, the forerunner of the Royal Society of London. Interestingly, the measurements of the Great Pyramid made by Greaves were later used by Isaac Newton in his stud- ies of Biblical Prophecy and in a calculation Newton made of the circumference of the Earth.11 But as we have seen, the 17th century was characterized by this curious mixture of science and magic, physics, and metaphysics. John Wilkins wished to create a universal language, primarily to facilitate international com- munication among scholars, but he also envisioned its use by diplomats, travelers, and merchants. Wilkins’ idea was to create a family of symbols corresponding to a complex classification scheme, which was intended to provide elementary building blocks which could be used to construct every possible object and idea. The Real Character is not a written representation of speech. Instead, each symbol directly represents a concept, without there being any way of speaking, or vocalizing it; each reader might, if he wished, give voice to the text in his or her own tongue. Later in his Essay, Wilkins introduces his Philosophical Language, which assigns phonetic values to the Real Characters, should it be desired to read the text aloud without using any of the existing natural languages. In this universal language, each word defines itself. Descartes had already noted in 1629 that using the decimal numbering system it was straightforward to name all the numbers up to infinity, and to write them in a new language—if one were so disposed. Descartes went on to suggest the creation of a language similar to this numbering system, but a general language, organizing and covering all human ideas. In 1664, Wilkins started to work on this task. John Wilkins divided everything in the Universe into 40 categories or genera, these being fur- ther subdivided into two hundred and 51 characteristic differences, which were subdivided into 2,030 species which appear in pairs. After depicting Nature in tables that occupy 270 folio pages, Wilkins began the construction of his philosophical grammar. Wilkins assigned to each genus a symbol con- sisting of a monosyllable of two letters; the characteristic differences are expressed by the consonants B, D, G, P, T, C, Z, S, N and the species by the addition of another letter; seven (Latin and Greek) vowels and two diphthongs. For example, De, signifies an element; Deb, the first difference, which according to Wilkins’ Tables is fire; and Debα will denote the first species, which is flame. Det will be 11 It was believed in the 17th and 18th Centuries that the Great Pyramid of Giza was a structure associated with magical and occult rites (Hermes Trismegistus again). In the same way that 18th Century surveyors were mea- suring the Meridian through Paris to define the universal measure of length (our modern meter), it was thought that the Ancient Egyptians had defined the near universal unit of length measurement in the Ancient world, the cubit from the base of the Great Pyramid (each base side is 440 cubits or 230.4 m) which was held to be 1/500 of one degree of the Earth’s circumference (222.639 m). 58 the fifth difference under that genus, which is appearing meteor, and Detα the first species, which is rainbow. The words in the analytical language of John Wilkins are full of meaning and information; however, there is a great deal of arbitrariness. Debα signifies flame, because α designates a species of the element fire. If we replace α with a, we obtain a new symbol, Deba, which according to Wilkins’ Tables designates comet; Deba and Debα are related but different.12 The “words” of Wilkins’ analytical language contain no arbitrary symbols. Each letter in the analytical language has significance and meaning, in the same manner that the text of Holy Scripture has various levels of meaning for the Kabbalists, and the long numerical sequences which regulate our lives such as social security numbers; telephone numbers; computer access codes; bank account numbers contain all that there is to know about each and every one of us. (For example, the IBAN bank code has 22 characters and the SWIFT code has 11 characters—these numbers contain the potential for vast numbers of combinations allowing all humanity to be numbered and sorted, and then monitored.) One could learn Wilkins’ language without knowing that it was artificial. Then later, one could be led to discover that it was also a universal key and a secret encyclopaedia. Not surprisingly, Wilkins’ language was not ideal, however, it was an extraordinary achievement for its time. But then, the impossibility of truly representing the entire scheme of the Universe should not and cannot stop us from planning human models, even though we are conscious that they are, at best, preliminary, and will, of necessity contain arbitrary and conjectural elements. The reason for this lack of perfec- tion in any human attempt at categorising all knowledge is because we do not truly know what the Universe is, or indeed, where it came from, and why it is here. And it was man’s speculation as to the origin and purpose of the visible world, that is, in God’s secret dictionary that started him off on his search for the perfect or universal language. We have perhaps been going around in circles, but coming to new wisdom at the completion of each circuit. It is with the advent of a more perfect analytical language, that is, the modern physical sciences that man has begun to truly penetrate the Divine scheme of the Universe. The analytic language of Wilkins is an example of a scheme intended to order all knowledge and relieve our memories of much unnecessary work. The word salmon, for example, tells us noth- ing, but zana, the corresponding word in Wilkins’ classification, defines (for one versed in the 40 categories of genera, and the differences and the species of those genera) a scaled river fish with reddish meat. It was a century later that the Swedish botanist Carl Linnaeus (1707–1778) would adopt the familiar binomial system of nomenclature for all creatures (see Chapter 13); the extant and the fossil. Man being Homo sapiens (“thinking man”) in the Linnaean classification, and the Atlantic salmon is Salmo salar (“leaping salmon”). 12 Umberto Eco gives a clear and fascinating description of the structure and use of Wilkins’ Analytical Language in his The Search for the Perfect Language. 6. NATURAL PHILOSOPHY6. NATURAL PHILOSOPHY 59 In the same way that Ramón Llull sought to use mechanical or logical devices to construct all possible combinations of the attributes of God (philosophical, theological and personal), thereby avoiding the tedious necessity of preparing ab initio lists, which would be very long and probably incomplete, and then trying to commit those lists to memory, Wilkins attempted to show how such a scheme could be used to order all human knowledge. We will see later (Chapter 9), how starting with a single universal measure (of length) it is possible to construct a self-contained system of units which is the basis of modern science. If you like, how a truly universal language may be constructed from a limited number of primitive semantic primes, or base units. John Wilkins did not so much wish to discover the language used by Adam in the Garden of Eden; he wished to be the new Adam, by turning the old mystical speculation of universal lan- guages on its head. As he wrote in the Introduction to his Essay of 1668, “This design would likewise contribute much to the clearing of some of our modern differences in Religion, by unmasking many wild errors, that shelter themselves under the disguise of affected phrases; which being Philosophically unfolded, and rendered according to the genuine and natural importance of Words, will appear to be inconsistencies and contradictions.” To fulfill this promise of reshaping language, of creating a tool for linguistic analysis and of providing a means of standardising religious understanding, it was not enough sim- ply to invent real characters for this new language; it was necessary to develop a criterion that would govern the primitive features that would compose these characters. In order to design characters that directly denote concepts and ideas, if not the things themselves that these concepts reflect (this was the problem which Adam was faced with when he was commanded by God, to name Creation), two conditions must be fulfilled: (1) the identification of the true primitive notions or semantic primes and (2) the organization of these primitives into a system which represents the organization of the model of the content. Thus, such a language is termed a priori. And the formulation of such a language requires a grammar of ideas that is independent of any natural language. John Wilkins’ ideas were widely circulated among the savants of his period. Unfortunately, his ideas were met mostly with derision, not only among ordinary people but also among fellow savants as being brilliant, but incomprehensible. The Ballad of Gresham College is a satirical ode on the Royal Society (originally called Gresham College) and refers directly to Wilkins’ project, A Doctor counted very able Designes that all Mankynd converse shall, Spite o’ th’ confusion made att Babell, By Character call’d Universall. How long this character will be learning, That truly passeth my discerning. Science is the reduction of an extraordinary and bewildering diversity of events and ob- servations into a manageable uniformity within one of a number of possible systems of symbols, 60 quantities, and units. Similarly, technology is the art of using those systems of quantities, units or symbols so as to be able to predict, control and organise events. The scientist always views things through the medium of a system of symbols, quantities, and units, and technology is the handling of information and materials in ways that have been predicted by the systems of symbols and units. To many this may seem like magic and, unfortunately, the more isolated the scientist be- comes from the general public, the more priest-like the scientist appears. But popular or not, communicative or not, science does evolve and impacts everyone. I am attempting to outline here how the modern language of science grew out of magic and the search for a mythical language of power that was used by God to create the Cosmos, and us. Indeed, it was not so long ago that the original search for the proto-language spoken in Eden was not so much abandoned, but subsumed into the search for a universal philosophical language which would better allow man to understand who he is, where he is, and why he is here. This change from the search for the language with which God created the physical world, to the creation of the language of science, probably arose because the later language actually worked at allowing man to speculate about Nature—it produced results. It was seen to be a language of authority, and not just a language of curiosity. The proto-language might have allowed God to create the Heavens and the Earth, but the philosophical languages allowed man to understand the Heavens and the Earth, and permitted him to dream that science might even allow him to one day be able to control Nature. Science works. But we scientists have still not completely shaken off the aura of the ma- gician or magus (whether we know that or not). As we are only too aware, all technologies are increasing in performance at an alarming rate; electronics and computers are becoming smaller, faster, and cheaper. But modern science and technology, and hence today’s scientist and the technician, have left the ordinary man far behind; and in the future, technology and magic will, perhaps again, become indistinguishable. But then this was the case in the 17th century, so there is nothing new there. 6.1 FURTHER READING For all aspects of the rise of science from an occult and magical background, the works of Frances Amelia Yates (1899–1981) are all worth reading. She was an English historian who focused on the study of the Renaissance, and also wrote books on the subject of the history of esotericism. In 1964, Yates published Giordano Bruno and the Hermetic Tradition, an examination of Bruno, which came to be seen as her most significant publication. In this book, she emphasised the role of Her- meticism in Bruno’s works, and the role that magic and mysticism played in Renaissance thinking. She wrote extensively on the occult or Neoplatonic philosophies of the Renaissance. Her books The Occult Philosophy in the Elizabethan Age (1979), The Art of Memory (1966), and The Rosicrucian En- lightenment (1972) are major contributions, where the author deals with the supposed remoteness 6. NATURAL PHILOSOPHYand inaccessibility of studies of magic and of the Hermetic arts. These volumes are available from Routledge Classics, Oxford, an imprint of Taylor & Francis. A truly remarkable history of languages, especially the more esoteric aspects of that history: The Search for the Perfect Language (1995); Umberto Eco; Great Britain, Blackwell Publishers Ltd. 6.1 FURTHER READING 61 CHAPTER 7 The Laws of Nature 63 Nature and Nature’s laws lay hid in night: God said, “Let Newton be!” and all was light. Alexander Pope: epitaph for Sir Isaac Newton A moment’s thought will demonstrate that science may be described as the quantitative study of the complex, coupled relationships that may or may not exist between observed events. Any phe- nomenon that is susceptible to investigation, that can be measured, that can be weighed, that can be numbered, and that can be expressed mathematically, the readings on laboratory dials, the clicks coming from a counter, or detector can all be considered as part of the enterprise of science. On the other hand, there is no room in the scientific worldview for the inexact, uncontingent, immea- surable, imponderable, or undefined. A process that can be repeated time after time, a system that can be reproduced and analyzed, these are the concepts which go to make up science, and not the individual, the unique, the elusive thing, or phenomenon that can never occur a second time. Our increasing understanding of ourselves and of the world within which we live comes from the myriad measurements scientists and technicians make each day. These measurements drive the evolution of our society. We realized in the 17th century that by studying and using the newly discovered Laws of Nature to make predictions about future events we no longer needed magicians or Shamans whose predictions about future events were correct only on a statistical basis. This ob- servation was a significant advance for mankind. Indeed, the history of science is an essential part of our political and economic freedom; it could be said to be the Palladium of our freedoms. One way of thinking about our present democracy is as an expanding mass of conflicting interests, which through the action of a solvent such as modern capitalism, spiked with a fascination for trivia, such as are readily available on the Internet, becomes resolved into what is, in essence, a thin vapor. That is, a dilute or rarefied, ideal gas of non-interacting particles that lose collective internal energy in proportion to the perfection of its aspiration. Like a perfect gas expanding into a vacuum… into nothing, losing all coherence and long-range structure. By using the prism of the scientific world- view to keep our views of how we came to be who we are in perspective, we might even be able to preserve our freedoms. When we know something of the origins and evolution of our assumed knowledge, or un- derstanding of the natural world, we are delivered from the thrall of preconceived opinions and the foolish, fabulous ideas into which man is all too willing to fall, and into which one may fall without even realizing it. In addition, we better understand the limited value, the limited shelf- 64 life of all our hypotheses about the unfolding of the visible universe, and on a smaller scale, about the evolution of our own society and of our own lives. When we study the history of science, we see how misunderstandings in science have arisen, and how they were resolved. And we are able to put the achievements of our own period in a more appropriate perspective; a more appropriate historical perspective. A study of history and particularly the history of science tells us how well we have been thinking, and whether what we have been thinking about is relevant and useful. And among other things, a study of the general scope of historical development affords the scrutiny of evidence, and the capacity to decide which particular version of an event seems most credible. It also allows one to observe the strange, almost unfathomable, metamorphosis that occurs in the interpretation and hallowing of a sacred text; invoked as if it were supernaturally ordained, and hence not available for contested examination and interpretation. That is, we may investigate the origins of the dogmas of science; it allows us to understand Nature and to live with less anxiety with the more violent aspects of the natural world (see Chapter 4). The essential and all-important characteristic of science is that it is predictive. Science fol- lows some established order; an order that was thought by our forebears, even as recently as the late 19th century, to be divinely inspired. Today, however, we hold that phenomena arise because of a set of transcendent fundamental laws, and the interaction between a set of unchanging forces that may be characterized by a set of inviolable constants of Nature, for example, the mass and charge of the electron, me and e, respectively. But where did this idea of a divine legislator for the Universe come from? If we can say that the natural world has arisen from, and is maintained by a set of fundamen- tal laws what is the similitude between these observed Laws of Nature and the laws promulgated by national parliaments? Where did the observed Laws of Nature come from? 7.1 THE COMPLEX RELATIONSHIP BETWEEN ASTROLOGY AND ASTRONOMY In earlier parts of this volume, I made much of the complex relationship between a magical way of looking at Nature, and a more rationalist or scientific way of looking at Nature, that is, the close relationship of natural philosophy, the Hermetic arts, and modern science. Nowhere is this com- plexity better seen than in a comparison of astrology and astronomy. In addition, in Chapter 5, we saw how the creation of complex, self-contained system such as the I Ching and the Houses of the Zodiac formed a system of study permitting a range of correspondences with the observed natural world to be constructed and maintained. If then one projects these theoretical, mystical intercon- nections onto other observations of Nature, one does have a system of sufficient flexibility to explain some aspects of Nature. But of course, this is a mystical theoretical model of Nature; one could say a mythological model. But this is where it all began. Ancient civilizations, such as the Sumerians, 7. THE LAWS OF NATURE7.1 THE COMPLEX RELATIONSHIP BETWEEN ASTROLOGY AND ASTRONOMY 65 were famous for their ability as both astronomers and as astrologers. You could not be an astrologer if you did not know something of the slow, reproducible, sacred dances of the planets and the stars. Consequently, we first need to consider the origins of the words astrology and astronomy. Table 7.1 gives a list of some alchemical and astrological/astronomical symbols commonly used by savants in the pre-scientific age (during and before the late 17th century). As can be seen (compare with Figure 3.1), there is a clear mixing of the symbols; the symbols used in alchemy also represent the metals that are associated with the seven planets that also give us our days of the week. The use of these symbols descends from ancient Greco-Roman astronomy/astrology, although their current shapes are a development of the 16th century. The symbols of Venus and Mars are also used to represent the female and the male in science, following a convention introduced by Linnaeus (see Chapter 13) in the 1750s. Even today, it is often difficult to separate the scientific and the magical description of Nature. Table 7.1: A table of symbols for celestial bodies (astrological and astronomical symbols) and chemical elements (alchemical symbols) Important Alchemical and Astrological Symbols According to the Swiss alchemist and chemist Paracelsus (1493–1541), the three primes or tria prima—of which material substances are composed are mercury, salt, and sulphur. Paracelsus reasoned that Aristotle’s four element theory appeared in all bodies as three principles. He saw these principles as fundamental, and justified them by recourse to the description of how wood burns. Mercury included the cohesive principle, so that when it left as smoke the initially solid wood fell apart. Smoke described the volatility (the mercurial principle), the heat-giving flames described flammability (sulphur), and the remnant ash described solidity (salt). Mercury (or mind) This is also the symbol for the planet Mercury Salt (base matter or body) Sulphur (or the soul) … continued on following page 66 Western alchemy makes use of the Hermetic elements. These are the four classical elements of Aristotle: air, earth, fire, and water Air Earth Fire Water The properties of the four classical elements are first discussed by the Islamic scholar Abū Mūsā Jābir ibn Hayyān (c.721–c.815). He has been widely described as the father, or the founder of early chemistry, in- venting many of the basic processes and equipment still used by chemists today. Seven metals are associated with the seven planets, which also give us our seven days of the week, and seven major deities, all figuring heavily in alchemical symbolism. Although the met- als occasionally have a glyph of their own, the planet’s symbol is most often used, and the sym- bolic and mythological septenary is consistent with Western astrology. The planetary symbolism is limited to the seven wandering stars visible to the naked eyes of ancient astronomers, the extra Saturnian planets. Uranus and Neptune are not included, as they were identified as plan- ets only in the late 18th and early 19th centuries, respectively. Lead dominated by Saturn Tin dominated by Jupiter Iron dominated by Mars Gold dominated by Sol (the Sun) Copper dominated by Venus Mercury (quicksilver) domi- nated by Mercury Silver dominated by Luna (the Moon) Also the symbol for the planet Saturn. Saturday is the day of Saturn or Kronos—dies Saturni. Also the symbol for the planet Jupiter. Thursday is the day of Zeus or Jupiter—dies Iovis. Also the symbol for the planet Mars, and for the male. Tuesday is the day of Mars—dies Martis. Also the symbol for the Sun. Sunday is the day of the Sun—dies Solis. Also the symbol for the planet Venus, and for the female. Friday is the day of Venus or Aphrodite—dies Veneris. Also the symbol for the planet Mercury. It is also used as a unisex symbol since the intersex Hermaph- roditus was a child of Hermes and Aphrodite (Mer- cury and Venus). Wednesday is the day or Mercurius or Hermes—dies Mercurii. Also the symbol for the Moon. Monday is the day of the Moon—dies Lunae. It was the Austrian-American, Marxist historian and sociologist Edgar Zilsel (1891–1944) who pointed out that the compound word, astronomy could not have been formed and used had 7. THE LAWS OF NATURE7.1 THE COMPLEX RELATIONSHIP BETWEEN ASTROLOGY AND ASTRONOMY 67 there not been, at that time a tacit recognition of the quasi-juridical nature of the laws which con- trol the motions of the heavenly bodies. That is, that there was a celestial law-giver who legislated for the Universe. [1] The de Legibus (On the laws) is a dialogue by Marcus Tullius Cicero (106–43 BCE) composed during the last years of the Roman Republic. Cicero wrote this work as a fictionalized dialogue between himself, his brother Quintus, and their mutual friend Titus Pomponius Atticus. The dia- logue begins with the trio taking a leisurely stroll through Cicero’s estate at Arpinum; they begin to discuss how laws should be made, and how they should be maintained. Cicero uses this text for expounding on his theories of natural laws of harmony among the social classes. But what Cicero also included was the comment, “The universe obeys god, seas and land obey the universe, and human life is subject to the decrees of the Supreme Law.” Cicero’s comment was certainly a Taoist view of the nature of all things, but it was a view that demonstrated a separation between divine laws (Laws of Nature) and the laws of men. Yet, in his de Natura Deorum (On the Nature of Gods), Cicero tells us that gods and men are influenced by the same laws, so we see there is an indication that there were laws of Nature which bind us all. The words astrology and astronomy were at first synonymous, and the later was familiar to Aristophanes in the 5th century BCE (Clouds, lines 194 and 201). Subsequent usage seemed to follow the personal preference of individual authors. Plato wished to settle on the word astrology for all investigations of the heavens, but astrology was already beginning to acquire the magical significance of astro-mancy. In the astrological literature of late antiquity, we sometimes encounter a mixing of terms, which today we take a great deal of care to separate; for example, “Laws of Na- ture” are mentioned in the context of a magical interpretation of phenomena. The astrologer Vettius Valens (120–175), while discussing an astrological predetermination (submission to fate), speaks of the legislation of Nature, of fate and of the stars. Vettius Valens’ surviving texts are particularly interesting, because he cites the views of a number of earlier authors and authorities who would otherwise be unknown. Although the astron- omer, mathematician, and astrologer Ptolemy of Alexandria (90–168), and author of Tetrabiblos (the most influential astrological text we possess), was generally regarded as the colossus of Helle- nistic astrology and astronomy for many centuries following his death, it is likely that the practical details of the astrology of the period resemble the methods elaborated in Valens’ Anthology. Mod- ern scholars tend to compare and contrast the two men since both were roughly contemporary and both lived in Alexandria. Yet Valens’ work elaborated the more practical techniques that arose from ancient tradition, while Ptolemy was more of a “modern” scientist, and tended to focus on creating a theoretically consistent model based on his Aristotelian interpretation of the Cosmos. Ptolemy’s model of the Cosmos persisted until the early 17th century. Deciding that the traditional Pagan religion (with all those sexually driven anthropomor- phic gods and goddesses) was useless, Valens found in fate a substitute religion. For him, absolute 68 pre-destination gave emotional satisfaction and aroused an almost mystical feeling of oneness with the Cosmos. Knowing that everything was already predetermined, apparently gave one a sense of freedom from anxiety (ataraxia or “unperturbedness”) and a sense of salvation. With such a view of Nature, we are not far from the Consolation of Philosophy by the late-Roman writer Boethius (480–524/525). In the 5th century AD, Latin encyclopaedias written for monks explain astronomy as, liter- ally, the “science dealing with the laws of the stars,” that is, lex astrorum.13 But these sources are not fully explained, and the significance might be that of the laws which the stars give to every man in fixing his fate, rather than that of the laws which the stars themselves had to obey in their eternal motions. So, we are no further forward. There is no clear distinction between astrology and astronomy until we get to the European Enlightenment, with even Isaac Newton being both an astrologer and an astronomer. Indeed, the idea of lex astrorum suggests that gravity is not only what keeps the stars in their courses, but also what carries astrological “influence.” Perhaps it was this later function that started Newton on his great quest for gravity. In short, there is no simple explanation or authority on the difference between astronomy and astrology other than one of personal belief in the influence of the stars on our fate, a fact that is emphasized when we consider how easily we make a Freudian lapsus when using the two words. 7.2 THE SEARCH FOR THE DIVINE LAWGIVER It is quite difficult to locate an exact moment when natural philosophers, savants, or magicians started using the term Law of Nature for a law or laws derived from observations of Nature, and which is considered to be inviolable; that is, a law which has absolute authority over all of us, and over our society. Archimedes (Figure 7.1) was probably the first to expound a Law of Nature, but he would probably have regarded what we call the law of the lever, as a principle rather than an inviolable law. But by the mid-18th century, the term Law of Nature was being widely used, cer- tainly as a result of the propagation of the Newtonian synthesis of mathematics, mechanics, and optics, although how many of those who used the term had much of an inkling of what it might mean is a moot point. Of course, there are the majestic lines of hymn, number 535 from the English Hymnal of 1796, Praise the Lord, for he hath spoken. Worlds’ his mighty voice obeyed; Laws that never shall be broken, For their guidance he hath made. 13 See Cassiodorus, Inst. 2, 7 and Isiodorus (Isidore of Seville), Diff. 2, 152. 7. THE LAWS OF NATURE7.2 THE SEARCH FOR THE DIVINE LAWGIVER 69 It is not entirely clear, however, if the author is here writing about God’s law as being a set of rules as given in the Bible, or a set of more fundamental rules stating how the Cosmos itself was to function. Such was the prestige of Newton in the late 18th century that this verse could just as well apply to the demi-god Newton, who had identified and presented to man a set of laws, or principles that he said were inviolable. Figure 7.1: The Fields Medal. This medal is awarded to those who achieve significant advances in mathematics (there being no Nobel Prize for mathematics), and it carries a portrait of Archimedes (c.287–c.212 BCE), as identified by the Greet text. The Greek natural philosopher was well ahead of his time in using the modern scientific techniques of observation, conjecture, and further confirmatory observations (and experiment) to understand the phenomena he saw around him. On the Equilibrium of Planes is a treatise in two volumes by Archimedes. The first book establishes the law of the lever, and locates the center of gravity of the triangle and the trapezoid. According to Pappus of Alexandria, Ar- chimedes’ work on levers caused him to remark: “Give me a place to stand on, and I will move the Earth.” The second book, which contains ten propositions, examines the centers of gravity of parabolic segments. The Latin phrase states: Transire suum pectus mundoque potiri (Rise above oneself and grasp the world). It is almost certain that the concept of a celestial lawgiver legislating for non-human, natu- ral phenomena goes back to the Ancient Sumerians. The Sun god, Marduk, was raised to central pre-eminence in Babylonian mythology about the same time that the sixth king of the First Dy- nasty of Babylon, Hammurabi (c.1810 BCE–c.1750 BCE), codified his society’s laws. We read how Marduk is he who prescribes the laws for the other gods, and it is he who fixes their bounds. Marduk is the lawgiver to the stars. It is he “who prescribes the laws for the lesser star-gods, Anu, Enlil and Ea and who fixes their bounds.” Marduk it is who “maintains the stars in their paths” by giving 70 “commands” and “decrees’” (from the Later Babylonian Creation Poem as given in Joseph Needham in Science and Civilization in China Volume II, P.533). Similar ideas of a supreme law-giving god may be found in Hindu literature; see the Rig Veda X, 121. Today, we know that it is the mass of the planetary and stellar bodies interacting with each other through the medium of gravity, which holds the stars in their courses; however, this idea of Isaac Newton is barely 300 years old, and received its latest refinement by Albert Einstein only a century ago. And although the ideas of Newton and Einstein are accepted by modern scientists as dogma, they are not widely understood. However, the concept of a primal lawgiving sky-god is still very much accepted by, perhaps, the majority of humanity. At an earlier period of scientific development and investigation, the pre-Socratic philoso- phers spoke about “necessity in Nature” but not about the “laws of Nature.” For example, Heraclitus (c.500 BCE) tells us that “The Sun will transgress his measures, otherwise the Erinyes, the bailiffs of Dike (Goddess of Justice) will find him out.’” Anaximander (c.560 BCE) also speaks of the forces of Nature paying fines and penalties to each other for slights and transgressions. But then is this not what the stories of Greek Mythology are really implying; that behind the lusty gods, goddesses, nymphs, and heroes whose stories are intended to instruct the unsophisticated, there was a complex philosophical picture about the nature of divine and human transgressions and actions. The Roman Stoics maintained, as did Zeno of Citium and Diogenes that Zeus, being immanent in the world was nothing other than universal law, an intelligent presence, or logos behind Nature—as with many ideas about the nature of the Monotheist god. Aristotle makes a separation between “positive law” which is obeyed by society, and “natural law.” In the Nicomachean Ethics (V, vii) we read “Some people think that all rules of justice are merely conventional, because whereas [a law of ] of Nature is immutable and has the same validity everywhere, as fire burns both here and in Persia, rules of justice are seen to vary.” Plato does use the phrase law of Nature in the Timaeus, but, unfortunately, he did not discuss the subject. It is the Stoics, particularly the domineering, law-conscious Roman stoics who developed the idea of a set of supreme natural laws common to all men, irrespective of their national or cultural heritage. One can see that just as the Babylonian idea of Laws of Nature grew out of a centralized, absolutist oriental monarchy or authority, so in the time of the Roman stoics, living within the world empire of Rome with its greatly increased centralization of power and of authority, it would be natural to view the Universe as a great empire ruled by a divine Logos, or intelligence. A supreme intelligence, which maintained the stars in their courses, and ruled the destinies of all men and of all empires. It is from the poet Ovid (43 BCE–17 AD) that we find the clearest statement of the belief in the existence of laws in the non-human world (in Pythagoras from Metamorphoses XV, 17). “What shakes the earth; what law the stars keep their courses under, and what so ever thing is hid from common sense;” that is, Pythagoras knew the laws according to which the stars move. Ovid does not hesitate to use the word lex (law) for stellar and planetary motions. In the Tristia, Ovid describes a supposed 7. THE LAWS OF NATURE7.3 A VERY DIFFERENT POINT OF VIEW 71 friend’s faithless behavior as being so appalling as to make rivers flow uphill, the Sun go backward, and all things proceed reversing Nature’s laws. Judaism, Christianity, and Islam are, of course, built on the idea of a single divine lawgiver. Perhaps it was during the Babylonian Captivity that the Jewish people came to adopt the idea of a single transcendent god. Certainly, it is with the Hebrew Bible that we first begin to glimpse a celestial lawgiver who influences both Nature and human society. “The Lord gave his decree to the sea, that the waters should not pass his commandment” (Psalm 104) and “He hath made them fast for ever and ever, he hath given them a law which shall not be broken” (Psalm 148). The problem with the monotheist view of natural laws, however, was that it quickly became identified with morality; human morality, particularly the do’s and don’ts of sex, as Saint Paul and Saint Augustine of Hippo inform us. Yet, even as late as the 4th century AD, the Christian apologist Arnobius of Sicca (died about 330) could argue that Christianity was not such a bad religion after all; as the adoption of Christianity by the Roman Empire had not changed the way the natural world worked. After all, the Sun still rose and the Moon still followed its traditional cycles. That is, that the Laws of Nature are implicit. The rotation of the stellar firmament, the cycles of the seasons had not altered with Constantine’s Edict of Milan of 313. Whatever was driving the Universe had little to do with the Christian religion; replacing Jupiter or Jove by God, Yahweh, or Allah in your affections did not change the visible world, it merely influenced your private life. 7.3 A VERY DIFFERENT POINT OF VIEW What of the idea of a celestial law-giver in the Orient? Following Needham (Science and Civiliza- tion in China, Volume II, P.554ff) we only need look at the Nei Ching which contains conversations between Chi Ni Tzu and Kou Chnen, the King of Yűeh in the late 4th century BCE. The king asks the sage about the origins of natural phenomena (he has already asked him about the forces that rule human society). “There are the Yin and the Yang. All things have their chi-kang [that is, their fixed position and motions with regard to other things]. (This chi-kang is what Needham translates as “Laws of Nature.”) The Sun, Moon and Stars signify punishment or virtue, and their change indicates fortune and misfortune. Metal, wood, water, fire and earth (the five elements of Classical Chinese thought; slightly different from the European quartet.) conquer each other successively; the Moon waxes and wanes completely. Yet these normal changes have no ruler or governor. If you follow it [heaven’s way] virtue will be attained; if you violate it there will be misfortune.” The Ancient Chinese viewed Nature as a great net, or vast pattern. There is a web of relation- ships throughout the Universe, the nodes of which are things and events. There is no ruler or gov- ernor. Nobody wove this great net; it is eternal, like the quantum mechanical view of the vacuum, but if you interfere with the texture of the net, you do so at your peril. The Ancient Chinese did not follow the Roman stoic’s love for celestial law-givers and law-enforcers. The Ancient Chinese did 72 not need the sense of security coming from the creation of an all-powerful, male deity who lived in the sky, who had a long white beard (a sign of wisdom according to Gnostic creation myths), and who would tell us all what to do and what to think; and of equal importance, what not to do, and who not to do it with. The idea that heaven does not command the processes of Nature to follow their regular courses is linked to the belief system and philosophy which we know today as Taoism, where, wu wei or non-action, or unforced action is central to the ways of heaven. The Tao of Heaven is a Ch- hang Tao, the order of Nature is an unvarying order, as was said by Hsűn Chhing in about 240 BCE, but that is not the same as affirming that anyone ordered it to be so. As Confucius (c.551 BCE–479 BCE) says in the Li Chi “The most important thing about [the ways of Heaven] is its ceaselessness... Without any action being taken, all things come to their completion; such is the Tao of Heaven.” There is a denial, if only an implied denial, of any heavenly creation or legislation. The heavens act according to wu wei; the Tao produces, feeds and clothes the myriads of things that compose our world, it does not lord it over them, and asks nothing in return. Back in Europe, it is not until the 17th century that savants or natural philosophers began to separate morality from the Laws of Nature, which were thought to be obeyed by animals, hu- manity... minerals, plants, chemical substances and planets alike. This separation could only have occurred with the advent of the Reformation, and the idea that there existed a “right of rebellion” against a supposedly un-Christian prince or authority. That is, a change in the worldview of Euro- pean man could not have begun until the absolutism of the pre-Reformation Catholic Church had been challenged and successfully broken by the Protestant Reformation; popes such as Alexander VI, Julius II, and Leo X were absolute “oriental” potentates. If it could be accepted that princes could act contrary to natural law, no matter how well or badly defined was that natural law, then a distinction could be made between natural or universal laws or authority, and man-made laws or authority. And, perhaps, in the case of man-made laws they should be more accurately termed as choices rather than as authority. Before the Reformation, the Christian world was in thrall to the greatest of Scholastic philosophers, Saint Thomas Aquinas. This Dominican friar and teacher envisaged a system of sets of laws: the lex aeterna, which governed all things for all time, the lex naturalis, which governed all men, and the lex positiva created by human legislators (-divina if canon law inspired by the Holy Ghost working through the church, and –humania, or common law laid down by princes and governments). Remarkably though, Johannes Kepler (1571–1630), who discovered the three empirical laws of planetary motion, one of the first occasions when Laws of Nature, or rules of observation were expressed in mathematical form, never referred to them as laws. Indeed, neither Galileo Galilei nor Nicolaus Copernicus (1473–1543) ever used the expression “Laws of Nature,” even though their work is the foundation of modern science. Perhaps, we see here the last vestige of the influence of the Roman Church on natural philosophers and the church’s desire not to separate the concepts of 7. THE LAWS OF NATUREuniversal laws and man-made (that is, church-sanctioned) laws for the governance of the Universe and society, respectively. Even Isaac Newton could not bring himself to totally decouple universal laws and society’s laws. 7.4 THAT FEARFUL PERFECTION 73 7.4 THAT FEARFUL PERFECTION But change was coming; the zeitgeist was moving in the direction of the creation of a God whose relationship to His creation could be examined. The Catholic heretic, Giordano Bruno, following Nicolas de Cusa (1401–1464), asserted that God was a perfect sphere. That is, the most perfect of solid (Platonic) bodies.14 Xenophanes of Colophon (c.570–c.475 BCE) was the first Classical philosopher to speak against the anthropomorphic nature of the gods, and spoke instead of a sin- gle transcendent god (“One god, greatest among gods and humans, like mortals neither in form nor in thought”). This perfect deity was conceived of as being a sphere. It was Plato who had told us that the sphere was the most perfect and uniform of all solid bodies; ideas that carried forward to dis- cussions of the shapes of atoms and molecules in the last century. For some Classical writers it was inconceivable that the transcendent god would not be spherical, because this shape was the best, or least inadequate to represent the Divine, the supernatural. But how did this abstract, geometrical image of God become established in the European mind? Alain de Lille (c1116/1117–1202/1203) was a French theologian and poet who studied and taught in the schools of Paris where he came under the influence of the philosophers and mystics attached to the Augustinian Abbey of Saint Victor. Alain was also influenced by ideas of material- ism, which could have condemned him to the flames; he wrote “God is an intelligible sphere, whose center is everywhere and whose circumference is nowhere.” This powerful, fearful image of the Divine sphere quickly became part of the European imagination. In Rabelais we read of, “that intellectual sphere, whose center is everywhere and whose circumference is nowhere, and which we call God” (Pan- tagruel). The mediaeval mind believed that God was in each of His creatures, but none of them limited Him, “The Heavens and the Heavens of the Heavens cannot contain thee” (1 Kings 8: 27). What better image for the Divine than the sphere? Nicolas de Cusa wrote in his De Docta Ignorantia (On Learned Ignorance) that, “Deus est absolutus;” no arguments or quibbles here. But he was following Saint Anselm of Canterbury (1033–1109), who gave us the first ontological proof of the existence of God, who said God is, “id cujus nihil majus cogitari possit” (something beyond which nothing greater can be envisaged). God can never fully be reached by the human intellect. One could say that invoking the geometric metaphor of the sphere that the relationship between our knowledge of God and our view of Nature is the same as that between a polygon made up of many (N) sides and the circumference of a circle. As 14 Interestingly, while Bruno was burned at the stake in Rome for such ideas, Nicolas de Cusa had gone on to be- come a Cardinal; evidently, the Middle Ages was a more easy-going time for cosmological speculation than the late Renaissance, but that difference was probably due to the intervening Reformation. 74 N increases, the polygon more closely resembles the circumference of the circle which may contain it, but they can never be commensurate. The circle cannot be squared. God is that circle (one slice through a sphere) whose center is everywhere, but whose circumference is nowhere. But whatever the difference in the disciplinary nature of the church for those who contem- plated the nature of God, between the end of the Middle Ages and the late 16th century, both Giordano Bruno and de Cusa demonstrated that there were no crystalline Ptolymeic Spheres between man and the Empyrean, where God was believed to dwell. There was just an immense, boundless emptiness filled with stars like our Sun. Bruno had finally overturned the Aristotelian model of the Universe by accepting the ideas of Copernicus. Before Copernicus and Bruno, when man looked into the heavens at the stars, he believed that he was looking inward toward God, toward the premium mobile as given in the cosmology of Dante, so wonderfully expressed in the Divine Comedy. After Bruno, when man looked at the stars, he looked into the depths of empty space, which Blaise Pascal (1623–1662) so eloquently and majestically told us terrified him, “Le silence Eternel des ces espaces infinis m’effraie” (Pensées 102), Dante thought that space was a cathedral containing God and man. Giordano Bruno, however, showed man that he was alone on a seashore looking out into the unknown. The Divine sphere, which contained all things, was fearful indeed. Giordano Bruno derived this geometric idea of the nature of God/the Universe from Nicolas de Cusa, who in turn had derived the idea from Alain de Lille. But from where or from whom did Alain de Lille get this idea? Interestingly, it seems as if the idea was derived from a 3rd century AD Corpus Hermeticum. That is, the idea of God as an infinite sphere filling the Universe, or if you like, by association, the Universe being an infinite sphere, an idea which made the Universe immense and homogeneous and removed man and his small planet from the central position assigned to them by theologians, came from Gnostic cosmology and the Hermetic writings which supposedly derived from the ancient Hellenistic-Egyptian magical writings of Hermes Trismegistus (see Page 55). That is, they date from Alexandria in Egypt and the 3rd century AD, but were supposedly an ancient tradition disappearing back into the mists of antiquity. In particular, from writings which derived from a secret or sealed, self-contained wisdom (Hermeticum) relating to alchemy, magic, and philosophy. Such an evolution of a science-like worldview evolving out of magic is not a unique event; it happened again in the 17th ventury. Such a change from magical to a more science-ori- ented worldview change can be thought of as the change from the use of a language of curiosity to a language of authority to describe the world within which we find ourselves. The next time this idea of spheres of infinite diameter, but with no ascertainable circumfer- ence, was heard of in the writings of the French mathematician, theologian, and philosopher Blaise Pascal who said that “Nature is an infinite sphere whose center is everywhere, whose circumference is no- where.” So, from Alain de Lille to de Cusa to Pascal, via Bruno, we have replaced God with Nature as being infinite. Not only has man lost his centrality from the Christian Cosmos, but even God seems to have got lost in this process. 7. THE LAWS OF NATURE7.4 THAT FEARFUL PERFECTION 75 The new feature of Bruno’s universe came from his blending of several philosophical ideas. The monk from Naples was attracted by the atomic theories of the Classical World, which had themselves been associated with the possibility of a plurality of worlds, formed by different combi- nations of the eternal, never-resting atoms passing in and out of various combinations. Bruno was also fascinated by the idea of Alain de Lille and de Cusa that the Universe had no center yet was infinitely vast. For Bruno, it was the Copernican system that best suited such an unbounded, infinite space, and also provided a model of planetary systems associated with stars extending away from us in all directions. In the same way that the mediaeval philosophers had developed a theology where God was infinite in all his attributes, Bruno correlated this infinite God with an infinite Universe, a physics of the infinite, which corresponded with a theology of the infinite. Bruno was only saying that the divine attributes of God be given physical meaning, just as Isaac Newton would do in the next century when he reconstructed God’s omnipotence in terms of an absolute space-time. Giordano Bruno had affirmed that the Universe was boundless and homogeneous, and that the same physical or natural laws would operate everywhere in this universe; this is still the standard view (dogma) of the physical sciences. Newton’s Universal Law of Gravitation is as valid on Earth as it would be in the Orion Nebulae, and Planck’s constant has the same value on Earth as it would have on a planet orbiting a star in a distant galaxy. Although Bruno does not use the phrase “Law of Nature” very often (he knew that the Holy Inquisition had their eyes on him), he did frequently refer to ratio (reason). He visualized the phenomena we see around us as a synthesis of freely de- veloping innate forces impelling an eternal growth and change. Bruno spoke of heavenly bodies as animalia pursuing their course through infinite space, believing in the Neo-Platonic ideal that both organic and inorganic entities and objects were in some sense animated. The anima constituted the ratio, or inherent law which, in contradiction to any outward force or constraint is responsible for all phenomena underlying motion. This was a very Taoist view of the Cosmos from a 16th-century Neapolitan Dominican friar. He may not have said it often, but Giordano Bruno said that God was to be found everywhere “... in inviolabili intermerabilique naturae lege..” (in inviolable laws of nature). This made Bruno a Pantheist as far as the church was concerned, although it did demonstrate that Bruno possessed a modern holistic, Taoist, or organic view of the character of natural phenomena. It was with the triumph of scientific rationalism of the 19th and 20th centuries that we move to definitively speaking about the Laws of Nature, and the advent of science as a language of au- thority capable of explaining the world around us, and the entire Cosmos. It could not be otherwise; we had removed God from our lives, and humanity wished to assume the divine mantle by showing that all Nature was subject to something that we had discovered and measured. We knew what was happening everywhere in Creation, because it happened in our laboratories here on Earth, partic- ularly, in the Cavendish Laboratories in Cambridge. Whereas to speak of rules or propositions of Nature would have been humbler, triumphalist scientists, however, wished to say that science (and by implication, the scientist) was omnipotent. 76 We are now at the position to ask why, after such a long period during which the Laws of Nature were viewed in Europe as a theological commonplace, they did attain such a position of central importance in the society of the late 17th century? For example, Pope’s epitaph for Isaac Newton in Westminster Abbey, quoted at the beginning of this chapter could not have been written for an earlier savant or natural philosopher. How was it that in the early-modern world, the idea of God’s sovereignty over the Cosmos shifted from the exceptions in Nature (comets which so terrified the mediaeval, and not so mediaeval mind) to unvarying, absolute, unbreakable rules? The answer is probably to be found in the political changes that were taking place in the wider society of this time. What was it that could lead men to look to an absolutist centralization of power over the Universe? Almost certainly a slow, but inevitable, seepage into Nature of man’s conception of an earthly ruler and his sovereignty. Perhaps with the decline in feudalism, and the rise of the capitalist mercantile state with a single central Royal Authority (Henry VIII or Elizabeth I), coupled with a widespread decline in the power of the aristocracy, and an increasing isolation of the monarch as absolute; best demonstrated by that most absolute of monarchs, Louis XIV of France. Perhaps it is no coincidence that the Cartesian idea of God as the supreme legislator for the Universe devel- oped during the lifetime of Thomas Hobbes (1588–1679), “Nature (the Art whereby God hath made and governs the World)” (Introduction to Leviathan, 1651). Thus, an idea which originated in early Bronze Age Mesopotamia of absolute oriental despotism, was preserved and evolved over three millennia to awake to new vigour in the world of early-capitalist absolutism. 7.5 FURTHER READING The Social Origins of Modern Science (Boston Studies in the Philosophy and History of Science) by Edgar Zilsel (2000); Boston, Kluwer Academic Publishers. The Grand Titration: Science and Society in East and West (1969), Joseph Needham; London, Routledge. In the sections of this present work, where I discuss Ancient China I, will be making use of the magisterial Science and Civilization in China (published 1956, re-published 1975), Joseph Needham; Cambridge, Cambridge University Press. In this chapter, I make reference to Volume II of this multi-volume work: The History of Scientific Thought. 7. THE LAWS OF NATURECHAPTER 8 Measuring the World 77 …une entreprise [the Metric System] dont le résultat doit appartenir un jour au monde en- tier. Charles-Maurice de Talleyrand-Périgord (1754–1838) One of the biggest changes to affect the lives of Europeans in the 16th century occurred in Febru- ary 1582, when Pope Gregory XIII reformed the solar calendar. This long-needed change should have been instantly accepted throughout the Christian world, but as the Reformation had already splintered Christendom, various nations adopted the new calendar in a piecemeal manner, based on national politics and religious sentiments, with England not adopting the changes until 1753. Russia only adopted the change in 1917. The new Gregorian calendar, named in honor of Pope Gregory XIII, was introduced because the old Julian calendar, introduced by Julius Caesar more that 16 centuries earlier, had made the solar year slightly too long. With the passage of the centu- ries, this accumulated additional time had become significant and had caused a drift of the seasons, which given the primordial place of agriculture in European society had lead to serious problems. In the Julian calendar, all years exactly divisible by four were leap years. To remedy the trend in the distortion of the solar calendar arising from the imprecision of the Julian calendar, an Italian savant Aloysius Lilius (1510–1576) devised a new calendar with new rules: Every year that is exactly di- visible by four is a leap year, except for years that are exactly divisible by 100, but the centurial years that are exactly divisible by 400 are still leap years. The changes proposed by Lilius corrected the drift in the civil calendar, but it was still nec- essary to delete ten days to bring the calendar back into synchronization with the seasons. This deletion of ten days lead to considerable consternation in Christendom, as ordinary people believed that the church, and the savants and natural philosophers who advised the Church were stealing ten days of their lives.15 The 16th century was also notable for the widespread introduction of a new idea to simplify everyday arithmetical operations; something that also impinged upon the lives of nearly everyone. That is, the use of decimal numbers (numbers to the base ten). In 1584, the Flemish engineer and surveyor, Simon Stevin (1548–1620) published a set of tables for the calculation of the amount of 15 And even when the new calendar was finally introduced into Great Britain in 1753 (when because of English procrastination it was now necessary to delete eleven not ten days of the year), there was similar popular anger. These events lead to a distinctly anti-science, or anti-expert, attitude in the UK, which persists to this day. 78 interest that banks would charge for lending money at various rates over various periods of time. As he was preparing these tables, Stevin realized that decimal numbers would greatly simplify calculations in every area of life. Consequently, in 1585, Stevin published De Thiende (Of Tenths) in Flemish and La Disme (The Tenth) in French. These were the first books where the simplicity of decimal numbering was fully explained and demonstrated. Thus, the invention of decimal arithme- tic is usually attributed to Simon Stevin, who, in addition to assisting people to understand how much interest they were paying to bankers, also found time to use his skill as a mathematician in the design a more efficient type of windmill, which was able to drain land more effectively, and so permitted the creation of the Netherlands. However, it was in Italy that the greatest scientific advances were being made in the 17th Century; scientific advances that would have a profound effect upon the science of measurement (metrology). The Italian mathematician, astronomer, and savant Galileo Galilei enjoyed daydream- ing in church. While attending Mass in the Cathedral of Pisa, he allowed his attention to wander from the Liturgy, and it was while contemplating the swaying motion of the heavy chandeliers suspended by long, fine chains from the high ceiling that he formulated several ideas about the pendulum. Galileo went on to conduct detailed experiments on pendulums, and eventually deter- mined the length of a pendulum swinging through its arc in exactly one second in Pisa. This became known as a seconds’ pendulum. It was subsequently shown that the seconds’ pendulum varied in length according to where it is on the Earth’s surface. For example, at the Equator the seconds’ pen- dulum is 991.00 mm in length, and at 45° north of the Equator it is slightly longer at 993.57 mm, this difference arising because of variation is the local value of gravity. The detailed study of the motion of a pendulum undertaken by Galileo made this humble object, a heavy mass attached to the end of a long piece of string, the world’s first precision measuring device. It also lead to ideas of occult magic being attached to the pendulum; primarily, but not wholly by Neo-Platonists; as it revealed characteristics of the invisible, hidden, and Hermetic part of Nature—the mysterious force of gravity. The pendulum is a simple measuring device. The period, T, in seconds of a pendulum of length, L (in meters) is given by T = (2π/√g) √L, where g is the local value of the acceleration due to gravity. The value of g varies by a few percent over the surface of the earth, and the pendulum is a sufficiently precise device that it is capable of determining the spatial variation of g (approximately, ). This relatively simple relationship yields the approximation, T = 2 √L. Thus, the period 9.806 m.s of oscillation of a pendulum is independent of the mass of the bob of the pendulum. This surprising finding from the 17th century linked the pendulum, in the imaginations of Occultists and those interested in the Hermetic arts with some, as yet undiscovered level of existence; which could well be the much sought-after link between the physical world and the world of the spirit. -2 An interesting aside on the presentation of decimal numbers, and one which has still to this day not been resolved, is the nature of the decimal marker. In 1615, John Napier (1550–1617) the 8. MEASURING THE WORLD8. MEASURING THE WORLD 79 Eighth Laird of Merchiston, Scotland, a mathematician, astronomer, and well-respected occultist and astrologer, used a comma as a decimal marker to separate the whole number part from the decimal number part of numbers in his book of multiplication tables Rabdologia. Here, Napier was following an idea put forward by the Frenchman François Viéte (1540–1603) who suggested that the comma be used as a separatrix between the whole number and the fraction. Unfortunately, for the scientific community, Napier later changed his mind, and replaced the comma as the decimal marker with the full stop. This change from the comma to the full stop as the decimal marker is still with us today. In the English-speaking world, the decimal marker is the full stop, but in the French-speaking world and in Continental Europe, the decimal marker is the comma. This confu- sion has become an unresolvable cultural identifier. We saw in Chapter 3 that in 1668 John Wilkins published An Essay Toward a Real Character and a Philosophical Language. Wilkins’ long essay included a four and a half page description of a proposed system of measurements based upon his idea for a single “universal measure” that could be used to define length, weight, volume, and money. John Wilkins suggested a decimal system of measurement, with a universal standard of length based on time and derived through the use of a swinging seconds’ pendulum, and that this standard length could then be used to define area, volume, and weight using a well-defined volume of pure, distilled rainwater. Wilkins’ Essay is the first description of a complete system of measurement intended to be used by all nations. Indeed, Wilkins’ proposal contained almost all of the essential elements of the Metric System of 1795, which could quite reasonably therefore be said to have originated in England in the 17th Century and not in France during the late 18th century (please note that national chauvinism is particularly strong in this debate). Following John Wilkins’ first description of an international system of measurement, the development of the decimal metric system of measurements was inevitable even though Wilkins himself was not confident of its success. Wilkins wrote about his plans for a universal measure, “I mention these particulars, not out of any hope or expectation that the World will ever make use of them, but only to show the possibility of reducing all Measures to one determined certainty.” Following the publication of John Wilkins’ essay, savants in several countries took up and promoted his ideas. The zeitgeist was waiting for this concept of a single system of units or weights and measures (and money) based on a single natural dimension. In 1670, Gabriel Mouton (1618–1694), a French cleric and astronomer, promoted a system of measurement that was to be based upon the physical dimensions of the Earth; rather than a measurement based on the length of a seconds’ pendulum, or one or other measurements of a human (all be it, Royal) body. Gabriel Mouton assumed that the Earth was a perfect sphere, and so a section along a Me- ridian would be a circle. Mouton proposed that this “great circle” should be divided into ever smaller angles, and that these small angles could be used to define a new system of measurement. What was also proposed was that the division of these angles should be made using decimal arithmetic; that 80 is, division by ten, rather than the old Babylonian sub-divisions of an angle based on arithmetic to the base 60 (an angle being divided into 60 min and each minute into 60 sec). Mouton suggested that a minute of arc along a Meridian be measured and defined as a unit of distance called a milliare; a linear distance that subtended this angle. The Abbé Mouton also suggested dividing the milliare into centuria, decuria, virga, virgula, decima, centesima, and millesima by successively dividing by fac- tors of ten. In short, Mouton suggested that Simon Stevin’s 1585 decimal system of tenths should be used to divide the Earth-based angular units into ever smaller parts. Interestingly, Abbé Mouton’s milliare is the modern definition of a Nautical Mile (that is, one minute of arc of Latitude along any Meridian), which given the importance of maritime trade to the world’s major powers accounts for the longevity of this system of measurement. Mouton’s virga would be one thousandth of a minute of arc, which would be about 1.11 m in today’s Met- ric System. In the same way that Wilkins suggested using a seconds’ pendulum beating 1 second, and hence having a length of about one meter, to define the universal measure of length, Mouton suggested using a shorter pendulum to measure the virgula (a tenth of a virga), or 0.111 m. A pendulum of this length would be beating or oscillating every 0.66 sec. However, the theoretical models of Wilkins and Mouton demonstrated that to make prog- ress in defining more precise units of measurement; that is, establishing a universal system of mea- surement to assist in the progress of science and society, one needed accurate measurements of our planet. Was the Earth a sphere, or not; and if not, what was the eccentricity of the planet? One of the first surveyors who undertook the task of precisely determining the curvature of the Earth was the founder of a dynasty of French mathematicians and astronomers, Jacques Cassini (1677–1756) who made measurements of the Earth based on minutes of arc. With his son, César-François (1714–1784), Jacques Cassini surveyed a portion of the Arc of the Meridian from Dunkirk on the coast of northern France to Barcelona in Spain; this is a line from Pole to Pole passing through Dunkirk and Barcelona. This particular Arc of the Meridian also passes through Paris (the Paris Observatory was built on the Meridian line in Paris) and is therefore called the Paris Meridian, and it would be surveyed many times over the following century. These repeated measurements of ever-increasing precision would finally yield the first standard meter, which is still preserved in Paris (the task would be completed by Jacques’ grandson Jean-Dominique, 1748–1845). 16 16 The Paris Meridian is not our present line of zero Latitude. The Prime Meridian runs through the Greenwich Royal Observatory, and so it is at Greenwich and not Paris that the world is bisected and the zero of Latitude established. This move to a Greenwich-based view of the world was decided by an international conference in 1884 (International Meridian Conference 1884, Washington DC,); and, as one can imagine, this move pleased the British, then at the zenith of Empire, and greatly displeased the French. Modern satellite measurements of the geographical coordinated of the Paris Observatory show how much the Meridian had been shifted by global geopolitics; the Paris Observatory is at 48°50’0’’N 2°21’14.025’’E. The Greenwich Royal Observatory is at 51°28’40.12’’N 0°00’0.5.31’’W. By using the Abbé Mouton’s system of units (given above) one can see how little the Meridian changed geographically, but the political repercussions where tremendous. The French did not begin to accept the 1884 change until after World War II. 8. MEASURING THE WORLD8. MEASURING THE WORLD 81 Between 1735 and 1737, the explorer, geographer, and mathematician Charles-Marie de La Condamine (1701–1774), the astronomer Louis Godin (1701–1780), and the naval architect, mathematician, astronomer, and geodesist Pierre Bouguer (1698–1758) measured an Arc of a Me- ridian in Peru where they also made equatorial measurements of the local value of the acceleration due to gravity (g). In addition, they returned to Europe with the first detailed map of the Amazon basin. And between 1739 and 1740, the astronomer Nicolas Louis de Lacaille (1713–1762) who had started his career in the church, but then moved to astronomy, together with Jacques Cassini again measured the Dunkirk-Barcelona Meridian. The northern and southern ends of the surveyed meridian were the belfry in the center of Dunkirk and the fortress of Montjuïc in Barcelona, respectively. Apart from defining the dimension of the universal measure or meter, these early surveyors refined the value of the Earth’s radius, and definitively established that the shape of the Earth is oblate or slightly flattened near the North and South Poles, which had been predicted by Isaac Newton. This observation lead to the Enlightenment cult of Newton as Universal Genius (see Figure 8.1). Figure 8.1: A medallion struck in Paris in 1840 to mark the final introduction of the Metric System in France, and to act as a souvenir to posterity of the manner in which the meter was determined in 1799 by a measurement of distance; the allegorical figure is measuring one quadrant of our planet. The reverse side of this medallion bears Condorcet’s famous rallying call for the Metric System, A TOUS LES TEMPS: A TOUS LES PEUPLES. This image is reproduced with the permission of the BIPM (https://www.bipm.org/en/about-us/), which retains full international copyright. While the French were surveying Latin America and Europe, the British finally got around to accepting the Gregorian calendar. Part of the reason given for the UK’s decision to finally adopt the Gregorian reforms to the Julian Calendar, and the necessary change in the date of the beginning of the new year, was the difficulty of calculating interest on loans which were outstanding. It was 82 noted, “…[the comparison of the date in England compared with the date on the Continent was] attended with divers inconveniences, not only as it differs from the usage of neighboring nations, but also from the legal method of computation in Scotland, and from the common usage throughout the whole king- dom, and thereby frequent mistakes are occasioned in the dates of deeds and other writings, and disputes arise therefrom…” And in 1753, the New Year in Britain actually began on January 1st rather than March 25th, to bring it into line with the rest of Europe because Great Britain (and the British Colonies, including America) began to use the Gregorian calendar (New Style or N.S.) rather than the Julian calendar (Old Style or O.S.).17 As the 18th century drew to its close, two political events occurred which would have a pro- found influence upon the nature of the various systems of weights and measures still used through- out the world today. In North America, the British colonists decided that they did not need to pay the government in London for protection against the French, Spaniards, and Native Peoples. The rebellion of these colonists was successful, and by 1791 a new nation was born, which was using the same system of weights and measures as they had inherited from England. But would they wish to continue using this system? In Europe, the major political event of this period was the bankruptcy of the Kingdom of France, and the collapse of the nation into the French Revolution of 1789. History tells us that systems of weights and measures are mostly reformed or changed during, or just after, major political upheavals. Well before the Revolution of 1789, everyone in France knew that the systems of weights and measures in France were tangled, convoluted, complex and an invitation to fraud, but no one thought that there was much to be gained by reform. Why re- form the system, it was only the ordinary people who suffered adversely from the complexity of the various systems of weights and measures, whose local variations were maintained for the personal advantage of the local aristocrats and church leaders. At the time when the French economy was beginning to industrialize in response to similar developments in England, which essentially had a national system of weights and measures by this time, France was unable to compete as it did not have any means of standardising and automating manufacture. In England, factories could out-pro- duce manual manufacture, because there was uniformity of measurement and standardisation of production based on the inch and the pound. The, as yet unborn, U.S. sent ambassadors to France, which was actively helping them in their struggle against Britain. Thomas Jefferson (1743–1826) served as Ambassador to France where he 17 Any reader of the letters of the Fourth Earl of Chesterfield to his sons will have remarked that the Earl of Ches- terfield was always fastidious in noting whether he was using the Old Style notation for dates, or the New Style notation when dating his letters. But then the reason why the Earl of Chesterfield paid so much attention to the change in calendar was because he was responsible for the change. The Calendar Act (also known as Chester- field’s Act) of 1753 made provision to ensure that monthly or yearly payments would not become due until the dates that they originally would have fallen due under the old Julian calendar. For this reason the UK tax year continued to operate on the Julian calendar and begins on the April 5th, which was the Old Style date for the New Style tax year that began on March 25th. 8. MEASURING THE WORLD8.1 DEFINING THE SIZE OF THE WORLD 83 was in regular contact with British and French savants as they formed their ideas about new, more natural systems of units of measurement for science and for society. Similarly, Benjamin Franklin (1706–1790) signed an alliance between France and America, but although the primary objective of this alliance was the raising of funds for the war against Britain, Franklin did not see any reason why he should not take the opportunity of this alliance to promote the cause of science. And it was from this exchange of ideas that the political leaders in America began to consider the best system of weights and measures for their young nation, which would ensure that they were able to com- pete effectively and independently on an international stage, and not be tied in any way to Britain. For example, in 1786, five years before the American Colonies gained their independence Thomas Jefferson proposed that the new nation adopt a decimal system for their currency. The Continental Congress established the silver dollar as the basis for decimal coins, although it was not minted until after independence in 1792. At the same time, Thomas Jefferson independently proposed a system of weights and mea- sures very similar to the proposed French decimal Metric System. He differed from the French in that he wanted the meter to be defined by the length of a pendulum that beat a second rather than surveying the surface of the Earth. Jefferson rightly reasoned that other countries could then readily duplicate such a standard at any time; thereby laying the foundations for a truly international sci- ence. Jefferson did not particularly like the idea that the meter would be based on a series of surveys made on French territory. Unfortunately, it was at this time that detailed measurements showed by how much gravity varied over the surface of the Earth, and the swinging pendulum definition for the universal measure of length was losing widespread support among savants. During his period as Ambassador to France (1785–1789), Jefferson visited London in 1789. While in London, the political situation in France deteriorated, and to avert bankruptcy King Louis XVI convened the États Généraux or States-General for the purpose of imposing new taxes on the nation. The États Généraux was a meeting of the three “states” or groups of people who were seen as constituting the nation: the First State was the clergy, the Second State was the nobility and the Third State was the bourgeoisie. The urban workers and the peasants were rather left out of things. 8.1 DEFINING THE SIZE OF THE WORLD Shortly after the fall of the Bastille in July 1789, but long before political stability was re-estab- lished throughout France, the science commission of the Académie des sciences in Paris recom- mended a measurement of the new standard of length, the meter, based on a detailed survey along the meridian arc extending from Dunkirk to Barcelona, which had already been surveyed and measured by de Lacaille and César-Francois Cassini in 1739. The commission calculated that if they could measure a significant piece of the Meridian, the rest could be estimated. Both ends of the line to be surveyed needed to be at sea level, and as near to the middle of the Pole-to-Equa- 84 tor Quadrant as possible to eliminate errors. Fortunately for them, the only one such meridian on Earth is about a tenth of the distance (about one thousand kilometers) from the Pole to the Equator and it runs through Dunkirk and Barcelona, so most of the distance to be surveyed lay conveniently inside France, a fact that did not escape the more nationalistic attention of observers such as Thomas Jefferson. Condorcet appreciated the potential for such nationalist views when he wrote “The Academy has done its best to exclude all arbitrary considerations—indeed, all that might have aroused the suspicion of its having advanced the particular interests of France; in a word, it sought to prepare such a plan that, were its principles alone to come down to posterity, no one could guess the country of its origin.” The Leg- islative Assembly endorsed the proposal from the Académie des sciences, directed that the detailed survey be made as soon as possible, and enacted the necessary legislation on March 26th, 1791. Although the Académie des sciences finally chose that the meter would be exactly a ten mil- lionth of the distance between the North Pole and the Equator, their choice also defined this distance as being precisely 10,000,000 m. Unfortunately, an error was made in the commission’s initial estimation, because the wrong value was used in correcting for our planet’s oblateness. We now know that this Quadrant of the Earth is actually 10,000,957 m. One should never forget that these savants were not only setting out to create what they saw as a new fundamental system of units based on the dimensions of the Earth, but they were also imposing models and views about the character of the Earth. In 1791, a handful of French Enlightenment mathematicians, guided by the writings of Isaac Newton, imposed a definite shape and size to our planet. The Earth shrank, and became precisely known. The Académie des sciences presented humanity with a fait accompli. The medallion shown in Figure 8.1 was struck to commemorate this standardization of the Earth. 8.2 OTHER SURVEYS The European Enlightenment had come up with the idea of constructing a new decimal metrol- ogy based on a single measurement of length. Such ideas, however, have a long history, and it is to Ancient China that we must turn for the first consistent use of decimal weights and measures; particularly, in the decrees of the first emperor, Chin Shih Huang Ti in 221 BCE. Also, given the size of China, it is perhaps not surprising that an early effort was also made in fixing terrestrial length measurements in terms of astronomical measurements or observations. It was an early idea of Chinese savants, going back before the time of Confucius (551–479 BCE), that the shadow-length of a standard height (an 8-ft gnomon), at the summer solstice increased by 1 inch for every thousand li (a length measurement equivalent to 1,500 chi or Chinese feet) north of the Earth’s “center,” and decreased by the same proportion as one went south. This rule of thumb remained current until the Han Dynasty (205 BCE–220), when detailed surveying of the expand- ing Chinese Empire showed it to be incorrect. But it was not until the Tang Dynasty (618–907) 8. MEASURING THE WORLD8.3 FURTHER READING 85 that a systematic effort was made to determine a range of latitudes. This extensive Tang survey had the objective of correlating the lengths of terrestrial and celestial measurements by finding the number of li that corresponded to 1° of polar altitude (that is, terrestrial latitude), thereby fixing the length of the li in terms of the Earth’s circumference. This Chinese meridian survey takes its place in history between the lines of Eratosthenes (c. 200 BCE), and those of the astronomers of the Ca- liph, al-Ma’mūm (c. 827), but more than 1,000 years before the French metric survey of the 1790s. The majority of these Chinese surveying measurements were undertaken between 723 and 726 by the Astronomer-Royal Nankung Yüeh and his assistant, I-Hsing, a Buddhist monk. The survey was carried out at 11 sites along a meridian running from the Great Wall in the north to Indo-China in the south, a distance of 7,973 li or about 2,500 km. The main result of this field work was that the difference in shadow length was found to be close to 4 inches for each 1,000 li north and south, and that the terrestrial distance corresponding to 1° of polar altitude was calculated to be 351 li and 80 bu (the bu was a measure of between 5–6 chi). The imperial surveyors had achieved their goal of defining a terrestrial unit of length, intended for use throughout the empire, in terms of the dimensions of “Heaven and Earth,” that is, 1/351 of a degree. This survey is today practically unknown, yet it represents an outstanding achievement given the spaciousness and amplitude of its plan and organization, and represents one of the earliest uses of advanced mathematics which was needed to compute the final result. These results were known in 18-century Europe, as they were commented upon by Leonard Euler and later by Pierre Simon in distance, de Laplace. While the metric survey obtained a routine precision of about 1 part in 10 . The Tang value of the much earlier Chinese survey could boast only of a precision of 1 part in 10 the li gives a modern equivalence of 323 m, but the earlier standard Han li is very different at 416 m. 3 6 8.3 FURTHER READING These books provide a readable background to the origins of the modern metric system. 1 Defining and Measuring Nature: The Make of all Things (2014); Jeffrey H. Williams; San Rafael, CA, Morgan & Claypool. This work contains an explanation of the recent redef- initions of several of the base units of the modern metric system. 2 3 Le nombre et la mesure : Logique des classifications métriques et prémétriques (1980); Franck Jedrzejewski; Diderot multimédia (in French.) The Measure of All Things: The Seven-Year Odyssey that Transformed the World (2002); Ken Alder; London, Abacus, an imprint of Little, Brown Book Group. This work describes in enjoyable details the problems of the two French surveyors who determined the value of the universal measure, or meter in Revolutionary France during the 1790s. CHAPTER 9 87 Dividing Apples with Oranges to Make the Language of Science In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei (1564–1642) Having looked at the evolution of the scientists’ worldview, that is, how science compartmenta- lises and classifies the phenomena and things we observe in the world, let us now turn to how the quantitative is introduced into this classification. After all, science would be nothing but magic without a means of quantifying as well as qualifying what we see around us. We have only words and numbers, the universal currency of humanity to interpret, describe, and record the wonders of Nature. Our various vernacular languages have evolved with our on-going, never-ending study of Nature; indeed, one could say that languages have created man, rather than man having created languages. The worldview of modern science has evolved by specialization of the basic language used to describe natural phenomena, but few understand what has become a highly specialized language. It has become a dialect of an elite. An elite as separate from the general mass of society, as any caste of priests. Previously, we saw something of the ideas of John Wilkins for a universal philosophical lan- guage, capable of being understood by all humanity. By the end of the 17th century, such ideas of a rational universal language were very much part of the European zeitgist. In 1666, the German polymath Gottfried Wilhelm Leibnitz published his Dissertatio de arte combinatoria in which he claimed that a proper or true philosophical language would be able to analyze all possible concepts into their simplest elements, into what Leibnitz termed “the alphabet of thought” (see Page X?). In such a philosophical or, as we would say today, scientific language, a proper symbol should indicate the nature of the animal, phenomenon, or whatever it was naming. In other words, it was a language which could define that thing, or that phenomenon by means of that thing’s appearance, or that phenomenon’s intrinsic properties. Leibnitz’s theoretical proposition presupposed that: (i) ideas can be analyzed into primitive notions or components; (ii) ideas can be represented symbolically; and (iii) it is possible to represent the relations between these ideas. Gottfried Leibnitz was writing in a century which had attempted the construction of many universal philosophical languages, and so presupposed that a complete enumeration of human knowledge could be achieved. The ques- 88 tion then arises as to how a relatively small number of fundamental primitive components or base units could be manipulated or combined to produce a true universal scientific language capable of describing all Creation. The philosophical languages of the 17th century attempted to reform natural languages by simplifying the complex, multiple meanings of some words and concepts. Consider an attempt at learning the definitions of all the words in a dictionary, or of attempting to comprehend all aspects of a discipline of science. In the dictionary, you will find every word defined in terms of other words; in the scientific discipline, you will find explanations involving other scientific terms. In your deter- mination to learn the meaning (or meanings) of every word, you may find that you need to consult the definitions of the words employed in the definitions of other words. Indeed, you soon realize that your initial attempt at learning the meaning of each word in the dictionary is futile. In fact, it is a circular task, because the dictionary contains only a closed set of words, finite in number, that enable descriptions of the meanings of each other. If you do not already have in your mind a set of basic words whose meanings you know independently, without the need of words to define them, you will remain forever in a continuous circular loop with your dictionary; and the same goes for seeking to learn a new scientific discipline. For this reason, the philosophical languages of the 17th century did not reform and simplify English, but they did give us the thesaurus. At the time of the French Revolution, savants who were familiar with the ideas of Wilkins assumed that the new fundamental unit of length, the meter, could be used to define all the scien- tific and technological concepts required by their society. This meter, or universal measure, was to be defined from the dimensions of the Earth, as one ten millionth of a quadrant running from the North Pole to the Equator. This universal unit of measurement may be thought of as a semantic prime of the new language of science. In fact, it is one of the seven base units, or semantic primes of the International System of Units (SI), which is the modern scientific version of the metric system of 1795; see Figure 9.1. [1]18 Having defined the basic unit of length, l, to define an area, a two-dimensional quantity, you simply multiplied two distances, that is, l.l = l2 . Similarly, when we go to three spatial dimensions to define a volume, we write algebraically l.l.l = l3 . Then, assuming that the density (that is, the mass of a known volume of a substance) of, for example, pure water is taken to be well defined as one gram for each cubic centimeter, one can define a base unit of mass as the weight of a precisely known volume of pure water. The kilogram was originally defined as the mass of 1,000 cubic centimeters or 1,000 cm , that is, one liter. 3 18 SI stands for Système international des unités, the French name for this set of units; in all matters relating to the metric system, French is the only official language. This point is rarely born in mind by English-speaking nations; but as is pointed out in Chapter 14, politics and science do not always sit well together. 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE 89 Figure 9.1: Medal commemorating the centenary of the Meter Convention of 1875, manufactured by R. Corbin, Monnaie de Paris. This face of the medal represents the seven base units of the SI (meter, kilogram, second, ampere, kelvin, mole, and the candela), and how the meter is defined in terms of the wavelength of light (in 1975 this was via the red light from a krypton discharge lamp) rather than by an artifact. This image is reproduced with the permission of the BIPM which retains full international copyright (https://www.bipm.org/en/about-us/) . But what happens when we wish to consider the combination of the universal measure of length with other quantities which are essential, in even some of the simplest ideas and concepts of technology, for example, how does one introduce time, the basic unit of which is the second into a system of mechanical quantities? [2]19 The speed, or velocity, of a planet flying through space, or of an ox ploughing a field, is de- fined in terms of distance and time; yet, how do we combine these two different base units? One might think of these two quantities as being as different as apples and oranges, so how can they be divided or multiplied together when they certainly cannot be added of subtracted? It is possible to mix and manipulate dimensions of distance and time, to divide or multiply meters and seconds, or even furlongs and fortnights. It is the mathematical definition of a unit that allows us to ma- nipulate distance and time, and generate new ideas such as the concept of speed or velocity, and of acceleration which is speed or velocity per unit time. First, consider what we mean by a unit. Any value of a physical quantity, Q, may be expressed as the multiplied product of a unit [Q] and a 19 The second is a base unit of the SI, and is the oldest measured quantity having been defined about 5,000 years ago by the Ancient Sumerians. 90 purely numerical factor (that is, a simple number). Written algebraically, we have Q = (a number). [Q], where [Q] is the unit, for example, meters or seconds, and there are a certain number of these meters or seconds; for example, Q = 10 meters or Q = 10 seconds. length time This convention of expressing a quantity as a unit and a numerical factor is used throughout science and is referred to as quantity calculus. When units are being manipulated, one may only add like terms, as with apples and oranges, but all units may be manipulated algebraically. When a unit is divided by itself (that is, meters/meters or seconds/seconds), the division yields a dimensionless number, which is one (1) and so intrinsically without dimension or unit. When two different units are multiplied or divided, the result is always a new unit, referred to by the combination of the indi- vidual units. For instance, in the SI, the unit of velocity is meters per second; that is, meters/seconds . This new unit is neither length nor is it time, but length divided by time. When or m/s or m.s dividing length by time, one is only dividing the numerical factors, which appear before the unit. The two original units are distinct, and cannot be divided but are left as a new unit, meters divided by seconds. Length and time are base units, but the new unit of speed, or velocity is said to be a derived unit, and may be deconstructed into base units. Likewise, density is defined as the mass of a known volume of something, or mass per unit volume. This derived unit is composed of two base units, the base unit of mass (kilogram) and the base unit of length (meter), which as we are dealing with a volume is cubed. Again, we have divided two base units together to create something new. -1 When the metric system was first introduced in April 1795, there were two base units, the meter and the kilogram; the second was already part of the social fabric. As science and technol- ogy advanced in the 19th century, the new profession of scientist (first defined in revolutionary France—scientifique) understood how the various manifestations of, for example, heat and work were all related to the concept of energy, and how this idea related to the established base units of length, mass and time. In fact, today we have seven base units which may be combined to explain every known scientific phenomenon, and which would be used to comprehend scientific discov- eries that have yet to be made. That is, it is through these seven base units that the true universal language, the language of authority that is science is formulated. By convention, all physical quantities are organized into a system of dimensions. Each of the seven base quantities used in the modern SI is regarded as having its own dimension. The symbols used for the base quantities or base units, and those which are used to denote their dimensions are given in Table 9.1. All other quantities, all the phenomena known to modern science are derived from these seven base quantities using the well-established equations, or Laws of Nature and are called derived quantities. As outlined above, the dimensions of the derived quantities are written as products of 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE9.1 CREATING EXPRESSIONS IN THE LANGUAGE OF SCIENCE 91 powers of the dimensions of the base quantities using the equations that relate the derived quan- tities to the base quantities.20 Table 9.1: Base quantities and their dimensions, and the base units of the SI Base Quantity Length Symbol of Base Quantity l Dimensional Symbol* L SI Base Unit Meter Symbol of SI Base Unit m Mass Time Electric current Temperature Amount of substance Light intensity * The dimension of a physical quantity does not include magnitude or units. The conventional symbolic rep- resentation of the dimension of a base quantity is a single uppercase letter in Roman (upright) sans-serif type (these specifications are part of the dogma of science [1]). Kilogram Second Ampere Kelvin Mole Candela kg s A K mol cd M T I Θ N J m t i T n I 9.1 CREATING EXPRESSIONS IN THE LANGUAGE OF SCIENCE Dimensional analysis, or the manipulation of quantity calculus is a powerful tool in understanding the properties of physical quantities, independent of the system of units used to measure them. Every physical quantity is some combination of the base units in Table 9.1, for example, speed, which may be measured in meters per second (m/s) or miles per hour (miles/h), has the dimension L/T, or L.T−1 , and pressure which is a mass pressing down on an area (as in pounds per square inch) is M/L2 . Dimensional symbols and exponents are manipulated using the rules of algebra; for example, the dimension of area is written as L2 (meter per second), the dimension of acceleration (the rate of change of velocity with respect to time) is writ- ten as L.T-2 (meter per second squared; that is, meter per second per second), and the dimension of density as M.L-3 , the dimension of velocity as L.T-1 (kilogram per meter cubed). or M.L-2 Dimensional analysis is routinely used to check the plausibility of newly derived equations, the design of experiments, and the results of calculations in engineering and science before money and effort is expended on detailed measurements. In this way, reasonable hypotheses about complex 20 As mentioned above, the dimension of any quantity Q is written in the form of a dimensional product; dimen- sions of Q = Lα Mβ Tγ Iδ Θε Nζ Jη , where the exponents α, β, γ, δ, ε, ζ, and η are generally small whole numbers (integers), they can be positive or negative, or even zero, and are termed dimensional exponents. This expression defines the make of all things [2]. 92 physical situations are examined theoretically, to see if they merit subsequent testing by experiment. And, it is also the means by which one seeks to determine appropriate equivalent values for a quan- tity in another system of units; for example, how you convert from the value of a quantity in metric units to the equivalent quantity in British customary units; for example, meters/second to miles/ ; that is, hour, or joules (the SI derived unit of energy, symbol J, where J is equivalent to kg.m L.M2.T-2 ) to British Thermal Units or BTU (a customary unit of energy equal to about 1,055 joules. A BTU is approximately the amount of energy needed to heat 1 lb (0.454 kg) of water, which is exactly one tenth of a UK gallon, or about 0.1198 U.S. gallons, from 39°F to 40°F , or 3.8°C to 4.4°C). Thus, dimensional analysis is the means of translating between the various dialects of the single, universal language of science. .s -2 2 Consider the concept of force, something that is done to an object to make it change its speed, or velocity through, for example, acceleration. In the SI, the unit of force is the newton (symbol, N), named after Isaac Newton in recognition of his fundamental work in mechanics. The newton is equal to the force required to accelerate a mass of one kilogram at a rate of one meter per second squared. In dimensional analysis using Newton’s famous formula where force (F) is given as being equal to a mass (m) multiplied by acceleration (a), that is F = m.a, multiplying m (kilo- ), the dimension of the newton is found to be M.L/T2 or gram) by an acceleration a (meter/second M.L.T-2 . The newton is derived from the base units of mass, length and time, and , that is, kg.m.s -2 2 so could have been derived by the savants of the late 18th century. These principles of dimensional analysis were known to Isaac Newton, who referred to them as the Great Principle of Similitude. The 19th-century French mathematician and Egyptologist Jo- seph Fourier (1768–1830) made important contributions to dimensional analysis based on the idea that physical laws like Newton’s famous law, F = m.a, should be independent of the systems of units employed to measure the physical variables. That is, the Laws of Nature and fundamental equations should be equally valid in the metric system of units as in a non-metric system of units. And when converting between these two systems of units, we need only be cognizant of the mathematical factors needed to convert between the base units to convert the entire quantity from one system to another. Thus, one should take care never to mix systems of units, as the consequences could be disastrous (see Page 97). But there is nothing stopping one defining force in Ancient Egyptian units of measurement; distance would be in terms of the Royal cubit (about 0.525 m), mass would be in deben (about 0.015 kg) and time would have been in unut (the hour, which is identical with our hour). Fourier showed how each of these base units would need to be converted to SI base units to convert the Ancient Egyptian unit of force to the newton or vice versa. 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE9.2 DERIVED UNITS 93 9.2 DERIVED UNITS The base quantities of the SI given in Table 9.1 are combined to generate derived units, which are products of powers of base units without any numerical factors (other than 1). Such a set of coherent derived units is, in principle, without limit and they represent the means by which all the phenomena of Nature are described. Table 9.2 lists some examples of derived quantities and how they are represented in the technical literature. Table 9.2: Derived quantities Quantity Area Volume Velocity or speed Acceleration Density Surface density Specific volume Representation as a Unit Derived Quantity 2 m square meter 3 m cubic meter meter per second m.s meter per second squared m.s kilogram per cubic meter kg.m kilogram per square meter kg.m 3 .kg cubic meter per kilogram m -3 -1 -2 -1 -2 In this way, the semantic primes of the universal language of science, the base units of the SI, are combined to produce a means of describing and quantifying Nature. Some important derived units are given a specific name, usually to honor the scientist most closely associated with that quantity. Some of these named derived units are given in Table 9.3. Table 9.3: Named derived quantities Quantity Frequency Force Pressure Energy (or work) Power (or light intensity) watt (W) Derived Unit (Symbol) hertz (Hz) newton (N) pascal (Pa) joule ( J) -2 Representation as a Unit -1 s m.kg.s -1 m m m .kg.s -2 .kg.s .kg.s -3 -2 2 2 Of particular interest are two derived quantities related to angles. The plane angle is a two-di- mensional quantity defined by two lines, and the solid angle (steradian) is a three-dimensional quantity defined by a cone with a certain cross-sectional area. When expressed in terms of base units of the SI, these two angles are: meter/meter and (meter squared)/(meter squared), respectively; 2 consequently, they are dimensionless, as m/m = 1 = m . The fact that quantities related to angles in the SI are essentially invisible, as far as the unit is concerned, needs to be remembered as we see in Table 9.4, which contains more derived quantities. 2 /m 94 Table 9.4: Further derived quantities Derived Unit (Symbol) Quantity newton meter (N.m) Moment of force pascal second (Pa.s) Viscosity Surface tension newton per meter (N/m) Angular velocity or torque radian per second (rad/s) Heat density Thermal conductivity Energy density watt per square meter (W/m ) watt per meter kelvin (W/m.K) joule per cubic meter ( J/m ) 2 3 Radian intensity watt per steradian (W/sr) -2 -1 -1 -1 = s .kg.s -1 .kg.s -2 Fuller Representation 2 m m kg.s (m/m)s -3 kg.s m.kg.s -1 m 2 m 2 m .kg.s -3 .kg.s .kg.s 2 /(m 2 /m ) = K -2 -3 -1 -3 Radiance watt per square meter steradian 2 (W/m .sr) 2 2 /m (m -3 ).kg.s = kg.s -3 These are only a handful of the phenomena of Nature described by a few of the base units of the SI. All the derived quantities listed above, except thermal conductivity, involve only the base quantities length (meter), mass (kilogram), and time (second); so these phenomena could, in principle, have been identified by the savants who created the metric system in 1795 who had the meter, kilogram, and second. They would not have had the kelvin as the base unit of temperature, as temperature was not included into the SI as a base unit until 1954, the 18th-century savants who created the metric system would have used the Centigrade scale of temperature. With only the meter, the kilogram and the second we can define energy, the driving force of Nature. Gottfried Leibnitz had pointed out that what he termed the vis visa of a body (kinetic energy) was propor- 2 (see Table tional to the product of the body’s mass and the square of its velocity; that is, kg.m 9.3). Likewise, Isaac Newton had said that a force (F) that causes a body to change its speed is equal 2 , which to the mass (kg) of the body multiplied by the acceleration (m/s is the definition of the newton in Table 9.2. -2 ); that is, F = m.a = kg.m.s -2 s By using the laws of physics as a grammar, and the base units as expressions or words, we may construct a language that allows us to make predictions about phenomena that have not yet been identified, but which should be observable. Looking at the above tables, a scientist could, for example, ask questions such as: What happens if a force tries to twist a body instead of pushing (repelling) or pulling (attracting) it?; What happens if a force acts upon an area, not simply along a line?; or Is there a real, measurable phenomenon that arises when one couples the next highest power of length with time? In the first case, one defines torque, which is a force that tries to rotate a body (as any inexperienced motorcyclist, who has applied his rear-break too harshly while going around a corner too quickly will tell you). In the SI, torque is termed angular velocity (see Table 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE9.2 DERIVED UNITS 95 -1 9.4) and is expressed in radian per second. But as the radian is dimensionless in the SI, it is written ). This can be confusing and is the reason why many engineers prefer to express as per second (s this important quantity in non-SI units. A force acting over an area would be newtons per square , which is meter, and from the Tables we see that this quantity would be m.kg.s the definition of pressure. Pressure is nothing more than the force exerted by something (a gas or a fluid) upon a well-defined area.21 2 /m or m .kg.s -1 -2 -2 As for the reasonableness of phenomena that have not yet been observed, as was mentioned above, one first has to consider the magnitude of the units and a dimensional analysis to see if such a new phenomenon is observable. A relatively recent example would be the pressure exerted by light, that is, radiation pressure. Could it exist? Is it measureable? The answer was yes, and it was discovered that the radiation of the Sun exerts a pressure of less than a billionth of an atmosphere at the Earth’s surface. But it was an examination of the existing language of science, which suggested to and allowed individuals to look for this new phenomenon. The complex interconnectedness of the base units that couple, to generate the phenomena of Nature is represented in Figure 9.2. This figure tells us, for example, that the present definition of the second is used in the present definition of kilogram, meter, candela, ampere, and kelvin, and that the definition of the unit of temperature, the kelvin is dependent upon mass, time, and length. This organic wholeness of the phenomena of Nature reminds us of the ideas underlying the I Ching and the Taoist view of Nature. [2] In linguistics, grammar is the set of rules governing the composition of clauses, phrases, and strings of words in any given natural or vernacular language. Individuals who use or speak a language have a set of internalized rules for using that language, and these rules constitute that lan- guage’s grammar. The vast majority of the information in the grammar is, at least in the case of one’s native language, acquired not by conscious study or instruction, but by observing other speakers. Much of this work is done during early childhood; learning a language later in life usually involves a greater degree of explicit instruction. But for all the emotion expended by those who understand and use the rules of grammar, as well as those who have no idea about grammar; grammar is the cognitive information underlying language use. And this is the same in the language of science, as it is in English. Grammar allows us to turn the lists of verbs, nouns, adjectives, adverbs, etc. that come into our minds, at a particular moment into comprehensive, information-conveying prose. Grammar is not a distraction or an irritation; grammar is magical. Indeed, grammar and grimoire are derived from the same root. Grammar is also glamour, and the primary meaning of glamour is enchantment or spell. While grimoire is a manual for the casting of spells. Through grammar we may define, explore, understand, and perhaps control some aspects of the Universe. 21 The British customary unit for pressure (still used in, for example, tyre pressures) is pounds per square inch, which gives clear indication of pressure as a force upon an area. The Meter: the base unit of length (defined by c) 96 The Candela: the base unit of light intensity The Mole: the base unit of amount of substance (defined by NA) The Kilogram: the base unit of mass (defined by h) The Second: the base unit of time (defined by the frequency of an atomic clock) The Kelvin: the base unit of temperature (defined by kB) The Ampere: the base unit of amound of electricity (defined by e) Figure 9.2: The interconnectedness of the seven base units of the SI, now that (since May 2019) the kilogram is redefined via Planck’s constant, h, the unit of thermodynamic temperature defined by Boltz- mann’s constant, kB, the mole defined by Avogadro’s number or constant, NA, and the ampere defined by the charge of the electron, e. As can be seen, the network of connections is complex, for example, the kelvin is connected to the physics underlying the SI and is defined as an energy, but is dependent on the definitions of length (L), mass (M), and time (T) as M.L2.T-2. In addition, the ampere is defined as a flow of electrons in a time interval and so is no longer a force (M.L.T-2) dependent on length, mass, and time, but only on time. The kilogram is now defined by h, which is dependent on energy and time. 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE 9.3 LOCATION: THE SURFACE OF MARS, SEPTEMBER 23, 1999 97 9.3 LOCATION: THE SURFACE OF MARS, SEPTEMBER 23, 1999 On the September 23, 1999, the Mars Climate Orbiter satellite was lost during a maneuver to place it in an orbit around Mars. Instead of entering a stable orbit from where it could monitor the Martian weather, it is believed that the satellite crashed onto the surface of the Red Planet. After the long crossing of interplanetary space, the satellite’s controllers would have needed to slow down the satellite for it to safely enter the Martian atmosphere. It is believed that it was this braking process, which led to the satellite’s loss. To slow down a body in motion requires the application of a force of the same order of magnitude as the velocity of the satellite, but applied in the opposite direction. Unfortunately for the satellite, and the scientists waiting to hear from it, something went seriously wrong. As it turned out, the problem for the Mars Climate Orbiter was that the force necessary to slow the satellite down for it to safely enter a stable orbit around Mars, was calculated in one set of units, but when the command was sent to the satellite to ignite the braking thrusters, it was applied in a different set of units. The two sets of software, on Earth and on the satellite hurtling toward Mars, were trying to communicate in different scientific units, and instead of entering a stable orbit well above the surface of the planet, it attempted to enter an orbit much closer to the surface and crashed. The principal cause of the disaster was traced to a thruster calibration table, in which British customary units instead of metric SI units had been used to define force. The navigation software expected the thruster impulse data to be expressed in newton seconds, but the satellite provided the values in pound-force seconds (a non-SI unit). This confusion in units caused the electric impulse to be interpreted as roughly one-fourth its actual value. Knowing the forward-moving force of the satellite, a calculation would have been undertaken to determine the force require to be applied in the reverse direction to reduce the forward force, but due to incompatible programming on earth and in the satellite, the satellite crashed. The pound-force (lbF) is a unit of force in the system of units, loosely term British customary units. There are many ways to define force in this system of units, which may be considered con- fusing to some, but actually tells one a great deal about the physics going on in a particular experi- mental situation. The pound-force is equal to the force exerted on a mass of one avoirdupois pound on the surface of Earth. Originally, this unit was used in low-precision measurements where small changes in the Earth’s gravity (which varies from place to place on the surface of the Earth by up to half a percent could be neglected. The acceleration of the standard gravitational field (g) and the international avoirdupois pound (lbm) define the pound-force as: 1lbF = 1lbm . g = 1lbm . 32.174 feet per second squared, which on converting to the SI is equal to 0.454 kilogram . 9.806 65 meter per second squared = 4.448 newton. (This factor of 4.448 was absent from the software that controlled the satellite, and so it crashed.) 98 Even after 200 years of the decimal metric system, the world of science and technology is still full of different systems of units. That is, different dialects of the same universal language of science. But provided one is aware of these different dialects, one may affect the necessary translation in a trivial line of computer code and everything will be fine. Assuming, blindly, that everyone is speak- ing exactly the same dialect by assuming that everyone is using the same system of units is risky. 9.4 A FINAL COMMENT ON THE VALUE OF A QUANTITY: SACRED GEOMETRIES The Book of Revelations is the Ur-text of a great deal of the nonsense one finds on the Internet. One example of the many Hermetic, or opaque subjects arising from Revelations often discussed at interminable length, but rarely with any clarity on the Internet are sacred geometries, or sacred architecture. Interestingly, these arcane concepts also reveal something of the nature of the way scientists look at the world. The concept of a sacred geometry, or a sacred architecture, comes from Saint John’s vision of the Heavenly Jerusalem given in Revelations 21:17. The King James Bible tells us about the dimensions of the future New Jerusalem, “And he measured the wall thereof—an hundred and forty and four cubits, according to the measure of man, that is, of the angel.” The cubit was a unit of length measurement common to the Ancient Mediterranean world, equal to the length of a man’s forearm (elbow to finger-tip). We immediately see from this obscure text from Revelations that the author is in fact referring directly to the 5th century BCE, pre-Socratic Greek philosopher Protagoras’ well-known comment that “man is the measure of all things,” but we are also given the actual height of the walls of the heavenly city, 144 cubits. This dimension has over the last two millennia, inspired many individuals, particularly, architects. The great gothic Cathedral of Amiens in northern France, where construction began in 1220, is built to a height of 144 pieds Romans (that is, 42.3 meters or 138.8 British feet). The near-by Cathedral of Beauvais, on the other hand, where construction began in 1225, is built to a height of 144 pieds du Roi (that is, 48.5 meters or 159 feet). These two mediaeval units, Roman feet (pieds Romans) and Royal feet (pieds du Roi), are different. The fact that Royal feet are longer than Roman feet means that the Cathedral of Beauvais is higher than the Cathedral of Amiens, which may well explain why it was an unstable building that partially collapsed in 1284, while the Cathedral of Amiens has never fallen down. As far as the mediaeval architects of these two neighboring cathedrals were concerned, it was the numerical value of the height of the City of God that was important. One hundred and forty-four units was to be the height of the cathedrals, because that was the height of the City of God given by Saint John in Revelations 21:17; it appears not to have mattered much which units was actually adopted. (Remember: any value of a physical quantity, Q, may be expressed as the 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCE9.5 FURTHER READING 99 product of a unit [Q] and a purely numerical factor or number.) The gothic architects of northern France were only interested in the numerical factor of this physical quantity taken from the Book of Revelations; as far as they were concerned, the unit was irrelevant. This addiction to the fetish value of a number is numerology, pure and simple; it is Hermeticism. That is, attempting to find some meaning or, perhaps, a secret hidden in a particular number. What precisely is the meaning of 144? Perhaps it is related to other celebrated biblical numbers such as 666? What is it about 144; the height of the walls and the number of the just (144,000)? When you put the heights of the two cathedrals into British feet or meters, any mystical significance or magic disappears in the very different light of the English Industrial Revolution and the French Enlightenment. Conversely from the architects of mediaeval France, the Ancient Sumerians had little concept of pure numbers, although they were well versed in the use of numbers to hide mystical significance and to work magic. Our earliest recorded list of objects comes from Ancient Sumeria, and when we look at these ancient lists (more than five millennia old) we see that the scribes used the same metrological symbol, or unit as many times as was required by the value of the numerical factor before the unit. Thus, instead of writing six oxen as the Sumerian form of the number six followed by, perhaps, a schematic of an ox, the scribes simply drew the pictorial schematic of the ox six times. The Ancient Sumerians used only the unit part of the definition of a quantity, while the me- diaeval French craftsmen only used the numerical part of the definition of a quantity. Neither is the correct approach. One can readily imagine the evolution of the Sumerian usage to a more sensible, modern approach arising because the lists were getting to be very long and tedious to compose, and those clay tablets were so very small. The magico-Christian architects, on the other hand, got caught up in looking for mystical significance in the numbers mentioned in religious-poetic texts of late antiquity, and as a consequence they lost their way in numerology, and like the Tower of Babel their cathedral collapsed. 9.5 FURTHER READING 1 Concerning the origins, since the late 19th century and the previous definitions of the base units of the SI, the best source for detailed information is the bilingual SI Brochure published by the Bureau international des poids et mesures (BIPM). This is a non-technical document intended for those already familiar with the science relating to the origin of the SI, and is essentially a list of rules concerning the use of SI units. The brochure is written by the Consultative Committee for Units of the BIPM; the most recent edition, the 8th, was published in May 2006. This substantial booklet is only available through the BIPM, but the text is freely available on the BIPM’s website (www.bipm.org/en/publications/). Also included are extensive lists of references as to when certain words or quantities were adopted for use with the SI. 100 The BIPM website also contains freely available information about the evolution of the definitions of the base units of the SI. The definitions of several of the base units changed in May 2019—full details may be found on the BIPM website (in English and in the official language, French) at https://www.bipm.org/en/measurement-units/. Also see https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units. 2 There is also a more recent history of metrology and of the metric system in this volume: Defining and Measuring Nature: The Make of all Things (2014); Jeffrey H. Williams; San Rafael, CA, Morgan & Claypool. 9. DIVIDING APPLES WITH ORANGES TO MAKE THE LANGUAGE OF SCIENCECHAPTER 10 What Powers Society? 101 We already know enough to begin to cope with all the major problems that are now threatening human life, and much of the rest of life on earth. Our crisis is not a crisis of information; it is a crisis of decision. George Wald (1906–1997) ἐνέργεια Having looked briefly at how the worldview of scientists has evolved, let us now briefly begin to consider the mutual influence of science and society. In particular, we will do this by looking at bulk thermodynamic properties (see Table 10.1, which is based on the tables in Chapter 9). In physics, energy—derived from the Greek (activity or operation) a term that first appears in Aris- totle—is an indirectly observable quantity. Energy powers, not only us and our society, but also the Universe and everything in the Universe; however, it cannot be measured as an absolute quantity. We may say that there is energy in a system, but we cannot quantify it precisely; as Saint Thomas Aquinas said in the 13th century, “I see motion, so I infer energy.” Indeed, there is so much energy in the Universe that we are only really able to quantify the influence of changes in quantities of energy, as they act upon matter. Table 10.1 lists four derived units from the International System of Units (see Chapter 9), for energy, work, force, power, and pressure. We can see from their rep- resentation in the language of science that they only differ by powers of length (m in meters) and time (s in seconds). The final column also demonstrates how interconnected are these four basic phenomena— as revealed in Figure 9.2. Table 10.1: Named derived closely related quantities Quantity Energy (and Work) Force Power Pressure Derived Unit (Symbol) joule ( J) newton (N) watt (W) pascal (Pa) 2 -2 Representation in the Language of Science s kg m -2 kg m s -3 2 s kg m -2 = kg m Nm = Jm -2 s -1 -3 James Prescott Joule (1818–1889), Figure 10.1, was an English brewer and amateur scientist, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to me- chanical work. This led to the law of conservation of energy, which in turn led to the development of the first Law of Thermodynamics. The SI-derived unit of energy, the joule, is named after him. 102 James Watt (1736–1819), Figure 10.2, was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen’s 1712 Newcomen steam engine with his Watt steam engine of 1776, which went on to become the driving force of the Industrial Revolution around the world. Figure 10.1: A photograph of James Prescott Joule, the Salford brewer and amateur scientist who defined and quantified energy. Image from: https://en.wikipe- dia.org/wiki/James_Prescott_Joule#/media/File:Joule_ James_sitting.jpg. When we look up at the sublime spectacle that is the night sky, all we see is energy and matter, nothing else, and as Einstein pointed out, energy and matter are proportional, and can be equated with a constant equaling the speed of light (c) squared (E = m.c2 ). All the things we see around us—form, texture, color, together with the sublimity and sense of the numinous that arise in our minds when we contemplate the Universe—all arise from the distribution of energy. But static quantities of energy and matter; stationary for all eternity can do nothing. It is only when energy and matter vary in quantities with distance that we can conceive of a Universe such as ours; a Universe capable of supporting life. If the Universe were not dynamic, in fact expanding, it would be a dark, dead gaseous nothing. In this, the Universe is like an economy. If we all kept our money in banks and spent nothing, there would be no global economy. Economic activity that generates jobs and opportunities, together with economic growth arises from the movement of money. That is, by money moving from one location to another. If it all stayed put in the bank accounts of a few billionaires, there would be no economic activity. Money only generates something useful to 10. WHAT POWERS SOCIETY? the wider society when it moves. The same with energy in a system. Everything we see around us, especially life, comes from the flow of energy.22 10. WHAT POWERS SOCIETY? 103 2 -2 -2 .s /m = kg.m.s When energy is channeled into a particular direction, we have a force; a force is energy/ as in Table 10.1. Again, the same can be said of money. distance, that is, kg.m When money flows into an economy, it can be said to be a powerful force. Consider a definition: a force is any influence that causes an object to undergo a change in its motion (for example its velocity or speed), the direction of its motion, or its shape (for example, compression). A force may thus cause a moving object to change its velocity (the force of gravity defining the trajectory of comets mov- ing around the Sun; or an injection of capital to change the direction of an economy) or even to begin to move if it were stationary (the force of the rocket engine accelerating against the force of gravity, or motion in a game of billiards, or a start-up grant) or it may compress the shape of an object (collapse or bankruptcy). While mechanical stress can often remain embedded in solids, gradually deforming them, mechanical stress in a fluid gives rise to changes in the fluid’s pressure if the volume is constrained. Work, energy, power, and force are all closely related, indeed, they are interconnected in physics (see Table 10.1). But they are also closely related concepts in the wider society. Work is described as the product of a force multiplied by the distance over which it acts. Only the compo- nent of a force (which is actually a field of potential action extending in many directions) in the direction of the movement of its point of application does work. The term work was first used in 1826 by the French mathematician Gaspard-Gustave Coriolis (1792–1843), who gave his name to the force responsible for the swirling form of hurricanes, and of the vortex of water as it disappears down a plughole. If a constant force of magnitude F acts on a point that moves a distance l in the direction of the force, then the work W done by this force is calculated from W=F.l. In the SI system of units, force is measured in the newton and it would act over a distance in meters, so the work done would equal newton meters, which (see Table 10.1) would be an energy, and so would be equal to joules. In the SI, work and energy have the same units. Power is the rate at which energy is transferred, used, or transformed into another form of energy. For example, the rate at which an electric heater transforms electrical energy (electrical current per unit time) into heat and light by passing the current through a heating element of high resistance, and is measured in watts, in honor of James Watt (Figure 10.2). The greater the power output or wattage, the more power, or equivalently the more electrical energy is used per unit time. Thus, power is the time-averaged use of energy (kg.m , as in Table 10.1). /s = kg.m .s .s -3 -2 2 2 22 As the British Nobel laureate in biochemistry, Frederick Gowland Hopkins (1861–1947) commented, “Life is a dynamic equilibrium in a polyphasic system.” 104 Figure 10.2: James Watt painted by Carl Frederik von Breda. Image from: https:// upload.wikimedia.org/wikipedia/com- mons/1/15/Watt_James_von_Breda.jpg. Energy transfer can be used to do work, so power is also the rate at which this work is per- formed. The output power of an electric motor is the product of the torque the motor generates and the angular velocity of its output shaft. The power expended to move a vehicle is the product of the traction force of the wheels against the ground and the velocity of the vehicle. The SI unit of power is the watt, which is equal to one joule per second. Older, more picturesque units of power include ergs per second, horsepower, metric horsepower (in German, Pferdestärke), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the power required to lift 550 pounds of weight by one foot in one second, and is equivalent to about 746 watts (and has nothing to do with carts and horses). 10.1 SOCIAL FORCES By the late 19th century, classical physics was triumphant. We understood how the Universe func- tioned because we understood how energy was transfered, conserved, and partitioned in our labo- ratories, particularly, the Cavendish Laboratory in Cambridge, and we merely extrapolated to the larger scale of the Universe. In 1864, Maxwell published A Dynamical Theory of the Electromagnetic Field, where he first proposed that light was composed of waves moving in the same medium that gives rise to electric and magnetic forces. Maxwell’s work in electromagnetism has been called the 10. WHAT POWERS SOCIETY? 10.1 SOCIAL FORCES 105 second great unification in physics, after the first great unification achieved by Isaac Newton. Max- well wrote, “The agreement of the results seems to show that light and [electro] magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.” Maxwell was proved right, and his quantitative connection between light and electromagnetism is considered one of the great accomplishments of the 19th century in any field of endeavor (see Section 12.2). By considering the propagation of electromagnetic radiation as a field emanating from some active source, Maxwell was able to advance his work on the nature of light. And by estimating what the speed of light should be, and observing that his prediction agreed with the best available exper- imental values, he was able to say that his initial assumption had been correct. In this way, he laid the foundations of the modern scientific methodology of solving complex interrelated problems. Even though Maxwell reconciled electricity, magnetism, and light, he did not live long enough to finalize the details of the character of the electromagnetic field. At that time, Maxwell and many others believed that the propagation of light required a medium which could support the waves, and through which the waves could move or propagate (as was the case for sound waves in air—sound waves cannot cross a vacuum). This proposed medium was called the luminiferous aether. Over time, however, the existence of such a medium permeating the Universe, and yet apparently undetectable by any mechanical means, proved more and more difficult to reconcile with experiment. Moreover, it seemed to require an absolute frame of reference in which the equations were valid, with the extraordinary result that the equations governing the phenomena of electromagnetism and optics would be different for a moving observer and for an observer at rest. These difficulties inspired Al- bert Einstein to formulate the theory of special relativity, and in the process Einstein demonstrated that one could dispense with the requirement for a sustaining luminiferous aether. The scientists of the late 19th century spoke about energy as the means of powering the Universe, and of forces operating everywhere throughout the Universe; they appeared to possess near-divine competence to explain and predict what was going on here on Earth as well as in the distant reaches of the Cosmos. The period from the mid-19th century to World War I was the great period of scientific triumphalism, and it is not surprising that this attitude of authority was copied by many social scientists and those involved in ordering and maintaining society. After all, the application of a quantitative way of looking at life was a wide-ranging consequence of the French Revolution; we were all now subject (whether we knew it or not) to a new tyranny, the tyranny of numbers and scientific concepts. Society was to be run efficiently, like a late 19th century laboratory. This quantitative view of society and of the evolution of society is best represented in the work of the German philosopher and economist, Karl Marx, especially his Das Kapital, published posthu- mously in 1885 and 1894. For those interested in the history of science, the concept of power is now inseparable from politics and economics. This confusion of terms began in the late 18th century when Matthew 106 Boulton, the financier who supported James Watt’s work to develop the steam engine that powered the Industrial Revolution wrote to Empress Catherine (the Great) of Russia, in an attempt to sell the new steam engines he was developing with Watt. He wrote to Her Imperial Majesty, “I am selling what the whole world wants: power.” He had given the game away. That was what it was all about. That a discussion of power in Nature is really inseparable from the idea of power in society. We could say that whereas the fundamental principle of physics is energy, power is the fundamental principle of the social sciences, and of politics and economics. Perhaps because power can be readily quantified, if only by demonstrating that one politician can command more votes than another, or that one bank, organization, or media Moghul is richer than another bank, organization or media Moghul, that they are deemed to be more powerful. Corporate power may have a different sense from physical power, but the units are exactly the same, and we have a confusion of terms. Such homonyms, are known in other areas. The ideas presented here are an attempt to point out that our society is really a microcosm of Nature, and concepts of what makes the Universe work the way it does, can be applied (perhaps without too much difficulty) to our society. Energy is the currency of Nature, and power and force drive nature; in society, money may be currency, but it is also the medium, the power and force that brings about change in society. When we come to forces, we are in an even more difficult position about possible confusion between politics, the social sciences, and the physical sciences. How many times have we heard a partisan journalist say of a politician that “he/she was a force of Nature.” A force is something that compels a molecule, or a planet to do something; that is, it is energy directed along a well-defined path, so perhaps certain politicians are able to act as forces. They order people to do this or that, they change society and use considerable resources in their endeavors. However, the big difference is that in Nature forces act in the most efficient manner, there is little wastage of energy; politicians, on the other hand, are less efficient and waste a great deal of the scarce currency of society. The age of scientific triumphalism came crashing down with the World War I, the advent of quantum mechanics and relativity in physics, and with modernism in the arts (cubism in the visual arts did more to advance the ideas of Einstein and Heisenberg than any number of textbooks written for a general readership). Sadly, the quantitative triumphalism of the social scientists and of politicians took a bit longer to dissipate, but another world war and several economic crashes; particularly, that of 2008, have revealed the final bankruptcy of all the standard models of economic growth; yet politicians still believe that we can all continue to have unlimited economic growth in a closed system of finite resources, that is, it is possible for politicians to repeal the Second Law of Thermodynamics. The force of politics has gone, and all we have left are politicians seen as a disruptive or, at best, an irrelevant force in social progress. 10. WHAT POWERS SOCIETY?10.2 INTERNATIONAL REGULATION OF TERMS AND NAMES 107 10.2 INTERNATIONAL REGULATION OF TERMS AND NAMES: DIALECTS ARE INEVITABLE I have spoken about the scientists’ desire to create a simple language to describe the world that would be universally understood; to permit a return to a Golden Age. But are such dreams practicable in the wider society? The followers of such projects always try, with greater or lesser cohesive power, to realize an international forum. But which authority has the competence to ad- judicate between these contending parties? Is it the richest or the most powerful nation on earth that decides for the rest of humanity? The beginning of the last century was the most optimistic epoch for the creation of Utopic ideas of international committees deciding on matters affecting and effecting humanity. This was an epoch when it still seemed realistic to believe that an inter- national body would be capable of coming to a fair and ecumenical conclusion, and imposing it on every nation by reason. But two world wars and numerous economic depressions put an end to all that Utopian nonsense. Anyway, if a committee did make a useful contribution; for example, inventing a good, new candidate for a universal language; as soon as it was made public, the language would spread through various countries. There would be clubs to propagate this new language, and these clubs would begin petitioning national governments to access national education systems. However, what invariably happens is that the original inventor discovers that his/her language has been subjected to, supposedly “heretical” modification(s), which might further simplify, restructure, and rearrange it—making it more useful as an international language. But the original inventor for, whatever reason will likely not be happy about this. The product of all their labor will have been modified by others. Their creation is not the final version. That honor will go to someone else. Such will in- evitably be the fate of artificial languages: the “word”’ remains pure only if it does not spread; if it spreads, it becomes the property of the community of its proselytes, and (since the best is the enemy of the good) the result is “Babelization.” After a few short years of rapid inflationary growth, the movement collapses, and continues only in an ever-shrinking state. One may make the observation that a universal language is impossible for a simple reason: Even if everybody on earth agreed to speak the same language from today, they would soon discover that, under the influence of their own use the single languag,e had begun to change, to modify itself in a multitude of different ways in each country, until it produced in each a different dialect, which gradually grew away from all the others. It is for this reason that the Portuguese spoken today in Brazil differs from the Portuguese spoken in Portugal and, more famously, the ever-widening sep- aration of English spoken in the UK and in the U.S. 108 10.3 SCIENCE AS A NEW TOWER OF BABEL By this point, I am sure that the reader will have appreciated that creating a universal language of science, or even a new system of weights and measures is no easy matter. Even ignoring political conflicts, it is rarely possible to achieve consensus between relatively small groups of scientists as to which units they should be using. And as for devising a scientifically coherent system of units that may be adopted and used by the wider society there is no simple answer. Creating a system of weights and measures, or a universal language capable of quantitative extension, is difficult due to conflicting requirements. • To facilitate everyday use, the units or nomenclature should be of a size or facility that is appropriate for use in specialist areas of science and technology, but they must also be appropriate for everyday use by the wider community. • To facilitate international use, the units or nomenclature should be defined in a man- ner that is both precise and capable of being reproduced anywhere in the world, and not be subject to reference to a prototype or artifact kept by a particular nation. • The units or nomenclature should be coherent; that is, all the subsidiary or derived units, which are needed to fully describe Nature, can be expressed as combinations of the basic units without the introduction of any numerical constants. Fortunately, compromise and even pragmatism are not entirely unknown in science, and some progress has been possible. The centimeter-gram-second (CGS) system of units was widely used until the electricity industry decided that the electromagnetic unit, or emu derived from Ampère’s Force Law, gave quantities which were too small for practical use by electrical engineers. They rescaled the electrical units to make them more “user friendly” for the electricity generation and supply companies, who needed units which referred directly to the large electric currents and the huge voltages found in industry, rather than the much smaller values used by research scientists. This resizing of units made the electrical engineers happy, but coherence with mechanical units was lost because of the numerical factors which were now needed to connect the units for large currents and voltages to related quantities. In 1948 it was decided that the centimeter, the gram and the erg (the CGS unit of energy) should be replaced by the larger meter, kilogram, and joule (one -3 kilogram, and one erg equals 10-7 joules). This centimeter equals 10 new system of units was called the meter-kilogram-second-ampere (MKSA) system of units, and it restored coherence to the whole system of units and quantities; that is, the numerical conversion factors introduced by electrical engineers disappeared. The MKSA system of units is also known as the SI system of units (see Chapter 9). meters, one gram equals 10 -2 So, why use these different systems of electrical units? Why was it deemed necessary to ap- pease the electricity industry? Well, it is not simply a reluctance to change. It is all about what you 10. WHAT POWERS SOCIETY?10.3 SCIENCE AS A NEW TOWER OF BABEL 109 hold to be important. Pragmatists favor the SI’s utilitarian approach to calculation, which actually keeps a lot of the underlying complex physics out of sight (which is useful for teachers when trying to instruct bored students, but is inappropriate for researchers); on the other hand, philosophically minded physicists want only the base units to better reflect the underlying science. This problem of fundamentally different systems of units and nomenclature being used con- currently by different communities of both scientists and non-scientists does, of course, extend far beyond the world of electrical engineering. A similar “confusion of tongues” applies in something as technically straightforward as pressure measurement. (Pressure is defined as the force per unit area applied in a direction perpendicular to the surface of a vessel. It can be thought of as arising from the molecules of gas striking the inner surface of the vessel containing that gas.) -1 -2 The SI unit for pressure is the pascal (Pa), named in honor of the 17th-century French mathematician and Catholic philosopher Blaise Pascal (1623–1662), which in the SI is equal to 2 ; pressure is a force). The name “pascal” or kg.m one newton per square meter (that is, N/m (symbol Pa; see Table 10.1) for the unit was adopted in 1971; before that date, pressure in the SI . The problems associated with pressure measurements begin was expressed simply as so many N/m with the SI unit of area; one square meter is a very large area, and so the values of even the modest pressures encountered in everyday life are very large numbers. For example, the pressure in your car tyre would be about 340,000 Pa; and successful systems of units usually express everyday quantities in small numbers, so as to facilitate familiarity with the size, and in recording and quoting the values (particularly, with non-physicists in places such as garages and tire shops). .s 2 On the other hand, non-SI units of pressure are legion. There are pounds per square inch (psi), or more precisely (given the distinction between mass and weight) pounds-force per square inch, and bars (that is, atmospheres) which are commonly used in the English-speaking world. The 2 or 0.1 Pa (a dyne, abbreviated as dyn, CGS unit of pressure is the barye (ba), equal to 1 dyn/cm newton). Then there being the unit of force in the CGS system of units, one dyne is equal to 10 is the universal measure of pressure used by the medical profession; your blood pressure of, for ex- ample, “130 over 82” is actually two measurements of pressure with each result given in millimeters of Mercury (mmHg). Here the pressure is defined as a force which would support a column of Mercury of uniform cross-section to that particular height.23 The standard atmosphere (atm) is a well-known and well-used constant. It is approximately equal to the air pressure at sea level and is equal to 101,325 Pa or 101.325 kPa or 1013.25 hPa, in the SI, or 14.696 psi or 760 mm of Mercury; so 1 mm of Mercury is equal to 133.3 Pa. -5 23 When millimeters of Mercury, or even inches of water, are quoted today as pressures, these units are not based on an actual physical column of Mercury or water; rather, they are measured by small electronic sensors or transduc- ers whose readings could be calibrated or expressed in any number of units (SI or non-SI) by an inbuilt computer chip, calibrated to behave as if it were a column of Mercury or of water. 110 Another point to bear in mind about this profusion of units of something as straightfor- ward as pressure is the difference between relative pressures (relative to atmospheric pressure) and absolute pressures (relative to a vacuum); for example, the pressure in your car tires is a relative pressure, or an overpressure and is often written as psig (pounds per square inch of gauge), which is one atmosphere or 14.696 psi above a vacuum. An absolute tire pressure would be written in psia (pounds per square inch absolute), and would be lower than a measurement of the same pressure given in psig by the amount 14.696 psi. These are all expressions of the same piece of information, but expressed in the various di- alects of the single language of science. This plethora of units for something as basic as pressure measurement is mirrored in measurements of many other common phenomena. This variety is not something that exists to confuse students and non-scientists. Such varieties of units exist for sound technical reasons: convenience in specialist branches of science, or convenience or facility of use in certain ranges of pressure, or because one profession refuses to change to another system of units, or because there is such an investment in technology that any change would be too expensive. The medical profession will, for example, not move away from using mmHg for blood pressure mea- surement,24 which is convenient for them and a sufficiently precise measurement for their patients, but this is not the case for the vast majority of physicists who gave up using mmHg as a unit for pressure early in the last century. However, the question we have to ask ourselves is whether there is anything to be gained by attempting to force a large body of professionals to give up a system of units with which they have become familiar over many generations. There is certainly the possibility of serious adverse consequences arising from such a move. It would be far better to encourage the ability to use and convert between many of these systems of units—to celebrate the diversity of the dialects of the single language of science. A scientist or a technician who can convert between these units will be someone who will truly understand the science underlying the phenomenon, and will be less likely to make foolish errors. Any common language for science would inevitably and rapidly grow distant from the lan- guage of literature, but we know that the language of science and the language of letters influence each other. But, in addition, an international language of purely scientific communication would soon become an instrument of secrecy, from which the humble speakers of their own native dialects, or regional languages would be excluded. And as to possible literary uses, if the authors were obliged to write in a common tongue, they would be exposed to international rivalries, fearing invidious comparisons with the works of foreign writers. Thus, it seems that circumspection was a disadvan- tage for science and an advantage for literature, as it was for the astute and cultivated traveler, more learned than his native and naïve interlocutors. In the background to the formation of a universal 24 In France, doctors define the blood pressure of their patients in terms of centimeters of Mercury, rather than millimeters of Mercury. That is only a factor ten to consider. 10. WHAT POWERS SOCIETY?language there is an 18th-century prejudice, which is still with us; that people simply do not wish to learn other languages, be they universal or merely foreign. There exists a sort of cultural deafness when faced with polyglottism, a deafness that continued on throughout the 19th century to leave visible traces in our own time. 10.4 FURTHER READING 111 10.4 FURTHER READING Defining and Measuring Nature: The Make of all Things (2014); Jeffrey H. Williams; San Rafael, CA, Morgan & Claypool. Order from Force: A Natural History of the Vacuum (2015); Jeffrey H. Williams; San Rafael, CA, Morgan & Claypool. CHAPTER 11 113 The Ghost of the Divine Language: The Theory of Everything Reality is merely an illusion, albeit a very persistent one. Albert Einstein (1879–1955) The Theory of Everything (TOE) is the final theory, the ultimate theory, or master theory. It is a hypothetical single, all-encompassing, coherent theoretical framework of physics that will fully ex- plain and link together all aspects of the Universe. Science fiction writers has long speculated about such an over-arching model of how the natural world functions, but let us consider what physicists mean by this fantastic, this sublime idea. Finding a TOE is one of the major unsolved problems in physics. Over the past two cen- turies, two theoretical frameworks have been developed that, as a whole, most closely resemble a TOE. These two theories, upon which all modern physics rests are general relativity and quantum field theory. General relativity is a theoretical framework that only focuses on one of the four fun- damental forces of Nature, gravity, for understanding the Universe on a large scale, and for objects kg), stars, galaxies (the mass of a of high mass: planets (the mass of the earth is about 6 × 10 kg), clusters of galaxies, etc. On the other hand, quantum field galaxy is estimated to be about 10 theory is a theoretical framework that focuses on the other three of the four fundamental forces of Nature (one of which is displayed in Figure 11.1), excluding gravity, and it holds for understand- ing the Universe at the small scale, and for objects of low mass: sub-atomic particles (the mass of kg), atoms, molecules, etc. Quantum field theory suc- a proton is 1.672 621 923 69(51) × 10 cessfully implemented the Standard Model and unified the interactions (so-called Grand Unified Theory) between the three non-gravitational forces: strong nuclear force, weak nuclear force, and electromagnetic force. −27 24 42 By merely suggesting that there is, somewhere… at some energy, a TOE, and that when we discover it all experimental science will become redundant (that is the implication), we are again in the world of the mediaeval and pre-mediaeval savants who searched for the Perfect Language (see Chapter 2). Both the poet Dante and his exact contemporaries, the Kabbalists of Spain searched for the language used by God to bring the Universe into existence from nothing (Ex nihilo). They believed that this language was merely lost, or perhaps, given that it was a language of power, had been hidden from man. But once man had re-discovered this language, all the secrets of Nature 114 would be revealed to him. He could re-order the world, and by implication humanity, bring about a new Golden Age of harmony, peace, and prosperity. Figure 11.1: Lightning or electromagnetism in action. Lightning is probably the most spectacular, frightening, and immediate demonstration of one of the four forces of Nature (electromagnetism). A great many of the most eminent physicists have confirmed with precision experiments virtually every prediction made by the two theories of general relativity and quantum field theory— when used in their appropriate domains of applicability. In accordance with their findings, scientists have also learned that general relativity and quantum field theory, as they are currently formulated are mutually incompatible; they cannot both be right. Since the domains of applicability of general relativity and quantum field theory are so different, most situations require that only one of the two theories be used. As it turns out, this incompatibility between general relativity and quantum field theory is apparently only an issue in regions of extremely small scale and high mass, such as those that exist within a Black Hole, or in the early stages of the Universe. To resolve this conflict, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three fundamental interactions, must be discovered to integrate, harmoniously the physics of the very large and of the very small into a seamless whole: a single theory that, in principle, is capable of describing all phenomena, at all length and mass scales. Today, it is string theory that has evolved into a candidate for this ultimate theory of the Universe, but not without limitations and controversy. String theory posits that at the beginning of second after the Big Bang, when the Universe was very small, and so at a the Universe (up to 10 very high temperature), the four fundamental forces were a single fundamental force. According to string theory, every particle in the Universe, at its most microscopic level (the Planck length scale), −43 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHING 11.1 SOME BACKGROUND 115 consists of varying combinations of vibrating strings with distinct patterns of vibration. String theory further claims that it is through these specific oscillations that a particle of a unique mass and charge is defined. Thus the electron (of mass, me = 9.109 383 56(11) ×10−31 kg and of charge, 1 e = 1.602 176 620 8(98) × 10−19 C = 4.803 204 51(10)×10−10 esu) is a string vibrating one way, while the up-quark, of charge = +(⅔) e and mass = (⅓)me, is a string vibrating in a different manner. 11.1 SOME BACKGROUND In Ancient Greece, philosophers such as Democritus (c.460–c.370 BCE) speculated that the ap- parent diversity of observed phenomena was due to a single type of interaction, namely the ability of the most fundamental particles, termed atoms, to move and collide with each other in the void that existed between the indivisible, eternal atoms. Archimedes (c.287–c.212 BCE) was possibly the first natural philosopher known to have described Nature with axioms (or principles), and then to have deduce new results from observations of these principles. In the late 17th century, Isaac Newton’s description of the force of gravity, which he knew operated over vast, astronomical distances implied that not all forces in Nature result from things coming into contact, or colliding. In his Mathematical Principles of Natural Philosophy of 1687, New- ton gave us an example of the unification of physical principles; in this case, unifying the mechanics of Galileo Galilei on terrestrial gravity, the laws of planetary motion of Nicolaus Copernicus (1473– 1543) and the phenomenon of tides by explaining these apparent actions at a distance under a sin- gle law: the Law of Universal Gravitation.25 The mid 19th century saw the unification of electrical and magnetic phenomenon to create electromagnetism. In his experiments of 1849–50, Michael Faraday was the first to search for a unification of gravity with electricity and magnetism, but he was unsuccessful. In 1900, the German mathematician David Hilbert (1862–1943) published a list of mathematical problems that became famous, and stimulated a great deal of research in the early years of the last century. In Hilbert’s sixth problem, he challenged researchers to find an axiomatic basis to all of physics. He asked the physics community to come up with a Theory of Everything. In the late 1920s, the recently invented quantum mechanics showed that the bonds between atoms, which are the basis of all chemistry and physiology were examples of electromagnetic forces (see Figure 11.1, where the lightning results from the energy released by atoms and molecules excited and ionized by huge electric and magnetic fields). This discovery led one of the inventors of quantum mechanics, Paul Dirac, to boast in the Preface of the first edition of his textbook on 25 Newton’s Law of Universal Gravitation states that every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. The equation for this law is: F = G(m1.m2/r2), where F is the gravitational force acting between two objects, m 2 are the masses of those objects, r is the distance between the centers of those masses, and G is the gravitational constant (6.674 × 10−11 m3kg−1s−2). We see immediately that this constant is known with considerably less precision that are the charge and mass of the electron given above. 1 and m 116 quantum mechanics (The Principles of Quantum Mechanics; Cambridge University Press, 1930) that “the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known.” Although Dirac predicted the end of experimental science, things turned out rather differently. During the great advances made in particle physics in the last century, that is, the elucidation of the menagerie of sub-atomic particles we know today, the search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces, which both differ from gravity and from electromagnetism. Gravity and electromagnetism could always coexist as entries in a list of classical forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone be unified with the other fundamental forces; the strong and the weak nuclear forces are purely quantum phenomena. For this reason, work on unification in the last century focused on understanding the three quantum forces: electromagnetism and the weak and strong nuclear forces. The first two were combined in 1967–68 by Sheldon Glashow (U.S., born 1932), Steven Weinberg (U.S., born 1933), and Abdus Salam (Pakistan, 1926–1996) into the electroweak force; see Figure 11.2. Electroweak unification is a broken symmetry; the electromagnetic and weak forces appear distinct at low-energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses of 80.4 GeV/c2 and 91.2 GeV/c2, respectively, whereas the photon, which carries the electromagnetic force, is without mass. At higher energies, the W and Z bosons can be created, and the unified nature of the force becomes apparent. A TOE would unify all the fundamental interactions of Nature: gravitation, strong nuclear interaction, weak nuclear interaction, and electromagnetism. Because the weak interaction can transform elementary particles from one kind into another, the TOE should also yield a deeper understanding of the various kinds of sub-atomic particles. The usual assumed path of these various theories is given in Figure 11.2, where each unification step (indicated in Figure 11.2 with a short vertical arrow (↑) from two horizontal pre-existing theories) leads to a higher level of sophistication and complexity. 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHING11.1 SOME BACKGROUND 117 Figure 11.2: A generalized and theoretical route to the creation/discovery (whether science develops a theory to explain Nature, or discovers a theory that explains Nature is a moot point, but one beyond the scope of the present volume) of the Theory of Everything, or the Perfect Language needed to characterize and explain every detail and phenomenon of Nature. Originally, electricity and magnetism were considered to be two separate forces. This view was overthrown by James Clerk Maxwell in 1873. Albert Einstein published his general theory of relativity in 1915. In 1961, Sheldon Glashow combined the electromagnetic and weak interactions. In 1967, Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow’s electroweak interaction, giving it its modern form. The Standard Model was developed in stages throughout the latter-half of the 20th century, through the work of many scientists with the current formulation being finalized in the mid-1970s with experimental confirmation of the existence of quarks. A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy the three gauge interactions of the Standard Model that define the electromagnetic, weak, 118 and strong interactions, or forces, are merged into a single force. Although this unified force has not been directly observed, the many GUT models theorize, or foretell its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct. The novel particles predicted by GUT models are expected to have extremely high masses of around the GUT energy scale of 10 GeV, and so are well beyond the reach of any foreseen particle collider experiments. The total energy range covered by the physics in this figure is a staggering, 30 orders of magnitude (10 GeV; that is, just not far below the Planck scale of 10 eV to 10 eV). 16 28 19 -2 The essential point to make about Figure 11.2, other than that it is a road map to an un- known destination (always the most exciting sort of journey); a destination that may not even exist, is that it represents a sequence of events at vastly different ranges of energy. From energies, of order, kBT for the unification of electricity and magnetism (here T is the temperature and kB the Boltzmann constant that relates temperature to energy; electromagnetic phenomena occur at ambient conditions) to vast energies way beyond the capabilities of our present high-energy particle GeV, Grand Unification is predicted to colliders. The electroweak unification occurs at around 10 GeV, and unification of the Grand Unified Theory force with gravity is expected at occur at 10 the Planck energy, roughly 10 GeV (that is, about 1028 eV).26 19 16 2 16 Several Grand Unified Theories (GUTs) have been proposed to unify electromagnetism and the weak and strong nuclear forces. Grand unification would imply the existence of an electronu- GeV, far greater than could be reached clear force; it is expected to set in at energies, of order, 10 by any present particle accelerator. The Large Hadron Collider is the world’s largest and most powerful particle collider, and the largest machine in the world. It was built by the European Orga- nization for Nuclear Research between 1998 and 2008 in collaboration with over 10,000 scientists, and hundreds of universities and laboratories from more than 100 countries. It lies in a tunnel 27 km in circumference, 175 m beneath the France–Switzerland border near Geneva. First collisions GeV) were achieved in 2010 at an energy of 3.5 teraelectronvolts (TeV; 1 T eV = 10 per beam, about four times the previous world record. After upgrades it reached 6.5 TeV per beam (13 TeV total collision energy, the present world record). At the end of 2018, it entered a two-year shutdown period for further upgrades; https://home.cern/. eV or 10 12 3 26 An electron volt (1 eV) is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 Joule/Coulomb, multiplied by the electron’s elementary charge e = 1.602 176 620 8(98) × 10−19 Coulomb. Therefore, one electron volt is equal to 1.602 176 620 8(98) × 10−19 Joule. By mass–energy equivalence, the electron volt is also a unit of mass (from Einstein’s celebrated equation). It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum. The mass equivalent of 1 eV/c2 is 1.782 × 10-36 kg. 1 eV corresponds to a temperature of about 11,604 K or 11,331°C. This system of units is useful for theoretical physicists, and the community of particle physicists but is wholly outside of the SI. 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHING11.2 STRING THEORY 119 The final step in Figure 11.2 requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity. Numerous researchers have concentrated their efforts on this specific step; nevertheless, no accepted theory of quantum gravity, and thus no accepted TOE have yet been formulated. In addition to explaining the forces mentioned in Figure 11.2, a TOE should also explain the status of, at least two candidate forces suggested by modern cosmology: an inflationary force for the Universe, and dark energy or dark matter. 11.2 STRING THEORY We believe there are four fundamental forces that govern the Universe: gravity, electromagnetism, the weak force, responsible for beta-decay, and the strong force which binds quarks into protons and neutrons. The physics community believe they understand all of these forces except for gravity. The word “understand” is used loosely, in that we may define the Lagrangian,27 which describes how these forces act upon matter and, at least in principle we know how to use these Lagrangians to make well-deﬁned predictions with which to test theories. But with gravity, our understanding is incomplete. Certainly, we understand gravity classically; that is, in the non-quantum limit of (h/2π) = 0, where h is Planck’s constant. And provided we do not ask questions about how gravity behaves m), we may calculate the effects of gravity. at very short distances (the Planck scale, of order, 10 It is sometimes said that physicists do not know how to combine quantum mechanics and gravity. In fact, physicists do understand how to include quantum mechanical effects into gravity, as long as we do not ask questions about what is going on at distances, less than the Planck length. For the other three fundamental forces we know how to include quantum effects, at all length scales. So, while we have a quantum mechanical understanding of gravity, we don’t have a complete theory of quantum gravity. And that is the problem, as the most interesting questions we wish to ask about gravity is what happen at very small length scales; for example, questions such as “What was the Big Bang” and “What happens at the singularity of a Black Hole?” So what is it that goes wrong with gravity at scales shorter than the Planck-length? The mathematical answer is that the force of gravity is not renormalizable; that is, at very short length scales, the gravitational energy become very large (we are trying to divide something by zero), and we can only avoid this mathematical divergence (that is, a number tending toward ∞) by constructing unnatural models. -35 27 Lagrangian mechanics is a reformulation of Newtonian mechanics, introduced by the Italian-French mathemati- cian and astronomer Joseph-Louis Lagrange (1736–1813) in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms; one separates terms involv- ing kinetic and potential energy. In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, and time; containing the information about the dynamics of the system. No new physics is necessarily introduced in applying Lagrangian mechanics, compared to Newtonian mechanics. It is, however, more sophisticated mathematically. 120 The force of gravity is a property of the scale over which it is being investigated. Consider an isolated electron in classical electromagnetism. The total energy (ET) of this electron (of rest mass, m) is given by the sum of a kinetic part and a potential part: ET ≈ m + ∫ d3x │E│2 ≈ m + 4π ∫ r2dr (e2/r4), where e is the charge of the electron and r is its radius. This integral defines the potential energy of the electron, and it diverges because you are dividing by a number going to zero at r = 0 (a point singularity). We may avoid this divergence by cutting the function off at some scale, Λ; so the total energy of the electron is now given by ET m + C (e2/Λ). ∼ Clearly, the second term still dominates in the limit which interest us; that is, small r. Naively, we speak of the rest mass of the electron, m, but we cannot measure m; we measure ET. That is, the inertial mass should include the electromagnetic self energy. Consequently, the physical mass m is given by the sum of the bare mass m and the mass derived from the electron’s ﬁeld energy (via E = mc2 ). This means that the bare mass is inﬁnite in the limit of interest. Note that we must make a measurement to ﬁx the bare mass. We cannot predict the electron mass. It also means that the bare mass must cancel the ﬁeld energy. That is, we have two huge numbers which cancel each other extremely precisely. To understand this better, note that it is natural to assume, using dimensional analysis (see Chapter 9) that the cut-off should be the Planck length. Which in turn means that the self-ﬁeld energy is, of order, the Planck mass. So the bare mass must have a value which cancels the ﬁeld energy. This cancellation is sometimes referred to as a hierarchy problem. This process of absorbing divergences in masses, or couplings (an analogous argument can be made for the charge e) is called renormalization. String theory, however, replaces point particles with minute strings, which can be either open or closed (depending on the particular type of particle that is being replaced by the string), whose length, or string length (denoted ls), is approximately 10 m. Moving from a point particle to a string avoids the problems of renormalisation. In string theory, one thus replaces Feynman diagrams by surfaces, and word-lines, or trajectories become world-sheets (see Figure 11.3). One increases the dimensionality of the problem. −35 All such theories use supersymmetry, which is a symmetry that relates elementary particles of one type of spin to another particle that differs by a half-unit of spin. These two partners are called superpartners. Thus, for every boson there exists its superpartner fermion and vice versa. For string theories to be physically consistent they require ten dimensions for space-time. However, our everyday world is only four-dimensional (three spatial dimensions and time) and so one is forced to assume that the extra six dimensions are extremely small, but must still be taken into consideration. To generalize about going from moving point particles (moving along a trajectory or world-line) 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHINGto strings we have a world-sheet instead of a world-line, which has the form of a curved sheet or a curved cylinder depending on whether the string is open or closed (see Figure 11.3). 11.2 STRING THEORY 121 e- e+ e+ World-Sheet World-Volume World-Line e m T i Space Space Particle String Brane Figure 11.3: (upper) In string theory, Feynman diagrams (the one displayed here describes the scatter- ing, or interaction of an electron, e- and a positron, e+) involving point entities are replaced by surfaces. (lower) World-line, world-sheet, and world-volume (denoting the trajectories of particles, strings or branes), as they are derived for particles, strings, and branes. What happens with gravity with this type of renormalization procedure? How does string theory solve the renormalization problem in gravity? Because the electron (now a string, not a point; one-dimensional rather than zero-dimensional) has ﬁnite extent lp, the divergent integral is cut-off at r = lp. We now have no need to introduce new parameters to absorb divergences, as they do not arise. String theory has only one unknown parameter, the string length, of order, lp, but this can be ﬁxed by the only measurement string theory requires before it can be used to make predictions. However, the hierarchy problem remains. String theory predicts that the electron mass is huge, of order, the inverse length of the string, but we still need an additional something to give a reasonable 122 value for the mass. It turns out that string theory can do more than just cut off the integral, it can also add an additional integral which cancels off a large part of the ﬁrst diverging integral, leaving a more realistic result for the electron mass. This cancellation is a consequence of supersymmetry which, as it turns out is necessary in some form for string theory to be mathematically consistent. So by working with objects of ﬁnite extent as opposed to point particles, we accomplish two things. All the integrals are ﬁnite and in, principle, if string theory were completely understood we would only need one measurement to make predictions for gravitational interactions at arbitrary length- scales. In addition, we also gain predictive power (at least, in principle). Indeed in the Standard Model of particle physics, which correctly describes all interactions to energies, of order, 200 GeV, there are 23 free parameters which need to be ﬁxed by experiment; for example, the electron mass. String theory, however, has only one such parameter in its Lagrangian, the string length. However, one must never forget that physics is a predictive science; it is not an end in itself. The less descriptive and the more predictive a theory becomes the better. In that sense, string the- ory has become a latter-day Holy Grail. We have a Lagrangian with one parameter, which would be ﬁxed by experiment. You would then have a TOE. You could, in principle, explain all possible phenomena. Particle physics tells us that there are a huge number of elementary particles, which can be split into two categories: matter and force-carriers. The set of particles that define matter is composed of six quarks: u, d, s, c, b, t (up, down, strange, charm, bottom, top), while the force carriers are the photon, the electroweak bosons, Z, W±, the graviton g, and eight gluons responsible for the strong force, and the recently discovered Higgs boson. So, in particle physics, we have a Lagrangian, which sums over all particle types and distinguishes between matter and force-carriers in some way. If we had a TOE, all the particles and forces should be uniﬁed in some way so that we could write down a Lagrangian for a “master entity,” and the particles mentioned would then just be different manifestations of this underlying entity. In string theory, the underlying entity is the string, and different excitations of the string represent different particles. Furthermore, uniﬁcation of the four fundamental forces is also built into the theory. In the world we perceive, there are three familiar dimensions of space: height, width, and depth. Einstein’s general theory of relativity treats time as a dimension on a par with the three spatial dimensions. In general relativity, space and time are not modeled as separate entities but are instead unified to a four-dimensional space-time; three spatial dimensions and one time dimension. In this framework, the phenomenon of gravity is viewed as a consequence of the geometry of space- time. In spite of the fact that the Universe is well described by four-dimensional space-time, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling space-time in a different number of dimensions, a theory becomes more tractable mathematically, and one can perform calculations to gain insights more readily. There are also situations where theories in two or three space-time dimensions are useful for describing phenomena in condensed 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHING11.3 REALITY 123 matter physics. Finally, there exist scenarios in which there could actually be more than four dimen- sions of space-time, which have nonetheless managed to escape detection.28 However, one should keep in mind that string theory is in some sense only in its infancy, and, as such, is nowhere near being able to answer any of the questions we would wish it to answer; especially regarding what happens at singularities. There are those who believe that, in the end, string theory will either have nothing to do with Nature, or will never be testable, and as such will be relegated to being a mathematical plaything, or a new branch of philosophy. 11.3 REALITY At present, there is no candidate TOE that includes the Standard Model of particle physics and general relativity. For example, no candidate theory is able to calculate the Fine Structure constant (α = 1/137.035 999 084(21)), or the mass of the electron (me = 9.109 383 56(11) ×10-31 kg), both of which are known very precisely from experiment (as can be seen by the error limits). We know these fundamental constants with extraordinary precision from experiment, and achieving that level of agreement with a theory, would be a significant test on the validity of any theory. Most particle physicists expect that the outcome of the ongoing experiments, the search for new particles at the large particle accelerators and for dark matter, are needed in order to provide further input for a TOE. However, there are many who take the view that the search for the TOE is a waste of time and resources. In fact, no better than the futile search for the Perfect Language by Dante and the Kabbalists, or Isaac Newton and Gottfried Leibniz. Kurt Friedrich Gödel (1906–1978) was an Austrian, and later American, logician, mathe- matician, and philosopher; he is considered to be one of the most significant of logicians. His in- completeness theorems define modern views of mathematical logic; they demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic. These results from 1931 are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that David Hilbert’s 1900 program to find a complete and consistent set of axioms for all physics, the TOE is impossible. A number of scholars claim that Gödel’s incompleteness theorem suggests that any attempt to construct a TOE is bound to fail. Gödel’s theorem, informally stated, asserts that any formal theory expressive enough for elementary arithmetical facts to be expressed, and strong enough for them to be proved is either inconsistent (both a statement and its denial can be derived from its axioms) or incomplete, in the sense that there is a true statement that can’t be derived in the for- mal theory. Stephen Hawking was originally a believer in the TOE but, after considering Gödel’s theorem, concluded that an ultimate theory is not possible: “Some people will be very disappointed if 28 There is a wonderfully imaginative use of such compactification and hidden dimensions in the science fiction of Liu Cixin; the technology of the Trisolarians and other alien species in The Three-body Problem of 2007, and its two sequels, The Dark Forest (2008) and Death’s End (2010). 124 there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.” Other physicists have argued against this view, pointing out that Gödel’s theorems are irrele- vant for computational physics; that is, purely model-based theoretical physics. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws. Whereas there may or there may not be an underlying philosophical/theoretical reason why a TOE may or may not exist, there is also a more prosaic argument about experimental uncertainty that clouds the search. How do you know if you have found a more fundamental model of physical reality, a higher syn- thesis of the Laws of Nature? To date, no physical theory is held to be precisely accurate. Physics proceeds by a series of successive approximations, allowing more and more accurate predictions and measurements of an ever-wider range of phenomena; see Table 11.1, which summarizes the evolution of the precision of the measured values of the speed of light, c. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in an “absolute truth.” Einstein himself expressed this view on several occa- sions. Following this view, we may reasonably hope for a TOE which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer. A motive for seeking a TOE apart from the pure intellectual satisfaction of completing a centuries-long quest, is that prior examples of unification have predicted new phenomena, some of which (for example, electrical generators and technology) have proved of great practical importance to our civilization. 11.4 FURTHER READING The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (2003); Brian Greene; New York: W.W. Norton & Company. The Road to Reality: A Complete Guide to the Laws of the Universe (2005); Roger Penrose; Knopf. The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next (2006); Lee Smolin; New York: Houghton Mifflin Co. Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law (2006); Peter Woit; London, Jonathan Cape. 11. THE GHOST OF THE DIVINE LANGUAGE: THE THEORY OF EVERYTHING11.4 FURTHER READING 125 Table 11.1: The evolution of the experimental value of the speed of light, c. We see how the value of this constant of Nature converged to its present day accepted value, but the size of the uncertainty associated with the measurements also fell with time and the increasing precision of the measurements. Today, the value of c is fixed by the definition of the meter in the modern Quantum-SI; hence, the present value of c is exact, and without error. But this “fixing” of the value of a constant of Nature has implications on our evolving understanding of other aspects of Nature. All Nature is interconnected (see Figure 9.2), and we should be careful in formally constraining some of those connections. Value of c Year Method 1675 Astronomical observations of the moons of Jupiter 220,000 km/s 301.000 km/s 1729 Studies of optics (parallax) 315,000 km/s 1849 Optics (interference) 298,000 ± 500 km/s 1862 Optics (rotating mirror) 299,710 ± 30 km/s 1907 Electromagnetism 299,796 ± 4 km/s 1926 Optics (interferometry) due to Albert Michelson 299,792.5 ± 3.0 km/s 1950 Electromagnetics (masers) 299,792.50 ± 0.10 km/s 1958 Radio interferometry 299,792.4562 ± 0.0011 km/s 1972 Laser interferometry 299,792.458 km/s (Exact, and so without error.) 1983 c fixed with the new definition of the meter CHAPTER 12 127 Changing the Paradigm: From Long Lists to Short Explanations One had to be a Newton to notice that the Moon is falling, when everyone else sees it doesn’t fall. Paul Valéry (1871–1945) So how did we go from the earliest stage of the creation of science, that is, the creation of long lists, to looking for an underlying principle to explain all the observations and information contained in those long lists? 12.1 THE GREAT PARADIGM SHIFT IN BIOLOGY In many ways, modern physics, or if you will modern physical sciences, is an unstable structure. While parts of the edifice of physics are solid enough, and have been around for centuries; rep- resenting a coherent story, there are other parts of the edifice that have been added in an ad-hoc manner. Quantum mechanics enables one to calculate many measureable atomic properties, and when the theoretical or calculated quantity is compared to the measured quantity, we have excep- tional agreement, and we say that the theory must therefore be true. This is, after all, the basis of the scientific method. Yet quantum mechanics does not fit in at all with astrophysics. These two areas of physics each apply to very different length scales-from galaxies to quarks. Consequently, we have at present two very different and successful, in their own domains, models of reality, but they do not come together. We have yet to construct, or find the Theory of Everything (see Chapter 11). When you look at physics today, you are looking at the state of biology in the early 1950s; that is, before the discovery of the structure of deoxyribonucleic acid or DNA, and the explanation of how this molecule and its self-replication explains evolution on earth. Before the early 1950s, we knew about the patterns of inheritance of characteristics such as eye color and hair color in animals, the breeding of horses and greyhounds, and the color of flowers in pea plants; and it was suspected that this strange mechanism of inheritance had something to do with the complex molecules found in the nuclei of all living cells. These large, complex molecules, which became known as nucleic acids, were investigated and found to be long polymers made up of a handful of smallish molecules. And so the race was on to try and determine the structure of the nucleic acid polymer to see if it could tell us something about inheritance and genetics. 128 The problem was solved in 1953. Francis Crick (1916–2004) and James Watson (born 1928) determined the double-helix structure of the major component of nucleic acid, deoxyribonucleic acid (DNA). Not only did they determine the position of the atoms within the double-helix, but they showed that when the DNA molecule divides, at the same time as the cell divides into two daughter cells, the two (helical) strands of the original DNA molecule unwind, and each strand as- sembles a new partner strand from small molecules available in the surrounding cell-fluid. And it is the rules that govern this assembling of a new stand of the double-helix DNA, based on the chem- ical structure of the original strand that allows physical characteristics to be passed from one gen- eration to the next. Two physicists, using the technique of x-ray crystallography, had demonstrated that the whole of biology could be re-interpreted from the view-point of the three-dimensional structure of the complex molecules found in the cells of every living organism. What was more, the work of these two young crystallographers demonstrated that if a mistake were made in building the daughter-DNA molecule; that is, in assembling the new DNA strand/molecule to be fitted into the daughter nucleus then there was the possibility of a mutation, or a change in the blue-print of life of that organism. Generating the possibility that the next generation of that organism would be ever so slightly different from their parents. At a stroke, the mechanism of Darwin’s theory of evolution by natural selection was discovered, and the pseudo-science of eugenics overturned. The paradigm of biology had changed. A new unity had been achieved out of a synthesis of diversity. Before the 1950s, biology consisted in learning the contents of some very long lists contained in a vast array of books. With reference to what was said in Chapter 1, when it comes to retrieving data and information we had moved from Homer’s Catalogue of Ships to the database of swift-footed Achilles. After the 1950s, biology consisted in looking at the observations contained in those long lists of book and re-interpreting them in terms of the structure and replication of DNA. The discovery of the structure of DNA, and how it replicated itself, revolutionized every aspect of biology and medicine. It opened up the possibility of designing life, and of significantly extending life-spans. The list of how the discovery of Crick and Watson will change our world is practically endless. This century will be the century of genetic engineering and genetic medicine, just as the last century was the century of the physical sciences. 12.2 ELECTROMAGNETISM When we use a mobile phone, listen to the radio, use a remote control, or heat food in the micro- wave, few are aware that it was the great Scottish physicist/mathematician, James Clerk Maxwell (1831–1879), who was responsible for making these technologies possible. In 1865, Maxwell published an article entitled “A Dynamical Theory of the Electromagnetic Field,” where he stated: “It seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic 12. CHANGING THE PARADIGM: FROM LONG LISTS TO SHORT EXPLANATIONS12.2 ELECTROMAGNETISM 129 field according to electromagnetic laws.” These ideas of Maxwell ushered in the great synthesis of electromagnetism. This paradigm change was a development of the metric system in Revolution- ary France (April, 1795). In the same way that the study of heat and energy had not reached a sufficiently mature stage to allow the savants who formulated the metric system to propose a base unit for temperature in 1795, the study of electricity was at an even more immature stage. Indeed, the study of electricity and magnetic phenomena in the 1790s had more in common with parlor tricks than laboratory investigations. The two names associated with the earliest investigations of the nature of electricity are the pious, conservative, Italian medical doctor Luigi Alyisio Galvani (1737–1798), and another Italian, the natural philosopher Alessandro Giuseppe Antonio Anastasio Volta (1745–1827). In 1791, Galvani famously discovered that the leg muscles of dead frogs twitched when they came in contact with an electrical spark. According to popular versions of the story, Galvani was dissecting a frog at a table where he had previously been investigating discharges of static electric- ity. Galvani’s assistant touched an exposed sciatic nerve of a dead frog with a metal scalpel, which had picked up a residual static (electrical) charge. At that moment, the two men saw the leg of the dead frog kick as if it were alive. Such laboratory-based observations made Galvani the first to consider the possible relationship between electricity and animation; that is, the creation of life, and the possibility of the re-animation of dead tissue. Indeed, Luigi Galvani used the term “animal electricity” to describe the force that animated the muscles of the dead frog. Along with many of his contemporaries, he regarded the activation of the supposedly dead muscles as being generated by an electrical fluid carried by the still functioning nerves of the frog to the inanimate muscles. Given his background, Galvani naturally assumed he had discovered something of the animating or vital force that was implanted in all creatures by their Creator. However, not everyone agreed with this conclusion. In particular, Alessandro Volta thought that the term “animal electricity” had a suggestion of superstition and magic, and that it was not an explanation of the dramatic phe- nomenon observed repeatedly by Galvani and co-workers. For his part, Galvani held that natural philosophers like Volta had no place in moving from the laboratory into God’s realm of vitalism and the nature of life itself. The argument between Galvani and Volta was a microcosm of the larger debate about the place of the Divine in Nature which was animating the European Enlightenment. Galvani spent years repeating his experiment on dead animals, and discovered that you did not need a traditional source of static electricity to cause the dead muscle tissue to twitch. A combination of two wires of different metals, for example, copper and zinc was sufficient, but Galvani could not explain these observations. The phenomenon observed by Galvani was subsequently named “galvanism,” on the sugges- tion of his sometime intellectual adversary, Volta. Today, the term galvanism is used only to describe someone who suddenly becomes excited, and it is likely that most people who use this word have no idea of its origin. Although at the beginning of the 19th century, the observations of Galvani 130 were the source of much discussion, most famously in the novel Frankenstein, or, The Modern Pro- metheus by Mary Shelley, which describes further investigations into the principles of animation and vitalism. Alessandro Volta was more of a scientist than Galvani. In the late 1770s, Volta had studied the chemistry of gases, and was the first person to investigate the origin and chemical composition of natural gas, or methane. However, it is for his investigations into the nature of electricity that Volta is most famous, in particular, for a systematic investigation of electrical capacitance. He de- veloped separate means of investigating both the electrical potential applied to the two plates of the capacitor, and the charge residing on the plates. Volta discovered that for a given pair of plates, the potential and the charge are proportional. This relationship is called Volta’s Law of Capacitance, and to honor his fundamental work on electrostatics the unit of electrical potential is named the volt. Alessandro Volta realized, from his own studies of Galvani’s observations that the frog’s leg merely served as both a conductor of electricity (the fluid in the dead muscle tissue is what today we would term an electrolyte) and a detector of the presence of a flowing electric current; all of which mimicked an instantaneous animation. Indeed, Volta realized that the two different metals (the electrodes) used by Galvani, inserted into the fluid of the frog’s leg formed an electrical circuit. Volta replaced the frog’s leg by paper saturated with another conducting electrolyte, e.g. salt solution, and detected a flow of electricity. In this way he invented the electrochemical cell, the forerunner of all chemical batteries. Luigi Galvani never perceived of electricity as being separable from biology. He always believed that animal electricity came from the muscle of the animal. Volta, on the other hand, reasoned that animal electricity was merely a physical phenomenon external to the dead frog, an electric current coming from the metals, which formed an electrochemical cell or battery (for ex- ample, zinc and copper), mediated by the fluid in the muscle tissue. There was no reanimation of dead tissue, merely a flow of electrical current from one electrode to the other electrode through the physiological fluid (the electrolyte) in the muscle of that poor dead frog. But Galvani’s ideas did give literature, and the cinema Dr Frankenstein and his splendid creature. In the early 19th century, electricity, magnetism, and optics were three independent disci- plines. However, the situation changed thanks to one invention and two discoveries. The invention was the electrical battery, a continuous source of electrical current created by Alessandro Volta in about 1800. The two discoveries were: (1) the demonstration of magnetic effects caused by the flow of electrical currents, observed by the Danish chemist and physicist Hans Christian Ørsted (1777– 1851) and by the French mathematician and one of the creators of the Metric system, André-Ma- rie Ampére (1775–1836) in 1820; and (2), the 1831 discovery by the British chemist and natural philosopher Michael Faraday (1791–1867) of the generation of electrical currents from magnetic fields, that is, electromagnetic induction. In September 1820, Ampére presented his results to the Académie des sciences: “mutual action between currents without the intervention of any magnet”; that is, 12. CHANGING THE PARADIGM: FROM LONG LISTS TO SHORT EXPLANATIONS12.2 ELECTROMAGNETISM 131 two parallel electrical currents attract, or repel each other depending on their polarity, as do per- manent magnets. In 1826, he published Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience, whereby he claimed that “magnetism is merely electricity in motion” and that magnetic phenomena depend only on the existence and motion of electrical charges (see the lines of force emanating from a bar magnet, which also represents the magnetic field generated by an electric current in Figure 12.1), thereby setting the stage for Faraday’s experiments. Figure 12.1: The invisible repulsive lines of force emanating from similar poles of two bar magnets; visualized by the use of iron fillings. Image from: https://commons.wikimedia.org/wiki/File:Magnetic_ field_of_bar_magnets_repelling.png. The three contributions mentioned above form the basis of modern electromagnetism, but required the insight of the Scot, James Clerk Maxwell to form a coherent single theory. Before Maxwell, electromagnetism still consisted of long lists of observations of supposedly disparate phenomena; Maxwell demonstrated the single underlying causation. Such a synthesis represents the most profound transformation of the fundamentals of physics since Newton, and is one of the greatest of scientific achievements, unifying electrical and magnetic phenomena, and enabling the development of the theory of electromagnetic waves, including light. James Clerk Maxwell published his major work, A Treatise on Electricity and Magnetism in 1873; a first step on the great journey to the Theory of Everything (see Figure 11.2). Here, Maxwell rationalized and unified all the then known phenomena involving electricity and magnetism. When we come to consider how matter interacts with light; that is, with an oscillating, or time-varying electromagnetic field, we have to consider the other great contribution to the final synthesis of elec- tromagnetism made by Maxwell, who, between 1861 and 1862, published a set of equations relating electricity and magnetism and demonstrated that light is another electromagnetic phenomenon. Classically, light scattering arises through secondary radiation from oscillating dipoles induced by 132 the incident electromagnetic wave. The simplest case occurs when the scattering medium is a gas, composed of randomly distributed molecules of dimensions that are small compared to the wave- length of the light.29 For a random distribution, the phase relationships between waves scattered from different molecules are uncorrelated in all but the forward direction, so that the total scat- tered intensity can be calculated directly as the sum of contributions from each molecule; thereby permitting study of the properties of individual scattering molecules. Figure 12.2 demonstrates the dramatic colors that are generated by the scattering, and absorption of the light coming from the Sun, by the molecules in the atmosphere. Figure 12.2: The blue color of the sky is caused by light scattered by atmospheric gas molecules (N2, O2, H2O, and CO2), and not by absorption. These molecules being much smaller than the wavelengths of visible light. The red color at sunset and sunrise (sunrise in Montpellier, France, in October 2019, in this photograph) comes from absorption, because at sunrise and sunset the Sun is low in the sky and so the sunlight is passing through the thickest section of atmosphere (that is, the path-length is at its longest). This absorption of blue light, leaving the red/pink color is due to molecules other than the normal com- ponents of air; that is, pollutants or dust. The grey/white color of clouds is caused by light scattered by water droplets, which are of a comparable size to the wavelengths of the incident visible light. The darker the color of the clouds, the larger are the water droplets, as liquid water does have a weak (electric dipole forbidden) absorption in the visible. 29 The molecules comprising air (principally, N2 and O2) have a “diameter” of about 1 Å; that is, 1 × 10 m. On the other hand, the wavelength of visible light; that is, the spacing between two successive maxima of the oscillating electromagnetic wave is about 5,100 Å (in the green where our eyes have evolved to be the most sensitive). -10 12. CHANGING THE PARADIGM: FROM LONG LISTS TO SHORT EXPLANATIONS 12.3 FURTHER READING 133 In the next two chapters, we will consider how the classification of information about life, and about natural phenomena is accomplished, and how this scientific classification assists scientists in comprehending Nature, and in developing theories to explain the world around us. First we will consider biology. As pointed out above, the paradigms of biology changed with the discovery of the structure and function of DNA, and the interpretation of evolution at a molecular level in terms of the hydrogen-bonding between the four nucleoside bases (the monomers) that compose the large (long) polymeric DNA molecule: adenine, cytosine, guanine, and thymine. The diversity and evolu- tion of life on earth arises from the coupling of these four smallish molecules, when they are bound into the DNA polymer. It is generally held that evolution is the most powerful and comprehensive idea ever formulated. 12.3 FURTHER READING 1 2 The Double Helix (1968); James D. Watson; New York, Touchstone. The Molecule as Meme (2018); Jeffrey H. Williams; San Rafael, CA:Morgan & Claypool. CHAPTER 13 135 The Classification of the Living and the Dead Nothing in biology makes sense except in the light of evolution. Theodosius Grygorovych Dobzhansky, (1900–1975) There are millions of species of organisms, both plants and animals living on this Earth. In addition, there are many millions of species preserved in the fossil record. These are plants and animals that lived once upon a time, and as a consequence of climate change, natural selection, and rogue large meteorites have become extinct. Given the scientist’s desire, and need for classification and list making, how is it possible to keep track of everything that is alive, or has ever been alive? This is not a dull academic question, as if we are to understand how we (Homo sapiens, or “thinking man”) evolved from less-advanced creatures; we must be able to locate ourselves, and our ancestors in the Great Scheme of Life on this planet. How then do we name and organize all of the long lists of the living and the dead, without getting confused, and without our imperfect memories leaving large embarrassing lacunae in our models of the evolutionary story of life on this planet? The answer to this question is straightforward; we use a complex, but elegant system of classification developed in the 18th century by Carolus Linnaeus (1707-1778).30 Linnaeus was a Swedish botanist, physician, and zoologist who formalized a binomial nomenclature of organisms; and we still use this system of naming and classifying organisms. Indeed, Linnaeus is known as the “father of modern taxonomy” (see Figure 13.1). Linnaeus was a product of, and became a towering figure in, the European Enlightenment. However, he is less well known,or remembered today than many of his scientific and philosophical contemporaries, particularly, those from France, Germany, and Scotland. 30 Many of his writings were in Latin, and his name Carl von Linné, is rendered in Latin as Carolus Linnaeus. In addition, we speak of the Linnaean system of classification (from the Latin form of his name), but the Linnean Society of London is named from the original Swedish spelling of the name. The Linnean Society of London are the custodians of Linnaeus’ specimen collection, and are the UK’s learned society responsible for taxonomy. It was in the rooms of the Linnean Society that the papers of Charles Darwin and Alfred Russel Wallace on evolution by natural selection were presented on July 1, 1858. 136 Figure 13.1: Painting of 1737 by Martin Hoffman showing Carl von Linné (Linnaeus) in his field-cos- tume; the traditional dress of the Sami people of Lapland. In his hand is the plant that Jan Frederik Gronovius named after him. Linnaea borealis is a spe- cies of flowering plant in the family Caprifoliaceae (the honeysuckle family). Until relatively recently, it was the only species in the genus Linnaea. It is a boreal to subarctic woodland subshrub; hence the specific name, and is commonly known as twinflower. This plant was a favorite of Carl Linnaeus, founder of the modern system of binomial nomenclature, for whom the genus was named (image from: https://en.wikipedia.org/wiki/ Carl_Linnaeus#/media/File:Naturalis_Biodiversity_ Center_-_Martin_Hoffman_-_Carl_von_Linné_(Lin- naeus)_in_his_Lapland_costume_-_painting.jpg). The European Enlightenment was the 18th century up to, but not including, the French Revolution; the great socio-political event that was the product of the Enlightenment. This was a period of intense philosophical and scientific investigation. Toward the end of the Enlightenment, in 1784, the German philosopher and mathematician Immanuel Kant (1724–1804) published his celebrated essay, “Answering the Question: What is the Enlightenment?,” where he told his readers that the Enlightenment was man’s emergence from a self-imposed immaturity that had led to his incapacity to use his understanding to explain Nature without guidance from another (higher) being. Kant told his readers that they had to be courageous to understand Nature, they had to “dare to know” (in Latin, sapere aude!). That man should investigate the world around him, and pursue his investigation to the limit of technology; and then use his mind to imagine what might happen be- yond his technical limitations. Although best known today for his work in ethics and metaphysics, Kant made significant contributions to other disciplines, especially, mathematical physics. In 1754, he was awarded the Berlin Academy Prize for his prediction of the inevitable slowing down of the Earth’s rotation. 13. THE CLASSIFICATION OF THE LIVING AND THE DEAD13. THE CLASSIFICATION OF THE LIVING AND THE DEAD 137 In his early mathematical studies, Kant pointed out that due to the gravitational attraction between the Earth and the Moon, the frictional resistance of the motion of the oceans on the Earth’s surface must lead to a slow decrease in the Earth’s speed of rotation. Energy was being generated as friction between the moving slabs of water, and the rotating solid Earth that supported and carried the oceans. Kant knew that energy was conserved; it cannot be made or be lost, so he reasoned that the frictional interaction of the oceans with the massive rotating crust had to come from somewhere, and Kant further reasoned that it was being taken from the speed of rotation of the Earth; that is, the Earth’s angular momentum. The position of the Moon relative to the Earth is determined by the sum of the attractive forces derived from the masses of the Earth and Moon and the much larger, but more distant, mass of the Sun. That is, the overall gravitational attraction of these three bodies. Through this mutual gravitational force, the Earth holds the Moon to itself and the Moon generates the tides seen on Earth; tides that are the origin of the inevitable slowing of the Earth’s rotation (2.3 milliseconds/century). This discovery attracted little or no attention until about 1840, when the concept of energy began to be widely and more fully comprehended. Yet, the slowing of the Earth is the reason that time-metrologists still insert “leap seconds” into the year to maintain coherence between Greenwich Mean Time (a measurement of when the sun rises at Greenwich) and atomic time (a measure of frequency of an excitation within the hydrogen atom). These early mathematical investigations had taught Kant that all the sciences are linked; that Nature is a seamless whole (see Figure 9.2). He looked at the energy of interaction of the oceans with the Earth’s rotating solid surface, then using mathematical logic he saw that the Earth is a complex but self-contained, and self-regulating system. He dared to use mathematics to follow, to its logical conclusion something that no one had previously considered: that the Earth is inevita- bly slowing down through the generation of frictional energy. A mechanical energy derived from the relative motion of the oceans to the Earth. Kant clearly demonstrated that one should look at Nature holistically; in much the same way that the Ancient Chinese Taoist sages had looked at the world around them. And in so doing, Kant came to a startling conclusion. What Kant and others achieved in the physical science, by building on the work and ideas of Isaac Newton, the Swedish botanist Carl Linnaeus attempted in the monumental task of trying to devise a system of classification capable of containing not only every living organism, but every organism that had ever lived. And in so doing provide a wealth of information about the interconnectedness of those living and extinct organisms; connections which proved invaluable after the appearance of Darwin’s explanation of the evolution of species in the mid-19th century. Carl von Linné (Carl Linnaeus) was born in the countryside of Småland in southern Swe- den. He received most of his higher education at Uppsala University and began giving lectures in botany in 1730. He lived abroad between 1735 and 1738, where he studied and published the first edition of his systematic classification of Nature, Systema Naturae, in the Netherlands. He returned to Sweden, where he became professor of medicine and botany at Uppsala. In the 1740s, he was 138 sent on several journeys through Sweden to find and classify plants and animals. In the 1750s and 1760s, he continued to collect and classify animals, plants, and minerals, while publishing several further volumes. At the end of his life, he was one of the most acclaimed scientists in Europe. Phi- losopher Jean-Jacques Rousseau sent him the message: “Tell him I know no greater man on earth.” Johann Wolfgang von Goethe wrote: “With the exception of Shakespeare and Spinoza, I know no one among the no longer living who has influenced me more strongly.” Swedish author August Strindberg wrote: “Linnaeus was in reality a poet who happened to become a naturalist.” Linnaeus has also been called Princeps botanicorum (Prince of Botanists), and is considered as one of the founders of mod- ern ecology. But it is as a taxonomist31 that he is remembered today. 13.1 A HIERARCHICAL SYSTEM OF CLASSIFICATION During his lifetime, Linnaeus collected around 40,000 specimens of plants, animals, and shells. He believed it was important to have a standard way of grouping and naming species. So in 1735, he published the first edition of Systema Naturae (The System of Nature), which was a small pamphlet explaining his new system of the classification of Nature. He continued to publish further editions of Systema Naturae that included increasing numbers of named species. In total, Linnaeus named 4,400 animal species and 7,700 plant species using his binomial system of nomenclature. The tenth edition of Systema Naturae was published in 1758 and is considered the most important edition; its full title in English is System of Nature through the Three Kingdoms of Nature, According to Classes, Orders, Genera, and Species, with Characters, Differences, Synonyms, Places. In Systema Naturae, Lin- naeus classified Nature into a hierarchy. In this, Linnaeus was following the classification of John Wilkins in his attempt to create a new philosophical universal language in 1688 (see Page 57). Linnaeus proposed that there were three broad groups, called kingdoms, into which the whole of Nature could be fitted. These kingdoms were animals and plants; he originally attempted to classify minerals within the same hierarchy, but this did not work. He divided each of these kingdoms into classes; classes were divided into orders. These were further divided into genera (genus is the singular) and then into species. We still use this system today, but we have made some changes. Today, we only use this system to classify living things, or things that were once alive. Also, we have added a few additional levels in the hierarchy. The broadest level of life is now a domain. All living things fit into only three domains: Archaea (single-celled microorganisms), Bacteria (prokaryotic microorganisms) and Eukarya (organisms whose cells have a nucleus enclosed within membranes, unlike prokaryotes (Bacteria and Archaea), which have no membrane-bound organelles). Within each of these domains there are kingdoms, for example, Eukarya includes the Kingdoms: Animalia, Fungi, Plantae (plants). Each kingdom contains phyla (the singular is 31 Taxonomy is the part of science that focuses on naming and classifying, or grouping organisms. Carolus Linnaeus developed a way of naming and organizing species that we still use today, and which is still expanding as new species of living and extinct organisms are discovered. 13. THE CLASSIFICATION OF THE LIVING AND THE DEAD13.1 A HIERARCHICAL SYSTEM OF CLASSIFICATION 139 phylum), followed by class, order, family, genus, and species. Each level of classification is called a taxon (the plural is taxa). According to this system, the tree of life consists of three domains: Archaea, Bacteria, and Eukarya. The first two are all prokaryotic microorganisms, or single-celled organisms whose cells have no nucleus. All life that is made up of cells containing a nucleus and membrane-bound or- ganelles, and multicellular organisms, is included in the Eukarya. Kingdom is the second highest taxonomic rank, just below domain. Kingdoms are divided into smaller groups called phyla (except the K. Plantae, which has “Divisions”).32 Some recent classifications based on modern cladistics33 have explicitly abandoned the term kingdom, noting that the traditional kingdoms are not monophyletic; that is, do not consist of all the descendants of a common ancestor. Depending on definitions, the animal kingdom Animalia or Metazoa contains approximately 35 phyla, the kingdom Plantae contains about 14, and the kingdom Fungi contains about 8 phyla. The total numbers of species in these phyla are estimates; figures from different authors vary wildly, not least because some are based on described species, some on extrapolations to numbers of undescribed species. And then there is the problem of es- timating, from the fossil record the number of species of a particular phylum that existed in the distant past. For instance, around 25,000–27,000 species of nematodes have been described, while published estimates of the total number of nematode species include 10,000–20,000; 500,000; 10 million; and 100 million. As mentioned above, animals, fungi, and plants are arranged into various groupings to assist with the classification of the great variety of life on Earth. Extinct organisms are treated in the same way as extant organisms (those which are still around today). All life on Earth belongs to one of three kingdoms: Animalia, Plantae, and another kingdom for the Fungi. Kingdoms are further sub-divided into other categories, organizing creatures, plants, and fungi in such a way that com- mon features lead to organisms being associated together until an individual species is defined; that is, until we arrive at the specific. This is the accepted method of classifying life (although cladistics has added a new dimension, or two), the principles of this form of classification were laid down by Carolus Linnaeus in the 18th century. To have achieved this level of hierarchical classification would have been impressive enough, but Linnaeus also demonstrated that by judicious choice of 32 Traditionally, some textbooks from the U.S. used a system of six kingdoms (Animalia, Plantae, Fungi, Protista (any eukaryotic organism (one with cells containing a nucleus) that is not an animal, plant or fungus), Archaea/ Archaebacteria, and Bacteria/Eubacteria) while textbooks in countries such as Great Britain, India, Greece, Austra- lia, Latin America used five kingdoms (Animalia, Plantae, Fungi, Protista, and Monera (a kingdom that contains unicellular organisms with a prokaryotic cell organization, having no nuclear membrane such as bacteria). 33 A method of classification of animals and plants that seeks to identify and take account of only those shared characteristics which can be deduced to have originated in the common ancestor of a group of species during evolution, not those arising by convergence. 140 names, for the various taxa, one could input into the classification a great deal of useful morphologic information; see Table 13.1. Table 13.1: Classification of man, an animal that lives with man, and an extinct carnivorous dinosaur Category (Taxon) Eukarya Animalia Chordata Mammalia Primates Hominidae Homo H. sapiens Domain Kingdom Phylum Class Order Family Genus Species The specimen of T. rex shown here is in the Field Museum in Chicago, IL, USA, and is affectionately known as Sue. There are many photos of Sue all over the Internet. The cat lives in south London. (Taxon) Eukarya Animalia Chordata Reptilia Saurischia (Theropoda) Tyrannosauroidea Tyrannosaurus T. rex (Taxon) Eukarya Animalia Chordata Mammalia Carnivora Felidae Felis F. catus We see from Table 13.1 that a human, a cat, and an extinct meat-eating dinosaur are all in the same domain, kingdom, and phylum. All three of us are, or were, multi-celled animals with backbones (the phylum Chordata: having a spine or backbone). It is after this level in the Great Hierarchy of Life that there is a divergence. The human and the cat are mammals (Mammalia), but the dinosaur was a reptile (Reptilia). Thereafter, the man and the cat diverge; we are Primates, and the cat is a Carnivore. The categories of classification from kingdom down to the species level is referred to as a taxonomic hierarchy. Organisms should be classified to reflect evolutionary relationships, with each taxon representing organisms that share a common ancestor; this is, the Tree of Life model of tax- onomy. It can be seen from Table 13.1 that the author, his neighbor’s cat, and a large meat-eating dinosaur all share the same domain, kingdom, and phylum. It is only there after that we start to separate; that is, the tree of life branches for us. The author and the cat, both being mammals, lie on a different line of descent from dinosaur T. rex, which derived from the chordates via reptiles. To be absolutely correct the name of all taxa should begin with a capital letter, except for the individual 13. THE CLASSIFICATION OF THE LIVING AND THE DEAD13.1 A HIERARCHICAL SYSTEM OF CLASSIFICATION 141 species name which should always begin with a lowercase letter.34 The scientific name for a partic- ular organism consists of two Latin or Latinized words that are always the genus followed by the species classification. Hence the term binomial classification. Such a standard system of nomencla- ture ensures that scientists from around the world can communicate effectively when describing the characteristics of an individual organism, or even of a single fossil. The genus, such as Tyrannosau- rus, can be used on its own but the species name; that is, rex without the genus associated with it has no meaning, as some species names may be used many times for organisms in different genera. It is at the level of order that the three creatures illustrated in Table 13.1 separate fully into primate, carnivore, and dinosaur. At the next level down in the hierarchy, family, we refer to Ho- minidae (whose members are known as great apes or hominids, are a taxonomic family of primates that includes eight extant species in four genera: Pongo, the Bornean, Sumatran, and Tapanuli orangutan; Gorilla, the eastern and western gorilla; Pan, the common chimpanzee and the bonobo; and Homo, which includes modern humans and their extinct relatives (e.g., the Neanderthal; Homo neanderthalensis), and ancestors, such as Homo erectus); for the cats, Felidae (a family of mammals in the order Carnivora, colloquially referred to as cats. A member of this family is also called a felid. The Felidae species exhibit the most diverse fur pattern of all terrestrial carnivores.); and Ty- rannosauroidea (meaning tyrant lizard forms is a group of coelurosaurian theropod dinosaurs that includes the family Tyrannosauridae as well as more basal relatives). The genus taxa in Table 13.1 become even more narrowly defined: Homo (from the Latin for human being, is the genus which emerged from the otherwise extinct genus Australopithecus, that encompasses the extant species Homo sapiens (modern thinking man), plus several extinct species classified as either ancestral to or closely related to modern humans (depending on a species), most notably Homo erectus and Homo neanderthalensis); Felis (genus of small and medium-sized cat species native to most of Africa and south of 60° latitude in Europe and Asia to Indochina). But it is with the specific taxon that we arrive at the specimens illustrated in Table 13.1. Homo sapiens (not, Homo neanderthalensis); Felis catus (not, Panthera tigris, the tiger) and Tyrannosaurus rex.35 In this way, all scientists, including palaeontologists work primarily with extinct species have a classification framework to use, and into which they may locate their particular specimen. That specimen will then be located in geological or evolutionary time, and in space; that is, in a partic- ular habitat. However, there are additional conventions to consider when classifying and naming animals such as dinosaurs, (or indeed all organisms for that matter). If a dispute arises as to the 34 This is some of the dogma of science that has attached itself to the technical advances of science. Such dogma, or “the way things should be done, as decided by an international group of elderly scientists” is also encountered in chemical nomenclature (see Chapter 14) and in the use of the International System of Units (SI, abbreviated from the French Système international d’unités), the modern form of the metric system, and the most widely used system of measurement (see Chapter 8). 35 Only species are real. Everything else is interpretation; that is, arbitrary and often subject to re-classification. But a species name should be eternal (unless a precedent turns up). 142 naming of an organism (and they do; see Chapter 14 on the naming of the chemical elements) then it is convention for the earliest name, the first description to take precedence. For example, the nomenclature of early hominids (our direct ancestors) is a minefield (see comment below). But this system of priority publishing does permit standardization; in this way, the name Brontosaurus was replaced by its older synonym Apatosaurus. There have, however, been some notable exceptions to this, and T. rex is one of them. In the late 19th century, many years before T. rex was named and described in 1905, the American palaeontologist, Edward Drinker Cope described two badly eroded fossil vertebrae as Manospondylus gigas; that is, “giant porous vertebra” in reference to the numerous openings for blood vessels he found in the fossilised bone. This strange honey-combed backbone was different to any known dinosaur fossils, and it was given this name. One of these bones has since been lost, however, the name stood and if scientific nomenclature was followed, as this bone is believed to represent a Tyrannosaurus rex then T. rex, the “Tyrant Lizard King” should be renamed Manospon- dylus gigas or “giant porous vertebrae,” but that is not quite such an exciting name. The debate as to the true name of Tyrannosaurus rex was brought to wider public attention when in 2000 a team from the Black Hills Institute of Geological Research, Hill City, South Da- kota, U.S., www.bhigr.com , claimed they had found the original site where Cope had unearthed the weathered fossil bones described as Manospondylus. Fossils found on this site, presumably from the same specimen that Cope studied almost a century earlier, turned out to be T. rex, so Tyrannosaurus rex should have been renamed based on this evidence. The International Code of Zoological Nomenclature (ICZN) states that if further remains are found and these are identical to those of the earlier discovery then the earlier name and description should be used. This led to much consternation among scientists (and among Hollywood directors, as Manospondylus sounds significantly less cool than Tyrannosaurus rex). However, in 2000 the ICZN ruled that T. rex should stay, as the name had been cited in numerous works by many authors and the case of mistaken identity was more than 50 years old. The creation of names, of naming things is an important and mysterious action, which is the origin of the attraction of the study of names, how to encapsulate in a word, or perhaps two words (as in the Linnaean system of biological nomenclature), the important characteristics of a newly discovered mineral, plant, animal or planet.36 36 A small bird like the thrush has very different names in different countries, yet even if you know all those names, you would still know nothing about the bird. You would only know something about the people who have observed that bird, and what they called the bird. The thrush sings, it teaches its young to fly, and it flies great distances; distances so large that we are not sure how this small bird is able to navigate using the Earth’s magnetic field as a guide. A true description of the thrush should provide some of this important information. The classifi- cation of the thrush: Kingdom: Animalia; Phylum: Chordata; Class: Aves; Order: Passeriformes; Suborder: Passeri; Family: Turdidae. Below this hierarchical level, the taxonomy of thrushes becomes complex because evolution is continually at work, leading to complex local characteristics. 13. THE CLASSIFICATION OF THE LIVING AND THE DEAD13.2 A WARNING TO THE UNWARY 143 13.2 A WARNING TO THE UNWARY The Linnaean system of biological nomenclature is in two parts, allowing some personal individu- ality while retaining some information on sample characteristics. The first name refers to the genus and is given to a set of distinct anatomical characteristics of the organism. The second, specific name can take this morphological characterisation further; for example, the large ammonite (a member of the phylum Mollusca (molluscs) similar to the still extant Nautilus, but the ammonites became extinct along with the dinosaurs at the end of the Cretaceous Period about 70 million years ago)37 found on Portland Isle, Dorset, UK, Titanites giganteus, is the largest representative of a genus of ammonite already well known for their size; see Figure 13.2. Although there are even larger am- monites in other genera. Figure 13.2: Giant Ammonite of the genus Titanities, in an organic limestone (the rock consists largely of a matrix of shells) of Portland stone ( Jurassic). Image from: http://www.southampton.ac.uk/~imw/ portfoss.htm. Thanks to Dr. Ian West for permission to reproduce this image; he retains full copyright. Alternatively, the second name in a Linnaean system of nomenclature may be the Latinized name of the person who first identified, or described the sample; the discoverer does not, however, 37 Classification of Ammonites: kingdom: Animalia; phylum: Mollusca; class: Cephalopoda; subclass: Ammonoidea. 144 propose his or her own name—this is discretely left to colleagues and vice versa. Thinking up such names might seem a good way to relax after all the hard work of obtaining the specimen. However, any slackness or lack of care in determining the taxonomy of a new specimen can have serious re- percussions; taxonomy is an important science as it explains and summarises the history of life on Earth. In 1995, an issue of Nature carried a scathing editorial condemnation of a research group who had, for whatever reason, ascribed a frozen corpse (affectionately named Ötzi, who died about 3345 BCE, and was found in an Austrian glacier) to a new species. The Nature editorial ran, “With breath-taking abandon, Lubec et al. assign Ötzi to a new species, Homo tirolensis. No reason is given for this casual designation. Readers will look in vain for the careful systematic and diagnostic argument that such nomenclature requires,” [1] Ötzi is as much a member of the species, Homo sapiens as is the author illustrated in Table 13.1. Such a colossal error in taxonomy (or, perhaps a lack of apprecia- tion for the details of taxonomy) will terminate your scientific career faster than a large incoming meteorite. 13.3 THE LIMITS OF LINNAEAN CLASSIFICATION: TWO UNCLASSIFIABLE SPECIES FOUND OFF AUSTRALIA As a final point, it is often the case that the limits of the Linnaean system of nomenclature are pushed by the discovery of new, exotic specimens. In this manner, the Linnaean system is contin- ually being expanded, and refined. The following is taken from a report in the Guardian newspa- per (www.theguardian.com/environment/2014/sep/04/two-unclassifiable-species-found-off-aus- tralian-coast) concerning a newly discovered organism. An organism that was so unusual that identifying the appropriate kingdom was problematic, and identifying the appropriate phylum almost impossible. The specimens displayed in Figure 13.3 were collected off the south-east coast of Australia in 1986. They were collected at water depths of 400 meters and 1,000 meters on the continental slope near Tasmania, using a sled that was dragged over the sea floor to collect bot- tom-dwelling organisms. The researchers were immediately struck by the unusual characteristics of the specimens collected. When initially discovered, the organism’s classification was difficult. The two specimens were assigned their own genus, Dendrogramma, and family, Dendrogrammatidae and the researchers even considered putting them in their own phylum. As they put it, however, “we refrain from erecting such a high-level taxon for the time being, because new material is needed to resolve many pertinent out- standing questions.” The lead scientist of the identification effort, Jørgen Olesen of the University of Copenhagen, suggested that they represent “an early branch on the tree of life, with similarities to the 600 million-year-old extinct Ediacara fauna.” The genus name Dendrogramma derives from the two Greek words déndron, meaning tree- like, and grámma meaning drawing, mathematical figure. Alluding to the branching pattern of 13. THE CLASSIFICATION OF THE LIVING AND THE DEADthe digestive canals, see Figure 13.3, which resemble dendrograms; that is, branching diagrams frequently used by biologists to illustrate the evolutionary relationships among organisms. The specific name enigmatica of the type species refers to the mysterious nature of the organisms, while discoides—the species epithet of the second species—alludes to the disc-like shape of the animals. 13.4 FURTHER READING 145 Figure 13.3: Enigmatic specimens dredged up from the ocean depths. Preserved specimens of Dendro- gramma. Images from: https://en.wikipedia.org/wiki/Dendrogramma#/media/File:Multiple_Dendro- gramma.png. 13.4 FURTHER READING The author is not a biologist, and is unfamiliar with texts used for teaching taxonomy; however, the author has found invaluable many of the articles available in the online encyclopaedia, Wiki- pedia (https://en.wikipedia.org/wiki/Wikipedia). In particular, the articles on Linnaean taxonomy (https://en.wikipedia.org/wiki/Linnaean_taxonomy) and taxonomy (https://en.wikipedia.org/ wiki/Taxonomy_(biology)) were helpful, as were the links they contain. 1 Nature, 1995, 373, 176. CHAPTER 14 147 Aspects of Chemical Nomenclature What’s in a name? that which we call a rose / By any other name would smell as sweet Romeo and Juliet, Act 2, Scene 2; William Shakespeare (1564–1616) The invention of modern biology began with the order introduced by Linnaeus, with his binomial nomenclature. In this way, biology became more that just long lists of organisms, fossils, and ob- servations of morphology and behavior. Biology became a system, which was developed further by Charles Darwin, and finally rationalized by the work of Crick and Watson in the 1950s. At a stroke, Darwin’s theory of evolution became a fact grounded in molecular physics. The myriad of books on everything from the breeding of horses and pigeons, to the genetics of pea plants and roses could be replaced by a new paradigm based on the interaction, and number of the hydrogen-bonds formed between the four DNA nucleoside bases. Biology and condensed matter physics were unified, and those long lists could be forgotten. This same type of rationalization is underway in chemistry. There are about 20 million known chemicals, with new molecules being synthesised every week. How do you construct a systematic chemical nomenclature, which removes the appalling idea of having to memorise all, or even a smallish part of those individual trivial names? Well, the subject of chemical nomenclature is truly vast. Indeed, the International Union of Pure and Applied Chemistry (IUPAC) was created over a century ago to address this very problem. But sadly, not everyone in the chemistry community follows the rules of nomenclature laid down by the committees of experts in IUPAC (see https:// iupac.org/what-we-do/nomenclature/ for details). Here we will consider the names of the chemical elements, which amply demonstrate the limitations of the present system of nomenclature. And of how the present system of nomenclature is not based purely on dispassionate scientific argument. Figure 14.1 and Table 14.1 give us a feeling for the arcane origins of chemistry, and of chemical nomenclature. We are taught that science is above politics; that it, science is truly international, but is this really true? The more one questions, for example, the names selected today for newly discovered chemical elements, phenomena, and units the more one seems to see the world of politics and the individual intrude into the world of science. But then the selection of a name is not a trivial matter. Old taboos about not revealing one’s name to a stranger, lest that stranger gain some magical hold over you, stem from the time when a person’s name represented a characteristic. That characteristic 148 defined the person under discussion, and if you knew that name you knew something, perhaps everything, about the person: “to name is to know.” Figure 14.1: A table of chemicals; including some chemical element constructed by the father of mod- ern chemistry, John Dalton (1766–1844); compare the symbols used for the entries in this table with the alchemical symbols, and planet symbols used by al- chemists and astrologers (see Table 14.1, Figure 14.2, and Figure 3.1); for example, Hydrogen has the same symbol as the Sun (see Table 7.1), but Dalton could not have known that the Sun is composed mostly of Hydrogen. Image from: https://en.wikipedia.org/wiki/ History_of_the_periodic_table. Names are at the heart of any classification of the world. They are therefore at the heart of science. A true name is the name of an object, or an animal that expresses, or is somehow identical to the true nature of that object or animal. The notion that language, or some specific sacred lan- guage, refers to things by their true names has been central to a great deal of literature, philosophy, as well as various traditions of magic, religious invocation, and mysticism (mantras) since antiquity (see Chapter 2). And thus the idea that if you know a person’s secret, or true name you can gain a magical power over that person, for example, the true name of the Egyptian Sun god, Ra, was revealed to Isis only through an elaborate trick. This knowledge gave Isis complete power over Ra, and allowed her to put her son Horus on the throne. Socrates in Plato’s Cratylus considers, with- out taking a position, the possibility as to whether names are “conventional” or “natural”; that is, whether language is a system of arbitrary signs, or whether words have an intrinsic relation to the things they signify. Odysseus, when captured by Polyphemus in Homer’s Odyssey is careful not to reveal his name; when asked for it, Odysseus tells the giant that he is “nobody.” But later, having escaped after blinding Polyphemus and thinking himself beyond Polyphemus’ power, Odysseus boastfully reveals his real name; an act of hubris that was to cause enormous problems later in the 14. ASPECTS OF CHEMICAL NOMENCLATURE14.1 THE PROBLEM OF NAMING THINGS IN CONTEMPORARY SCIENCE 149 story. Knowing his name, Polyphemus was able to call down upon Odysseus the revenge of his father, the god of the sea Poseidon. 14.1 THE PROBLEM OF NAMING THINGS IN CONTEMPORARY SCIENCE Today in astronomy, celestial objects are often named after individuals as we have exhausted the Classical pantheons of pagan gods and goddesses. It is likely that in some cases, using a personal name is justified. One can well imagine, for example, the relief of the European nations in Septem- ber 1683 when the King of Poland, Jan (III) Sobieski, defeated the armies of the Ottoman Sultan, Mehmed IV at Kahlenberg, thereby saving Christian Europe from the Turks. In recompense, So- bieski’s name was given to a newly discovered constellation of Stars, a rare honor for someone who did not live on Mount Olympus. However, when we learn that there are comet and small planet hunters who scan the heavens for new objects so that they may name them after family members and friends, one wonders at the seriousness with which they regard their enterprise. Astronomy is a field crying out for a totally rational system of nomenclature, although the International Astro- nomical Union does have a numbering system for asteroids, and has adopted a numerical system for comets, they continue to use a personal name in parentheses. Figure 14.2: The first modern tabulation of the chemical elements, by Dimitri Mendeleev (1834–1907); dating from 1869–71. Image from: https://en.wikipedia.org/wiki/History_of_the_periodic_table. Perhaps the most rarefied branch of experimental chemistry is the synthesis of new chemical elements. As one might imagine, this is not easy but nuclear chemists are continually attempting such syntheses. At present there are 118 named chemical elements, but the naming process is not 150 always straightforward. And we will see that in an investigation of the relevance and appropri- ateness of naming new chemical elements after towns, laboratories, and scientists, one begins to question that oft-stated description of science as being supranational; particularly, science related to nuclear physics and the disintegration of radioactive nuclei. The International Union of Pure and Applied Chemistry (IUPAC) is the body, which since 1919 has been charged with organizing a systematic nomenclature of chemistry, and this includes the naming of the chemical elements. Figure 14.2 gives a picture of the classification of the chem- ical elements in the middle of the 19th century. Today, the naming of a new element is complex. Gone are the days when early chemists such as Humphrey Davy (1778–1829) isolated whole col- umns of the Periodic Table,38 and assigned the names we still use. Today, when a discovery is first published a temporary systematic element name is assigned, by IUPAC to the newly synthesized chemical element. In chemistry, a transuranic element (heavier than Uranium) receives a permanent name and symbol only after its synthesis has been confirmed by a second laboratory (there are only two or three laboratories in the world capable of doing these experiments). In some cases, however, such as the Transfermium Wars, controversies about priority and the naming of the elements have arisen; and there have been protracted international disagreements. Such controversies are not only deeply embarrassing for the laboratories concerned (questioning the science), but also embarrassing politically because non-scientists get involved to further their own ends by boosting national pride and chauvinism, which should have no place in science. The IUPAC systematic, but temporary, names for a new element are derived from the ele- ment’s atomic number, and are only applicable for elements between atomic number (Z) 101 ≤ Z ≤ 999. Each digit is translated to a numerical root, according to published rules. The roots are con- catenated, and the name is completed with the ending-suffix -ium. Some of the roots are Latin and others are Greek to avoid two digits starting with the same letter (for example, the Greek-derived pent is used instead of the Latin derived quint to avoid confusion with quad for 4). There are elision rules designed to prevent odd-looking names. The suffix -ium overrides traditional chemical suffix rules, thus elements 117 and 118 were ununseptium and ununoctium, not ununseptine and ununocton. This does not apply to the final trivial names these elements receive once their existence has been confirmed; thus element 117 and 118 are now Tennessine and Oganesson. For these trivial names, all elements receive the suffix -ium, except those in group 17 which receive -ine (like the other Halogens) and those in group 18 which receive -on (like the other Noble Gases). The systematic symbol is formed by taking the first letter of each root, converting the first to a capital. This results in three-letter symbols instead of the one- or two-letter symbols used for named elements. 38 If you look at Mendeleev’s Table of the Chemical Elements, Figure 14.2, you will see most of the elements iso- lated and named by Davy (sodium, potassium, calcium, strontium, magnesium, barium) in the first two columns or groups ( I and II). Группа 14. ASPECTS OF CHEMICAL NOMENCLATURE14.1 THE PROBLEM OF NAMING THINGS IN CONTEMPORARY SCIENCE 151 After many years and a great deal of discussion in the appropriate IUPAC committee, the scientists responsible for the experiments that created these ephemeral species (few of the most re- cently discovered chemical elements exist for anything approaching a second; they are all radioactive species, and their half-lives are very short—usually fractions of a millisecond) will eventually agree on a true trivial name; that is, a name that can be used to identify this element in the non-specialist literature. Table 14.1 gives the names of the Transfermium chemical elements; Fermium is element number 100, and it can be clearly seen that these chemical elements have been named in accordance with the pre-eminent geo-political struggle of that period, the Cold War. There are about as many Russian as American names, with a few European names thrown in for good measure; to make it look as if it is not a Cold War club. It is not for nothing that the two largest laboratories involved in this type of nuclear synthe- sis are the Lawrence Livermore (element 116) National Laboratory in California (element 96 is named after California) and the Flerov (element 114) Laboratory of Nuclear Reactions in Dubna (element 105) near Moscow (element 115), where the centers for Cold War research into nuclear weapons. Table 14.1: Names and origin of the elements after Fermium in the Periodic Table of the Elements (see Figure 14.3) Number in Periodic Table 100 Final Trivial Name (and symbol) Fermium (Fm) Origin of Trivial Name Named in honor of the Italian-American physicist, En- rico Fermi (1901–1954). 101 102 103 104 105 106 107 108 Mendelevium (Md) Named in honor of the Russian chemist, Demitri Men- Nobelium (No) Larwrencium (Lr) deleev (1834–1907). Named for the founder of the Nobel prizes and arma- ments manufacturer, Alfred Nobel (1833–1896). Named in honor of the American physicist, Ernest O. Lawrence (1901–1958). Rutherfordium (Rf ) Named in honor of the British (New Zealand born) Dubnium (Db) Seaborgium (Sg) Bohrium (Bh) Hassium (Hs) physicist, Lord Ernest Rutherford (1871–1937). Named after the town of Dubna in Russia. Named in honor of the American chemist, Glenn T. Seaborg (1912–1999). Named in honor of the Danish physicist Niels Bohr (1885–1962). Named for the German state of Hesse 152 109 110 111 112 113 114 115 116 117 118 Meitnerium (Mt) Named in honor of the German chemist, Lise Meitner (1878–1968). Copernicium (Cn) Nihonium (Nh) Flerovium (Fl) Darmstadtium (Ds) Named for the German city of Darmstadt. Roentgenium (Rg) Named in honor of the German physicist, Wilhelm Conrad Röntgen (1845–1923). Named in honor of the Polish astronomer, Nicolaus Copernicus (1473–1543). Named for Japan. Named for the Flerov Laboratory of Nuclear Reactions, Dubna, Russia. Named for the city of Moscow, Russia. Named for the Lawrence Livermore National Labora- tory, CA, U.S. Named for the state of Tennessee, USA. Named in honor of the Russian chemist, Yuri Oganes- sian (born 1933). Moscovium (Mc) Livermorium (Lv) Tennessine (Ts) Oganesson (Og) Speaking personally, the origins and meaning of the names given to the chemical elements is sometimes the first romantic attachment formed by young chemists with their future career. Many of us are fascinated by the way that the various names have been derived. For example, some are taken from the name of the mineral from which the element was extracted (for example, Sodium (from soda), Potassium (from potash), or Carbon; carbo being Latin for charcoal), and some from the locality where the mineral containing the element was found (for example, Strontium, from Strontian in Scotland, or Copper derived from Cuprum, the Latin name for Cyprus,). Other names of elements derive from the name of the city where the discoverer lived (for example, Hafnium, Hafnia being Latin for Copenhagen), or from the color of the purified element (for example, Chlo- rine, from chloros, meaning greenish-yellow in Greek). The element’s name might also be derive from some characteristic of the chemical properties of the element, thereby providing information about its chemistry. This may include inertness (for example, Argon; in Greek argos means inactive), or reactivity (for example, Bromine, bromos being Greek for stench, or Fluorine, where in Latin fluere means flux). Indeed, the name may even derive from the difficulty of extracting the element from the naturally occurring source, again imparting important chemical information. Examples of these include the Greek lanthanein (Lanthanum, element number 57) which means to “lie hidden,” and dysprositos (Dysprosium, element number 66) meaning “hard to get at.” If one is familiar with the Greek myths, it is easy to understand why Niobium (element number 41) and Tantalum (element number 73) are so named. Niobe was the 14. ASPECTS OF CHEMICAL NOMENCLATURE14.1 THE PROBLEM OF NAMING THINGS IN CONTEMPORARY SCIENCE 153 daughter of Tantalus, and the two elements are found together in the same ore. It was only in 1844 that they were shown to be two distinct elements. The element Tantalum was first isolated in 1802, but Niobium was not isolated until 1864, when it was extracted from a purified ore of Tantalum. Sir Humphry Davy and JÖns Jacob Berzelius (1779–1848) isolated and named almost whole columns of chemical elements. Davy was the first to isolate and name eight of the elements: Boron, Barium, Calcium, Chlorine, Magnesium, Potassium, Sodium, and Strontium, whereas Berzelius only managed to isolate and name four elements: Cerium, Selenium, Silicon, and Thorium. Other well-known chemists who figure in this list of discoveries include Friedrich WÖhler (1800–1882), who isolated Aluminium and Beryllium, and Robert Wilhelm Bunsen (1811–1899) who, in a tri- umph of early analytical chemistry, spectroscopically identified Caesium and Rubidium, without even isolating weighable quantities of the pure metals. Bunsen named these elements from the color of the principal spectral line; caesius, Latin for sky-blue, and rubidus, Latin for deepest-red. These early chemists did not simply add extra elements to the list of elements already known, they put de- tailed information about the structure and properties of the newly discovered elements into the new names; just as Linnaeus did in his system of binomial nomenclature of organisms (see Chapter 13). Recently, however, there has been a trend to name elements after individuals. Cynics might say that this trend has arisen because few of today’s nuclear chemists know the Greek myths, or any Classical languages. Probably the last element named from a distinctive characteristic, as opposed to merely adopting the Latinized name of the university or state where it was discovered, was the man-made metal Technetium (element number 43), discovered in 1937 and named, appropriately, from the Greek technetos, meaning artificial; although Dimitri Mendeleev knew that such an el- ement must exist when he was putting together the first pictorial representation of the Periodic Table, he left a gap for it (see Figure 14.2 where the gap is at number 44). Unfortunately, the modern desire to name elements after scientists has allowed politics and nationalism to creep into the Periodic Table. During the Cold War, Russian scientists suggested the name of an eminent Russian scientist for an element they claimed to have discovered, U.S. scientists suggested the name of a U.S. scientist, and Germans suggested a German scientist, or town. As a result, the naming of the most recently discovered chemical elements required more international compromise than classical erudition. Such national disagreements over the name of a chemical el- ement are unfortunately not new, and can never improve the public perception of science or, more importantly of scientists. In 1950, IUPAC had to intervene, after almost a century of controversy, to recommend that the name of element number 41 be Niobium. The first specimen of the ore containing this element was found in the American Colonies by John Winthrop (1714–1779), pro- fessor of natural philosophy at Harvard College, but this specimen was sent to England for study. However, many American institutions continued, after its isolation in 1864, to refer to this element as Columbium (Cb), after the spirit of America. Nevertheless, it is the name Niobium that is today universally accepted by working scientists. 154 14.2 THE TRANSFERMIUM WAR Given the nature of American-Soviet rivalry in the forty years following the World War II, it is perhaps not surprising that this rivalry carried over into the world of scientific research. Although given that the particular area of research, which interests us here involved the investigation of the stability of atomic nuclei, and that the research was largely carried out in laboratories better known for their research into developing nuclear weapons, this Cold War rivalry is probably not unex- pected. But there was more to this competition than simple, international political posturing; there also no small measure of personal vanity. After all, the naming of new chemical elements is a rare event, unlike the discovery of a new asteroid or a new comet. And if your name is chosen, you join one of the most hallowed clubs in all of science. The lucky few who are immortalised by having their name adopted as a chemical element. Consequently, the names for the chemical elements beyond number 100 were the subject of a major international controversy starting in the 1960s, described by some nuclear chemists as the Transfermium War. This controversy was only resolved in 1997, and only by a significant weak- ening of one of the international organizations created early in the 20th century to permit science to continue internationally, even when nations were at war. The controversy arose from disputes between American scientists and Soviet scientists as to which had first made these particular elements. One cannot be said to have isolated these elements as Humphrey Davy did back in the late 18th century as they are ephemeral; they are unstable and their half-life is usually only a few milliseconds, or even a few microseconds. Consider element 112, Copernicium (112Cn). This element was first observed in the Heavy Ion Research Laboratory (Ge- sellschaft für Schwerionenforschung, GSI) in Darmstadt (element number 110), Germany (element number 32), where researchers were attempting to fuse the nuclei of Lead and Zinc (named by the alchemist Paracelsus after the form of its crystals) atoms. The reaction scheme for the generation of element 112 and its subsequent decay via neutron and alpha-particle emission are given in the following scheme (where the superscripted number refers to the atomic weight of a particular iso- 82Pb + tope of the element, and the subscripted number refers to the element’s atomic number): 70 112Cn → -(alpha) [losses an alpha-particle39] 108Hs → -(alpha) [losses another 100Fm. 277 110Ds → -(alpha) [losses another alpha-particle] → 106Sg → -(3 alpha) [losses three alpha-particles] → → alpha-particle] → 0n) [loses a neutron] → The scientists undertaking these experiments observed a single atom of 112Cn on Febru- 110Ds decays after ary 9, 1996. It should be noted that 108Hs is relatively long-lived, decaying after 19.7 seconds. These are all 110 microseconds, and ephemeral materials made in quantities so small they cannot be weighed. The same research group 39 An α-particle (alpha-particle) is a doubly-ionized Helium atom; that is, He 112Cn decays after 280 microseconds, (a bare Helium nucleus) with a 30Zn → 273 112Cn → -( 277 273 253 269 208 278 265 277 269 2+ 1 mass of 4 amu (or 6.644 657 230(82) × 10 −27 kg) 14. ASPECTS OF CHEMICAL NOMENCLATURE14.2 THE TRANSFERMIUM WAR 155 were the first to observe element 111 by fusing Bismuth nuclei with Nickel nuclei, and were re- warded by seeing three atoms of the desired product over the period December 8–18, 1994. By convention, the right to suggest a name for a newly discovered chemical element goes to their discoverers. However, for the elements 104, 105, and 106 there was a controversy between a Soviet/Russian laboratory and an American laboratory regarding priority. Both parties suggested their own names for elements 104 and 105, neither recognizing the names suggested by the other laboratory. This is what brought IUPAC into the debate. In addition, the American name of Sea- borgium for element 106, chosen by the American Chemical Society to honor Glenn T. Seaborg (1912–1999) of University of California, Berkley (a Nobel laureate chemist who had also been a science adviser to U.S. presidents during the Cold War) was objectionable to some, because it referred to an individual who was still alive at the time his name was proposed. Einsteinium (ele- ment number 99) and Fermium (element number 100) had also been proposed as names for new elements while Einstein and Fermi were still living, but by the time that the names of these two eminent physicists were adopted, both scientists were dead. So, there was no precedent at this time for naming a chemical element after a living person. However, Seaborg wanted this fame while still living. And this caused serious international tensions; reviving much of the rivalry that had existed during the Cold War, and with no little Cold War rhetoric.40 In addition, the Soviet Union wished to name element 104 after Igor Kurchatov (1903–1960), builder of the Soviet atomic bomb, which was another reason the name was objectionable to Americans. The two principal groups which were involved in the conflict over element naming were: an American group at Lawrence Berkeley Laboratory, California, and a Russian group at Joint Insti- tute for Nuclear Research in Dubna, Russia. And between these two national teams, the referee, or arbiter, was the IUPAC Commission on Nomenclature of Inorganic Chemistry, which introduced its own proposal to the IUPAC General Assembly (the Union’s highest decision making body) for the names of these elements. The German group at the GSI in Darmstadt, who had undisputedly discovered elements 107 to 109, were dragged into the controversy when the IUPAC Commission suggested that the name “Hahnium” (in honor of the German physicist Otto Hahn (1879–1968), who won the Nobel physics-prize in 1944 and, although opposed to the Nazi Party, had remained in Germany throughout WWII); a name already proposed for element 105 by the Americans, be used instead for GSI’s element 108. In short, no national laboratory was happy, and it was in fact a major blow to the prestige of IUPAC. In 1994, the IUPAC Commission on Nomenclature of Inorganic Chemistry proposed the names given in column six of Table 14.2. Thus attempting to resolve the international disagreement by sharing the naming of the disputed elements between Russians and Americans, replacing the name for 104 with one honoring the Dubna research center, but not naming 106 after Seaborg. 40 The author was, at this time, the Deputy Executive Secretary and editor of IUPAC and saw, read, and heard the voluminous correspondence and exchanges concerning this sad affair. 156 However, this solution drew objections from the American Chemical Society on the grounds that the right of the American group to propose the name for element 106 was not in question, and that group should have the right to name the element. IUPAC further confused things by deciding that the credit for the discovery of element 106 should be shared between Berkeley and Dubna, but the Dubna group had not come forward with a name. Along the same lines, the German group protested against naming element 108 with the American suggestion Hahnium, mentioning the long-standing convention that an element is named by its discoverers. In addition, given that many American textbooks had already used the names Rutherfordium and Hahnium for elements 104 and 105, the ACS objected to those names being used for other elements. Finally in 1997, the 39th IUPAC General Assembly in Geneva put forward the names given in the last column of Table 14.2. Professor Glenn Seaborg died in 1999, however this attempt at creating a tradition of naming chemical elements after living people has continued with the Russian chemist, Yuri Oganessian whose name is given to element 118, Oganesson. Thus, the convention of the discoverer’s right to name their elements was respected for elements 106 to 109, and the two disputed claims were shared between the two opponents. Table 14.2: A summary of the evolution of the names of some of the transfermium elements Atomic Systematic Proposed Proposed Proposed Suggested Final Name Number IUPAC American Soviet/ German IUPAC in (IUPAC 1997) Name Name Russian Name 1994 Name 104 105 106 107 108 109 unnilqua- Rutherfordium Kurchatovium - Dubnium Rutherfordium dium unnilpentium Hahnium Neilsbohrium - Joliotium Dubnium unnilhexium Seaborgium unnilseptium - unniloctium - unnilennium - - - - - - Rutherfordium Seaborgium Neilsbohrium Bohrium Hassium Hahnium Bohrium Hassium Meitnerium Meitnerium Meitnerium This modern personality cult is inappropriate and inherently nationalistic, laying itself open to political problems. It was a lot simpler, and more appropriate, when the names of mythological char- acters or names derived from chemical properties were used for the elements. Myths and legends are the common heritage of all mankind and tell us, by analogy, more about the element, for example the chemical affinity between Niobium and Tantalum, than do Fermium or Nobelium, which were never associated with Enrico Fermi or Alfred Nobel. And unlike Niobium—a relatively common, naturally occurring, element whose salts are key materials used in modern electronics—element 106 has a half-life of a few hundred microseconds and will only ever be available in the minutest of quantities. 14. ASPECTS OF CHEMICAL NOMENCLATURE14.2 THE TRANSFERMIUM WAR 157 The name Iridium, derived from the Latin iris, meaning color, as exemplified by the salts of this element, and Iodine, from the Greek iodes meaning violet; both impart chemical information. Likewise with Antimony, derived from the Greek anti monos—“a metal not found alone,” savants of the Ancient World are telling us that this element is unreactive enough to be found as a native metal, but always associated with its chemically similar neighbors in the Periodic Table. This is quite a lot of information for the Ancient World (Antimony salts were used as cosmetics by the Ancient Egyptians). In comparison, the names Tennessine, Nihonium, Hahnium, and Meitner- ium tell us nothing and create confusion because we would need to consult textbooks of history, or English–Japanese dictionary to identify the origins of their names—let alone their discoverers. Berzelius refused to name elements after people; when the discoverer of Tungsten (element number 74), Carl Wilhelm Scheele, was to be immortalized as the discoverer of this new element, Berzelius remarked “The immortality of our compatriot does not need this support.” Thus, today we have Tungsten and not Scheelium. Figure 14.3: The well-known Periodic Table of the Elements (source: https://en.wikipedia.org/wiki/ Periodic_table). Hydrogen (H) is element number 1; Uranium (U) is number 92; Iron (Fe) is in the middle at number 26. Compare with the image in Figure 14.1; it took two centuries for scientists to shake off the last vestiges of alchemy. However, many modern scientists prefer the names of scientists as labels for the chemical ele- ments. Unfortunately, the choice of scientist to be so honored is arbitrary and illogical—why choose Lawrence, who was not a chemist, while Humphry Davy, who discovered eight elements, and Fred- 158 erick Soddy, who discovered and explained the existence of isotopes, have not been so honored? If only truly great scientists are to be so honored, why not Newton, Maxwell, Faraday, or Galileo? 14.3 FURTHER READING The International Union of Pure and Applied Chemistry (IUPAC) was founded in 1919 by chem- ists from industry and academia who recognized the need for international standardization in their area. As I have pointed out in this volume, the standardization of weights, quantities, names, and symbols is essential to the successful advance of the scientific enterprise, and to the smooth devel- opment and growth of international trade and commerce. IUPAC is the authority on chemical nomenclature and terminology, and two IUPAC bodies take leading roles in this activity: Division VIII—Chemical Nomenclature and Structure Repre- sentation and the Inter-divisional Committee on Terminology, Nomenclature, and Symbols (see https://iupac.org/ for more details). As one of its major activities, IUPAC develops Recommenda- tions to establish unambiguous, uniform, and consistent nomenclature and terminology for specific scientific fields, usually presented as: glossaries of terms for specific chemical disciplines; definitions of terms relating to a group of properties; nomenclature of chemical compounds and their classes; terminology, symbols, and units in a specific field; classifications and uses of terms in a specific field; and conventions and standards of practice for presenting data in a specific field. Information on chemical terminology can also be accessed through the IUPAC Color Books, which may be consulted on-line at https://iupac.org/what-we-do/books/color-books/. 14. ASPECTS OF CHEMICAL NOMENCLATURECHAPTER 15 159 The Evolving Science of History Social media: Websites and applications that enable users to create and share content or to par- ticipate in social networking. The premise of this volume is that scientists (but not social scientists) have a worldview that is different from that of non-scientists, particularly, for example, historians. Whether this is a good thing or a bad thing, given the predictive power of science, it is irrelevant. Science is in the world, and it cannot be removed. We have seen how science has evolved over the last few millennia, how it has extended human life, and how it is capable of extending it a lot further. There is no problem that has arisen from some aspect of the misuse of science that cannot be corrected by application of more science. This is true whether we are considering nuclear power, or the influence of man-made greenhouse gases in the Earth’s atmosphere. Our errors catalyze future progress. Ordinary people may not understand science, particularly, the physical sciences, and they may also be in awe and fearful of the power of science and of the scientist, but it is to science and the scientist that politicians must turn when they need a solution to a technical (non-social or non-po- litical) problem. After all, there is no one else to turn to; and science has already transformed the world and society on a number of occasions. For example, the rise of science and medicine in the early-modern age of the 17th century; the Victorian Internet of the international telegraph (Wil- liam Thomson became Lord Kelvin for his invention of the equipment needed to lay conducting cables between the UK and the U.S.); atomic power; genetic medicine; and the creation of the mod- ern Internet.41 These things cannot be undone; scientific discoveries once made cannot be forgotten. Society will have been transformed, and if the technical details of an advance become lost; then it will survive in the form of legend and myth, which will catalyse its re-invention. History waits for no one; it is always on the move, somewhere. The Second Law of Thermodynamics tells us that the arrow of time can only point in one direction—into the future. Scientific advances are the ratchets in the mechanism of history that prevent history, and social advance running backwards. But what of history, that subject that fascinates all thoughtful individuals? Anyone who has read, at least, two history texts by different authors on the same period of history will know that historians can be maddening people. Yet asked if history has a pattern or a plan, they will usually assert that such a question is offensive; history is but the record of the chaotic events that come about because people’s hopes and ambitions are invariably modified by external circumstances— 41 Question: how did we organize holidays and trips to the theater before the invention of the Internet? 160 often the hopes and ambitions of other people. As Edward Gibbon put it, “History is but the record of crimes and misfortunes.” You will likely be told that an historian’s job, is not to find a pattern, let alone a fundamental law, but to ensure by research that the record is accessible and intelligible. There are, however, var- ious schools of historians. There are Marxist historians, who look preferentially for patterns in the data of events, which they believe reveal the signature of the perpetual struggle between the prole- tariat and their economic masters. Other historians hold to the idea of progress, or the notion that the improvement of the human condition in recent centuries can, with ingenuity be extrapolated into the future. Physical scientists who have an interest in history often fall into this camp. Without realizing it, however, these physical scientists are adopting the ideas of the science fiction writer, Isaac Asimov (1920–1992); best expressed in his invented science of psychohistory. That the future may be predicted, if only we had sufficient data and powerful enough computers. Irrespective of the desires of even the most ardent of anti-scientists, whether their dislike of science arises from their religion, their politics, or their limited education, science is here to stay. As an example of the now unavoidable influence of the mathematical or physical sciences on society, let us consider the mining of personal data on social media. This study will also demonstrate how techniques of mathematical physics are used to analyze a set of data. This is a topic that will likely remake our society over the next generation. It will certainly do away with conventional politics; there will still be elections in the future, but there will be no need to go to a polling office to vote. We will all like or dislike a particular politician, or a particular proposal for a law on social media. 15.1 SOCIAL MEDIA While it may seem premature to associate history with something as new and vibrant as Facebook, it must be commented that a great many people, of a variety of political views, religious persuasions and commercial interests are sifting through; that is, mining the data we have all (well over 2.5 billion of us… and increasing) carelessly left littering social media. Before writing was invented, there was only one way for an individual to leave behind a record of himself for future generations. They would place their hand on cave walls and blown a mouthful of pigment over it; leaving behind a stenciled handprint. It was a successful strategy, as a great many of these haunting cave paintings survive. With time, our civilization evolved, as did an individual’s ambitions and desires. We have now become amazingly adept at recording our lives. We have built mausoleums and libraries, and filled those libraries with books; we have written books of history and compiled sophisticated records of our ancestors. Then a college student developed an extraordinarily simple and useful tool to convey our personal histories, and interests to future generations—Facebook. 15. THE EVOLVING SCIENCE OF HISTORY15.1 SOCIAL MEDIA 161 Historians have always struggled to tell the stories of our everyday ancestors, even those who lived only a few generations ago. Historical records offer great insight into a handful of important and powerful people, but piecing together the lives of ordinary people has always been difficult. Facebook changes all this. In little more than a decade, Facebook’s users have contributed to a massive depository of personal information that documents both our reactions to events and our evolving customs with a scale and intimacy earlier historians could only dream about. It’s hard to estimate just how substantial this database of personalities could become. Presently, more than 2.5 billion people are regular users of Facebook. Assuming people will continue to use the site regularly, this means most of these users will document more of their lives over the coming years, leaving behind photos, details of friendships and love affairs, their likes and dislikes, and their reactions to news-worthy events. In addition, there are tens of millions of deceased Facebook users; individuals who have left behind digital remains. It is estimated that if Facebook stopped growing tomorrow, the number of deceased users “on” (perhaps one should say “in”) the site would be well over a billion by the end of the century. If the site were to continue growing as it is now, that number could reach about 5 billion users by 2100. All this data, this information is there to be mined and exploited—for whatever reason. Today, these “dead” accounts offer a virtual environment for mourning. However, the data they contain will be invaluable to future historians and sociologists. They will be able to investigate the events surrounding the election of Donald Trump, and the online culture wars that facilitated and followed this election. Similarly, with the great saga of Brexit, future historians will be able to study what ordinary people thought about Brexit and the politicians who desired Brexit, rather than merely what the politicians who desired Brexit thought about Brexit. Of course, future re- searchers will see lots of pictures of dead cats and puppies, of homemade cakes, and Game of Thrones memes with which users distracted themselves from the daily grind of work. But, this potential utility complicates, rather than resolves, the problems of security already plaguing Facebook: How much privacy do the dead deserve? How do we guarantee that those who wish to be forgotten are allowed this right—is it a right? This matters because, for the first time, we all have the power to leave behind far more personalized histories than any previous generation. We don’t have to rely on the recollection of our descendants for our memory to survive, and we don’t have to accept that our collective experiences will fade away with time. This is our chance to leave far more than our handprints on the digital walls of history. Let us now look briefly at the possible misuse of the data of the living, and of the dead. What is happening to our data, to our likes and dislikes, our loves and hates that we all leave all over social media? If I, for example, like a friend’s post about what he and his boyfriend did on the weekend, who outside of a list of our mutual friends looks at this information, and for what purpose may this information (data) be used by parties unknown to anyone actually involved? If these data miners restricted themselves to collecting recipes for chocolate cookies, there would be no problem, but it appears that this is not what data mining on social media is all about. 162 15.2 SOME DETAILS OF THE ANALYSIS OF PERSONAL DATA ON SOCIAL MEDIA The first study of Facebook data, that is, data mined from the personal profiles of Facebook users, was based on a sample of 58,466 volunteers (thus in Table 15.1, N = 58,466) from the U.S.; this data was obtained through the myPersonality Facebook application (no longer available), which included their Facebook profile information, a list of their likes (with, on average n = 170 likes per person; totalling about 10 million likes, and one assumes dislikes), psychometric test scores, and survey information. Users and their likes were represented as a sparse user–like matrix, the entries of which were set to 1 if there existed an association between a user and a like, and to 0 otherwise. The modelers selected a wide range of traits and personal attributes from users that clearly re- veal how accurate and potentially intrusive such an analysis could be; these characteristics included: sexual orientation, ethnic origin, political views, religion, personality, intelligence, satisfaction with life, substance use (alcohol, drugs, cigarettes), whether an individual’s parents stayed together until the individual was 21, and basic demographic attributes such as age, gender, relationship status, and size and density of the friendship network. This data was then represented in the form of a matrix (see Table 15.1), and standard statistical methods of analysis were used for their manipulation. Table 15.1: A representation of the raw data mined from social media sites such as Facebook. The N users are represented as the first column, and the various characteristics of each of these N users form the columns of the table or matrix; for example, the user either likes (1) Mickey Mouse or he/she dislikes (0) Donald Trump. There can be as many columns as there are data-fields available for personal traits and characteristics: ethnicity, sexual orientation, religion, etc. [1] t r A s e k i L x e s - y a G s e k i L y t i n a i t s i r h C s e k i L l a c i l e g n a v E s e k i L y t i n a i t s i r h C d l a n o D s e k i L p m u r T t i x e r B s e k i L g n i t o v o t s t i m d A t i x e r B r o f s g u r d s e k i L s e k i L g n i t a r t s n o m e d y e k c i M s e k i L e s u o M Facebook user 1 Facebook user 2 …. Facebook user N 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 15. THE EVOLVING SCIENCE OF HISTORY 15.2 SOME DETAILS OF THE ANALYSIS OF PERSONAL DATA ON SOCIAL MEDIA 163 Matrix decomposition, also known as matrix factorization, is the standard initial procedure in the analysis of any large body of data from which researchers wish to make predictions. Perhaps the best-known and widely used matrix decomposition method is the singular-value decomposition (SVD). All matrices have an SVD, and as such it is used in a huge range of applications. The SVD takes a rectangular matrix of, for example, likes and dislikes from a selection of users of Facebook; defined as M, where M is an m by n matrix, see Figure 15.1, in which the m rows represents the N social media users being studied, and the n columns represents those users’ likes and dislikes (see Table 15.1). The SVD theorem states: M = U Σ V* Here, U is an m by n unitary matrix; Σ is a diagonal m by n matrix; V is a symmetric n by n matrix, and V* is the conjugate transpose of V. The SVD represents an expansion of the original data in a coordinate system where the covariance matrix is diagonal, and so more amenable to statistical analysis. 0 0 0 0 0 0 Σ m × n 0 0 0 1 0 0 0 = = V* n × n 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 Im 0 1 0 In M m × n = U m × m U U* V V* Figure 15.1: Details of the matrix algebra involved in the singular-value decomposition by which the raw data of our likes and dislikes on social media are turned into a set of linear equations, from which the likelihood of our “behavior” may be calculated. (The lowercase, italicized letters denote the type of matrix—symmetric or non-symmetric.) 164 Having now prepared the data in a standard statistical format, it is possible to make predic- tions about the group under study; the users of social media such as Facebook, as a representation of humanity in general, or just the voting population of the U.S. or the UK. In statistical model- ing, regression analysis is a set of statistical processes used for calculating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or predictors). More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held constant. Let us consider an example of such an analysis that could be readily applied to data available on social media: the influence of education upon voting intention. To obtain the raw data we take a large sample of individuals of similar age and ask them how long they spent in full-time education and what are their political likes and dislikes. Clearly, when graphed such raw data will generate a plot with an enormous range of uncertainty, or scatter. But the question of interest is: Is there a relationship between education level and voting pattern? The scatter of points on the graph may suggest that people with higher values of education tend to follow a more liberal voting pattern, but the relationship is not perfect; and it would be clear that knowledge of education level does not suffice for an accurate prediction of voting intention. To apply regression analysis to this particular problem, and to obtain a smoother curve of the data when plotted (for better predictions) requires that we first hypothesize that voting intentions for each individual are determined by education, and by a collection of other factors (race, locality, sex, sexuality, profession, etc.) that we term “con- tributing noise.” This noise is the background against which one is trying to derive a clear cause and effect relationship, upon which to base extension and prediction. First, we write a hypothesized model relationship (a linear regression model) or equation between education level (E) and voting intention (I, where a particular numerical value, or range can be correlated with right-wing or left-wing voting intentions) as, for example, I = α + βE + ε, where α is a constant (how one would vote with zero education), β is the coefficient relating how an additional year of education influences voting intention (assumed to be either positive or negative), and ε is the noise term representing other factors that influence voting intention (for example, age, postal address, religious beliefs, etc.). The parameters α and β are not observed, and regression anal- ysis is used to produce an estimate of their value, based upon the information contained in the raw data set; for example, in Table 15.1. What we have hypothesized is that there is a straight line, or linear relationship, between E and I. Thus, somewhere in the cloud of data points derived from our social media user-like matrix we expect to find a line defined by the equation I = α + β E + ε. The task of estimating α and β is equivalent to the task of estimating where this line is located relative to the axes, I and E. The answer depends in part upon what we think about the nature of the noise term, ε. To estimate ε, one would look at the solutions (eigenvalues) of the matrix of likes and dis- 15. THE EVOLVING SCIENCE OF HISTORY15.2 SOME DETAILS OF THE ANALYSIS OF PERSONAL DATA ON SOCIAL MEDIA 165 likes for various groups of individuals. The predictive modeling undertaken by organizations such as Cambridge Analytica (now bankrupt) involved fitting various models of correlations (such as education, age, or sexuality with voting intention, or liberal sentiments, or lack of liberal sentiments) using standard techniques of linear regression. Variables such as age or intelligence were predicted using a linear regression model, whereas dichotomous variables such as gender or sexual orientation were predicted using logistic regression [2]. So how close are we to a precise science of prediction based on the analysis of the personali- ties of individuals comprising large groups? To my mind, the present furore about the actions of the now defunct company Cambridge Analytica in the UK and the U.S., and Facebook in seeking to gain personal data on hundreds of millions of individual voters with the desire to target individual voters with the most appropriate publicity material, so as to influence elections, and thereby direct the course of history, is merely a first overt attempt at creating something akin to Isaac Asimov’s psychohistory. But perhaps it is too premature—it only just worked and has been revealed to public scrutiny and condemnation, which was probably not the intention. Perhaps there are not yet enough individuals on social media; we are still a long way from the assumptions of Asimov about the ap- propriate size of the group being examined and modeled. But this new form of democracy is only in its infancy; it works, and that is a great stimulant for further development. Intrusion into one’s Internet-space, is happening everywhere, and will only become worse. Sadly or happily, depending upon one’s point of view, we have a long way to go before we can approach the perfect state required for a true statistical modeling of society. The transition from the non-statistical behaviour of individual molecules (or individual humans in Asimov’s fiction) to the more mathematically friendly statistical behaviour of large groups of molecules, i.e., solids and liquids (or human society in Asimov’s fiction), is not so easily identified. However, the American historian Henry Adams (1838–1918), the grandson and great-grandson of American presidents, attempted such a modeling of human history at the beginning of the last century. In his Degrada- tion of the Democratic Dogma (1919), Adams proposed two laws of history: All civilization is central- ization and All centralization is economy. It is difficult to find fault with the first law; however, the second law says that resources; particularly, energy sources must be adequate to sustain the energy needs of the civilization or empire. Therefore, all civilization is the survival of the most economic system; for example, the nation that has an ample source of energy (coal, oil, gas, nuclear, etc.) and is able to control access to all major sources of energy for all other nations will necessarily dom- inate the world. There is a strange closeness between physics and history; a closeness that always moves out of focus when you seek to examine it in detail. In both physics and history, all is cause and effect; in history as in physics, there is no action without a reaction. The problem is that in any predictive, quantitative estimation derived from history and from physics, the error bars are larger for the former than for the latter. 166 15.3 FURTHER READING 1 The full details of such analyses are to be found in Private traits and attributes are pre- dictable from digital records of human behavior; Michal Kosinskia, David Stillwella, and Thore Graepel; Proceedings National Academy of Sciences (2013); 110(15): 5802–5805. 2 This topic is discussed in detail in any textbook on the statistical analysis of experimen- tal data; for example, Linear Algebra and Matrix Analysis for Statistics (2014): Sudipto Banerjee and Anindya Roy; Texts in Statistical Science; Boca Raton, FL:Chapman and Hall/CRC Press. And Quantifying Measurements: The Tyranny of Numbers; Jeffrey H. Williams (2016); San Rafael, CA:Morgan & Claypool, and references therein. 15. THE EVOLVING SCIENCE OF HISTORY CHAPTER 16 167 Obfuscation: Why Are We Not Living in a New Golden Age? Where is the wisdom we have lost in knowledge, and the knowledge we have lost in information? T.S. Eliot, What is a Classic?; Presidential address to the Virgil Society of London, 1944. In this book, I have tried to show the evolution of science was an attempt to classify, understand, and contain Nature. Originally, this involved the creation and memorising of long lists of natural events, things and phenomena; then we abandoned the lists and looked for the coherences that existed behind the observations. We searched for the rule or universal law that gave rise to, or led to, the observed thing or phenomenon. Why man wished to understand his environment is simply stated; he wished to protect himself and his extended family, or tribe in a hostile and indifferent world. We invented religions and social systems to further enable this protection. Science, as we know it today, grew out of the failure of religion and magic, that is, pre-scientific natural philosophy, to explain and predict natural events. Science worked on a regular basis, unlike magic and religion that only worked on a statistical basis. But this triumph of science has not eliminated magic and religion; they are still with us today, and in the case of religion still play an important role in the stability of the wider society. All this effort to create a scientific worldview was directed toward improving the lot of hu- manity. Men imitated the divine lawgivers in our mythologies and religions, demonstrating that religion always develops before science in an evolving society, and thereby formulated the idea of Laws of Nature, which we all had to obey. Scientists believed that a codification and explanation of natural laws would help man return to that Golden Age when everything was perfect; when men were at peace with each other, and at one with Nature. This search for a better world goes on. The ultimate discovery, the Theory of Everything should enable man to cease struggling against Nature, as all would finally be revealed; there would be no questions left unanswered. Figure 11.2 shows that we are well along on the roadmap to the Theory of Everything. So, the question we must now ask is why are we not living in a new Golden Age? What has gone wrong? Or, are we living in a 168 Golden Age, and we just haven’t noticed?42 What happened to all that optimism and enthusiasm that gave birth to the first tentative steps of the great endeavor of science? 16.1 THE SCIENCE WARS Sadly, it is true to say that not everyone wishes to be liberated from their narrow, limited, obscure way of looking at Nature. It is not universally assumed that scientists have the only correct way of interpreting the world we see around us. The fractious disputes or disagreements between scientists and some non-scientists as to who has a monopoly on objective truth have always generated a lot of heat. Scientists, particularly physical scientists, find sociologists, historians, and “critics of culture” tedious in their attempts to rub the gloss off the enterprise of science. In good relativistic fashion, non-scientists usually look askance at scientists’ claims of an absolute objectivity and the ultimate truth, and regard scientists in the same way they would regard any other anthropological group. Social scientists often regard scientists as a tribe, whose structures of supposed authority, of peer review, as a means of maintaining their integrity, of training and initiation and peer-acceptance, should be subjected to the same levels of criticism, as would be the behaviour of any tribe of non-in- dustrialised people to be found in the Amazonian jungle. Needless to say, this does not go down too well with the professional tribe who have given us: atomic power, aeroplanes, antibiotics, weapons of mass destruction, mobile phone, spaceflight, and genetic engineering. But then to contemporary cultural critics, such as the French philosopher and literary theorist Jean-Francois Lyotard, science is nothing more than another grand narrative, with a structure just like, and no better than history, sociology or semiotics. That is, science should be treated as an object of study in itself, not as an enterprise that provides a transcendental view of Nature. Scientists (especially physicists) will, however, tell you that their view of Nature is the real, or the most real view of the world around us, that it is possible to gain. Scientists like to call them- selves realists, but even some of the greatest of physicists have had doubts as to the transcendental viewpoint of the scientist. Niels Bohr, one of the founders of quantum mechanics, said that “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” Nothing transcendental here; description, rather than explanation. This is a more realistic viewpoint; but, unfortunately, not one shared by all scientists. So, when it comes to understanding the world in all its wonderful complexity, should we be- lieve our ardent, zealous physical scientists, or the majority of mankind? The philosopher, physicist Karl Raimund Popper (1902–1994) held that all science provides are hypotheses that have, so far defied attempts to falsify them. Of course, this argument does not take account of the “trust” we put in the technological products of science. We design things not in accord with a fundamental 42 Granted we have yet to find the Theory of Everything, but we are well on the way to glimpsing its spectral form in extreme events in Space and here on Earth, as in the discovery of gravity waves and of the Higgs boson. 16. OBFUSCATION: WHY ARE WE NOT LIVING IN A NEW GOLDEN AGE?16.2 ANTI-SCIENCE 169 principle of a theory, but with a theory that has survived rigorous examination, and which we fully expect to continue to survive ever more detailed examination. When you agree to have major sur- gery, you expect to wake up cured, and when you buy an airline ticket to Australia, you expect to get there, and so you buy a return ticket. Modern medicine is successful, because it is based upon the scientific method of observation, hypothesis and testing. When we design jet engines, we do so in the context for which they are intended. In saying these things, we are not able to step outside our skins, or outside the Universe and attempt a majestic, dispassionate, transcendental examination. We are merely repeating sci- ence’s own explanation of events and observations. There is a world of difference between observing and recording something, and an a priori explanation of a phenomenon. There is, in fact, no getting behind the explanation of science, because we are in the world we describe, we are part of it and cannot stand outside that world. As modern quantum mechanics tells us, the experimenter is part of the experiment; Schrödinger’s cat again. Whereas a sociologist does often stand outside of society and deliver himself/herself of sweeping generalisations. 16.2 ANTI-SCIENCE The problem between scientists and non-scientists is, today, often termed anti-science; this is a term that has arisen in our contemporary world of alt-truth and climate change sceptics. Anti-science is an extreme form of a suspicion of science; a position that rejects science and the scientific method. People holding antiscientific views do not accept science as an objective method that can generate anything of use to them—let alone universal knowledge. The more thoughtful, contend that scien- tific reductionism is an inherently limited means to reach an in-depth understanding of a complex world in continuous evolution. At the beginnings of the scientific revolution, proto-scientists or savants such as Robert Boyle found themselves in conflict with non-practical thinkers, such as Thomas Hobbes, who were skeptical as to whether or not science was a satisfactory way of arriving at real, or genuine knowl- edge of the world. Hobbes’ stance is sometimes regarded as an early anti-science position. And we saw in Chapter 4, that this disagreement between the experimental scientist and the rationalist is not a new phenomenon; it goes back to the Taoist Sages of the Waring States Period of Ancient China. We also saw that it was nature mysticism that allowed the experimental sciences to over- come the opposition of the dogmatic theologians, theoreticians, and philosophers. However, in our modern world, Nature and a study of Nature is often invoked by those opposed to science. Perhaps it is in the world of artistic inspiration that we find some of the most thoughtful, and therefore useful (perhaps even persuasive) arguments for anti-science. The poet and mystic, William Blake (1757–1827) reacted particularly strongly against the ideas of Isaac Newton in his paintings and writings, and is seen as being perhaps the earliest, and almost certainly the most 170 prominent and enduring, example of what is seen by historians as the aesthetic, or romantic re- sponse against science. In Blake’s 1795 poem Auguries of Innocence, the poet describes that beautiful exemplar of Nature, the robin redbreast imprisoned by the materialistic cage of Newtonian mathe- matics and philosophy. In Blake’s painting (1795) of Newton (Figure 16.1), Newton is depicted as a misguided hero whose attention was only directed to the drawing of sterile, geometrical patterns on the ground, while the beauty of Nature was all around him; as Blake put it, “May God us keep / From single vision and Newton’s sleep!” Blake thought that Newton, Bacon, and Locke with their emphasis on mechanistic reasoning were nothing more than “the three great teachers of atheism, or Satan’s Doctrine.” Blake’s painting of Newton, progresses from exuberance and color on the left-side, to sterility and darkness on the right-side. In Blake’s view, Newton brings not light, but night. In a poem, W.H. Auden summarizes Blake’s anti-scientific views by saying that he “[broke] off relations in a curse, with the Newtonian Universe.” But Newton was a complex, universal personality. As we saw in Chapter 1, Isaac Newton was as much at home in the Kabbalah, and other such metaphysics as he was in classical mechanics, but this was not widely appreciated in Blake’s day. Figure 16.1: William Blake’s Newton (1795) demonstrates his opposition to the “single-vision” of scientific materialism. Image from: https://en.wikipedia.org/wiki/William_Blake#/media/File:New- ton-WilliamBlake.jpg. 16. OBFUSCATION: WHY ARE WE NOT LIVING IN A NEW GOLDEN AGE? 16.2 ANTI-SCIENCE 171 Issues of anti-science are best seen as a consideration in the on-going transition from pre-science or proto-science to present-day science. This is what we spoke about in the continued use of the I Ching and Astrology as means of divination, and as limited models of the complexity of the natural world. This same argument is evident in the evolution of alchemy (a mystical and an experimental art) into purely functional experimental chemistry. Many disciplines that pre-date the widespread adoption and acceptance of the quantitative scientific method (early 18th century in Europe), such as mathematics and astronomy, are not seen as anti-science. However, some of the orthodoxies within those disciplines that predate a scientific approach, for example, those orthodox- ies repudiated by the discoveries of Galileo are seen as being a product of an antiscientific stance. Of course, an ardent or zealous belief in the central importance, the universality and the unfailing potential of science can be considered as a new religion. A religion in which scientists would be the priestly caste. But this would be a religion based upon reproducible miracles. And if everyone could see and benefit from a miracle, then all would become believers.43 The derogatory term “scientism” derives from the study of science, and is a term invented and used by social scientists and philosophers of science to describe the views, beliefs, and behavior of strong supporters of science; those who speak of science triumphalism, the science of the late 19th century. It is commonly used in a pejorative sense, for individuals who seem to be treating science in a manner similar to that used by believers in their particular religion.44 Of course, it is often the case that a difference arises between scientists and non-social sci- entists, because of a difference of perception. Some supporters of anti-science may have presented unreal images of science that threaten the believability of scientific knowledge, or appear to have gone too far in their anti-science deconstructions. The question often lies in how much scientists conform to the standard ideal of communalism, universalism, disinterestedness, originality, and skepticism. Unfortunately, scientists don’t always conform; scientists do get passionate about pet theories; they do rely on reputation in judging another scientist’s work; they do pursue fame and fortune via research. Thus, they may show inherent biases in their work. Indeed, many scientists are not as rational and logical as legend would have them, but then neither are they as illogical or irrational as some supporters of anti-science might say. We are all human. A point of contention often presented by supporters of anti-science involves the inappropri- ate, or inadequate nature of the mathematical models used to model real systems. That these models do not capture the full reality of existence. Scientists would be told that the formulae of mathemat- ical models are artificial constructions, logical figments with no necessary relation to the outside 43 This is the premise behind a great deal of science fiction, particularly, the novels of H.G. Wells, such as The War in the Air of 1908 and his writings such as The Shape of Things to Come of 1933, which were turned into the 1936 movie, Things to Come. 44 Thomas Henry Huxley (1825–1895) was an English biologist and anthropologist specialising in comparative anatomy. He is known as “Darwin’s Bulldog” for his aggressive advocacy of Charles Darwin’s theory of evolution, an ardent advocate, who would not have been out of place in a mediaeval search for heretics. 172 world. That such models always leave out the richest and most important part of human experience: daily life, history, human laws and institutions, the modes of human self-expression. That these models fail to appreciate the subtle complexity of the social world; so a great deal of what is best in society is excluded from the model, which, not surprisingly only generates oversimplifications. A great deal of this criticism is true—our models of the world are limited. But they are limited by the ability of present-day computers to solve the equations that describe the model; that is, the models we use are limited by the present limitations of technology. Today’s computers are fast, but the computers of the mid-century will be a lot faster, and so better for solving the types of complex social problems that supporters of anti-science criticise scientists for not solving—just be patient. This difficulty in communicating the evolving interaction of science and the wider society is as the heart of the problem about the public understanding of science, and the vanquishing of anti-science. For my part, I continue to believe in science, and that science has done incalculably more good than harm to mankind. I have not lost faith in science as part of the highest civilization, and its development as one single epic story for all humanity. It might have been the American taxpayers who paid for the journey of the first men to the Moon half a century ago, but it was all mankind who exalted in the achievement (see Figure 16.2). 16.3 THE LIMITATIONS OF THE ENLIGHTENMENT Supposedly, the Enlightenment of the 18th century was the moment when the light of reason was focused into the obscure corners and occult recesses of the human mind. Yet, the 19th century saw an extraordinary revival of interest in magic, spirituality, and religion. True, there was also the great synthesis by James Clerk Maxwell of electromagnetism, and the first steps toward the triumphs of 20th-century physics, but why was it that so much enchantment survived the Enlightenment’s rational examination? Why was it that the Enlightenment’s spirit of “daring to know” failed? This question is at the heart of why it is that man has not been translated into a new Golden Age by the extraordinary achievements of science over the three centuries since science came into its own.The German philosopher, Emmanuel Kant, who was the man who told us to “dare to know” also said that man, because of his reason was fated to propose and worry about questions he could never an- swer or dismiss. Kant regarded this fruitless search after mysteries to be an aspect of human reason. An irritating aspect that may be deflected or ignored, but cannot be fully denied. The Enlightenment’s quest for any truth that may have been hidden within the occult sci- ences was not a search for magic per se. It was a process of copying scientific investigations that in the fields of natural sciences were yielding new useful, verifiable discoveries in Nature. The natural world was seen to be yielding up her secrets to the empirically minded scientist. Those 18th-century occultists and Neo-Platonists would have considered themselves as men of science. It was just that the sciences they pursued were not limited to chemistry, physics, botany, etc., but also include 16. OBFUSCATION: WHY ARE WE NOT LIVING IN A NEW GOLDEN AGE?16.3 THE LIMITATIONS OF THE ENLIGHTENMENT 173 necromancy, alchemy, and magic. Everything was being studied; the practitioners were daring to know everything, and by so doing gave to the more esoteric and recondite subjects a veneer of re- spectability. The Book of Nature had no forbidden chapters. The rationality of the Enlightenment collapsed into a myth of the type that rationality was intended to banish. Physics became mixed up with metaphysics, and it was Isaac Newton who had warned us to avoid such a mixing, even though his Neo-Platonic outlook told a very different story. Figure 16.2: Neil Armstrong (1930–2012) became the first human to step onto the surface of the Moon (image from: https://en.wikipedia.org/wiki/Moon_landing#/media/File:Apollo_11_first_step.jpg). He was Commander of NASA’s Apollo 11 mission, and is here seen descending the ladder of the Apollo Lunar Module to step onto the Lunar surface. During this descent he spoke one of the most celebrated of all phrases; a phrase that still inspires and transcends tedious earth-bound politics. The video of this event, which the author watched live on TV as an impressionable 13-year-old, may be found at: https:// commons.wikimedia.org/wiki/File:Apollo_11_Landing_-_first_steps_on_the_moon.ogv. It was in the last century that we witnessed the most significant re-appraisal of our well-es- tablished way of looking at Nature. At the dawn of the 20th century, we began to finally get to grips with the question of the nature of light, which is just as well as it is via light that we perceive the world around us; and so try to begin to disentangle our perceived sensations from our real and imaginary fears. Physics had shown that light could be thought of as a wave when it propagated freely, yet could also be analyzed successfully if it were considered a stream of tiny particles. Which 174 was true? Was light continuous, or was it particulate? The same could also be said for electrons, so what was the relationship between electrons and light? Such debates led to the creation of quantum theory, and then the rationalization of quantum theory by Paul Dirac (1902–84) and Werner Heisenberg (1901–76); involving the interpretation of radiation-matter interactions in terms of an uncertainty as to the precise values of the velocity and position of the quantum particles; the problem of complementarity. This rationalization means, that at the quantum level of Nature, measuring something will interfere with the actual validity of the measurement. Niels Bohr (1885–1962), one of the founders of quantum mechanics, thought that the apparatus in which an experiment was performed should be described in the mathemat- ical equations defining what was being measured. Thus, scientific objectivity disappeared. Albert Einstein, the other founder of early quantum mechanics was not happy with Bohr’s ideas, and he could never bring himself to abandon belief in the reality of an external world controlled by cau- sality; a world that could be investigated in an objective manner by science. For the purely classical, pre-quantum view of the Universe, we must go back to Pierre-Simon Laplace (1749–1827), who thought in purely classical terms, and who said that from the known laws of mechanics and from a full knowledge of the present state of the Universe, every future state could, in principle, be pre- dicted. But that conceit of Laplace was the view of the European Enlightenment; it was based on their devotion to the mechanical universe of Isaac Newton. The European Enlightenment did not long survive the Revolutionary Wars of Napoléon Bonaparte. The restoration of the French monarch in 1815 was part of the rapid return to the in- fluence of religion in the political affairs of Europe. For many people, the European Enlightenment was supposed to have done away with ideas of magic and the occult, yet it is true to say that Paris at the end of the 19th century was filled with individuals searching for new ways of looking at Nature. Not only did fin de siècle Paris have Picasso inventing cubism, but the greatest, and the most famous physicists in the city at this time were the husband and wife team of Pierre (1859–1906) and Marie Curie (1867–1934), who investigated radioactivity. Yet for all the tremendous research carried out by scientists like the Curies, and the supposed triumph of the Enlightenment, Paris in the period 1880–1914 was also the world center for occultism and mysticism. There was the revival of Rosi- crucianism, Helena Blavatsky was attempting a synthesis of eastern and western Hermeticism into what she termed Theosophy (God’s wisdom), and symbolism was a dominant idea in literature and music. Why this revival of occultism and spirituality in the City of Light and science? Perhaps because the Curies were investigating radioactivity and radioactive decay; that is, the transforma- tion of one chemical element into another element. This was something that science had always said was impossible, yet was now the hottest topic in physics. How could, supposedly indivisible, eternal atoms such as Uranium decay to form other indivisible, eternal atoms such as Radium and Polonium; what was going on in that atom of Uranium (see Figure 16.3)? 16. OBFUSCATION: WHY ARE WE NOT LIVING IN A NEW GOLDEN AGE? 16.3 THE LIMITATIONS OF THE ENLIGHTENMENT 175 238 226 Uranium, the progenitor of Figure 16.3: Decay chain of Radium. Since the early modern period, Hermeticists and other followers of Hermes Trismegistus had been told they were crazy, and that there was no such thing as the transmutation of the chemical elements. Yet at the end of the 19th century in Paris, the Curies were unravelling the decomposition of a particular isotope of Uranium, and discovering that it transformed into many different chemical elements. Image from: https://en.wikipedia.org/wiki/ Radium#/media/File:Decay_chain(4n+2,_Uranium_series).svg. As far as the 19th-century Hermeticists and alchemists were concerned, the Curies were in- vestigating and seeking an explanation for the transmutation of the chemical elements, something 176 they had always believed in. The Curies were painstakingly showing that many, supposedly eternal, indestructible atoms, could transmute into atoms of other elements releasing huge amounts of en- ergy in the process. Marie Curie even demonstrated how Radium, or rather the radiation emitted by Radium as it transmuted, could cure cancer. All these strange and magical new discoveries in science were to the occultists a vindication of alchemy, and if alchemy was now seen to be true what other occult, or Hermetic sciences, would also be vindicated? But then, man’s passion for the fantastic is such that he is only too ready to suspend belief in the rational and the mundane. In this intellectual ferment, it was not surprising that Einstein and Picasso began coinciden- tally exploring notions of space and time. Relativity in its overthrow of absolute space and time teaches us that in thinking about perspective, we cannot simply trust our senses; and the cubism of Picasso destroyed the primacy of perspective in art. Indeed, one could say that cubism is art inspired by a redefinition of space and time; a technique for reducing the artistic form to geometry, of representing three dimensions in two dimensions. In their different ways, both Einstein and Pi- casso discarded the empiricist view—what you see is what you get—in favor of an intellectualized view of the world. But, of course, this re-intellectualization of our study of Nature was the opposite of what had happened in the Middle Ages when modern science had been born in Europe (see Chapter X?). Then a combination of empiricism and nature mysticism had overturned the Aristo- telian-Scholasticism of the Middle Ages. At the beginning of the last century, some of the leading figures in the arts were returning to a cerebral, scholastic interpretation of Nature. Proclaiming that thinking, not seeing leads us closer to the truth. Yet the purpose of science is not to provide the most economical representation of the facts, and the purpose of art is not to provide the most accurate representation of what we can see—why compete with photography? The purpose of both science and art is to discover the reality that lies hidden behind the appearances. After all, what is today considered to be magic and science fiction could well become scientific dogma in another half century. 16. OBFUSCATION: WHY ARE WE NOT LIVING IN A NEW GOLDEN AGE?177 Author Biography Jeffrey H. Williams was born in Swansea, UK, in 1956. He attended the University College of Wales, Aberystwyth and Cambridge University, being awarded a Ph.D. in chemical physics from the University of Cambridge in 1981. Subse- quently, his career as a research scientist was in the physical sciences. First, as a research scientist in the universities of Cambridge, Oxford, Harvard, and Illinois, and subsequently as an experimental physicist at the Institute Laue-Langevin, Grenoble, which remains one of the world’s leading centers for research involving neutrons, especially, neutron scattering and diffraction. During this research career, the author pub- lished more than seventy technical papers and invited review articles in the peer-reviewed literature. However, after much thought, the author chose to leave research in 1992 and moved to the world of science publishing and the communication of science by becoming the European editor for the physical sciences for the AAAS’s Science. Subsequently, the author was Assistant Executive Secretary of the International Union of Pure and Applied Chemistry; the agency responsible for the world-wide advancement of chemistry through international collaboration. And most recently, 2003–2008, he was the head of publications and communications at the Bureau International des Poids et Mesures (BIPM), Sèvres. The BIPM is charged by the Meter Convention of 1875 with ensuring world-wide uniformity of measurements, and their traceability to the International System of Units (SI). It was during these years at the BIPM that the author became interested in, and familiar with the origin of the Metric System, its subsequent evolution into the SI, and the coming transformation into the Quantum-SI. Since retiring, the author has devoted myself to writing. In 2014, he published Deﬁning and Measuring Nature: The Make of All Things in the IOP Concise Physics series. This publication out- lined the coming changes to the deﬁnitions of several of the base units of the SI, and the evolution of the SI into the Quantum-SI. In 2015, he published Order from Force: A Natural History of the Vacuum in the IOP Concise Physics series. This title looks at intermolecular forces, but also explores how ordered structures, whether they are galaxies or crystalline solids, arise via the application of a force. Then in 2016, he published Quantifying Measurement: The Tyranny of Number, again the IOP Concise Physics series. This title is intended to explain the concepts essential in an understanding of the origins of measurement uncertainty. No matter how well an experiment is done, there is 178 always an uncertainty associated with the final result—something that is often forgotten. In 2017, he published Crystal Engineering: How Molecules Build Solids in the IOP Concise Physics series. This title looks at how the many millions of molecules, of hugely varying shapes and size can all be packed into a handful of crystal symmetries. Most recently, 2018, the author published Molecules as Memes, again in the IOP Concise Physics Series. This title explains how the onetime separate sciences of physics and chemistry became one science, with the advent of quantum mechanics and the acceptance of the existence of molecules. In addition, retirement has allowed the author to return to the research laboratory and he is again publishing technical papers, this time in the fields of crystal design and structure determina- tion via x-ray diffraction, in particular, the architecture and temperature stability of co-crystals and molecular adducts. AUTHOR BIOGRAPHY
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=8737906.pdf&bkn=8737905&pdfType=book	Synthesis Lectures on Engineering Series ISSN 1939-5221 Transformative Teaching A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam, Arizona State University Brooke Coley, Arizona State University Audrey Boklage, University of Texas at Austin The journey to becoming an exemplary engineering educator is one that is rarely simple and straightforward. Simply being exposed to active learning strategies or innovative pedagogies rarely leads to a transformation of one’s own teaching. In this book, we present a collection of stories from exemplary engineering educators that are told in their own voices. These stories are shared to enable readers to immerse themselves in first-person recollections of transformation, involving engineering educators who changed their teaching strategies from the ways that they were taught as engineering undergraduate students to ways that more effectively fostered a conducive learning atmosphere for all students. It is our hope that providing stories of successful engineering educators might stimulate thoughtful and productive self-reflection on ways that we can each change our own teaching.These stories are not simple, linear stories of transformation. Instead, they highlight the complexities and nuances inherent to transforming the way that engineering faculty teach. Through our strategy of narrative storytelling, we hope to inspire future and current engineering educators to embark on their own journeys of teaching transformations. We conclude the book with some lessons that we learned during our readings of these stories, and invite readers to extract lessons of their own. ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For more information, visit our website: http://store.morganclaypool.com store.morganclaypool.com K E L L A M • C O L E Y • B O K L A G E T R A N S F O R M A T I V E T E A C H I N G M O R G A N & C L A Y P O O L Transformative Teaching A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Synthesis Lectures on Engineering Each book in the series is written by a well known expert in the ﬁeld. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience. In addition, the series includes several titles written on very speciﬁc topics not covered elsewhere in the Synthesis Digital Library. Transformative Teaching: A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam, Brooke Coley, and Audrey Boklage 2019 Ancient Hindu Science: Its Transmission and Impact of World Cultures Alok Kumar 2019 Value Relational Engineering Shuichi Fukuda 2018 Strategic Cost Fundamentals: for Designers, Engineers, Technologists, Estimators, Project Managers, and Financial Analysts Robert C. Creese 2018 Concise Introduction to Cement Chemistry and Manufacturing Tadele Assefa Aragaw 2018 Data Mining and Market Intelligence: Implications for Decision Making Mustapha Akinkunmi 2018 Empowering Professional Teaching in Engineering: Sustaining the Scholarship of Teaching John Heywood 2018 iii The Human Side of Engineering John Heywood 2017 Geometric Programming for Design Equation Development and Cost/Proﬁt Optimization (with illustrative case study problems and solutions), Third Edition Robert C. Creese 2016 Engineering Principles in Everyday Life for Non-Engineers Saeed Benjamin Niku 2016 A, B, See... in 3D: A Workbook to Improve 3-D Visualization Skills Dan G. Dimitriu 2015 The Captains of Energy: Systems Dynamics from an Energy Perspective Vincent C. Prantil and Timothy Decker 2015 Lying by Approximation: The Truth about Finite Element Analysis Vincent C. Prantil, Christopher Papadopoulos, and Paul D. Gessler 2013 Simpliﬁed Models for Assessing Heat and Mass Transfer in Evaporative Towers Alessandra De Angelis, Onorio Saro, Giulio Lorenzini, Stefano D’Elia, and Marco Medici 2013 The Engineering Design Challenge: A Creative Process Charles W. Dolan 2013 The Making of Green Engineers: Sustainable Development and the Hybrid Imagination Andrew Jamison 2013 Crafting Your Research Future: A Guide to Successful Master’s and Ph.D. Degrees in Science & Engineering Charles X. Ling and Qiang Yang 2012 Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronald E. Terry 2012 iv A Little Book on Teaching: A Beginner’s Guide for Educators of Engineering and Applied Science Steven F. Barrett 2012 Engineering Thermodynamics and 21st Century Energy Problems: A Textbook Companion for Student Engagement Donna Riley 2011 MATLAB for Engineering and the Life Sciences Joseph V. Tranquillo 2011 Systems Engineering: Building Successful Systems Howard Eisner 2011 Fin Shape Thermal Optimization Using Bejan’s Constructal Theory Giulio Lorenzini, Simone Moretti, and Alessandra Conti 2011 Geometric Programming for Design and Cost Optimization (with illustrative case study problems and solutions), Second Edition Robert C. Creese 2010 Survive and Thrive: A Guide for Untenured Faculty Wendy C. Crone 2010 Geometric Programming for Design and Cost Optimization (with Illustrative Case Study Problems and Solutions) Robert C. Creese 2009 Style and Ethics of Communication in Science and Engineering Jay D. Humphrey and Jeﬀrey W. Holmes 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Analog Multimedia Explorations Lina J. Karam and Naji Mounsef 2008 Introduction to Engineering: A Starter’s Guide with Hands-On Digital Multimedia and Robotics Explorations Lina J. Karam and Naji Mounsef 2008 CAD/CAM of Sculptured Surfaces on Multi-Axis NC Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 v Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Robert G. Watts 2007 Project Management for Engineering Design Charles Lessard and Joseph Lessard 2007 Relativistic Flight Mechanics and Space Travel Richard F. Tinder 2006 Copyright © 2019 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Transformative Teaching: A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam, Brooke Coley, and Audrey Boklage www.morganclaypool.com ISBN: 9781681735450 ISBN: 9781681735467 ISBN: 9781681735474 paperback ebook hardcover DOI 10.2200/S00911ED1V01Y201903ENG035 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON ENGINEERING Lecture #35 Series ISSN Print 1939-5221 Electronic 1939-523X Cover image by Pexels on Pixabay (https://pixabay.com/users/Pexels-2286921/). Image retrived from https://pixabay.com/photos/mountains-dawn-dusk-grass-hills-1868715/ Transformative Teaching A Collection of Stories of Engineering Faculty’s Pedagogical Journeys Nadia Kellam Arizona State University Brooke Coley Arizona State University Audrey Boklage University of Texas at Austin SYNTHESIS LECTURES ON ENGINEERING #35 CM&cLaypoolMorganpublishers&ABSTRACT The journey to becoming an exemplary engineering educator is one that is rarely simple and straightforward. Simply being exposed to active learning strategies or innovative pedagogies rarely leads to a transformation of one’s own teaching. In this book, we present a collection of stories from exemplary engineering educators that are told in their own voices. These stories are shared to enable readers to immerse themselves in ﬁrst-person recollections of transformation, involving engineering educators who changed their teaching strategies from the ways that they were taught as engineering undergraduate students to ways that more eﬀectively fostered a con- ducive learning atmosphere for all students. It is our hope that providing stories of successful engineering educators might stimulate thoughtful and productive self-reﬂection on ways that we can each change our own teaching. These stories are not simple, linear stories of transfor- mation. Instead, they highlight the complexities and nuances inherent to transforming the way that engineering faculty teach. Through our strategy of narrative storytelling, we hope to inspire future and current engineering educators to embark on their own journeys of teaching transfor- mations. We conclude the book with some lessons that we learned during our readings of these stories, and invite readers to extract lessons of their own. KEYWORDS engineering teaching journeys, engineering teaching stories, innovative engineer- ing teaching, engineering active learning, narrative interviews of engineering fac- ulty, exemplary engineering teachers, exemplary engineering educators, innovative engineering teachers, innovative engineering educators, innovation in engineering education, engineering teaching inspiration, engineering educator inspiration, en- gineering faculty teaching stories Contents ix Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii 1 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Nadia Kellam, Audrey Boklage, and Brooke Coley Motivation for this Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 How we Structured These Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Developing a Liberative Pedagogy in Engineering . . . . . . . . . . . . . . . . . . . . . . . . 9 Donna Riley Call to Adventure: Why Can’t Engineering be Taught the Way Religion is Taught? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Supernatural Aid: You Have to Read Teaching to Transgress . . . . . . . . . . . . . 11 Belly of the Whale: The Start of a 10-Year Period of Experimentation in Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Supernatural Aid: Learning about a CAREER Award in Engineering Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Road of Trials: Becoming Comfortable with Critique in Thermodynamics . . 13 Refusal of the Call: Becoming a Feminist Activist . . . . . . . . . . . . . . . . . . . . . . 14 Stories from My Class: The Montreal Massacre as a Case Study . . . . . . . . . . . 15 Road of Trials: Pushback from Students and Colleagues . . . . . . . . . . . . . . . . . 17 Road of Trials: Required Service Learning in Thermodynamics . . . . . . . . . . . 18 Return Threshold: Protesting a Nuclear Power Plant . . . . . . . . . . . . . . . . . . . . 20 Return Threshold: Challenging the Powers that Be . . . . . . . . . . . . . . . . . . . . . 21 Road of Trials: Creative Solutions to Constraining Policies . . . . . . . . . . . . . . . 22 Apotheosis: Pushing the Boundaries in any Context . . . . . . . . . . . . . . . . . . . . 22 Master of Both Worlds and Freedom to Live: The Importance of Reﬂection . 23 Additional Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 x 3 Experiencing Vulnerability and Empowerment in Teaching . . . . . . . . . . . . . . . 27 Sara Atwood Call to Adventure: From Childhood to Undergraduate, Becoming an Educator First . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Call to Adventure and Supernatural Aid: Experiences as an Undergraduate TA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Call to Adventure: Experiencing Faculty who Prioritize Research First . . . . . 29 Supernatural Aid: Finding My Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 First Threshold: Finding the Right College and Connecting with the Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Supernatural Aid: Learning from Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Belly of the Whale: Not Enough Time During the Lecture . . . . . . . . . . . . . . 31 Road of Trials: Theory vs. Solving Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Road of Trials: Just-in-Time vs. Established Preparation . . . . . . . . . . . . . . . . . 33 Road of Trials: Students with Learning Disabilities . . . . . . . . . . . . . . . . . . . . . 34 Belly of the Whale: A Particularly Challenging Semester . . . . . . . . . . . . . . . . 35 Supernatural Aid and Meeting with the All Knower: A Community of Academic STEM Women . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Master of Both Worlds and Freedom to Live: A Balance of Vulnerability and Empowerment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 From the Armed Services to the Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Brad Hyatt The Call to Adventure: A True Learner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Refusal of the Call: Deciding to Leave Industry . . . . . . . . . . . . . . . . . . . . . . . . 40 Road of Trails: Connecting Classroom to Industry . . . . . . . . . . . . . . . . . . . . . 40 Crossing the First Threshold: Flipping the Classroom . . . . . . . . . . . . . . . . . . 41 Apotheosis/Freedom to Live: Learning Together . . . . . . . . . . . . . . . . . . . . . . . 41 Supernatural Aid: Professional Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Master of Two Worlds/Return Threshold: Real-World Examples . . . . . . . . . . 42 Freedom to Live/Ultimate Boone: Constructive Criticism . . . . . . . . . . . . . . . 42 Supernatural Aid: Faculty Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Road of Trials: Resisting Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Freedom to Live: Embracing the Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Master of Two Worlds: Investing Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Freedom to Live: Gamiﬁcation in the Classroom . . . . . . . . . . . . . . . . . . . . . . . 44 xi 5 Engaging Students through Service Learning and Innovation . . . . . . . . . . . . . 45 Chris Swan Call to Adventure: The Ten-Year Plan to Become a Professor with Practical Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Crossing the Threshold: Helping Students Connect the Theoretical and Practical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Apotheosis: Seeing an Explosion in the Desire of the Students to Learn . . . . 47 Road of Trials: Researching New Ways to Engage and Deepen Learning . . . 48 Ultimate Boon: Becoming the Best Faculty Member through Student Engagement and Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6 From Food to Simulation with Legos: Engaging Students in Hands-On Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Thais Alves Call to Adventure: Creating a Community . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Road of Trials: A Lack of In-Situ Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 54 First Threshold: Building a Language Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Belly of The Whale: The Task of Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Acceptance of the Call: Food, Handmade Legos, and Presentations . . . . . . . . 55 Ultimate Boone: Positive Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Apotheosis: More Pluses than Deltas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Master of Two Worlds/Freedom to Live: Pedagogical Flexibility . . . . . . . . . . 57 Meeting with the All Knower: Like-Minded Educators . . . . . . . . . . . . . . . . . 57 Master of Two Worlds: Legos Aren’t a Waste of Time . . . . . . . . . . . . . . . . . . 58 7 Finding Her Niche with Hands-On, Practical, and Real-World Pedagogy . . . 59 Fernanda Leite Call to Adventure: Combining Passions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Supernatural Aid: Figuring Out How To Become a Professor . . . . . . . . . . . . . 60 Meeting with the All Knower: A Visiting Professor and Future Advisor . . . . 60 Road of Trials: Experience Teaching in Graduate School . . . . . . . . . . . . . . . . 60 Apotheosis: Developing an Interconnected Course . . . . . . . . . . . . . . . . . . . . . 61 Return Threshold: Bringing the Real World into the Classroom . . . . . . . . . . . 64 xii Master of Both Worlds and Freedom to Live: Encouraging Other Academics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Stories from My Class: Teaching with Legos . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Master of Both Worlds and Freedom to Live: Integrating Teaching and Research Through an Industry Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8 Creating a Community of Collaborators to Achieve Curriculum Change . . . . 69 Charles Pierce Call to Adventure: Teaching Runs in the Family . . . . . . . . . . . . . . . . . . . . . . . 69 Supernatural Aid: Graduate School Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Supernatural Aid: Push to Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Meeting with the All Knower: An Opportunity to Teach Autonomously . . . . 71 Supernatural Aid: Funding Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Road of Trials: New(ish) Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Atonement: Student Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Road of Trials: Communication in the Classroom . . . . . . . . . . . . . . . . . . . . . . 73 Ultimate Boone: Concepts not Schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Supernatural Aid: Classmate Assistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Ultimate Boone: Candy and Personality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Freedom to Live: Flexible Syllabi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Master of Two Worlds: Problem Solving in the Classroom . . . . . . . . . . . . . . . 75 Road of Trials: Improving the Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Ultimate Boone: With Funding Comes Change . . . . . . . . . . . . . . . . . . . . . . . 77 Apotheosis: Encouraging Critical Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Ultimate Boone: Teaching Award and Reﬂecting on My Journey . . . . . . . . . . 79 Master of Two Worlds: Collaboration is Key . . . . . . . . . . . . . . . . . . . . . . . . . . 80 9 Teaching with Advocacy: Buﬃng the Talent to Break the Mold of the Monolithic Engineer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Matthew Fuentes The Call to Adventure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Supernatural Aid: Learning to Teach in a Student-Centered Way . . . . . . . . . 82 The Call to Adventure: Aspiring to Teach Students Who are Less Privileged 83 Supernatural Aid: A Mentor Who Helped Encourage Experimenting Educationally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Stories from My Class: Going Outside to Bring out the Inquisitive Mind . . . 84 xiii Road of Trials: Finding a Faculty Position at a Place Where I Can Make a Diﬀerence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Road of Trials: Becoming Transparent About Who I Am . . . . . . . . . . . . . . . . 86 Stories from My Class: Helping Students Overcome Imposter Syndrome and Become More Engaged . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Stories From My Class: Teaching Through Making and Failure . . . . . . . . . . . 87 Road of Trials: Introducing Simulink® Before it Had Been Debugged . . . . . . 88 Road of Trials: Uncovering Biases and Expectations and a Need for Engineering to Change, Culturally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Road of Trials: Experiencing Marginalization Through a Last Name Change and Becoming an Advocate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Apotheosis: Empowering Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 10 Conclusion and Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Nadia Kellam Lesson 1: Importance of Having a Community . . . . . . . . . . . . . . . . . . . . . . . . 91 Lesson 2: The Power of Reﬂection in Improving Our Courses . . . . . . . . . . . . 92 Lesson 3: Take it Slow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Lesson 4: Improving Teaching and Learning is a lot of Work, but it is Fulﬁlling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Lesson 5: Tradeoﬀs Between Teaching and Research, or Not? . . . . . . . . . . . . 93 Lesson 6: Consider an Asset-Based Approach to your Teaching . . . . . . . . . . . 94 Lesson 7: Empower Engineering Students who have Otherwise been Marginalized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Lesson 8: Connecting Theory to the Real World in the Classroom . . . . . . . . . 97 Lesson 9: Using Ideas from Entrepreneurship in Engineering Education . . . 97 Lesson 10: Comfort with Ambiguity and Relinquishing Control are Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Lesson 11: Learn Something New . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Authors’ Biographies (in order of appearance) . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Preface xv When I was interviewing for my ﬁrst engineering tenure-track faculty position in 2006, the department head asked me which classes I could teach in the program. Conﬁdently, I responded that I could teach anything I had taken. A few months later, in the summer before I started, I learned I would be teaching something I had never taken before—a computational engineering methods class for ﬁrst-year engineering students. After talking to a few people, I understood that the undergraduate program coordinator wanted to get someone into the classroom who was nice to ﬁrst-year students. The current teacher, an Associate Professor, had structured the entire class around programming and was known to get frustrated with the students with rumors of him throwing chalk at students. I could be nice, I thought, but I’m not sure about teaching the course with my degrees in mechanical engineering. I managed to get by through changing the course to focus on learning programming structures (through storytelling using Alice), learning relative and absolute referencing in Microsoft Excel, learning html to create websites, and learning basic programming using MatLAB. I ended up teaching a few sections of this class for two years and eventually became comfortable teaching computational engineering methods to ﬁrst-year students. I even ended up having some fun with the class with a challenge at the end of the course for the students to use MatLAB to create artwork for an art exhibit. Students created music, edited photographs, created fractals, and created stop motion animations. During the art exhibit, I overheard one of my senior colleagues make a comment to the students saying that this was not engineering and seemed like a waste of time to him. This was my ﬁrst experience teaching as an engineering faculty member. After that ﬁrst semester teaching my own class, I quickly realized how diﬃcult and com- plicated teaching could be. While I had read many books preparing me to be a teacher, it was hard to truly prepare for experiences like this. I did not expect to be asked to teach something that I had not learned myself as a student. I also expected that senior faculty members in the department would be supportive of a junior faculty member. In hindsight, I was a bit naïve and probably should not have been surprised to experience some pushback for my alternative ways of teaching. I was, after all, the second woman faculty in our department of around 50 faculty members. In addition, I was the youngest faculty. The composition of our faculty was about to change, but when I ﬁrst joined it was pretty homogeneous. Because the teaching books that I read did not seem to be helping prepare me for the realities of teaching, I sought out additional opportunities to develop my teaching skills. These included workshops such as the National Eﬀective Teaching Institute (NETI) that Rich Felder and Rebecca Brent hosted before the American Society for Engineering Education (ASEE) conference. However, in spite of these intensive experiences to help me as a teacher, it felt diﬃcult xvi PREFACE to reconcile the actual experience of teaching with what I was learning from the experts. I would learn helpful strategies for teaching, but some of the diﬃculties I faced were not addressed in these workshops. In this book, we are going to share the messy and sometimes complicated stories of faculty as they embark on journeys to become better teachers. I hope that, through immersing yourself in these stories, that you will learn more about the journeys that faculty take to become better teachers and feel better prepared as you embark on your own journey. Nadia Kellam April 2019 Acknowledgments xvii We wish to thank our fellow research team members, Joachim Walther, Stephan Durham, San- dra Bird, and Kathleen DeMarrais at the University of Georgia for support during the early stages of this project. We would also like to thank more recent research team members includ- ing Madeleine Jennings, Joshua Cruz, Michael Sheppard, and Anna Cirell at Arizona State University for their support during the later stages of this book preparation. We would espe- cially like to thank Madeleine Jennings for helping with copy-editing many of the chapters of this book. In addition, we would like to thank the research participants in this study, including those whose stories were not included in this book. This material is based upon work supported by the National Science Foundation under grant numbers 1329300 and 1542531. Any opinions, ﬁndings, and conclusions or recommen- dations expressed in this material are those of the authors and do not necessarily reﬂect the views of the National Science Foundation. Nadia Kellam, Brooke Coley, and Audrey Boklage April 2019 C H A P T E R 1 Introduction Nadia Kellam, Audrey Boklage, and Brooke Coley 1 Anyone who has been an undergraduate engineering student knows that exemplary engineering educators are rare to ﬁnd but can make a big diﬀerence in engineering students’ development, sometimes being the diﬀerence between persisting in engineering or changing majors. As some of us continue through school and then become engineering faculty members, it can be daunting to ﬁgure out how to become good teachers ourselves, especially when our own Master’s and Ph.D. programs tend to focus on research and engineering sciences with little, if any, focus on our development as teachers. In this book, we (in this chapter, “we” refers to Nadia, Audrey, and Brooke) hope to provide an opportunity for engineering educators to learn about engineering teaching through becoming immersed in the stories of exemplary engineering faculty. These are not polished and overly edited stories of engineering faculty, but instead are somewhat raw and uncut stories as told by the faculty themselves. These stories were developed from transcriptions of narrative interviews and are kept in the spoken words of the engineering faculty. We wanted to explore ways of sharing the experience of hearing these inspirational stories, and thus the concept of this book was born. These stories promise to humanize teachers and show that good teachers are not just “born that way,” but face many obstacles on their own journeys of becoming exemplary teachers. From the outset of this project, we were interested in using narrative research strategies (narrative interviews and analysis), to develop an understanding of the stories of successful engi- neering faculty who have embraced active learning strategies [Meyers and Jones, 1993]. Stories are powerful ways of learning from others and are inherent to the way that we communicate, think, and learn. “We think in story. It’s hardwired in our brain. It’s how we make strategic sense of the otherwise overwhelming world around us” [Cron, 2012, p. 8]. We wholeheartedly agree that people are “hardwired” for stories and hope that by sharing these faculty stories others can be inspired and better prepared to embark on their own teaching journeys. As you immerse yourself into the stories shared in this book, in addition to providing inspiration, we hope the stories resonate with you and help you as you navigate your own personal teaching journeys. Through experiencing these stories, we can all learn from these stories, and, possibly, see teaching in a diﬀerent way than we did before. I know for me (in this chapter, “I” refers to Nadia), they impacted my understanding of what it means to be a good teacher. Somewhere in the back of my mind, I thought there were some teachers who were simply born 2 1. INTRODUCTION amazing teachers. From my experience, I knew I was not one of these fortunate people but hoped that with enough work I could become better. Through these stories, I began to see that other’s journeys are not simple and that even amazing teachers experience trials and diﬃculties throughout their journeys. MOTIVATION FOR THIS PROJECT When reading literature about STEM or engineering faculty and how they become exemplar teachers, much focuses on why faculty do not embrace active learning strategies. For example, in the Discipline Based Educational Research report, the committee describes barriers to chang- ing teaching practices including institutional priorities, local leadership, peers, reward systems, students’ attitudes, perceived importance of teaching, and faculty members’ beliefs [National Research Council, 2012]. While we recognize the importance of identifying and understand- ing these barriers, we are also interested in understanding faculty who have successfully changed their teaching practices. We decided to focus this research on these faculty who have successfully transitioned to active learning strategies and to uncover insights and lessons learned from their stories. The interviews that were used as the basis for these stories came from a research project focused on engineering faculty change. When we conducted these interviews, we did so for the purpose of the research project, and not with the goal of writing a book that included their stories. However, as we began conducting interviews, we quickly became inspired by the stories of the interviewees. Many of the interviews were conducted by Brooke and Audrey, who were, at the time of the data collection, postdoctoral researchers. In our team meetings after interviews, they were both very excited about the stories that they were hearing. We began to see the power of hearing the inspirational stories of these engineering faculty. In addition, I, who had been a faculty member for about 10 years, would listen to the interviews and become just as inspired and excited as Brooke and Audrey. These stories were powerful and we began to consider ways that these could be shared in a more complete form so that more people could become inspired and empowered by these stories. Another observation when conducting interviews for this research project was that the stories of faculty change were complex stories. They were not stories of faculty who just happened to be amazing teachers from day one. Nor were they stories of faculty who decided to make a change to their teaching, made their change, and succeeded easily. Instead, they were stories of faculty who wanted to make changes to their teaching for diﬀerent reasons, and they all encountered successes and struggles. In other words, these were not simple or linear stories of change. Instead, they were messy and complicated stories of change. In a few of the cases, these stories had reached a conclusion, and in others, the journey was ongoing and the engineering faculty members were continuously evolving as teachers. In Chapters 2–9 of this book, we will present these stories of faculty who have successfully transitioned to active learning strategies in their classes. These stories were developed based on interviews with these faculty and are kept in their words as spoken. 1. INTRODUCTION 3 HOW WE STRUCTURED THESE STORIES As described above, these stories were captured as part of a research project where we interviewed exemplar teachers to develop an understanding of how they got to where they are today in spite of all the challenges and obstacles along the way. As part of our methods, we constructed stories, in the spoken word of the participants, as we felt this format had the most resonance with the reader. We used Joseph Campbell’s Hero’s Journey [2008] as a way to structure these stories. We then analyzed the data for patterns across the stories. However, when we disseminated this work in journal articles, most of the participants’ stories and voices were lost. Their stories were reduced to a few pages, at most, with a few supporting quotes from their interviews [Boklage, Coley, and Kellam, 2018]. Because we were unable to share these complete stories in traditional dissemination venues, we began considering nontraditional ways of sharing these stories. After some con- sideration, we decided to prepare a book that would include faculty stories in their entirety. The hope is that these stories will serve as an inspiration to help teachers as they embark on or grow in their own personal journeys of transformation. Prior to sharing these stories, we will describe the Hero’s Journey, as the stories in this book are all organized using this structure. The idea behind the Hero’s Journey is that all stories follow similar structural patterns. In Joseph Campbell’s book, Hero with a Thousand Faces, he introduces the monomyth [2008]. The monomyth is a universal structure that all epic myths are claimed to follow. In Campbell’s book, he considers over 100 stories from multiple cultures and times and shows that these stories follow a similar trajectory. Campbell proposes 17 stages that stories generally follow. We have interpreted these stages that were intended for written or told stories or epic myths for lived stories of engineering faculty. Below are brief descriptions of the stages that we used in structuring stories that were told in interviews. 1. The call to adventure marks the beginning of the faculty’s story and includes their purpose or reason for embarking on a journey. 2. The refusal of the call occurs after the call to adventure and involves the faculty member changing their mind and deciding to not begin their journey. This is typically a considera- tion and, at least in the stories of faculty who have successfully transitioned their teaching practices highlighted in this book, is only a consideration that does not result in the end of the journey. 3. Supernatural aid occurs when the faculty member receives unexpected help from a mentor, colleague, or other resource (e.g., a book or website). This aid helps the faculty member prepare for the journey that they are about to take. 4 1. INTRODUCTION 4. The ﬁrst threshold is experienced when the faculty member continues forward in their jour- ney and experiences their ﬁrst trial or challenge on their journey. This challenge is typically expected by the faculty member, as they anticipate some diﬃculties when embarking on the journey. 5. During the belly of the whale, the faculty member experiences a very low point in their journey. Oftentimes, this experience becomes transformative for the faculty member as they have a realization of the importance of this journey as they recover from this low point. 6. During the road of trials, the faculty member experiences and overcomes many challenges. This could be student resistance to active learning strategies, or colleagues questioning the eﬀort being put into teaching. 7. The meeting with the all-knower structure represents the faculty member meeting with a mentor who passes critical knowledge onto the faculty member. Without this interaction, it could be imagined that the journey might have ended very diﬀerently for the faculty member. 8. The meeting with temptation occurs when the faculty member has an experience that could keep them from reaching their personal goal. This temptation could be in the form of focusing eﬀorts on research instead of teaching, beginning to lecture again because of the potential of earning higher teaching evaluations, or following traditional course approaches after some students express frustration with the new approaches. 9. In the apotheosis stage, the faculty member reaches a new level of understanding where their journey becomes routine and their teaching innovations come with fewer surprises. 10. The ultimate boon occurs near the end of the journey as the journey reaches resolution. As could be imagined, many of the faculty in this book do not reach the end of their story, but do reach some boon where they attain a steady state in their goals. 11. The return threshold occurs when the faculty member begins communicating with peers, colleagues, students, and administrators, telling them what they learned during their jour- ney and beginning to reconcile their new identity with the one they left behind as they embarked on their journey. 12. The ﬁnal phase, master of both worlds and freedom to live, represents when the faculty mem- ber moves back to the “ordinary” world that they left when embarking on their journey to the “special” world that they inhabited while on their journey. This can involve shar- ing their story of change with people who have not embarked on their own journey. It can also involve becoming integrated back into the “ordinary” world with the knowledge gained while on their journey. 1. INTRODUCTION 5 There are ﬁve additional stages that were not used in these journeys, and will not be ex- plained in detail. These include some that are less applicable to lived stories, including, for ex- ample, the magic ﬂight which involved the hero rushing home in a pursuit. Others were just not included in the stories highlighted in this book and include, for example, the refusal of the return, where a faculty member would refuse to move back into their “ordinary” world after experiencing the “special” world. As you begin reading the chapters, you will notice that many of the stories only include some of the stages in the journey. These stages were only used to structure the stories as they were constructed from the spoken interview. These stages will be used to help organize the subsequent chapters. For those interested in journal articles, we outline this process in Cruz and Kellam [2017] and use this structure in an article exploring the beginning of engineering students’ journeys [Cruz and Kellam, 2018]. In addition to the stages described above, we added some stages to the stories. One com- mon addition is named stories from my class. While the monomyth provided a helpful structure for organizing and constructing narratives from the interview transcripts, we found that some parts of the story were excluded because they did not follow neatly into one of the structures. While the stories from my class structure did not involve a particular trial or challenge, we felt it was important to include this part of their story as it showed innovations in their teaching and provided more texture and context to their particular journey. In each participant’s story we will use headings to denote each stage in the journey. This will help the reader move more easily between stories to compare, for example, speciﬁc stages for each engineering educator. OVERVIEW OF THE BOOK The participants’ stories are told in their spoken voice as transcribed from the interview. By keep- ing the stories true to their voice, we believe that the stories are more engaging than they would be if we rephrased them. This does mean that there are some run-on sentences and colloquial terms used in their stories. Occasionally, we include a few additional words to help improve the ﬂow of the story. These words are denoted with square brackets in the text. In addition, we provide some clarifying details in parentheses (e.g., the meaning of an acronym). In Chapter 2, Donna Riley, the Kamyar Haghighi Head of the School of Engineering Education at Purdue University, shares her teaching story. At the time of the interview, Donna was a faculty member at Virginia Tech. Donna tells her story of integrating a liberative pedagogy into engineering education. After she started her ﬁrst faculty appointment at Smith College, she began a 10-year experiment in a Thermodynamics course where she challenged the power dy- namics common to engineering courses and pushed students to begin thinking critically about the subject. Her story is one that includes social activism and is one that will serve as an inspi- ration to many faculty as she challenged the status quo in engineering education. 6 1. INTRODUCTION In Chapter 3, Sara Atwood, an Associate Professor and Chair of Engineering and Physics at Elizabethtown College, shares her teaching story. Her undergraduate studies at Dartmouth College, a liberal arts setting, provided her foundation for student-centered learning. Sara’s jour- ney was one that elevated the evolution, process, and development of implementing this peda- gogical approach. Among her main supports were the colleagues and community created around these eﬀorts, like-minds committed to enhancing the education of engineering students. In Chapter 4, Brad Hyatt, an Associate Professor of Construction Management at Fresno State University, shares his story. Prior to being a faculty member, Brad worked for 12 years in industry, both as a Civil Engineering Oﬃcer in the Navy and as a Project Management and Construction Management Consultant. When he was a new faculty member, Brad approached teaching with a lot of energy and a “just do it” attitude where he adopted project-based learning, ﬂipping the classroom, and bringing case studies into the class. In Chapter 5, Chris Swan, an Associate Professor in Civil and Environmental Engineer- ing at Tufts University, shares his story. His belief is that students should experience knowledge and he works to connect content with applications. He ﬁnds seeing the application in a real- world context to be especially critical in students’ ability to truly grasp material and he facilitates this by oﬀering students service-learning based projects. In Chapter 6, Thais Alves, an Associate Professor of Construction Engineering at San Diego State University, shares her story. Thais brings an international experience as she is from Brazil, completed her Ph.D. at UC Berkeley, and returned to Brazil again prior to becoming a faculty member in San Diego. When Thais became a faculty member in San Diego, she had to become creative with her teaching because she did not have the access to construction sites that she had in Brazil. She began to take an entrepreneurial approach to her teaching and considered her students as clients to ﬁnd a way that students begin to value what they were learning in class. Now, she integrates site visits, food, and Lego simulations into her classes. In Chapter 7, Fernanda Leite, an Associate Professor in Civil, Architectural, and En- vironmental Engineering in the Cockrell School of Engineering at The University of Texas in Austin, shares her story. Throughout her experiences, Fernanda has always been passionate about teaching and as a graduate student she revamped a lab course while she worked as a Teaching Assistant (TA). At UT Austin, Fernanda has developed courses where she created modules that connect lectures, lab classes, and reﬂections across topics in the course. She brings real-world scenarios into the classroom where students have to make assumptions and estimates. She also discusses how her teaching and research have been inseparable with each one enhancing the other. In Chapter 8, Charles Pierce, an Associate Professor of Civil and Environmental En- gineering at the University of South Carolina, shares his story. Charlie had a strong passion for teaching and pursued his Ph.D. so that he could become a teacher. As he began teaching, he initially emulated some of his professors who were engaging and entertaining. He quickly transitioned from trying to cover content in his classes to ensuring that students were develop- 1. INTRODUCTION 7 ing conceptual understandings. He describes using activities to help explain concepts in class, including activities involving candy, demonstration activities, and problem-based learning. He also describes a group of faculty in his department who continue to inspire and motivate him as he continues in his journey to become an exemplary engineering educator and an engineering education researcher. In Chapter 9, Matthew Fuentes, an Engineering Faculty member at Everett Community College, shares his story. Matthew uses his quirky zeal for learning to create student engage- ment in his classrooms anchored in a belief in equity and opportunity for all. In recognizing his own privilege in the world as a White, male engineer, he envisions the classroom as a place where all students should be able to see themselves. Through his student-centered approaches, Matthew hopes to change what engineers look like, one student at a time. Matthew’s willingness to challenge meritocracy with an appreciation for the process of developing potential positions him as a rare and refreshing advocate for a just education. In ﬁnding comfort amid situations of ambiguity, Matthew has enhanced student learning while also cultivating a culture of inclusion that empowers students to reach their fullest potential. In Chapter 10, we provide a set of lessons learned from the stories. These lessons include taking it slow when innovating in the classroom, ﬁnding a community of educators with simi- lar visions and goals, and using reﬂection to help improve classes. Another take-away from the stories is that innovative teaching can require a lot of work, but can also prove very fulﬁlling and worth the extra time and eﬀort. One lesson was around focusing on teaching or research, with on story demonstrating that these two aspects of faculty roles can be symbiotic. Other lessons focus around concepts of inclusivity, with one focusing on considering the assets of students when they come into the classroom, valuing their experiences, and being intentional to empower stu- dents who have been marginalized in engineering education programs. Moreover, there were many examples in the stories of engineering educators connecting theory through teaching ap- proches to the real world in the classroom through case studies, projects, service learning, and open-ended problems. There were a few examples of engineering educators using concepts from entrepreneurship to improve their classrooms, with a focus on value propositions, considering our customer segments, and pushing on boundaries. Finally, there were many engineering edu- cators who were motivated and inspired to become better teachers because of their experiences as undergraduate or graduate students. The last lesson learned includes a challenge to consider learning something new and trying new things, to help faculty relate better to students in their classrooms who are learning something new and to help expose them to diﬀerent pedagogies and ways of teaching. As you begin reading these stories, we encourage you to think about lessons or take-aways that can help inform your own teaching journeys. 8 1. INTRODUCTION REFERENCES Boklage, A., Coley, B., and Kellam, N. (2018). Understanding engineering educators’ pedagog- ical transformations through the hero’s journey. European Journal of Engineering Education. DOI: 10.1080/03043797.2018.1500999. 3 Campbell, J. (2008). The Hero with a Thousand Faces, 3rd ed., Novato, New World Library. 3 Cron, L. (2012). Wired for Story: The Writer’s Guide to Using Brain Science to Hook Readers from the Very First Sentence, Ten Speed Press. 1 Cruz, J. and Kellam, N. (2017). Restructuring structural narrative analysis using Camp- bell’s monomyth to understand participant narratives. Narrative Inquiry, 27(1). DOI: 10.1075/ni.27.1.09cru. 5 Cruz, J. and Kellam, N. (2018). Beginning an engineer’s journey: A narrative examination of how, when, and why students choose the engineering major. Journal of Engineering Education, 107(4), pp. 556–582. DOI: 10.1002/jee.20234. 5 Meyers, C. and Jones, T.B. (1993). Promoting Active Learning Strategies for the College Classroom, Jossey-Bass Inc., Publishers, San Francisco, CA. 1 National Research Council. (2012). Discipline-Based Education Research: Understanding and Im- proving Learning in Undergraduate Science and Engineering, The National Academies Press, Washington, DC. 2 C H A P T E R 2 9 Developing a Liberative Pedagogy in Engineering Donna Riley Narrative constructed by Brooke Coley and Nadia Kellam It’s just recognizing that [change] doesn’t happen trivially. [It] takes a lot of thought. [It] takes a lot of adjustment. It takes a lot of troubleshooting. And small changes can be tremen- dously huge… Letting [change] play out organically, it allows for students to shape the class. That’s part of it. Donna Riley is currently the Kamyar Haghighi Head of the School of Engineering Ed- ucation at Purdue University. At the time of the interview in November of 2016, Donna was Professor and Interim Head of the Department of Engineering Education at Virginia Tech. CALL TO ADVENTURE: WHY CAN’T ENGINEERING BE TAUGHT THE WAY RELIGION IS TAUGHT? I think it all started basically in undergrad where I went to Princeton and we had very old school professors there. A lot of them were Oxford and Cambridge educated. They would do the classic thing of taking out notes that were yellowed and 30 years old and write what was in the notes on the chalk board, and we wrote what was on the chalkboard in our notes, and rarely were we ever asked a question in class. The biggest exception to that was a professor who was in a wheelchair and he wrote what was in his notes on a transparency that was projected on a screen rather than on a chalk board, that was the variation. It was extremely passive, and we all had to sort it out later. We learned to work together in groups because all we had was what we wrote down in lecture and we had to ﬁgure out how to understand that and make sense of it. Meanwhile, I took other classes, and this was just kind of my own interest that I thought, well, if I’m only going to have 8 or 10 classes outside of engineering that I’m going to be able to take, I wanted to make them count. I took these upper-level classes in the humanities and social sciences which were over my head, but I just wanted to do that, so I took a class on ﬁve romantic poets, so I took a class on women’s history in the United States, or something like 10 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING that. Just because it was interesting to me. I was taking a class, I think it was probably my junior year; no, it was [the] spring of my sophomore year, from Elaine Pagels on Gnosticism and Early Christianity. She had this way of teaching the class where on the Monday we would...She would give her perspective on the reading and we would turn in a reﬂection paper that was just a couple of pages long. On Wednesday, she would basically facilitate a conversation among all of us in the seminar, there were probably a dozen of us. She would facilitate this conversation among us. What always surprised me was that I felt like I belonged in the room. I felt like I had something important to say. Despite my not having had any of the prerequisites for this class—I didn’t speak Greek. I couldn’t read things—she’d come in and read, on Monday, she’d be translating from original Aramaic and stuﬀ and everybody would sort of be nodding and I’d be like “How is she even doing this?” Just feeling completely both in over my head, but supported at the same time that I had actually something important to say. Contrast that with engineering [for] which I had all the prerequisites and yet every single time I was in there, they made us feel like we didn’t know anything. I became curious [around] that time about why engineering couldn’t be taught in the same way that my religion classes were being taught. I didn’t really get to pursue that question, it just kind of rested in the back of my mind for a while. When I got [into] grad school, I found that in chemical engineering at Carnegie Mellon there were people that were much more interested in some pedagogical innovations. They were doing project-based learning and problem-based learning, and they were just more engaged with the literature. A professor named Ed Ko was at Carnegie Mellon at the time, he ended up moving, changing universities later, but at that time he was there, and he was pretty well known in engineering education circles at the time. It was a campus that was just more engaged with conversations about active learning and so on. I was educated in how to do that. There was a certiﬁed program for Ph.D. students from the Center for Teaching and Learning and I went and pursued that. They taught us Bloom’s taxonomy. They taught us the basics of what it would take to do active learning. I felt, at the time, I was like “Okay, I can do these things.” I was teaching a project-based course that was community-based as well, so we were working with the city of Pittsburgh on Pittsburgh’s urban forest. We had seniors in the engineering and public policy program and some Master’s students from the policy school working together in teams on how to assess the value of Pittsburgh’s urban forest from an environmental perspective. What was it doing to mitigate climate change, having all these trees around? What did it mean for property values? and so on; What did it mean in diﬀerent neighborhoods? And so on… We were looking at some environmental justice aspects of that problem. I was coaching these teams and really enjoying doing that, and thinking “Gosh, I think I really want to become a teacher.” Still not really getting at the heart of what I wanted to understand about the classroom. It wasn’t until I got to Smith College for my ﬁrst faculty appointment…Smith is a lib- eral arts college, it’s a women’s college.… In the fall semester, I taught an intro class, intro to engineering with two other people, so a team-taught class. I stepped in and taught the class 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 11 the way the other people taught it, but then in the spring I taught thermodynamics. That was really the ﬁrst time I had my own class, where there wasn’t someone else setting the syllabus, the curriculum, whatever. It was just me. SUPERNATURAL AID: YOU HAVE TO READ TEACHING TO TRANSGRESS I contacted a friend of mine who I knew through other relationships. This was someone [that] I was an activist with who taught sociology at Grinnell College in Iowa. I said, “Look, I need to understand, like it’s time for me to really unpack this. What was diﬀerent about what Elaine Pagels was doing in my Gnosticism class compared with this other stuﬀ? Because I know some- thing about active learning, I know something about project-based and problem-based learn- ing, but that’s not what this is. This is something else that she was doing. What was she doing? What’s it called?” I didn’t even know the name for it. I couldn’t research it on my own because I didn’t know what the keywords were. She said “Oh, you have to read bell hooks’ book Teaching to Transgress. By that point it was spring break, it was March, and I got the book and started reading it. It completely changed how I thought about what was going on in my classroom.” It was the key to understanding, not exactly what Elaine Pagels was doing, because I think she might describe her pedagogy diﬀerently, but it did talk about the power relationships in a class- room. It talked about viewing students in a holistic way. It talked about valuing the authority of experience and what students bring into a classroom. All of those things were things that were elements that Elaine Pagels was doing in our classroom that were never being done in engineering classes. BELLY OF THE WHALE: THE START OF A 10-YEAR PERIOD OF EXPERIMENTATION IN THERMODYNAMICS I noticed that I was repeating some of the very same problematic relationships that existed in my prior experience with thermo. This was true even though I wasn’t doing this passive lecture thing. I was doing active learning. I was doing the stuﬀ I was taught to do, but I could tell there were students in front of the class that were engaged, and the students in the back of the class weren’t engaged. I could just see it all unfolding in those same ways that I had been taught. The ﬁrst thing I did was I went back to my class after spring break and said “Here’s the problem I’ve been noticing. I’ve noticed that some of you are sitting in the back of the class and you don’t seem as engaged. I’d like to change the way that we’re sitting and so that we can actually face each other. What do you think?” They said “Okay.” We started doing that. They felt that was better. I tried this experiment that completely failed which was having them teach each other the material. I said “Oh, well, why don’t you just prepare chapter eight and come in and let’s talk about it.” That didn’t work so well, so I abandoned that. It started this 10-year period of experimentation in this thermodynamics class. I was fortunate to be at a place that was, ﬁrst of all, a brand-new 12 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING engineering curriculum where we were encouraged to experiment and encouraged to go to the ASEE conference, learn about the state of the art in engineering. The other really fortunate thing that happened is [that] bell hooks happened to come to Smith College while I was doing this. That was the same semester. There was some connection with the program in Buddhist Studies. She’s Buddhist, and they brought her to campus a couple of times over the next few years and one of her visits would happen to be that semester, so because it’s a small campus, I was able to go to her. They had a reception for her after her talk. I went to her talk and then went to the reception after. I just walked up to her and said, “Is anybody doing your pedagogy in a science or engineering class?” She said “Well, yes, but nobody has written about it.” Then she said, “Whatever you do make sure that you publish what you do.” I said “Okay.” She didn’t really give me any names, so I was able to kind of, I sort of Googled around and tried to ﬁnd some other folks and I found [a] couple things in science education but nothing in engineering. What’s interesting about that is, I wrote up the thermodynamics class, and submitted it to the Journal of Women and Minorities in Science and Engineering. It’s the only time I’ve ever had a paper published without any revisions at all. I fell into this ability to continue to innovate in that class because I applied for a CAREER award to the National Science Foundation. My research area was actually risk-assessment and risk-communication. I was doing technical research in this but my research, because my Ph.D. was in engineering and public policy, was always interdisciplinary…. When I went to meet with the program oﬃcers at NSF, I met with the environmental engineering program oﬃcer and he said “Well, this isn’t really…this sounds more like social behavior and economic sciences, you should go over there.” I went over to SBE [Directorate for Social, Behavioral, and Economic Sciences], and the person there was actually someone from my research group, so she had gone on to be a policy school professor in risk communication and was doing a rotation as a program oﬃcer at NSF that year. When I met with her, I said “Look, I mean, you know exactly the work I do.” She’s published in the same area, she knows the area really well. She said “Look, I’ve got to tell you, don’t waste your time. As much as I’d love to fund this, this doesn’t ﬁt what SBE funds and I can tell for sure it’s not going to ﬁt what engineering does.” She said “Don’t waste your time writing this proposal. It’s not for CAREER,” basically. I was upset because I didn’t know, you know, what can I do? They told us for tenure, we don’t expect to get a CAREER award, but we expect you to apply for them. I was feeling this urgency that I had to submit one but had no idea how or where. SUPERNATURAL AID: LEARNING ABOUT A CAREER AWARD IN ENGINEERING EDUCATION Just again by luck, Rich Felder was in the oﬃce [of ] a colleague of mine. He was in Glenn Ellis’ oﬃce. I was just walking by, stopped in to talk to Glenn about something else, and Rich, he’s just a mentor to everybody, and he took an interest and he said, “How’s it going? What are you working on?” and just asked me how it’s going. I said, “Well, it’s not going so well, frankly, 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 13 because they told me I have to apply for this CAREER award.” Rich has this very famous resource called, “So You Want to Get a CAREER Award,” and it tells faculty how to write their CAREER grant. I was like, “I’ve been told by NSF that my topic doesn’t ﬁt.” He said “Well, you know you can apply in engineering education.” And I said “No, I didn’t know that.” This was in 2004, and Rich said “Well, you know, they’re giving CAREER awards in engineering education now.” And, so I wouldn’t have known that if he hadn’t been there. I had two weeks to write the thing. I wrote it. I submitted it. It wasn’t the best grant proposal ever written but they funded it. It was probably a risk for Sue Kemnitzer to do it, but I suddenly had a ﬁve-year funded research program that would enable me to explore what it would mean to do bell hooks-like pedagogies in engineering education. I had used the word liberative to describe these pedagogies because bell hooks did and that turned out to be really interesting. I wasn’t quite aware of what that would mean, and it was an interesting move, because apparently that’s not a commonly used term. I used it because I wanted to group together various kinds of critical pedagogies—feminist pedagogies, anti-racist pedagogies, pedagogies that are considering class. All of these are grouped together under some label, but probably the term ought to be critical pedagogies. All of that happened. That allowed me to do these little experiments. ROAD OF TRIALS: BECOMING COMFORTABLE WITH CRITIQUE IN THERMODYNAMICS The best thing was that grant allowed me to hire a colleague, and so I had this great half time, actually he was quarter time in the beginning, a Research Associate named Lionel Claris. I hired [Lionel] when he was a Master’s student in Education at Smith. He had been at Hampshire College before that and did his undergraduate degree on political philosophy, so he knew all of the social theory, and he had an education Master’s, and he was now teaching in the K-12 schools in Springﬁeld, Massachusetts. As we started talking, I was thinking about power relationships in the classroom and the fact that I could ask the students to share power, and they would do it. They would go through the motions of what I asked them to do. I want you to talk to each other more. They would do those things, but they never really seemed to internalize what that was for. Why that was happening? That [it] was about trying to change this fundamental set of assumptions that I knew stuﬀ that they didn’t know. That I had some position, the privilege in the classroom, and I was trying to challenge that and mess with that in some way. They didn’t understand that, so he was like “Well, why don’t you have them read something about that.” I started having them read this piece [that Lionel brought in] from Michel Foucault [1980] on truth and power in science. So, it’s speciﬁc to science, it lets them think about it in a very concrete way that they can access. It was just three pages. Even if they found it impenetrable, it was short. They would read it and we would unpack it. They took a whole day of class to just talk about that reading and what it meant for the syllabus. What it meant about who decided what 14 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING was in the thermodynamics class, who decided what was in their textbook, who decided what the discipline of thermodynamics constituted. This ended up being the most fruitful change, and I didn’t realize all of the ways it was going to be so important, because at the time I had this focus on pedagogy and I realized with this assignment that in order to change the pedagogy, to really change it, I had to change the curriculum to an extent, and I had to change it at least enough to insert this one reading. I realized that once I did that, then I had students reading the textbook critically and saying “Well, wait a minute.” The textbook that I picked was a textbook that had a lot of real-world examples, so [it was] trying to relate to students. There’s this whole unit when they taught the ﬁrst law of thermodynamics, they taught this piece about energy and exercise and diet, so they’d be like “You’re burning calories, you can do an energy balance on your calories in, calories out,” kind of thing. But some of the problems that [the book] had them do were problematic from a gender perspective and problematic from a women’s health or anybody’s health perspective. An example problem was like, “Jack and Jill go to Burger King and Jack orders a Whopper and a large fry and a large Coke, and Jill orders a Whopper Junior and a small fries and a Diet Coke. If Jill weighs this much and Jack weighs that much, how much do they have to exercise to work oﬀ their meal?” And Jill has to work way more because she’s smaller or whatever. You’re learning all these gendered ideas about exercise. Then you’ve got these other problems where someone diets and loses like 13 pounds in a week, and this one student of mine who was [an] eating disorder survivor wrote a piece. The student was a survivor of Anorexia and she had read this one problem that was about somebody losing 13 pounds in a week and she pointed out that that’s really unhealthy weight loss, and so that enabled us to, ﬁrst, we talked about it as a class, but then that turned into an assignment where I asked the students to pick some of the problems from that section, because a lot of them were really problematic on diﬀerent grounds, and just talk about them. They could do the problem and then critique what it is saying about health, exercise, whatever, and then write their own new version of that problem, or a wholly diﬀerent problem if they wanted to, that related to their interest in some other way. That was a really great opening, because the students became comfortable with critique. REFUSAL OF THE CALL: BECOMING A FEMINIST ACTIVIST And it led to a second thing where a student came up to me that same semester and said “You know, I read about this thing on the Internet and I don’t believe everything I read on the Internet so I just wanted to ask you, have you ever heard of this thing called the Montreal Massacre?” I had heard of the Montreal Massacre because I was a ﬁrst-year engineering student when [it] happened, and it left a big impression on me, because it was a critical moment where, for me, there was a microaggression associated with the event, so I had read about the event, heard about it. There was a vigil that the women’s center on my campus was organizing about [the Montreal Massacre]. I had a chemistry exam that night, so I went to take the chemistry exam, and we 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 15 were all talking before the exam and this guy in front of me had turned around to see. We were talking and he said “Oh, what’s your major?” And I said “Oh, chemical engineering.” And he said “Oh, you’re an engineer. Where’s my gun? Ha ha ha ha.” Everybody is laughing. I’m just like did I hear him right? Right. I’m like did he really just say that? Then right then, it was like “Pencils up, take the test.” I spent a good amount of time going, “What else could he have said. What the hell?” I walked out of that exam and this vigil was still going on and so I went to the vigil and what was upsetting to me was there was [only] one engineering faculty member there at all, and he was there in his role as, they had these things at Princeton called Masters of residential colleges. There were four or ﬁve residential colleges where students live their ﬁrst two years and they had faculty that had an administrative role at the college. He was in that role, so he was there because he was involved in student aﬀairs. He wasn’t just there because he was a concerned engineering faculty member. …. He was the only representative of the entire engineering school. The Society of Women Engineers wasn’t there. Nothing. It was all about the Women’s Center. That radicalized me in undergrad, and it was a big moment for me because it is pretty much directly how I became a feminist activist. The head of the Women Center found me at that event because I said something [like], “I’m an engineer, this shit just happened to me.” She approached me after and said, “You should really come to the Women’s Center.” And so that started my engagement with the Women’s Center at Princeton. Anyway, [back to the conversation with the Smith student] the Montreal Massacre, I was like “Yes, I have heard of this thing.” She’s like “Well, how come we’re at the ﬁrst women’s college engineering program. Like why are we not learning about this event? This is important.” Anyway, I said “Oh yeah, sure.” STORIES FROM MY CLASS: THE MONTREAL MASSACRE AS A CASE STUDY I went in the literature, there was a women’s studies class that used a case study, like a memorial to the women from the Montreal Massacre as a way to talk about violence against women. I read [the case study], it was in Feminist Teacher, it’s a journal, and so I picked up that journal, read her lesson plan that involved doing a memorial to the women [by] saying their names, and then talk about violence against women. I picked up some important pieces from that, like not talking about the shooter being an essential thing. You don’t want to give airtime to that because then you end up in this criminology conversation that you don’t want to be having. I took the basic structure and some tips from that and then found a bunch of videos from the Canadian broadcasting company that just had the basics of what happened that night and a really poignant survivor retrospective. Because one of the things, the guy literally yelled [was], “You’re all women who are going to be engineers. You’re all a bunch of fucking feminists. I hate feminists.” Right when he shot them. There was a woman who said “No, we’re not feminists. We’re just trying to get an education.” She’s pleading with him not to kill them and she was in the original group of ... There’s this classroom of about 60 people, and about 50 of them are 16 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING men, and he orders the men out of the room and there’s maybe 10 women left, and he opens ﬁre on them. Most of those women died. She was shot but survived. They had an interview with her ﬁve years later where she’s working as an engineer. The woman that’s interviewing her is this famous feminist journalist. [The shooter’s] suicide note, had this list of women that he wanted to kill that day, but he couldn’t access those women. Her name, this journalist’s name is on that list. They’re having this conversation and [the journalist] goes, “What does he represent to you?” And [the survivor] said “He’s just a poor guy.” She said, “That’s all.” She said “Yeah. Yeah. He’s just a poor guy.” The journalist says “Well, what did you represent to him?” She says “You.” She’s like “Yeah. You know, like you.” And then she starts naming these other Canadian feminists. You, so and so, so and so, but I was easier to take, and then she goes “Well, maybe what we were doing is the same as what you all were ﬁghting for.” She’s like thinking out loud about, like, “Is being a woman in engineering a feminist act?” She’s thinking through this out loud to herself. It’s this incredible moment. It’s like a ﬁve-minute clip. I played the clip. I’m like “Okay, so what do you think about this?” You get all these diﬀerent perspectives about people’s comfort or lack of comfort with the idea of feminism and they talk about that, and they start talking about their internships. They start talking about intersectional ideas of feminism. They’re not just talking about their experiences as women [with] internships. They start talking about how race intersects with that, how class intersects with that, sexuality. They have this incredibly rich conversation that all I had to do was spend maybe 15 minutes [at the] beginning of the class presenting this incident to them, and they didn’t get hung up on the violence part of it. They didn’t talk about murder. They immediately got the relationship and just started talking about the stuﬀ. I think it helped that I was in a liberal arts environment because I think they had more tools to talk about this stuﬀ than they might have elsewhere, and this was true of the Foucault reading as well, that they all had heard of Foucault. None of them had read him except one or two that took a sociology class or something. Most of them, they knew their roommates were reading him. They were like “Oh, yeah, I know what this is.” There were people they could talk to in their dorms about it. Now they have this opening for conversation outside of class that gave them, I think, a lot of good common ground with other folks to talk about everything and what it means for them to be an engineer and put together their identity with what other people are doing. That’s all [a] big aside, those are the kinds of things I was able to do in my classroom that were really a departure from what, at least at that time, anybody else was doing to my knowledge in their classes. This did empower them to raise questions in other classes. They would come back to me and tell me stories about “Well, so and so teaches really traditionally and I asked him about it.” They did learn to push a little harder on some of the other faculty. In the early years of engineering at Smith, I think the other faculty were pretty receptive to that. Everybody was in 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 17 an experimental place. Everybody was willing to play around with stuﬀ. “Yeah, I’ll take your suggestion. Let’s shape the assignment this way, whatever, whatever.” ROAD OF TRIALS: PUSHBACK FROM STUDENTS AND COLLEAGUES As time went on and people got more and more busy with other stuﬀ and less willing or less rewarded for doing stuﬀ with their teaching—whatever it was, they became less interested in that conversation. There was a real shift from this kind of open place to a more like, well, “This isn’t how I teach” kind of thing. “This isn’t how engineering is.” There was this other pushback that happened where some of the time and in the later years I started to get more and more pushback from the students that what we were doing in that class wasn’t engineering...when I asked them to do the Montreal Massacre exercise, when I asked them to think about ethics. The most shocking thing occurred the very last time I taught that class at Smith, [which] was the fall of 2012. [The students] entered a National Academy of Engineering [NAE] competition that was making engineering energy ethics videos. I had the whole class do it. The requirement wasn’t that they had to enter the competition, but they had to make the video in teams. That was a semester-long project, [which] was to make a video about some issue of energy ethics, you pick, totally open. They didn’t see how any of that related to thermodynamics. This was despite my spending a lot of time trying to address it explicitly and having those conversations about what [ethics has] to do with thermo. They all entered it. I explained to them what the NAE was, I didn’t assume that they knew that. They all entered it, and they won, four teams won awards from the National Academy of Engineering that year. It was a big deal. They won money. They got to go to a conference. They told the NAE that they didn’t think ethics belonged in a thermodynamics class, and then the NAE people got back to me, and they’re like “Do you know that they’re saying this?” And I’m like “Yeah, I know.” It had gotten to the point where there was more pushback. This is a really interesting possible result of the pedagogies I was using. One of my favorite examples of this happened pretty early on. It was right before Thanks- giving break and everybody is really stressed out. There’s a lot of stuﬀ due in all of the classes. She came in and I had handed back a couple diﬀerent assignments. I was asking them to do learning reﬂections, which were written, or ethics essays, which were written. And then they always had problem sets, which were shorter because I wanted them to spend less time on them to make room for the reﬂections. I had this theory, which I would explain to them. It was the rule of the nth problem, a law of diminishing returns. We have you do so many problems that there’s a learning curve and as you approach the nth problem, you don’t really learn as much when you do it because you already got it by that point. I want them to stop there and then spend their time doing something else. Anyway, I was handing back assignments, and this stu- dent got really mad and held up her essay and said, “This isn’t thermodynamics.” Then she held 18 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING up the problem set and said, “This is thermodynamics.” Or maybe she said engineering, I forget. This is engineering. This is thermodynamics, not this. It was a really poignant moment because that’s what I wanted them to do. I want them to be authoritative. I want them to feel like they can decide what belongs in the class, to the point where they’re telling me this doesn’t belong in this class. That’s a good thing. Though maybe the irony of it, I guess, is that they’re reasserting a traditional view of engineering in doing that I thought, “Well this is good, I want her to be able to do that.” It was a perfect setup because right after Thanksgiving—and I had the weekend to think about it—right after Thanksgiving, the next topic was co-generation. And they learned it, it’s in their textbook, and they’re learning how to analyze co-generation power plants. They had taken a tour of the Smith campus plant and we had a heating plant that did not generate any electricity. All it did was, they’d burn fuel oil and then use the steam to heat the whole campus. There had been a lot of talk [about] whether or not they wanted to retroﬁt that facility to generate electricity and feed some back to the grid. They hadn’t done it and there was a widespread belief on campus that they ought to do this and they should have done it yesterday. I was able to talk about it and the students said “Yeah, why don’t we have co-generation on this campus, that’s so stupid.” And I would say “Well, why do you think?” They’d say, “The [Board of ] Trustees.” So, OK, say I’m on the [Board of ] Trustees. What do you need to communicate to convince me? Suddenly they realized that this was about communication that you had to be able to articulate to someone who’s not an engineer, why co-generation was going to save money, why it was going to be more environmental, why it was going to be good PR, why it was the right thing to do. I was able to, the very next class, make the case again for why all of these things were engineering and were really important things for them to know in a thermodynamics class. I was able to continue to have the conversation with the class, and I liked having that tension because it was a productive tension. There’s a type of resistance going on that I was able to make sure that it stayed a learning moment, but then toward the later years, it stopped feeling that way because, I’m not sure. I think some of it was less direct, like the students weren’t coming to me directly and saying this in class. They were sort of going sideways, they were telling the NAE, not me, that kind of thing. It became harder to bring stuﬀ back for conversation. As I said, [I] just got, for whatever reason toward the end, I got more and more pushback. A student told me at one point that one of my colleagues, her advisor, told her that I just didn’t like thermodynamics; I didn’t like the material, so I taught other stuﬀ, because I didn’t like the technical stuﬀ, which wasn’t true at all. They said that and that became widespread belief among students so it’s hard to refute that one, it’s very political in some ways. ROAD OF TRIALS: REQUIRED SERVICE LEARNING IN THERMODYNAMICS One of the things that really didn’t go over well was the time I did a service learning or community-based learning project where all of [the students] had to go to Springﬁeld, Mas- 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 19 sachusetts. I thought it was a really cool project. It was about the energy density and energy cost of food, and so we were looking at, we were in a food desert in Springﬁeld. There was a women’s studies class that was looking at women’s role in organizing this urban farmer’s market, where it was a struggle to get the folks from the surrounding farms to drive the extra distance into Springﬁeld. They were ﬁlling this critical need for fresh vegetables because there was no grocery store in this neighborhood at all. There were a couple convenience stores, and you just couldn’t get fresh vegetables at these places for any reasonable price anyway, and so these women organized the farmer’s market there. My class was looking at doing an energy analysis, because there’s this fascinating study that these folks at the University of Washington did—this analysis where on a per calorie basis, vegetables like lettuce cost up to 100 times more per calorie than fats and oils or potato chips. There’s this whole explanation of hunger, about why it’s cheaper to buy fast food and junk food, and they just have a lot of interesting data. Taking that as the model, can we collect the local data for the farmer’s market and compare it to the convenience store that people could get to and then the nearest grocery store which you had to take a bus to, and sort of look at, okay, what are the energy costs of food in this community? There were some really interesting things that came out of [the energy analysis project] which were that there’s an assumption that farmer’s market vegetables are more expensive. That wasn’t always true and there were places where the vegetables were either cheaper or there were vegetables that they just couldn’t get elsewhere. There were a lot of Puerto Rican and other Caribbean families there. They were looking for particular kinds of greens, the farmer’s market had those, like to make callaloo. They couldn’t get that otherwise. There were a bunch of things the farmer’s market was able to provide, and then we presented the results to this larger group of folks, including food bank people, and some of the farmers, and the women that organized this farmer’s market. What was fascinating was the farmers started talking about the policies of the grocery stores in underselling them. Corn comes in season [and] the grocery stores will sell corn at a loss, just to bring people into the grocery store. They started talking about how [we can] counter that. Because the farmer’s market is in a food desert, it actually gave them an opportunity, like a market for their corn that they wouldn’t have otherwise. There were some really interesting pieces that wouldn’t have come out without the analysis that the students provided, but the students had to travel 25 minutes to go to the farmer’s market. At the end of the day, the students hated it. They hated it because it was required, I think. Most service learning classes are elective classes, where students sign up for it, knowing they’re signing up for it. I said “Okay. Clearly, I can’t keep doing that in this class because it’s pissing them oﬀ.” I couldn’t justify continuing to do that in a required course. I did service learning in my elective courses, but I didn’t do it in thermo anymore after that. 20 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING RETURN THRESHOLD: PROTESTING A NUCLEAR POWER PLANT The pedagogy that I was doing in the early 2000s led directly to my meeting a couple of people who are part of this network on engineering, social justice, and peace. Early on when I was presenting about my thermodynamics stuﬀ, I was in a session with the liberal education division at ASEE with an engineering professor named George Catalano at SUNY Binghamton. He was presenting on peace pedagogy, basically how to teach peace in engineering classes. I was talking about, I think that particular time I was talking about globalization and how to teach critical perspectives on global engineering. We were in the same session and we were like “You! I found a kindred spirit.” I invited him to my very ﬁrst kickoﬀ meeting for the critical pedagogy project, and then he invited me the next year to go to this engineering, social justice, and peace meeting. I was part of that network of folks and I began thinking more and more about community- based learning and after I did that community-based project with the food bank, I did a diﬀerent community-based project in my engineering ethics class, which was an elective on the ethics of nuclear power. It was during a critical point where the Vermont Yankee Nuclear Power Plant had just had its license extended by the Nuclear Regulatory Commission. Its life had been extended by 20 years, but there were serious problems with how the plant was being managed, and they had had a number of problems like a cooling tower collapsing. It was rotted wood and rusted bolts that caused that thing to collapse. It should never have happened. I think they were just totally deferring maintenance on that thing. There was a series of ridiculous things that happened. The state came to take an oﬃcial position of opposition to the nuclear power plant continuing to operate. They didn’t renew its public utilities license and said, “You can’t continue to operate in the state of Vermont.” Well, they challenged this and said “Well, if the Nuclear Regulatory Commission has approved us, we should be able to operate regardless of what the state says.” And that went through to federal court and they made a ruling that they could continue to operate. The state of Vermont actually lost that case, and so then on the day that the state’s license expired, there was a massive protest, over a thousand people in the street, and 138 people got arrested, including me. That fall the plant was still operating and the community was interested in continuing to take data. There had been little tritium leaks here and there. Stuﬀ leaking from this plant. People were like, “What’s happening when they release steam?” “What’s in the river?” “We know it’s really hot when they’re releasing steam into the river, but what happens downstream, how are ﬁsh being aﬀected?” A bunch of questions that were ripe for citizen science projects. My students started thinking about, okay, “What can we do as engineers to help support what the citizens want to do?” “What questions do they want to ask, how do we do this?” It was fascinating because the students were coming up against diﬀerences in what the nuclear industry was saying was valid data and what the citizens (some of whom also possessed expertise 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 21 in nuclear power) wanted to take as data. They had to confront these diﬀerent ways of knowing. What did they think was valid, and who do they believe and why? Lots of really critical thinking processes [were] going on and all in this context of citizen science, or as I would call it, citizen engineering. This is coming up against my own questions about, how do I as a citizen and an engineer oppose this nuclear power plant or get involved in other kinds of projects. My involvement in the engineering, social justice, and peace network led me [to] ask... where are the places that engineers ought to be acting? That was one way that I found that was very concrete and local to me that I could be out there as an engineer and say “Look, I’m a risk analyst. You know, I’m in risk assessment, risk communication. I know about nuclear power risk. You know, people talk about how low the risks of nuclear power are. And after Chernobyl and Fukushima, those numbers were re-calculated. Because they had been based on models, not on experience, but once you factor in all the diﬀerent accidents that have taken place, the probabilities go up from what the early nuclear reactor safety studies said.” It’s not to be alarmist or create undue concern, but the Vermont Yankee plant is a Fukushima clone. It has the same containment problems that the Fukushima plant has, and, no, there’s not likely to be a big earthquake, but there are hurricanes, there are ﬂoods, and a lot of the same questions apply when you start really looking at the risk and what the evacuation plans are, and so on and so forth. Long story short, I was involved in that and then I went to NSF and the plant closed by the way, they’re decommissioning it, which is good. RETURN THRESHOLD: CHALLENGING THE POWERS THAT BE I think the cultures in the diﬀerent places I’ve worked are more similar than they are diﬀer- ent in that there’s always a creative tension with traditionalists, however that manifests itself. There’s always people who think, “Well this is the way you have to do it.” There are unchal- lenged assumptions everywhere, and I’m sure they exist in my class as well. When you’re trying to do something diﬀerent, you’re always pushing against those and you have to push. That is the whole for me, that’s the deﬁnition of it. If you’re not pushing against those, you’re probably not being truly innovative. If you’re not getting resistance, you probably aren’t challenging the right things. You’re not being really challenging of the powers that be, if you’re not getting pushed back. That was true at Smith, and it is true at Virginia Tech. You want to be supported. You have to ﬁnd where your support is, so that you can continue to do that work and I think at Smith, I had that support from day one from the top down because we were doing this new engineering program. I think I didn’t have to build it because it was given to me at the beginning. Getting the CAREER award bolstered that support in a big way, so NSF was able to support that work in important ways so that the critics couldn’t descend until toward the end of my grant. 22 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING At Virginia Tech, there’s the same thing of well, we are funded to do this. Stephanie Adams had this huge grant, so sure, I can do it. We’re trying to be good citizens to this new roll out of the new general ed curriculum, with backing from the Provost. There are ways in which you go, and you ﬁnd your support where you can and then go with that. And yeah, if you’re doing it right, you’re going to hit some pushback. Then depending on who that’s from, you address it in diﬀerent ways, and if it’s from students, well, you want to morph and change and do things that are going to be responsive to their concerns like I did with the service learning thing. If it’s from the powers that be, well, [you’ve] got to really think about, how do you work with them going forward, if it’s [that] you’re not meeting this requirement or spending too much time here. Well, you always want to just continue to be creative, is the way that I think about it, so there’s a new constraint, well, you work creatively with, around, and through that. ROAD OF TRIALS: CREATIVE SOLUTIONS TO CONSTRAINING POLICIES One of the big constraints at Smith with doing the collaboration with the women’s studies faculty was that if you team-taught, you got half a course credit. We knew that team teaching was going to be twice the work for us because we’d have to somehow join women’s studies and engineering intellectually. What we decided to do instead was [say], “Look let’s each teach our separate classes, we’ll enroll them separately, but we’ll have them do joint meetings together, we’ll have them do this joint project together.” By doing that with a couple diﬀerent classes, we found a workaround that was successful. We didn’t directly challenge this constraint even though it is really prohibitive of collaborative work to say that team-teaching is half the credit. We found a way around it. It’s just that attitude of ﬁnding the creative solution to stuﬀ. You do want to always be in that give and take of pushing the boundary. APOTHEOSIS: PUSHING THE BOUNDARIES IN ANY CONTEXT I don’t want to downplay the importance of the institution because I do think I was able to do what I did at Smith in part because I was at Smith. I really do think that played a role. That said, I think there’s other ways I would have pushed the boundaries if I had been at a traditional engineering school from the beginning. It would have looked really diﬀerent but there is this, it does ultimately come from within the individual to do this creative work because it’s your class. You’re the one that’s generating the ideas that are going to push the boundaries. If I’m advising a new faculty member that’s going to one of these places, yeah, you want to go to the institution that’s going to let you do the work that you can do without getting in your way too much, but at the end of the day, every institution is going to get in your way somehow. It is about recognizing that and not seeing it in too black-and-white a way. I know a lot of junior faculty are like “Oh, I just have to get tenure. I’m going to just mind my own business, I’m going 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 23 to get tenure, then I’m going to do what I want.” But that never works. Look at all the senior people. How did that strategy work out for them? Clearly, this gets drummed out of you if you take that path. You always have to keep within you the sense that, “Well, okay, I’m going to push the boundaries.” Sure, you don’t want to do something that’s going to get you ﬁred but there’s so many things in between doing the one thing that’s going to be a bridge too far, and doing all these other things that are going to push boundaries and make people think and challenge the status quo, and maybe make real change as you go. Or maybe you do want to make that stand that gets you ﬁred. There might be reasons to do that. I would never rule that out, but I think most of the time that’s not going to happen. Many people fear that way more than it actually happens, so you do good work, you do what you love. Sometimes, changing institutions ends up being the best route. At Smith, I had a great cadre of folks that I could stir stuﬀ up with, despite the pushback. And, as I engaged more on a national level, I started thinking more about the bigger picture of what was I doing in the ﬁeld of engineering education, and how could I have an impact outside of my institution. As the Smith experiment wore on, people paid less and less attention to what was going on there, and kept saying “Well, you can do that because you’re at Smith. You’re a special case.” Doing something at Virginia Tech would obviously directly impact a large number of engineers right away and have more inﬂuence on the rest of the enterprise of engineering education. That made the move make a lot of sense. MASTER OF BOTH WORLDS AND FREEDOM TO LIVE: THE IMPORTANCE OF REFLECTION I think there’s something about the reﬂection of the faculty member that matters in this story. I had a lot of opportunity and still do have a lot of opportunity to talk with others about what I’m doing and why. Having Lionel at Smith and having my other colleagues at Smith too, both inside and outside of engineering, who were able to talk stuﬀ through with me and just be supportive and help troubleshoot and help creatively was essential. The process of reﬂection, of really taking the time at the end of the semester, and at Smith this was built into our ABET processes and I still think it’s a really worthwhile exercise, and it was built into our grant in NSF too with the science and engineering project. At the end of the term, you stop, and you say well, what worked, what didn’t, what’s the student feedback, what am I thinking. About how to do this better the next time, what are my goals, how do I think about how I’m going to push the envelope next, that keeps the spirit of innovation alive. You’re not just doing the same thing every year, good, that’s done. You’re actually taking the time to have a reﬂective practice about what you’re doing and say I need to change this [next] time, more of this, less of that, tweak this, try this new thing here, whatever. It’s a constant pro- cess. The thermodynamics class over 10 years became almost unrecognizable from the original 24 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING one, but I never changed more than one or two things a semester. I never completely overhauled the class. It was about asking just what am I capable of doing and doing well? If I’m going to create a new type of assignment, well, I’m going to do that and take something else out to put it in and just do that and not ... It’s just a sustainability thing. You don’t want to completely, yeah, you just don’t want to make yourself so distraught. I did that community-based learning thing with the food bank, and that’s basically the only thing I changed that semester, because it was a big deal to do that. It’s just recognizing that these things don’t happen trivially. They take a lot of thought. They take a lot of adjustment. They take a lot of troubleshooting. And small changes can be tremendously huge, like that Foucault change [that] led to all these other changes and all I did was add one assignment. I added one thing. Read these three pages, talk about it in class, write an essay about it. That led to a whole bunch of other stuﬀ, and so that’s being open to that too, and not predetermining. Well, I’m changing this, this, this, this, and this. No, I’m just changing this one thing, let’s see what happens. Letting that play out organically, it allows for students to shape the class. That’s part of it. ADDITIONAL RESOURCES American Society for Engineering Education (ASEE), annual conference. https://www.asee .org/conferences-and-events/conferences/ 12 Felder, R. (2005). Resources in science and engineering education,. http://www4.ncsu.edu/u nity/lockers/users/f/felder/public/ Felder, R. (2002). So you want to win a CAREER award. Chemical Engineering Education, 36(1), pp. 32–33. http://www4.ncsu.edu/unity/lockers/users/f/felder/public/Columns /Career-Award.html Foucault, M. (1980). Truth and power, Alessandro Fontana and Pasquale Pasquino, interview- ers. In Power/Knowledge: Selected Interviews and Other Writings 1972–1977, C. Gordon, Ed., pp. 131–133, New York, Pantheons. 13 Hooks, B. (1994). Teaching to Transgress: Education as the Practice of Freedom, New York, Rout- ledge. Riley, D. (2003). Employing liberative pedagogies in engineering education. Journal of Women and Minorities in Science and Engineering, 9(2). DOI: 10.1615/jwomenminor- scieneng.v9.i2.20. 2. DEVELOPING A LIBERATIVE PEDAGOGY IN ENGINEERING 25 Riley, D. and Claris, L. (2006). Power/knowledge: Using Foucault to promote critical under- standings of content and pedagogy in engineering thermodynamics. Proc. of the ASEE Annual Conference, Chicago. https://peer.asee.org/155 C H A P T E R 3 27 Experiencing Vulnerability and Empowerment in Teaching Sara Atwood Narrative constructed by Brooke Coley Whereas my walking around and coaching them and challenging them and saying, “Now, how does that work?” they didn’t perceive that [as teaching]. So, I did get comments, es- pecially from ﬁrst-years, of, “She didn’t teach us anything. I taught myself.” Well, yeah. I coached you to learn how to learn. That’s the point. Sara Atwood is an Associate Professor and Chair of Engineering and Physics at Eliza- bethtown College with specialization in mechanical and biomedical engineering. CALL TO ADVENTURE: FROM CHILDHOOD TO UNDERGRADUATE, BECOMING AN EDUCATOR FIRST I think when—you know, hindsight’s 20-20, but when I look back at it, I think that I’m kind of an educator ﬁrst and an engineer second in a lot of ways. Growing up, I never played with dolls, I actually lectured to my stuﬀed animals and had a little chalkboard easel. My mom was a teacher, second grade, and a lot of people in my family were K-12 educators. So, I grew up around that and always enjoyed school, obviously. In high school, I tutored math for some extra money, and word spread through teachers. I was always really good at math and science, although my favorite class in high school was actually English and Literature. But people told me, “Oh, you’re good at math and science, maybe you should consider engineering.” I went to Dartmouth for undergrad, and part of why I liked that institution [were the variety of options]. I didn’t look at any institutions that were engineering-speciﬁc, so I wasn’t really thinking about my major or engineering going into college, necessarily. It was kind of in the back of my mind, but I wasn’t going for that. Then, at Dartmouth—a liberal arts school, you didn’t declare a major until [your] second year, and at that point, enough people had said, “You’re good at math and science, consider engineering,” that I took the introductory engineering courses, and I really liked that and really 28 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT found a home. At Dartmouth, it was a very close—and it’s grown a lot now—so at the time that I went, we had maybe 30 students in a cohort, so it was pretty small. I found that it was comfortable, [a] home environment and that’s, I think, a big reason why I went in that direction. I feel like, looking back, maybe I could have gone in diﬀerent directions. But, I liked that. [I] liked the impact that engineering has on the world. And [I] had some professors that were very good mentors to me. And so there at Dartmouth, I really got that experience of more of the teaching-focused, rather than research-focused. Now, I think it’s transitioning a little bit more away from that, which I think is sad. But at the time, the faculty were really teachers ﬁrst. It was still more lecture-based, but I feel like they were all very aware of doing a good job of educating; it wasn’t secondary to them, it was their primary thing. So, I think that they were starting to do [active learning], we would certainly work through a lot of examples and things like that, it wasn’t necessarily what I would call active learning now with small group examples. But, it was not just like you only saw the professor’s back the entire lecture, and you were just scribbling notes the whole time. CALL TO ADVENTURE AND SUPERNATURAL AID: EXPERIENCES AS AN UNDERGRADUATE TA [At Dartmouth] I had a couple of professors who encouraged me, “Hey, you would be a really good professor.” And I did some TAing [teaching assisting] there, so I think that might have ac- tually been formative in my ease with embracing active learning, because I ran problem sessions each week. So maybe more like a grad student would do at an institution with more grad stu- dents. And in those problem sessions, it was really just small group, walking around [to] people, explaining how to do problems, basically doing that more small-group, problem-solving, active learning model in my problem sessions. And I did grading for them, and had a couple of faculty that kind of brought me under their wing, putting together exams and things like that. So, I got some mentorship there. So then when I was looking for grad school, I was really speciﬁcally looking to go to grad school to become an educator. And I didn’t know anything about engineering education pro- grams at that time. I graduated Dartmouth undergrad in 2003, then I stayed for my Master’s—so [I] graduated in 2005, then was looking for Ph.D. programs around that time. I think at that time there might have only been Purdue and Virginia Tech, [engineering education] was not a big thing at all and I feel like those were even pretty new, is my sense. I just hadn’t heard of that, I hadn’t heard of the [American Society for Engineering Education] (ASEE). None of that. So, I was looking speciﬁcally at engineering programs in mechanical engineering. Dartmouth was a general engineering degree undergrad, so I had [a] broad base. So, I thought, “Okay, I’m going to apply to a couple places and be selective, or I’ll just go and be an engineer, or even teach high school physics or math, or something like that if I don’t get into these grad schools.” I applied to UT Austin because I’m originally from Texas, 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT 29 and then Berkeley, because for some reason, I had in my head I wanted to try out the west coast, and I had a professor at Dartmouth who had done a sabbatical there and knew an advisor that he thought would be a really good mentor to me and was doing work I was interested in. CALL TO ADVENTURE: EXPERIENCING FACULTY WHO PRIORITIZE RESEARCH FIRST I ended up going to Berkeley, and that was a huge shock because the diﬀerence in teaching and student focus from Dartmouth to Berkeley was enormous. My ﬁrst semester I was like, “Oh my gosh these are the worst teachers I’ve ever had in my life.” And in fact, I feel like there was almost a pride in that [teaching] wasn’t their thing. I’ve known some people who have gone to R1 type places and they’ve been told that, “If your teaching evaluations are high, you’re not doing things right. That’s not where you should be focusing your time and eﬀort.” So [I] was just thrown into the deep end of the traditional lecture style. No working examples. You know, the professor’s back, working on the boards the whole time. They ﬁnish the one [board], they scroll it up, just keep going on to the next one. And I had a really rough time my ﬁrst semester, transitioning to that. It was very diﬃcult going into professors’ oﬃce hours and they wouldn’t even be there at their posted oﬃce hours. And I was like, “What is this?” At Dartmouth, it was an open-door policy. [At Berkeley] you didn’t know where they were, you couldn’t track them down. I had a really hard time. And honestly, the problem sessions with TAs also were like recitation sessions and not that great either because most of the TAs were not that interested in teaching, either. I think it was a little bit of that rude awakening into that style. It made me, ﬁrst of all, not want to work at an R1 (very high research activity university) and secondly, really kind of reject that more traditional lecture format, because that was such a rude awakening and it took me a while to adjust to that. SUPERNATURAL AID: FINDING MY HOME Then when I was at Berkeley for a longer time, I did some TA-ing [Teaching Assisting] and had courses with a few professors who cared about teaching. I luckily had a mentor (Dr. Lisa Pruitt) who did focus a lot on education, and she sent me to ASEE, even though I didn’t have any conference presentation, just to expose me to it because I wanted to go in that direction. I TA’d for her… several times. And through that, I sort of really enjoyed the time that I spent on that, more than on my research. So that was kind of a big clue for me as to what I should do in the future. And, actually, right after I passed my quals [qualifying exams] they had a professor that went on medical leave, and another was going on Sabbatical or something. [As a result] I got to teach a course at Berkeley all on my own. I was the primary instructor. And I used more of what I had learned at Dartmouth. It was a 115-person class, so it was not the style where you could really do small group/walk around to very easily, and I didn’t have, at that time, any exposure for how to do active learning in a larger setting, because I had never 30 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT instructed in a larger setting. But I did try to do some aspects of it in terms of, my lectures were a lot more on solving example problems, and stopping [for questions]. I didn’t know that it was called active learning, then, and I didn’t know what the right way to do it was, but stopping and saying, “Okay, now you do the next two steps of this derivation to try to get down to where we only have this and this left,” and throwing it back to them a bit. And at the end of that, I got the highest teaching evaluations in the department, and my comments were things like, “Wow, she works examples!” And, “This is like having a discussion section every lecture, it’s great! I’m learning so much!” And so that was also pretty formative to me. It was at the end of my time at Berkeley that I started going to the ASEE sessions and conferences. And I was like, “Oh, this is home, this is heaven, this is amazing!” Every session [I wanted to attend]. So that was huge for me. FIRST THRESHOLD: FINDING THE RIGHT COLLEGE AND CONNECTING WITH THE STUDENTS Then I knew, when I was looking at schools [after my Ph.D.], I wanted a teaching focus. I was looking for a liberal arts college, an accredited program, small residential college. There are not many of those, actually. Just kind of a handful. I ended up here at Elizabethtown. And right from the beginning, I was doing a lot more of [the student centered, active learning]. I had been successful doing what I did at Berkeley in terms of just working through more example problems and throwing those [out] to the students in small chunks or whatever. [At Elizabethtown] it was much smaller classes, so that was a little more natural. And I think another thing that really helped was I was closer to my students’ age, being a newly graduated grad student. And my advisor had told me that, back at Berkeley, she said, “The years that you are seeming just like an older sister, or someone who could be kind of in their friend group, embrace that. Kind of use that to your advantage.” I think that also made it natural to kind of walk around and work on problems with them, and be a little more on their level because we were so much closer in age. And that has changed a little bit over the years, and that’s a little bit hard sometimes to deal with, that I’m just getting further away from them socially, so that sometimes makes that gap a little bit harder to close. SUPERNATURAL AID: LEARNING FROM OTHERS My advisor had done NETI [National Eﬀective Teaching Institute] with Rich Felder and Re- becca Brent. And she had done that right when I was graduating. I knew of it, and I knew to look out for it, even though our college, Elizabethtown College was not on their list, because we were a newer program and just not all hooked into everything or well known. I knew my ﬁrst year [at Elizabethtown] to look out for the NETI invitation, and I think I reached out to Rich Felder and made sure that my dean got the invite. And so, myself and another colleague who started at the same time went and did NETI after our ﬁrst year. And I think that it was 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT 31 actually better after our ﬁrst year, rather than before you start, because you have a year to sort of see what’s natural, see what works, see where you need to pay attention to like, “Oh, that’s how I could be tweaking that a little bit.” Whereas I think if you get it before you ever do the classroom all yourself, you don’t quite know what the more important parts are, the subtler parts, or where you know you have a little bit of trouble and you need to make sure and pay attention to that. But [NETI] was huge. That was very, very formative in my embracing of active learning. But I do think everything that had come before that had sort of primed me to want to do [active learning, and NETI] deﬁnitely reﬁned that technique. Then my second year [at Elizabethtown], we hired another young faculty, and we then sent her to NETI right after her ﬁrst year because it had been so great. And she came back and she actually embraced the gap notes piece (see Felder and Brent [2015] for more details about gap notes), which I had never done before just because I was doing all new preps. [With gap notes,] what I’m talking about there is basically having a note packet that has blank spaces for where the students ﬁll in, but it provides kind of a structure, a scaﬀolding, and then there are certain things the students ﬁll in. So, I tend to just type out, if it’s a deﬁnition or something, I don’t want them wasting their time writing out a sentence. Or what’s been really helpful to me, I have the objectives right up top, the ﬁrst page of the gap notes, and then the last page I just have a blank gray box that says “summary.” So, at the end of each notes packet, we do a summary and they write it there. And then, a lot of what [the notes] consist of are pictures and problem set-ups. So, instead of them writing down all the given information and the ﬁgure, just giving them that information and then spending that time working on the problem. That’s sort of what the gap notes are. At the time that [my colleague] did it—she did it in the fall after she came back and really liked it—and had a lot of success, and I was like, “Ooh, I love this. And now, I’m actually teaching things for the second time, and I feel like I can handle doing that.” So, then I really embraced doing gap notes, and that has been really formative in being able to [implement active learning]. BELLY OF THE WHALE: NOT ENOUGH TIME DURING THE LECTURE One of my challenges, which I think is probably everyone’s challenge, is it always seems like there’s not enough time during the lecture. So, you’re always kind of rushing to get through what you want to and I am a very structured person—disciplined, very ordered and structured. I deﬁnitely have an approach of, “I want to get through this amount of stuﬀ on this day because we have weekly homework, and I already have my quizzes set, my exams set, and everything like that.” The use of gap notes was really big to me, because it does take more time to let the students work on problems, walk around and talk to them, [and] let them struggle in some places before you then pull them back together and say, “Okay, you tried this out. I see some of you were having trouble with this stuﬀ. Here’s how to do that.” That’s always a challenge. 32 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT So, I think before NETI, I was doing a lot of group problem solving, but not in small chunks. It was more, give the class an entire problem and have them work it through, and walk around and talk to them and then come back up to the board and go through it. But, I remember this one student particularly who was very talented, and he always had a paperback book—he liked Clive Cussler. He would get done with the problem so quickly and then he would just open his book. He wasn’t being disrespectful, he just [grasped the concepts quickly]. And that was one of the things when I went to NETI that I mentioned that I need to look out for. “How does this work with the timing?” Because at Berkeley and at Dartmouth students were more at the same level, and so people would tend to ﬁnish more in the same amount of time. We have a wide range of students’ preparation and backgrounds here at Etown, because we don’t have a pre-selection program. I was having a lot of trouble with some students would ﬁnish a problem really quickly, some would take a long time, and how do I handle that? With active learning after NETI, one thing the gap notes enabled [was it] put everyone on at least an even playing ﬁeld to start, because some people just take a really long time to write down the problem and focus and get on it. Some students have learning challenges around writing and processing that make them take longer. And two is that the idea of saying, “Okay now just do this step. Okay let’s come back together and go over that. Now do this next step and let’s come back together. Okay now ﬁnish it up and I’ll walk around and help everybody with it.” That was kind of a big change. Now it’s more back and forth, whereas before it was more like me lecturing a chunk, and then problem solving a chunk, but in a bigger chunk. Now, I guess the engagement is more dispersed. Like me, them, me, them. So that’s become kind of my steady state of where I am now. I’ve done a little bit of dipping my toe into a ﬂipped classroom kind of thing, so I have recorded some videos. And I try to keep those, I know the literature says about seven minutes is about max for those. I’ll try to have two videos each week, which is about a packet or a chapter or whatever, and post those and then just do a 5-minute summary of that, the most important equations, and get right into problem solving. And this is something that I kind of swing the pendulum on, too. Because I’ve had students that have responded that they actually like some lecture, and I think one of my strengths is being able to explain things fairly clearly and logically and in a neat, ordered way. So, I’ve had students that say, “We actually like it when you lecture maybe half an hour and then go to the problem solving,” because also a ﬂipped classroom is depending on them to watch the video, which you can’t always… And, I think it depends on your style as well. I go a little bit back and forth between, I guess in my lower-level class I do less lecture, more problem-solving because I feel like the concepts are a little easier to grasp quickly. In my upper-level class, I tend to do a little more lecture with problem solving sprinkled in. That’s something that I still sort of go back and forth on as well. How much ﬂipping to do and how much outside of class time are students really going to spend with that? ROAD OF TRIALS: THEORY VS. SOLVING PROBLEMS 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT 33 One of the things that I still struggle with a bit in terms of active learning—I think that it’s best suited with working problems. I swing back and forth like a pendulum semester to semester on the importance of the derivation versus the application in working problems. And so I try to use active learning and say, “Okay, for the next step of this derivation we want to reduce this down to one term, or something,” and then try to have them do that for the next 30 seconds or so, and then come in with it and engage them in the derivation. But, there’s just a little bit of a debate in my mind about how much [undergraduates] get out of a derivation. I do want them to see where things come from, so it’s not just some black box. But, a lot of our engineers also—now we’re getting a steady state where we graduate probably 30, 35 a year and two of those will go to grad school—so most of them go out and become practicing engineers. They may be more like construction management, or project managers or things like that. I just kind of struggle with the balance between the theory and the derivation versus the practical and applied problem- solving piece. And active learning, I think, is a little better suited for the problem-solving piece, at least the way that I tend to use it. So that’s something that, potentially if I did a redo of NETI, I’d be paying a little more attention to that balance. ROAD OF TRIALS: JUST-IN-TIME VS. ESTABLISHED PREPARATION [There have deﬁnitely been some trade-oﬀs to this journey]. My ﬁrst three years was basically all new preps all of the time. Because we’re a general engineering program—and when I ﬁrst got here we were smaller—so my ﬁrst three or so years, we were teaching classes every other year, a lot of them, like the upper level ones, so each time was new. And, of those courses I was teaching, only one was in my Ph.D. area. So, I was teaching something that I hadn’t looked at since undergrad and a Physics 3 course with optics that I had never done in my life. I was doing new labs that I had never done before. So that was like drinking out of a ﬁre hose. It’s hard to even say what that was like because it was just so much prep all of the time. I was just a lecture ahead of the students, essentially. But, in some ways that was better, because now I feel like it’s a little hard to get motivated to go back and rework the example problems that I’ve already got prepped. It seems like you shouldn’t be spending your time on regenerating new example problems all of the time. I always do new quiz problems and switch out a couple of homework problems. But, when it was just-in-time, and I was learning it almost alongside them, I feel like I was better in some ways because it was a little fresher and I was getting a better fresh perspective on trying to understand the material. And so, there’s been some tradeoﬀs. I’m teaching things now for the third or fourth time. Things are more settled, so I spend a lot less time on prep and getting to where I’m barely making any changes to [my gap notes]. I’m hoping that I can turn them into a reader. And so that part is nice, but sometimes I feel a little bit disconnected because I’m at the point where now I can kind 34 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT of go in on Monday and I haven’t really looked at the stuﬀ for a year. And I’m familiar enough with it. But then sometimes, it’s just a little diﬀerent than when you’re learning it alongside with them two days before. So that’s been a bit of a tradeoﬀ, actually. I feel like I’ve had enough years now that I’ve been able to chip away at it. I’ve been able to sort of add something that I wanted to do every year. But I certainly, even though I wanted to do those things, I knew that I couldn’t do them all at once. Is there anything still left? I mean the gap notes have taken me several years to get the way that I want them. I’d like to make more videos. I wish that I could see it more from the students’ perspective again. When I was just learning material for a class, it made me closer to their experience. And so that’s one thing that I really miss, and I don’t know exactly how to get that back. I taught a class I hadn’t taught since my very ﬁrst year, and I changed the format to being mastery-based. It was really energizing to get that new perspective back again, but it was a lot of time. I’m looking forward to tackling that course again next year. I also think doing more open-ended work would capture that fun again. When I ﬁrst started, homework solutions were not out there in public. They just weren’t accessible like they are now. Students [would] learn a lot doing the problems and would come in and work with me and we would learn a lot through that process. And now, the solution manuals are so readily available online, that only a few students get the same learning out of it. That may be the thing that I would do [to improve as a teacher is] ﬁgure out open-ended, interesting, design-analysis problems to do for problem sets, that help them meet the learning objectives, but are really interesting, higher- level struggles for them. I think I might still keep example problems and quizzes simple. But, I feel like the homework sets—in a way—the students who use them correctly, learn a lot from them. But, now with solutions readily available they’re set up in a way that students don’t have to use them correctly. I’ve tried doing a couple of “Epic Finales” where students in groups work through an open-ended problem in place of a traditional ﬁnal exam. It’s gone really well. ROAD OF TRIALS: STUDENTS WITH LEARNING DISABILITIES I just read “Tomorrow’s Professor,” [and] it was talking about one of the pitfalls of active learning being those with learning disabilities. It was very interesting. We actually do have a number of students, and I think everyone has increasing students with learning disabilities, partly because of the higher K-12 education system, and our cultural expectation that everyone goes to college. So, [Tomorrow’s Professor] mentions though—that these students that have visual or auditory processing issues, or slow processing, or dyslexia—that active learning might not be good for them because it might take a long time for them to process it. So, then, they kind of miss out on the problem-solving piece and it makes them feel worse because their peers are able to do it and they really have no idea what that 15-minute lecture that you just gave was on because they have not gotten time to process it. 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT 35 Actually, the email was kind of a call for more studies into how active learning might be able to be tweaked for those with learning disabilities or processing speed diﬃculties or things like that. And that really struck me because we do have a number of those students, and I do wonder if maybe those are some of the ones who are resistant or who don’t even make it past the ﬁrst year of the program because of that way of teaching. I can see [how] psychologically they [could] just feel like, “This isn’t for me. I don’t get it. Everybody else around me gets it, and I have no idea what she’s talking about.” One thing that occurs to me, actually, is [with] the little videos that I do. They are posted and can be accessed any time in the semester on the learning management system. That might be one thing that could help a lot. And I actually have a student who’s struggling with English, and that occurred to me, too. “Oh, yeah, the international students, too, who have a hard time grasping the English. They don’t have time to translate or really understand what’s been said, and now I’m asking them to do something with it like work a problem.” So what I’ve been doing with a student who’s been having trouble with English is I actually send him the gap notes a few days ahead so that he has a few days to look at them, to run them through his translation, to look up any terms that he’s not familiar with and try to translate it so that he comes into class [better prepared]. That might be a way that students with learning disabilities could come into class more prepared to see it for a second time or a third time and then be able to jump in on the working of a problem better. Especially if those [videos] are closed-captioned or whatever. I can imagine where yeah, that could be some tweaks [to the student-centered teaching] that could have a bit impact. BELLY OF THE WHALE: A PARTICULARLY CHALLENGING SEMESTER So many things have changed throughout the years, I guess. I did the Intro to Engineering class for about four years. One semester I had only Intro to Engineering course, and it was just 70 ﬁrst-years (we expected 50)—all ﬁrst-years, all of the time—and it was miserable. That was probably my darkest semester because I just did not have much joy in it. And I actually did a workshop with a STEM-UP PA group for academic women in STEM that was funded by the National Science Foundation (NSF) through the Advance Grant. And I remember I was doing this workshop and the facilitator said something like, “What do you take joy in in your job?” And I remember writing down, “encouraging students,” and I realized that that semester I was just not doing that, because I had so many discipline problems and [was] on the phone with Learning Services and ﬁrst-year advisors all the time. And so, for the last about three weeks of that semester after that workshop, I made a point to really reach out and encourage students and write nice emails to them and notes and things. And that kind of got some of the joy back, I guess. But it had just been, like, stamped out of me with that semester. That was a pretty miserable semester, to be honest. I never want to teach all ﬁrst semester students again nor just one class with so many sections. I enjoy the variety of topics and student 36 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT populations. After that the department faculty started sharing the Intro class, which I think was more appropriate—team teaching the ﬁrst-years. SUPERNATURAL AID AND MEETING WITH THE ALL KNOWER: A COMMUNITY OF ACADEMIC STEM WOMEN One of the big supports was the STEM-Up PA group, funded by an advance grant. There was one semester that I did the STEM-UP PA Oasis program. Rutgers [University] has an Oasis program, and it’s like an Objective Analysis of Self and Institution Seminar. And so, the STEM- Up program of Central PA teaching-focused group adapted that. And now I think they call it their leadership development program. It was one semester, and it was four meetings during that semester, Friday nights or Sat- urdays, for about ﬁve hours, so it was pretty intensive. All women, maybe about 25, 30 women. And they also formed peer groups of four women and you also had to meet in person and get din- ner or something with those peer groups in between the other sessions. So it was eight sessions during a semester, which was basically every other week. So that was a lot of time commitment, but a lot of support. And a lot of that support, it wasn’t necessarily the content of the workshops, it was just hearing other women faculty suﬀering through some of the same problems and being like, “Oh, it’s not just me, I’m not alone.” I certainly have experienced it where you return things twice as fast as a male colleague and students have this perception that, “Ugh, she’s still grading those?” And you’re like, “What about him?” And they’re like, “We love him!” Just sharing some of those experiences was key, I think, to getting me through that. We did a negotiation seminar. It gave me a little bit more empowerment to feel like, okay, next semester, if they try to assign me all of the ﬁrst-years, I’m going to say, “No, that doesn’t work for me. Someone else needs to take some of this on.” And not just be like, “Sure! I’ll do all of the ﬁrst-years.” And that course content is so much writing and soft skills. The department put me with something that was non-technical, and I didn’t appreciate that because it made me look like a kindergarten teacher that was teaching the soft skills, not like someone who was teaching the upper level technical stuﬀ. Historically the class had been taught by the one other female lecturer in the department. After me we started team-teaching with male faculty as well. MASTER OF BOTH WORLDS AND FREEDOM TO LIVE: A BALANCE OF VULNERABILITY AND EMPOWERMENT Do I feel like I’m better at teaching now? I feel like my focus has changed a little bit. So that’s the other thing about my trajectory. My ﬁrst few years, the department, the college, the emphasis was really on teaching, so I was really focusing on that. The last few years, then, going up for tenure, I was sort of shifting because my teaching evaluations were very good and very solid. I was willing to accept a little bit of a dip, and some vulnerability in how well I thought I was doing in teaching to get some papers written and get those out the door for tenure. And now, 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT 37 I’m actually Chair of the department. So now some of my research is really taking oﬀ and I’ve got that going on, and I’ve got Chair. So, I’m also right now willing to accept a little bit of a lower standard in teaching. Return of teaching evaluations has really evolved, too. In my ﬁrst years of teaching, I used to get just so devastated, even though they were really good. But I would get so devastated when there was any sort of negative comment on something. I remember our Dean of Faculty saying, “Well, for tenure, we just want to see that you’re reacting to those [evaluations] and you’re taking them seriously.” And I remember joking to my friend, I was like, “Yeah, let me send you the empty bottle of wine and empty chocolate bar wrapper, that shows you that I’m taking them seriously.” My husband was always like, “Oh, did you get your evaluations today?” He knew it would be a couple of rough days. And now, I get them and I read them and I guess I feel a little more evened out about the response to my teaching, and can use them more formatively without negative emotion. I keep a list of positive student comments on my bulletin board for those occasional bad days. One evolution is in prep work, when I walk in and I feel 80% prepared, I’m okay with, “Well, I’ll wing it on the other 20%,” that’s a little bit of a diﬀerence. And I think there’s also that realization that the 80-20 rule or whatever, you know, my ﬁrst few years—I guess I was feeling sort of vulnerable, too, because I was new and the students didn’t really know me yet, and I was young, and I got mistaken for a student all the time, and being a woman also walking into the classroom and not having much authority. That’s the positive about getting older. I’m like, “Well, I’m going to get gray hair, but I’ll get some authority, too.” But, yes, I think, just personally, knowing that I didn’t know the material that well, I would work extra hard to make sure that I was prepared. I think that I allowed myself to be vulnerable, too, and say, “I’m not sure. Let me get back to you.” And the students were pretty good about that. But then, over the years, I felt a little less vulnerable in terms of how good of a teacher I am, or whatever, and so have allowed that whole, “It doesn’t have to be perfect. Good enough is good enough.” But, it’s really satisfying because I still have days where I walk in and I just absolutely kill it on a lecture, and it just goes really well for whatever reason. And I have to tell the students, “It’s actually time to leave now, we [have to] go.” So those are deﬁnitely good days that I still appreciate, but I guess I don’t get upset anymore when days aren’t like that. I will say that one of the trade-oﬀs, I think, is some students really like the active learning. But, one thing that strikes me, is that some students are pretty resistant to it. And particularly, when they’re ﬁrst years, you get a lot of the comments of, “They didn’t teach us anything,” because I think that they have a very speciﬁc way of thinking about what teaching looks like. [Students] think teaching is, “Open my brain, pour in your brain” kind of thing, rather than the sort of self- discovery together. So, I’ve had some students that tell me, “I would rather you just lecture the whole time, and I just want to sit back and take notes.” So, there are some that I think remain all four years a bit resistant to that, and would rather be passively lectured at, even though all of the literature shows diﬀerently. And I think that might have been my challenge, too, with having 38 3. EXPERIENCING VULNERABILITY AND EMPOWERMENT ﬁrst year students, is their perception of what they thought I should be delivering to them as a consumer because education has gotten very consumerized, especially at a private, high-cost institution, [which] was very diﬀerent than what I felt like my role was in the classroom. And I wonder if, in a more traditional sense, they might have felt like they were getting what they perceived as teaching. Whereas my walking around and coaching them and challenging them and saying, “Now, how does that work?” they didn’t perceive that [as teaching]. So, I did get comments, especially from ﬁrst-years, of, “She didn’t teach us anything. I taught myself.” Well, yeah. I coached you to learn how to learn. That’s the point. So, I will say that I have seen that resistance. It has not, certainly, been enough to stop me. And I think, when I ﬁrst got to Etown, part of why I was so successful is because I was teaching some students that had been taught by a visiting instructor that was very lecture-based. So, all of a sudden, when I came in, and now they had that alternative, and I was teaching upperclassmen, they appreciated that a lot. Same thing at Berkeley. I think my evaluations were honestly artiﬁcially high there because I was just doing something diﬀerent than what they saw in all of their other classes. Now that we sort of almost all do it at Etown, I think some of them almost want the alternative where they would rather just sit there and be passive and be given the information. I think when I look back, I guess the main thing that was formative for me was that experience at Dartmouth, kind of small, with a teaching focus, and then going to Berkeley and seeing the alternative. And I wanted to make that journey, that was intentional on my part, but I didn’t realize quite how diﬀerent the experiences would be. So, I think that that was one of the most formative things in my student-centered active learning teaching style. REFERENCES Felder, R. M. and Brent, R. (2015). Random thoughts… handouts with gaps. Chemical En- gineering Education, 49(4), pp. 239–240. https://www.engr.ncsu.edu/wp-content/up loads/drive/1l5p3UW6e7oQ_JBOpvMEPcpz8APhxj2Ph/2015-r_HandoutsWithGaps.pdf 31 C H A P T E R 4 39 From the Armed Services to the Classroom Brad Hyatt Narrative constructed by Audrey Boklage It wasn’t just something from a book that was 10 years old, but it was something that was currently happening. It was very relevant. Those are the type of opportunities that make me excited, that we can provide students once we make it focused on them and engage technology or bring that technology into class as much as possible. Brad Hyatt is an Associate Professor of Construction Management at Fresno State Uni- versity. THE CALL TO ADVENTURE: A TRUE LEARNER I’ve been teaching now full-time for 7 years. Prior to that, I spent about 12 years in the industry, ﬁrst as a civil engineering oﬃcer in the Navy and then a couple years as a project management, construction management consultant, working on large construction projects. When I came and started teaching, I was really interested in bringing my experience to the classroom, and really the only way that I thought I could do that eﬀectively is by talking about projects. I’ve always enjoyed teaching. Even when I was in the Navy, I taught some college classes, and then I did some training in which I would instruct other people. I always enjoyed that. I’ve always enjoyed mentoring others along the way and being a part of that. I think a lot of it has to do with just my makeup, and the way that I am, and I enjoy that. I also enjoy learning new things. I think any of us that are in academia, that’s a big part of why we do what we do, is that we really, we have those questions, and we want those questions answered. We’re really good at learning. A lot of us wouldn’t be in this position if we weren’t. For me, the process has been to really try new things, and always having that goal of “How can I improve?” “How can I be better?” “How can I take the feedback from students and from my peers?” “How can I look at the examples of what else is going on and try that?” 40 4. FROM THE ARMED SERVICES TO THE CLASSROOM One of my personal goals had always been to teach at the college level or a university level. I’ll be honest, I never thought it would happen this soon. I had envisioned it would be something that I would be a consultant for 10, 15, 20 years, and then go back and teach 1 or 2 classes as an adjunct. The opportunity came 7 years ago. This position came open. My background is the Navy. As a civil engineer in the Navy, they send you to graduate school, so I went to the University of Texas, got my Master’s degree in construction engineering and project management. At the time, here at Fresno State for this position with construction management, they were looking for someone that had industry experience and a Master’s degree as a minimum. It was just one of those things that the door opened, I went and interviewed with it, it worked out, and they oﬀered me the position. REFUSAL OF THE CALL: DECIDING TO LEAVE INDUSTRY Quite honestly, it was a very, very hard decision, because I loved my job. I loved the company I worked for. I loved the project that I was assigned to. It was a very exciting project, probably one of the best projects that I had ever been a part of. It was a hospital project in Riverside, California, just a great team. There was about a year and a half left in the project. I just looked at really what I wanted to do. As far as my professional experience goes, speciﬁcally with the Navy, as an oﬃcer in the Navy, I think what that has allowed me to do, it’s given me the conﬁdence to try new things. It’s allowed me to understand and know that I can try new things. I went and talked to my boss. He said, “Really you should take it. It’s a unique opportunity that may not come along in the future, at least the way it’s designed.” I took his advice, and it’s been the best decision that, one of the best decisions I’ve ever made in my career. ROAD OF TRAILS: CONNECTING CLASSROOM TO INDUSTRY I would say that, when I ﬁrst started [the faculty position], it was a huge transition, not just for me but for the students as a whole. I got lots of negative feedback from students, comments, you know, “I’m not paying to work in class. I’m paying you to lecture and teach me things. You’re not like other faculty members. Your class is too hard. I don’t like the style where I have to do homework or problems in class. I’d rather do it on my own time.” There were a lot of comments that I got back initially that were discouraging. What I found after my ﬁrst semester of teaching was that I just didn’t like lecturing. I didn’t like being the person in the front that talked 90% of the time, and students weren’t paying attention or asleep or just not engaged overall in the classroom. It was very frustrating. I decided quickly that I needed to do something diﬀerent. I needed to engage the students more. I needed to get them more excited about my profession and what they were going to do 4. FROM THE ARMED SERVICES TO THE CLASSROOM 41 eventually. At that point, I started to do some research, reach out to people here on campus and other places to see what they did. What I quickly found was that there were other ways, primarily project-based learning and things like that, but the feedback that I kept on getting [from other professors] was that it’s just a lot more challenging to do that. CROSSING THE FIRST THRESHOLD: FLIPPING THE CLASSROOM Being a new faculty member, and with lots of vigor and excitement, I decided, “You know what, I’m going to go ahead and do it anyway, and see how it goes.” The next semester, the second semester that I was here, I started to think about and utilize project-based learning. You bring in projects into the class and have the students work on speciﬁc projects and do more hands- on work, and a lot less lecturing. Then the next year, I found out about ﬂipped teaching. I decided I really liked that approach where the students would still get the content, but it would be delivered outside of class. Then when they came into class, we would do things with that content, whether it be work on problems or work on a project itself. I really started to see my students get the content and get the problems and do much better on the exams than what they had previously done. Ever since then, that’s really the approach that I’ve taken. APOTHEOSIS/FREEDOM TO LIVE: LEARNING TOGETHER As a civil engineer in the Navy and also a project consultant, that has given me a very broad- based experience. When I go into the classroom and I talk about certain things, I just have a very broad background in which I can pull from, not that I know everything, because I don’t. That’s the very ﬁrst thing that I tell students is I don’t know everything. If I don’t know the answer, then we’re going to ﬁnd the answer together. Luckily with technology, computers, and Google, you can get an answer to almost any question. It may not be the right answer. You may have to dig for the right answer, but we can get an answer and really try to discern what the correct solution is or answer that question. Again, having that broad-based background gives me the conﬁdence to step into a classroom and know that either any question that a student asks, either I’m going to be able to pull it from my background or I’m going to know the resource that we can use to answer that question. It may not happen in the class, but soon after class, we can get that solution or answer. SUPERNATURAL AID: PROFESSIONAL KNOWLEDGE If I hadn’t had that professional experience, if I hadn’t been in the Navy for over 9 years, and then been a project consultant for a couple years after that, I don’t think I would have had [professional 42 4. FROM THE ARMED SERVICES TO THE CLASSROOM knowledge]. I wouldn’t be able to do those things as conﬁdently as I can do now. It’s really a culmination of all my experience and just a willingness to try. One of the things, especially in our discipline, in construction management, in construc- tion engineering, and management, that we always tell students is that our discipline is one in which you work with people all the time. We do not have the opportunity to work in a silo. We don’t get to work by ourselves in a cubicle without ever having any human interaction. That is not the reality of our career path. I try to explain to them that the classroom itself, I am doing my best not just to deliver the content, have them learn the content, and learn some of that technical and management aspects of what their job’s going to be, but also I want them to learn those soft skills of how to interrelate, how to work in teams, how to articulate your position and work with others. Really having this focus on student interaction, group work, project-based learning, it provides that opportunity. MASTER OF TWO WORLDS/RETURN THRESHOLD: REAL-WORLD EXAMPLES What’s been most rewarding in this process has been not necessarily what I had planned students to get out of it, but when we go beyond what was planned in the class, and we really start to talk about or do work problems or look at projects that have much more depth than what was originally planned. A prime example of this would be when we talk about construction law in our classes. Sometimes law can be a very tricky subject, especially for a student that’s fairly early on in their curriculum. We do an introductory law class, construction law class, at the sophomore level. They’re very challenging topics a lot of times, but by giving students the tablet, what we allow them to do is do some research. When we have a speciﬁc topic in law, have them go and do a web search and ﬁnd some examples, and then we can talk about those examples. The examples then are contemporary examples. I can think of one example where it was a case that had come out within the last month, and we can really talk about what that case was, and how it applied to our topic, and it became something very real that the students understood. It wasn’t just something from a book that was 10 years old, but it was something that was currently happening. It was very relevant. Those are the type of opportunities that make me excited, that we can provide students once we make it focused on them and engage technology or bring that technology into class as much as possible. FREEDOM TO LIVE/ULTIMATE BOONE: CONSTRUCTIVE CRITICISM Do I still get negative comments [about my teaching]? Absolutely. I always do. There’s always some. There’s always 1 or 2 that just don’t ... that really don’t like that style, especially the students that are used to learning on their own and used to not having to work in groups. Really, they like to process things by themselves. What I see with those students, and it could be students 4. FROM THE ARMED SERVICES TO THE CLASSROOM 43 that are really good, and it could be students that aren’t as adept academically, but I always get some feedback from them. “Why do I have to do this? I can do this work on my own. Once I get the problem right, why do I have to help someone else? I have other things to do.” Maybe I’m unrealistic in thinking that I’m never going to have a semester where I don’t have some kind of comment that really critiques what I’m doing. Come to think of it, really, one of the things that I always tell students is I want your feedback. I want your critical feedback on my class, on the content, and on myself. If you think that there are things that I can do better, I want to hear it. I welcome it. I feel conﬁdent that I can try new things, that I can do something diﬀerent. That’s reassuring. I’m not afraid to fail. I’m not afraid to try something new. SUPERNATURAL AID: FACULTY SUPPORT The past two years really has been the most exciting, because here at Fresno State, our new pres- ident, President Castro, had an initiative to bring tablets into the classroom. The way that the university approached that is to have faculty really decide how they were going to do that, and they provided us with the training and the resources to explore new ways to bring tablets, tech- nology, into the class, engage students more, and hopefully improve the learning atmosphere. This is the third semester in which I’ve done that. It’s been extremely exciting. What Fresno State has done is they have created programs in which they provide all kinds of workshops and opportunities for you to become a better teacher. Like a lot of institutions, they provide these faculty learning committees or faculty learning groups that focus on a speciﬁc topic. I’ve been involved in a number of those, one on ﬂipped teaching, one on using e-portfolios. Then they also have a lot of programs that allow faculty to redesign courses, to integrate technology or new teaching practices. Those oftentimes are a full-year program. You meet about once a month for a couple hours each meeting, and then you go to a “summer institute,” which is a week-long intensive program in which you do the heavy lifting and redesign your course. It’s a really good program that Fresno State has created. Even if you come in and don’t have a lot of teaching experience, they provide a lot of resources to help you get better at it. ROAD OF TRIALS: RESISTING CHANGE Again, there’s a lot of bumps in the road. There’s a lot of frustration. There are some students that just don’t like [changes]. What I’ve seen this semester is that almost every single student engages it. They’re excited to have a tablet. They’re excited to have a tablet, because when I do problems, when I do activities in class, they have something in their hands that allows them to leverage what I’m talking about and do more than just what they could do with a piece of paper and a pen. Really, I view it as the next step of having technology in the hands of all students and engaging them more, and really moving away from what I’m doing in the class more to what I want students to do and what they can do. 44 4. FROM THE ARMED SERVICES TO THE CLASSROOM FREEDOM TO LIVE: EMBRACING THE CHANGE I just truly believe it’s so important to have the conﬁdence to try new things. A faculty colleague of mine, he and I were talking about it yesterday in that it’s so much easier to do lecture. It really is. In the big scheme of things, if I was solely focused just on myself and not really…not that I wouldn’t care about the students, but if I was less focused on the students and really focused on me and my time and being eﬃcient, I would lecture every single period. I would lecture and give quizzes and give an exam. It’s just so much easier that way, but I don’t learn that way well myself, and I ﬁnd that I have to be engaged and I have to be interested. The work load is immensely higher than traditional teaching, but I think, just from my standpoint, I really see huge beneﬁts to the students. The feedback I get from the majority of the students is, “Wow, this is great. It’s one of my favorite classes. You’re a great instructor. I appreciate you.” Then to see them in a next class down the line really understand the concepts and be able to apply the concepts, that just makes such a huge diﬀerence. I think that, by trying something new, using technology, using project-based learning, doing some of these things that are innovative and out there, it takes a lot more time and energy. MASTER OF TWO WORLDS: INVESTING TIME I would say, for anyone, if they try something new, really put the time and energy, know that it’s going to take a lot of time and energy. Any time you try something new, outside the box, it’s going to take a lot more time, more time than you probably anticipate, but if you stick with it, if you get feedback from students, if you have them involved in the overall process, it really does pay dividends. FREEDOM TO LIVE: GAMIFICATION IN THE CLASSROOM My next step is I’m really interested in gamiﬁcation, and ﬁnding a way to integrate points, [badges] into our courses. I tried a little bit of it in the past, and it’s challenging. It adds a little bit more complexity to the classes, but I’m really interested in ﬁnding a way to streamline that. Hopefully that will take the students further and get them more excited about it, the course itself, and the content that’s created and the projects that come out of it. C H A P T E R 5 45 Engaging Students through Service Learning and Innovation Chris Swan Narrative constructed by Brooke Coley To me, a faculty member is someone who actually provides the best education that they can for their students. So, doing it where people are engaged is a key part, at least to me… What I really think is engaging the students [is] doing it in such a way that allows them to take the technical expertise that they’ve mastered in the classroom and apply it to real-world situations and learning as well. Not just doing the technical expertise, but actually learning about both their technical and non-technical professional skills. That’s the best education I think we can provide to our students. Chris Swan is Dean of Undergraduate Education for the School of Engineering and an Associate Professor in Civil and Environmental Engineering at Tufts University. CALL TO ADVENTURE: THE TEN-YEAR PLAN TO BECOME A PROFESSOR WITH PRACTICAL EXPERIENCE I started oﬀ at UT-Austin. I grew up in Texas and always dreamed to go to college, period. I chose engineering because I found it to be closest to my own interests and capabilities. I always enjoyed math and science, and since my father was an excavating contractor, I said “let me do something in the construction ﬁeld,” and civil engineering ﬁt best as a direction. So, I pursued that as my degree. Struggled through it as a lot of people do, but by the time I was a junior, I ﬁnally got the hang of all this stuﬀ because it became more applied. And that was the key for me, was that all of a sudden, I started to see the application of all that math, science, and other often abstract things that they require you to take. [I] ﬁnished with a Bachelor’s, went straight through for a Master’s with the particular disciplinary aspects of geotechnical engineering. My plan was to then work for a while and 46 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION return for a doctorate and then an academic career. [I] graduated in 1986, turned in my Master’s thesis, loaded up my car and drove to Massachusetts from Texas. I arrived here to work for a company. Originally, [it] was going to be for 4 years, but it turned out to be only 3. Then, went back to school (MIT) to get my doctorate so that I could actually go on to the academic profession. After MIT, and 5 years of doctorate education, I was lucky enough to get a position here at Tufts. Amazingly, I did have a 10-year plan after my Bachelor’s to actually become a professor and it happened. It was just a number I threw out at the end of my senior year saying, “Yeah, I want to pursue a Ph.D., but I want to pursue a Ph.D. with practical experience because that’s what’s helped me to learn things.” So, I wanted to go out and work for a little bit and take the knowledge that I gained from working…It [was] 3 years of practical “apprenticeship,” knowledge that I could bring back into engineering education. CROSSING THE THRESHOLD: HELPING STUDENTS CONNECT THE THEORETICAL AND PRACTICAL I’ve [now] been teaching here at Tufts for [more than] 24 years. What and how I began teaching were basically the same way that I was taught. But I always had valued, at least in my own learning, the application aspect. So, it wasn’t just “Here’s the formula” and trying to get to the mathematics of the formula, but saying, “Here’s the formula, let me tell you why it works and how it works and where it is applied.” And then you can work from the “I’ve applied it” to “Oh, let me try and understand the mathematics of it, or even the science of it,” so it was a reversed direction. What that has shown me is that the math and the science is so important to understanding many of our engineering principles, but engineering is still something that students need to also experience—to the point that the application is so important that it makes the math and the science that much more interesting to them. In other words, I can actually apply that calculus to that, or the diﬀerential equations to that. But they also get to see this particular principle, if you will, and its real-world aspects and its applied aspects. The fact to me is that connecting the theoretical and practical aspects is important. It’s not necessary, I don’t think, for all students to experience engineering as such a connection, but for me, it made the experience that much stronger. [Students think], “Oh I just learned this formula, and I can easily plug and chug in this formula, but I don’t understand what that means in reality,” so, [I] try to bring in real situations where that can happen. And the real situation could be that you do a video, or something that they actually have to do themselves. To me, the tactile [nature] of actually making something makes a diﬀerence in how students will engage with a particular topic. As a civil and environmental engineer, let’s say [the lecture topic] is water resource related, I can’t have them build an actual dam. [Nor can I] really have them do watershed analysis from the standpoint of delineating its location for a particular river or stream. That’s a good ﬁeld eﬀort, but it’s not what I’m doing. And I would say [in] environmental studies people can do 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION 47 that, that actually ﬁts very well. But for me, I can show it in a planned situation, and then talk about the situations as they arise in reality. Not just, “here’s a plan,” but we also can see that, here we are in Massachusetts, close to the Aberjona River watershed. So, what does that mean? Well, the Aberjona River watershed is the same one that is in the book (and later movie) Civil Action from the 1980s/late 90s. But it has real-world implications because understanding the Aberjona River watershed was an important aspect of this case of contaminating a community’s drinking water, leading to an increase of cases of leukemia. But it makes a connection because this is real, the people are less than 20 miles from Tufts, and that impact is real. So, if I can make those connections between the abstract concept of watershed analysis and the concrete reality of understanding a watershed so that you can see its impacts on the community, I think that it just brings home the topic. It makes it deeper for a student to go into how they can understand the subject. APOTHEOSIS: SEEING AN EXPLOSION IN THE DESIRE OF THE STUDENTS TO LEARN So, my teaching was not completely hands-on, but I did a lot of projects at that point to make it hands-on. But it was still, and I would say, it still is, strongly lecture-based. But, the evolution of my lectures is another piece that’s interesting ...I would say that the real evolution in my teaching, and almost revolution in my teaching, occurred when the projects started to become real projects instead of ones that I had made up and controlled the data. In [the] spring of 1999, I was still teaching a course called Site Remediation Techniques, which are basically methods in which we clean up hazardous waste sites or toxic waste sites. Previously, I had always used projects for which I knew the result; either the site had been cleaned up and I had the data, or I had made up the data to lead to a speciﬁc solution. For example, here’s the soil proﬁle, here’s the chemicals of concern, let’s think of a method [with] which you can clean it. How would you go about cleaning up this thing? The “switch” in 1999 was that we were working on real sites with no known or given solutions. Additionally, remediation of these sites would have impact on the economies, the social fabric, all diﬀerent aspects that weren’t traditionally seen, nor taught as an engineering aspect, beyond just technical [aspects]. So, these projects were basically service learning-based projects. We were doing projects in service to a community, working with clients, working with regulators, working with the community. And so, when I introduced those as projects, I saw the change more so in the students [with] what they learned than anything else. So, all of a sudden, the students became extremely attached to the project. It wasn’t just because it was a real-world aspect, but because it had real people. Students just seemed to love it. They loved it to the point where they were learning things beyond what I taught them in class. Instead of saying, “Oh, we learned this in class, we’ll do this method of analysis,” it’s like “Well, we did talk about that, but that’s not what you need to do here.” They would actually think about how to implement solutions that we had not talked about. And therefore, they had to get the details I did not talk about—excavation support systems, or 48 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION methods of remediation, or decision-making processes; items that we had not even discussed in class. Seeing this explosion in the desire of students to learn is what ﬁrst got me interested in the pedagogy of service learning. For a number of years, it was just trying to orchestrate the class so that all planned subjects could be completed. Now, it became the logistics for ﬁnding potential sites with potential clients and stakeholders and getting students to interact with them. I will say that one of the most powerful achievements of these service-based projects was in the Spring 2000 term, where we had a group of students who not only took a hold of the site, but they actually became advocates for the community. They would go to community meetings and act as technical advocates for the community, and in some cases, get into arguments with the contractors about what should be done and shouldn’t be done. They basically provided a tremendous service, in that case. And it just so happened that those students were also graduate students, they were all Master’s level students, many of them had worked for environmental agencies or environmental groups in the past, and so they already had a passion for this, and now they had the technical knowledge to go with their eagerness, passion, and desire for social justice and fairness; [they were] a very good group. Once I started seeing the students who were performing at an enhanced level technically, as well as otherwise, I started to ask the question: Why does this approach—having these service learning-based projects—really engage these students? And, therefore, it went from the way that I taught, to the research direction. ROAD OF TRIALS: RESEARCHING NEW WAYS TO ENGAGE AND DEEPEN LEARNING The thing that I’ve been working on for the last few years is how to make sure that I am not only achieving technical learning outcomes through service-based eﬀorts, but that this achievement is equal in level as found using traditional, non-service-based pedagogical approaches. So, now I’m doing research on the impacts of service on engineering students. How that sort of engagement can actually, hopefully, lead to a better prepared engineer, both technically as well as all other aspects. I call [these impacts] professional skills, other people call them soft skills, but I tend to say you communicate better because you know who your client is [and] you can actually communicate with them as opposed to just talking at them. You will take into consideration things such as social issues and economic issues and political issues, and not just say that that’s someone else’s job. In doing the research, it became clear that there’s more than just service learning that can engage a student. And so now I’m ﬁnding ways to engage students throughout the course, instead of just saying, “Oh, you’re going to have this really cool project, just wait. 8 weeks of lecture stuﬀ, and it’ll pay oﬀ, believe me, you’ll get to see it.” For example, I now look for ways of engaging and deepening the learning without the eﬀort being service-based nor a long-term project. It’s engaging them in the moment; within a class period or about a particular topic. For example, you say to the class “let’s design a ﬂagpole,” 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION 49 so the class will do that design very quickly; back-of-the-envelope style, using quick and simple calculations, by assuming the ﬂagpole is a simple cantilever beam. You do the calculation, and now you’re done—technically. Let’s think deeper about this. Is that ﬂagpole supposed to be there? What’s the ﬂagpole for? We’re now getting to questions not of the design’s technical aspects—how big should it be, what type of material should it be, etc.—but, into the why it should be. Is the client really looking for a ﬂagpole, or are they really looking for something else? Would the neighborhood accept that particular location for a ﬂagpole? Does the town have the money to pay for said ﬂagpole? So, other issues start to be seen. And I don’t dwell on them, I don’t make them the entire discussion, I just make them a part of the topic of designing the ﬂagpole. A speciﬁc case that I used to do was a bridge. I had a project in a sophomore engineer- ing course for the students to design a bridge. But they’re not designing the entire bridge, just designing an element; [a] straightforward, simply supported beam. I’d push on the technical analysis by asking them to do things beyond what they know. “It’s reinforced concrete. We’re not going to talk about it, you’re going to have to ﬁgure it out.” The project then asked for stu- dents to create a miniature model of their design, using concrete and created formwork. This is now getting closer to real-world implementation. But then I add other considerations that are not strictly technical. Questions such as, how do we make this sustainable? Should we consider this with the neighborhood or the community’s input as to what’s necessary? The goal is to get students to recognize that such questions should be a part of the design. So, when they get into their senior year and do their senior capstone design, if they have to do a bridge, or any structure, they will start to ask those questions. Hopefully, students realized that it comes down to, “what does the client want?” [These are] the ﬁrst questions that should be asked [along with] why do they want it? How does that structure “ﬁt” with the client, the neighborhood, the bankers, whomever else is involved? ULTIMATE BOON: BECOMING THE BEST FACULTY MEMBER THROUGH STUDENT ENGAGEMENT AND INNOVATION I think what [students] did recognize was that the remediation course and the course’s material became much more interesting and connected for them because the class changed. It increased in number, essentially doubling in size once the service-based eﬀorts were integrated into it. Ad- ditionally, its audience changed. When I ﬁrst started teaching, it was predominately graduate students who did not have strong technical backgrounds. Then, it switched over to be under- graduate seniors who had stronger engineering background, but little practical experience. Then when I started doing these real, service-based projects, it became more balanced; about half undergraduate and half graduate students. What I was seeing was graduate students coming into the course because it had a stronger connection to actual case studies for them. That is, at this time, many of our graduate students were part-time [students] holding full-time jobs. 50 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION So, the course was taught in the late afternoon/evening, allowing them to be involved. Many of them were working for environmental agencies and consultants, but they saw that this was a good course that would help to hone in some of the things they had seen out in practice. What I found really interesting was they were getting technical aspects from me, but they were bringing to the classroom their real-world experiences. So, in essence they were co-teachers. [Graduate students] could talk about, “I remember this site, we actually pumped it, and we actually found this and this ...” Yes, real world. They may not have understood the theoretical or technical aspects of pumping; that is, as you pump and you get a draw down and you can actually ﬁgure out the change in height of the water at diﬀerent points, that technical detail [was] not there. But then they could make the connection of, “Okay, when we pumped, we saw the water level being diﬀerent across the site.” They could make that connection to what a technical analysis was saying. So, I think it created an opportunity for students who had real- world experience to make those connections. It also created, especially in this mixed classroom that I had, an opportunity for more ‘default’ instructors to be there, and to be educators to those whom [had not yet had] such real-life experiences. After doing it for 2 or 3 years, [I could] see the value. These people [were] not just picking up a real-world project, they were actually providing their expertise and their knowledge in a non-technical sense to what the technical issue was. So, the undergraduates that could do the technical work, calculations out [of ] the kazoo, but they didn’t understand what the calculations were for. Whereas these graduate students, especially the experienced ones, they could and they could run with it. The impact on me and my time was substantial. Because, to do that, to maintain that same level of technical competence, and to expose these other things, was additional work— additional work on the faculty, additional work on the TA, additional work on the students. But the students won’t see it as work, if they see it as learning. So, there are barriers; I call them self-imposed. It depends on your own personal value proposition. I don’t have a personal value proposition that says I need to become a full professor and then write papers all the time and have a graduate [cohort] of 10–15 students. That’s not my personal value proposition. Mine is delivering an education to all students. And this allows me to do that. Yes, it takes a lot of time. More so than what some people say I should be doing, probably. I agree with that. So, the barrier in my case has been my own personal goals and interests. They are internal as opposed to external. Intrinsic versus extrinsic. To me, a faculty member is someone who actually provides the best education that they can for their students. So, doing it where people are engaged is a key part, at least to me. Do I ﬁnd colleagues that pursue this as well? Yes, and more and more of them are coming. But it’s not an overnight sensation and everybody wants to do it, no. Not that way. What I really think is, [engage] the students in such a way that allows them to take the technical expertise that they’ve mastered in the classroom and apply it to real-world situations and learning, as well. Not just doing the technical expertise, but actually learning about both their technical and non-technical professional skills. That’s the best education I think we can provide to our students. 5. ENGAGING STUDENTS THROUGH SERVICE LEARNING AND INNOVATION 51 So, that’s where I am right now, I have academic evidence to show that [service learning] works. [This thing I did in 1999] is still impacting [my ability] to continue on these diﬀerent pathways. [I’m] still working on things, got an entrepreneurial side to it, too. Most people look at entrepreneurship as another way to say, “I want to make a lot of money and I want to make a lot of money fast.” To me, entrepreneurship is ﬁnding out what your client wants—basically their values—and saying how do I satisfy those values? And you may ﬁnd out that what is currently available doesn’t satisfy them. So, you have to be innovative in the process. Entrepreneurship is truly a mindset where you really evaluate if something can be grown, scaled and sustained. Why not be entrepreneurial in applying an educational concept? An educational innovation? When most of the education that we still receive today is the traditional lecture style, when people can deliver it in a diﬀerent way, why can’t that be an entrepreneurial eﬀort? My value proposition is that service-based eﬀorts enhance student’s learning outcomes. I’m looking at service learning as something that engages them so much, and they continue to be engaged by it throughout their lives, that they say, “I picked that up at Tufts.” Same thing at another institution, “I picked that up, at Institution X.” Long term, [service learning] could have broad and deep beneﬁts—[and] this is really long-term thinking—[as] an engaged student leads to an engaged alum, which leads to [a] continued ﬂow of institutional support. [Such eﬀorts will inﬂuence a] diﬀerent student body, hopefully more engaged with learning, but also more engaged with the institution. I want to say that it really comes down to wanting to deliver the education that I think is appropriate and most impactful to the students. What I’m seeing just by doing it and being involved in it, is that [service learning] is impactful. C H A P T E R 6 53 From Food to Simulation with Legos: Engaging Students in Hands-On Learning Thais Alves Narrative constructed by Audrey Boklage Right now, I hope I can better manage this struggle that I can just smoothly put these innovations in the class and still be able to move on with the content. This was another thing that the CTL (Center for Teaching and Learning) changed in my mind before I wanted to go and bang, bang, bang, bang, cover the syllabus. Right now, I said, “ You know what? If they learn this and this and this and they really know well about this, I can skip a topic or two and maybe have a smaller amount of time dedicated to that.” I think that my battle is to change a little bit at a time but still cover the material. Thais Alves is an Associate Professor of Construction Engineering at San Diego State University. CALL TO ADVENTURE: CREATING A COMMUNITY It started all the way when I did my Master’s in [lean construction] in Brazil. Then I went to UC Berkeley and I had more exposure to [teaching]. Through my time there I also TA’d for my advisor and I really enjoyed being a TA and working with the students and seeing how the assignments were prepared from the other end. After my Ph.D. studies, I had to go to Brazil because I had a scholarship, a full ride. I had to go there [Brazil] and spend some time. Then when this opening showed up at San Diego (San Diego State University, SDSU), it was in an environment very similar to the one I had in Brazil in the sense that the industry there is extremely supportive of our program. Whatever we need, if we structure the call or the request nicely, we’ll get help. Projects that we send people to collect data, research, whatever, you name it. It was the same thing when I was in Brazil. The interesting thing when I was [in Brazil, there] was this group that was very close to the university 54 6. FROM FOOD TO SIMULATION WITH LEGOS down there, they had their own learning community, so there were 10, 12 companies that paid money every month to become a member of an innovation type of community, and they would bring experts from other parts of the world to see what they were doing, and they were very creative in how they implemented lean construction, so much so that people from around the world, we were often hosting people just to show what they are doing. One of the things that caught my attention very early was that people who were trying to explain lean [construction] to us, they would always have diﬀerent ways of explaining. It was not your traditional “I teach, you sit and learn.” There were a lot of fun exercises outside of the classroom and games and the sheer volume of discussion and how we were trying to understand it, because we are engineers and we were trying to understand all this philosophy behind lean. I think the ingenuity that they have in the U.S., everything has to have a computer and a laptop and a tablet and a projector. [In Brazil], this is not [the case]. People [become] very creative in terms of how they [do] things with paper and pencil and conversations because of [the lack of a computer and other technology]. That was very good, too, because when I was there, I had a bunch of examples that I could give to my students and they could step out of the university and see it. ROAD OF TRIALS: A LACK OF IN-SITU EXAMPLES When I came here to San Diego in 2009, I was talking about some of the concepts that I taught in my graduate course [in Brazil], and people had never heard about them. I didn’t even have construction sites to send [students] to see because [they were] not here. That forced me to be even more creative on how these things were going to be put together because they couldn’t step out of campus and say, “Oh, we are going to go to a construction site and see these.” Some of the concepts that I teach them, to this day, they haven’t seen anywhere. My students back in Brazil, they could actually go to a construction site and talk to somebody who didn’t know how to read, and they were implementing some of those things. The barrier to change some of the mindset there was much lower at the construction site level because some of these people, they didn’t know how to read and write, but once they were brought into the discussion, and were given some ideas, they would use it. If it beneﬁted them, they would do it. It was a very big shock when I came from there to here and I had to adopt my teaching and the sites were not there for them to see, and people here, they seemed to be more reluctant to accepting some of these things. One of the most interesting things was that the terms that we were using to teach lean to engineers, some of them were not translated to Portuguese. When you talk about certain terms, the students had to learn what those terms meant in English. The term was in English or in Japanese or whatever language and they had to learn the term. I didn’t think that that was actually a problem for them. You would just say what the look-ahead schedule is, and they would get that the look-ahead schedule was whatever I was explaining. They would call it as such in English. 6. FROM FOOD TO SIMULATION WITH LEGOS 55 FIRST THRESHOLD: BUILDING A LANGUAGE BRIDGE When I came back to U.S., I started seeing that some of those terms that I was trying to teach back in Brazil and those students would just learn a term like “look-ahead” and they would make sense of it, when I got back to U.S., I realized that some of those terms were not commonplace here either. It was interesting to ﬁgure out how I was going to teach that because there was not this, let’s say, inertia, right. The term “inertia,” is translated into many diﬀerent languages and there are formulas that are associated with it. Well, with what I was teaching, there was not. It was interesting when I came back here to see that those students were having trouble getting some of these concepts that I thought, “Okay, it’s in their language, they are going to capture it better.” That pushed me to be ever more creative in terms of how I was teaching these things. I had to become very creative as my other instructors were in the past. That’s how I got into this track, if you will. BELLY OF THE WHALE: THE TASK OF TEACHING [I realized that] I have to adapt whatever I’m doing and see what kind of population I have here. SDSU is a university that is supposed to form people to go to the market, so they are not going to become researchers. Going to the Center for Teaching and Learning [CTL] lunches here, they said, “Remember that your goal is for students to learn. Do whatever you have to do, but they have to learn.” I think that was that “aha” moment that I can do whatever I want, but these people are my clients and if they are not happy or if this is not useful for them, I have to do something. I have to ﬁnd the happy medium, which I think I ended up ﬁnding after going to the CTL meetings and seeing the diﬀerent approaches and using Blackboard and working on my syllabi to make sure it’s clear and they know when the assignments are coming, when we have simulations and just keep reminding them. I had to become this person that serves more of the students and tailor my teaching to their needs. ACCEPTANCE OF THE CALL: FOOD, HANDMADE LEGOS, AND PRESENTATIONS I like food. I would always start talking about some food related stuﬀ [in my classes]. I would catch their attention right away. I was talking about something that was very personal and I would say, “I like this, I like that, and now imagine that you are in a restaurant and that’s what’s happening.” I would always try to anchor the concepts into something that they already knew and they were familiar with on a daily basis. To this day, when I teach, I talk about all the food places on campus. In one of my classes I used to send them to do studies in these places before I would send them to a construction site. That was one way. The other way was the simulation with Legos. Probably you heard about many of them, and I created my own with, I asked the students to cut dice, small dice, and I would give very simple instructions and they would do it, and then we would move on to 56 6. FROM FOOD TO SIMULATION WITH LEGOS diﬀerent problems of the game with them, making dice and making the airplane game that you might come across as you talk to some people in this ﬁeld. I remember a professor in Berkeley who used to bring some ingredients to class and mix in front of the students. He taught construction materials, and he would show how those things will add glue to the mix or become more watery or harder. Usually we see a lot of that in construction, but I don’t see [it] in the other disciplines in my department, unfortunately. They might have other things that they do that I don’t know, but as far as these Lego simulations go and stuﬀ like this, it’s just construction people. In my grad class, which is the one that I teach these concepts the most, I created an assignment that they have to create a video or an animation or a game that explains a concept. They have to ﬁgure out, I just tell them what the parameters are. They have to pick a concept. They have to do a lesson plan. They have ten minutes to present and the video has to be up to ﬁve minutes within that presentation. It’s something very focused, and they presented that. ULTIMATE BOONE: POSITIVE FEEDBACK A few weeks ago, and every time they have a presentation, I ask them to post on Blackboard a positive thing, a negative thing that can be improved, and a lesson learned. By far and large, they love this assignment because they could see the concepts, the abstraction that the metaphor for diﬀerent concepts in each group presented in a diﬀerent way. Some people presented washing dishes. Some people presented how they prepare to go surf. Some people presented how they are getting ready to organize a new production line in their company. The comments on Blackboard overwhelmingly tell me that they enjoy that because they could see diﬀerent ways of applying the same concepts. APOTHEOSIS: MORE PLUSES THAN DELTAS [These comments are] usually very positive because we still have the traditional lecture [when] I’m in front of them and I’m lecturing the traditional way, but we have a lot of guest speakers and we have these simulations. Every time we have a guest speaker or we have a simulation, or they present, they have to do this plus/delta of lessons learned. This plus/delta lesson learned is open for everybody to see, so they see what other people write, and it’s a safe environment, it’s free of criticism. They post whatever they want and I put my comments as well, but they can all see what they’re saying. The only negative comment that I got that I would say for my video animation assignment is that they want more time to present. I’m saying, “No. I’m not going to let you get more time because you’re going to be rambling there and people are going to get bored.” That’s the only negative thing that I have gotten so far. They want more time. MASTER OF TWO WORLDS/FREEDOM TO LIVE: PEDAGOGICAL FLEXIBILITY 6. FROM FOOD TO SIMULATION WITH LEGOS 57 I feel that every time I’m going to lecture, I have my slides that are ready, but I never have the same exact lesson. Never, ever. Every time I go to a class, not only I have to see my notes, but whatever I’m listening on NPR, if I have a chance, or I read the news, I always try to bring something that is contemporary, if nothing else, just to catch their attention. They might be distracted and say, “Oh, did you guys see this and that?” This relates to the class. I want to keep using that and I want to ﬂip the class a little bit more moving forward. It’s very hard to come to grips with the idea that you want to introduce these things and you want to give freedom for them to lead the class, and at the same time cover the course material. Right now, I hope I can better manage this struggle that I can just smoothly put these innovations in the class and still be able to move on with the content. This was another thing that the CTL changed in my mind before I wanted to go and bang, bang, bang, bang, cover the syllabus. Right now, I said, “You know what? If they learn this and this and this and they really know well about this, I can skip a topic or two and maybe have a smaller amount of time dedicated to that.” I think that’s my battle is to change a little bit at a time but still cover the material. MEETING WITH THE ALL KNOWER: LIKE-MINDED EDUCATORS [I also received support from the ASCE workshop.] That was the best work week of my life, because we would work from 8 o’clock [in the morning] to 8 o’clock, maybe 9, 10, 11 [in the evening], and we were all so happy, so excited, and that was another thing that I appreciate having a chance to go there and have this support that you are mentioning, because that’s another thing they said. You have to think about ways to teach your students, and engineering professors are very, “You teach like this or teach like this.” We went to West Point [for the workshop], and you had all these military professors that you would think are very structured. It’s very structured, but it’s also very fun. They had all these diﬀerent things that they would do. That was a huge help for me to be part of that and to accept that those things are accepted in engineering, because some people, I have the impression that when you say that you are doing these things, people think, “Are these people really learning? Is she really teaching something?” With my comments, my reviews, right, you will see that the students enjoy and that they like this approach. That was a huge help. 58 6. FROM FOOD TO SIMULATION WITH LEGOS MASTER OF TWO WORLDS: LEGOS AREN’T A WASTE OF TIME As far as the CTL help here, the director of the CTL here just invited me recently to be part of their ﬁrst advisory board that they are putting together, so I’m having a chance to actually look at some of the schedules and workshops and things that are more hands-on. They are doing that and whoever is part of the board is trying to say, “Yeah, we prefer to have hands-on things that we can bring to class immediately.” I just wish more people [who teach engineering] spent the time to do these things, because I have the impression that sometimes when some of the students from other disciplines, when they land into my class and they say, “We are going to work with Legos,” they are like, “Oh, there it comes.” They think that it’s something that I’m just doing to kill time, that I’m not prepared for class and then I’m going to play a game or something, and then some of this perception changes, and when I say we are going to play a simulation, and they know that it’s serious and they will be engaged and I’m not just trying to kill time. I think that it will be good if more people had this mindset, that they could try and use these other experiments in class. C H A P T E R 7 59 Finding Her Niche with Hands-On, Practical, and Real-World Pedagogy Fernanda Leite Narrative constructed by Nadia Kellam I think I’m still a work in progress. You said [that I’m a] rock star, but I just see myself as somebody that’s just constantly learning, and constantly trying to provide our students the best education that they deserve to have. That just is a work in progress. Honestly, there are still days that I come out of a class and I said, “I could have done that better. Next time I’ll do it better.” It’s always a work in progress. That keeps me motivated. Fernanda Leite is an Associate Professor in Civil, Architectural and Environmental En- gineering in the Cockrell School of Engineering at The University of Texas at Austin. CALL TO ADVENTURE: COMBINING PASSIONS My father is an educator. He’s a professor in Brazil in agricultural engineering. I grew up actually in College Station, Texas. I knew what it was like to live the academic life from my observa- tions of my father. I also was very passionate about construction, which was my grandfather’s profession. He was a developer of high residential/commercial construction in Brazil. My ﬁrst teaching experience was teaching English as a foreign language in an afterschool program. That’s where I fell in love with teaching, when I was an undergrad [in Brazil, where I’m from.] I knew that I wanted to teach, but I knew I didn’t want to be an English teacher in an afterschool program as a full-time career. I put all these little pieces together. Really, the passion that sparked that, that was ignited when I was just teaching. It was better than ﬂipping burgers. I had the skills. Why not use that? The research observations of my father, and the construction domain from my grandfather. I wanted to combine the two [professions.] 60 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD SUPERNATURAL AID: FIGURING OUT HOW TO BECOME A PROFESSOR [When teaching English in the afterschool program,] I just had lots of fun… just seeing people, observing people grow, and how a small intervention could really impact people. That, for me, was really encouraging, and it just gave me a high. The same thing that I feel after teaching a good lecture. Endorphins go oﬀ in your brain, or something like that. It just feels really good. [However,] I knew that that wasn’t the domain where I wanted to be doing that, in terms of teaching English. I wanted to teach my chosen profession. My father really helped me shape how [to reach my goal.] That’s where I traced out my plan of, “What do I need to do to be this person, in terms of getting the right degrees?” I sat with my dad and said, “What do I have to do?” He said, “Well, if you want to be a university professor, you’ve got to have a Ph.D.” That’s where it started. From there, I went into a Master’s program in the south of Brazil. I’m from the north-east [of Brazil.] In Brazil, at least, at that time, I didn’t know I was going to get a Ph.D. in the U.S., or become a professor in the U.S. My plan was more, “How do I become a professor in Brazil?” Because that wasn’t in my radar, that this would be a possibility. My dad’s like, “Well, you need a master’s ﬁrst, and then a Ph.D. Then you can apply for a faculty position in Brazil.” MEETING WITH THE ALL KNOWER: A VISITING PROFESSOR AND FUTURE ADVISOR During my Master’s [degree], a professor from Carnegie Mellon University went and taught a one-week short course over the U.S. summer, our winter in Brazil. At the end of that course, he basically said, “Would you like to get a Ph.D. at Carnegie Mellon?” I said, “Sure. Are there two positions, one for me and one for my husband?” Because my husband was also in the same path. We were both Master’s students together. We ended up going to Carnegie Mellon for our PhDs, as well. He said, “Sure, I’ll get a position for the two of you.” We applied, and it worked out. We actually only applied to two U.S. universities for our Ph.D.s: UT Austin and Carnegie Mellon. We were accepted to both, but we decided to go to Carnegie Mellon in the end. [Eventually,] I ended up here [at UT Austin] anyway. Because I grew up here in Texas, so I had a big connection with the state. ROAD OF TRIALS: EXPERIENCE TEACHING IN GRADUATE SCHOOL I’ve always served as a teaching assistant in classes in grad school. I’ve always done research, which was my primary responsibility in grad school. I’ve always been really, really passionate about teaching. What I noticed [when I taught in graduate school] is that a one hour lab was pretty limited and it was, most of the times, very disconnected to what was happening in the 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD 61 three hours of lecture in the week. My Ph.D. advisor taught those, and then I taught the one- hour lab. There was that disconnect. That was the ﬁrst thing. My desire was that it would be all connected, better connected. I was frustrated [then,] because I didn’t [teach in a hands-on] way as a graduate student, as a TA. I was supposed to teach the lab, and teach them how to press the buttons. That just frustrated me. But you only had one hour a week, and it was not connected to the lecture slides. You really couldn’t do a lot more than that anyway. That’s the ﬁrst thing that I said. “If I’m going to do this, I’m going to do it right, the way that I really believe how this should be done.” For me, since I’m in such a practical ﬁeld, which is construction, I don’t understand how I can teach without it being hands on, and very practical, and very real-world oriented. I just don’t know how to do it a diﬀerent way, honestly. When I was a teaching assistant, I think the hands-on component was very limited. I tried to develop my advising style, my teaching style, based on my own experiences working with other people. APOTHEOSIS: DEVELOPING AN INTERCONNECTED COURSE When I came here to UT, that was one of the things that I created was this BIM (Building Information Modeling) course. The way I thought of creating those connections better was by dividing the course into modules. The modules would be a lecture, two lab classes, and then a reﬂection class. All on that same theme. They’re all very interconnected. The ﬁrst lab class, we teach them, they’re able to use ﬁve or six diﬀerent software systems to be able to do applied BIM for diﬀerent application areas in construction. There’s a lot of new software that they’re learning throughout the semester. Each module has at least one or two [types of software]. That ﬁrst lab class is getting them up to speed in those software systems. Then they typically have one week between that lab and the second lab. The second lab, I call it Time for Questions. There’s no teaching component. We’re not showing them anything. We’re just walking around the classroom answering questions. Most of the teams have done about 80% of the work between that ﬁrst lab and then the second lab. That way we’re just really helping them connect what they’ve been doing to the general theme of that module, and answering questions. I tell them that, “I don’t answer button-related questions. Don’t ask me a button-related question. Personally, I don’t really care about teaching how to press the right button in the right order in the software system. For me, I care about what are you getting out of that deci- sion support, that software system, the output that you’re getting? How is that changing your decision-making process to solve that problem?” I tend to focus more on the process of the module, because I really believe that they can pick up the software, wherever they go. Whatever software I’m teaching them here might not be 62 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD the one that they’re going to be using when they go out in industry. I really don’t put too much emphasis on that. That, I think, is the main diﬀerence between how I teach them in class. Over the summer of 2015, I participated in an academic BIM symposium, where faculty from all over the U.S. that teach BIM shared how they teach it. Most people tend to focus on ... One of the major softwares that [we] use is called Autodesk Revit. They said, “Oh, I teach Revit. How to draw a column, how to draw a wall.” Well that’s not really ... You’re teaching them how to use a program. For me, that is a disservice to our students. Because there are tons of YouTube tutorials online that they can learn that through. You really have to teach them how to make decisions with those systems. Then the second component is [that] it’s got to be all based on real-world problems. See those large drawing sets over there? They actually use that. That’s a commercial building in a diﬀerent state, in Pennsylvania. That’s what they use for two of their homework assignments in my BIM class. They literally walk around with those giant sets of drawings. It’s a real building that has been built. Another homework assignment is another building under construction. The fourth homework assignment is this building we are in [at UT Austin], ECJ (Ernest Cockrell Jr. Hall). They do diﬀerent things with these real-world projects. That’s important, because [the stu- dents] need to understand project complexity. In engineering, we tend to over-simplify problems and provide and spoon-feed a lot of the boundaries of problems in a way that, in the end, there’s only one right answer. You give them all the assumptions that they’re supposed to make, you spoon feed all of the inputs. That’s not how it is in the real world. When I show up in class with the ﬁrst module and show them these drawings, and tell them homework 1, which is a model-based cost estimating assignment, that they’re not going to ﬁnd the specs exactly like it’s stated in that project, in those drawings, in the speciﬁcations for that project, in the National Standard for Cost Estimating. They have to make assumptions, they have to interpolate, they have to ﬁnd approximations. Some students go crazy, because they are just not used to that world. [They say], “What do you mean I have to make an assumption? What is the right answer? What is the number that I’m supposed to get?” This is a cost estimate, it’s an estimate. There is no one right answer. Everybody’s going to have a diﬀerent answer in the end, based on their assumptions. If two teams come back to me with the same answer, that’s when I know there’s a problem. At the beginning, they’re a little shocked in the ﬁrst assignment of the semester, but then they get used to it. When they understand that, they really ﬂourish in the class. I notice that a lot, especially with students that have had no internship, no industry experience, a lot of our undergrads are like that. This is a cross-listed course, with graduate and undergraduate students. It’s about half undergrad/half grad. I see that reaction a lot with undergraduate students. Each module is basically the same structure. Lecture, which is the theoretical basis for that module. We typically have a reading associated with that. The two labs, the ﬁrst lab to get them jump-started; second lab, time for questions. Then the reﬂection class. Which is, if there 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD 63 are eight teams in that semester and four homework assignments, then two teams would present for every homework assignment. Each team has speciﬁc points to cover in their presentation, so that the presentations are not really repeated. It’s more meant as a discussion. Everybody is expected to participate in the discussion and chime in, because everyone has had that experience. It’s not like a project that only that [one] team did that one thing. They’re presenting everybody else’s, that’s all new information, no. In this case, everyone had that same experience, so they’re all expected to provide their input, as well. There tends to be a lot of interaction and discussion in this class. Even in the ﬁrst lecture- type class, I start the lecture, I just leave the PowerPoint up in the background, and we’re dis- cussing the assigned reading for that class. There’s no PowerPoint, it’s just the ﬁrst slide is up, but I’m sitting there trying to get their perspective on what were the main take-home messages from that reading. I really try to cement the important concepts in that reading. Then we get into the lecture. Then I basically tell them what the structure of that assignment, that module, is going to be after that. The reﬂection just caps it all oﬀ. We’re able to provide some closure for that module, and then discuss: “What were the limitations?” “How would you do this diﬀerently if you had this other piece of information?” And so forth. There’s a lot of discussion that happens. It’s very, very interactive. [There are] four modules that are structured that way throughout the semester, and then there are several guest lecturers. I’m very much a believer of real-world knowledge. I invite people to come and guest lecture to talk about how they’re using BIM in the ﬁeld. We actually have two site visits. We’re actually going to observe people using BIM in the ﬁeld. We’ve already done this two weeks ago on our ﬁrst site visit. This is a high-rise project on West Campus, a residential tower. We went and visited their BIM oﬃce to see how they’re using the models in their ﬁeld oﬃce, and then visited the job site to see here’s what they did, talk about in the virtual world, in the 3D model, here’s what they’re doing in the ﬁeld. When they actually see it, and see other people using it in the ﬁeld, it really sparks their interest. All of these diﬀerent perspectives help them cement these concepts. It’s not like they’re just getting a one-sided perspective, it’s [that] other people are showing them how they do this as well. It’s not just one true reality. People apply this in diﬀerent ways. It’s important for them to see that experience. Also, each team of students also has an assigned industry mentor. They work with that mentor throughout the semester developing a case study on a real-world project that uses BIM. As you can see, all of these assignments, there’s nothing that’s very spoon fed, like assump- tions. Everything [assigned requires that] you’ve got to go out and try it. There’s some structure. There’s some material. But you’ve got to make decisions on your own. You’ve got to understand that, in the end, you’re the professional. You have to take ownership for your work. We’re not going to spoon feed you. You’ve got to go after all this data. 64 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD RETURN THRESHOLD: BRINGING THE REAL WORLD INTO THE CLASSROOM Before the semester started in January 2015, in December 2014, I held a brainstorming ses- sion with an industry group called Safety Community Practice. These are about 32 professional safety engineers in this group from all over the world. We had a brainstorming session, over Go- ToMeeting, on what the next generation of safety engineers should know. That’s how I created the topics, the structure of the lectures. It’s not my domain, expertise, but I really wanted to teach that class. But I also wanted to reach out to people that it is their domain of expertise. That’s how the lectures came about. I put together the syllabus. Then for each lecture, I thought about, “How can they do that reﬂection in the class?” Because I don’t want to just read lecture slides, I want them to be able to reﬂect on their own, on that theme. For each lecture, I did something hands-on. It was either a case analysis, which happened a lot, and they really loved it. A real-world case and they have to deal with, let’s say, an accident investigation. What were the diﬀerent steps? How they would do an accident investigation for that case? One day, we used the intersection of Dean Keeton and San Jacinto, right here, [outside] of our building. We considered that an active job site. Each time somebody crossed, J-walked, basically, that was considered a near miss. They basically classiﬁed how many near misses were in that intersection. We were doing behavioral-based safety, that was a theme. They were using a lot of concepts that we had learned throughout the semester applied to something that’s not a construction job site, but you could, literally, think about it as a job site. Because you still have behavioral issues. You could think about a car as being a construction equipment, and pedestrians as being the laborers on the job site. We also went to this job site here, the new engineering building, and we did job hazard analysis, a theme in one of the classes. We went and looked at a set of workers that were doing a speciﬁc task around a column, we just identiﬁed all of the hazards in the ﬁeld, in person. I got several exam questions just from [a] picture I took of this construction site from my oﬃce window that they had to do an analysis on, of a real-world problem. Nothing is memorizing and applying, it’s really understanding the problem, and how do you connect the concepts that we covered in class to that real-world problem? How do you do something that people in the real world, a safety engineer, is actually doing? Like an accident investigation, a hazard analysis, and so forth. MASTER OF BOTH WORLDS AND FREEDOM TO LIVE: ENCOURAGING OTHER ACADEMICS I think the biggest barrier when I presented my approach in the summer of 2015 to other aca- demics teaching BIM all over the U.S., people are just shocked at the amount of work. I think that’s the ﬁrst thing. It’s too much work. Because you have all these mentors, you have all these 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD 65 case studies, you have these site visits, you have all these modules. It’s ﬁve or six diﬀerent soft- ware systems. If people just look at it from a distance, they are overwhelmed, because they’re going to think it’s too much work. I think people are scared of things like that. Most faculty want to be able to not depend on other people. “I want to be able to go to my lecture and just do my thing. If I have to depend on other people, then it’s a bottleneck.” The type of support that I have found helps is a teaching assistant; I have always had one. The teaching assistant helps update the tutorial material for the lab, and helps teach the button pressing in the lab. Because if I had to update all of these, because the software systems are updated every year, every single year... I’ve got to make sure that the right version is installed in the lab, I’ve got to make sure that the tutorial material’s up to date. If I were to do that myself every year, that would be a huge barrier for me to keep doing it this way, because it’s just a huge amount of time. Frankly, I’m not even interested in that part of the process. I do all the other [parts] of identifying the real-world problem that they’re going to be using for the assignment. Identifying the mentors, connecting them to the mentors. Frankly, updating the material, I think, is the barrier. If people don’t have that same kind of support, it becomes overwhelming to teach a class like this. I try to do something, a smaller version of this, in my required undergraduate course, that we have ﬁve diﬀerent structures on teaching. I try to make it very problem-based as well in class, but I don’t use any software systems, which also minimizes that barrier as well. Same thing, I have a real-world project—they do an estimating project. I pick some area around campus, so they can actually go and see it. Normally, it’s little plazas like the Barbara Jordan statue plaza. They do a quantity take oﬀ and a cost estimate for that. Then they have a panel of judges that are all UT project managers that actually worked in the construction of that plaza, and they evaluate the student’s work, the student’s cost estimate. That mini-project is probably the highlight of that course. I still do it. That takes about two to three weeks in a semester. Very hands-on, and it’s completely real world. It’s much better than teaching them how to cost estimate using a very standard problem from the book. It’s boring, and it doesn’t really show them the multiple dimensions that go into the problem. It’s too simpliﬁed. It’s nice to get the students out of their comfort zone, to really make them think, and not just blindly apply things. I’m the only one that [teaches in a hands-on way.] Because most people will say that, “Oh, it’s a lot of work, because we have to get all those projects, you have to get those plans, then you have to get that panel of judges.” Honestly, I don’t think it’s a lot of work. I think the beneﬁt is much larger than the work involved. Once you have a structure in place, all I change every year is the project. But this general structure is pretty much the same. I know if you build relationships with the right people, you can rely on them every time you teach that class. If you just plan ahead, people are happy to help. It doesn’t become that overwhelming. The students really value that, and they really enjoyed something that they can say, “I’ve worked on that project right there.” Barbara Jordan statue plaza, or the Cesar Chavez plaza, or whatever it is on campus. They’re really going to take that and remember that for the rest of their careers. 66 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD Again, people will say, “Oh, that’s too much work.” It is much easier to just get a book, walk to a lecture hall, and just teach straight from a book. Yeah, that’s easy. For me, that’s not fulﬁlling, and that’s not why I chose this profession. That wouldn’t make me happy. I would feel very frustrated. STORIES FROM MY CLASS: TEACHING WITH LEGOS Last Thursday in class, we did a Lego exercise. I can send you the examples. Basically, it’s like a 2D set of drawings, elevations, plans, section cuts, of a 3D model made in Lego. They are in teams of 4, and there are 4 colors in this exercise. Each student is a diﬀerent color. They have to build that model in 3D, but all they have are the 2D drawings. We timed them. We basically see how long it takes for them to build a 3D model. It takes them between 7–10 minutes, which is a pretty long time, if you think about it. But it’s to make a point. There are about 30 pieces, 4 colors, 4 team members per group. They worked together, and they have to communicate their ideas to make sure they’re putting their pieces in the right place. But also the fact that they have to interpret that 2D information, translate that into 3D, that’s also the point of this assignment. The second round of it is I give them a 3D perspective of another model. They have to repeat the same exercise. They still have the same colors, same number of pieces. Now they’re able to build that in 55 seconds to a minute and a half. It really decreases the amount of time. That’s to make the point that if you’re able to communicate in 3D, which is part of BIM, building information modelling, if you’re able to communicate in 3D, your crews in the ﬁeld that are building that will have a very clear understanding of your design, of what you’re trying to build. They’re able to work more eﬃciently, because they’re not spending a lot of time trying to translate something in 2D, which was already translated from your 3D original idea. We run those through, two simulations. Between each one, we reﬂect. We think, “Okay, what did you learn?” In the end, we reﬂect again: “What did you learn?” This whole process was just this exercise, and reﬂection on what they learned. Little things like that I sprinkle throughout the semester as well. I do a Lego exercise in my required project management and economics class too. It’s literally two teams of students, one on one side of the table, another one on the other side of the table. There’s 10 Lego pieces, that start with the ﬁrst person on each end. Each team has a die, they roll it. If you get one, that means that your productivity rate for that day was one unit. You pass one Lego piece to the person next to you. The person next to you rolls their die, and they get three. That means their maximum productivity rate would have been three that day. But since the previous person was a bottleneck, they can only pass on one. Then the next person... We keep doing that exercise. Say the ﬁrst person on the other side got six at the ﬁrst roll of the die, so he or she passes on six. The second person got four. He passes on four, he keeps two in his station. All of the pieces that are left over after that round, then I ask the class, “What do they mean in the concepts that we covered?” Because the pieces that stayed in your 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD 67 station, they’re called work in progress, in construction. The roll [of ] the die of one, that’s a low productivity rate, that’s a bottleneck. If they’re able to play that and see those concepts, it cements it in a much better way. It’s a very simple exercise that takes less than 10 minutes with a discussion in class. It’s more eﬀective than me going through those deﬁnitions in a regular lecture. Then they’re able to really see it, and experience it, and they tend to quickly learn it. And they’ll probably never forget it. MASTER OF BOTH WORLDS AND FREEDOM TO LIVE: INTEGRATING TEACHING AND RESEARCH THROUGH AN INDUSTRY FOCUS I have my niche, which is, I’m very much connected to industry, even from my research as well. My department supports me. I can be productive and can build these connections. People respect me for what I am, because this is what I am, this is who I am. I’m just one person. I can’t separate my teaching person from my research person. I’m one person. My experiences are all combined experience. That’s what’s important. I have to put in the same dedication that I do for teaching in research. That’s the only way to keep teaching cutting-edge as well. Especially teaching something that’s very much information technology. That gets old really fast. You really, really have to be connected to research to keep students engaged, and what’s the most innovative piece of it? Keep them ahead of the curve. That’s the last thing. Just always maintaining that connection between research and teaching. I actually have a student right now, one of Mary’s (pseudonym) Ph.D. students. He’s observing every single one of my classes for his research. One thing that he’s probably noticing is that whenever I ask a question, out of the 21 students in the class, I see at least 7 or 8 hands go up. One third of the class, they immediately put their hands up when I ask a question, because they’ve had plenty of time to reﬂect on the question that I’m asking. I get to know all of them individually, so I tend to ask questions sometimes about their speciﬁc experience. They’ll share that. They’ll be able to communicate that well, because they’ve lived it as well. That’s one thing that’s amazing. You get a lot more participation that way, because they feel more conﬁdent. All I know is that it’s not going to stay the same. My hope is that a class like the one that I teach, the BIM class, is not going to be needed in the future, because it’s just going to be industry practice. That’s what I tell my students. My ultimate goal, my dream, is that I’m not going to be teaching this class in 10 years, because this is just industry practice, there’s not going to be a need. I’m going to have to come up with something new that’s going to be the next big thing in the industry. I’m going to adapt with time. Luckily, I have that luxury of being able to tweak things throughout the semester, between semesters, and think about new courses as well. I think it’s stimulating, also, to teach new courses, because it forces me to think diﬀerently, and to teach things in a diﬀerent way. Because each domain has their own speciﬁcities that require you to adapt to that and try to deliver that material in a diﬀerent way. 68 7. FINDING HER NICHE WITH HANDS-ON, PRACTICAL, AND REAL-WORLD I think I’m still a work in progress. You said [that I’m a] rock star, but I just see myself as somebody that’s just constantly learning, and constantly trying to provide our students the best education that they deserve to have. That just is a work in progress. Honestly, there are still days that I come out of a class and I said, “I could have done that better. Next time I’ll do it better.” It’s always a work in progress. That keeps me motivated. Doing that also makes me come up with ideas for research. Ideas that I have in research become modules, or lectures, in my course. For me, a lot of people say, “Teaching takes away from research. That’s just taking up too much time. I don’t want to do that, because I’m so busy with research.” For me, it’s all one thing. The way that I see it is that I build oﬀ of the experiences that I have in the classroom. That gives me lots of ideas for research, and vice versa. C H A P T E R 8 69 Creating a Community of Collaborators to Achieve Curriculum Change Charles Pierce Narrative constructed by Audrey Boklage, Brooke Coley, and Nadia Kellam I want to share what I think engineering is, because that certainly has changed over time… Engineering is helping people. That’s what I think of it as. We solve problems for [the] purpose [of ] trying to help come up with solutions to problems that impact society. That’s kind of by deﬁnition what we do. Charles Pierce is an Associate Professor of Civil and Environmental Engineering at The University of South Carolina. CALL TO ADVENTURE: TEACHING RUNS IN THE FAMILY My dad was a civil engineer and also taught years ago back when you could teach with your Master’s degree, which is what he had. He taught at URI (the University of Rhode Island) for a few years. I bring that up because I was aware of what his professional trajectory was, [and] most of his time was [in] professional practice, but I know he had some teaching experience. My mom was a nurse, which is important. I think in many ways, I’m a perfect blend of my parents, because I’ve got the technical side from my dad and my mom helped people. I had a pretty good idea that I wanted to go into engineering from high school, [and] into college. My parents never pushed, but I was well aware of what my dad did and I seemed to have those interests. I earned a civil engineering degree from the University of New Hampshire (UNH). It was a reasonably small state program, which was a good choice for me, and I really got to know a lot of the faculty. I had some very important relationships with professors as an undergraduate student. 70 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE SUPERNATURAL AID: GRADUATE SCHOOL ADVICE I was pretty involved at UNH. I joined ASCE (American Society of Civil Engineering) and became president and all those things. I do remember one professor in particular during my junior year encouraged me to look into doing a Research Experience for Undergraduates (REU) program. Of course, at that time, I knew almost nothing about [doing research]. I applied to an REU program at Cornell and was accepted. I did that the summer after my junior year. As a junior, I already had a sense that I would go to graduate school. When the opportunity to gain research experience [was presented to me], I ﬁgured it was a smart move. Plus, at the time, [the market for] ﬁnding part-time jobs in engineering was really bad. Even with my dad being in the industry, he was unsuccessful at ﬁnding an opportunity for me to do an internship. It’s not like I had other options. I went and had the summer experience at Cornell University, which was very favorable. I got a sense for what graduate students did. I think that really set the stage for me to apply to grad school my senior year. I even went to one of my professors and asked him, “Hey, I think I’m interested in geotechnical [engineering]. Are there some programs that you would recommend for me?” Northwestern University was one of them and Purdue University was another where he also had a classmate. I applied to four schools. I applied to Virginia Tech, where my uncle was on the faculty in mechanical engineering, so there was a connection there. I applied to Purdue University, Northwestern University, and Cornell, of course, where I had gained the summer experience. I was accepted at all four and received funding from two. I distinctly remember having a conversation with one of my professors at UNH. He sug- gested, “go where there’s funding. You should be funded to go to grad school.” That meant deciding between Northwestern and Cornell, which were the two that had made me oﬀers. Ultimately, I thought Northwestern was a better ﬁt for me than Cornell, partly because I had attended a fairly rural, small town school in New Hampshire. The thought of being able to go to Chicago and go to school there was appealing. I visited all four schools my senior year to make a decision. I remember visiting North- western [and] meeting the faculty in the geotechnical program, which was my speciﬁc interest within civil and, more importantly, meeting the graduate students. Of course, I didn’t know what to expect, so I’m like, “I’m going to meet all of these really intellectual, you know, above me kinds of students.” I was pleasantly surprised to ﬁnd that there were students I thought were very much like me, which was important in making that decision. That’s not to say that [it] wasn’t the same at Cornell. But, for whatever reason, at Northwestern that really struck me. SUPERNATURAL AID: PUSH TO PH.D. [I decided to attend Northwestern] for the purpose of getting a Master’s degree. [One day after I had applied to] the Master’s program, I received a phone call from a professor there. He said, “Hey, I saw your application. I saw that you applied for a Master’s degree. I really encourage you 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE 71 to apply for the Ph.D., because then you’re eligible for fellowships.” I would not have otherwise been eligible for such funding. I remember thinking, “Sure, I’ll do that. Why not?” [I’m unsure whether I had an] inkling to get a Ph.D. [at that time]. I remember really having to think about that decision, though I was intrigued by the idea of getting a Ph.D. My goal at the time was [to] get a Master’s degree, be like my dad, go into professional practice. That was my intent. I now had a better sense of what a Ph.D. was, which I did not as an undergraduate, and could see what I could do with it, which was to go into academia. I enjoyed doing research, but never thought that was my strength. I really did like teaching. I should probably rephrase that... I liked having good teachers. I liked being a student in classes where I resonated with professors that I thought helped me learn. I do believe much of that wasn’t necessarily from my graduate program, but much of that was from my undergraduate program, because I feel to this day that I had some absolutely fantastic engineering professors in my undergraduate program. I knew very clearly, I could not go do that unless I had a Ph.D. I think [that] had there been more options, like it was back in the day with my dad, I might have stopped at the master’s and then tried to pursue getting a teaching position. But I knew those opportunities didn’t really exist anymore, in large part. That was a big part of my decision making to get the Ph.D. knowing that I had to go through the research process. My end goal was I wanted to be a teacher. I think during my Ph.D. program, one of the things that resonated with me was having the opportunity to be a Teaching Assistant (TA). I think most of us that were Ph.D. students had at least one opportunity to TA. I don’t think it was a requirement, but [being a TA] was certainly an opportunity. MEETING WITH THE ALL KNOWER: AN OPPORTUNITY TO TEACH AUTONOMOUSLY I was asked to TA the soils lab which is pretty common in geotechnical. Once I knew I was going to TA, [I went to the] professor who normally teaches that class and asked him, “What do I need to cover? Just tell me and I’ll do it.” [His response was], “This is your class. You do what you want.” I was ﬂabbergasted by [being given] that amount of responsibility. I was like, “Okay. All right, I can do that.” He just told me to run with it. I mean, he didn’t hold my hand in any way, shape, or form. I don’t think he even came down to the lab with me. He said, “You know where the lab is. Go ﬁnd the equipment. Figure out what tests you need to run.” I mean, he completely left it up to me. Whether he knew it or not, I have no idea, but that was the perfect thing to do for me, because it really did make me think about how the decisions about what to do in a lab class or any class [are made]. Just all the planning that’s required for managing students and managing equipment and thinking about what you want them to get out of it. I’m sure I didn’t do a particularly good job with that at the time, but I remember having to think about it. That was really important, because it conﬁrmed for me that I liked doing those things. Given everything else I was supposed to be 72 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE doing with research, I was spending too much time TA-ing. But it was important to me, so I did. [After ﬁnishing my Ph.D.], I was interested in ﬁnding a place that had more of a balance with research and teaching. I knew I didn’t want to go to a top tier research institution. I just didn’t feel like that suited me the best. To be honest, I don’t even know how I made that distinc- tion. How [was I even deﬁning] a good teaching institution? I don’t know. I think it was more a process of elimination than anything else. Like, “Okay, I know that’s not what I would consider a top tier research institution, so if it’s not, then maybe it’s more teaching oriented. I’ll apply there.” I was minimally informed back then in that process, but probably not as [informed] as I wish I had been. I ended up getting an oﬀer here at The University of South Carolina (USC), which seemed like a good ﬁt. I had a sense from most of the faculty here at the time that teaching was important, and it was valued within the department. That was signiﬁcant for me. SUPERNATURAL AID: FUNDING SUPPORT I came into USC knowing I wanted to be a good teacher. I [was also aware] of the research expectations and [knew that I’d have to] balance that. I was reasonably fortunate to get some grants funded early on. In fact, I think the ﬁrst NSF proposal I wrote was funded. That, in large part, had to do with my collaborator. I was set up with a senior person living in Georgia at the time who had been a faculty member elsewhere and was looking to get back into academia. We were connected and wrote a joint proposal together. He was phenomenally helpful in that process in terms of learning how to write a proposal, which I knew very little about. I had some experience as a graduate student, but not enough. I was fortunate to have had that. I was also able to get some local funding through the Department of Transportation. I was getting grants and [using them to support] students. I felt like I was doing the things I was supposed to be doing at the time, which was good. ROAD OF TRIALS: NEW(ISH) CONTENT I think the [funding success] allowed me to feel less pressured about the [research process] enabling me to spend time on teaching. I came in and was asked to teach a little bit outside of my comfort zone. I was asked to come in and teach a civil materials class with the associated lab. I had a little experience working with cement-based materials and concrete, which was part of this course, but I was not that familiar with a lot of the other content [without referring] back to my undergraduate days. I needed a lot of prep time to learn [the course content] on my own and [be able] to share that with the students. Then I also had the corresponding lab, which I think was very good because it really forced me to understand material behavior. Not only did I have to teach it, but I had to be able to demonstrate it in the lab. I spent a lot of time working on that and then that 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE 73 next semester, I was [put in a similar situation]. I was asked to teach our soils class, which is a junior level class, and the corresponding lab as well. In some ways, that was good because it was the same type of teaching, just diﬀerent material. ATONEMENT: STUDENT FEEDBACK [Starting oﬀ ] at 28 or 29 [years old], I really enjoyed meeting the students, talking to the stu- dents, and trying to get to know them. I wanted to ﬁnd out as best I could whether or not they were learning anything from me. There was one student who was also very willing to get to know me. During the middle of the ﬁrst semester when I was teaching that civil materials class and the lab, I individually asked him, “Hey, how do you think the lab is going? Is this helping you learn?” He was actually honest and said, “Yeah, but I think you could do this, you could do that.” [I found his critical feedback to be] great and was actually happy to receive it. It made a big diﬀerence for me by [enabling me to] understand [his perspective] of what was working or was not working. From that point forward, I always felt comfortable trying to solicit that kind of information from students. That was always an important thing for me, to try to get a sense from the student of what they thought they were learning. ROAD OF TRIALS: COMMUNICATION IN THE CLASSROOM Here I am, ﬁrst year, teaching two classes, teaching two labs. I felt okay about that process. I know I worked hard in developing materials and strategies, although I don’t know if that’s really what I was thinking of at the time. [My conscious focus was more], “How do I try to get this information across?” The teachers that I liked as an undergraduate student were ones that I thought made the class engaging and entertaining. One of my environmental engineering professors, I particularly loved. She was hard and I did not do well in her classes, but I really liked her and I liked her classes, regardless of how I did. I was not ever really good at having a plan for content to cover [during the class period]. [The plan consisted of ] compartmentalized units of notes that [enabled me to know] exactly what was to be taught, [and] when. I quickly realized that [such structure] didn’t suit me, because if students had questions on a concept that took 15 minutes of class discussion, I was okay with that. Many of them were still struggling with basics. I really needed to spend more time making sure they really understand the stress-strain curve, where the stress came from, how it could be calculated, and the diﬀerence between load and stress. I also took for granted students could make the connections on their own. ULTIMATE BOONE: CONCEPTS NOT SCHEDULES I realized I had to step back and make sure they understood the basics. Eventually, [I accepted that] if all I did was get them to understand those basics, [that would be] really good. As long 74 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE as I feel like what we’ve covered they’ve learned pretty well, I feel like I’ve done my job. But it’s still a challenge. SUPERNATURAL AID: CLASSMATE ASSISTANCE A former classmate of mine was also teaching a civil materials class that was more his back- ground. We were classmates at Northwestern and he knew a lot more about cement and con- crete than I did. I asked him for help with notes. He mentioned that he used this little exercise when teaching cement hydration. Cement hydration basically is looking at a chemical reaction between cement particles when they become in contact with water. They go through a hydration process and it’s exothermic; there’s heat released. Sure, I made sure I understood the reactions so I could explain them in class. But I remember thinking, “How do I get the students to better understand what’s happening?” He shared with me that he used atomic ﬁreballs, little candies, to illustrate that process. Basically, it’s a little exercise where you just go through showing several of the chemical reactions while [the students are] sucking on an atomic ﬁreball. You associate where the ﬁreball gets spicy to the heat release. Then once that wears oﬀ, you don’t really notice it anymore, and that is correlated to a decrease in the heat released. I just thought [the exercise] was the coolest thing. I used it in class and I remember people loved it. So I’m like, “Yeah, that’s a really neat idea. I need to do more of this, whatever this is.” ULTIMATE BOONE: CANDY AND PERSONALITY I ended up teaching that civil materials class for a number of years, and over that period of time, I ended up developing a whole series of mostly food-related activities to try to illustrate certain concepts. I have one where I’ve [heated and frozen samples] of Laﬀy Taﬀy. When you pull on the heated sample, it really stretches, and so I tried to use that to very grossly exaggerate ductile behavior. [In comparison, the frozen samples] would become brittle and just fracture demonstrating that behavior. In doing a whole series of little things like that I recognized that students always appreciated when you did things that were a little bit diﬀerent. Whether or not it was actually helping them learn, I don’t know that I knew that at the time, but it seemed like the right thing to do. I ended up trying to create a number of these kinds of activities in all courses I was teach- ing. Never in my graduate courses interestingly enough, but in all of the undergraduate courses I was teaching. I think having been a slightly above average student, I feel like that has dictated a lot of how I teach. I teach in such a way that I’m trying to reach everyone knowing that I won’t necessarily reach everyone. I’m trying to really make sure students understand the most basic principles ﬁrst and then build on those. Maybe that was just going to be my personality in the classroom anyway, but it felt like, “I want to make it interesting and entertaining.” I tend to talk fast and loudly. I deﬁnitely tend 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE 75 to not stand still, and that’s just how I am. Even back then the students commented, “Can’t you just stand still? I’m having a hard time following you walking around the classroom.” [I’m] pretty animated in the classroom. That seemed to go over well, so that was reassurance for me, that I was at least approaching this the right way. Although, I feel like that was just my nature anyway. It might have been hard to change it. I don’t know, but I felt like I was getting the feedback that worked well. FREEDOM TO LIVE: FLEXIBLE SYLLABI I wasn’t teaching things like statics or solid mechanics, which are largely solving problems, doing calculations. I was sort of in this middle, more conceptual. The textbook for my civil materials course was very conceptual. There were certainly problems and equations, but not all the way [throughout the text. In the text] you’re learning about concrete, what it is, what it is made of, and how you construct it. What is steel, what it is made of, how you construct it, so on and so forth. I think it made sense to me [at the time] that I had to do these sort of demonstration activities for them to understand the concepts. It wasn’t just a matter of using calculations to solve problems, that was part of it. But they had to understand the concepts, too. I think that was the breeding ground for me, through what I now know as active learning, to realize that conceptual understanding was really important. I’d always been asking students questions in class like, “Do something. Do you understand that? Are you sure? Let’s discuss it again.” If I was asked a question, I would try to explain it in a diﬀerent way if I could. I think it was always more natural for me to do that. [I no longer] have a schedule in [the course syllabus] that says, “Day one or week one, do this. Week two, do that.” With the way I teach now, I can’t do that because I let my class evolve. Early on, my struggle was internal. I wanted to be that good professor that taught them everything. I would say, “Okay, no more questions. We got to move on. I need to cover this stuﬀ.” I was very good about covering material because I was fast. MASTER OF TWO WORLDS: PROBLEM SOLVING IN THE CLASSROOM I think what’s happened over time is [that] I ﬁnd [questions I pose during class] become more of the emphasis than a side note. That, of course, in turn, has evolved into doing things like work- sheets associated with an activity. Not only do we do the activity, but I may have them complete a worksheet. Maybe that’s individual. Maybe it’s group. Where I am—on the conceptual side in terms of how things have changed—I do a lot more of those sorts of things. I also do a lot more in-class problem solving and I never used to do that. I guess this was somewhat initiated by the idea of wanting to ﬂip a classroom. I got very intrigued by this concept a few years ago. I like problem-based learning. “Here’s a problem. I haven’t touched everything about this, but dissect it. Here’s the problem statement. What do you need? What’s given to you? Ask me 76 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE questions.” That’s what I like to do. I walk around in the room and get questions. Once I get a question that’s been asked a couple of times, I raise it with the class. I love that. It is so much more suited for me. Again, I guess I have just gotten to a point where it’s also [the] content I’m comfortable with, which I think makes all the diﬀerence. I feel like I should be able to answer any question they ask me, but I also feel like if they ask me and I don’t know, I’ll go try to ﬁgure that one out. Again, if it’s in-class problem solving, I usually have a pretty good sense of what kind of questions are going to come up beforehand. I guess that experience helps me. I’ll pick a speciﬁc problem for a reason, because I know it’s going to teach them X and Y when they go through this problem. Instead of me just writing stuﬀ on the board, they’re going to learn it by going through this problem. [I’ll ask], “Does everybody understand the X and Y? Because that’s what’s important from this problem.” I always try to make sure to emphasize that when we’re done. I do a lot of that. ROAD OF TRIALS: IMPROVING THE CLASSROOM There was a group of us in the department, sort of like-minded, who enjoyed teaching but really wanted a better sense of what students were learning, [and] how to do a better job. We sat down to put together an NSF proposal for what was the Course Curriculum and Laboratory Improvement (CCLI) grant program at the time. The purpose of the grant proposal was to develop a new course. We wanted to develop an introduction to civil engineering course that we did not have [yet]. It was driven by wanting to improve the curriculum. We knew we needed a ﬁrst-year course for our students to have a better sense of what they were getting into in the major. That was the purpose, but at the same time, we knew, “Okay, what can we do diﬀerent? What can we do to make this class more unique?” We didn’t want it to be a class with a whole series of PowerPoint presentations on the diﬀerent disciplines of civil engineering and oﬀ you go. We didn’t want to do that. We really wanted to make it a more engaging class. I can’t remember now exactly how we arrived at this, but we did want to introduce technology. More speciﬁcally, we wanted to introduce sensors. I think part of the reason [we wanted to introduce sensors] was that most of us on the proposal did experimental research, understood the value of sensors, and wanted to get that concept across to the students, thinking that [introducing sensors] would help them learn some of the things that we do in civil engineering, some of the things we measure, why we measure them, and how we measure them. We were captured with this idea of critical thinking. I’m not sure that any of us really understood what that meant in the context of engineering learning, but we knew that was an important thing. I do think a lot of it was driven by [reﬂecting on] most of our classes in the curriculum, how students could go through calculations, solve problems and almost never think about the output—never think about the number, the value, does it make sense within some bounds of reasonableness, never think about the units... Of course, we complain about that all the time. Students don’t really have a good understanding of units and how it’s associated with 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE 77 the answer. One of my colleagues, I heard him say this in a class one time a few years ago and I loved it—I steal it and use it now—he explains that in engineering problems, the solutions have a name. They have a ﬁrst name and a last name. The ﬁrst name is the value and the last name is the unit. I just thought that was really cool. I like that because I think it really emphasizes that both are equally important and one depends on the other. You have to understand what units you’re dealing with to make some sense of the numbers. I think that was a big driver for what we wanted to introduce [to] civil engineering students coming into the major—how important that was. Ultimately, that evolved [into recognizing that] in order to do that, you almost have to think beforehand what would make sense for an answer to a problem. I think what we realized is [that] we never give our students a chance to do that [before]. We never ask them in advance, “Okay, here’s a problem. What do you think would be a reasonable answer to this? Don’t calculate anything. Look at it. Try to dissect it. What do you think is going to be a reasonable answer? What’s the order of magnitude? Are you going to be in the thousands? Are you going to be in the thousandths? Like, where are you?” It’s amazing when you start really stepping back and asking students these questions, how far oﬀ some of them can be. You realize, “Oh my gosh, I really need to help these students understand. Get a sense of what they’re doing.” ULTIMATE BOONE: WITH FUNDING COMES CHANGE I think we were fortunate to get that grant funded to develop that course. I think we oﬀered it for the ﬁrst time in 2007, if I remember correctly. That changed everything for me. Getting that grant, having to develop this novel course in a very unique, problem-based learning teaching style [was a signiﬁcant opportunity. Additionally], working on that proposal with my co-investigators gave me a new appreciation for collaboration and what that could really mean. I don’t think we even knew that at the time to be honest. I don’t know that we even used that terminology in the proposal, but that’s essentially what we were doing. [We were giving] students these realistic engineering problems and ask them to estimate a solution knowing that they knew nothing other than any prior knowledge they might have had about how [to approach the problem] and solve. Our purpose was [to] get them to think about the problem, what are the factors, and what’s even important. One of the problems I developed for the class was to introduce students to what geotechnical engineering is within civil engineering. I wanted to pick something that would resonate with the students. Again, this was ’07. I picked a problem that was set in the context of Hurricane Katrina and the levee failures, because that was very recent at the time. I knew that was something that students would understand and were aware of. Basically, through a long process we decided we wanted to ask the students a problem related to the failed levee section in New Orleans. It needed to be rebuilt and we speciﬁed the length. We said, “It’s a 100-foot long section of earthen levee that needs to be rebuilt. How much soil do you need?” I speciﬁed in tons because we had a long discussion about assigning 78 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE units. We said, “Okay, just to keep it consistent, let’s ask for tons of soil,” which is something that would probably be used in the ﬁeld, thinking in those terms. “Okay, I didn’t give you much other information. What do you need to ﬁgure out? First and foremost, draw me a levee. What does it look like?” We had a little bit of discussion about what they were, but not a lot. I wanted them to see what they visualized, [which the research team] thought this was important, this whole concept of visualization. What they saw in their mind when they thought of a levee was fascinating stuﬀ. You’d get some really nice two-dimensional drawings with dimensions and units as well as some abstract looking things that I wasn’t sure what I was looking at. You’d get some that were asymmetrical versus symmetrical. You’d even get students who would draw three-dimensional drawings. Then you’d start to realize, “Wow. Now, you can start asking questions about why did you think about that or why did you choose this?” As part of that, getting to think about, “Okay, so you have a shape. How do you ﬁgure out the weight?” Keep in mind this was for freshmen. Really, we were just trying to introduce them to what civil engineering was and what we felt like was the process of engineering problem solving. The whole purpose of that course was to have opportunities for the students to explore and reﬁne their answers. Clearly, one of the things we realized very quickly is students can’t really visualize a ton of anything. You asked them this fairly large magnitude unit, it’s hard for them to think about. The other thing that was very interesting and that was dealing with earth and a levee. One of the things I wanted them to learn from this whole exercise was, “Okay, in civil engineering, when you’re a geotechnical engineer, you work with building and designing earth structures using diﬀerent types of soil.” There are diﬀerent types of soil from an engineering perspective. There are gravels, there are sands, there are silts, there are clays, primarily what we work with. The [diﬀerent types of soil] have diﬀerent properties, which is ultimately what they would learn later on as a junior, but I always wanted to expose them to that. What was interesting was how many students were like, “Oh yeah, soil that’s like the stuﬀ in your yard with the grass, the top.” They thought that you’re building this whole levee out of top soil, organics and grass. But, it didn’t occur to me that that’s what a lot of students would think. You don’t want to work with organics at all, so it was perfect. It ultimately [presented the] opportunity for them to ﬁgure out, and me to reinforce, why you would never want to build using these kinds of soils. They actually ended up working with some soils. I basically brought the four types of soils: the gravels, sands, silts, and clays. They would work with them and learn what the density was. They also learned what aﬀected the density, which was the other thing I wanted them to ﬁgure out. APOTHEOSIS: ENCOURAGING CRITICAL THINKING One of the most important things for them to walk away with for me conceptually is that when you work with soil, soil density changes. It’s not a constant. That for me was a huge change from the activities and trying to get students engaged. I realized that capturing what they thought they 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE 79 knew, like actually getting that written on paper, was so important. Until you get them to write the stuﬀ down, you have no idea. It enabled me to look at it and see what they thought, giving me the opportunity to correct, or better yet, giving them the opportunity to self correct, which [was the intent behind] how we set up a lot of those exercises. From that point forward, it made me realize that doing worksheets and those sorts of things in class, not for grading purposes, [but for understanding], was critical. It’s participation. I make that clear. “Do your best. Provide me your best set of answers. That’s what I’m interested in. This is not for a grade,” which in that freshman course, it actually works reasonably well because they’re ﬁrst year students and they don’t know what to expect. We tell them, “Hey, this is how this class goes.” They’re okay, they’re on board with it. Ultimately, we didn’t grade them until the very end documenting this whole process of what they’d learned. We essentially did [what ended up being] a report. “Write a report. Give me a ﬁnal answer. Explain to me why you think that’s a good answer.” What we also did in those reports, which I really like, is explain the process of how your answer changed during that time period. Of course, some of them were better at this than others, but we forced them to say, “Okay, the ﬁrst day I guessed it was one ton and then I realized that’s not possible because I was assuming this, that or the other.” Whatever they thought they knew. “Now, I know a better answer is, let’s say, 5,000 tons.” We wanted to force them to step back and think about what they’d actually learned through that process and document it. I think that process has become infused in basically every class that I teach now, [and every class I teach now] is using that approach. Active learning, worksheets to document [the learning experience], and in-class problem solving. ULTIMATE BOONE: TEACHING AWARD AND REFLECTING ON MY JOURNEY [My teaching has been recognized by my academic peers]. I was nominated for the Mungo Undergraduate Teaching Award, USC’s highest level award for teaching, and I had to prepare a statement. I spent a lot of time thinking about that statement [for the Mungo Undergraduate Teaching Award] and [decided that I] wanted to share [about] why I got into teaching. Maybe this was subconscious until that time, but it made me realize that, I think in many ways, I’m a perfect blend of my parents because I got the technical side from my dad and my mom helped people. I had no teachers necessarily in the family, but I think those two characteristics brought together sort of described me, because I do look at teaching as more than that. I don’t necessarily want to be a good teacher. I want to be thought of as a good mentor. As a person who’s there to help students in this whole process of being an engineering student. I’ve been working more in the past few years with K-12 teachers and students, and part of the reason for that is I want to share what I think engineering is, because that certainly has changed over time. You know what? Engineering is helping people. That’s what I think of it as. 80 8. CREATING A COMMUNITY OF COLLABORATORS TO ACHIEVE CHANGE We solve problems for [the] purpose [of ] trying to help come up with solutions to problems that impact society. That’s kind of by deﬁnition what we do. MASTER OF TWO WORLDS: COLLABORATION IS KEY I’m tenured, [but I value collaboration]. I almost don’t want to write any proposal that isn’t a true collaborative eﬀort with people that I know are just as bought into the research idea as I am. [My colleagues and I] always put out a proposal I’m very pleased with, whether it’s funded or not. I feel like we do a nice job. Man, I love that. It’s interesting, because for me, that is so intellectually stimulating, which is what I think most people want out of being in academia. You have that freedom, that opportunity to choose how you want to be intellectually engaged. This stuﬀ is fascinating to me because I feel like I don’t know enough about it, so I want to explore it more. Having people to share those thoughts and not having a single concern whatsoever that someone is going to say, “That’s a stupid idea.” Someone may say, “I don’t think that’s a good idea and here’s why…” I’m ﬁne with that. To be able to do this type of work on pedagogical strategies and curriculum change, [you want to be a force]. I cannot do this solo. What’s the impact going to be if I do one thing in my class? The collaboration with the seven or eight faculty I’ve worked with has been the best part. It makes a huge diﬀerence for me personally to know that there’s a decent size group of faculty that I brought into writing these kinds of proposals, to doing this kind of work, to [recognizing its] meaning and potential impact. That goes a long way. I feel like I am constantly learning about learning. I’m at the point where I’m gaining some knowledge about student learning, how students learn, what’s eﬀective for them, but not nearly enough. I deﬁnitely feel like the next step for me is getting a better handle on how to assess that—how to really determine that what I’m doing is eﬀective in the learning process for the student. We’ve been very successful in developing the classes in the way we intended to and have collected data on that. Now, I feel like we have so much data that while we’ve looked at some of it, I need a better sense of how do I extract from this solid evidence of what worked and what did not work? It is interesting. I question myself all the time now when I do something in class. I ask, “I wonder how eﬀective that was...” I still have tests to see what concepts they’ve learned or what kinds of problems they can solve. That’s all good, but I want to know more about the process the students go through. I think that’s where I want to move forward—getting a better handle on how to do those things, which I think should make me, and others, a better instructor. C H A P T E R 9 81 Teaching with Advocacy: Buﬃng the Talent to Break the Mold of the Monolithic Engineer Matthew Fuentes Narrative constructed by Brooke Coley [I want to] empower others to do those things. I don’t need my face on the cover of X, Y, Z. I would like my students’ faces to be there, wherever they are, and to be representative of those talents that are really sitting around, and not being polished, if you will. Yeah. So, I kind of think of faculty as more of park rangers, and this information as just kind of like the parks. It’s not that faculty are less important. It’s just this idea that there’s this huge landscape of information that students have to navigate. They can consume it anyway they want, but it’s really damn nice sometimes to have a park ranger around to ask those questions, to make those connections, to see stuﬀ that maybe you would not have really looked for or at before. I think that’s really the role of the faculty member, is that guide, that park ranger if you will, to this information. Matthew Fuentes is an Engineering Faculty member at Everett Community College. THE CALL TO ADVENTURE When I was an undergrad, I was hyper-focused. I wanted to be an aerospace engineer. Nothing was going to stop that. This was what I wanted to do. It’s sort of like when I started exploring in grad school, which is completely reverse of what most people do, it was, oh maybe I don’t want to do, not that I don’t want to do this, but I am interested in a lot of things now. So, I started exploring more, taking more computer science stuﬀ, taking some more advanced math, and some algorithms, and just kind of going all over the place. 82 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD I think I got the hook for teaching when I was a tutor back in undergrad. I was a math tutor, [for the] math department, and that’s where I started to really focus more on student- centered learning than just the faculty- or teacher-centered learning paradigm. That more one- on-one, walking you through the process. I’m a pretty social person, so I think that [the] social aspect of it—the human aspect of it—was what really kind of struck me at the time. I guess fast forward a little bit. When I started teaching, I started teaching actually in graduate school when I was working on my Ph.D. I’m a Ph.D. dropout by the way, so you don’t have to call me doctor or anything. I guess I realized I didn’t know what I wanted to do, which probably scared me a lot. Because at the time I guess I wouldn’t admit to myself that that was true, and I wouldn’t admit that I wanted to change. The reason I left was not because I didn’t feel supported. Actually, that’s kind of an odd thing. I deﬁnitely felt supported. The reason I left was because I guess I ﬁnally recognized that I wasn’t there because I wanted to do this particular research. I was there for the glitz and the glamour, and I didn’t know exactly what it was that I wanted to focus on at that moment. And I really liked teaching, so why was I hyper focused on this if I wanted to teach? I made the choice to move out West with my wife and just quit everything. I thought, “hmmm, I’ll take a wild risk.” I had never really taken a risk like that, so I’ll give this up. Of course, friends and family were like, “What the hell is wrong with you? You’re giving up your RA [Research Assistant] fellowship to go live in an apartment in Seattle?” [I was] like, “Yeah, but my wife will work at Microsoft, so we’re ﬁne, and I get to plan the wedding. That sounds fun.” It was nice. It was nice to change. I think it was really good for me to make that change. I think it was hard at ﬁrst for me to make that change, because I had always been the hyper focused, motivated ... I don’t know, win with all costs comes to mind. It’s like, you know, publish as many papers kind of person, to what am I doing again? [I] started to reﬂect and [tried] to recognize what motivated me and made me really happy and appreciate things. I think it made me a better person doing that. One, it’s fun to say that I’m a dropout from college. It at least starts an interesting conversation, but I think it helps me sort of make peace with the fact that I didn’t need to be in that role to do what I loved to do. I didn’t need to be a tier-one research faculty leading a research team, especially since I thought there was a lot of really talented people that didn’t do that, or really didn’t get that opportunity. I started to feel like, well I wonder how much of my success also is because people trust me because I look like a typical engineer? SUPERNATURAL AID: LEARNING TO TEACH IN A STUDENT-CENTERED WAY So, when I was working on my Ph.D. I really liked the teaching aspect, and my advisor at the time, he was pretty big into engineering and pedagogy. In particular, [he was big on] bringing things into the classroom to make it more, I guess, student-centered. More hands-on was his real approach. What was kind of interesting about that experience was I was his student at one 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD 83 point in time, and then I was kind of his colleague at some point in time where I was in the classroom with him. I kind of saw both sides to it, which was kind of a cool experience. The class that I got him for, and that he was really interested in, was Mechanics of Materials. [At] some places they call it Mechanics of Solids or Solid Mechanics. It’s kind of, I’d say, one of the more visual of the engineering courses. It’s pretty hands-on. It’s pretty visual. [And], it’s a pretty old part of engineering. His take was, “Well, why are we teaching such a hands-oﬀ methodology, you know, this lecture based [approach]? Let’s talk about these problems, and let’s really bring in some tangibility to this.” That’s probably where I started to really switch [my approach]. I not only liked teaching from the standpoint of bringing stuﬀ into the students, but I liked learning in that environment as well. I think the way that I have approached it is more along the lines of, in today’s world, faculty aren’t this big ball of knowledge anymore. You can ﬁnd that information anywhere in the world. It’s accessible by anyone. So, I kind of think of faculty as more of park rangers, and this information as just kind of like the parks. It’s not that faculty are less important. It’s just this idea that there’s this huge landscape of information that students have to navigate. They can consume it anyway they want, but it’s really damn nice sometimes to have a park ranger around to ask those questions, to make those connections, to see stuﬀ that maybe you would not have really looked for or at before. I think that’s really the role of the faculty member, is that guide, that park ranger if you will, to this information. I think making them more self-suﬃcient and self-reliant is important for when they get out into the working world and get to do their own things. They become lifelong learners. THE CALL TO ADVENTURE: ASPIRING TO TEACH STUDENTS WHO ARE LESS PRIVILEGED So, I started teaching Physics at a community college. Why did I start teaching at a commu- nity college? I think for me one of the other big light bulb moments was recognizing that not everybody’s educational experience was smooth. Not everybody had the same opportunities as I did—a middle-class white man going into engineering—people kind of expected that of me in some ways. [As an example], I met a guy in the computer lab in the middle of the night, [who would later end] up becoming my best friend, and he was struggling with some stuﬀ, with some programming. I ended up helping him out and chit-chatting. Long story short, what I sort of came to realize from him was [after spending] three years at a community college, he transferred to the University of Tennessee, where I was, to ﬁnish his aerospace degree. [He] now works for NASA. The part of the story that really stuck out to me was when he started, he was an auto mechanic and he told the guys in his shop, “I’m [going to] work for NASA as a rocket scien- tist.” Of course, they thought he was a little crazy. What I really appreciate about his story was starting from essentially [the] pre-college math level, and then becoming essentially an active rocket scientist at NASA. That’s what he does now, and we actually collaborate. And that’s the kind of opportunity I wanted everyone to have. 84 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD And so, when I realized how much of a diﬀerence faculty really made in his life and him transitioning from that world into university, I sort of changed my focus on going to more of a four-year school to, all right, what can I do to be in this, I’ll call it the transitional college—the open enrollment colleges? Universities know [their] baseline, student-wise, because you have entrance and admissions processes to go through. [But], what about all those other people that want to get to that point? That’s where I really—I kind of [decided], ‘You know what, I should really try out this community college thing,’ and so I started teaching at a small school. [I] started teaching physics at Cascadia Community College. I think they hired me mostly because they had an emergency ﬁll. Let’s see, I was hired a week before classes started, and it was courses that I was pretty familiar with, so I was ready to go. It was a pretty easy thing for me to start up. I think it was really in Cascadia that I guess I experimented a lot with diﬀerent styles of teaching, and moving into the, how can I best empower my students to be these self-centered learners? How can I get my students to be empowered? SUPERNATURAL AID: A MENTOR WHO HELPED ENCOURAGE EXPERIMENTING EDUCATIONALLY What I really liked about the college that I started in was Cheryl Barnes (pseudonym)—the faculty member that recommended me—was actually the person that hired me. She’s the type of person that’s sort of like, “Yeah, try out whatever you want, go for whatever…experiment.” She’s very much into experimenting educationally. I think [her inﬂuence] and that experience just really helped me grow into an I-can-do-whatever-I-want [believer], teaching wise. Let me try some stuﬀ out. Let’s see how students react. What I really liked about what Cheryl did was she used the Physics by Inquiry, I think is the name of the little textbooks. It’s really this motto of getting students to, in some ways, answer their own questions. You can ask probing questions, get them to work in groups, and get them to sort of discover all of these nuanced ideas to make the “aha” connections. I think growing up academically in that teaching system with her gave me the framework to start branching out from that. Because that [was] physics, but engineering has been very traditional. And so, it brought out more of the, “huh, well I wonder what kind of things actually do work in engineering?” STORIES FROM MY CLASS: GOING OUTSIDE TO BRING OUT THE INQUISITIVE MIND And so, I started doing strange things. When I say strange, [an example is], I took the class outside. I taught Mechanics of Materials in the spring and it wasn’t raining here. So, I went outside, I brought some sidewalk chalk out, and we had lecture on the sidewalk. Part of the fun was we got [to be] outside. But, [also], there was some interesting spirit of literally walking 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD 85 through the steps, because you could write down a problem, have it ﬂow, and really make students walk through the steps of a process. They couldn’t fall asleep standing up, so that’s a good thing. It actually, what I found was, it somewhat brought out this, I don’t want to say childlike experience, but kind of the inquisitive nature of the child mind, like this “oh, huh, I wonder what would happen with this,” when we did that kind of experiment. It took them out of the classroom, “I’m just going to be absorbing knowledge brain,” to “huh, okay yeah I can do this!” That was kind of one [part]. I think another part of that was bringing engineering from an enclosed room [to] out in the open, too. Maybe in some ways to socialize engineering and engineers. My real hope was that passersby’s, which sometimes happened, would just kind of stop, and listen, and be interested in engineering, and ask students questions, and the students would answer questions. That’s my utopia that didn’t quite take shape, but it did have some strange impact in that other people would notice, and they’d say, “Oh, that looks complicated.” Then it would be an opportunity for me to say, “Well, you know, if you take this path and learn these things, it’s interesting. It might be complex, but you can, you can totally learn this, too.” I don’t have any data to say it totally reshaped all of these mindsets. But, I did like the camaraderie it created with my students. I did notice that they felt a whole lot more comfortable when they saw me doing these kinds of strange things to ask questions—to ask questions maybe they had been afraid to ask before. ROAD OF TRIALS: FINDING A FACULTY POSITION AT A PLACE WHERE I CAN MAKE A DIFFERENCE I was associate faculty at Cascadia for over three years, and they didn’t really have the funding to put in a new faculty position. We were right in the ﬁnancial crisis of 2000 something or other. I don’t remember the date now. The state had frozen the budget, and so they had a hiring freeze for a few years. By the time they actually did have a position open, there was a position open at Everett, which was just north of us. I started teaching at Everett again, hmmm, this is a theme. I got a phone call over the weekend and a faculty member was pretty ill in Everett, and I had made some pretty good contact with the faculty up at Everett, and they were like, “Uh, so Matthew, we know that you teach these particular classes down at Cascadia. Is there any way you could come ﬁll in midway through a quarter on a class? Because we trust that you could do that.” I’m like, “Wow, I appreciate that you trust me.” And, “Sure, why not?” I did, and it worked out. One of the reasons that I left Cascadia and went to Everett was really the students I felt like they were—the word raw comes to mind or scrappy. So, Everett in many ways is a pretty rough city. Maybe in the news you’ve seen the city of Everett actually sued the drug company for the opioid epidemic, so we have a really nasty epidemic in Everett, and really—Snohomish County, which is the county that this particular school lives in. One of the kinds of interesting things is almost all [of ] the students there start out in pre-college math, pre-college English, so not very prepared students. I guess in many 86 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD ways they are the students that represented my best friend, the kid from Flint. It really kind of felt like that same group of students. The rough and tumble group as I call it sometimes. I do feel like in many ways the program was a diamond in the rough, too—the engineering program out there. It was one faculty member when I started. No, I guess it was two, two faculty members when I started, to now we have ﬁve tenure-track faculty. Some of us are tenured, some of the others are still tenure track. And four associate faculty, so we’re a really big department now, and just becoming this kind of center of hands-on engineering education. ROAD OF TRIALS: BECOMING TRANSPARENT ABOUT WHO I AM In one of our intro engineering classes—so one of the things that my colleague and I did when we ﬁrst joined Everett was—we completely changed the ﬁrst-year experience. We made it a lot more hands-on, a lot more tiered, so that we’re taking you from wherever you’re at and getting you up to sophomore-level engineering courses, in theory of course. But, not just we’re going to spray you with a bunch of knowledge and expect you to grow from there. I appreciated the challenge. It deﬁnitely pushed my teaching limits I would say, going to Everett. I don’t want to say the students were less receptive of my quirkiness, but they were, I guess, more suspicious of it. Who is this weird guy? It felt like it took longer for students to buy into sort of my oddball schemes. Yeah, and I think I had to adapt a little bit, too. I had to better understand that a big chunk of my students in Everett are on the verge of homelessness every day. I guess the point is I had to academically grow, and change with that group, and meet whatever that need was, but still maintain this idea of empowering, and student-centered learning, because it felt like that was one of those things that could help a lot of these students out. I think a lot of students at Everett just, I don’t know if they’re not good at reading between the lines, or if they’re not ... They don’t know, so it’s really good for you just to tell them what it is you’re thinking, and why you’re doing stuﬀ. Because a lot of them don’t have experience with college, or really very good experiences with the education system at all. I guess I became a lot more honest and open about who I was. STORIES FROM MY CLASS: HELPING STUDENTS OVERCOME IMPOSTER SYNDROME AND BECOME MORE ENGAGED I usually talk, so that brings me to the whole conversation of, “Hey what I expect in the classroom is to have conversations. If something comes up, you need to talk to me, we need to communicate. We’re a team here. I know that all kinds of things happen throughout the quarter. The big thing that you can do is communicate with me. Let me know if something’s going on, this, that, or the other because I’m here to help you.” I give them the speech about, this class is all about you learning something new, so it requires that you ask questions, don’t be afraid to ask questions. 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD 87 I have a little stamp card that my wife and I came up with, a system. She’s a professor as well. So, we came up with this little participation stamp card, and I give the spiel to the students like, “Oh, you need three stamps on this card.” It’s like a frequent coﬀee customer card is what it looks like that I put pictures of bunnies or my pets on, so they already know I’m a little diﬀerent, right, when I’m giving them these. So, I give them the card and I say, you need three by the end of the quarter to earn your participation points, and anything above the three you can earn potentially bonus points on assignments. I explain to them I really want a way to incentivize you participating. It’s good for me and for them because it’s something tangible for the students that they can sort of validate themselves that they participated—that they are doing more stuﬀ. It’s also a way for me to point at something physical to say, “Hey, yeah, um, you want, you want me to go out of the way to help you with this, yet you really haven’t shown a lot of eﬀort in the course. You know, what gives here?” And now, I have sort of a physical record of what you’ve been doing or what you haven’t been doing. I think they appreciate maybe that I’m just honest with who I am. At least that’s my hope, that they recognize that you don’t have to be afraid to be an individual, and you don’t have to be afraid to learn. There’s no stereotypical type of person that needs to be in this classroom. So, it can come around to the maybe they have the imposter syndrome, or something like that, then we can have a conversation. I think it’s that aspect and those conversations—really directed conversations with my individual students—that have helped me transition, I would say. I think even if I were to go back to Cascadia and teach again, I would probably take all of that new stuﬀ, and directly apply it to Cascadia as well. Yeah. Now I think I’m a little bit more focused on what I want as outcomes, and what I want for them in terms of helping them develop. STORIES FROM MY CLASS: TEACHING THROUGH MAKING AND FAILURE A good example of things that I think work pretty well is in the last of our series of intro classes, it’s really kind of a maker’s class, so all the students get a kit of sensors, an Arduino, and we have a 3D printer in the room. We set up the teams to be essentially, I would say, startups. They build two prototypes throughout the course, so two projects, and along with those two prototypes they learn how to program. They learn some basic team building skills. They learn how to problem solve. What I like about that class and what I think works pretty well, is giving students this freedom to search, try, ﬁnd, explore, experiment, and have things fail. Failure is totally an option, and I think a great way for them to learn [is with awareness of ] how hard sometimes things are to implement. Of course, you don’t want it to be so much of a failure they learn nothing and they sort of unlearn everything. But, if I can, in those projects, get them to at least keep trying stuﬀ—and to get stuﬀ to work pretty well, and to have some failures along the way and ﬁx those failures—that’s the success. 88 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD ROAD OF TRIALS: INTRODUCING Simulink® BEFORE IT HAD BEEN DEBUGGED One of the things that was a total disaster in that class early on was we had this—well there were a couple of disasters that happened. One, well, I think it was my doing here. I thought we were going to do this awesome thing. We were going to teach them MATLAB®, but I was going to teach them how to use Simulink®, and we were going to have the hardware software interaction. It was going to be amazing. [Instead] it was a disaster. Because Simulink®, at the time, had just unlocked the capabilities for Arduino, and I should’ve talked to the company beforehand, before making that decision to have students go down that route. There had to be a lot more debugging that was advanced for them that they couldn’t really handle with the tools that we gave them. It wasn’t such a seamless experience for what we were trying to have them do. I guess early on it was a reminder to me that something that was important for students in the early part of their career was having something that was challenging, but didn’t sort of make it seem like it was impossible. In this, I think, early iteration, my guess is that some students sort of felt like some of the robotics stuﬀ was impossible, right? Unattainable. That was not the message I wanted them to get. So, like, crap, I made this worse, great. I tried to contextualize it and say that, “This class is an alpha prototype,” you know at the time, “and we’re going to do some things that probably won’t work, and let’s just play. Let’s see how it goes.” I tried to remind them like, “Yeah this was terrible. I’m sorry.” I think they got okay with that. They got through that. ROAD OF TRIALS: UNCOVERING BIASES AND EXPECTATIONS AND A NEED FOR ENGINEERING TO CHANGE, CULTURALLY I used to get interesting feedback all [of ] the time in my course reviews, was something like, Matthew is really approachable, blah, blah, blah, awesome. His tests were crazy hard. He expects a lot. What I was getting in this feedback was students felt blindsided by, I’m a really relaxed person face-to-face, but not technical competency wise. That was hard for me to deal with, especially at ﬁrst. I was like, wait, being nice and being technically competent are exclusive? I don’t understand. It started to click a little bit more I think when I started seeing what my wife’s experiences were. Interestingly enough, we’ve taught the same class before, in the same quarter. She would get dramatically diﬀerent [evaluations]. I think one of the interesting things that happened was seeing how her students, I guess, expected her to be nice, like personality wise [because she was a woman]. Seeing how students reacted to her, because she’s deﬁnitely ﬁrmer than I am, I guess what I noticed was, if I were ﬁrm or looking at some of my coworkers who are pretty, I don’t want to say they’re rough, but they’re very strict—they have very strict schedules, they have a very strict classroom, style-wise—students never complain[ed] about it. But, when someone like my wife is strict, she’s not really that strict, but she runs the classroom in a diﬀerent way than maybe I 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD 89 do, the students react, I’ll say, quite negatively to that personality type. I guess what it’s kind of started clicking in was students’ expectations on things like the gender role of the faculty member in charge of the classroom. When I back up to that mismatch of me face-to-face versus the technical competency or capabilities on exams—back to those ﬁrst comments—I guess I started to recognize that it was some kind of me peering into their biases or expectations. I don’t have a good answer for that, but I think it helped. Those comments happened early in my tenure process at Everett, and I think that’s where I started to become a lot more upfront with who I am at the beginning of the course, and lay it out, and not be afraid to talk about things if it arises. It’s just that I feel like the world is changing, and engineering needs to change, culturally. ROAD OF TRIALS: EXPERIENCING MARGINALIZATION THROUGH A LAST NAME CHANGE AND BECOMING AN ADVOCATE I can’t lie, having seen the world through my wife’s eyes a lot more, she was at Microsoft for ﬁve years, and I saw indirectly how people reacted to her. I guess it sort of broke down my utopian vision of everybody lives with kitty cats and unicorns, and everything works great, right? [I went from thinking] there [are] no real problems, to wow, there’s a lot more to this than I ever realized. There’s a lot more to what people deal with on a day-to-day basis then I realized. I think the other part of that picture, of changing our expectations for what an engineer looks like is even a small part of what I experienced in changing my last name. Until I changed my last name, and I guess I started to feel—a couple of experiences. It’s not uncommon that people ask where I’m from. I’ve had people say, “Wow, you’re really white.” Like, no one has ever commented on my race. What the hell? It was such, I guess, a shock. I really didn’t expect that. For 30-plus years of my life, I had never had any comments like that. Now to suddenly, by a switch like that, [be exposed to people], I could see why it was annoying and why it was qualifying. It was sort of that kicking in like, well now, are you going to qualify that? I mean like now do I become a Hispanic engineer instead of an engineer? I think it was really eye opening for me. It was kind of like trying on something new. It’s like putting on a new face almost. I never anticipated having those experiences in that way, and being so directed. That’s what was so shocking. But I think honestly looking at myself, I don’t think I fully understood it, until I experienced it. While I can take that with the knowledge that I have of going through life I guess in a diﬀerent skin, if you will. I can parse that now because I kind of know better. But, I can’t imagine going through the educational system and having to deal with that and learning new things all at the same time. I guess to bring it all back to the classroom environment, it’s that kind of conversation that I want to have happen in engineering classrooms, because I think those are important conversations along with the technical. Now, I know that you can’t spend all the time in the classroom talking about these experiences, but it’s important for students to at least be aware. For a long time, I struggled with, “well, all right 90 9. TEACHING WITH ADVOCACY: BUFFING THE TALENT TO BREAK THE MOLD yeah, but what do I do?” I really thank my wife for saying, “Yeah, but you have a unique role as the stereotypical white male in engineering to be able to stand up and do something about that, right? You can be an advocate.” I’ve tried to do a lot of soul searching on [diversity and people assuming everyone else is like them]. Quite frankly, I was thinking back to one of my roommates in college. He was also an engineer. He ended up quitting. [He is] African American, he was my neighbor at one point in time and we were really good friends. Now I go back to that a lot and think why was he not successful? What was it? I really wish I would have just asked him the provocative questions like, “Hey man, what’s going on? You feel alright? Something going on?” Maybe I just am forever guilty. I guess I still always come back to I think people just don’t have enough real conversations. They don’t ask about how certain actions or things might make someone uncomfortable or something of the sort. I don’t have an answer for changing [that]. But, I at least want to have those conversations in the classroom. So, it may be over the course of my lifetime the needle is moved, right? If we make some progress, then we’re stepping in the right direction. Maybe it’s some part of me like, “Oh, he took his wife’s last name, hmmm, maybe I should think about women diﬀerently, or relationships diﬀerently. He’s interested in other cultures…” You know, maybe some part of my spectrum they’ll at least take away from the classroom and maybe change a little bit, I’m hoping. Plus, being technically competent. APOTHEOSIS: EMPOWERING STUDENTS I recently met with a few of my former students from those—this is kind of an interesting aside—some of my former students that I had during that timeframe at Cascadia. And quite a few of them [now] have advanced degrees. One of them is ﬁnishing up his Ph.D. in civil engineering. Another one I just spoke to a couple weeks ago, he ﬁnished his Master’s in four quarters in mechanical engineering. I think the great thing about these students, in particular, was that they were not very engaged. They didn’t know what they wanted. They were pretty sloppy with their work. If you looked at them as a snapshot in a particular quarter you would say, “Yeah, they’re not going to be successful.” What I really liked was that they ... I don’t know how much a part I was in this transition, but at least I appreciate Cascadia being a part of this transition in them to let’s say develop. Yeah, so I think that was just kind of looking back and seeing how I was as an educator, and seeing where those students ended up, yeah it feels good. [I want to] empower others to do those things. I don’t need my face on the cover of X, Y, Z. I would like my students’ faces to be there, wherever they are, and to be representative of those talents that are really sitting around, and not being polished, if you will. Yeah. C H A P T E R 10 91 Conclusion and Lessons Learned Nadia Kellam I hope you have enjoyed reading these stories of engineering faculty and their diverse stories of embracing active learning strategies. To me, these stories highlight the complexities inherent in stories of change. Of these eight stories, there was not a single one that was simple and straightforward. This was part of the impetus for sharing these stories as people are not born good teachers; it requires work to become good teachers. While these stories show the diﬃculties in becoming exemplary engineering educators, they also highlight the beneﬁts of changing our ways of teaching. As I was reading through the chapters I noted some emergent take-aways that strongly resonated with me. This is not meant to be a comprehensive list of lessons learned. In fact, I am very interested in lessons that struck you as you read through the stories and anticipate that people at diﬀerent points will appreciate varied aspects of these stories. LESSON 1: IMPORTANCE OF HAVING A COMMUNITY A lesson that appeared throughout many of the narratives is the importance of having a com- munity throughout the process of improving your teaching. Sara reﬂected explicitly on this in her narrative when she acknowledged the support of her teaching-focused group of all women where she was able to hear the accounts of others suﬀering through the same challenges and feeling assured that, “Oh, it’s not just me, I’m not alone.” This larger network of women enabled her to not only learn content that would aid her in her pedagogical approach, but also serve as a critical body of support that would empower her to “get through that” period of her journey. Charlie also described the importance of collaboration and community in his journey. Much of his personal satisfaction came from, for example, writing collaborative proposals with his colleagues in support of their teaching. He found that to be intellectually stimulating. He also discussed that making changes in a silo would not likely prove eﬀective in achieving the scale of changes possible within an engineering program; Charlie wanted to have impact and learned early on that to do so required a community of like-minded individuals. 92 10. CONCLUSION AND LESSONS LEARNED How can we all incorporate this lesson into our teaching journeys? One way is to ﬁnd others who are also interested in improving their teaching. You may ﬁnd some people like this within your department or program, or you may have to look more broadly to ﬁnd others to work with so that you can inspire each other to continue to improve your teaching. LESSON 2: THE POWER OF REFLECTION IN IMPROVING OUR COURSES Sometimes as faculty we get so busy that we do not take a step back to reﬂect. As we all embark on our journeys in becoming better engineering educators, we can learn a lot through reﬂecting on our goals for a class, how the class went, how the students responded to the class, and con- siderations of ways to improve it in future semesters. Donna recommended taking time at the end of the semester to reﬂect on what worked well, what did not work so well, how you have progressed toward your goals, and, ﬁnally, what you will change moving forward. She describes this as keeping “the spirit of innovation alive.” Most engineering programs have ABET require- ments for continuous improvement, and this can be a good opportunity to reﬂect on a class and develop goals and ideas for future iterations of the same course. How can we all incorporate reﬂection into our courses? There are many ways this can be achieved, both individually and collaboratively. One way is to write up your reﬂection and include it with your course ﬁles so that you can read through it when planning for the class in the future. Another idea is to have a discussion with peers in your community so that you can spend time sharing experiences from your class, what went well, and what did not go so well. This way your community can help you brainstorm ideas of improving the course or be able to anticipate areas they may wish to invest more energy into if they are to oﬀer that same course in the future. While it is always helpful to reﬂect at the end of a course, it can also be helpful to reﬂect as the course is happening so that minor corrections and improvements can be made in real-time throughout the semester. Deploying a course evaluation while the course is happening can help provide some input from the students in reﬂecting on the course and to identify some opportunities for improvement. Another option is to ask a colleague to observe your class so that you can have another person’s perspective on the strengths of your classes and areas for improvement. LESSON 3: TAKE IT SLOW In many of the stories, the engineering educators discussed taking things slowly and not chang- ing everything at once. In Donna’s story, she made some signiﬁcant changes to her thermody- namics course over 10 years that made it “unrecognizable from the original one.” Even though there were large changes over a longer time period, she explains that she “never completely overhauled the class.” She would make one or two changes each semester. She explains that by changing one thing at a time, it did not become so overwhelming. By taking a slower pace, you 10. CONCLUSION AND LESSONS LEARNED 93 are probably more likely to continue on the journey of changing your teaching. If you change everything at once, you could easily become overwhelmed and the teaching “experiment” could end. How can we take it slower in introducing innovations? When planning our classes, we can think about our vision for the class and one or two things that we can do to help realize that vision. Through the stories, we learned that starting with one small change can initiate a series of beneﬁcial changes. What are the one or two changes that you can make to your class next semester? How can you learn from those changes for future iterations of the course? LESSON 4: IMPROVING TEACHING AND LEARNING IS A LOT OF WORK, BUT IT IS FULFILLING Many of the stories highlighted in this book admit that their journeys of becoming better educa- tors is a lot of work. In particular, Chris, Fernanda, and Brad describe their journey as diﬃcult. While they felt that this journey was a lot of work, there was consensus around the idea that it was worth it. For example, Fernanda talks about how it would be a lot easier to teach directly from a textbook, but for her it would not be fulﬁlling. She explains that if she took this easy route, she would ﬁnd herself frustrated and not happy in her position. She also talks about how she is constantly learning herself. She explains, “Honestly, there are still days that I come out of a class and I said, ‘I could have done that better. Next time I’ll do it better.’ It’s always a work in progress. That keeps me motivated.” Brad also discusses this idea that trying new things is a more diﬃcult route, but that it is worth it. Brad explains, “Any time you try something new, outside the box, it’s going to take a lot more time, more time than you probably anticipate.” It will take a lot of time and energy, but “if you stick with it…it really does pay dividends.” What would our roles as engineering educators look like if we took the extra time and energy to become better educators? Would it make our faculty roles more intrinsically satisfying? These stories serve as an inspiration to try new things and continuously improve our teaching and student learning in our classes. They also help us see the importance of getting feedback, both formally and informally, from students to help improve the learning experience in the classroom and also serve as extra motivation to persist through the diﬃcult times. LESSON 5: TRADEOFFS BETWEEN TEACHING AND RESEARCH, OR NOT? In the stories shared in this book, there was some tension between those that felt that they needed to decide between being a good teacher and a good researcher with others feeling that your teaching can inform your research and vice versa. Both Matthew and Charlie discuss being intentional about ﬁnding a faculty position at an institution that valued teaching. Inherent in these stories is the idea that there is a tradeoﬀ between teaching and research, you are either a 94 10. CONCLUSION AND LESSONS LEARNED good teacher or a good researcher, but not likely both. Fernanda pushes on this idea by saying that teaching and research can be symbiotic. In other words, teaching can help give ideas for research and research can help give ideas for teaching. What could faculty roles become if we started integrating our teaching and research ef- forts? How can we have teaching inform our research and our research inform our teaching? How can we begin to see these not as roles that are pitted against one another, but rather with each as integral parts of our roles as faculty members? If we are in administrative roles, how can we value both teaching and research in a way that encourages faculty to integrate these two aspects of their role. LESSON 6: CONSIDER AN ASSET-BASED APPROACH TO YOUR TEACHING An asset-based approach to teaching is one in which students are seen as having strengths and prior knowledge when they come into a classroom [Llopart and Esteban-Guitart, 2018]. They are seen as individuals with a myriad of experiences that will add to the class. In my experience, this approach is critical in improving our engineering education systems because many engi- neering faculty take a deﬁcit-based approach, where they believe that students are not “cut-out” for engineering and lack the prerequisite knowledge (from K-12 or prior engineering classes) to do well in the class [Secules et al., 2018]. I have had many conversations in curriculum commit- tees, faculty meetings, and hallways where faculty explain to me that our students are not smart enough to be engineering students, that our students are not adequately prepared to be engi- neering students, or that our students should be weeded out of their engineering programs. It was refreshing to read through stories of engineering faculty who do not take this deﬁcit-based approach, but instead take an asset-based approach. Fernanda discussed incorporating real-world projects into her courses. In one example, she describes asking questions in class and 1/3 of the student’s hands go up immediately. The students have learned that she is interested in their particular experiences and know that the classroom is a space where they can share those experiences. She talks about how engaged they become, how well they can communicate when discussing something they know so well (their experiences), and how they seem to be more conﬁdent. Also, Chris discussed his Site Remediation Techniques course that he transitioned to include real-world projects. The students became very engaged in the project as the projects in- volved real stakeholders in a real community. His students were distributed in this class with some having substantial practical experience and weaker technical backgrounds while others had strong technical backgrounds and limited practical experience. The students with practical experience were encouraged to bring their experience into the classroom to help teach the stu- dents with little practical experience about real-world engineering. This is diﬀerent than many engineering classes, where technical knowledge is valued more than practical experience. 10. CONCLUSION AND LESSONS LEARNED 95 Donna took an asset-based approach in a deliberate way as she incorporated a liberative pedagogy in her classroom where she worked to change the power imbalance in the classroom. She adopted several strategies to give students agency and power in the class, primarily by having students critically reﬂect and critique the class. How can we incorporate this lesson into our classrooms? For one, we can start asking explicitly about students’ experiences as they relate to the course. In some courses it may be easy to value students’ experiences, but in others it may appear more diﬃcult at ﬁrst glance. First, we can think about who has power in our classrooms and consider ways of giving the students agency within our classes. We could try having students read a handout by Foucalt or we can think about how to integrate real-world projects that build on experiences students bring into the classroom. LESSON 7: EMPOWER ENGINEERING STUDENTS WHO HAVE OTHERWISE BEEN MARGINALIZED Another transformative lesson emerged around the ability to empower engineering students who have traditionally been marginalized through our teaching approaches and Matthew was an exemplar of this. Early on in his own academic pursuits, Matthew befriended a guy who had ambitious goals with humble beginnings who would later become his best friend. His friend started as an auto mechanic attending community college and struggling academically. However, his desire was to land at NASA as a Rocket Scientist and with persistence and resilience, that is exactly where he ended up. This relationship was Matthew’s ﬁrst impactful exposure enabling him to recognize that not everyone had access to the same opportunities and access, and yet, where and/or how one started oﬀ on their journeys did not limit how far they could climb. Matthew realized that with the right support, encouragement and conﬁdence, students could have a greater potential of achieving such laudable goals—inclusive of the “raw and scrappy” talent and not just those sought-after students that arrived prepared and ready to soar. Matthew acknowledged that many of these students had not had much experience with college or positive experiences with the education system. He made a conscious decision that through his teaching, he would make a way for these students—the atypical recruit for engineering—to be able to see themselves as engineers. Through his openness and the cama- raderie created through his teaching approaches, the students would be empowered “to ask ques- tions maybe they had been afraid to ask before.” The students were representations of his best friend and he chose to use his position to support them by meeting them where they were to help them develop and realize their fullest potential. It was important for Matthew that students learn “there’s no stereotypical type of person that needs to be in this classroom.” The other experience that solidiﬁed the necessity of becoming an advocate for the marginalized engineering student occurred when Matthew changed his own last name. He took the last name of his wife, which happened to be a name of Hispanic origin. With this change, his identity of decades was suddenly challenged and he questioned, “I mean like now do I be- 96 10. CONCLUSION AND LESSONS LEARNED come a Hispanic engineer instead of an engineer?” Through the microaggressions that started to become commonplace for Matthew after changing his last name, he gained a diﬀerent under- standing of what “people deal with on a day-to-day basis” in terms of being underrepresented in engineering, and in society, in general. This shift in experience for a “stereotypical, white male in engineering” created a level of awareness that made Matthew want to create a space for dia- logue, transparency and real conversations. Matthew reﬂected in his heightened awareness and position for advocacy, “But, I can’t imagine going through the educational system and having to deal with that and learning new things all at the same time. I guess to bring it all back to the classroom environment, it’s that kind of conversation that I want to have happen in engineering classrooms, because I think those are important conversations along with the technical.” How can we strive to have an awareness of the experiences of all students in our classrooms and empower those who have been marginalized in engineering? We learn through Matthew’s story that there are several tangible actions we can take that can stand to have a signiﬁcant impact on the students we encounter. The most critical of those being a self-reﬂection and acknowledg- ment of our own privilege and position (i.e., race, gender, education, socioeconomic status). We should challenge ourselves to use our position to push back against the systemic barriers facing students every day rather than being an added barrier to their load. We can also be open about our own identity with our students and unapologetic about who we are as Matthew exempliﬁed, “I think they appreciate maybe that I’m just honest with who I am. At least that’s my hope, that they recognize that you don’t have to be afraid to be an individual, and you don’t have to be afraid to learn.” The last suggestion in fostering empowerment in the classroom is to encourage real conversations. Matthew urged that this didn’t happen enough and people just “don’t ask about how certain actions or things might make someone uncomfortable or something of the sort.” We can learn a lot from Matthew’s example. What seems most encouraging is knowing that there is no perfect approach, it just takes a true desire and commitment to making a diﬀer- ence. Matthew was focused on helping students develop and what he envisioned as outcomes. At the end of his narrative, he describes a recent meeting with former students of his from his ﬁrst transitional college. Most compelling is Matthew clearly remembers that perceiving these particular students through a deﬁcit lens at a snapshot in time could have easily rendered, “Yeah, they’re not going to be successful” for a lack of demonstrating traditional metrics of success. However, the students came to him—one ﬁnishing a Ph.D. in civil engineering and another a Master’s in mechanical engineering—both of which most would regard as extremely successful. We cannot stop at how students show up in our classrooms, but as exemplar educators, must challenge ourselves to identify ways to empower them beyond the barriers to reach their fullest potential. It is our jobs as educators to help every student envision themselves as the engineer they wish to be. We are grateful for educators like Matthew and hope that others can be inspired and learn from his insight. LESSON 8: CONNECTING THEORY TO THE REAL WORLD IN THE CLASSROOM 10. CONCLUSION AND LESSONS LEARNED 97 In some of the stories, there was a focus on providing opportunities for students to experience engineering practice. In many engineering classrooms, there tends to be a focus on technical solutions only, with no consideration of the complexity of solutions, especially when embedded in our social systems. Fernanda discusses a need to understand project complexity as we tend to over-simplify problems in engineering classes. She pushes students to think about “How do you connect the concepts that we covered in class to that real-world problem? How do you do something that people in the real world, e.g., a safety engineer, are actually doing?” To do this, she has strong connections with industry and includes real-world projects in her classes. Chris also brings socio-technical problems into his classroom. For example, when he has students do watershed analysis he embeds that discussion with the impacts that watersheds can have on communities. For example, he discussed the Aberjona River watershed, as it is an example where there was contamination of a community’s water which led to increased cases of leukemia. While this case is well known, it is also a case that is less than 20 miles from his university. Chris helps students make “connections between the abstract concept of watershed analysis and the concrete reality of understanding a watershed so that you can see its impacts on the community.” What are ways that we can make more explicit connections between the course curricula and our surrounding community? How can we begin to embed engineering problems into the real world? How can we begin to focus on the assumptions that we are making to teach engi- neering science courses? In research done by Erin Cech [2014], she found that students become more disengaged as they continue in an engineering program. Speciﬁcally, students’ concerns about public welfare diminish as they continue in their studies. Through an attempt to make more connections between engineering and design and the communities that could be impacted by those designs, we could shift the paradigm to graduate engineers who are more engaged in public welfare. LESSON 9: USING IDEAS FROM ENTREPRENEURSHIP IN ENGINEERING EDUCATION Throughout many of the faculty stories, there was discussion of an entrepreneurial mindset help- ing teaching. Chris explains that to him, taking an entrepreneurial approach means thinking about the values of your students and developing ways of satisfying their values. Thais also ex- plains that she had an “aha” moment when she realized that the students are her clients “and if they are not happy or if this is not useful for them, I have to do something.” She then began at- tending Center for Teaching and Learning meetings and learning diﬀerent teaching approaches so that she could begin to serve “more of the students and tailor my teaching to their needs.” 98 10. CONCLUSION AND LESSONS LEARNED Donna also encourages other engineering educators us to be entrepreneurial in her advice. She explains that you will always have constraints as you are trying to do things diﬀerently and push the boundaries, and advises you to “work creatively with, around, and through” those con- straints. She explains that this creative “attitude” will help you continue to push boundaries and do things diﬀerently. Donna explains that “there are unchallenged assumptions everywhere” and that as innovative engineering educators, we have to begin pushing against those assumptions to truly be innovative. She also advises engineering educators to not be surprised when you en- counter pushback from your peers, students, or administrators. This may actually be a sign that you are doing something right. In Chris’ story, he poses some questions for us to consider as educators, Why not be entrepreneurial in applying an educational concept? An educational in- novation? When most of the education that we still receive today is the traditional lecture style, when people can deliver it in a diﬀerent way, why can’t that be an en- trepreneurial eﬀort? Maybe considering ways of being more entrepreneurial or innovative in our approaches to teach- ing could help us become stronger teachers. When we are trying something new and it does not seem to be working well, when should we pivot to something new? When we are truly propos- ing something transformative in our teaching, should we expect to get some pushback from colleagues and students? These ideas of value propositions, customer segments, and pivots could be helpful as we begin pushing the boundaries of traditional engineering teaching and learning to do something truly innovative as engineering educators. LESSON 10: COMFORT WITH AMBIGUITY AND RELINQUISHING CONTROL ARE REQUIRED As faculty members, one natural tendency is to aim to cover all of the material as designated by the course syllabus. However, in the implementation of student-centered pedagogies, and par- ticularly active learning, the proposed presentation of content does not always execute according to plan and this was one of the adjustments that the faculty in these stories had to get used to. These approaches necessitate a ﬂexibility that challenges the certainty of knowing—whether it’s the faculty’s conﬁdence in adequately covering the material or knowing exactly which topics the students will walk away from the class having mastered—there is a comfort with ambiguity and a relinquishing of control that essentially has to happen for faculty to shift their teaching. This was demonstrated in Thais’ story when she described the lack of a consistent expec- tation, “I never have the same exact lesson. Never, ever.” For many faculty, the thought of such variation would be daunting. In fact, one of the reasons we invest such time and eﬀort into developing a given lesson is the notion that the material will be repeatable and reusable. Brad mentioned that lecturing would simply be easier and that if he was solely focused on self, lec- turing would be the rational choice. Thais acknowledged this tension when she admitted, “It’s 10. CONCLUSION AND LESSONS LEARNED 99 very hard to come to grips with the idea that you want to introduce these things and you want to give freedom for them to lead the class, and at the same time cover the course material.” How can we can as faculty learn to be open to the ambiguity and surrendering of control that is required when the outcomes of teaching approaches are less predictable? As we learn from Thais and Brad, having the conﬁdence to try new things is imperative. Additionally, another way to navigate this struggle involves simply learning to accept that adopting active learning strategies may come with tradeoﬀs and/or require compromises. Students may not cover every single item in the course as they have historically, but the hope is that they will leave the class with a richer experience of engagement through thinking critically that ﬁlls those gaps all the same. In the words of Brad, “The workload is immensely higher than traditional teaching, but I think, just from my standpoint, I really see huge beneﬁts to the students.” LESSON 11: LEARN SOMETHING NEW A possible way to become better teachers is to become learners ourselves. In many of the stories, the faculty discussed becoming inspired when they were a student themselves. As a child, Sara knew she wanted to be a teacher. She had positive experiences as she pursued her undergraduate degree at Dartmouth, where she also served as a Teaching Assistant and experienced engineering faculty who cared about teaching. When she began to pursue her Ph.D. at a research-focused university, she was shocked by the poor quality of teaching she was experiencing. This, in part, motivated her even further to become a good teacher herself. Donna was also inspired, not when taking her engineering courses, but when taking humanities and social science courses as an undergraduate student. She discusses faculty from non-engineering departments that created an environment where she felt that she had something important to say, even though she had not taken some of the prerequisites for the course. While many of these examples are of faculty becoming initially inspired to become better teachers through their experiences as students themselves, it makes me wonder if we can emulate those inspirations as the time between being students ourselves increases. Brad discusses that he enjoys learning and trying new things, and maybe we can take some inspiration from Brad. We can continue to learn new things and experience being a student throughout our lives. Recently, I began to learn to play the guitar. For me, this has been a huge inspiration as I get to experience ﬁrst-hand being a complete novice and having so much to learn. In trying diﬀerent ways of learning guitar, I have experienced diﬀerent types of instructors. Some instructors have a ﬁxed mindset and believe that either you can be a guitar player or you cannot, that somehow some people are born good guitar players. Another instructor who teaches online, goes to great lengths to explain that anyone can learn to play the guitar. He explains that babies are not born as guitar players and that everyone has to work at it. While it may come easier to some people, some of the greatest guitar players worked very hard to become the guitar players that they are today. Teaching using this growth mindset is an inspiration and helps you feel like you belong and that you, too, can become a guitar player. This has inspired me to change the way I talk about learning 100 10. CONCLUSION AND LESSONS LEARNED Statics in one of my classes. Using this growth mindset explicitly in the class may help many of my students who were not as prepared academically as others in the class. Students need to be empowered and not held to the limitations of their preparation. How can we continue to be inspired in our teaching? Maybe one way is to become a student ourselves. What is something that you’ve always wanted to learn, but never found the time? You could even extend the challenge to learn something completely diﬀerent than your background—possibly learning to dance or paint. Maybe in learning something new you can become more inspired to become a stronger engineering educator. Maybe you can also begin to have more empathy for students who are struggling in your classes or those whose backgrounds have not equipped them with the tools of success. CONCLUSION Hopefully sharing the raw and real stories of engineering faculty in their transformations in teaching has inspired you in your own personal journey toward becoming an exemplary en- gineering educator. This book can serve as a catalyst for you to begin learning about others’ teaching stories. Many of us have worked towards becoming better teachers, have encountered obstacles, while also experiencing some success. Continue these conversations by asking engi- neering educators about their stories of change and sharing your own journey. REFERENCES Cech, E. A. (2014). Culture of disengagement in engineering education? Science, Technology, and Human Values, 39(1), pp. 42–72. DOI: 10.1177/0162243913504305. 97 Llopart, M. and Esteban-Guitart, M. (2018). Funds of knowledge in 21st century societies: Inclusive educational practices for under-represented students. A literature review. Journal of Curriculum Studies. DOI: 10.1080/00220272.2016.1247913. 94 Secules, S., Gupta, A., Elby, A., and Turpen, C. (2018). Zooming out from the struggling individual student: An account of the cultural construction of engineering ability in an un- dergraduate programming class. Journal of Engineering Education. DOI: 10.1002/jee.20191. 94 Authors’ Biographies (in order of appearance) 101 NADIA KELLAM Nadia Kellam is an Associate Professor in the Polytechnic School of the Ira A. Fulton Schools of Engineering at Arizona State University. She is a qualitative researcher who primarily uses narrative research methods. In her research, Dr. Kellam is broadly interested in developing critical understandings of the culture of engineering education and, especially, the ex- periences of underrepresented undergraduate engineering stu- dents and engineering educators. In addition to teaching un- dergraduate engineering courses and a graduate course on en- trepreneurship, she also enjoys teaching qualitative research methods in engineering education in the Engineering Educa- tion Systems and Design Ph.D. program at ASU. Nadia serves as Deputy Editor of the Journal of Engineering Education. 102 AUTHORS’ BIOGRAPHIES BROOKE COLEY Brooke Coley is an Assistant Professor in Engineering at the Polytechnic School of the Ira A. Fulton Schools of Engineer- ing at Arizona State University. Dr. Coley is Principal Inves- tigator of the Shifting Perceptions, Attitudes and Cultures in Engineering (SPACE) Lab that aspires to elevate the expe- riences of marginalized populations, dismantle systematic in- justices, and transform the way inclusion is cultivated in engi- neering through the implementation of novel technologies and methodologies in engineering education. Intrigued by the in- tersections of engineering education, mental health, and social justice, Dr. Coley’s primary research interest focuses on virtual reality as a tool for developing empathetic and inclusive mindsets among engineering faculty. She is also interested in hidden populations in engineering education and innovation for more inclusive pedagogies. AUDREY BOKLAGE Audrey Boklage is a Research Assistant in the Center for En- gineering Education of the Cockrell School of Engineering at The University of Texas at Austin. Prior to entering graduate school, she taught high school science in Texas for seven years. During this time, she redesigned curriculum and served as a mentor for new to profession educators. Upon receiving her doctorate degree in Curriculum and Instruction with a focus on STEM education, she became speciﬁcally interested in narra- tive research methods and faculty development within schools of engineering. Her current research interests include creating inclusive spaces within university engineering environments, speciﬁcally makerspaces and asset-based pedagogies. DONA RILEY AUTHORS’ BIOGRAPHIES 103 Donna Riley is Kamyar Haghighi Head of the School of En- gineering Education and Professor of Engineering Education at Purdue University. She is the author of two books, Engi- neering and Social Justice and Engineering Thermodynamics and 21st Century Energy Problems, both published by Morgan & Claypool. Riley earned a B.S.E. in Chemical Engineering from Princeton University and a Ph.D. from Carnegie Mellon University in Engineering and Public Policy. She is a fellow of the American Society for Engineering Education. SARA ATWOOD Sara Atwood is an Associate Professor and Chair of Engineer- ing and Physics at Elizabethtown College. She received a B.A. and M.S. in Engineering Sciences from Dartmouth College and a Ph.D. in Mechanical Engineering from the University of California at Berkeley. She is passionate about engaging un- derrepresented students in engineering education, teaching en- gineers in a liberal arts setting, and encouraging students to use their engineering skills to be empowered citizens. 104 AUTHORS’ BIOGRAPHIES BRAD HYATT Brad Hyatt is an Associate Professor and the Chair of the Department of Construction Management in the Lyles Col- lege of Engineering at California State University, Fresno (Fresno State). He has an M.S. in Engineering with a focus on Construction Engineering and Project Management from The University of Texas at Austin and a B.S. in Civil Engi- neering from the University of Kentucky. He teaches courses in construction estimating, scheduling, documents, and project controls. He actively conducts research on data and predictive analytics in construction, leadership in construction, lean con- struction practices, and integrating technology into construc- tion pedagogy. Professor Hyatt continuously participates in leadership roles at Fresno State. He is a DISCOVERe Faculty Fellow and serves on the steering committee for the President’s Leadership Academy. These transformational programs provide innovative solutions to mobile technology in the classroom and to the development of future leaders at Fresno State. Addi- tionally, Professor Hyatt led a group of faculty to review learning management systems for the campus during the 2017/2018 academic year. Professor Hyatt is a Registered Professional En- gineer in California and LEED Accredited Professional (Building, Design & Construction) with over 20 years of professional experience in program and project management of facilities, engineering, and construction projects. Professor Hyatt spent nearly ten years as a U.S. Navy Civil Engineer Corps Oﬃcer prior to his academic career. He also worked as a Construction Project Management consultant in between his military service and academic career. His broad industry expertise includes sustainable design and construction, facilities management, construc- tion management, capital improvements planning, energy management, disaster response, and construction workforce shaping. He has managed a variety of projects from a large, complex replacement hospital to small fuel tank renovations. AUTHORS’ BIOGRAPHIES 105 CHRIS SWAN Chris Swan is Dean of Undergraduate Education in the School of Engineering at Tufts University and an Associate Professor in its Civil and Environmental Engineering Depart- ment. He is also a senior fellow in Tisch College of Civic Life. Previously, he has served as CEE department chair. He re- ceived a ScD degree in Civil and Environmental Engineering from MIT in 1994 and both B.S. and M.S. degrees in Civil Engineering from the University of Texas at Austin in 1984 and 1986, respectively. An initiator of explicitly incorporating components of service-learning into engineering curriculum at Tufts, he continues to champion the development and imple- mentation of civic engagement in engineering education. For example, he currently serves as an advisor to Tufts student chapter of Engineers Without Borders. Current engineering edu- cation research eﬀorts focus on evaluating the impact of service-based learning in engineering education, as well as applying entrepreneurial principles in examining sustainable and scalable pathways for innovations in engineering education. He was also an inaugural Faculty Fellow of Tisch College and of the Center for the Enhancement of Learning and Teaching (CELT). In addition, Chris researches the development of reuse strategies for waste materials. Most no- tably, his research eﬀorts have focused on the reuse of ﬂy ash from coal burning facilities with waste plastics. This has led to the development of synthetic lightweight aggregates (SLA), an innovative construction material that can be used in place of traditional sand and gravel. 106 AUTHORS’ BIOGRAPHIES THAIS ALVES Thais Alves specializes in construction management and project-based production systems. Her areas of interest in- clude the application of Lean production/construction con- cepts, principles, and tools to improve the performance of production systems and products in diﬀerent stages of their life-cycle and supply chains. Additionally, she is interested in how contracts and delivery methods support collaboration across supply chains in the Owner-Architecture-Engineering- Construction industry. For more than 15 years, Thais has been teaching, advising students, researching, and collaborat- ing with construction companies toward the dissemination and implementation of Lean, especially in the ﬁeld of production planning and control at construc- tion sites. She is currently the AGC—Paul S. Roel Chair in Construction Engineering and Management at the J.R. Filanc Construction Engineering and Management Program at San Diego State University. FERNANDA LEITE Fernanda Leite is an Associate Professor in Construction En- gineering and Project Management, in the Civil, Architectural and Environmental Engineering (CAEE) Department at the University of Texas at Austin. She has a Ph.D. in Civil and Environmental Engineering from Carnegie Mellon Univer- sity. Prior to her graduate education, she worked as a Project Manager in her home country of Brazil, in multiple gov- ernment infrastructure and commercial building construction projects. Her technical interests include information technol- ogy for project management, building information modeling, collaboration and coordination technologies, and information technology-supported construction safety management. She has taught four unique courses at UT and has integrated project-based and experiential learning to all of her courses, through class projects, industry mentorships, and interactive exercises. She serves as Graduate Program Coordinator for CAEE’s Sustainable Systems graduate program and on the Executive Com- mittee for the University-wide Grand Challenges eﬀort called Planet Texas 2050. She currently supervises 8 Ph.D. and 5 M.S. students. She has graduated 7 Ph.D. and 36 M.S. students. AUTHORS’ BIOGRAPHIES 107 CHARLES E. PIERCE Charles E. Pierce is an Associate Professor in the Department of Civil and Environmental En- gineering at the University of South Carolina (USC), where he has been teaching since 1998. He has an M.S. and Ph.D. in Civil Engineering from Northwestern University and a B.S. de- gree in Civil Engineering from the University of New Hampshire. He is the current Director for Diversity and Inclusion in his department and a USC Connect Faculty Fellow for Integrative Learning. He was awarded the Michael J. Mungo Undergraduate Teaching Award for USC in 2006, and he is also the recipient of the Samuel P. Litman Award and Bell South Teaching Fellowship in recognition of his contributions to engineering education. Dr. Pierce is an ac- tive member of ASEE and serves as the campus representative for USC. He is committed to improving engineering education across the K-20 spectrum. His contributions include leading professional development activities on engineering for middle and high school math and science teachers and creating programs for graduate students in engineering to integrate research and teaching. His undergraduate educational interests include the facilitation and assessment of crit- ical thinking through problem-based learning using the Environments for Fostering Eﬀective Critical Thinking (EFFECTs) framework developed with his colleagues at USC. MATTHEW FUENTES Matthew Fuentes is currently a member of the engineering faculty at Everett Community Col- lege. He has been teaching at community colleges for 10 years. He earned a B.S. and M.S. in Aerospace Engineering from the University of Tennessee.
huggingface/hf-endpoints-documentation/blob/main/docs/source/guides/create_endpoint.mdx	Create an Endpoint After your first login, you will be directed to the [Endpoint creation page](https://ui.endpoints.huggingface.co/new). As an example, this guide will go through the steps to deploy [distilbert-base-uncased-finetuned-sst-2-english](https://huggingface.co/distilbert-base-uncased-finetuned-sst-2-english) for text classification. ## 1. Enter the Hugging Face Repository ID and your desired endpoint name: <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/1_repository.png" alt="select repository" /> ## 2. Select your Cloud Provider and region. Initially, only AWS will be available as a Cloud Provider with the `us-east-1` and `eu-west-1` regions. We will add Azure soon, and if you need to test Endpoints with other Cloud Providers or regions, please let us know. <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/1_region.png" alt="select region" /> ## 3. Define the [Security Level](security) for the Endpoint: <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/1_security.png" alt="define security" /> ## 4. Create your Endpoint by clicking Create Endpoint. By default, your Endpoint is created with a medium CPU (2 x 4GB vCPUs with Intel Xeon Ice Lake) The cost estimate assumes the Endpoint will be up for an entire month, and does not take autoscaling into account. <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/1_create_cost.png" alt="create endpoint" /> ## 5. Wait for the Endpoint to build, initialize and run which can take between 1 to 5 minutes. <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/overview.png" alt="overview" /> ## 6. Test your Endpoint in the overview with the Inference widget 🏁 🎉! <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/1_inference.png" alt="run inference" />
huggingface/evaluate/blob/main/docs/source/choosing_a_metric.mdx	Choosing a metric for your task So you've trained your model and want to see how well it’s doing on a dataset of your choice. Where do you start? There is no “one size fits all” approach to choosing an evaluation metric, but some good guidelines to keep in mind are: ## Categories of metrics There are 3 high-level categories of metrics: 1. Generic metrics, which can be applied to a variety of situations and datasets, such as precision and accuracy. 2. Task-specific metrics, which are limited to a given task, such as Machine Translation (often evaluated using metrics [BLEU](https://huggingface.co/metrics/bleu) or [ROUGE](https://huggingface.co/metrics/rouge)) or Named Entity Recognition (often evaluated with [seqeval](https://huggingface.co/metrics/seqeval)). 3. Dataset-specific metrics, which aim to measure model performance on specific benchmarks: for instance, the [GLUE benchmark](https://huggingface.co/datasets/glue) has a dedicated [evaluation metric](https://huggingface.co/metrics/glue). Let's look at each of these three cases: ### Generic metrics Many of the metrics used in the Machine Learning community are quite generic and can be applied in a variety of tasks and datasets. This is the case for metrics like [accuracy](https://huggingface.co/metrics/accuracy) and [precision](https://huggingface.co/metrics/precision), which can be used for evaluating labeled (supervised) datasets, as well as [perplexity](https://huggingface.co/metrics/perplexity), which can be used for evaluating different kinds of (unsupervised) generative tasks. To see the input structure of a given metric, you can look at its metric card. For example, in the case of [precision](https://huggingface.co/metrics/precision), the format is: ``` >>> precision_metric = evaluate.load("precision") >>> results = precision_metric.compute(references=[0, 1], predictions=[0, 1]) >>> print(results) {'precision': 1.0} ``` ### Task-specific metrics Popular ML tasks like Machine Translation and Named Entity Recognition have specific metrics that can be used to compare models. For example, a series of different metrics have been proposed for text generation, ranging from [BLEU](https://huggingface.co/metrics/bleu) and its derivatives such as [GoogleBLEU](https://huggingface.co/metrics/google_bleu) and [GLEU](https://huggingface.co/metrics/gleu), but also [ROUGE](https://huggingface.co/metrics/rouge), [MAUVE](https://huggingface.co/metrics/mauve), etc. You can find the right metric for your task by: - Looking at the [Task pages](https://huggingface.co/tasks) to see what metrics can be used for evaluating models for a given task. - Checking out leaderboards on sites like [Papers With Code](https://paperswithcode.com/) (you can search by task and by dataset). - Reading the metric cards for the relevant metrics and see which ones are a good fit for your use case. For example, see the [BLEU metric card](https://github.com/huggingface/evaluate/tree/main/metrics/bleu) or [SQuaD metric card](https://github.com/huggingface/evaluate/tree/main/metrics/squad). - Looking at papers and blog posts published on the topic and see what metrics they report. This can change over time, so try to pick papers from the last couple of years! ### Dataset-specific metrics Some datasets have specific metrics associated with them -- this is especially in the case of popular benchmarks like [GLUE](https://huggingface.co/metrics/glue) and [SQuAD](https://huggingface.co/metrics/squad). <Tip warning={true}> 💡 GLUE is actually a collection of different subsets on different tasks, so first you need to choose the one that corresponds to the NLI task, such as mnli, which is described as “crowdsourced collection of sentence pairs with textual entailment annotations” </Tip> If you are evaluating your model on a benchmark dataset like the ones mentioned above, you can use its dedicated evaluation metric. Make sure you respect the format that they require. For example, to evaluate your model on the [SQuAD](https://huggingface.co/datasets/squad) dataset, you need to feed the `question` and `context` into your model and return the `prediction_text`, which should be compared with the `references` (based on matching the `id` of the question) : ``` >>> from evaluate import load >>> squad_metric = load("squad") >>> predictions = [{'prediction_text': '1976', 'id': '56e10a3be3433e1400422b22'}] >>> references = [{'answers': {'answer_start': [97], 'text': ['1976']}, 'id': '56e10a3be3433e1400422b22'}] >>> results = squad_metric.compute(predictions=predictions, references=references) >>> results {'exact_match': 100.0, 'f1': 100.0} ``` You can find examples of dataset structures by consulting the "Dataset Preview" function or the dataset card for a given dataset, and you can see how to use its dedicated evaluation function based on the metric card.
gradio-app/gradio/blob/main/guides/cn/01_getting-started/02_key-features.md	主要特点让我们来介绍一下 Gradio 最受欢迎的一些功能！这里是 Gradio 的主要特点： 1. [添加示例输入](#example-inputs) 2. [传递自定义错误消息](#errors) 3. [添加描述内容](#descriptive-content) 4. [设置旗标](#flagging) 5. [预处理和后处理](#preprocessing-and-postprocessing) 6. [样式化演示](#styling) 7. [排队用户](#queuing) 8. [迭代输出](#iterative-outputs) 9. [进度条](#progress-bars) 10. [批处理函数](#batch-functions) 11. [在协作笔记本上运行](#colab-notebooks) ## 示例输入您可以提供用户可以轻松加载到 "Interface" 中的示例数据。这对于演示模型期望的输入类型以及演示数据集和模型一起探索的方式非常有帮助。要加载示例数据，您可以将嵌套列表提供给 Interface 构造函数的 `examples=` 关键字参数。外部列表中的每个子列表表示一个数据样本，子列表中的每个元素表示每个输入组件的输入。有关每个组件的示例数据格式在[Docs](https://gradio.app/docs#components)中有说明。 $code_calculator $demo_calculator 您可以将大型数据集加载到示例中，通过 Gradio 浏览和与数据集进行交互。示例将自动分页（可以通过 Interface 的 `examples_per_page` 参数进行配置）。继续了解示例，请参阅[更多示例](https://gradio.app/more-on-examples)指南。 ## 错误您希望向用户传递自定义错误消息。为此，with `gr.Error("custom message")` 来显示错误消息。如果在上面的计算器示例中尝试除以零，将显示自定义错误消息的弹出模态窗口。了解有关错误的更多信息，请参阅[文档](https://gradio.app/docs#error)。 ## 描述性内容在前面的示例中，您可能已经注意到 Interface 构造函数中的 `title=` 和 `description=` 关键字参数，帮助用户了解您的应用程序。 Interface 构造函数中有三个参数用于指定此内容应放置在哪里： - `title`：接受文本，并可以将其显示在界面的顶部，也将成为页面标题。 - `description`：接受文本、Markdown 或 HTML，并将其放置在标题正下方。 - `article`：也接受文本、Markdown 或 HTML，并将其放置在界面下方。 ![annotated](/assets/guides/annotated.png) 如果您使用的是 `Blocks` API，则可以 with `gr.Markdown(...)` 或 `gr.HTML(...)` 组件在任何位置插入文本、Markdown 或 HTML，其中描述性内容位于 `Component` 构造函数内部。另一个有用的关键字参数是 `label=`，它存在于每个 `Component` 中。这修改了每个 `Component` 顶部的标签文本。还可以为诸如 `Textbox` 或 `Radio` 之类的表单元素添加 `info=` 关键字参数，以提供有关其用法的进一步信息。 ```python gr.Number(label='年龄', info='以年为单位，必须大于0') ``` ## 旗标默认情况下，"Interface" 将有一个 "Flag" 按钮。当用户测试您的 `Interface` 时，如果看到有趣的输出，例如错误或意外的模型行为，他们可以将输入标记为您进行查看。在由 `Interface` 构造函数的 `flagging_dir=` 参数提供的目录中，将记录标记的输入到一个 CSV 文件中。如果界面涉及文件数据，例如图像和音频组件，将创建文件夹来存储这些标记的数据。例如，对于上面显示的计算器界面，我们将在下面的旗标目录中存储标记的数据： ```directory +-- calculator.py +-- flagged/ \| +-- logs.csv ``` _flagged/logs.csv_ ```csv num1,operation,num2,Output 5,add,7,12 6,subtract,1.5,4.5 ``` 与早期显示的冷色界面相对应，我们将在下面的旗标目录中存储标记的数据： ```directory +-- sepia.py +-- flagged/ \| +-- logs.csv \| +-- im/ \| \| +-- 0.png \| \| +-- 1.png \| +-- Output/ \| \| +-- 0.png \| \| +-- 1.png ``` _flagged/logs.csv_ ```csv im,Output im/0.png,Output/0.png im/1.png,Output/1.png ``` 如果您希望用户提供旗标原因，可以将字符串列表传递给 Interface 的 `flagging_options` 参数。用户在进行旗标时必须选择其中一个字符串，这将作为附加列保存到 CSV 中。 ## 预处理和后处理 (Preprocessing and Postprocessing) ![annotated](/assets/img/dataflow.svg) 如您所见，Gradio 包括可以处理各种不同数据类型的组件，例如图像、音频和视频。大多数组件都可以用作输入或输出。当组件用作输入时，Gradio 自动处理预处理，将数据从用户浏览器发送的类型（例如网络摄像头快照的 base64 表示）转换为您的函数可以接受的形式（例如 `numpy` 数组）。同样，当组件用作输出时，Gradio 自动处理后处理，将数据从函数返回的形式（例如图像路径列表）转换为可以在用户浏览器中显示的形式（例如以 base64 格式显示图像的 `Gallery`）。您可以使用构建图像组件时的参数控制预处理。例如，如果您使用以下参数实例化 `Image` 组件，它将将图像转换为 `PIL` 类型，并将其重塑为`(100, 100)`，而不管提交时的原始大小如何： ```py img = gr.Image(shape=(100, 100), type="pil") ``` 相反，这里我们保留图像的原始大小，但在将其转换为 numpy 数组之前反转颜色： ```py img = gr.Image(invert_colors=True, type="numpy") ``` 后处理要容易得多！Gradio 自动识别返回数据的格式（例如 `Image` 是 `numpy` 数组还是 `str` 文件路径？），并将其后处理为可以由浏览器显示的格式。请查看[文档](https://gradio.app/docs)，了解每个组件的所有与预处理相关的参数。 ## 样式 (Styling) Gradio 主题是自定义应用程序外观和感觉的最简单方法。您可以选择多种主题或创建自己的主题。要这样做，请将 `theme=` 参数传递给 `Interface` 构造函数。例如： ```python demo = gr.Interface(..., theme=gr.themes.Monochrome()) ``` Gradio 带有一组预先构建的主题，您可以从 `gr.themes.` 加载。您可以扩展这些主题或从头开始创建自己的主题 - 有关更多详细信息，请参阅[主题指南](https://gradio.app/theming-guide)。要增加额外的样式能力，您可以 with `css=` 关键字将任何 CSS 传递给您的应用程序。 Gradio 应用程序的基类是 `gradio-container`，因此以下是一个更改 Gradio 应用程序背景颜色的示例： ```python with `gr.Interface(css=".gradio-container {background-color: red}") as demo: ... ``` ## 队列 (Queuing) 如果您的应用程序预计会有大量流量，请 with `queue()` 方法来控制处理速率。这将排队处理调用，因此一次只处理一定数量的请求。队列使用 Websockets，还可以防止网络超时，因此如果您的函数的推理时间很长（> 1 分钟），应使用队列。 with `Interface`： ```python demo = gr.Interface(...).queue() demo.launch() ``` with `Blocks`： ```python with gr.Blocks() as demo： #... demo.queue() demo.launch() ``` 您可以通过以下方式控制一次处理的请求数量： ```python demo.queue(concurrency_count=3) ``` 查看有关配置其他队列参数的[队列文档](/docs/#queue)。在 Blocks 中指定仅对某些函数进行排队： ```python with gr.Blocks() as demo2： num1 = gr.Number() num2 = gr.Number() output = gr.Number() gr.Button("Add").click( lambda a, b: a + b, [num1, num2], output) gr.Button("Multiply").click( lambda a, b: a b, [num1, num2], output, queue=True) demo2.launch() ``` ## 迭代输出 (Iterative Outputs) 在某些情况下，您可能需要传输一系列输出而不是一次显示单个输出。例如，您可能有一个图像生成模型，希望显示生成的每个步骤的图像，直到最终图像。或者您可能有一个聊天机器人，它逐字逐句地流式传输响应，而不是一次返回全部响应。在这种情况下，您可以将生成器函数提供给 Gradio，而不是常规函数。在 Python 中创建生成器非常简单：函数不应该有一个单独的 `return` 值，而是应该 with `yield` 连续返回一系列值。通常，`yield` 语句放置在某种循环中。下面是一个简单示例，生成器只是简单计数到给定数字： ```python def my_generator(x): for i in range(x): yield i ``` 您以与常规函数相同的方式将生成器提供给 Gradio。例如，这是一个（虚拟的）图像生成模型，它在输出图像之前生成数个步骤的噪音： $code_fake_diffusion $demo_fake_diffusion 请注意，我们在迭代器中添加了 `time.sleep(1)`，以创建步骤之间的人工暂停，以便您可以观察迭代器的步骤（在真实的图像生成模型中，这可能是不必要的）。将生成器提供给 Gradio 需要在底层 Interface 或 Blocks 中启用队列（请参阅上面的队列部分）。 ## 进度条 Gradio 支持创建自定义进度条，以便您可以自定义和控制向用户显示的进度更新。要启用此功能，只需为方法添加一个默认值为 `gr.Progress` 实例的参数即可。然后，您可以直接调用此实例并传入 0 到 1 之间的浮点数来更新进度级别，或者 with `Progress` 实例的 `tqdm()` 方法来跟踪可迭代对象上的进度，如下所示。必须启用队列以进行进度更新。 $code_progress_simple $demo_progress_simple 如果您 with `tqdm` 库，并且希望从函数内部的任何 `tqdm.tqdm` 自动报告进度更新，请将默认参数设置为 `gr.Progress(track_tqdm=True)`！ ## 批处理函数 (Batch Functions) Gradio 支持传递批处理函数。批处理函数只是接受输入列表并返回预测列表的函数。例如，这是一个批处理函数，它接受两个输入列表（一个单词列表和一个整数列表），并返回修剪过的单词列表作为输出： ```python import time def trim_words(words, lens): trimmed_words = [] time.sleep(5) for w, l in zip(words, lens): trimmed_words.append(w[:int(l)]) return [trimmed_words] for w, l in zip(words, lens): ``` 使用批处理函数的优点是，如果启用了队列，Gradio 服务器可以自动批处理传入的请求并并行处理它们，从而可能加快演示速度。以下是 Gradio 代码的示例（请注意 `batch=True` 和 `max_batch_size=16` - 这两个参数都可以传递给事件触发器或 `Interface` 类） with `Interface`： ```python demo = gr.Interface(trim_words, ["textbox", "number"], ["output"], batch=True, max_batch_size=16) demo.queue() demo.launch() ``` with `Blocks`： ```python import gradio as gr with gr.Blocks() as demo: with gr.Row(): word = gr.Textbox(label="word") leng = gr.Number(label="leng") output = gr.Textbox(label="Output") with gr.Row(): run = gr.Button() event = run.click(trim_words, [word, leng], output, batch=True, max_batch_size=16) demo.queue() demo.launch() ``` 在上面的示例中，可以并行处理 16 个请求（总推理时间为 5 秒），而不是分别处理每个请求（总推理时间为 80 秒）。许多 Hugging Face 的 `transformers` 和 `diffusers` 模型在 Gradio 的批处理模式下自然工作：这是[使用批处理生成图像的示例演示](https://github.com/gradio-app/gradio/blob/main/demo/diffusers_with_batching/run.py) 注意：使用 Gradio 的批处理函数 requires 在底层 Interface 或 Blocks 中启用队列（请参阅上面的队列部分）。 ## Gradio 笔记本 (Colab Notebooks) Gradio 可以在任何运行 Python 的地方运行，包括本地 Jupyter 笔记本和协作笔记本，如[Google Colab](https://colab.research.google.com/)。对于本地 Jupyter 笔记本和 Google Colab 笔记本，Gradio 在本地服务器上运行，您可以在浏览器中与之交互。（注意：对于 Google Colab，这是通过[服务工作器隧道](https://github.com/tensorflow/tensorboard/blob/master/docs/design/colab_integration.md)实现的，您的浏览器需要启用 cookies。）对于其他远程笔记本，Gradio 也将在服务器上运行，但您需要使用[SSH 隧道](https://coderwall.com/p/ohk6cg/remote-access-to-ipython-notebooks-via-ssh)在本地浏览器中查看应用程序。通常，更简单的选择是使用 Gradio 内置的公共链接，[在下一篇指南中讨论](/sharing-your-app/#sharing-demos)。
huggingface/transformers/blob/main/docs/source/en/perf_train_tpu_tf.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Training on TPU with TensorFlow <Tip> If you don't need long explanations and just want TPU code samples to get started with, check out [our TPU example notebook!](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) </Tip> ### What is a TPU? A TPU is a Tensor Processing Unit. They are hardware designed by Google, which are used to greatly speed up the tensor computations within neural networks, much like GPUs. They can be used for both network training and inference. They are generally accessed through Google’s cloud services, but small TPUs can also be accessed directly for free through Google Colab and Kaggle Kernels. Because [all TensorFlow models in 🤗 Transformers are Keras models](https://huggingface.co/blog/tensorflow-philosophy), most of the methods in this document are generally applicable to TPU training for any Keras model! However, there are a few points that are specific to the HuggingFace ecosystem (hug-o-system?) of Transformers and Datasets, and we’ll make sure to flag them up when we get to them. ### What kinds of TPU are available? New users are often very confused by the range of TPUs, and the different ways to access them. The first key distinction to understand is the difference between TPU Nodes and TPU VMs. When you use a TPU Node, you are effectively indirectly accessing a remote TPU. You will need a separate VM, which will initialize your network and data pipeline and then forward them to the remote node. When you use a TPU on Google Colab, you are accessing it in the TPU Node style. Using TPU Nodes can have some quite unexpected behaviour for people who aren’t used to them! In particular, because the TPU is located on a physically different system to the machine you’re running your Python code on, your data cannot be local to your machine - any data pipeline that loads from your machine’s internal storage will totally fail! Instead, data must be stored in Google Cloud Storage where your data pipeline can still access it, even when the pipeline is running on the remote TPU node. <Tip> If you can fit all your data in memory as `np.ndarray` or `tf.Tensor`, then you can `fit()` on that data even when using Colab or a TPU Node, without needing to upload it to Google Cloud Storage. </Tip> <Tip> 🤗Specific Hugging Face Tip🤗: The methods `Dataset.to_tf_dataset()` and its higher-level wrapper `model.prepare_tf_dataset()` , which you will see throughout our TF code examples, will both fail on a TPU Node. The reason for this is that even though they create a `tf.data.Dataset` it is not a “pure” `tf.data` pipeline and uses `tf.numpy_function` or `Dataset.from_generator()` to stream data from the underlying HuggingFace `Dataset`. This HuggingFace `Dataset` is backed by data that is on a local disc and which the remote TPU Node will not be able to read. </Tip> The second way to access a TPU is via a TPU VM. When using a TPU VM, you connect directly to the machine that the TPU is attached to, much like training on a GPU VM. TPU VMs are generally easier to work with, particularly when it comes to your data pipeline. All of the above warnings do not apply to TPU VMs! This is an opinionated document, so here’s our opinion: Avoid using TPU Node if possible. It is more confusing and more difficult to debug than TPU VMs. It is also likely to be unsupported in future - Google’s latest TPU, TPUv4, can only be accessed as a TPU VM, which suggests that TPU Nodes are increasingly going to become a “legacy” access method. However, we understand that the only free TPU access is on Colab and Kaggle Kernels, which uses TPU Node - so we’ll try to explain how to handle it if you have to! Check the [TPU example notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) for code samples that explain this in more detail. ### What sizes of TPU are available? A single TPU (a v2-8/v3-8/v4-8) runs 8 replicas. TPUs exist in pods that can run hundreds or thousands of replicas simultaneously. When you use more than a single TPU but less than a whole pod (for example, a v3-32), your TPU fleet is referred to as a pod slice. When you access a free TPU via Colab, you generally get a single v2-8 TPU. ### I keep hearing about this XLA thing. What’s XLA, and how does it relate to TPUs? XLA is an optimizing compiler, used by both TensorFlow and JAX. In JAX it is the only compiler, whereas in TensorFlow it is optional (but mandatory on TPU!). The easiest way to enable it when training a Keras model is to pass the argument `jit_compile=True` to `model.compile()`. If you don’t get any errors and performance is good, that’s a great sign that you’re ready to move to TPU! Debugging on TPU is generally a bit harder than on CPU/GPU, so we recommend getting your code running on CPU/GPU with XLA first before trying it on TPU. You don’t have to train for long, of course - just for a few steps to make sure that your model and data pipeline are working like you expect them to. <Tip> XLA compiled code is usually faster - so even if you’re not planning to run on TPU, adding `jit_compile=True` can improve your performance. Be sure to note the caveats below about XLA compatibility, though! </Tip> <Tip warning={true}> Tip born of painful experience: Although using `jit_compile=True` is a good way to get a speed boost and test if your CPU/GPU code is XLA-compatible, it can actually cause a lot of problems if you leave it in when actually training on TPU. XLA compilation will happen implicitly on TPU, so remember to remove that line before actually running your code on a TPU! </Tip> ### How do I make my model XLA compatible? In many cases, your code is probably XLA-compatible already! However, there are a few things that work in normal TensorFlow that don’t work in XLA. We’ve distilled them into three core rules below: <Tip> 🤗Specific HuggingFace Tip🤗: We’ve put a lot of effort into rewriting our TensorFlow models and loss functions to be XLA-compatible. Our models and loss functions generally obey rule #1 and #2 by default, so you can skip over them if you’re using `transformers` models. Don’t forget about these rules when writing your own models and loss functions, though! </Tip> #### XLA Rule #1: Your code cannot have “data-dependent conditionals” What that means is that any `if` statement cannot depend on values inside a `tf.Tensor`. For example, this code block cannot be compiled with XLA! ```python if tf.reduce_sum(tensor) > 10: tensor = tensor / 2.0 ``` This might seem very restrictive at first, but most neural net code doesn’t need to do this. You can often get around this restriction by using `tf.cond` (see the documentation [here](https://www.tensorflow.org/api_docs/python/tf/cond)) or by removing the conditional and finding a clever math trick with indicator variables instead, like so: ```python sum_over_10 = tf.cast(tf.reduce_sum(tensor) > 10, tf.float32) tensor = tensor / (1.0 + sum_over_10) ``` This code has exactly the same effect as the code above, but by avoiding a conditional, we ensure it will compile with XLA without problems! #### XLA Rule #2: Your code cannot have “data-dependent shapes” What this means is that the shape of all of the `tf.Tensor` objects in your code cannot depend on their values. For example, the function `tf.unique` cannot be compiled with XLA, because it returns a `tensor` containing one instance of each unique value in the input. The shape of this output will obviously be different depending on how repetitive the input `Tensor` was, and so XLA refuses to handle it! In general, most neural network code obeys rule #2 by default. However, there are a few common cases where it becomes a problem. One very common one is when you use label masking, setting your labels to a negative value to indicate that those positions should be ignored when computing the loss. If you look at NumPy or PyTorch loss functions that support label masking, you will often see code like this that uses [boolean indexing](https://numpy.org/doc/stable/user/basics.indexing.html#boolean-array-indexing): ```python label_mask = labels >= 0 masked_outputs = outputs[label_mask] masked_labels = labels[label_mask] loss = compute_loss(masked_outputs, masked_labels) mean_loss = torch.mean(loss) ``` This code is totally fine in NumPy or PyTorch, but it breaks in XLA! Why? Because the shape of `masked_outputs` and `masked_labels` depends on how many positions are masked - that makes it a data-dependent shape. However, just like for rule #1, we can often rewrite this code to yield exactly the same output without any data-dependent shapes. ```python label_mask = tf.cast(labels >= 0, tf.float32) loss = compute_loss(outputs, labels) loss = loss * label_mask # Set negative label positions to 0 mean_loss = tf.reduce_sum(loss) / tf.reduce_sum(label_mask) ``` Here, we avoid data-dependent shapes by computing the loss for every position, but zeroing out the masked positions in both the numerator and denominator when we calculate the mean, which yields exactly the same result as the first block while maintaining XLA compatibility. Note that we use the same trick as in rule #1 - converting a `tf.bool` to `tf.float32` and using it as an indicator variable. This is a really useful trick, so remember it if you need to convert your own code to XLA! #### XLA Rule #3: XLA will need to recompile your model for every different input shape it sees This is the big one. What this means is that if your input shapes are very variable, XLA will have to recompile your model over and over, which will create huge performance problems. This commonly arises in NLP models, where input texts have variable lengths after tokenization. In other modalities, static shapes are more common and this rule is much less of a problem. How can you get around rule #3? The key is padding - if you pad all your inputs to the same length, and then use an `attention_mask`, you can get the same results as you’d get from variable shapes, but without any XLA issues. However, excessive padding can cause severe slowdown too - if you pad all your samples to the maximum length in the whole dataset, you might end up with batches consisting endless padding tokens, which will waste a lot of compute and memory! There isn’t a perfect solution to this problem. However, you can try some tricks. One very useful trick is to pad batches of samples up to a multiple of a number like 32 or 64 tokens. This often only increases the number of tokens by a small amount, but it hugely reduces the number of unique input shapes, because every input shape now has to be a multiple of 32 or 64. Fewer unique input shapes means fewer XLA compilations! <Tip> 🤗Specific HuggingFace Tip🤗: Our tokenizers and data collators have methods that can help you here. You can use `padding="max_length"` or `padding="longest"` when calling tokenizers to get them to output padded data. Our tokenizers and data collators also have a `pad_to_multiple_of` argument that you can use to reduce the number of unique input shapes you see! </Tip> ### How do I actually train my model on TPU? Once your training is XLA-compatible and (if you’re using TPU Node / Colab) your dataset has been prepared appropriately, running on TPU is surprisingly easy! All you really need to change in your code is to add a few lines to initialize your TPU, and to ensure that your model and dataset are created inside a `TPUStrategy` scope. Take a look at [our TPU example notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) to see this in action! ### Summary There was a lot in here, so let’s summarize with a quick checklist you can follow when you want to get your model ready for TPU training: - Make sure your code follows the three rules of XLA - Compile your model with `jit_compile=True` on CPU/GPU and confirm that you can train it with XLA - Either load your dataset into memory or use a TPU-compatible dataset loading approach (see [notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb)) - Migrate your code either to Colab (with accelerator set to “TPU”) or a TPU VM on Google Cloud - Add TPU initializer code (see [notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb)) - Create your `TPUStrategy` and make sure dataset loading and model creation are inside the `strategy.scope()` (see [notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb)) - Don’t forget to take `jit_compile=True` out again when you move to TPU! - 🙏🙏🙏🥺🥺🥺 - Call model.fit() - You did it!
gradio-app/gradio/blob/main/demo/blocks_random_slider/run.ipynb	Gradio Demo: blocks_random_slider ``` !pip install -q gradio ``` ``` import gradio as gr def func(slider_1, slider_2): return slider_1 * 5 + slider_2 with gr.Blocks() as demo: slider = gr.Slider(minimum=-10.2, maximum=15, label="Random Slider (Static)", randomize=True) slider_1 = gr.Slider(minimum=100, maximum=200, label="Random Slider (Input 1)", randomize=True) slider_2 = gr.Slider(minimum=10, maximum=23.2, label="Random Slider (Input 2)", randomize=True) slider_3 = gr.Slider(value=3, label="Non random slider") btn = gr.Button("Run") btn.click(func, inputs=[slider_1, slider_2], outputs=gr.Number()) if __name__ == "__main__": demo.launch() ```
huggingface/hub-docs/blob/main/docs/hub/security-git-ssh.md	Git over SSH You can access and write data in repositories on huggingface.co using SSH (Secure Shell Protocol). When you connect via SSH, you authenticate using a private key file on your local machine. Some actions, such as pushing changes, or cloning private repositories, will require you to upload your SSH public key to your account on huggingface.co. You can use a pre-existing SSH key, or generate a new one specifically for huggingface.co. ## Checking for existing SSH keys If you have an existing SSH key, you can use that key to authenticate Git operations over SSH. SSH keys are usually located under `~/.ssh` on Mac & Linux, and under `C:\\Users\\<username>\\.ssh` on Windows. List files under that directory and look for files of the form: - id_rsa.pub - id_ecdsa.pub - id_ed25519.pub Those files contain your SSH public key. If you don't have such file under `~/.ssh`, you will have to [generate a new key](#generating-a-new-ssh-keypair). Otherwise, you can [add your existing SSH public key(s) to your huggingface.co account](#add-a-ssh-key-to-your-account). ## Generating a new SSH keypair If you don't have any SSH keys on your machine, you can use `ssh-keygen` to generate a new SSH key pair (public + private keys): ``` $ ssh-keygen -t ed25519 -C "[email protected]" ``` We recommend entering a passphrase when you are prompted to. A passphrase is an extra layer of security: it is a password that will be prompted whenever you use your SSH key. Once your new key is generated, add it to your SSH agent with `ssh-add`: ``` $ ssh-add ~/.ssh/id_ed25519 ``` If you chose a different location than the default to store your SSH key, you would have to replace `~/.ssh/id_ed25519` with the file location you used. ## Add a SSH key to your account To access private repositories with SSH, or to push changes via SSH, you will need to add your SSH public key to your huggingface.co account. You can manage your SSH keys [in your user settings](https://huggingface.co/settings/keys). To add a SSH key to your account, click on the "Add SSH key" button. Then, enter a name for this key (for example, "Personal computer"), and copy and paste the content of your public SSH key in the area below. The public key is located in the `~/.ssh/id_XXXX.pub` file you found or generated in the previous steps. Click on "Add key", and voilà! You have added a SSH key to your huggingface.co account. ## Testing your SSH authentication Once you have added your SSH key to your huggingface.co account, you can test that the connection works as expected. In a terminal, run: ``` $ ssh -T [email protected] ``` If you see a message with your username, congrats! Everything went well, you are ready to use git over SSH. Otherwise, if the message states something like the following, make sure your SSH key is actually used by your SSH agent. ``` Hi anonymous, welcome to Hugging Face. ```
huggingface/transformers/blob/main/examples/research_projects/layoutlmv3/README.md	!--- Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # Token classification with LayoutLMv3 (PyTorch version) This directory contains a script, `run_funsd_cord.py`, that can be used to fine-tune (or evaluate) LayoutLMv3 on form understanding datasets, such as [FUNSD](https://guillaumejaume.github.io/FUNSD/) and [CORD](https://github.com/clovaai/cord). The script `run_funsd_cord.py` leverages the 🤗 Datasets library and the Trainer API. You can easily customize it to your needs. ## Fine-tuning on FUNSD Fine-tuning LayoutLMv3 for token classification on [FUNSD](https://guillaumejaume.github.io/FUNSD/) can be done as follows: ```bash python run_funsd_cord.py \ --model_name_or_path microsoft/layoutlmv3-base \ --dataset_name funsd \ --output_dir layoutlmv3-test \ --do_train \ --do_eval \ --max_steps 1000 \ --evaluation_strategy steps \ --eval_steps 100 \ --learning_rate 1e-5 \ --load_best_model_at_end \ --metric_for_best_model "eval_f1" \ --push_to_hub \ --push_to_hub°model_id layoutlmv3-finetuned-funsd ``` 👀 The resulting model can be found here: https://huggingface.co/nielsr/layoutlmv3-finetuned-funsd. By specifying the `push_to_hub` flag, the model gets uploaded automatically to the hub (regularly), together with a model card, which includes metrics such as precision, recall and F1. Note that you can easily update the model card, as it's just a README file of the respective repo on the hub. There's also the "Training metrics" [tab](https://huggingface.co/nielsr/layoutlmv3-finetuned-funsd/tensorboard), which shows Tensorboard logs over the course of training. Pretty neat, huh? ## Fine-tuning on CORD Fine-tuning LayoutLMv3 for token classification on [CORD](https://github.com/clovaai/cord) can be done as follows: ```bash python run_funsd_cord.py \ --model_name_or_path microsoft/layoutlmv3-base \ --dataset_name cord \ --output_dir layoutlmv3-test \ --do_train \ --do_eval \ --max_steps 1000 \ --evaluation_strategy steps \ --eval_steps 100 \ --learning_rate 5e-5 \ --load_best_model_at_end \ --metric_for_best_model "eval_f1" \ --push_to_hub \ --push_to_hub°model_id layoutlmv3-finetuned-cord ``` 👀 The resulting model can be found here: https://huggingface.co/nielsr/layoutlmv3-finetuned-cord. Note that a model card gets generated automatically in case you specify the `push_to_hub` flag.
gradio-app/gradio/blob/main/guides/03_building-with-blocks/03_state-in-blocks.md	State in Blocks We covered [State in Interfaces](https://gradio.app/interface-state), this guide takes a look at state in Blocks, which works mostly the same. ## Global State Global state in Blocks works the same as in Interface. Any variable created outside a function call is a reference shared between all users. ## Session State Gradio supports session state, where data persists across multiple submits within a page session, in Blocks apps as well. To reiterate, session data is _not_ shared between different users of your model. To store data in a session state, you need to do three things: 1. Create a `gr.State()` object. If there is a default value to this stateful object, pass that into the constructor. 2. In the event listener, put the `State` object as an input and output. 3. In the event listener function, add the variable to the input parameters and the return value. Let's take a look at a game of hangman. $code_hangman $demo_hangman Let's see how we do each of the 3 steps listed above in this game: 1. We store the used letters in `used_letters_var`. In the constructor of `State`, we set the initial value of this to `[]`, an empty list. 2. In `btn.click()`, we have a reference to `used_letters_var` in both the inputs and outputs. 3. In `guess_letter`, we pass the value of this `State` to `used_letters`, and then return an updated value of this `State` in the return statement. With more complex apps, you will likely have many State variables storing session state in a single Blocks app. Learn more about `State` in the [docs](https://gradio.app/docs#state).
gradio-app/gradio/blob/main/guides/cn/05_tabular-data-science-and-plots/plot-component-for-maps.md	如何使用地图组件绘制图表 Related spaces: Tags: PLOTS, MAPS ## 简介本指南介绍如何使用 Gradio 的 `Plot` 组件在地图上绘制地理数据。Gradio 的 `Plot` 组件可以与 Matplotlib、Bokeh 和 Plotly 一起使用。在本指南中，我们将使用 Plotly 进行操作。Plotly 可以让开发人员轻松创建各种地图来展示他们的地理数据。点击[这里](https://plotly.com/python/maps/)查看一些示例。 ## 概述我们将使用纽约市的 Airbnb 数据集，该数据集托管在 kaggle 上，点击[这里](https://www.kaggle.com/datasets/dgomonov/new-york-city-airbnb-open-data)。我已经将其上传到 Hugging Face Hub 作为一个数据集，方便使用和下载，点击[这里](https://huggingface.co/datasets/gradio/NYC-Airbnb-Open-Data)。使用这些数据，我们将在地图上绘制 Airbnb 的位置，并允许基于价格和位置进行筛选。下面是我们将要构建的演示。 ⚡️ $demo_map_airbnb ## 步骤 1-加载 CSV 数据 💾 让我们首先从 Hugging Face Hub 加载纽约市的 Airbnb 数据。 ```python from datasets import load_dataset dataset = load_dataset("gradio/NYC-Airbnb-Open-Data", split="train") df = dataset.to_pandas() def filter_map(min_price, max_price, boroughs): new_df = df[(df['neighbourhood_group'].isin(boroughs)) & (df['price'] > min_price) & (df['price'] < max_price)] names = new_df["name"].tolist() prices = new_df["price"].tolist() text_list = [(names[i], prices[i]) for i in range(0, len(names))] ``` 在上面的代码中，我们先将 CSV 数据加载到一个 pandas dataframe 中。让我们首先定义一个函数，这将作为 gradio 应用程序的预测函数。该函数将接受最低价格、最高价格范围和筛选结果地区的列表作为参数。我们可以使用传入的值 (`min_price`、`max_price` 和地区列表) 来筛选数据框并创建 `new_df`。接下来，我们将创建包含每个 Airbnb 的名称和价格的 `text_list`，以便在地图上使用作为标签。 ## 步骤 2-地图图表 🌐 Plotly 使得处理地图变得很容易。让我们看一下下面的代码，了解如何创建地图图表。 ```python import plotly.graph_objects as go fig = go.Figure(go.Scattermapbox( customdata=text_list, lat=new_df['latitude'].tolist(), lon=new_df['longitude'].tolist(), mode='markers', marker=go.scattermapbox.Marker( size=6 ), hoverinfo="text", hovertemplate='<b>Name</b>: %{customdata[0]}<br><b>Price</b>: $%{customdata[1]}' )) fig.update_layout( mapbox_style="open-street-map", hovermode='closest', mapbox=dict( bearing=0, center=go.layout.mapbox.Center( lat=40.67, lon=-73.90 ), pitch=0, zoom=9 ), ) ``` 上面的代码中，我们通过传入经纬度列表来创建一个散点图。我们还传入了名称和价格的自定义数据，以便在鼠标悬停在每个标记上时显示额外的信息。接下来，我们使用 `update_layout` 来指定其他地图设置，例如缩放和居中。有关使用 Mapbox 和 Plotly 创建散点图的更多信息，请点击[这里](https://plotly.com/python/scattermapbox/)。 ## 步骤 3-Gradio 应用程序 ⚡️ 我们将使用两个 `gr.Number` 组件和一个 `gr.CheckboxGroup` 组件，允许用户指定价格范围和地区位置。然后，我们将使用 `gr.Plot` 组件作为我们之前创建的 Plotly + Mapbox 地图的输出。 ```python with gr.Blocks() as demo: with gr.Column(): with gr.Row(): min_price = gr.Number(value=250, label="Minimum Price") max_price = gr.Number(value=1000, label="Maximum Price") boroughs = gr.CheckboxGroup(choices=["Queens", "Brooklyn", "Manhattan", "Bronx", "Staten Island"], value=["Queens", "Brooklyn"], label="Select Boroughs:") btn = gr.Button(value="Update Filter") map = gr.Plot() demo.load(filter_map, [min_price, max_price, boroughs], map) btn.click(filter_map, [min_price, max_price, boroughs], map) ``` 我们使用 `gr.Column` 和 `gr.Row` 布局这些组件，并为演示加载时和点击 " 更新筛选 " 按钮时添加了事件触发器，以触发地图更新新的筛选条件。以下是完整演示代码： $code_map_airbnb ## 步骤 4-部署 Deployment 🤗 如果你运行上面的代码，你的应用程序将在本地运行。如果要获取临时共享链接，可以将 `share=True` 参数传递给 `launch`。但如果你想要一个永久的部署解决方案呢？让我们将我们的 Gradio 应用程序部署到免费的 HuggingFace Spaces 平台。如果你以前没有使用过 Spaces，请按照之前的指南[这里](/using_hugging_face_integrations)。 ## 结论 🎉 你已经完成了！这是构建地图演示所需的所有代码。链接到演示：[地图演示](https://huggingface.co/spaces/gradio/map_airbnb)和[完整代码](https://huggingface.co/spaces/gradio/map_airbnb/blob/main/run.py)（在 Hugging Face Spaces）
huggingface/pytorch-image-models/blob/main/hfdocs/source/models/se-resnet.mdx	SE-ResNet SE ResNet is a variant of a [ResNet](https://www.paperswithcode.com/method/resnet) that employs [squeeze-and-excitation blocks](https://paperswithcode.com/method/squeeze-and-excitation-block) to enable the network to perform dynamic channel-wise feature recalibration. ## How do I use this model on an image? To load a pretrained model: ```py >>> import timm >>> model = timm.create_model('seresnet152d', pretrained=True) >>> model.eval() ``` To load and preprocess the image: ```py >>> import urllib >>> from PIL import Image >>> from timm.data import resolve_data_config >>> from timm.data.transforms_factory import create_transform >>> config = resolve_data_config({}, model=model) >>> transform = create_transform(**config) >>> url, filename = ("https://github.com/pytorch/hub/raw/master/images/dog.jpg", "dog.jpg") >>> urllib.request.urlretrieve(url, filename) >>> img = Image.open(filename).convert('RGB') >>> tensor = transform(img).unsqueeze(0) # transform and add batch dimension ``` To get the model predictions: ```py >>> import torch >>> with torch.no_grad(): ... out = model(tensor) >>> probabilities = torch.nn.functional.softmax(out[0], dim=0) >>> print(probabilities.shape) >>> # prints: torch.Size([1000]) ``` To get the top-5 predictions class names: ```py >>> # Get imagenet class mappings >>> url, filename = ("https://raw.githubusercontent.com/pytorch/hub/master/imagenet_classes.txt", "imagenet_classes.txt") >>> urllib.request.urlretrieve(url, filename) >>> with open("imagenet_classes.txt", "r") as f: ... categories = [s.strip() for s in f.readlines()] >>> # Print top categories per image >>> top5_prob, top5_catid = torch.topk(probabilities, 5) >>> for i in range(top5_prob.size(0)): ... print(categories[top5_catid[i]], top5_prob[i].item()) >>> # prints class names and probabilities like: >>> # [('Samoyed', 0.6425196528434753), ('Pomeranian', 0.04062102362513542), ('keeshond', 0.03186424449086189), ('white wolf', 0.01739676296710968), ('Eskimo dog', 0.011717947199940681)] ``` Replace the model name with the variant you want to use, e.g. `seresnet152d`. You can find the IDs in the model summaries at the top of this page. To extract image features with this model, follow the [timm feature extraction examples](../feature_extraction), just change the name of the model you want to use. ## How do I finetune this model? You can finetune any of the pre-trained models just by changing the classifier (the last layer). ```py >>> model = timm.create_model('seresnet152d', pretrained=True, num_classes=NUM_FINETUNE_CLASSES) ``` To finetune on your own dataset, you have to write a training loop or adapt [timm's training script](https://github.com/rwightman/pytorch-image-models/blob/master/train.py) to use your dataset. ## How do I train this model? You can follow the [timm recipe scripts](../scripts) for training a new model afresh. ## Citation ```BibTeX @misc{hu2019squeezeandexcitation, title={Squeeze-and-Excitation Networks}, author={Jie Hu and Li Shen and Samuel Albanie and Gang Sun and Enhua Wu}, year={2019}, eprint={1709.01507}, archivePrefix={arXiv}, primaryClass={cs.CV} } ``` <!-- Type: model-index Collections: - Name: SE ResNet Paper: Title: Squeeze-and-Excitation Networks URL: https://paperswithcode.com/paper/squeeze-and-excitation-networks Models: - Name: seresnet152d In Collection: SE ResNet Metadata: FLOPs: 20161904304 Parameters: 66840000 File Size: 268144497 Architecture: - 1x1 Convolution - Batch Normalization - Bottleneck Residual Block - Convolution - Global Average Pooling - Max Pooling - ReLU - Residual Block - Residual Connection - Softmax - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA Titan X GPUs ID: seresnet152d LR: 0.6 Epochs: 100 Layers: 152 Dropout: 0.2 Crop Pct: '0.94' Momentum: 0.9 Batch Size: 1024 Image Size: '256' Interpolation: bicubic Code: https://github.com/rwightman/pytorch-image-models/blob/a7f95818e44b281137503bcf4b3e3e94d8ffa52f/timm/models/resnet.py#L1206 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-weights/seresnet152d_ra2-04464dd2.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 83.74% Top 5 Accuracy: 96.77% - Name: seresnet50 In Collection: SE ResNet Metadata: FLOPs: 5285062320 Parameters: 28090000 File Size: 112621903 Architecture: - 1x1 Convolution - Batch Normalization - Bottleneck Residual Block - Convolution - Global Average Pooling - Max Pooling - ReLU - Residual Block - Residual Connection - Softmax - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA Titan X GPUs ID: seresnet50 LR: 0.6 Epochs: 100 Layers: 50 Dropout: 0.2 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 1024 Image Size: '224' Interpolation: bicubic Code: https://github.com/rwightman/pytorch-image-models/blob/a7f95818e44b281137503bcf4b3e3e94d8ffa52f/timm/models/resnet.py#L1180 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-weights/seresnet50_ra_224-8efdb4bb.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 80.26% Top 5 Accuracy: 95.07% -->
huggingface/evaluate/blob/main/metrics/poseval/README.md	-- title: poseval emoji: 🤗 colorFrom: blue colorTo: red sdk: gradio sdk_version: 3.19.1 app_file: app.py pinned: false tags: - evaluate - metric description: >- The poseval metric can be used to evaluate POS taggers. Since seqeval does not work well with POS data that is not in IOB format the poseval is an alternative. It treats each token in the dataset as independant observation and computes the precision, recall and F1-score irrespective of sentences. It uses scikit-learns's classification report to compute the scores. --- # Metric Card for peqeval ## Metric description The poseval metric can be used to evaluate POS taggers. Since seqeval does not work well with POS data (see e.g. [here](https://stackoverflow.com/questions/71327693/how-to-disable-seqeval-label-formatting-for-pos-tagging)) that is not in IOB format the poseval is an alternative. It treats each token in the dataset as independant observation and computes the precision, recall and F1-score irrespective of sentences. It uses scikit-learns's [classification report](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html) to compute the scores. ## How to use Poseval produces labelling scores along with its sufficient statistics from a source against references. It takes two mandatory arguments: `predictions`: a list of lists of predicted labels, i.e. estimated targets as returned by a tagger. `references`: a list of lists of reference labels, i.e. the ground truth/target values. It can also take several optional arguments: `zero_division`: Which value to substitute as a metric value when encountering zero division. Should be one of [`0`,`1`,`"warn"`]. `"warn"` acts as `0`, but the warning is raised. ```python >>> predictions = [['INTJ', 'ADP', 'PROPN', 'NOUN', 'PUNCT', 'INTJ', 'ADP', 'PROPN', 'VERB', 'SYM']] >>> references = [['INTJ', 'ADP', 'PROPN', 'PROPN', 'PUNCT', 'INTJ', 'ADP', 'PROPN', 'PROPN', 'SYM']] >>> poseval = evaluate.load("poseval") >>> results = poseval.compute(predictions=predictions, references=references) >>> print(list(results.keys())) ['ADP', 'INTJ', 'NOUN', 'PROPN', 'PUNCT', 'SYM', 'VERB', 'accuracy', 'macro avg', 'weighted avg'] >>> print(results["accuracy"]) 0.8 >>> print(results["PROPN"]["recall"]) 0.5 ``` ## Output values This metric returns a a classification report as a dictionary with a summary of scores for overall and per type: Overall (weighted and macro avg): `accuracy`: the average [accuracy](https://huggingface.co/metrics/accuracy), on a scale between 0.0 and 1.0. `precision`: the average [precision](https://huggingface.co/metrics/precision), on a scale between 0.0 and 1.0. `recall`: the average [recall](https://huggingface.co/metrics/recall), on a scale between 0.0 and 1.0. `f1`: the average [F1 score](https://huggingface.co/metrics/f1), which is the harmonic mean of the precision and recall. It also has a scale of 0.0 to 1.0. Per type (e.g. `MISC`, `PER`, `LOC`,...): `precision`: the average [precision](https://huggingface.co/metrics/precision), on a scale between 0.0 and 1.0. `recall`: the average [recall](https://huggingface.co/metrics/recall), on a scale between 0.0 and 1.0. `f1`: the average [F1 score](https://huggingface.co/metrics/f1), on a scale between 0.0 and 1.0. ## Examples ```python >>> predictions = [['INTJ', 'ADP', 'PROPN', 'NOUN', 'PUNCT', 'INTJ', 'ADP', 'PROPN', 'VERB', 'SYM']] >>> references = [['INTJ', 'ADP', 'PROPN', 'PROPN', 'PUNCT', 'INTJ', 'ADP', 'PROPN', 'PROPN', 'SYM']] >>> poseval = evaluate.load("poseval") >>> results = poseval.compute(predictions=predictions, references=references) >>> print(list(results.keys())) ['ADP', 'INTJ', 'NOUN', 'PROPN', 'PUNCT', 'SYM', 'VERB', 'accuracy', 'macro avg', 'weighted avg'] >>> print(results["accuracy"]) 0.8 >>> print(results["PROPN"]["recall"]) 0.5 ``` ## Limitations and bias In contrast to [seqeval](https://github.com/chakki-works/seqeval), the poseval metric treats each token independently and computes the classification report over all concatenated sequences.. ## Citation ```bibtex @article{scikit-learn, title={Scikit-learn: Machine Learning in {P}ython}, author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.}, journal={Journal of Machine Learning Research}, volume={12}, pages={2825--2830}, year={2011} } ``` ## Further References - [README for seqeval at GitHub](https://github.com/chakki-works/seqeval) - [Classification report](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html) - [Issues with seqeval](https://stackoverflow.com/questions/71327693/how-to-disable-seqeval-label-formatting-for-pos-tagging)
huggingface/blog/blob/main/large-language-models.md	-- title: "Large Language Models: A New Moore's Law?" thumbnail: /blog/assets/33_large_language_models/01_model_size.jpg authors: - user: juliensimon --- # Large Language Models: A New Moore's Law? A few days ago, Microsoft and NVIDIA [introduced](https://www.microsoft.com/en-us/research/blog/using-deepspeed-and-megatron-to-train-megatron-turing-nlg-530b-the-worlds-largest-and-most-powerful-generative-language-model/) Megatron-Turing NLG 530B, a Transformer-based model hailed as "the world’s largest and most powerful generative language model." This is an impressive show of Machine Learning engineering, no doubt about it. Yet, should we be excited about this mega-model trend? I, for one, am not. Here's why. <kbd> <img src="assets/33_large_language_models/01_model_size.jpg"> </kbd> ### This is your Brain on Deep Learning Researchers estimate that the human brain contains an average of [86 billion neurons](https://pubmed.ncbi.nlm.nih.gov/19226510/) and 100 trillion synapses. It's safe to assume that not all of them are dedicated to language either. Interestingly, GPT-4 is [expected](https://www.wired.com/story/cerebras-chip-cluster-neural-networks-ai/) to have about 100 trillion parameters... As crude as this analogy is, shouldn't we wonder whether building language models that are about the size of the human brain is the best long-term approach? Of course, our brain is a marvelous device, produced by millions of years of evolution, while Deep Learning models are only a few decades old. Still, our intuition should tell us that something doesn't compute (pun intended). ### Deep Learning, Deep Pockets? As you would expect, training a 530-billion parameter model on humongous text datasets requires a fair bit of infrastructure. In fact, Microsoft and NVIDIA used hundreds of DGX A100 multi-GPU servers. At $199,000 a piece, and factoring in networking equipment, hosting costs, etc., anyone looking to replicate this experiment would have to spend close to $100 million dollars. Want fries with that? Seriously, which organizations have business use cases that would justify spending $100 million on Deep Learning infrastructure? Or even $10 million? Very few. So who are these models for, really? ### That Warm Feeling is your GPU Cluster For all its engineering brilliance, training Deep Learning models on GPUs is a brute force technique. According to the spec sheet, each DGX server can consume up to 6.5 kilowatts. Of course, you'll need at least as much cooling power in your datacenter (or your server closet). Unless you're the Starks and need to keep Winterfell warm in winter, that's another problem you'll have to deal with. In addition, as public awareness grows on climate and social responsibility issues, organizations need to account for their carbon footprint. According to this 2019 [study](https://arxiv.org/pdf/1906.02243.pdf) from the University of Massachusetts, "training BERT on GPU is roughly equivalent to a trans-American flight". BERT-Large has 340 million parameters. One can only extrapolate what the footprint of Megatron-Turing could be... People who know me wouldn't call me a bleeding-heart environmentalist. Still, some numbers are hard to ignore. ### So? Am I excited by Megatron-Turing NLG 530B and whatever beast is coming next? No. Do I think that the (relatively small) benchmark improvement is worth the added cost, complexity and carbon footprint? No. Do I think that building and promoting these huge models is helping organizations understand and adopt Machine Learning ? No. I'm left wondering what's the point of it all. Science for the sake of science? Good old marketing? Technological supremacy? Probably a bit of each. I'll leave them to it, then. Instead, let me focus on pragmatic and actionable techniques that you can all use to build high quality Machine Learning solutions. ### Use Pretrained Models In the vast majority of cases, you won't need a custom model architecture. Maybe you'll want a custom one (which is a different thing), but there be dragons. Experts only! A good starting point is to look for [models](https://huggingface.co/models) that have been pretrained for the task you're trying to solve (say, [summarizing English text](https://huggingface.co/models?language=en&pipeline_tag=summarization&sort=downloads)). Then, you should quickly try out a few models to predict your own data. If metrics tell you that one works well enough, you're done! If you need a little more accuracy, you should consider fine-tuning the model (more on this in a minute). ### Use Smaller Models When evaluating models, you should pick the smallest one that can deliver the accuracy you need. It will predict faster and require fewer hardware resources for training and inference. Frugality goes a long way. It's nothing new either. Computer Vision practitioners will remember when [SqueezeNet](https://arxiv.org/abs/1602.07360) came out in 2017, achieving a 50x reduction in model size compared to [AlexNet](https://papers.nips.cc/paper/2012/hash/c399862d3b9d6b76c8436e924a68c45b-Abstract.html), while meeting or exceeding its accuracy. How clever that was! Downsizing efforts are also under way in the Natural Language Processing community, using transfer learning techniques such as [knowledge distillation](https://en.wikipedia.org/wiki/Knowledge_distillation). [DistilBERT](https://arxiv.org/abs/1910.01108) is perhaps its most widely known achievement. Compared to the original BERT model, it retains 97% of language understanding while being 40% smaller and 60% faster. You can try it [here](https://huggingface.co/distilbert-base-uncased). The same approach has been applied to other models, such as Facebook's [BART](https://arxiv.org/abs/1910.13461), and you can try DistilBART [here](https://huggingface.co/models?search=distilbart). Recent models from the [Big Science](https://bigscience.huggingface.co/) project are also very impressive. As visible in this graph included in the [research paper](https://arxiv.org/abs/2110.08207), their T0 model outperforms GPT-3 on many tasks while being 16x smaller. <kbd> <img src="assets/33_large_language_models/02_t0.png"> </kbd> You can try T0 [here](https://huggingface.co/bigscience/T0pp). This is the kind of research we need more of! ### Fine-Tune Models If you need to specialize a model, there should be very few reasons to train it from scratch. Instead, you should fine-tune it, that is to say train it only for a few epochs on your own data. If you're short on data, maybe of one these [datasets](https://huggingface.co/datasets) can get you started. You guessed it, that's another way to do transfer learning, and it'll help you save on everything! * Less data to collect, store, clean and annotate, * Faster experiments and iterations, * Fewer resources required in production. In other words: save time, save money, save hardware resources, save the world! If you need a tutorial, the Hugging Face [course](https://huggingface.co/course) will get you started in no time. ### Use Cloud-Based Infrastructure Like them or not, cloud companies know how to build efficient infrastructure. Sustainability studies show that cloud-based infrastructure is more energy and carbon efficient than the alternative: see [AWS](https://sustainability.aboutamazon.com/environment/the-cloud), [Azure](https://azure.microsoft.com/en-us/global-infrastructure/sustainability), and [Google](https://cloud.google.com/sustainability). Earth.org [says](https://earth.org/environmental-impact-of-cloud-computing/) that while cloud infrastructure is not perfect, "[it's] more energy efficient than the alternative and facilitates environmentally beneficial services and economic growth." Cloud certainly has a lot going for it when it comes to ease of use, flexibility and pay as you go. It's also a little greener than you probably thought. If you're short on GPUs, why not try fine-tune your Hugging Face models on [Amazon SageMaker](https://aws.amazon.com/sagemaker/), AWS' managed service for Machine Learning? We've got [plenty of examples](https://huggingface.co/docs/sagemaker/train) for you. ### Optimize Your Models From compilers to virtual machines, software engineers have long used tools that automatically optimize their code for whatever hardware they're running on. However, the Machine Learning community is still struggling with this topic, and for good reason. Optimizing models for size and speed is a devilishly complex task, which involves techniques such as: * Specialized hardware that speeds up training ([Graphcore](https://www.graphcore.ai/), [Habana](https://habana.ai/)) and inference ([Google TPU](https://cloud.google.com/tpu), [AWS Inferentia](https://aws.amazon.com/machine-learning/inferentia/)). * Pruning: remove model parameters that have little or no impact on the predicted outcome. * Fusion: merge model layers (say, convolution and activation). * Quantization: storing model parameters in smaller values (say, 8 bits instead of 32 bits) Fortunately, automated tools are starting to appear, such as the [Optimum](https://huggingface.co/hardware) open source library, and [Infinity](https://huggingface.co/infinity), a containerized solution that delivers Transformers accuracy at 1-millisecond latency. ### Conclusion Large language model size has been increasing 10x every year for the last few years. This is starting to look like another [Moore's Law](https://en.wikipedia.org/wiki/Moore%27s_law). We've been there before, and we should know that this road leads to diminishing returns, higher cost, more complexity, and new risks. Exponentials tend not to end well. Remember [Meltdown and Spectre](https://meltdownattack.com/)? Do we want to find out what that looks like for AI? Instead of chasing trillion-parameter models (place your bets), wouldn't all be better off if we built practical and efficient solutions that all developers can use to solve real-world problems? Interested in how Hugging Face can help your organization build and deploy production-grade Machine Learning solutions? Get in touch at [[email protected]](mailto:[email protected]) (no recruiters, no sales pitches, please).
huggingface/transformers/blob/main/docs/source/en/model_doc/vision-text-dual-encoder.md	!--Copyright 2021 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # VisionTextDualEncoder ## Overview The [`VisionTextDualEncoderModel`] can be used to initialize a vision-text dual encoder model with any pretrained vision autoencoding model as the vision encoder (e.g. [ViT](vit), [BEiT](beit), [DeiT](deit)) and any pretrained text autoencoding model as the text encoder (e.g. [RoBERTa](roberta), [BERT](bert)). Two projection layers are added on top of both the vision and text encoder to project the output embeddings to a shared latent space. The projection layers are randomly initialized so the model should be fine-tuned on a downstream task. This model can be used to align the vision-text embeddings using CLIP like contrastive image-text training and then can be used for zero-shot vision tasks such image-classification or retrieval. In [LiT: Zero-Shot Transfer with Locked-image Text Tuning](https://arxiv.org/abs/2111.07991) it is shown how leveraging pre-trained (locked/frozen) image and text model for contrastive learning yields significant improvement on new zero-shot vision tasks such as image classification or retrieval. ## VisionTextDualEncoderConfig [[autodoc]] VisionTextDualEncoderConfig ## VisionTextDualEncoderProcessor [[autodoc]] VisionTextDualEncoderProcessor <frameworkcontent> <pt> ## VisionTextDualEncoderModel [[autodoc]] VisionTextDualEncoderModel - forward </pt> <tf> ## FlaxVisionTextDualEncoderModel [[autodoc]] FlaxVisionTextDualEncoderModel - __call__ </tf> <jax> ## TFVisionTextDualEncoderModel [[autodoc]] TFVisionTextDualEncoderModel - call </jax> </frameworkcontent>
huggingface/course/blob/main/subtitles/en/raw/chapter3/02d_dynamic-padding.md	hat is dynamic padding? In the "Batching Inputs together" video, we have seen that to be able to group inputs of different lengths in the same batch, we need to add padding tokens to all the short inputs until they are all of the same length. Here for instance, the longest sentence is the third one, and we need to add 5, 2 and 7 pad tokens to the other to have four sentences of the same lengths. When dealing with a whole dataset, there are various padding strategies we can apply. The most obvious one is to pad all the elements of the dataset to the same length: the length of the longest sample. This will then give us batches that all have the same shape determined by the maximum sequence length. The downside is that batches composed from short sentences will have a lot of padding tokens which introduce more computations in the model we ultimately don't need. To avoid this, another strategy is to pad the elements when we batch them together, to the longest sentence inside the batch. This way batches composed of short inputs will be smaller than the batch containing the longest sentence in the dataset. This will yield some nice speedup on CPU and GPU. The downside is that all batches will then have different shapes, which slows down training on other accelerators like TPUs. Let's see how to apply both strategies in practice. We have actually seen how to apply fixed padding in the Datasets Overview video, when we preprocessed the MRPC dataset: after loading the dataset and tokenizer, we applied the tokenization to all the dataset with padding and truncation to make all samples of length 128. As a result, if we pass this dataset to a PyTorch DataLoader, we get batches of shape batch size (here 16) by 128. To apply dynamic padding, we must defer the padding to the batch preparation, so we remove that part from our tokenize function. We still leave the truncation part so that inputs that are bigger than the maximum length accepted by the model (usually 512) get truncated to that length. Then we pad our samples dynamically by using a data collator. Those classes in the Transformers library are responsible for applying all the final processing needed before forming a batch, here DataCollatorWithPadding will pad the samples to the maximum length inside the batch of sentences. We pass it to the PyTorch DataLoader as a collate function, then observe that the batches generated have various lenghs, all way below the 128 from before. Dynamic batching will almost always be faster on CPUs and GPUs, so you should apply it if you can. Remember to switch back to fixed padding however if you run your training script on TPU or need batches of fixed shapes.
huggingface/diffusers/blob/main/docs/source/en/api/pipelines/kandinsky3.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # Kandinsky 3 Kandinsky 3 is created by [Vladimir Arkhipkin](https://github.com/oriBetelgeuse),[Anastasia Maltseva](https://github.com/NastyaMittseva),[Igor Pavlov](https://github.com/boomb0om),[Andrei Filatov](https://github.com/anvilarth),[Arseniy Shakhmatov](https://github.com/cene555),[Andrey Kuznetsov](https://github.com/kuznetsoffandrey),[Denis Dimitrov](https://github.com/denndimitrov), [Zein Shaheen](https://github.com/zeinsh) The description from it's Github page: Kandinsky 3.0 is an open-source text-to-image diffusion model built upon the Kandinsky2-x model family. In comparison to its predecessors, enhancements have been made to the text understanding and visual quality of the model, achieved by increasing the size of the text encoder and Diffusion U-Net models, respectively. Its architecture includes 3 main components: 1. [FLAN-UL2](https://huggingface.co/google/flan-ul2), which is an encoder decoder model based on the T5 architecture. 2. New U-Net architecture featuring BigGAN-deep blocks doubles depth while maintaining the same number of parameters. 3. Sber-MoVQGAN is a decoder proven to have superior results in image restoration. The original codebase can be found at [ai-forever/Kandinsky-3](https://github.com/ai-forever/Kandinsky-3). <Tip> Check out the [Kandinsky Community](https://huggingface.co/kandinsky-community) organization on the Hub for the official model checkpoints for tasks like text-to-image, image-to-image, and inpainting. </Tip> <Tip> Make sure to check out the schedulers [guide](../../using-diffusers/schedulers) to learn how to explore the tradeoff between scheduler speed and quality, and see the [reuse components across pipelines](../../using-diffusers/loading#reuse-components-across-pipelines) section to learn how to efficiently load the same components into multiple pipelines. </Tip> ## Kandinsky3Pipeline [[autodoc]] Kandinsky3Pipeline - all - __call__ ## Kandinsky3Img2ImgPipeline [[autodoc]] Kandinsky3Img2ImgPipeline - all - __call__
huggingface/datasets-server/blob/main/services/worker/README.md	Datasets server - worker > Workers that pre-compute and cache the response to /splits, /first-rows, /parquet, /info and /size. ## Configuration Use environment variables to configure the workers. The prefix of each environment variable gives its scope. ### Uvicorn The following environment variables are used to configure the Uvicorn server (`WORKER_UVICORN_` prefix). It is used for the /healthcheck and the /metrics endpoints: - `WORKER_UVICORN_HOSTNAME`: the hostname. Defaults to `"localhost"`. - `WORKER_UVICORN_NUM_WORKERS`: the number of uvicorn workers. Defaults to `2`. - `WORKER_UVICORN_PORT`: the port. Defaults to `8000`. ### Prometheus - `PROMETHEUS_MULTIPROC_DIR`: the directory where the uvicorn workers share their prometheus metrics. See https://github.com/prometheus/client_python#multiprocess-mode-eg-gunicorn. Defaults to empty, in which case every uvicorn worker manages its own metrics, and the /metrics endpoint returns the metrics of a random worker. ## Worker configuration Set environment variables to configure the worker. - `WORKER_CONTENT_MAX_BYTES`: the maximum size in bytes of the response content computed by a worker (to prevent returning big responses in the REST API). Defaults to `10_000_000`. - `WORKER_DIFFICULTY_MAX`: the maximum difficulty of the jobs to process. Defaults to None. - `WORKER_DIFFICULTY_MIN`: the minimum difficulty of the jobs to process. Defaults to None. - `WORKER_HEARTBEAT_INTERVAL_SECONDS`: the time interval between two heartbeats. Each heartbeat updates the job "last_heartbeat" field in the queue. Defaults to `60` (1 minute). - `WORKER_JOB_TYPES_BLOCKED`: comma-separated list of job types that will not be processed, e.g. "dataset-config-names,dataset-split-names". If empty, no job type is blocked. Defaults to empty. - `WORKER_JOB_TYPES_ONLY`: comma-separated list of the non-blocked job types to process, e.g. "dataset-config-names,dataset-split-names". If empty, the worker processes all the non-blocked jobs. Defaults to empty. - `WORKER_KILL_LONG_JOB_INTERVAL_SECONDS`: the time interval at which the worker looks for long jobs to kill them. Defaults to `60` (1 minute). - `WORKER_KILL_ZOMBIES_INTERVAL_SECONDS`: the time interval at which the worker looks for zombie jobs to kill them. Defaults to `600` (10 minutes). - `WORKER_MAX_DISK_USAGE_PCT`: maximum disk usage of every storage disk in the list (in percentage) to allow a job to start. Set to 0 to disable the test. Defaults to 90. - `WORKER_MAX_JOB_DURATION_SECONDS`: the maximum duration allowed for a job to run. If the job runs longer, it is killed (see `WORKER_KILL_LONG_JOB_INTERVAL_SECONDS`). Defaults to `1200` (20 minutes). - `WORKER_MAX_LOAD_PCT`: maximum load of the machine (in percentage: the max between the 1m load and the 5m load divided by the number of CPUs \100) allowed to start a job. Set to 0 to disable the test. Defaults to 70. - `WORKER_MAX_MEMORY_PCT`: maximum memory (RAM + SWAP) usage of the machine (in percentage) allowed to start a job. Set to 0 to disable the test. Defaults to 80. - `WORKER_MAX_MISSING_HEARTBEATS`: the number of hearbeats a job must have missed to be considered a zombie job. Defaults to `5`. - `WORKER_SLEEP_SECONDS`: wait duration in seconds at each loop iteration before checking if resources are available and processing a job if any is available. Note that the loop doesn't wait just after finishing a job: the next job is immediately processed. Defaults to `15`. - `WORKER_STORAGE_PATHS`: comma-separated list of paths to check for disk usage. Defaults to empty. Also, it's possible to force the parent directory in which the temporary files (as the current job state file and its associated lock file) will be created by setting `TMPDIR` to a writable directory. If not set, the worker will use the default temporary directory of the system, as described in https://docs.python.org/3/library/tempfile.html#tempfile.gettempdir. ### Datasets based worker Set environment variables to configure the datasets-based worker (`DATASETS_BASED_` prefix): - `DATASETS_BASED_HF_DATASETS_CACHE`: directory where the `datasets` library will store the cached datasets' data. If not set, the datasets library will choose the default location. Defaults to None. Also, set the modules cache configuration for the datasets-based worker. See [../../libs/libcommon/README.md](../../libs/libcommon/README.md). Note that this variable has no `DATASETS_BASED_` prefix: - `HF_MODULES_CACHE`: directory where the `datasets` library will store the cached dataset scripts. If not set, the datasets library will choose the default location. Defaults to None. Note that both directories will be appended to `WORKER_STORAGE_PATHS` (see [../../libs/libcommon/README.md](../../libs/libcommon/README.md)) to hold the workers when the disk is full. ### Numba library Numba requires setting the `NUMBA_CACHE_DIR` environment variable to a writable directory to cache the compiled functions. Required on cloud infrastructure (see https://stackoverflow.com/a/63367171/7351594): - `NUMBA_CACHE_DIR`: directory where the `numba` decorators (used by `librosa`) can write cache. Note that this directory will be appended to `WORKER_STORAGE_PATHS` (see [../../libs/libcommon/README.md](../../libs/libcommon/README.md)) to hold the workers when the disk is full. ### Huggingface_hub library If the Hub is not https://huggingface.co (i.e., if you set the `COMMON_HF_ENDPOINT` environment variable), you must set the `HF_ENDPOINT` environment variable to the same value. See https://github.com/huggingface/datasets/pull/5196#issuecomment-1322191411 for more details: - `HF_ENDPOINT`: the URL of the Hub. Defaults to `https://huggingface.co`. ### First rows worker Set environment variables to configure the `first-rows` worker (`FIRST_ROWS_` prefix): - `FIRST_ROWS_MAX_BYTES`: the max size of the /first-rows response in bytes. Defaults to `1_000_000` (1 MB). - `FIRST_ROWS_MAX_NUMBER`: the max number of rows fetched by the worker for the split and provided in the /first-rows response. Defaults to `100`. - `FIRST_ROWS_MIN_CELL_BYTES`: the minimum size in bytes of a cell when truncating the content of a row (see `FIRST_ROWS_ROWS_MAX_BYTES`). Below this limit, the cell content will not be truncated. Defaults to `100`. - `FIRST_ROWS_MIN_NUMBER`: the min number of rows fetched by the worker for the split and provided in the /first-rows response. Defaults to `10`. - `FIRST_ROWS_COLUMNS_MAX_NUMBER`: the max number of columns (features) provided in the /first-rows response. If the number of columns is greater than the limit, an error is returned. Defaults to `1_000`. Also, set the assets-related configuration for the first-rows worker. See [../../libs/libcommon/README.md](../../libs/libcommon/README.md). ### Parquet and info worker Set environment variables to configure the `parquet-and-info` worker (`PARQUET_AND_INFO_` prefix): - `PARQUET_AND_INFO_COMMIT_MESSAGE`: the git commit message when the worker uploads the parquet files to the Hub. Defaults to `Update parquet files`. - `PARQUET_AND_INFO_COMMITTER_HF_TOKEN`: the HuggingFace token to commit the parquet files to the Hub. The token must be an app token associated with a user that has the right to 1. create the `refs/convert/parquet` branch (see `PARQUET_AND_INFO_TARGET_REVISION`) and 2. push commits to it on any dataset. [Datasets maintainers](https://huggingface.co/datasets-maintainers) members have these rights. The token must have permission to write. If not set, the worker will fail. Defaults to None. - `PARQUET_AND_INFO_MAX_DATASET_SIZE_BYTES`: the maximum size in bytes of the dataset to pre-compute the parquet files. Bigger datasets, or datasets without that information, are partially streamed to get parquet files up to this value. Defaults to `100_000_000`. - `PARQUET_AND_INFO_MAX_EXTERNAL_DATA_FILES`: the maximum number of external files of the datasets. Bigger datasets, or datasets without that information, are partially streamed to get parquet files up to `PARQUET_AND_INFO_MAX_DATASET_SIZE_BYTES` bytes. Defaults to `10_000`. - `PARQUET_AND_INFO_MAX_ROW_GROUP_BYTE_SIZE_FOR_COPY`: the maximum size in bytes of the row groups of parquet datasets that are copied to the target revision. Bigger datasets, or datasets without that information, are partially streamed to get parquet files up to `PARQUET_AND_INFO_MAX_DATASET_SIZE_BYTES` bytes. Defaults to `100_000_000`. - `PARQUET_AND_INFO_SOURCE_REVISION`: the git revision of the dataset to use to prepare the parquet files. Defaults to `main`. - `PARQUET_AND_INFO_TARGET_REVISION`: the git revision of the dataset where to store the parquet files. Make sure the committer token (`PARQUET_AND_INFO_COMMITTER_HF_TOKEN`) has the permission to write there. Defaults to `refs/convert/parquet`. - `PARQUET_AND_INFO_URL_TEMPLATE`: the URL template to build the parquet file URLs. Defaults to `/datasets/%s/resolve/%s/%s`. ### Duckdb Index worker Set environment variables to configure the `duckdb-index` worker (`DUCKDB_INDEX_` prefix): - `DUCKDB_INDEX_CACHE_DIRECTORY`: directory where the temporal duckdb index files are stored. Defaults to empty. - `DUCKDB_INDEX_COMMIT_MESSAGE`: the git commit message when the worker uploads the duckdb index file to the Hub. Defaults to `Update duckdb index file`. - `DUCKDB_INDEX_COMMITTER_HF_TOKEN`: the HuggingFace token to commit the duckdb index file to the Hub. The token must be an app token associated with a user that has the right to 1. create the `refs/convert/parquet` branch (see `DUCKDB_INDEX_TARGET_REVISION`) and 2. push commits to it on any dataset. [Datasets maintainers](https://huggingface.co/datasets-maintainers) members have these rights. The token must have permission to write. If not set, the worker will fail. Defaults to None. - `DUCKDB_INDEX_MAX_DATASET_SIZE_BYTES`: the maximum size in bytes of the dataset's parquet files to index. Datasets with bigger size are ignored. Defaults to `100_000_000`. - `DUCKDB_INDEX_TARGET_REVISION`: the git revision of the dataset where to store the duckdb index file. Make sure the committer token (`DUCKDB_INDEX_COMMITTER_HF_TOKEN`) has the permission to write there. Defaults to `refs/convert/parquet`. - `DUCKDB_INDEX_URL_TEMPLATE`: the URL template to build the duckdb index file URL. Defaults to `/datasets/%s/resolve/%s/%s`. - `DUCKDB_INDEX_EXTENSIONS_DIRECTORY`: directory where the duckdb extensions will be downloaded. Defaults to empty. ### Descriptive statistics worker Set environment variables to configure the `descriptive-statistics` worker (`DESCRIPTIVE_STATISTICS_` prefix): - `DESCRIPTIVE_STATISTICS_CACHE_DIRECTORY`: directory to which a dataset in parquet format is downloaded. Defaults to empty. - `DESCRIPTIVE_STATISTICS_HISTOGRAM_NUM_BINS`: number of histogram bins (see examples below for more info). - `DESCRIPTIVE_STATISTICS_MAX_PARQUET_SIZE_BYTES`: maximum size in bytes of the dataset's parquet files to compute statistics. Datasets with bigger size are ignored. Defaults to `100_000_000`. #### How descriptive statistics are computed Descriptive statistics are currently computed for the following data types: strings, floats, and ints (including `ClassLabel` int). Response has two fields: `num_examples` and `statistics`. `statistics` field is a list of dicts with three keys: `column_name`, `column_type`, and `column_statistics`. `column_type` is one of the following values: `class_label` - for `datasets.ClassLabel` feature * `float` - for float dtypes ("float16", "float32", "float64") * `int` - for integer dtypes ("int8", "int16", "int32", "int64", "uint8", "uint16", "uint32", "uint64") * `string_label` - for string dtypes ("string", "large_string") - if there are less than or equal to `MAX_NUM_STRING_LABELS` unique values (hardcoded in worker's code, for now it's 30) * `string_text` - for string dtypes ("string", "large_string") - if there are more than `MAX_NUM_STRING_LABELS` unique values * `bool` - for boolean dtype ("bool") `column_statistics` content depends on the feature type, see examples below. ##### class_label <details><summary>example: </summary> <p> ```python { "column_name": "class_col", "column_type": "class_label", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "no_label_count": 0, # number of -1 values - special value of the `datasets` lib to encode `no label` "no_label_proportion": 0.0, "n_unique": 5, # number of unique values (excluding `no label` and nan) "frequencies": { # mapping value -> its count "this": 19834, "are": 20159, "random": 20109, "words": 20172, "test": 19726 } } } ``` </p> </details> ##### float Bin size for histogram is counted as `(max_value - min_value) / DESCRIPTIVE_STATISTICS_HISTOGRAM_NUM_BINS` <details><summary>example: </summary> <p> ```python { "column_name": "delay", "column_type": "float", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "min": -10.206, "max": 8.48053, "mean": 2.10174, "median": 3.4012, "std": 3.12487, "histogram": { "hist": [ 2, 34, 256, 15198, 9037, 2342, 12743, 45114, 14904, 370 ], "bin_edges": [ -10.206, -8.33734, -6.46869, -4.60004, -2.73139, -0.86273, 1.00592, 2.87457, 4.74322, 6.61188, 8.48053 # includes maximum value, so len is always len(hist) + 1 ] } } } ``` </p> </details> ##### int As bin edges for integer values also must be integers, bin size is counted as `np.ceil((max_value - min_value + 1) / DESCRIPTIVE_STATISTICS_HISTOGRAM_NUM_BINS)`. Rounding up means that there might be smaller number of bins in response then provided `DESCRIPTIVE_STATISTICS_HISTOGRAM_NUM_BINS`. The last bin's size might be smaller than that of the others if the feature's range is not divisible by the rounded bin size. <details><summary>examples: </summary> <p> ```python { "column_name": "direction", "column_type": "int", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "min": 0, "max": 1, "mean": 0.49925, "median": 0.0, "std": 0.5, "histogram": { "hist": [ 50075, 49925 ], "bin_edges": [ 0, 1, 1 # if the last value is equal to the last but one, that means that this bin includes only this value ] } } }, { "column_name": "hour", "column_type": "int", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "min": 0, "max": 23, "mean": 13.44402, "median": 14.0, "std": 5.49455, "histogram": { "hist": [ 2694, 2292, 16785, 16326, 16346, 17809, 16546, 11202 ], "bin_edges": [ 0, 3, 6, 9, 12, 15, 18, 21, 23 ] } } }, { "column_name": "humidity", "column_type": "int", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "min": 54, "max": 99, "mean": 83.89878, "median": 85.0, "std": 8.65174, "histogram": { "hist": [ 554, 1662, 3823, 6532, 12512, 17536, 23871, 20355, 12896, 259 ], "bin_edges": [ 54, 59, 64, 69, 74, 79, 84, 89, 94, 99, 99 ] } } }, { "column_name": "weekday", "column_type": "int", "column_statistics": { "nan_count": 0, "nan_proportion": 0.0, "min": 0, "max": 6, "mean": 3.08063, "median": 3.0, "std": 1.90347, "histogram": { "hist": [ 10282, 15416, 15291, 15201, 15586, 15226, 12998 ], "bin_edges": [ 0, 1, 2, 3, 4, 5, 6, 6 ] } } } ``` </p> </details> ##### string_label If the number of unique values in a column (within requested split) is <= `MAX_NUM_STRING_LABELS` (currently 30), the column is considered to be a category and the categories counts are computed. <details><summary>examples: </summary> <p> ```python { 'column_name': 'string_col', 'column_type': 'string_label', 'column_statistics': { "nan_count": 0, "nan_proportion": 0.0, "n_unique": 5, # number of unique values (excluding nan) "frequencies": { # mapping value -> its count "this": 19834, "are": 20159, "random": 20109, "words": 20172, "test": 19726 } } } ``` </p> </details> ##### string_text If the number of unique values in a column (within requested split) is > `MAX_NUM_STRING_LABELS` (currently 30), the column is considered to be text and the distribution of text lengths is computed. <details><summary>example: </summary> <p> ```python { 'column_name': 'text_col', 'column_type': 'string_text', 'column_statistics': { 'max': 296, 'mean': 97.46649, 'median': 88.0, 'min': 11, 'nan_count': 0, 'nan_proportion': 0.0, 'std': 55.82714, 'histogram': { 'bin_edges': [ 11, 40, 69, 98, 127, 156, 185, 214, 243, 272, 296 ], 'hist': [ 171, 224, 235, 180, 102, 99, 53, 28, 10, 2 ] }, } } ``` </p> </details> ##### bool <details><summary>example: </summary> <p> ```python { 'column_name': 'bool__nan_column', 'column_type': 'bool', 'column_statistics': { 'nan_count': 3, 'nan_proportion': 0.15, 'frequencies': { 'False': 7, 'True': 10 } } } ``` </p> </details> ### Splits worker The `splits` worker does not need any additional configuration. ### Common See [../../libs/libcommon/README.md](../../libs/libcommon/README.md) for more information about the common configuration.
huggingface/datasets/blob/main/docs/source/about_mapstyle_vs_iterable.mdx	Differences between Dataset and IterableDataset There are two types of dataset objects, a [`Dataset`] and an [`IterableDataset`]. Whichever type of dataset you choose to use or create depends on the size of the dataset. In general, an [`IterableDataset`] is ideal for big datasets (think hundreds of GBs!) due to its lazy behavior and speed advantages, while a [`Dataset`] is great for everything else. This page will compare the differences between a [`Dataset`] and an [`IterableDataset`] to help you pick the right dataset object for you. ## Downloading and streaming When you have a regular [`Dataset`], you can access it using `my_dataset[0]`. This provides random access to the rows. Such datasets are also called "map-style" datasets. For example you can download ImageNet-1k like this and access any row: ```python from datasets import load_dataset imagenet = load_dataset("imagenet-1k", split="train") # downloads the full dataset print(imagenet[0]) ``` But one caveat is that you must have the entire dataset stored on your disk or in memory, which blocks you from accessing datasets bigger than the disk. Because it can become inconvenient for big datasets, there exists another type of dataset, the [`IterableDataset`]. When you have an `IterableDataset`, you can access it using a `for` loop to load the data progressively as you iterate over the dataset. This way, only a small fraction of examples is loaded in memory, and you don't write anything on disk. For example, you can stream the ImageNet-1k dataset without downloading it on disk: ```python from datasets import load_dataset imagenet = load_dataset("imagenet-1k", split="train", streaming=True) # will start loading the data when iterated over for example in imagenet: print(example) break ``` Streaming can read online data without writing any file to disk. For example, you can stream datasets made out of multiple shards, each of which is hundreds of gigabytes like [C4](https://huggingface.co/datasets/c4), [OSCAR](https://huggingface.co/datasets/oscar) or [LAION-2B](https://huggingface.co/datasets/laion/laion2B-en). Learn more about how to stream a dataset in the [Dataset Streaming Guide](./stream). This is not the only difference though, because the "lazy" behavior of an `IterableDataset` is also present when it comes to dataset creation and processing. ## Creating map-style datasets and iterable datasets You can create a [`Dataset`] using lists or dictionaries, and the data is entirely converted to Arrow so you can easily access any row: ```python my_dataset = Dataset.from_dict({"col_1": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]}) print(my_dataset[0]) ``` To create an `IterableDataset` on the other hand, you must provide a "lazy" way to load the data. In Python, we generally use generator functions. These functions `yield` one example at a time, which means you can't access a row by slicing it like a regular `Dataset`: ```python def my_generator(n): for i in range(n): yield {"col_1": i} my_iterable_dataset = IterableDataset.from_generator(my_generator, gen_kwargs={"n": 10}) for example in my_iterable_dataset: print(example) break ``` ## Loading local files entirely and progressively It is possible to convert local or remote data files to an Arrow [`Dataset`] using [`load_dataset`]: ```python data_files = {"train": ["path/to/data.csv"]} my_dataset = load_dataset("csv", data_files=data_files, split="train") print(my_dataset[0]) ``` However, this requires a conversion step from CSV to Arrow format, which takes time and disk space if your dataset is big. To save disk space and skip the conversion step, you can define an `IterableDataset` by streaming from the local files directly. This way, the data is read progressively from the local files as you iterate over the dataset: ```python data_files = {"train": ["path/to/data.csv"]} my_iterable_dataset = load_dataset("csv", data_files=data_files, split="train", streaming=True) for example in my_iterable_dataset: # this reads the CSV file progressively as you iterate over the dataset print(example) break ``` Many file formats are supported, like CSV, JSONL, and Parquet, as well as image and audio files. You can find more information in the corresponding guides for loading [tabular](./tabular_load), [text](./nlp_load), [vision](./image_load), and [audio](./audio_load]) datasets. ## Eager data processing and lazy data processing When you process a [`Dataset`] object using [`Dataset.map`], the entire dataset is processed immediately and returned. This is similar to how `pandas` works for example. ```python my_dataset = my_dataset.map(process_fn) # process_fn is applied on all the examples of the dataset print(my_dataset[0]) ``` On the other hand, due to the "lazy" nature of an `IterableDataset`, calling [`IterableDataset.map`] does not apply your `map` function over the full dataset. Instead, your `map` function is applied on-the-fly. Because of that, you can chain multiple processing steps and they will all run at once when you start iterating over the dataset: ```python my_iterable_dataset = my_iterable_dataset.map(process_fn_1) my_iterable_dataset = my_iterable_dataset.filter(filter_fn) my_iterable_dataset = my_iterable_dataset.map(process_fn_2) # process_fn_1, filter_fn and process_fn_2 are applied on-the-fly when iterating over the dataset for example in my_iterable_dataset: print(example) break ``` ## Exact and fast approximate shuffling When you shuffle a [`Dataset`] using [`Dataset.shuffle`], you apply an exact shuffling of the dataset. It works by taking a list of indices `[0, 1, 2, ... len(my_dataset) - 1]` and shuffling this list. Then, accessing `my_dataset[0]` returns the row and index defined by the first element of the indices mapping that has been shuffled: ```python my_dataset = my_dataset.shuffle(seed=42) print(my_dataset[0]) ``` Since we don't have random access to the rows in the case of an `IterableDataset`, we can't use a shuffled list of indices and access a row at an arbitrary position. This prevents the use of exact shuffling. Instead, a fast approximate shuffling is used in [`IterableDataset.shuffle`]. It uses a shuffle buffer to sample random examples iteratively from the dataset. Since the dataset is still read iteratively, it provides excellent speed performance: ```python my_iterable_dataset = my_iterable_dataset.shuffle(seed=42, buffer_size=100) for example in my_iterable_dataset: print(example) break ``` But using a shuffle buffer is not enough to provide a satisfactory shuffling for machine learning model training. So [`IterableDataset.shuffle`] also shuffles the dataset shards if your dataset is made of multiple files or sources: ```python # Stream from the internet my_iterable_dataset = load_dataset("deepmind/code_contests", split="train", streaming=True) my_iterable_dataset.n_shards # 39 # Stream from local files data_files = {"train": [f"path/to/data_{i}.csv" for i in range(1024)]} my_iterable_dataset = load_dataset("csv", data_files=data_files, split="train", streaming=True) my_iterable_dataset.n_shards # 1024 # From a generator function def my_generator(n, sources): for source in sources: for example_id_for_current_source in range(n): yield {"example_id": f"{source}_{example_id_for_current_source}"} gen_kwargs = {"n": 10, "sources": [f"path/to/data_{i}" for i in range(1024)]} my_iterable_dataset = IterableDataset.from_generator(my_generator, gen_kwargs=gen_kwargs) my_iterable_dataset.n_shards # 1024 ``` ## Speed differences Regular [`Dataset`] objects are based on Arrow which provides fast random access to the rows. Thanks to memory mapping and the fact that Arrow is an in-memory format, reading data from disk doesn't do expensive system calls and deserialization. It provides even faster data loading when iterating using a `for` loop by iterating on contiguous Arrow record batches. However as soon as your [`Dataset`] has an indices mapping (via [`Dataset.shuffle`] for example), the speed can become 10x slower. This is because there is an extra step to get the row index to read using the indices mapping, and most importantly, you aren't reading contiguous chunks of data anymore. To restore the speed, you'd need to rewrite the entire dataset on your disk again using [`Dataset.flatten_indices`], which removes the indices mapping. This may take a lot of time depending of the size of your dataset though: ```python my_dataset[0] # fast my_dataset = my_dataset.shuffle(seed=42) my_dataset[0] # up to 10x slower my_dataset = my_dataset.flatten_indices() # rewrite the shuffled dataset on disk as contiguous chunks of data my_dataset[0] # fast again ``` In this case, we recommend switching to an [`IterableDataset`] and leveraging its fast approximate shuffling method [`IterableDataset.shuffle`]. It only shuffles the shards order and adds a shuffle buffer to your dataset, which keeps the speed of your dataset optimal. You can also reshuffle the dataset easily: ```python for example in enumerate(my_iterable_dataset): # fast pass shuffled_iterable_dataset = my_iterable_dataset.shuffle(seed=42, buffer_size=100) for example in enumerate(shuffled_iterable_dataset): # as fast as before pass shuffled_iterable_dataset = my_iterable_dataset.shuffle(seed=1337, buffer_size=100) # reshuffling using another seed is instantaneous for example in enumerate(shuffled_iterable_dataset): # still as fast as before pass ``` If you're using your dataset on multiple epochs, the effective seed to shuffle the shards order in the shuffle buffer is `seed + epoch`. It makes it easy to reshuffle a dataset between epochs: ```python for epoch in range(n_epochs): my_iterable_dataset.set_epoch(epoch) for example in my_iterable_dataset: # fast + reshuffled at each epoch using `effective_seed = seed + epoch` pass ``` ## Switch from map-style to iterable If you want to benefit from the "lazy" behavior of an [`IterableDataset`] or their speed advantages, you can switch your map-style [`Dataset`] to an [`IterableDataset`]: ```python my_iterable_dataset = my_dataset.to_iterable_dataset() ``` If you want to shuffle your dataset or [use it with a PyTorch DataLoader](./use_with_pytorch#stream-data), we recommend generating a sharded [`IterableDataset`]: ```python my_iterable_dataset = my_dataset.to_iterable_dataset(num_shards=1024) my_iterable_dataset.n_shards # 1024 ```
huggingface/deep-rl-class/blob/main/units/en/unit2/q-learning-recap.mdx	Q-Learning Recap [[q-learning-recap]] Q-Learning is the RL algorithm that : - Trains a Q-function, an action-value function encoded, in internal memory, by a Q-table containing all the state-action pair values. - Given a state and action, our Q-function will search its Q-table for the corresponding value. <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit3/Q-function-2.jpg" alt="Q function" width="100%"/> - When the training is done, we have an optimal Q-function, or, equivalently, an optimal Q-table. - And if we have an optimal Q-function, we have an optimal policy, since we know, for each state, the best action to take. <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit3/link-value-policy.jpg" alt="Link value policy" width="100%"/> But, in the beginning, our Q-table is useless since it gives arbitrary values for each state-action pair (most of the time we initialize the Q-table to 0 values). But, as we explore the environment and update our Q-table it will give us a better and better approximation. <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/notebooks/unit2/q-learning.jpeg" alt="q-learning.jpeg" width="100%"/> This is the Q-Learning pseudocode: <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit3/Q-learning-2.jpg" alt="Q-Learning" width="100%"/>
huggingface/transformers/blob/main/docs/source/en/tasks/zero_shot_object_detection.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Zero-shot object detection [[open-in-colab]] Traditionally, models used for [object detection](object_detection) require labeled image datasets for training, and are limited to detecting the set of classes from the training data. Zero-shot object detection is supported by the [OWL-ViT](../model_doc/owlvit) model which uses a different approach. OWL-ViT is an open-vocabulary object detector. It means that it can detect objects in images based on free-text queries without the need to fine-tune the model on labeled datasets. OWL-ViT leverages multi-modal representations to perform open-vocabulary detection. It combines [CLIP](../model_doc/clip) with lightweight object classification and localization heads. Open-vocabulary detection is achieved by embedding free-text queries with the text encoder of CLIP and using them as input to the object classification and localization heads. associate images and their corresponding textual descriptions, and ViT processes image patches as inputs. The authors of OWL-ViT first trained CLIP from scratch and then fine-tuned OWL-ViT end to end on standard object detection datasets using a bipartite matching loss. With this approach, the model can detect objects based on textual descriptions without prior training on labeled datasets. In this guide, you will learn how to use OWL-ViT: - to detect objects based on text prompts - for batch object detection - for image-guided object detection Before you begin, make sure you have all the necessary libraries installed: ```bash pip install -q transformers ``` ## Zero-shot object detection pipeline The simplest way to try out inference with OWL-ViT is to use it in a [`pipeline`]. Instantiate a pipeline for zero-shot object detection from a [checkpoint on the Hugging Face Hub](https://huggingface.co/models?other=owlvit): ```python >>> from transformers import pipeline >>> checkpoint = "google/owlvit-base-patch32" >>> detector = pipeline(model=checkpoint, task="zero-shot-object-detection") ``` Next, choose an image you'd like to detect objects in. Here we'll use the image of astronaut Eileen Collins that is a part of the [NASA](https://www.nasa.gov/multimedia/imagegallery/index.html) Great Images dataset. ```py >>> import skimage >>> import numpy as np >>> from PIL import Image >>> image = skimage.data.astronaut() >>> image = Image.fromarray(np.uint8(image)).convert("RGB") >>> image ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_1.png" alt="Astronaut Eileen Collins"/> </div> Pass the image and the candidate object labels to look for to the pipeline. Here we pass the image directly; other suitable options include a local path to an image or an image url. We also pass text descriptions for all items we want to query the image for. ```py >>> predictions = detector( ... image, ... candidate_labels=["human face", "rocket", "nasa badge", "star-spangled banner"], ... ) >>> predictions [{'score': 0.3571370542049408, 'label': 'human face', 'box': {'xmin': 180, 'ymin': 71, 'xmax': 271, 'ymax': 178}}, {'score': 0.28099656105041504, 'label': 'nasa badge', 'box': {'xmin': 129, 'ymin': 348, 'xmax': 206, 'ymax': 427}}, {'score': 0.2110239565372467, 'label': 'rocket', 'box': {'xmin': 350, 'ymin': -1, 'xmax': 468, 'ymax': 288}}, {'score': 0.13790413737297058, 'label': 'star-spangled banner', 'box': {'xmin': 1, 'ymin': 1, 'xmax': 105, 'ymax': 509}}, {'score': 0.11950037628412247, 'label': 'nasa badge', 'box': {'xmin': 277, 'ymin': 338, 'xmax': 327, 'ymax': 380}}, {'score': 0.10649408400058746, 'label': 'rocket', 'box': {'xmin': 358, 'ymin': 64, 'xmax': 424, 'ymax': 280}}] ``` Let's visualize the predictions: ```py >>> from PIL import ImageDraw >>> draw = ImageDraw.Draw(image) >>> for prediction in predictions: ... box = prediction["box"] ... label = prediction["label"] ... score = prediction["score"] ... xmin, ymin, xmax, ymax = box.values() ... draw.rectangle((xmin, ymin, xmax, ymax), outline="red", width=1) ... draw.text((xmin, ymin), f"{label}: {round(score,2)}", fill="white") >>> image ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_2.png" alt="Visualized predictions on NASA image"/> </div> ## Text-prompted zero-shot object detection by hand Now that you've seen how to use the zero-shot object detection pipeline, let's replicate the same result manually. Start by loading the model and associated processor from a [checkpoint on the Hugging Face Hub](https://huggingface.co/models?other=owlvit). Here we'll use the same checkpoint as before: ```py >>> from transformers import AutoProcessor, AutoModelForZeroShotObjectDetection >>> model = AutoModelForZeroShotObjectDetection.from_pretrained(checkpoint) >>> processor = AutoProcessor.from_pretrained(checkpoint) ``` Let's take a different image to switch things up. ```py >>> import requests >>> url = "https://unsplash.com/photos/oj0zeY2Ltk4/download?ixid=MnwxMjA3fDB8MXxzZWFyY2h8MTR8fHBpY25pY3xlbnwwfHx8fDE2Nzc0OTE1NDk&force=true&w=640" >>> im = Image.open(requests.get(url, stream=True).raw) >>> im ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_3.png" alt="Beach photo"/> </div> Use the processor to prepare the inputs for the model. The processor combines an image processor that prepares the image for the model by resizing and normalizing it, and a [`CLIPTokenizer`] that takes care of the text inputs. ```py >>> text_queries = ["hat", "book", "sunglasses", "camera"] >>> inputs = processor(text=text_queries, images=im, return_tensors="pt") ``` Pass the inputs through the model, post-process, and visualize the results. Since the image processor resized images before feeding them to the model, you need to use the [`~OwlViTImageProcessor.post_process_object_detection`] method to make sure the predicted bounding boxes have the correct coordinates relative to the original image: ```py >>> import torch >>> with torch.no_grad(): ... outputs = model(inputs) ... target_sizes = torch.tensor([im.size[::-1]]) ... results = processor.post_process_object_detection(outputs, threshold=0.1, target_sizes=target_sizes)[0] >>> draw = ImageDraw.Draw(im) >>> scores = results["scores"].tolist() >>> labels = results["labels"].tolist() >>> boxes = results["boxes"].tolist() >>> for box, score, label in zip(boxes, scores, labels): ... xmin, ymin, xmax, ymax = box ... draw.rectangle((xmin, ymin, xmax, ymax), outline="red", width=1) ... draw.text((xmin, ymin), f"{text_queries[label]}: {round(score,2)}", fill="white") >>> im ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_4.png" alt="Beach photo with detected objects"/> </div> ## Batch processing You can pass multiple sets of images and text queries to search for different (or same) objects in several images. Let's use both an astronaut image and the beach image together. For batch processing, you should pass text queries as a nested list to the processor and images as lists of PIL images, PyTorch tensors, or NumPy arrays. ```py >>> images = [image, im] >>> text_queries = [ ... ["human face", "rocket", "nasa badge", "star-spangled banner"], ... ["hat", "book", "sunglasses", "camera"], ... ] >>> inputs = processor(text=text_queries, images=images, return_tensors="pt") ``` Previously for post-processing you passed the single image's size as a tensor, but you can also pass a tuple, or, in case of several images, a list of tuples. Let's create predictions for the two examples, and visualize the second one (`image_idx = 1`). ```py >>> with torch.no_grad(): ... outputs = model(inputs) ... target_sizes = [x.size[::-1] for x in images] ... results = processor.post_process_object_detection(outputs, threshold=0.1, target_sizes=target_sizes) >>> image_idx = 1 >>> draw = ImageDraw.Draw(images[image_idx]) >>> scores = results[image_idx]["scores"].tolist() >>> labels = results[image_idx]["labels"].tolist() >>> boxes = results[image_idx]["boxes"].tolist() >>> for box, score, label in zip(boxes, scores, labels): ... xmin, ymin, xmax, ymax = box ... draw.rectangle((xmin, ymin, xmax, ymax), outline="red", width=1) ... draw.text((xmin, ymin), f"{text_queries[image_idx][label]}: {round(score,2)}", fill="white") >>> images[image_idx] ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_4.png" alt="Beach photo with detected objects"/> </div> ## Image-guided object detection In addition to zero-shot object detection with text queries, OWL-ViT offers image-guided object detection. This means you can use an image query to find similar objects in the target image. Unlike text queries, only a single example image is allowed. Let's take an image with two cats on a couch as a target image, and an image of a single cat as a query: ```py >>> url = "http://images.cocodataset.org/val2017/000000039769.jpg" >>> image_target = Image.open(requests.get(url, stream=True).raw) >>> query_url = "http://images.cocodataset.org/val2017/000000524280.jpg" >>> query_image = Image.open(requests.get(query_url, stream=True).raw) ``` Let's take a quick look at the images: ```py >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 2) >>> ax[0].imshow(image_target) >>> ax[1].imshow(query_image) ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_5.png" alt="Cats"/> </div> In the preprocessing step, instead of text queries, you now need to use `query_images`: ```py >>> inputs = processor(images=image_target, query_images=query_image, return_tensors="pt") ``` For predictions, instead of passing the inputs to the model, pass them to [`~OwlViTForObjectDetection.image_guided_detection`]. Draw the predictions as before except now there are no labels. ```py >>> with torch.no_grad(): ... outputs = model.image_guided_detection(**inputs) ... target_sizes = torch.tensor([image_target.size[::-1]]) ... results = processor.post_process_image_guided_detection(outputs=outputs, target_sizes=target_sizes)[0] >>> draw = ImageDraw.Draw(image_target) >>> scores = results["scores"].tolist() >>> boxes = results["boxes"].tolist() >>> for box, score, label in zip(boxes, scores, labels): ... xmin, ymin, xmax, ymax = box ... draw.rectangle((xmin, ymin, xmax, ymax), outline="white", width=4) >>> image_target ``` <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/zero-sh-obj-detection_6.png" alt="Cats with bounding boxes"/> </div> If you'd like to interactively try out inference with OWL-ViT, check out this demo: <iframe src="https://adirik-owl-vit.hf.space" frameborder="0" width="850" height="450" ></iframe>
huggingface/deep-rl-class/blob/main/units/en/unit6/quiz.mdx	Quiz The best way to learn and [to avoid the illusion of competence](https://www.coursera.org/lecture/learning-how-to-learn/illusions-of-competence-BuFzf) is to test yourself. This will help you to find where you need to reinforce your knowledge. ### Q1: Which of the following interpretations of bias-variance tradeoff is the most accurate in the field of Reinforcement Learning? <Question choices={[ { text: "The bias-variance tradeoff reflects how my model is able to generalize the knowledge to previously tagged data we give to the model during training time.", explain: "This is the traditional bias-variance tradeoff in Machine Learning. In our specific case of Reinforcement Learning, we don't have previously tagged data, but only a reward signal.", correct: false, }, { text: "The bias-variance tradeoff reflects how well the reinforcement signal reflects the true reward the agent should get from the enviromment", explain: "", correct: true, }, ]} /> ### Q2: Which of the following statements are true, when talking about models with bias and/or variance in RL? <Question choices={[ { text: "An unbiased reward signal returns rewards similar to the real / expected ones from the environment", explain: "", correct: true, }, { text: "A biased reward signal returns rewards similar to the real / expected ones from the environment", explain: "If a reward signal is biased, it means the reward signal we get differs from the real reward we should be getting from an environment", correct: false, }, { text: "A reward signal with high variance has much noise in it and gets affected by, for example, stochastic (non constant) elements in the environment", explain: "", correct: true, }, { text: "A reward signal with low variance has much noise in it and gets affected by, for example, stochastic (non constant) elements in the environment", explain: "If a reward signal has low variance, then it's less affected by the noise of the environment and produce similar values regardless the random elements in the environment", correct: false, }, ]} /> ### Q3: Which of the following statements are true about Monte Carlo method? <Question choices={[ { text: "It's a sampling mechanism, which means we don't analyze all the possible states, but a sample of those", explain: "", correct: true, }, { text: "It's very resistant to stochasticity (random elements in the trajectory)", explain: "Monte Carlo randomly estimates everytime a sample of trajectories. However, even same trajectories can have different reward values if they contain stochastic elements", correct: false, }, { text: "To reduce the impact of stochastic elements in Monte Carlo, we take `n` strategies and average them, reducing their individual impact", explain: "", correct: true, }, ]} /> ### Q4: How would you describe, with your own words, the Actor-Critic Method (A2C)? <details> <summary>Solution</summary> The idea behind Actor-Critic is that we learn two function approximations: 1. A `policy` that controls how our agent acts (π) 2. A `value` function to assist the policy update by measuring how good the action taken is (q) <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit8/step2.jpg" alt="Actor-Critic, step 2"/> </details> ### Q5: Which of the following statements are true about the Actor-Critic Method? <Question choices={[ { text: "The Critic does not learn any function during the training process", explain: "Both the Actor and the Critic function parameters are updated during training time", correct: false, }, { text: "The Actor learns a policy function, while the Critic learns a value function", explain: "", correct: true, }, { text: "It adds resistance to stochasticity and reduces high variance", explain: "", correct: true, }, ]} /> ### Q6: What is `Advantage` in the A2C method? <details> <summary>Solution</summary> Instead of using directly the Action-Value function of the Critic as it is, we could use an `Advantage` function. The idea behind an `Advantage` function is that we calculate the relative advantage of an action compared to the others possible at a state, averaging them. In other words: how taking that action at a state is better compared to the average value of the state <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit8/advantage1.jpg" alt="Advantage in A2C"/> </details> Congrats on finishing this Quiz 🥳, if you missed some elements, take time to read the chapter again to reinforce (😏) your knowledge.
huggingface/hf-endpoints-documentation/blob/main/docs/source/guides/logs.mdx	Access and read Logs Hugging Face Endpoints provides access to the logs of your Endpoints through the UI in the “Logs” tab of your Endpoint. You will have access to the build logs of your Image artifacts as well as access to the Container Logs during inference. <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/9_selection.png" alt="select logs" /> The Container Logs are only available when your Endpoint is in the “Running” state. _Note: If your Endpoint creation is in the “Failed” state, you can check the Build Logs to see what the reason was, e.g. wrong version of a dependency, etc._ Build Logs: <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/9_build_logs.png" alt="build logs" /> Container Logs: <img src="https://raw.githubusercontent.com/huggingface/hf-endpoints-documentation/main/assets/9_logs.png" alt="container logs" />
gradio-app/gradio/blob/main/demo/examples_component/run.ipynb	Gradio Demo: examples_component ``` !pip install -q gradio ``` ``` # Downloading files from the demo repo import os os.mkdir('images') !wget -q -O images/cheetah1.jpg https://github.com/gradio-app/gradio/raw/main/demo/examples_component/images/cheetah1.jpg !wget -q -O images/lion.jpg https://github.com/gradio-app/gradio/raw/main/demo/examples_component/images/lion.jpg !wget -q -O images/lion.webp https://github.com/gradio-app/gradio/raw/main/demo/examples_component/images/lion.webp !wget -q -O images/logo.png https://github.com/gradio-app/gradio/raw/main/demo/examples_component/images/logo.png ``` ``` import gradio as gr import os def flip(i): return i.rotate(180) with gr.Blocks() as demo: with gr.Row(): with gr.Column(): img_i = gr.Image(label="Input Image", type="pil") with gr.Column(): img_o = gr.Image(label="Output Image") with gr.Row(): btn = gr.Button(value="Flip Image") btn.click(flip, inputs=[img_i], outputs=[img_o]) gr.Examples( [ os.path.join(os.path.abspath(''), "images/cheetah1.jpg"), os.path.join(os.path.abspath(''), "images/lion.jpg"), ], img_i, img_o, flip, ) demo.launch() ```
huggingface/deep-rl-class/blob/main/units/en/unit4/additional-readings.mdx	Additional Readings These are optional readings if you want to go deeper. ## Introduction to Policy Optimization - [Part 3: Intro to Policy Optimization - Spinning Up documentation](https://spinningup.openai.com/en/latest/spinningup/rl_intro3.html) ## Policy Gradient - [https://johnwlambert.github.io/policy-gradients/](https://johnwlambert.github.io/policy-gradients/) - [RL - Policy Gradient Explained](https://jonathan-hui.medium.com/rl-policy-gradients-explained-9b13b688b146) - [Chapter 13, Policy Gradient Methods; Reinforcement Learning, an introduction by Richard Sutton and Andrew G. Barto](http://incompleteideas.net/book/RLbook2020.pdf) ## Implementation - [PyTorch Reinforce implementation](https://github.com/pytorch/examples/blob/main/reinforcement_learning/reinforce.py) - [Implementations from DDPG to PPO](https://github.com/MrSyee/pg-is-all-you-need)
huggingface/optimum/blob/main/docs/source/onnxruntime/package_reference/quantization.mdx	!--Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # Quantization ## ORTQuantizer [[autodoc]] onnxruntime.quantization.ORTQuantizer - all
gradio-app/gradio/blob/main/demo/number_component/run.ipynb	Gradio Demo: number_component ``` !pip install -q gradio ``` ``` import gradio as gr with gr.Blocks() as demo: gr.Number() demo.launch() ```
gradio-app/gradio/blob/main/demo/map_airbnb/run.ipynb	Gradio Demo: map_airbnb ### Display an interactive map of AirBnB locations with Plotly. Data is hosted on HuggingFace Datasets. ``` !pip install -q gradio plotly ``` ``` import gradio as gr import plotly.graph_objects as go from datasets import load_dataset dataset = load_dataset("gradio/NYC-Airbnb-Open-Data", split="train") df = dataset.to_pandas() def filter_map(min_price, max_price, boroughs): filtered_df = df[(df['neighbourhood_group'].isin(boroughs)) & (df['price'] > min_price) & (df['price'] < max_price)] names = filtered_df["name"].tolist() prices = filtered_df["price"].tolist() text_list = [(names[i], prices[i]) for i in range(0, len(names))] fig = go.Figure(go.Scattermapbox( customdata=text_list, lat=filtered_df['latitude'].tolist(), lon=filtered_df['longitude'].tolist(), mode='markers', marker=go.scattermapbox.Marker( size=6 ), hoverinfo="text", hovertemplate='<b>Name</b>: %{customdata[0]}<br><b>Price</b>: $%{customdata[1]}' )) fig.update_layout( mapbox_style="open-street-map", hovermode='closest', mapbox=dict( bearing=0, center=go.layout.mapbox.Center( lat=40.67, lon=-73.90 ), pitch=0, zoom=9 ), ) return fig with gr.Blocks() as demo: with gr.Column(): with gr.Row(): min_price = gr.Number(value=250, label="Minimum Price") max_price = gr.Number(value=1000, label="Maximum Price") boroughs = gr.CheckboxGroup(choices=["Queens", "Brooklyn", "Manhattan", "Bronx", "Staten Island"], value=["Queens", "Brooklyn"], label="Select Boroughs:") btn = gr.Button(value="Update Filter") map = gr.Plot() demo.load(filter_map, [min_price, max_price, boroughs], map) btn.click(filter_map, [min_price, max_price, boroughs], map) if __name__ == "__main__": demo.launch() ```
huggingface/pytorch-image-models/blob/main/hfdocs/source/models/res2net.mdx	Res2Net Res2Net is an image model that employs a variation on bottleneck residual blocks, [Res2Net Blocks](https://paperswithcode.com/method/res2net-block). The motivation is to be able to represent features at multiple scales. This is achieved through a novel building block for CNNs that constructs hierarchical residual-like connections within one single residual block. This represents multi-scale features at a granular level and increases the range of receptive fields for each network layer. ## How do I use this model on an image? To load a pretrained model: ```py >>> import timm >>> model = timm.create_model('res2net101_26w_4s', pretrained=True) >>> model.eval() ``` To load and preprocess the image: ```py >>> import urllib >>> from PIL import Image >>> from timm.data import resolve_data_config >>> from timm.data.transforms_factory import create_transform >>> config = resolve_data_config({}, model=model) >>> transform = create_transform(**config) >>> url, filename = ("https://github.com/pytorch/hub/raw/master/images/dog.jpg", "dog.jpg") >>> urllib.request.urlretrieve(url, filename) >>> img = Image.open(filename).convert('RGB') >>> tensor = transform(img).unsqueeze(0) # transform and add batch dimension ``` To get the model predictions: ```py >>> import torch >>> with torch.no_grad(): ... out = model(tensor) >>> probabilities = torch.nn.functional.softmax(out[0], dim=0) >>> print(probabilities.shape) >>> # prints: torch.Size([1000]) ``` To get the top-5 predictions class names: ```py >>> # Get imagenet class mappings >>> url, filename = ("https://raw.githubusercontent.com/pytorch/hub/master/imagenet_classes.txt", "imagenet_classes.txt") >>> urllib.request.urlretrieve(url, filename) >>> with open("imagenet_classes.txt", "r") as f: ... categories = [s.strip() for s in f.readlines()] >>> # Print top categories per image >>> top5_prob, top5_catid = torch.topk(probabilities, 5) >>> for i in range(top5_prob.size(0)): ... print(categories[top5_catid[i]], top5_prob[i].item()) >>> # prints class names and probabilities like: >>> # [('Samoyed', 0.6425196528434753), ('Pomeranian', 0.04062102362513542), ('keeshond', 0.03186424449086189), ('white wolf', 0.01739676296710968), ('Eskimo dog', 0.011717947199940681)] ``` Replace the model name with the variant you want to use, e.g. `res2net101_26w_4s`. You can find the IDs in the model summaries at the top of this page. To extract image features with this model, follow the [timm feature extraction examples](../feature_extraction), just change the name of the model you want to use. ## How do I finetune this model? You can finetune any of the pre-trained models just by changing the classifier (the last layer). ```py >>> model = timm.create_model('res2net101_26w_4s', pretrained=True, num_classes=NUM_FINETUNE_CLASSES) ``` To finetune on your own dataset, you have to write a training loop or adapt [timm's training script](https://github.com/rwightman/pytorch-image-models/blob/master/train.py) to use your dataset. ## How do I train this model? You can follow the [timm recipe scripts](../scripts) for training a new model afresh. ## Citation ```BibTeX @article{Gao_2021, title={Res2Net: A New Multi-Scale Backbone Architecture}, volume={43}, ISSN={1939-3539}, url={http://dx.doi.org/10.1109/TPAMI.2019.2938758}, DOI={10.1109/tpami.2019.2938758}, number={2}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Gao, Shang-Hua and Cheng, Ming-Ming and Zhao, Kai and Zhang, Xin-Yu and Yang, Ming-Hsuan and Torr, Philip}, year={2021}, month={Feb}, pages={652–662} } ``` <!-- Type: model-index Collections: - Name: Res2Net Paper: Title: 'Res2Net: A New Multi-scale Backbone Architecture' URL: https://paperswithcode.com/paper/res2net-a-new-multi-scale-backbone Models: - Name: res2net101_26w_4s In Collection: Res2Net Metadata: FLOPs: 10415881200 Parameters: 45210000 File Size: 181456059 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net101_26w_4s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L152 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net101_26w_4s-02a759a1.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 79.19% Top 5 Accuracy: 94.43% - Name: res2net50_14w_8s In Collection: Res2Net Metadata: FLOPs: 5403546768 Parameters: 25060000 File Size: 100638543 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net50_14w_8s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L196 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net50_14w_8s-6527dddc.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 78.14% Top 5 Accuracy: 93.86% - Name: res2net50_26w_4s In Collection: Res2Net Metadata: FLOPs: 5499974064 Parameters: 25700000 File Size: 103110087 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net50_26w_4s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L141 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net50_26w_4s-06e79181.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 77.99% Top 5 Accuracy: 93.85% - Name: res2net50_26w_6s In Collection: Res2Net Metadata: FLOPs: 8130156528 Parameters: 37050000 File Size: 148603239 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net50_26w_6s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L163 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net50_26w_6s-19041792.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 78.57% Top 5 Accuracy: 94.12% - Name: res2net50_26w_8s In Collection: Res2Net Metadata: FLOPs: 10760338992 Parameters: 48400000 File Size: 194085165 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net50_26w_8s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L174 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net50_26w_8s-2c7c9f12.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 79.19% Top 5 Accuracy: 94.37% - Name: res2net50_48w_2s In Collection: Res2Net Metadata: FLOPs: 5375291520 Parameters: 25290000 File Size: 101421406 Architecture: - Batch Normalization - Convolution - Global Average Pooling - ReLU - Res2Net Block Tasks: - Image Classification Training Techniques: - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 4x Titan Xp GPUs ID: res2net50_48w_2s LR: 0.1 Epochs: 100 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 256 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/res2net.py#L185 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-res2net/res2net50_48w_2s-afed724a.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 77.53% Top 5 Accuracy: 93.56% -->
huggingface/course/blob/main/subtitles/en/raw/chapter5/03a_slice-and-dice.md	ow to slice and dice a dataset. Most of the time, the data you work with won’t be perfectly prepared for training models. In this video we’ll explore various features that Datasets provides to clean up your datasets. The Datasets library provides several built-in methods that allow you to wrangle your data. In this video we'll see how you can shuffle and split your data, select the rows you're interested in, tweak the columns, and apply processing functions with the map() method. Let's start with shuffling. It is generally a good idea to apply shuffling to the training set so that your model doesn't learn any artificial ordering in the data. If you want to shuffle the whole dataset, you can apply the appropriately named shuffle() method to your dataset. You can see an example of this method in action here, where we've downloaded the training split of the SQUAD dataset and shuffled all the rows randomly.Another way to shuffle the data is to create random train and test splits. This can be useful if you have to create your own test splits from raw data. To do this, you just apply the train_test_split method and specify how large the test split should be. In this example, we've specified that the test set should be 10% of the total dataset size. You can see that the output of train_test_split is a DatasetDict object, whose keys correspond to the new splits. Now that we know how to shuffle a dataset, let's take a look at returning the rows we're interested in. The most common way to do this is with the select method. This method expects a list or generator of the dataset's indices, and will then return a new Dataset object containing just those rows. If you want to create a random sample of rows, you can do this by chaining the shuffle and select methods together. In this example, we've created a sample of 5 elements from the SQuAD dataset. The last way to pick out specific rows in a dataset is by applying the filter method. This method checks whether each rows fulfills some condition or not. For example, here we've created a small lambda function that checks whether the title starts with the letter "L". Once we apply this function with the filter method, we get a subset of the data consisting of just these titles. So far we've been talking about the rows of a dataset, but what about the columns? The Datasets library has two main methods for transforming columns: a rename_column method to change the name of a column, and a remove_columns method to delete them. You can see examples of both these method here. Some datasets have nested columns and you can expand these by applying the flatten method. For example in the SQUAD dataset, the answers column contains a text and answer_start field. If we want to promote them to their own separate columns, we can apply flatten as shown here. Of course, no discussion of the Datasets library would be complete without mentioning the famous map method. This method applies a custom processing function to each row in the dataset. For example,here we first define a lowercase_title function that simply lowercases the text in the title column and then we feed that to the map method and voila! we now have lowercase titles. The map method can also be used to feed batches of rows to the processing function. This is especially useful for tokenization, where the tokenizers are backed by the Tokenizers library can use fast multithreading to process batches in parallel.
gradio-app/gradio/blob/main/demo/question-answering/run.ipynb	Gradio Demo: question-answering ``` !pip install -q gradio torch transformers ``` ``` import gradio as gr from transformers import AutoModelForQuestionAnswering, AutoTokenizer, pipeline model_name = "deepset/roberta-base-squad2" nlp = pipeline("question-answering", model=model_name, tokenizer=model_name) context = "The Amazon rainforest, also known in English as Amazonia or the Amazon Jungle, is a moist broadleaf forest that covers most of the Amazon basin of South America. This basin encompasses 7,000,000 square kilometres (2,700,000 sq mi), of which 5,500,000 square kilometres (2,100,000 sq mi) are covered by the rainforest. This region includes territory belonging to nine nations. The majority of the forest is contained within Brazil, with 60% of the rainforest, followed by Peru with 13%, Colombia with 10%, and with minor amounts in Venezuela, Ecuador, Bolivia, Guyana, Suriname and French Guiana. The Amazon represents over half of the planet's remaining rainforests, and comprises the largest and most biodiverse tract of tropical rainforest in the world, with an estimated 390 billion individual trees divided into 16,000 species." question = "Which continent is the Amazon rainforest in?" def predict(context, question): res = nlp({"question": question, "context": context}) return res["answer"], res["score"] gr.Interface( predict, inputs=[ gr.Textbox(lines=7, value=context, label="Context Paragraph"), gr.Textbox(lines=2, value=question, label="Question"), ], outputs=[gr.Textbox(label="Answer"), gr.Textbox(label="Score")], ).launch() ```
huggingface/diffusers/blob/main/docs/source/en/api/loaders/ip_adapter.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # IP-Adapter [IP-Adapter](https://hf.co/papers/2308.06721) is a lightweight adapter that enables prompting a diffusion model with an image. This method decouples the cross-attention layers of the image and text features. The image features are generated from an image encoder. Files generated from IP-Adapter are only ~100MBs. <Tip> Learn how to load an IP-Adapter checkpoint and image in the [IP-Adapter](../../using-diffusers/loading_adapters#ip-adapter) loading guide. </Tip> ## IPAdapterMixin [[autodoc]] loaders.ip_adapter.IPAdapterMixin
huggingface/peft/blob/main/docs/source/package_reference/config.md	!--⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Configuration [`PeftConfigMixin`] is the base configuration class for storing the adapter configuration of a [`PeftModel`], and [`PromptLearningConfig`] is the base configuration class for soft prompt methods (p-tuning, prefix tuning, and prompt tuning). These base classes contain methods for saving and loading model configurations from the Hub, specifying the PEFT method to use, type of task to perform, and model configurations like number of layers and number of attention heads. ## PeftConfigMixin [[autodoc]] config.PeftConfigMixin - all ## PeftConfig [[autodoc]] PeftConfig - all ## PromptLearningConfig [[autodoc]] PromptLearningConfig - all
huggingface/transformers/blob/main/README_ru.md	!--- Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> <p align="center"> <picture> <source media="(prefers-color-scheme: dark)" srcset="https://huggingface.co/datasets/huggingface/documentation-images/raw/main/transformers-logo-dark.svg"> <source media="(prefers-color-scheme: light)" srcset="https://huggingface.co/datasets/huggingface/documentation-images/raw/main/transformers-logo-light.svg"> <img alt="Hugging Face Transformers Library" src="https://huggingface.co/datasets/huggingface/documentation-images/raw/main/transformers-logo-light.svg" width="352" height="59" style="max-width: 100%;"> </picture> <br/> <br/> </p> <p align="center"> <a href="https://circleci.com/gh/huggingface/transformers"> <img alt="Build" src="https://img.shields.io/circleci/build/github/huggingface/transformers/main"> </a> <a href="https://github.com/huggingface/transformers/blob/main/LICENSE"> <img alt="GitHub" src="https://img.shields.io/github/license/huggingface/transformers.svg?color=blue"> </a> <a href="https://huggingface.co/docs/transformers/index"> <img alt="Documentation" src="https://img.shields.io/website/http/huggingface.co/docs/transformers/index.svg?down_color=red&down_message=offline&up_message=online"> </a> <a href="https://github.com/huggingface/transformers/releases"> <img alt="GitHub release" src="https://img.shields.io/github/release/huggingface/transformers.svg"> </a> <a href="https://github.com/huggingface/transformers/blob/main/CODE_OF_CONDUCT.md"> <img alt="Contributor Covenant" src="https://img.shields.io/badge/Contributor%20Covenant-v2.0%20adopted-ff69b4.svg"> </a> <a href="https://zenodo.org/badge/latestdoi/155220641"><img src="https://zenodo.org/badge/155220641.svg" alt="DOI"></a> </p> <h4 align="center"> <p> <a href="https://github.com/huggingface/transformers/blob/main/README.md">English</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_zh-hans.md">简体中文</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_zh-hant.md">繁體中文</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_ko.md">한국어</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_es.md">Español</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_ja.md">日本語</a> \| <a href="https://github.com/huggingface/transformers/blob/main/README_hd.md">हिन्दी</a> \| <b>Русский</b> <a href="https://github.com/huggingface/transformers//blob/main/README_te.md">తెలుగు</a> \| <p> </h4> <h3 align="center"> <p>Современное машинное обучение для JAX, PyTorch и TensorFlow</p> </h3> <h3 align="center"> <a href="https://hf.co/course"><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/course_banner.png"></a> </h3> 🤗 Transformers предоставляет тысячи предварительно обученных моделей для выполнения различных задач, таких как текст, зрение и аудио. Эти модели могут быть применены к: * 📝 Тексту для таких задач, как классификация текстов, извлечение информации, ответы на вопросы, обобщение, перевод, генерация текстов на более чем 100 языках. * 🖼️ Изображениям для задач классификации изображений, обнаружения объектов и сегментации. * 🗣️ Аудио для задач распознавания речи и классификации аудио. Модели transformers также могут выполнять несколько задач, такие как ответы на табличные вопросы, распознавание оптических символов, извлечение информации из отсканированных документов, классификация видео и ответы на визуальные вопросы. 🤗 Transformers предоставляет API для быстрой загрузки и использования предварительно обученных моделей, их тонкой настройки на собственных датасетах и последующего взаимодействия ими с сообществом на нашем [сайте](https://huggingface.co/models). В то же время каждый python модуль, определяющий архитектуру, полностью автономен и может быть модифицирован для проведения быстрых исследовательских экспериментов. 🤗 Transformers опирается на три самые популярные библиотеки глубокого обучения - [Jax](https://jax.readthedocs.io/en/latest/), [PyTorch](https://pytorch.org/) и [TensorFlow](https://www.tensorflow.org/) - и легко интегрируется между ними. Это позволяет легко обучать модели с помощью одной из них, а затем загружать их для выводов с помощью другой. ## Онлайн демонстрация Большинство наших моделей можно протестировать непосредственно на их страницах с [сайта](https://huggingface.co/models). Мы также предлагаем [привтаный хостинг моделей, контроль версий и API для выводов](https://huggingface.co/pricing) для публичных и частных моделей. Вот несколько примеров: В области NLP ( Обработка текстов на естественном языке ): - [Маскированное заполнение слов с помощью BERT](https://huggingface.co/bert-base-uncased?text=Paris+is+the+%5BMASK%5D+of+France) - [Распознавание сущностей с помощью Electra](https://huggingface.co/dbmdz/electra-large-discriminator-finetuned-conll03-english?text=My+name+is+Sarah+and+I+live+in+London+city) - [Генерация текста с помощью GPT-2](https://huggingface.co/gpt2?text=A+long+time+ago%2C+) - [Выводы на естественном языке с помощью RoBERTa](https://huggingface.co/roberta-large-mnli?text=The+dog+was+lost.+Nobody+lost+any+animal) - [Обобщение с помощью BART](https://huggingface.co/facebook/bart-large-cnn?text=The+tower+is+324+metres+%281%2C063+ft%29+tall%2C+about+the+same+height+as+an+81-storey+building%2C+and+the+tallest+structure+in+Paris.+Its+base+is+square%2C+measuring+125+metres+%28410+ft%29+on+each+side.+During+its+construction%2C+the+Eiffel+Tower+surpassed+the+Washington+Monument+to+become+the+tallest+man-made+structure+in+the+world%2C+a+title+it+held+for+41+years+until+the+Chrysler+Building+in+New+York+City+was+finished+in+1930.+It+was+the+first+structure+to+reach+a+height+of+300+metres.+Due+to+the+addition+of+a+broadcasting+aerial+at+the+top+of+the+tower+in+1957%2C+it+is+now+taller+than+the+Chrysler+Building+by+5.2+metres+%2817+ft%29.+Excluding+transmitters%2C+the+Eiffel+Tower+is+the+second+tallest+free-standing+structure+in+France+after+the+Millau+Viaduct) - [Ответы на вопросы с помощью DistilBERT](https://huggingface.co/distilbert-base-uncased-distilled-squad?text=Which+name+is+also+used+to+describe+the+Amazon+rainforest+in+English%3F&context=The+Amazon+rainforest+%28Portuguese%3A+Floresta+Amaz%C3%B4nica+or+Amaz%C3%B4nia%3B+Spanish%3A+Selva+Amaz%C3%B3nica%2C+Amazon%C3%ADa+or+usually+Amazonia%3B+French%3A+For%C3%AAt+amazonienne%3B+Dutch%3A+Amazoneregenwoud%29%2C+also+known+in+English+as+Amazonia+or+the+Amazon+Jungle%2C+is+a+moist+broadleaf+forest+that+covers+most+of+the+Amazon+basin+of+South+America.+This+basin+encompasses+7%2C000%2C000+square+kilometres+%282%2C700%2C000+sq+mi%29%2C+of+which+5%2C500%2C000+square+kilometres+%282%2C100%2C000+sq+mi%29+are+covered+by+the+rainforest.+This+region+includes+territory+belonging+to+nine+nations.+The+majority+of+the+forest+is+contained+within+Brazil%2C+with+60%25+of+the+rainforest%2C+followed+by+Peru+with+13%25%2C+Colombia+with+10%25%2C+and+with+minor+amounts+in+Venezuela%2C+Ecuador%2C+Bolivia%2C+Guyana%2C+Suriname+and+French+Guiana.+States+or+departments+in+four+nations+contain+%22Amazonas%22+in+their+names.+The+Amazon+represents+over+half+of+the+planet%27s+remaining+rainforests%2C+and+comprises+the+largest+and+most+biodiverse+tract+of+tropical+rainforest+in+the+world%2C+with+an+estimated+390+billion+individual+trees+divided+into+16%2C000+species) - [Перевод с помощью T5](https://huggingface.co/t5-base?text=My+name+is+Wolfgang+and+I+live+in+Berlin) В области компьютерного зрения: - [Классификация изображений с помощью ViT](https://huggingface.co/google/vit-base-patch16-224) - [Обнаружение объектов с помощью DETR](https://huggingface.co/facebook/detr-resnet-50) - [Семантическая сегментация с помощью SegFormer](https://huggingface.co/nvidia/segformer-b0-finetuned-ade-512-512) - [Сегментация паноптикума с помощью MaskFormer](https://huggingface.co/facebook/maskformer-swin-small-coco) - [Оценка глубины с помощью DPT](https://huggingface.co/docs/transformers/model_doc/dpt) - [Классификация видео с помощью VideoMAE](https://huggingface.co/docs/transformers/model_doc/videomae) - [Универсальная сегментация с помощью OneFormer](https://huggingface.co/shi-labs/oneformer_ade20k_dinat_large) В области звука: - [Автоматическое распознавание речи с помощью Wav2Vec2](https://huggingface.co/facebook/wav2vec2-base-960h) - [Поиск ключевых слов с помощью Wav2Vec2](https://huggingface.co/superb/wav2vec2-base-superb-ks) - [Классификация аудиоданных с помощью траснформера аудиоспектрограмм](https://huggingface.co/MIT/ast-finetuned-audioset-10-10-0.4593) В мультимодальных задачах: - [Ответы на вопросы по таблице с помощью TAPAS](https://huggingface.co/google/tapas-base-finetuned-wtq) - [Визуальные ответы на вопросы с помощью ViLT](https://huggingface.co/dandelin/vilt-b32-finetuned-vqa) - [Zero-shot классификация изображений с помощью CLIP](https://huggingface.co/openai/clip-vit-large-patch14) - [Ответы на вопросы по документам с помощью LayoutLM](https://huggingface.co/impira/layoutlm-document-qa) - [Zero-shot классификация видео с помощью X-CLIP](https://huggingface.co/docs/transformers/model_doc/xclip) ## 100 проектов, использующих Transformers Transformers - это не просто набор инструментов для использования предварительно обученных моделей: это сообщество проектов, созданное на его основе, и Hugging Face Hub. Мы хотим, чтобы Transformers позволил разработчикам, исследователям, студентам, профессорам, инженерам и всем желающим создавать проекты своей мечты. Чтобы отпраздновать 100 тысяч звезд Transformers, мы решили сделать акцент на сообществе, и создали страницу [awesome-transformers](./awesome-transformers.md), на которой перечислены 100 невероятных проектов, созданных с помощью transformers. Если вы являетесь владельцем или пользователем проекта, который, по вашему мнению, должен быть включен в этот список, пожалуйста, откройте PR для его добавления! ## Если вы хотите получить индивидуальную поддержку от команды Hugging Face <a target="_blank" href="https://huggingface.co/support"> <img alt="HuggingFace Expert Acceleration Program" src="https://cdn-media.huggingface.co/marketing/transformers/new-support-improved.png" style="max-width: 600px; border: 1px solid #eee; border-radius: 4px; box-shadow: 0 1px 2px 0 rgba(0, 0, 0, 0.05);"> </a><br> ## Быстрый гайд Для использования модели на заданном входе (текст, изображение, звук, ...) мы предоставляем API `pipeline`. Конвейеры объединяют предварительно обученную модель с препроцессингом, который использовался при ее обучении. Вот как можно быстро использовать конвейер для классификации положительных и отрицательных текстов: ```python >>> from transformers import pipeline # Выделение конвейера для анализа настроений >>> classifier = pipeline('sentiment-analysis') >>> classifier('Мы очень рады представить конвейер в transformers.') [{'label': 'POSITIVE', 'score': 0.9996980428695679}] ``` Вторая строка кода загружает и кэширует предварительно обученную модель, используемую конвейером, а третья оценивает ее на заданном тексте. Здесь ответ "POSITIVE" с уверенностью 99,97%. Во многих задачах, как в НЛП, так и в компьютерном зрении и речи, уже есть готовый `pipeline`. Например, мы можем легко извлечь обнаруженные объекты на изображении: ``` python >>> import requests >>> from PIL import Image >>> from transformers import pipeline # Скачиваем изображение с милыми котиками >>> url = "https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/coco_sample.png" >>> image_data = requests.get(url, stream=True).raw >>> image = Image.open(image_data) # Выделение конвейера для обнаружения объектов >>> object_detector = pipeline('object-detection') >>> object_detector(image) [{'score': 0.9982201457023621, 'label': 'remote', 'box': {'xmin': 40, 'ymin': 70, 'xmax': 175, 'ymax': 117}}, {'score': 0.9960021376609802, 'label': 'remote', 'box': {'xmin': 333, 'ymin': 72, 'xmax': 368, 'ymax': 187}}, {'score': 0.9954745173454285, 'label': 'couch', 'box': {'xmin': 0, 'ymin': 1, 'xmax': 639, 'ymax': 473}}, {'score': 0.9988006353378296, 'label': 'cat', 'box': {'xmin': 13, 'ymin': 52, 'xmax': 314, 'ymax': 470}}, {'score': 0.9986783862113953, 'label': 'cat', 'box': {'xmin': 345, 'ymin': 23, 'xmax': 640, 'ymax': 368}}] ``` Здесь мы получаем список объектов, обнаруженных на изображении, с рамкой вокруг объекта и оценкой достоверности. Слева - исходное изображение, справа прогнозы: <h3 align="center"> <a><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/coco_sample.png" width="400"></a> <a><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/coco_sample_post_processed.png" width="400"></a> </h3> Подробнее о задачах, поддерживаемых API `pipeline`, можно узнать в [этом учебном пособии](https://huggingface.co/docs/transformers/task_sum) В дополнение к `pipeline`, для загрузки и использования любой из предварительно обученных моделей в заданной задаче достаточно трех строк кода. Вот версия для PyTorch: ```python >>> from transformers import AutoTokenizer, AutoModel >>> tokenizer = AutoTokenizer.from_pretrained("bert-base-uncased") >>> model = AutoModel.from_pretrained("bert-base-uncased") >>> inputs = tokenizer("Привет мир!", return_tensors="pt") >>> outputs = model(inputs) ``` А вот эквивалентный код для TensorFlow: ```python >>> from transformers import AutoTokenizer, TFAutoModel >>> tokenizer = AutoTokenizer.from_pretrained("bert-base-uncased") >>> model = TFAutoModel.from_pretrained("bert-base-uncased") >>> inputs = tokenizer("Привет мир!", return_tensors="tf") >>> outputs = model(inputs) ``` Токенизатор отвечает за всю предварительную обработку, которую ожидает предварительно обученная модель, и может быть вызван непосредственно с помощью одной строки (как в приведенных выше примерах) или на списке. В результате будет получен словарь, который можно использовать в последующем коде или просто напрямую передать в модель с помощью оператора распаковки аргументов . Сама модель представляет собой обычный [Pytorch `nn.Module`](https://pytorch.org/docs/stable/nn.html#torch.nn.Module) или [TensorFlow `tf.keras.Model`](https://www.tensorflow.org/api_docs/python/tf/keras/Model) (в зависимости от используемого бэкенда), который можно использовать как обычно. [В этом руководстве](https://huggingface.co/docs/transformers/training) рассказывается, как интегрировать такую модель в классический цикл обучения PyTorch или TensorFlow, или как использовать наш API `Trainer` для быстрой тонкой настройки на новом датасете. ## Почему необходимо использовать transformers? 1. Простые в использовании современные модели: - Высокая производительность в задачах понимания и генерации естественного языка, компьютерного зрения и аудио. - Низкий входной барьер для преподавателей и практиков. - Небольшое количество абстракций для пользователя и всего три класса для изучения. - Единый API для использования всех наших предварительно обученных моделей. 1. Более низкие вычислительные затраты, меньший "углеродный след": - Исследователи могут обмениваться обученными моделями вместо того, чтобы постоянно их переобучать. - Практики могут сократить время вычислений и производственные затраты. - Десятки архитектур с более чем 60 000 предварительно обученных моделей для всех модальностей. 1. Выбор подходящего фреймворка для каждого этапа жизни модели: - Обучение самых современных моделей за 3 строки кода. - Перемещайте одну модель между фреймворками TF2.0/PyTorch/JAX по своему усмотрению. - Беспрепятственный выбор подходящего фреймворка для обучения, оценки и производства. 1. Легко настроить модель или пример под свои нужды: - Мы предоставляем примеры для каждой архитектуры, чтобы воспроизвести результаты, опубликованные их авторами. - Внутренние компоненты модели раскрываются максимально последовательно. - Файлы моделей можно использовать независимо от библиотеки для проведения быстрых экспериментов. ## Почему я не должен использовать transformers? - Данная библиотека не является модульным набором строительных блоков для нейронных сетей. Код в файлах моделей специально не рефакторится дополнительными абстракциями, чтобы исследователи могли быстро итеративно работать с каждой из моделей, не погружаясь в дополнительные абстракции/файлы. - API обучения не предназначен для работы с любой моделью, а оптимизирован для работы с моделями, предоставляемыми библиотекой. Для работы с общими циклами машинного обучения следует использовать другую библиотеку (возможно, [Accelerate](https://huggingface.co/docs/accelerate)). - Несмотря на то, что мы стремимся представить как можно больше примеров использования, скрипты в нашей папке [примеров](https://github.com/huggingface/transformers/tree/main/examples) являются именно примерами. Предполагается, что они не будут работать "из коробки" для решения вашей конкретной задачи, и вам придется изменить несколько строк кода, чтобы адаптировать их под свои нужды. ## Установка ### С помощью pip Данный репозиторий протестирован на Python 3.8+, Flax 0.4.1+, PyTorch 1.10+ и TensorFlow 2.6+. Устанавливать 🤗 Transformers следует в [виртуальной среде](https://docs.python.org/3/library/venv.html). Если вы не знакомы с виртуальными средами Python, ознакомьтесь с [руководством пользователя](https://packaging.python.org/guides/installing-using-pip-and-virtual-environments/). Сначала создайте виртуальную среду с той версией Python, которую вы собираетесь использовать, и активируйте ее. Затем необходимо установить хотя бы один бекенд из Flax, PyTorch или TensorFlow. Пожалуйста, обратитесь к страницам [TensorFlow установочная страница](https://www.tensorflow.org/install/), [PyTorch установочная страница](https://pytorch.org/get-started/locally/#start-locally) и/или [Flax](https://github.com/google/flax#quick-install) и [Jax](https://github.com/google/jax#installation), где описаны команды установки для вашей платформы. После установки одного из этих бэкендов 🤗 Transformers может быть установлен с помощью pip следующим образом: ```bash pip install transformers ``` Если вы хотите поиграть с примерами или вам нужен самый современный код и вы не можете ждать нового релиза, вы должны [установить библиотеку из исходного кода](https://huggingface.co/docs/transformers/installation#installing-from-source). ### С помощью conda Начиная с версии Transformers v4.0.0, у нас появилсась поддержка conda: `huggingface`. Установить Transformers с помощью conda можно следующим образом: ```bash conda install -c huggingface transformers ``` О том, как установить Flax, PyTorch или TensorFlow с помощью conda, читайте на страницах, посвященных их установке. > _ЗАМЕТКА:_ В операционной системе Windows вам может быть предложено активировать режим разработчика, чтобы воспользоваться преимуществами кэширования. Если для вас это невозможно, сообщите нам об этом [здесь](https://github.com/huggingface/huggingface_hub/issues/1062). ## Модельные архитектуры [Все контрольные точки моделей](https://huggingface.co/models), предоставляемые 🤗 Transformers, беспрепятственно интегрируются с huggingface.co [model hub](https://huggingface.co/models), куда они загружаются непосредственно [пользователями](https://huggingface.co/users) и [организациями](https://huggingface.co/organizations). Текущее количество контрольных точек: ![](https://img.shields.io/endpoint?url=https://huggingface.co/api/shields/models&color=brightgreen) 🤗 В настоящее время Transformers предоставляет следующие архитектуры (подробное описание каждой из них см. [здесь](https://huggingface.co/docs/transformers/model_summary)): 1. [ALBERT](https://huggingface.co/docs/transformers/model_doc/albert) (from Google Research and the Toyota Technological Institute at Chicago) released with the paper [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://arxiv.org/abs/1909.11942), by Zhenzhong Lan, Mingda Chen, Sebastian Goodman, Kevin Gimpel, Piyush Sharma, Radu Soricut. 1. [ALIGN](https://huggingface.co/docs/transformers/model_doc/align) (from Google Research) released with the paper [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://arxiv.org/abs/2102.05918) by Chao Jia, Yinfei Yang, Ye Xia, Yi-Ting Chen, Zarana Parekh, Hieu Pham, Quoc V. Le, Yunhsuan Sung, Zhen Li, Tom Duerig. 1. [AltCLIP](https://huggingface.co/docs/transformers/model_doc/altclip) (from BAAI) released with the paper [AltCLIP: Altering the Language Encoder in CLIP for Extended Language Capabilities](https://arxiv.org/abs/2211.06679) by Chen, Zhongzhi and Liu, Guang and Zhang, Bo-Wen and Ye, Fulong and Yang, Qinghong and Wu, Ledell. 1. [Audio Spectrogram Transformer](https://huggingface.co/docs/transformers/model_doc/audio-spectrogram-transformer) (from MIT) released with the paper [AST: Audio Spectrogram Transformer](https://arxiv.org/abs/2104.01778) by Yuan Gong, Yu-An Chung, James Glass. 1. [Autoformer](https://huggingface.co/docs/transformers/model_doc/autoformer) (from Tsinghua University) released with the paper [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://arxiv.org/abs/2106.13008) by Haixu Wu, Jiehui Xu, Jianmin Wang, Mingsheng Long. 1. [Bark](https://huggingface.co/docs/transformers/model_doc/bark) (from Suno) released in the repository [suno-ai/bark](https://github.com/suno-ai/bark) by Suno AI team. 1. [BART](https://huggingface.co/docs/transformers/model_doc/bart) (from Facebook) released with the paper [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://arxiv.org/abs/1910.13461) by Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Ves Stoyanov and Luke Zettlemoyer. 1. [BARThez](https://huggingface.co/docs/transformers/model_doc/barthez) (from École polytechnique) released with the paper [BARThez: a Skilled Pretrained French Sequence-to-Sequence Model](https://arxiv.org/abs/2010.12321) by Moussa Kamal Eddine, Antoine J.-P. Tixier, Michalis Vazirgiannis. 1. [BARTpho](https://huggingface.co/docs/transformers/model_doc/bartpho) (from VinAI Research) released with the paper [BARTpho: Pre-trained Sequence-to-Sequence Models for Vietnamese](https://arxiv.org/abs/2109.09701) by Nguyen Luong Tran, Duong Minh Le and Dat Quoc Nguyen. 1. [BEiT](https://huggingface.co/docs/transformers/model_doc/beit) (from Microsoft) released with the paper [BEiT: BERT Pre-Training of Image Transformers](https://arxiv.org/abs/2106.08254) by Hangbo Bao, Li Dong, Furu Wei. 1. [BERT](https://huggingface.co/docs/transformers/model_doc/bert) (from Google) released with the paper [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://arxiv.org/abs/1810.04805) by Jacob Devlin, Ming-Wei Chang, Kenton Lee and Kristina Toutanova. 1. [BERT For Sequence Generation](https://huggingface.co/docs/transformers/model_doc/bert-generation) (from Google) released with the paper [Leveraging Pre-trained Checkpoints for Sequence Generation Tasks](https://arxiv.org/abs/1907.12461) by Sascha Rothe, Shashi Narayan, Aliaksei Severyn. 1. [BERTweet](https://huggingface.co/docs/transformers/model_doc/bertweet) (from VinAI Research) released with the paper [BERTweet: A pre-trained language model for English Tweets](https://aclanthology.org/2020.emnlp-demos.2/) by Dat Quoc Nguyen, Thanh Vu and Anh Tuan Nguyen. 1. [BigBird-Pegasus](https://huggingface.co/docs/transformers/model_doc/bigbird_pegasus) (from Google Research) released with the paper [Big Bird: Transformers for Longer Sequences](https://arxiv.org/abs/2007.14062) by Manzil Zaheer, Guru Guruganesh, Avinava Dubey, Joshua Ainslie, Chris Alberti, Santiago Ontanon, Philip Pham, Anirudh Ravula, Qifan Wang, Li Yang, Amr Ahmed. 1. [BigBird-RoBERTa](https://huggingface.co/docs/transformers/model_doc/big_bird) (from Google Research) released with the paper [Big Bird: Transformers for Longer Sequences](https://arxiv.org/abs/2007.14062) by Manzil Zaheer, Guru Guruganesh, Avinava Dubey, Joshua Ainslie, Chris Alberti, Santiago Ontanon, Philip Pham, Anirudh Ravula, Qifan Wang, Li Yang, Amr Ahmed. 1. [BioGpt](https://huggingface.co/docs/transformers/model_doc/biogpt) (from Microsoft Research AI4Science) released with the paper [BioGPT: generative pre-trained transformer for biomedical text generation and mining](https://academic.oup.com/bib/advance-article/doi/10.1093/bib/bbac409/6713511?guestAccessKey=a66d9b5d-4f83-4017-bb52-405815c907b9) by Renqian Luo, Liai Sun, Yingce Xia, Tao Qin, Sheng Zhang, Hoifung Poon and Tie-Yan Liu. 1. [BiT](https://huggingface.co/docs/transformers/model_doc/bit) (from Google AI) released with the paper [Big Transfer (BiT): General Visual Representation Learning](https://arxiv.org/abs/1912.11370) by Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Joan Puigcerver, Jessica Yung, Sylvain Gelly, Neil Houlsby. 1. [Blenderbot](https://huggingface.co/docs/transformers/model_doc/blenderbot) (from Facebook) released with the paper [Recipes for building an open-domain chatbot](https://arxiv.org/abs/2004.13637) by Stephen Roller, Emily Dinan, Naman Goyal, Da Ju, Mary Williamson, Yinhan Liu, Jing Xu, Myle Ott, Kurt Shuster, Eric M. Smith, Y-Lan Boureau, Jason Weston. 1. [BlenderbotSmall](https://huggingface.co/docs/transformers/model_doc/blenderbot-small) (from Facebook) released with the paper [Recipes for building an open-domain chatbot](https://arxiv.org/abs/2004.13637) by Stephen Roller, Emily Dinan, Naman Goyal, Da Ju, Mary Williamson, Yinhan Liu, Jing Xu, Myle Ott, Kurt Shuster, Eric M. Smith, Y-Lan Boureau, Jason Weston. 1. [BLIP](https://huggingface.co/docs/transformers/model_doc/blip) (from Salesforce) released with the paper [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://arxiv.org/abs/2201.12086) by Junnan Li, Dongxu Li, Caiming Xiong, Steven Hoi. 1. [BLIP-2](https://huggingface.co/docs/transformers/model_doc/blip-2) (from Salesforce) released with the paper [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://arxiv.org/abs/2301.12597) by Junnan Li, Dongxu Li, Silvio Savarese, Steven Hoi. 1. [BLOOM](https://huggingface.co/docs/transformers/model_doc/bloom) (from BigScience workshop) released by the [BigScience Workshop](https://bigscience.huggingface.co/). 1. [BORT](https://huggingface.co/docs/transformers/model_doc/bort) (from Alexa) released with the paper [Optimal Subarchitecture Extraction For BERT](https://arxiv.org/abs/2010.10499) by Adrian de Wynter and Daniel J. Perry. 1. [BridgeTower](https://huggingface.co/docs/transformers/model_doc/bridgetower) (from Harbin Institute of Technology/Microsoft Research Asia/Intel Labs) released with the paper [BridgeTower: Building Bridges Between Encoders in Vision-Language Representation Learning](https://arxiv.org/abs/2206.08657) by Xiao Xu, Chenfei Wu, Shachar Rosenman, Vasudev Lal, Wanxiang Che, Nan Duan. 1. [BROS](https://huggingface.co/docs/transformers/model_doc/bros) (from NAVER CLOVA) released with the paper [BROS: A Pre-trained Language Model Focusing on Text and Layout for Better Key Information Extraction from Documents](https://arxiv.org/abs/2108.04539) by Teakgyu Hong, Donghyun Kim, Mingi Ji, Wonseok Hwang, Daehyun Nam, Sungrae Park. 1. [ByT5](https://huggingface.co/docs/transformers/model_doc/byt5) (from Google Research) released with the paper [ByT5: Towards a token-free future with pre-trained byte-to-byte models](https://arxiv.org/abs/2105.13626) by Linting Xue, Aditya Barua, Noah Constant, Rami Al-Rfou, Sharan Narang, Mihir Kale, Adam Roberts, Colin Raffel. 1. [CamemBERT](https://huggingface.co/docs/transformers/model_doc/camembert)** (from Inria/Facebook/Sorbonne) released with the paper [CamemBERT: a Tasty French Language Model](https://arxiv.org/abs/1911.03894) by Louis Martin, Benjamin Muller, Pedro Javier Ortiz Suárez, Yoann Dupont, Laurent Romary, Éric Villemonte de la Clergerie, Djamé Seddah and Benoît Sagot. 1. [CANINE](https://huggingface.co/docs/transformers/model_doc/canine)* (from Google Research) released with the paper [CANINE: Pre-training an Efficient Tokenization-Free Encoder for Language Representation](https://arxiv.org/abs/2103.06874) by Jonathan H. Clark, Dan Garrette, Iulia Turc, John Wieting. 1. [Chinese-CLIP](https://huggingface.co/docs/transformers/model_doc/chinese_clip) (from OFA-Sys) released with the paper [Chinese CLIP: Contrastive Vision-Language Pretraining in Chinese](https://arxiv.org/abs/2211.01335) by An Yang, Junshu Pan, Junyang Lin, Rui Men, Yichang Zhang, Jingren Zhou, Chang Zhou. 1. [CLAP](https://huggingface.co/docs/transformers/model_doc/clap) (from LAION-AI) released with the paper [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://arxiv.org/abs/2211.06687) by Yusong Wu, Ke Chen, Tianyu Zhang, Yuchen Hui, Taylor Berg-Kirkpatrick, Shlomo Dubnov. 1. [CLIP](https://huggingface.co/docs/transformers/model_doc/clip) (from OpenAI) released with the paper [Learning Transferable Visual Models From Natural Language Supervision](https://arxiv.org/abs/2103.00020) by Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, Ilya Sutskever. 1. [CLIPSeg](https://huggingface.co/docs/transformers/model_doc/clipseg) (from University of Göttingen) released with the paper [Image Segmentation Using Text and Image Prompts](https://arxiv.org/abs/2112.10003) by Timo Lüddecke and Alexander Ecker. 1. [CodeGen](https://huggingface.co/docs/transformers/model_doc/codegen) (from Salesforce) released with the paper [A Conversational Paradigm for Program Synthesis](https://arxiv.org/abs/2203.13474) by Erik Nijkamp, Bo Pang, Hiroaki Hayashi, Lifu Tu, Huan Wang, Yingbo Zhou, Silvio Savarese, Caiming Xiong. 1. [CodeLlama](https://huggingface.co/docs/transformers/model_doc/llama_code) (from MetaAI) released with the paper [Code Llama: Open Foundation Models for Code](https://ai.meta.com/research/publications/code-llama-open-foundation-models-for-code/) by Baptiste Rozière, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Tal Remez, Jérémy Rapin, Artyom Kozhevnikov, Ivan Evtimov, Joanna Bitton, Manish Bhatt, Cristian Canton Ferrer, Aaron Grattafiori, Wenhan Xiong, Alexandre Défossez, Jade Copet, Faisal Azhar, Hugo Touvron, Louis Martin, Nicolas Usunier, Thomas Scialom, Gabriel Synnaeve. 1. [Conditional DETR](https://huggingface.co/docs/transformers/model_doc/conditional_detr) (from Microsoft Research Asia) released with the paper [Conditional DETR for Fast Training Convergence](https://arxiv.org/abs/2108.06152) by Depu Meng, Xiaokang Chen, Zejia Fan, Gang Zeng, Houqiang Li, Yuhui Yuan, Lei Sun, Jingdong Wang. 1. [ConvBERT](https://huggingface.co/docs/transformers/model_doc/convbert) (from YituTech) released with the paper [ConvBERT: Improving BERT with Span-based Dynamic Convolution](https://arxiv.org/abs/2008.02496) by Zihang Jiang, Weihao Yu, Daquan Zhou, Yunpeng Chen, Jiashi Feng, Shuicheng Yan. 1. [ConvNeXT](https://huggingface.co/docs/transformers/model_doc/convnext) (from Facebook AI) released with the paper [A ConvNet for the 2020s](https://arxiv.org/abs/2201.03545) by Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, Saining Xie. 1. [ConvNeXTV2](https://huggingface.co/docs/transformers/model_doc/convnextv2) (from Facebook AI) released with the paper [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://arxiv.org/abs/2301.00808) by Sanghyun Woo, Shoubhik Debnath, Ronghang Hu, Xinlei Chen, Zhuang Liu, In So Kweon, Saining Xie. 1. [CPM](https://huggingface.co/docs/transformers/model_doc/cpm) (from Tsinghua University) released with the paper [CPM: A Large-scale Generative Chinese Pre-trained Language Model](https://arxiv.org/abs/2012.00413) by Zhengyan Zhang, Xu Han, Hao Zhou, Pei Ke, Yuxian Gu, Deming Ye, Yujia Qin, Yusheng Su, Haozhe Ji, Jian Guan, Fanchao Qi, Xiaozhi Wang, Yanan Zheng, Guoyang Zeng, Huanqi Cao, Shengqi Chen, Daixuan Li, Zhenbo Sun, Zhiyuan Liu, Minlie Huang, Wentao Han, Jie Tang, Juanzi Li, Xiaoyan Zhu, Maosong Sun. 1. [CPM-Ant](https://huggingface.co/docs/transformers/model_doc/cpmant) (from OpenBMB) released by the [OpenBMB](https://www.openbmb.org/). 1. [CTRL](https://huggingface.co/docs/transformers/model_doc/ctrl) (from Salesforce) released with the paper [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://arxiv.org/abs/1909.05858) by Nitish Shirish Keskar, Bryan McCann, Lav R. Varshney, Caiming Xiong and Richard Socher. 1. [CvT](https://huggingface.co/docs/transformers/model_doc/cvt) (from Microsoft) released with the paper [CvT: Introducing Convolutions to Vision Transformers](https://arxiv.org/abs/2103.15808) by Haiping Wu, Bin Xiao, Noel Codella, Mengchen Liu, Xiyang Dai, Lu Yuan, Lei Zhang. 1. [Data2Vec](https://huggingface.co/docs/transformers/model_doc/data2vec) (from Facebook) released with the paper [Data2Vec: A General Framework for Self-supervised Learning in Speech, Vision and Language](https://arxiv.org/abs/2202.03555) by Alexei Baevski, Wei-Ning Hsu, Qiantong Xu, Arun Babu, Jiatao Gu, Michael Auli. 1. [DeBERTa](https://huggingface.co/docs/transformers/model_doc/deberta) (from Microsoft) released with the paper [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://arxiv.org/abs/2006.03654) by Pengcheng He, Xiaodong Liu, Jianfeng Gao, Weizhu Chen. 1. [DeBERTa-v2](https://huggingface.co/docs/transformers/model_doc/deberta-v2) (from Microsoft) released with the paper [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://arxiv.org/abs/2006.03654) by Pengcheng He, Xiaodong Liu, Jianfeng Gao, Weizhu Chen. 1. [Decision Transformer](https://huggingface.co/docs/transformers/model_doc/decision_transformer) (from Berkeley/Facebook/Google) released with the paper [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://arxiv.org/abs/2106.01345) by Lili Chen, Kevin Lu, Aravind Rajeswaran, Kimin Lee, Aditya Grover, Michael Laskin, Pieter Abbeel, Aravind Srinivas, Igor Mordatch. 1. [Deformable DETR](https://huggingface.co/docs/transformers/model_doc/deformable_detr) (from SenseTime Research) released with the paper [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://arxiv.org/abs/2010.04159) by Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, Jifeng Dai. 1. [DeiT](https://huggingface.co/docs/transformers/model_doc/deit) (from Facebook) released with the paper [Training data-efficient image transformers & distillation through attention](https://arxiv.org/abs/2012.12877) by Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, Hervé Jégou. 1. [DePlot](https://huggingface.co/docs/transformers/model_doc/deplot) (from Google AI) released with the paper [DePlot: One-shot visual language reasoning by plot-to-table translation](https://arxiv.org/abs/2212.10505) by Fangyu Liu, Julian Martin Eisenschlos, Francesco Piccinno, Syrine Krichene, Chenxi Pang, Kenton Lee, Mandar Joshi, Wenhu Chen, Nigel Collier, Yasemin Altun. 1. [DETA](https://huggingface.co/docs/transformers/model_doc/deta) (from The University of Texas at Austin) released with the paper [NMS Strikes Back](https://arxiv.org/abs/2212.06137) by Jeffrey Ouyang-Zhang, Jang Hyun Cho, Xingyi Zhou, Philipp Krähenbühl. 1. [DETR](https://huggingface.co/docs/transformers/model_doc/detr) (from Facebook) released with the paper [End-to-End Object Detection with Transformers](https://arxiv.org/abs/2005.12872) by Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, Sergey Zagoruyko. 1. [DialoGPT](https://huggingface.co/docs/transformers/model_doc/dialogpt) (from Microsoft Research) released with the paper [DialoGPT: Large-Scale Generative Pre-training for Conversational Response Generation](https://arxiv.org/abs/1911.00536) by Yizhe Zhang, Siqi Sun, Michel Galley, Yen-Chun Chen, Chris Brockett, Xiang Gao, Jianfeng Gao, Jingjing Liu, Bill Dolan. 1. [DiNAT](https://huggingface.co/docs/transformers/model_doc/dinat) (from SHI Labs) released with the paper [Dilated Neighborhood Attention Transformer](https://arxiv.org/abs/2209.15001) by Ali Hassani and Humphrey Shi. 1. [DINOv2](https://huggingface.co/docs/transformers/model_doc/dinov2) (from Meta AI) released with the paper [DINOv2: Learning Robust Visual Features without Supervision](https://arxiv.org/abs/2304.07193) by Maxime Oquab, Timothée Darcet, Théo Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, Mahmoud Assran, Nicolas Ballas, Wojciech Galuba, Russell Howes, Po-Yao Huang, Shang-Wen Li, Ishan Misra, Michael Rabbat, Vasu Sharma, Gabriel Synnaeve, Hu Xu, Hervé Jegou, Julien Mairal, Patrick Labatut, Armand Joulin, Piotr Bojanowski. 1. [DistilBERT](https://huggingface.co/docs/transformers/model_doc/distilbert) (from HuggingFace), released together with the paper [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://arxiv.org/abs/1910.01108) by Victor Sanh, Lysandre Debut and Thomas Wolf. The same method has been applied to compress GPT2 into [DistilGPT2](https://github.com/huggingface/transformers/tree/main/examples/research_projects/distillation), RoBERTa into [DistilRoBERTa](https://github.com/huggingface/transformers/tree/main/examples/research_projects/distillation), Multilingual BERT into [DistilmBERT](https://github.com/huggingface/transformers/tree/main/examples/research_projects/distillation) and a German version of DistilBERT. 1. [DiT](https://huggingface.co/docs/transformers/model_doc/dit) (from Microsoft Research) released with the paper [DiT: Self-supervised Pre-training for Document Image Transformer](https://arxiv.org/abs/2203.02378) by Junlong Li, Yiheng Xu, Tengchao Lv, Lei Cui, Cha Zhang, Furu Wei. 1. [Donut](https://huggingface.co/docs/transformers/model_doc/donut) (from NAVER), released together with the paper [OCR-free Document Understanding Transformer](https://arxiv.org/abs/2111.15664) by Geewook Kim, Teakgyu Hong, Moonbin Yim, Jeongyeon Nam, Jinyoung Park, Jinyeong Yim, Wonseok Hwang, Sangdoo Yun, Dongyoon Han, Seunghyun Park. 1. [DPR](https://huggingface.co/docs/transformers/model_doc/dpr) (from Facebook) released with the paper [Dense Passage Retrieval for Open-Domain Question Answering](https://arxiv.org/abs/2004.04906) by Vladimir Karpukhin, Barlas Oğuz, Sewon Min, Patrick Lewis, Ledell Wu, Sergey Edunov, Danqi Chen, and Wen-tau Yih. 1. [DPT](https://huggingface.co/docs/transformers/master/model_doc/dpt) (from Intel Labs) released with the paper [Vision Transformers for Dense Prediction](https://arxiv.org/abs/2103.13413) by René Ranftl, Alexey Bochkovskiy, Vladlen Koltun. 1. [EfficientFormer](https://huggingface.co/docs/transformers/model_doc/efficientformer) (from Snap Research) released with the paper [EfficientFormer: Vision Transformers at MobileNetSpeed](https://arxiv.org/abs/2206.01191) by Yanyu Li, Geng Yuan, Yang Wen, Ju Hu, Georgios Evangelidis, Sergey Tulyakov, Yanzhi Wang, Jian Ren. 1. [EfficientNet](https://huggingface.co/docs/transformers/model_doc/efficientnet) (from Google Brain) released with the paper [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://arxiv.org/abs/1905.11946) by Mingxing Tan, Quoc V. Le. 1. [ELECTRA](https://huggingface.co/docs/transformers/model_doc/electra) (from Google Research/Stanford University) released with the paper [ELECTRA: Pre-training text encoders as discriminators rather than generators](https://arxiv.org/abs/2003.10555) by Kevin Clark, Minh-Thang Luong, Quoc V. Le, Christopher D. Manning. 1. [EnCodec](https://huggingface.co/docs/transformers/model_doc/encodec) (from Meta AI) released with the paper [High Fidelity Neural Audio Compression](https://arxiv.org/abs/2210.13438) by Alexandre Défossez, Jade Copet, Gabriel Synnaeve, Yossi Adi. 1. [EncoderDecoder](https://huggingface.co/docs/transformers/model_doc/encoder-decoder) (from Google Research) released with the paper [Leveraging Pre-trained Checkpoints for Sequence Generation Tasks](https://arxiv.org/abs/1907.12461) by Sascha Rothe, Shashi Narayan, Aliaksei Severyn. 1. [ERNIE](https://huggingface.co/docs/transformers/model_doc/ernie) (from Baidu) released with the paper [ERNIE: Enhanced Representation through Knowledge Integration](https://arxiv.org/abs/1904.09223) by Yu Sun, Shuohuan Wang, Yukun Li, Shikun Feng, Xuyi Chen, Han Zhang, Xin Tian, Danxiang Zhu, Hao Tian, Hua Wu. 1. [ErnieM](https://huggingface.co/docs/transformers/model_doc/ernie_m) (from Baidu) released with the paper [ERNIE-M: Enhanced Multilingual Representation by Aligning Cross-lingual Semantics with Monolingual Corpora](https://arxiv.org/abs/2012.15674) by Xuan Ouyang, Shuohuan Wang, Chao Pang, Yu Sun, Hao Tian, Hua Wu, Haifeng Wang. 1. [ESM](https://huggingface.co/docs/transformers/model_doc/esm) (from Meta AI) are transformer protein language models. ESM-1b was released with the paper [Biological structure and function emerge from scaling unsupervised learning to 250 million protein sequences](https://www.pnas.org/content/118/15/e2016239118) by Alexander Rives, Joshua Meier, Tom Sercu, Siddharth Goyal, Zeming Lin, Jason Liu, Demi Guo, Myle Ott, C. Lawrence Zitnick, Jerry Ma, and Rob Fergus. ESM-1v was released with the paper [Language models enable zero-shot prediction of the effects of mutations on protein function](https://doi.org/10.1101/2021.07.09.450648) by Joshua Meier, Roshan Rao, Robert Verkuil, Jason Liu, Tom Sercu and Alexander Rives. ESM-2 and ESMFold were released with the paper [Language models of protein sequences at the scale of evolution enable accurate structure prediction](https://doi.org/10.1101/2022.07.20.500902) by Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Allan dos Santos Costa, Maryam Fazel-Zarandi, Tom Sercu, Sal Candido, Alexander Rives. 1. [Falcon](https://huggingface.co/docs/transformers/model_doc/falcon) (from Technology Innovation Institute) by Almazrouei, Ebtesam and Alobeidli, Hamza and Alshamsi, Abdulaziz and Cappelli, Alessandro and Cojocaru, Ruxandra and Debbah, Merouane and Goffinet, Etienne and Heslow, Daniel and Launay, Julien and Malartic, Quentin and Noune, Badreddine and Pannier, Baptiste and Penedo, Guilherme. 1. [FLAN-T5](https://huggingface.co/docs/transformers/model_doc/flan-t5) (from Google AI) released in the repository [google-research/t5x](https://github.com/google-research/t5x/blob/main/docs/models.md#flan-t5-checkpoints) by Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Eric Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, Albert Webson, Shixiang Shane Gu, Zhuyun Dai, Mirac Suzgun, Xinyun Chen, Aakanksha Chowdhery, Sharan Narang, Gaurav Mishra, Adams Yu, Vincent Zhao, Yanping Huang, Andrew Dai, Hongkun Yu, Slav Petrov, Ed H. Chi, Jeff Dean, Jacob Devlin, Adam Roberts, Denny Zhou, Quoc V. Le, and Jason Wei 1. [FLAN-UL2](https://huggingface.co/docs/transformers/model_doc/flan-ul2) (from Google AI) released in the repository [google-research/t5x](https://github.com/google-research/t5x/blob/main/docs/models.md#flan-ul2-checkpoints) by Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Eric Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, Albert Webson, Shixiang Shane Gu, Zhuyun Dai, Mirac Suzgun, Xinyun Chen, Aakanksha Chowdhery, Sharan Narang, Gaurav Mishra, Adams Yu, Vincent Zhao, Yanping Huang, Andrew Dai, Hongkun Yu, Slav Petrov, Ed H. Chi, Jeff Dean, Jacob Devlin, Adam Roberts, Denny Zhou, Quoc V. Le, and Jason Wei 1. [FlauBERT](https://huggingface.co/docs/transformers/model_doc/flaubert) (from CNRS) released with the paper [FlauBERT: Unsupervised Language Model Pre-training for French](https://arxiv.org/abs/1912.05372) by Hang Le, Loïc Vial, Jibril Frej, Vincent Segonne, Maximin Coavoux, Benjamin Lecouteux, Alexandre Allauzen, Benoît Crabbé, Laurent Besacier, Didier Schwab. 1. [FLAVA](https://huggingface.co/docs/transformers/model_doc/flava) (from Facebook AI) released with the paper [FLAVA: A Foundational Language And Vision Alignment Model](https://arxiv.org/abs/2112.04482) by Amanpreet Singh, Ronghang Hu, Vedanuj Goswami, Guillaume Couairon, Wojciech Galuba, Marcus Rohrbach, and Douwe Kiela. 1. [FNet](https://huggingface.co/docs/transformers/model_doc/fnet) (from Google Research) released with the paper [FNet: Mixing Tokens with Fourier Transforms](https://arxiv.org/abs/2105.03824) by James Lee-Thorp, Joshua Ainslie, Ilya Eckstein, Santiago Ontanon. 1. [FocalNet](https://huggingface.co/docs/transformers/model_doc/focalnet) (from Microsoft Research) released with the paper [Focal Modulation Networks](https://arxiv.org/abs/2203.11926) by Jianwei Yang, Chunyuan Li, Xiyang Dai, Lu Yuan, Jianfeng Gao. 1. [Funnel Transformer](https://huggingface.co/docs/transformers/model_doc/funnel) (from CMU/Google Brain) released with the paper [Funnel-Transformer: Filtering out Sequential Redundancy for Efficient Language Processing](https://arxiv.org/abs/2006.03236) by Zihang Dai, Guokun Lai, Yiming Yang, Quoc V. Le. 1. [Fuyu](https://huggingface.co/docs/transformers/model_doc/fuyu) (from ADEPT) Rohan Bavishi, Erich Elsen, Curtis Hawthorne, Maxwell Nye, Augustus Odena, Arushi Somani, Sağnak Taşırlar. Released with the paper [blog post](https://www.adept.ai/blog/fuyu-8b) 1. [GIT](https://huggingface.co/docs/transformers/model_doc/git) (from Microsoft Research) released with the paper [GIT: A Generative Image-to-text Transformer for Vision and Language](https://arxiv.org/abs/2205.14100) by Jianfeng Wang, Zhengyuan Yang, Xiaowei Hu, Linjie Li, Kevin Lin, Zhe Gan, Zicheng Liu, Ce Liu, Lijuan Wang. 1. [GLPN](https://huggingface.co/docs/transformers/model_doc/glpn) (from KAIST) released with the paper [Global-Local Path Networks for Monocular Depth Estimation with Vertical CutDepth](https://arxiv.org/abs/2201.07436) by Doyeon Kim, Woonghyun Ga, Pyungwhan Ahn, Donggyu Joo, Sehwan Chun, Junmo Kim. 1. [GPT](https://huggingface.co/docs/transformers/model_doc/openai-gpt) (from OpenAI) released with the paper [Improving Language Understanding by Generative Pre-Training](https://blog.openai.com/language-unsupervised/) by Alec Radford, Karthik Narasimhan, Tim Salimans and Ilya Sutskever. 1. [GPT Neo](https://huggingface.co/docs/transformers/model_doc/gpt_neo) (from EleutherAI) released in the repository [EleutherAI/gpt-neo](https://github.com/EleutherAI/gpt-neo) by Sid Black, Stella Biderman, Leo Gao, Phil Wang and Connor Leahy. 1. [GPT NeoX](https://huggingface.co/docs/transformers/model_doc/gpt_neox) (from EleutherAI) released with the paper [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://arxiv.org/abs/2204.06745) by Sid Black, Stella Biderman, Eric Hallahan, Quentin Anthony, Leo Gao, Laurence Golding, Horace He, Connor Leahy, Kyle McDonell, Jason Phang, Michael Pieler, USVSN Sai Prashanth, Shivanshu Purohit, Laria Reynolds, Jonathan Tow, Ben Wang, Samuel Weinbach 1. [GPT NeoX Japanese](https://huggingface.co/docs/transformers/model_doc/gpt_neox_japanese) (from ABEJA) released by Shinya Otani, Takayoshi Makabe, Anuj Arora, and Kyo Hattori. 1. [GPT-2](https://huggingface.co/docs/transformers/model_doc/gpt2) (from OpenAI) released with the paper [Language Models are Unsupervised Multitask Learners](https://blog.openai.com/better-language-models/) by Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei and Ilya Sutskever. 1. [GPT-J](https://huggingface.co/docs/transformers/model_doc/gptj) (from EleutherAI) released in the repository [kingoflolz/mesh-transformer-jax](https://github.com/kingoflolz/mesh-transformer-jax/) by Ben Wang and Aran Komatsuzaki. 1. [GPT-Sw3](https://huggingface.co/docs/transformers/model_doc/gpt-sw3) (from AI-Sweden) released with the paper [Lessons Learned from GPT-SW3: Building the First Large-Scale Generative Language Model for Swedish](http://www.lrec-conf.org/proceedings/lrec2022/pdf/2022.lrec-1.376.pdf) by Ariel Ekgren, Amaru Cuba Gyllensten, Evangelia Gogoulou, Alice Heiman, Severine Verlinden, Joey Öhman, Fredrik Carlsson, Magnus Sahlgren. 1. [GPTBigCode](https://huggingface.co/docs/transformers/model_doc/gpt_bigcode) (from BigCode) released with the paper [SantaCoder: don't reach for the stars!](https://arxiv.org/abs/2301.03988) by Loubna Ben Allal, Raymond Li, Denis Kocetkov, Chenghao Mou, Christopher Akiki, Carlos Munoz Ferrandis, Niklas Muennighoff, Mayank Mishra, Alex Gu, Manan Dey, Logesh Kumar Umapathi, Carolyn Jane Anderson, Yangtian Zi, Joel Lamy Poirier, Hailey Schoelkopf, Sergey Troshin, Dmitry Abulkhanov, Manuel Romero, Michael Lappert, Francesco De Toni, Bernardo García del Río, Qian Liu, Shamik Bose, Urvashi Bhattacharyya, Terry Yue Zhuo, Ian Yu, Paulo Villegas, Marco Zocca, Sourab Mangrulkar, David Lansky, Huu Nguyen, Danish Contractor, Luis Villa, Jia Li, Dzmitry Bahdanau, Yacine Jernite, Sean Hughes, Daniel Fried, Arjun Guha, Harm de Vries, Leandro von Werra. 1. [GPTSAN-japanese](https://huggingface.co/docs/transformers/model_doc/gptsan-japanese) released in the repository [tanreinama/GPTSAN](https://github.com/tanreinama/GPTSAN/blob/main/report/model.md) by Toshiyuki Sakamoto(tanreinama). 1. [Graphormer](https://huggingface.co/docs/transformers/model_doc/graphormer) (from Microsoft) released with the paper [Do Transformers Really Perform Bad for Graph Representation?](https://arxiv.org/abs/2106.05234) by Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, Tie-Yan Liu. 1. [GroupViT](https://huggingface.co/docs/transformers/model_doc/groupvit) (from UCSD, NVIDIA) released with the paper [GroupViT: Semantic Segmentation Emerges from Text Supervision](https://arxiv.org/abs/2202.11094) by Jiarui Xu, Shalini De Mello, Sifei Liu, Wonmin Byeon, Thomas Breuel, Jan Kautz, Xiaolong Wang. 1. [HerBERT](https://huggingface.co/docs/transformers/model_doc/herbert) (from Allegro.pl, AGH University of Science and Technology) released with the paper [KLEJ: Comprehensive Benchmark for Polish Language Understanding](https://www.aclweb.org/anthology/2020.acl-main.111.pdf) by Piotr Rybak, Robert Mroczkowski, Janusz Tracz, Ireneusz Gawlik. 1. [Hubert](https://huggingface.co/docs/transformers/model_doc/hubert) (from Facebook) released with the paper [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://arxiv.org/abs/2106.07447) by Wei-Ning Hsu, Benjamin Bolte, Yao-Hung Hubert Tsai, Kushal Lakhotia, Ruslan Salakhutdinov, Abdelrahman Mohamed. 1. [I-BERT](https://huggingface.co/docs/transformers/model_doc/ibert) (from Berkeley) released with the paper [I-BERT: Integer-only BERT Quantization](https://arxiv.org/abs/2101.01321) by Sehoon Kim, Amir Gholami, Zhewei Yao, Michael W. Mahoney, Kurt Keutzer. 1. [IDEFICS](https://huggingface.co/docs/transformers/model_doc/idefics) (from HuggingFace) released with the paper [OBELICS: An Open Web-Scale Filtered Dataset of Interleaved Image-Text Documents](https://huggingface.co/papers/2306.16527) by Hugo Laurençon, Lucile Saulnier, Léo Tronchon, Stas Bekman, Amanpreet Singh, Anton Lozhkov, Thomas Wang, Siddharth Karamcheti, Alexander M. Rush, Douwe Kiela, Matthieu Cord, Victor Sanh. 1. [ImageGPT](https://huggingface.co/docs/transformers/model_doc/imagegpt) (from OpenAI) released with the paper [Generative Pretraining from Pixels](https://openai.com/blog/image-gpt/) by Mark Chen, Alec Radford, Rewon Child, Jeffrey Wu, Heewoo Jun, David Luan, Ilya Sutskever. 1. [Informer](https://huggingface.co/docs/transformers/model_doc/informer) (from Beihang University, UC Berkeley, Rutgers University, SEDD Company) released with the paper [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://arxiv.org/abs/2012.07436) by Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. 1. [InstructBLIP](https://huggingface.co/docs/transformers/model_doc/instructblip) (from Salesforce) released with the paper [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://arxiv.org/abs/2305.06500) by Wenliang Dai, Junnan Li, Dongxu Li, Anthony Meng Huat Tiong, Junqi Zhao, Weisheng Wang, Boyang Li, Pascale Fung, Steven Hoi. 1. [Jukebox](https://huggingface.co/docs/transformers/model_doc/jukebox) (from OpenAI) released with the paper [Jukebox: A Generative Model for Music](https://arxiv.org/pdf/2005.00341.pdf) by Prafulla Dhariwal, Heewoo Jun, Christine Payne, Jong Wook Kim, Alec Radford, Ilya Sutskever. 1. [LayoutLM](https://huggingface.co/docs/transformers/model_doc/layoutlm) (from Microsoft Research Asia) released with the paper [LayoutLM: Pre-training of Text and Layout for Document Image Understanding](https://arxiv.org/abs/1912.13318) by Yiheng Xu, Minghao Li, Lei Cui, Shaohan Huang, Furu Wei, Ming Zhou. 1. [LayoutLMv2](https://huggingface.co/docs/transformers/model_doc/layoutlmv2) (from Microsoft Research Asia) released with the paper [LayoutLMv2: Multi-modal Pre-training for Visually-Rich Document Understanding](https://arxiv.org/abs/2012.14740) by Yang Xu, Yiheng Xu, Tengchao Lv, Lei Cui, Furu Wei, Guoxin Wang, Yijuan Lu, Dinei Florencio, Cha Zhang, Wanxiang Che, Min Zhang, Lidong Zhou. 1. [LayoutLMv3](https://huggingface.co/docs/transformers/model_doc/layoutlmv3) (from Microsoft Research Asia) released with the paper [LayoutLMv3: Pre-training for Document AI with Unified Text and Image Masking](https://arxiv.org/abs/2204.08387) by Yupan Huang, Tengchao Lv, Lei Cui, Yutong Lu, Furu Wei. 1. [LayoutXLM](https://huggingface.co/docs/transformers/model_doc/layoutxlm) (from Microsoft Research Asia) released with the paper [LayoutXLM: Multimodal Pre-training for Multilingual Visually-rich Document Understanding](https://arxiv.org/abs/2104.08836) by Yiheng Xu, Tengchao Lv, Lei Cui, Guoxin Wang, Yijuan Lu, Dinei Florencio, Cha Zhang, Furu Wei. 1. [LED](https://huggingface.co/docs/transformers/model_doc/led) (from AllenAI) released with the paper [Longformer: The Long-Document Transformer](https://arxiv.org/abs/2004.05150) by Iz Beltagy, Matthew E. Peters, Arman Cohan. 1. [LeViT](https://huggingface.co/docs/transformers/model_doc/levit) (from Meta AI) released with the paper [LeViT: A Vision Transformer in ConvNet's Clothing for Faster Inference](https://arxiv.org/abs/2104.01136) by Ben Graham, Alaaeldin El-Nouby, Hugo Touvron, Pierre Stock, Armand Joulin, Hervé Jégou, Matthijs Douze. 1. [LiLT](https://huggingface.co/docs/transformers/model_doc/lilt) (from South China University of Technology) released with the paper [LiLT: A Simple yet Effective Language-Independent Layout Transformer for Structured Document Understanding](https://arxiv.org/abs/2202.13669) by Jiapeng Wang, Lianwen Jin, Kai Ding. 1. [LLaMA](https://huggingface.co/docs/transformers/model_doc/llama) (from The FAIR team of Meta AI) released with the paper [LLaMA: Open and Efficient Foundation Language Models](https://arxiv.org/abs/2302.13971) by Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, Aurelien Rodriguez, Armand Joulin, Edouard Grave, Guillaume Lample. 1. [Llama2](https://huggingface.co/docs/transformers/model_doc/llama2) (from The FAIR team of Meta AI) released with the paper [Llama2: Open Foundation and Fine-Tuned Chat Models](https://ai.meta.com/research/publications/llama-2-open-foundation-and-fine-tuned-chat-models/XXX) by Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, Dan Bikel, Lukas Blecher, Cristian Canton Ferrer, Moya Chen, Guillem Cucurull, David Esiobu, Jude Fernandes, Jeremy Fu, Wenyin Fu, Brian Fuller, Cynthia Gao, Vedanuj Goswami, Naman Goyal, Anthony Hartshorn, Saghar Hosseini, Rui Hou, Hakan Inan, Marcin Kardas, Viktor Kerkez Madian Khabsa, Isabel Kloumann, Artem Korenev, Punit Singh Koura, Marie-Anne Lachaux, Thibaut Lavril, Jenya Lee, Diana Liskovich, Yinghai Lu, Yuning Mao, Xavier Martinet, Todor Mihaylov, Pushka rMishra, Igor Molybog, Yixin Nie, Andrew Poulton, Jeremy Reizenstein, Rashi Rungta, Kalyan Saladi, Alan Schelten, Ruan Silva, Eric Michael Smith, Ranjan Subramanian, Xiaoqing EllenTan, Binh Tang, Ross Taylor, Adina Williams, Jian Xiang Kuan, Puxin Xu, Zheng Yan, Iliyan Zarov, Yuchen Zhang, Angela Fan, Melanie Kambadur, Sharan Narang, Aurelien Rodriguez, Robert Stojnic, Sergey Edunov, Thomas Scialom. 1. [Longformer](https://huggingface.co/docs/transformers/model_doc/longformer) (from AllenAI) released with the paper [Longformer: The Long-Document Transformer](https://arxiv.org/abs/2004.05150) by Iz Beltagy, Matthew E. Peters, Arman Cohan. 1. [LongT5](https://huggingface.co/docs/transformers/model_doc/longt5) (from Google AI) released with the paper [LongT5: Efficient Text-To-Text Transformer for Long Sequences](https://arxiv.org/abs/2112.07916) by Mandy Guo, Joshua Ainslie, David Uthus, Santiago Ontanon, Jianmo Ni, Yun-Hsuan Sung, Yinfei Yang. 1. [LUKE](https://huggingface.co/docs/transformers/model_doc/luke) (from Studio Ousia) released with the paper [LUKE: Deep Contextualized Entity Representations with Entity-aware Self-attention](https://arxiv.org/abs/2010.01057) by Ikuya Yamada, Akari Asai, Hiroyuki Shindo, Hideaki Takeda, Yuji Matsumoto. 1. [LXMERT](https://huggingface.co/docs/transformers/model_doc/lxmert) (from UNC Chapel Hill) released with the paper [LXMERT: Learning Cross-Modality Encoder Representations from Transformers for Open-Domain Question Answering](https://arxiv.org/abs/1908.07490) by Hao Tan and Mohit Bansal. 1. [M-CTC-T](https://huggingface.co/docs/transformers/model_doc/mctct) (from Facebook) released with the paper [Pseudo-Labeling For Massively Multilingual Speech Recognition](https://arxiv.org/abs/2111.00161) by Loren Lugosch, Tatiana Likhomanenko, Gabriel Synnaeve, and Ronan Collobert. 1. [M2M100](https://huggingface.co/docs/transformers/model_doc/m2m_100) (from Facebook) released with the paper [Beyond English-Centric Multilingual Machine Translation](https://arxiv.org/abs/2010.11125) by Angela Fan, Shruti Bhosale, Holger Schwenk, Zhiyi Ma, Ahmed El-Kishky, Siddharth Goyal, Mandeep Baines, Onur Celebi, Guillaume Wenzek, Vishrav Chaudhary, Naman Goyal, Tom Birch, Vitaliy Liptchinsky, Sergey Edunov, Edouard Grave, Michael Auli, Armand Joulin. 1. [MADLAD-400](https://huggingface.co/docs/transformers/model_doc/madlad-400) (from Google) released with the paper [MADLAD-400: A Multilingual And Document-Level Large Audited Dataset](https://arxiv.org/abs/2309.04662) by Sneha Kudugunta, Isaac Caswell, Biao Zhang, Xavier Garcia, Christopher A. Choquette-Choo, Katherine Lee, Derrick Xin, Aditya Kusupati, Romi Stella, Ankur Bapna, Orhan Firat. 1. [MarianMT](https://huggingface.co/docs/transformers/model_doc/marian) Machine translation models trained using [OPUS](http://opus.nlpl.eu/) data by Jörg Tiedemann. The [Marian Framework](https://marian-nmt.github.io/) is being developed by the Microsoft Translator Team. 1. [MarkupLM](https://huggingface.co/docs/transformers/model_doc/markuplm) (from Microsoft Research Asia) released with the paper [MarkupLM: Pre-training of Text and Markup Language for Visually-rich Document Understanding](https://arxiv.org/abs/2110.08518) by Junlong Li, Yiheng Xu, Lei Cui, Furu Wei. 1. [Mask2Former](https://huggingface.co/docs/transformers/model_doc/mask2former) (from FAIR and UIUC) released with the paper [Masked-attention Mask Transformer for Universal Image Segmentation](https://arxiv.org/abs/2112.01527) by Bowen Cheng, Ishan Misra, Alexander G. Schwing, Alexander Kirillov, Rohit Girdhar. 1. [MaskFormer](https://huggingface.co/docs/transformers/model_doc/maskformer) (from Meta and UIUC) released with the paper [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://arxiv.org/abs/2107.06278) by Bowen Cheng, Alexander G. Schwing, Alexander Kirillov. 1. [MatCha](https://huggingface.co/docs/transformers/model_doc/matcha) (from Google AI) released with the paper [MatCha: Enhancing Visual Language Pretraining with Math Reasoning and Chart Derendering](https://arxiv.org/abs/2212.09662) by Fangyu Liu, Francesco Piccinno, Syrine Krichene, Chenxi Pang, Kenton Lee, Mandar Joshi, Yasemin Altun, Nigel Collier, Julian Martin Eisenschlos. 1. [mBART](https://huggingface.co/docs/transformers/model_doc/mbart) (from Facebook) released with the paper [Multilingual Denoising Pre-training for Neural Machine Translation](https://arxiv.org/abs/2001.08210) by Yinhan Liu, Jiatao Gu, Naman Goyal, Xian Li, Sergey Edunov, Marjan Ghazvininejad, Mike Lewis, Luke Zettlemoyer. 1. [mBART-50](https://huggingface.co/docs/transformers/model_doc/mbart) (from Facebook) released with the paper [Multilingual Translation with Extensible Multilingual Pretraining and Finetuning](https://arxiv.org/abs/2008.00401) by Yuqing Tang, Chau Tran, Xian Li, Peng-Jen Chen, Naman Goyal, Vishrav Chaudhary, Jiatao Gu, Angela Fan. 1. [MEGA](https://huggingface.co/docs/transformers/model_doc/mega) (from Meta/USC/CMU/SJTU) released with the paper [Mega: Moving Average Equipped Gated Attention](https://arxiv.org/abs/2209.10655) by Xuezhe Ma, Chunting Zhou, Xiang Kong, Junxian He, Liangke Gui, Graham Neubig, Jonathan May, and Luke Zettlemoyer. 1. [Megatron-BERT](https://huggingface.co/docs/transformers/model_doc/megatron-bert) (from NVIDIA) released with the paper [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://arxiv.org/abs/1909.08053) by Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper and Bryan Catanzaro. 1. [Megatron-GPT2](https://huggingface.co/docs/transformers/model_doc/megatron_gpt2) (from NVIDIA) released with the paper [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://arxiv.org/abs/1909.08053) by Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper and Bryan Catanzaro. 1. [MGP-STR](https://huggingface.co/docs/transformers/model_doc/mgp-str) (from Alibaba Research) released with the paper [Multi-Granularity Prediction for Scene Text Recognition](https://arxiv.org/abs/2209.03592) by Peng Wang, Cheng Da, and Cong Yao. 1. [mLUKE](https://huggingface.co/docs/transformers/model_doc/mluke) (from Studio Ousia) released with the paper [mLUKE: The Power of Entity Representations in Multilingual Pretrained Language Models](https://arxiv.org/abs/2110.08151) by Ryokan Ri, Ikuya Yamada, and Yoshimasa Tsuruoka. 1. [MMS](https://huggingface.co/docs/transformers/model_doc/mms) (from Facebook) released with the paper [Scaling Speech Technology to 1,000+ Languages](https://arxiv.org/abs/2305.13516) by Vineel Pratap, Andros Tjandra, Bowen Shi, Paden Tomasello, Arun Babu, Sayani Kundu, Ali Elkahky, Zhaoheng Ni, Apoorv Vyas, Maryam Fazel-Zarandi, Alexei Baevski, Yossi Adi, Xiaohui Zhang, Wei-Ning Hsu, Alexis Conneau, Michael Auli. 1. [MobileBERT](https://huggingface.co/docs/transformers/model_doc/mobilebert) (from CMU/Google Brain) released with the paper [MobileBERT: a Compact Task-Agnostic BERT for Resource-Limited Devices](https://arxiv.org/abs/2004.02984) by Zhiqing Sun, Hongkun Yu, Xiaodan Song, Renjie Liu, Yiming Yang, and Denny Zhou. 1. [MobileNetV1](https://huggingface.co/docs/transformers/model_doc/mobilenet_v1) (from Google Inc.) released with the paper [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://arxiv.org/abs/1704.04861) by Andrew G. Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, Hartwig Adam. 1. [MobileNetV2](https://huggingface.co/docs/transformers/model_doc/mobilenet_v2) (from Google Inc.) released with the paper [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://arxiv.org/abs/1801.04381) by Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, Liang-Chieh Chen. 1. [MobileViT](https://huggingface.co/docs/transformers/model_doc/mobilevit) (from Apple) released with the paper [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://arxiv.org/abs/2110.02178) by Sachin Mehta and Mohammad Rastegari. 1. [MobileViTV2](https://huggingface.co/docs/transformers/model_doc/mobilevitv2) (from Apple) released with the paper [Separable Self-attention for Mobile Vision Transformers](https://arxiv.org/abs/2206.02680) by Sachin Mehta and Mohammad Rastegari. 1. [MPNet](https://huggingface.co/docs/transformers/model_doc/mpnet) (from Microsoft Research) released with the paper [MPNet: Masked and Permuted Pre-training for Language Understanding](https://arxiv.org/abs/2004.09297) by Kaitao Song, Xu Tan, Tao Qin, Jianfeng Lu, Tie-Yan Liu. 1. [MPT](https://huggingface.co/docs/transformers/model_doc/mpt) (from MosaiML) released with the repository [llm-foundry](https://github.com/mosaicml/llm-foundry/) by the MosaicML NLP Team. 1. [MRA](https://huggingface.co/docs/transformers/model_doc/mra) (from the University of Wisconsin - Madison) released with the paper [Multi Resolution Analysis (MRA) for Approximate Self-Attention](https://arxiv.org/abs/2207.10284) by Zhanpeng Zeng, Sourav Pal, Jeffery Kline, Glenn M Fung, Vikas Singh. 1. [MT5](https://huggingface.co/docs/transformers/model_doc/mt5) (from Google AI) released with the paper [mT5: A massively multilingual pre-trained text-to-text transformer](https://arxiv.org/abs/2010.11934) by Linting Xue, Noah Constant, Adam Roberts, Mihir Kale, Rami Al-Rfou, Aditya Siddhant, Aditya Barua, Colin Raffel. 1. [MusicGen](https://huggingface.co/docs/transformers/model_doc/musicgen) (from Meta) released with the paper [Simple and Controllable Music Generation](https://arxiv.org/abs/2306.05284) by Jade Copet, Felix Kreuk, Itai Gat, Tal Remez, David Kant, Gabriel Synnaeve, Yossi Adi and Alexandre Défossez. 1. [MVP](https://huggingface.co/docs/transformers/model_doc/mvp) (from RUC AI Box) released with the paper [MVP: Multi-task Supervised Pre-training for Natural Language Generation](https://arxiv.org/abs/2206.12131) by Tianyi Tang, Junyi Li, Wayne Xin Zhao and Ji-Rong Wen. 1. [NAT](https://huggingface.co/docs/transformers/model_doc/nat) (from SHI Labs) released with the paper [Neighborhood Attention Transformer](https://arxiv.org/abs/2204.07143) by Ali Hassani, Steven Walton, Jiachen Li, Shen Li, and Humphrey Shi. 1. [Nezha](https://huggingface.co/docs/transformers/model_doc/nezha) (from Huawei Noah’s Ark Lab) released with the paper [NEZHA: Neural Contextualized Representation for Chinese Language Understanding](https://arxiv.org/abs/1909.00204) by Junqiu Wei, Xiaozhe Ren, Xiaoguang Li, Wenyong Huang, Yi Liao, Yasheng Wang, Jiashu Lin, Xin Jiang, Xiao Chen and Qun Liu. 1. [NLLB](https://huggingface.co/docs/transformers/model_doc/nllb) (from Meta) released with the paper [No Language Left Behind: Scaling Human-Centered Machine Translation](https://arxiv.org/abs/2207.04672) by the NLLB team. 1. [NLLB-MOE](https://huggingface.co/docs/transformers/model_doc/nllb-moe) (from Meta) released with the paper [No Language Left Behind: Scaling Human-Centered Machine Translation](https://arxiv.org/abs/2207.04672) by the NLLB team. 1. [Nyströmformer](https://huggingface.co/docs/transformers/model_doc/nystromformer) (from the University of Wisconsin - Madison) released with the paper [Nyströmformer: A Nyström-Based Algorithm for Approximating Self-Attention](https://arxiv.org/abs/2102.03902) by Yunyang Xiong, Zhanpeng Zeng, Rudrasis Chakraborty, Mingxing Tan, Glenn Fung, Yin Li, Vikas Singh. 1. [OneFormer](https://huggingface.co/docs/transformers/model_doc/oneformer) (from SHI Labs) released with the paper [OneFormer: One Transformer to Rule Universal Image Segmentation](https://arxiv.org/abs/2211.06220) by Jitesh Jain, Jiachen Li, MangTik Chiu, Ali Hassani, Nikita Orlov, Humphrey Shi. 1. [OpenLlama](https://huggingface.co/docs/transformers/model_doc/open-llama) (from [s-JoL](https://huggingface.co/s-JoL)) released on GitHub (now removed). 1. [OPT](https://huggingface.co/docs/transformers/master/model_doc/opt) (from Meta AI) released with the paper [OPT: Open Pre-trained Transformer Language Models](https://arxiv.org/abs/2205.01068) by Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen et al. 1. [OWL-ViT](https://huggingface.co/docs/transformers/model_doc/owlvit) (from Google AI) released with the paper [Simple Open-Vocabulary Object Detection with Vision Transformers](https://arxiv.org/abs/2205.06230) by Matthias Minderer, Alexey Gritsenko, Austin Stone, Maxim Neumann, Dirk Weissenborn, Alexey Dosovitskiy, Aravindh Mahendran, Anurag Arnab, Mostafa Dehghani, Zhuoran Shen, Xiao Wang, Xiaohua Zhai, Thomas Kipf, and Neil Houlsby. 1. [Pegasus](https://huggingface.co/docs/transformers/model_doc/pegasus) (from Google) released with the paper [PEGASUS: Pre-training with Extracted Gap-sentences for Abstractive Summarization](https://arxiv.org/abs/1912.08777) by Jingqing Zhang, Yao Zhao, Mohammad Saleh and Peter J. Liu. 1. [PEGASUS-X](https://huggingface.co/docs/transformers/model_doc/pegasus_x) (from Google) released with the paper [Investigating Efficiently Extending Transformers for Long Input Summarization](https://arxiv.org/abs/2208.04347) by Jason Phang, Yao Zhao, and Peter J. Liu. 1. [Perceiver IO](https://huggingface.co/docs/transformers/model_doc/perceiver) (from Deepmind) released with the paper [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://arxiv.org/abs/2107.14795) by Andrew Jaegle, Sebastian Borgeaud, Jean-Baptiste Alayrac, Carl Doersch, Catalin Ionescu, David Ding, Skanda Koppula, Daniel Zoran, Andrew Brock, Evan Shelhamer, Olivier Hénaff, Matthew M. Botvinick, Andrew Zisserman, Oriol Vinyals, João Carreira. 1. [Persimmon](https://huggingface.co/docs/transformers/main/model_doc/persimmon) (from ADEPT) released in a [blog post](https://www.adept.ai/blog/persimmon-8b) by Erich Elsen, Augustus Odena, Maxwell Nye, Sağnak Taşırlar, Tri Dao, Curtis Hawthorne, Deepak Moparthi, Arushi Somani. 1. [Phi](https://huggingface.co/docs/main/transformers/model_doc/phi) (from Microsoft Research) released with the papers - [Textbooks Are All You Need](https://arxiv.org/abs/2306.11644) by Suriya Gunasekar, Yi Zhang, Jyoti Aneja, Caio César Teodoro Mendes, Allie Del Giorno, Sivakanth Gopi, Mojan Javaheripi, Piero Kauffmann, Gustavo de Rosa, Olli Saarikivi, Adil Salim, Shital Shah, Harkirat Singh Behl, Xin Wang, Sébastien Bubeck, Ronen Eldan, Adam Tauman Kalai, Yin Tat Lee and Yuanzhi Li, [Textbooks Are All You Need II: phi-1.5 technical report](https://arxiv.org/abs/2309.05463) by Yuanzhi Li, Sébastien Bubeck, Ronen Eldan, Allie Del Giorno, Suriya Gunasekar and Yin Tat Lee. 1. [PhoBERT](https://huggingface.co/docs/transformers/model_doc/phobert) (from VinAI Research) released with the paper [PhoBERT: Pre-trained language models for Vietnamese](https://www.aclweb.org/anthology/2020.findings-emnlp.92/) by Dat Quoc Nguyen and Anh Tuan Nguyen. 1. [Pix2Struct](https://huggingface.co/docs/transformers/model_doc/pix2struct) (from Google) released with the paper [Pix2Struct: Screenshot Parsing as Pretraining for Visual Language Understanding](https://arxiv.org/abs/2210.03347) by Kenton Lee, Mandar Joshi, Iulia Turc, Hexiang Hu, Fangyu Liu, Julian Eisenschlos, Urvashi Khandelwal, Peter Shaw, Ming-Wei Chang, Kristina Toutanova. 1. [PLBart](https://huggingface.co/docs/transformers/model_doc/plbart) (from UCLA NLP) released with the paper [Unified Pre-training for Program Understanding and Generation](https://arxiv.org/abs/2103.06333) by Wasi Uddin Ahmad, Saikat Chakraborty, Baishakhi Ray, Kai-Wei Chang. 1. [PoolFormer](https://huggingface.co/docs/transformers/model_doc/poolformer) (from Sea AI Labs) released with the paper [MetaFormer is Actually What You Need for Vision](https://arxiv.org/abs/2111.11418) by Yu, Weihao and Luo, Mi and Zhou, Pan and Si, Chenyang and Zhou, Yichen and Wang, Xinchao and Feng, Jiashi and Yan, Shuicheng. 1. [Pop2Piano](https://huggingface.co/docs/transformers/model_doc/pop2piano) released with the paper [Pop2Piano : Pop Audio-based Piano Cover Generation](https://arxiv.org/abs/2211.00895) by Jongho Choi and Kyogu Lee. 1. [ProphetNet](https://huggingface.co/docs/transformers/model_doc/prophetnet) (from Microsoft Research) released with the paper [ProphetNet: Predicting Future N-gram for Sequence-to-Sequence Pre-training](https://arxiv.org/abs/2001.04063) by Yu Yan, Weizhen Qi, Yeyun Gong, Dayiheng Liu, Nan Duan, Jiusheng Chen, Ruofei Zhang and Ming Zhou. 1. [PVT](https://huggingface.co/docs/transformers/model_doc/pvt) (from Nanjing University, The University of Hong Kong etc.) released with the paper [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://arxiv.org/pdf/2102.12122.pdf) by Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, Ling Shao. 1. [QDQBert](https://huggingface.co/docs/transformers/model_doc/qdqbert) (from NVIDIA) released with the paper [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://arxiv.org/abs/2004.09602) by Hao Wu, Patrick Judd, Xiaojie Zhang, Mikhail Isaev and Paulius Micikevicius. 1. [RAG](https://huggingface.co/docs/transformers/model_doc/rag) (from Facebook) released with the paper [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://arxiv.org/abs/2005.11401) by Patrick Lewis, Ethan Perez, Aleksandara Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Küttler, Mike Lewis, Wen-tau Yih, Tim Rocktäschel, Sebastian Riedel, Douwe Kiela. 1. [REALM](https://huggingface.co/docs/transformers/model_doc/realm.html) (from Google Research) released with the paper [REALM: Retrieval-Augmented Language Model Pre-Training](https://arxiv.org/abs/2002.08909) by Kelvin Guu, Kenton Lee, Zora Tung, Panupong Pasupat and Ming-Wei Chang. 1. [Reformer](https://huggingface.co/docs/transformers/model_doc/reformer) (from Google Research) released with the paper [Reformer: The Efficient Transformer](https://arxiv.org/abs/2001.04451) by Nikita Kitaev, Łukasz Kaiser, Anselm Levskaya. 1. [RegNet](https://huggingface.co/docs/transformers/model_doc/regnet) (from META Platforms) released with the paper [Designing Network Design Space](https://arxiv.org/abs/2003.13678) by Ilija Radosavovic, Raj Prateek Kosaraju, Ross Girshick, Kaiming He, Piotr Dollár. 1. [RemBERT](https://huggingface.co/docs/transformers/model_doc/rembert) (from Google Research) released with the paper [Rethinking embedding coupling in pre-trained language models](https://arxiv.org/abs/2010.12821) by Hyung Won Chung, Thibault Févry, Henry Tsai, M. Johnson, Sebastian Ruder. 1. [ResNet](https://huggingface.co/docs/transformers/model_doc/resnet) (from Microsoft Research) released with the paper [Deep Residual Learning for Image Recognition](https://arxiv.org/abs/1512.03385) by Kaiming He, Xiangyu Zhang, Shaoqing Ren, Jian Sun. 1. [RoBERTa](https://huggingface.co/docs/transformers/model_doc/roberta) (from Facebook), released together with the paper [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://arxiv.org/abs/1907.11692) by Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, Veselin Stoyanov. 1. [RoBERTa-PreLayerNorm](https://huggingface.co/docs/transformers/model_doc/roberta-prelayernorm) (from Facebook) released with the paper [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://arxiv.org/abs/1904.01038) by Myle Ott, Sergey Edunov, Alexei Baevski, Angela Fan, Sam Gross, Nathan Ng, David Grangier, Michael Auli. 1. [RoCBert](https://huggingface.co/docs/transformers/model_doc/roc_bert) (from WeChatAI) released with the paper [RoCBert: Robust Chinese Bert with Multimodal Contrastive Pretraining](https://aclanthology.org/2022.acl-long.65.pdf) by HuiSu, WeiweiShi, XiaoyuShen, XiaoZhou, TuoJi, JiaruiFang, JieZhou. 1. [RoFormer](https://huggingface.co/docs/transformers/model_doc/roformer) (from ZhuiyiTechnology), released together with the paper [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://arxiv.org/abs/2104.09864) by Jianlin Su and Yu Lu and Shengfeng Pan and Bo Wen and Yunfeng Liu. 1. [RWKV](https://huggingface.co/docs/transformers/model_doc/rwkv) (from Bo Peng), released on [this repo](https://github.com/BlinkDL/RWKV-LM) by Bo Peng. 1. [SegFormer](https://huggingface.co/docs/transformers/model_doc/segformer) (from NVIDIA) released with the paper [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://arxiv.org/abs/2105.15203) by Enze Xie, Wenhai Wang, Zhiding Yu, Anima Anandkumar, Jose M. Alvarez, Ping Luo. 1. [Segment Anything](https://huggingface.co/docs/transformers/model_doc/sam) (from Meta AI) released with the paper [Segment Anything](https://arxiv.org/pdf/2304.02643v1.pdf) by Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alex Berg, Wan-Yen Lo, Piotr Dollar, Ross Girshick. 1. [SEW](https://huggingface.co/docs/transformers/model_doc/sew) (from ASAPP) released with the paper [Performance-Efficiency Trade-offs in Unsupervised Pre-training for Speech Recognition](https://arxiv.org/abs/2109.06870) by Felix Wu, Kwangyoun Kim, Jing Pan, Kyu Han, Kilian Q. Weinberger, Yoav Artzi. 1. [SEW-D](https://huggingface.co/docs/transformers/model_doc/sew_d) (from ASAPP) released with the paper [Performance-Efficiency Trade-offs in Unsupervised Pre-training for Speech Recognition](https://arxiv.org/abs/2109.06870) by Felix Wu, Kwangyoun Kim, Jing Pan, Kyu Han, Kilian Q. Weinberger, Yoav Artzi. 1. [SpeechT5](https://huggingface.co/docs/transformers/model_doc/speecht5) (from Microsoft Research) released with the paper [SpeechT5: Unified-Modal Encoder-Decoder Pre-Training for Spoken Language Processing](https://arxiv.org/abs/2110.07205) by Junyi Ao, Rui Wang, Long Zhou, Chengyi Wang, Shuo Ren, Yu Wu, Shujie Liu, Tom Ko, Qing Li, Yu Zhang, Zhihua Wei, Yao Qian, Jinyu Li, Furu Wei. 1. [SpeechToTextTransformer](https://huggingface.co/docs/transformers/model_doc/speech_to_text) (from Facebook), released together with the paper [fairseq S2T: Fast Speech-to-Text Modeling with fairseq](https://arxiv.org/abs/2010.05171) by Changhan Wang, Yun Tang, Xutai Ma, Anne Wu, Dmytro Okhonko, Juan Pino. 1. [SpeechToTextTransformer2](https://huggingface.co/docs/transformers/model_doc/speech_to_text_2) (from Facebook), released together with the paper [Large-Scale Self- and Semi-Supervised Learning for Speech Translation](https://arxiv.org/abs/2104.06678) by Changhan Wang, Anne Wu, Juan Pino, Alexei Baevski, Michael Auli, Alexis Conneau. 1. [Splinter](https://huggingface.co/docs/transformers/model_doc/splinter) (from Tel Aviv University), released together with the paper [Few-Shot Question Answering by Pretraining Span Selection](https://arxiv.org/abs/2101.00438) by Ori Ram, Yuval Kirstain, Jonathan Berant, Amir Globerson, Omer Levy. 1. [SqueezeBERT](https://huggingface.co/docs/transformers/model_doc/squeezebert) (from Berkeley) released with the paper [SqueezeBERT: What can computer vision teach NLP about efficient neural networks?](https://arxiv.org/abs/2006.11316) by Forrest N. Iandola, Albert E. Shaw, Ravi Krishna, and Kurt W. Keutzer. 1. [SwiftFormer](https://huggingface.co/docs/transformers/model_doc/swiftformer) (from MBZUAI) released with the paper [SwiftFormer: Efficient Additive Attention for Transformer-based Real-time Mobile Vision Applications](https://arxiv.org/abs/2303.15446) by Abdelrahman Shaker, Muhammad Maaz, Hanoona Rasheed, Salman Khan, Ming-Hsuan Yang, Fahad Shahbaz Khan. 1. [Swin Transformer](https://huggingface.co/docs/transformers/model_doc/swin) (from Microsoft) released with the paper [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://arxiv.org/abs/2103.14030) by Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, Baining Guo. 1. [Swin Transformer V2](https://huggingface.co/docs/transformers/model_doc/swinv2) (from Microsoft) released with the paper [Swin Transformer V2: Scaling Up Capacity and Resolution](https://arxiv.org/abs/2111.09883) by Ze Liu, Han Hu, Yutong Lin, Zhuliang Yao, Zhenda Xie, Yixuan Wei, Jia Ning, Yue Cao, Zheng Zhang, Li Dong, Furu Wei, Baining Guo. 1. [Swin2SR](https://huggingface.co/docs/transformers/model_doc/swin2sr) (from University of Würzburg) released with the paper [Swin2SR: SwinV2 Transformer for Compressed Image Super-Resolution and Restoration](https://arxiv.org/abs/2209.11345) by Marcos V. Conde, Ui-Jin Choi, Maxime Burchi, Radu Timofte. 1. [SwitchTransformers](https://huggingface.co/docs/transformers/model_doc/switch_transformers) (from Google) released with the paper [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://arxiv.org/abs/2101.03961) by William Fedus, Barret Zoph, Noam Shazeer. 1. [T5](https://huggingface.co/docs/transformers/model_doc/t5) (from Google AI) released with the paper [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://arxiv.org/abs/1910.10683) by Colin Raffel and Noam Shazeer and Adam Roberts and Katherine Lee and Sharan Narang and Michael Matena and Yanqi Zhou and Wei Li and Peter J. Liu. 1. [T5v1.1](https://huggingface.co/docs/transformers/model_doc/t5v1.1) (from Google AI) released in the repository [google-research/text-to-text-transfer-transformer](https://github.com/google-research/text-to-text-transfer-transformer/blob/main/released_checkpoints.md#t511) by Colin Raffel and Noam Shazeer and Adam Roberts and Katherine Lee and Sharan Narang and Michael Matena and Yanqi Zhou and Wei Li and Peter J. Liu. 1. [Table Transformer](https://huggingface.co/docs/transformers/model_doc/table-transformer) (from Microsoft Research) released with the paper [PubTables-1M: Towards Comprehensive Table Extraction From Unstructured Documents](https://arxiv.org/abs/2110.00061) by Brandon Smock, Rohith Pesala, Robin Abraham. 1. [TAPAS](https://huggingface.co/docs/transformers/model_doc/tapas) (from Google AI) released with the paper [TAPAS: Weakly Supervised Table Parsing via Pre-training](https://arxiv.org/abs/2004.02349) by Jonathan Herzig, Paweł Krzysztof Nowak, Thomas Müller, Francesco Piccinno and Julian Martin Eisenschlos. 1. [TAPEX](https://huggingface.co/docs/transformers/model_doc/tapex) (from Microsoft Research) released with the paper [TAPEX: Table Pre-training via Learning a Neural SQL Executor](https://arxiv.org/abs/2107.07653) by Qian Liu, Bei Chen, Jiaqi Guo, Morteza Ziyadi, Zeqi Lin, Weizhu Chen, Jian-Guang Lou. 1. [Time Series Transformer](https://huggingface.co/docs/transformers/model_doc/time_series_transformer) (from HuggingFace). 1. [TimeSformer](https://huggingface.co/docs/transformers/model_doc/timesformer) (from Facebook) released with the paper [Is Space-Time Attention All You Need for Video Understanding?](https://arxiv.org/abs/2102.05095) by Gedas Bertasius, Heng Wang, Lorenzo Torresani. 1. [Trajectory Transformer](https://huggingface.co/docs/transformers/model_doc/trajectory_transformers) (from the University of California at Berkeley) released with the paper [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://arxiv.org/abs/2106.02039) by Michael Janner, Qiyang Li, Sergey Levine 1. [Transformer-XL](https://huggingface.co/docs/transformers/model_doc/transfo-xl) (from Google/CMU) released with the paper [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://arxiv.org/abs/1901.02860) by Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V. Le, Ruslan Salakhutdinov. 1. [TrOCR](https://huggingface.co/docs/transformers/model_doc/trocr) (from Microsoft), released together with the paper [TrOCR: Transformer-based Optical Character Recognition with Pre-trained Models](https://arxiv.org/abs/2109.10282) by Minghao Li, Tengchao Lv, Lei Cui, Yijuan Lu, Dinei Florencio, Cha Zhang, Zhoujun Li, Furu Wei. 1. [TVLT](https://huggingface.co/docs/transformers/model_doc/tvlt) (from UNC Chapel Hill) released with the paper [TVLT: Textless Vision-Language Transformer](https://arxiv.org/abs/2209.14156) by Zineng Tang, Jaemin Cho, Yixin Nie, Mohit Bansal. 1. [UL2](https://huggingface.co/docs/transformers/model_doc/ul2) (from Google Research) released with the paper [Unifying Language Learning Paradigms](https://arxiv.org/abs/2205.05131v1) by Yi Tay, Mostafa Dehghani, Vinh Q. Tran, Xavier Garcia, Dara Bahri, Tal Schuster, Huaixiu Steven Zheng, Neil Houlsby, Donald Metzler 1. [UMT5](https://huggingface.co/docs/transformers/model_doc/umt5) (from Google Research) released with the paper [UniMax: Fairer and More Effective Language Sampling for Large-Scale Multilingual Pretraining](https://openreview.net/forum?id=kXwdL1cWOAi) by Hyung Won Chung, Xavier Garcia, Adam Roberts, Yi Tay, Orhan Firat, Sharan Narang, Noah Constant. 1. [UniSpeech](https://huggingface.co/docs/transformers/model_doc/unispeech) (from Microsoft Research) released with the paper [UniSpeech: Unified Speech Representation Learning with Labeled and Unlabeled Data](https://arxiv.org/abs/2101.07597) by Chengyi Wang, Yu Wu, Yao Qian, Kenichi Kumatani, Shujie Liu, Furu Wei, Michael Zeng, Xuedong Huang. 1. [UniSpeechSat](https://huggingface.co/docs/transformers/model_doc/unispeech-sat) (from Microsoft Research) released with the paper [UNISPEECH-SAT: UNIVERSAL SPEECH REPRESENTATION LEARNING WITH SPEAKER AWARE PRE-TRAINING](https://arxiv.org/abs/2110.05752) by Sanyuan Chen, Yu Wu, Chengyi Wang, Zhengyang Chen, Zhuo Chen, Shujie Liu, Jian Wu, Yao Qian, Furu Wei, Jinyu Li, Xiangzhan Yu. 1. [UPerNet](https://huggingface.co/docs/transformers/model_doc/upernet) (from Peking University) released with the paper [Unified Perceptual Parsing for Scene Understanding](https://arxiv.org/abs/1807.10221) by Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, Jian Sun. 1. [VAN](https://huggingface.co/docs/transformers/model_doc/van) (from Tsinghua University and Nankai University) released with the paper [Visual Attention Network](https://arxiv.org/abs/2202.09741) by Meng-Hao Guo, Cheng-Ze Lu, Zheng-Ning Liu, Ming-Ming Cheng, Shi-Min Hu. 1. [VideoMAE](https://huggingface.co/docs/transformers/model_doc/videomae) (from Multimedia Computing Group, Nanjing University) released with the paper [VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training](https://arxiv.org/abs/2203.12602) by Zhan Tong, Yibing Song, Jue Wang, Limin Wang. 1. [ViLT](https://huggingface.co/docs/transformers/model_doc/vilt) (from NAVER AI Lab/Kakao Enterprise/Kakao Brain) released with the paper [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://arxiv.org/abs/2102.03334) by Wonjae Kim, Bokyung Son, Ildoo Kim. 1. [Vision Transformer (ViT)](https://huggingface.co/docs/transformers/model_doc/vit) (from Google AI) released with the paper [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://arxiv.org/abs/2010.11929) by Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby. 1. [VisualBERT](https://huggingface.co/docs/transformers/model_doc/visual_bert) (from UCLA NLP) released with the paper [VisualBERT: A Simple and Performant Baseline for Vision and Language](https://arxiv.org/pdf/1908.03557) by Liunian Harold Li, Mark Yatskar, Da Yin, Cho-Jui Hsieh, Kai-Wei Chang. 1. [ViT Hybrid](https://huggingface.co/docs/transformers/model_doc/vit_hybrid) (from Google AI) released with the paper [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://arxiv.org/abs/2010.11929) by Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby. 1. [VitDet](https://huggingface.co/docs/transformers/model_doc/vitdet) (from Meta AI) released with the paper [Exploring Plain Vision Transformer Backbones for Object Detection](https://arxiv.org/abs/2203.16527) by Yanghao Li, Hanzi Mao, Ross Girshick, Kaiming He. 1. [ViTMAE](https://huggingface.co/docs/transformers/model_doc/vit_mae) (from Meta AI) released with the paper [Masked Autoencoders Are Scalable Vision Learners](https://arxiv.org/abs/2111.06377) by Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, Ross Girshick. 1. [ViTMatte](https://huggingface.co/docs/transformers/main/model_doc/vitmatte) (from HUST-VL) rreleased with the paper [ViTMatte: Boosting Image Matting with Pretrained Plain Vision Transformers](https://arxiv.org/abs/2305.15272) by Jingfeng Yao, Xinggang Wang, Shusheng Yang, Baoyuan Wang. 1. [ViTMSN](https://huggingface.co/docs/transformers/model_doc/vit_msn) (from Meta AI) released with the paper [Masked Siamese Networks for Label-Efficient Learning](https://arxiv.org/abs/2204.07141) by Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Michael Rabbat, Nicolas Ballas. 1. [VITS](https://huggingface.co/docs/transformers/model_doc/vits) (from Kakao Enterprise) released with the paper [Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech](https://arxiv.org/abs/2106.06103) by Jaehyeon Kim, Jungil Kong, Juhee Son. 1. [ViViT](https://huggingface.co/docs/transformers/model_doc/vivit) (from Google Research) released with the paper [ViViT: A Video Vision Transformer](https://arxiv.org/abs/2103.15691) by Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, Cordelia Schmid. 1. [Wav2Vec2](https://huggingface.co/docs/transformers/model_doc/wav2vec2) (from Facebook AI) released with the paper [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://arxiv.org/abs/2006.11477) by Alexei Baevski, Henry Zhou, Abdelrahman Mohamed, Michael Auli. 1. [Wav2Vec2-Conformer](https://huggingface.co/docs/transformers/model_doc/wav2vec2-conformer) (from Facebook AI) released with the paper [FAIRSEQ S2T: Fast Speech-to-Text Modeling with FAIRSEQ](https://arxiv.org/abs/2010.05171) by Changhan Wang, Yun Tang, Xutai Ma, Anne Wu, Sravya Popuri, Dmytro Okhonko, Juan Pino. 1. [Wav2Vec2Phoneme](https://huggingface.co/docs/transformers/model_doc/wav2vec2_phoneme) (from Facebook AI) released with the paper [Simple and Effective Zero-shot Cross-lingual Phoneme Recognition](https://arxiv.org/abs/2109.11680) by Qiantong Xu, Alexei Baevski, Michael Auli. 1. [WavLM](https://huggingface.co/docs/transformers/model_doc/wavlm) (from Microsoft Research) released with the paper [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://arxiv.org/abs/2110.13900) by Sanyuan Chen, Chengyi Wang, Zhengyang Chen, Yu Wu, Shujie Liu, Zhuo Chen, Jinyu Li, Naoyuki Kanda, Takuya Yoshioka, Xiong Xiao, Jian Wu, Long Zhou, Shuo Ren, Yanmin Qian, Yao Qian, Jian Wu, Michael Zeng, Furu Wei. 1. [Whisper](https://huggingface.co/docs/transformers/model_doc/whisper) (from OpenAI) released with the paper [Robust Speech Recognition via Large-Scale Weak Supervision](https://cdn.openai.com/papers/whisper.pdf) by Alec Radford, Jong Wook Kim, Tao Xu, Greg Brockman, Christine McLeavey, Ilya Sutskever. 1. [X-CLIP](https://huggingface.co/docs/transformers/model_doc/xclip) (from Microsoft Research) released with the paper [Expanding Language-Image Pretrained Models for General Video Recognition](https://arxiv.org/abs/2208.02816) by Bolin Ni, Houwen Peng, Minghao Chen, Songyang Zhang, Gaofeng Meng, Jianlong Fu, Shiming Xiang, Haibin Ling. 1. [X-MOD](https://huggingface.co/docs/transformers/model_doc/xmod) (from Meta AI) released with the paper [Lifting the Curse of Multilinguality by Pre-training Modular Transformers](http://dx.doi.org/10.18653/v1/2022.naacl-main.255) by Jonas Pfeiffer, Naman Goyal, Xi Lin, Xian Li, James Cross, Sebastian Riedel, Mikel Artetxe. 1. [XGLM](https://huggingface.co/docs/transformers/model_doc/xglm) (From Facebook AI) released with the paper [Few-shot Learning with Multilingual Language Models](https://arxiv.org/abs/2112.10668) by Xi Victoria Lin, Todor Mihaylov, Mikel Artetxe, Tianlu Wang, Shuohui Chen, Daniel Simig, Myle Ott, Naman Goyal, Shruti Bhosale, Jingfei Du, Ramakanth Pasunuru, Sam Shleifer, Punit Singh Koura, Vishrav Chaudhary, Brian O'Horo, Jeff Wang, Luke Zettlemoyer, Zornitsa Kozareva, Mona Diab, Veselin Stoyanov, Xian Li. 1. [XLM](https://huggingface.co/docs/transformers/model_doc/xlm) (from Facebook) released together with the paper [Cross-lingual Language Model Pretraining](https://arxiv.org/abs/1901.07291) by Guillaume Lample and Alexis Conneau. 1. [XLM-ProphetNet](https://huggingface.co/docs/transformers/model_doc/xlm-prophetnet) (from Microsoft Research) released with the paper [ProphetNet: Predicting Future N-gram for Sequence-to-Sequence Pre-training](https://arxiv.org/abs/2001.04063) by Yu Yan, Weizhen Qi, Yeyun Gong, Dayiheng Liu, Nan Duan, Jiusheng Chen, Ruofei Zhang and Ming Zhou. 1. [XLM-RoBERTa](https://huggingface.co/docs/transformers/model_doc/xlm-roberta) (from Facebook AI), released together with the paper [Unsupervised Cross-lingual Representation Learning at Scale](https://arxiv.org/abs/1911.02116) by Alexis Conneau, Kartikay Khandelwal, Naman Goyal, Vishrav Chaudhary, Guillaume Wenzek, Francisco Guzmán, Edouard Grave, Myle Ott, Luke Zettlemoyer and Veselin Stoyanov. 1. [XLM-RoBERTa-XL](https://huggingface.co/docs/transformers/model_doc/xlm-roberta-xl) (from Facebook AI), released together with the paper [Larger-Scale Transformers for Multilingual Masked Language Modeling](https://arxiv.org/abs/2105.00572) by Naman Goyal, Jingfei Du, Myle Ott, Giri Anantharaman, Alexis Conneau. 1. [XLM-V](https://huggingface.co/docs/transformers/model_doc/xlm-v) (from Meta AI) released with the paper [XLM-V: Overcoming the Vocabulary Bottleneck in Multilingual Masked Language Models](https://arxiv.org/abs/2301.10472) by Davis Liang, Hila Gonen, Yuning Mao, Rui Hou, Naman Goyal, Marjan Ghazvininejad, Luke Zettlemoyer, Madian Khabsa. 1. [XLNet](https://huggingface.co/docs/transformers/model_doc/xlnet) (from Google/CMU) released with the paper [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://arxiv.org/abs/1906.08237) by Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Ruslan Salakhutdinov, Quoc V. Le. 1. [XLS-R](https://huggingface.co/docs/transformers/model_doc/xls_r) (from Facebook AI) released with the paper [XLS-R: Self-supervised Cross-lingual Speech Representation Learning at Scale](https://arxiv.org/abs/2111.09296) by Arun Babu, Changhan Wang, Andros Tjandra, Kushal Lakhotia, Qiantong Xu, Naman Goyal, Kritika Singh, Patrick von Platen, Yatharth Saraf, Juan Pino, Alexei Baevski, Alexis Conneau, Michael Auli. 1. [XLSR-Wav2Vec2](https://huggingface.co/docs/transformers/model_doc/xlsr_wav2vec2) (from Facebook AI) released with the paper [Unsupervised Cross-Lingual Representation Learning For Speech Recognition](https://arxiv.org/abs/2006.13979) by Alexis Conneau, Alexei Baevski, Ronan Collobert, Abdelrahman Mohamed, Michael Auli. 1. [YOLOS](https://huggingface.co/docs/transformers/model_doc/yolos) (from Huazhong University of Science & Technology) released with the paper [You Only Look at One Sequence: Rethinking Transformer in Vision through Object Detection](https://arxiv.org/abs/2106.00666) by Yuxin Fang, Bencheng Liao, Xinggang Wang, Jiemin Fang, Jiyang Qi, Rui Wu, Jianwei Niu, Wenyu Liu. 1. [YOSO](https://huggingface.co/docs/transformers/model_doc/yoso) (from the University of Wisconsin - Madison) released with the paper [You Only Sample (Almost) Once: Linear Cost Self-Attention Via Bernoulli Sampling](https://arxiv.org/abs/2111.09714) by Zhanpeng Zeng, Yunyang Xiong, Sathya N. Ravi, Shailesh Acharya, Glenn Fung, Vikas Singh. 1. Want to contribute a new model? We have added a detailed guide and templates to guide you in the process of adding a new model. You can find them in the [`templates`](./templates) folder of the repository. Be sure to check the [contributing guidelines](./CONTRIBUTING.md) and contact the maintainers or open an issue to collect feedbacks before starting your PR. Чтобы проверить, есть ли у каждой модели реализация на Flax, PyTorch или TensorFlow, или связанный с ней токенизатор, поддерживаемый библиотекой 🤗 Tokenizers, обратитесь к [этой таблице](https://huggingface.co/docs/transformers/index#supported-frameworks). Эти реализации были протестированы на нескольких наборах данных (см. примеры скриптов) и должны соответствовать производительности оригинальных реализаций. Более подробную информацию о производительности можно найти в разделе "Примеры" [документации](https://github.com/huggingface/transformers/tree/main/examples). ## Изучи больше \| Секция \| Описание \| \|-\|-\| \| [Документация](https://huggingface.co/docs/transformers/) \| Полная документация по API и гайды \| \| [Краткие описания задач](https://huggingface.co/docs/transformers/task_summary) \| Задачи поддерживаются 🤗 Transformers \| \| [Пособие по предварительной обработке](https://huggingface.co/docs/transformers/preprocessing) \| Использование класса `Tokenizer` для подготовки данных для моделей \| \| [Обучение и доработка](https://huggingface.co/docs/transformers/training) \| Использование моделей, предоставляемых 🤗 Transformers, в цикле обучения PyTorch/TensorFlow и API `Trainer`. \| \| [Быстрый тур: Тонкая настройка/скрипты использования](https://github.com/huggingface/transformers/tree/main/examples) \| Примеры скриптов для тонкой настройки моделей на широком спектре задач \| \| [Совместное использование и загрузка моделей](https://huggingface.co/docs/transformers/model_sharing) \| Загружайте и делитесь с сообществом своими доработанными моделями \| ## Цитирование Теперь у нас есть [статья](https://www.aclweb.org/anthology/2020.emnlp-demos.6/), которую можно цитировать для библиотеки 🤗 Transformers: ```bibtex @inproceedings{wolf-etal-2020-transformers, title = "Transformers: State-of-the-Art Natural Language Processing", author = "Thomas Wolf and Lysandre Debut and Victor Sanh and Julien Chaumond and Clement Delangue and Anthony Moi and Pierric Cistac and Tim Rault and Rémi Louf and Morgan Funtowicz and Joe Davison and Sam Shleifer and Patrick von Platen and Clara Ma and Yacine Jernite and Julien Plu and Canwen Xu and Teven Le Scao and Sylvain Gugger and Mariama Drame and Quentin Lhoest and Alexander M. Rush", booktitle = "Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations", month = oct, year = "2020", address = "Online", publisher = "Association for Computational Linguistics", url = "https://www.aclweb.org/anthology/2020.emnlp-demos.6", pages = "38--45" } ```
huggingface/transformers/blob/main/docs/source/en/model_sharing.md	!--Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Share a model The last two tutorials showed how you can fine-tune a model with PyTorch, Keras, and 🤗 Accelerate for distributed setups. The next step is to share your model with the community! At Hugging Face, we believe in openly sharing knowledge and resources to democratize artificial intelligence for everyone. We encourage you to consider sharing your model with the community to help others save time and resources. In this tutorial, you will learn two methods for sharing a trained or fine-tuned model on the [Model Hub](https://huggingface.co/models): - Programmatically push your files to the Hub. - Drag-and-drop your files to the Hub with the web interface. <iframe width="560" height="315" src="https://www.youtube.com/embed/XvSGPZFEjDY" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> <Tip> To share a model with the community, you need an account on [huggingface.co](https://huggingface.co/join). You can also join an existing organization or create a new one. </Tip> ## Repository features Each repository on the Model Hub behaves like a typical GitHub repository. Our repositories offer versioning, commit history, and the ability to visualize differences. The Model Hub's built-in versioning is based on git and [git-lfs](https://git-lfs.github.com/). In other words, you can treat one model as one repository, enabling greater access control and scalability. Version control allows revisions, a method for pinning a specific version of a model with a commit hash, tag or branch. As a result, you can load a specific model version with the `revision` parameter: ```py >>> model = AutoModel.from_pretrained( ... "julien-c/EsperBERTo-small", revision="v2.0.1" # tag name, or branch name, or commit hash ... ) ``` Files are also easily edited in a repository, and you can view the commit history as well as the difference: ![vis_diff](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/vis_diff.png) ## Setup Before sharing a model to the Hub, you will need your Hugging Face credentials. If you have access to a terminal, run the following command in the virtual environment where 🤗 Transformers is installed. This will store your access token in your Hugging Face cache folder (`~/.cache/` by default): ```bash huggingface-cli login ``` If you are using a notebook like Jupyter or Colaboratory, make sure you have the [`huggingface_hub`](https://huggingface.co/docs/hub/adding-a-library) library installed. This library allows you to programmatically interact with the Hub. ```bash pip install huggingface_hub ``` Then use `notebook_login` to sign-in to the Hub, and follow the link [here](https://huggingface.co/settings/token) to generate a token to login with: ```py >>> from huggingface_hub import notebook_login >>> notebook_login() ``` ## Convert a model for all frameworks To ensure your model can be used by someone working with a different framework, we recommend you convert and upload your model with both PyTorch and TensorFlow checkpoints. While users are still able to load your model from a different framework if you skip this step, it will be slower because 🤗 Transformers will need to convert the checkpoint on-the-fly. Converting a checkpoint for another framework is easy. Make sure you have PyTorch and TensorFlow installed (see [here](installation) for installation instructions), and then find the specific model for your task in the other framework. <frameworkcontent> <pt> Specify `from_tf=True` to convert a checkpoint from TensorFlow to PyTorch: ```py >>> pt_model = DistilBertForSequenceClassification.from_pretrained("path/to/awesome-name-you-picked", from_tf=True) >>> pt_model.save_pretrained("path/to/awesome-name-you-picked") ``` </pt> <tf> Specify `from_pt=True` to convert a checkpoint from PyTorch to TensorFlow: ```py >>> tf_model = TFDistilBertForSequenceClassification.from_pretrained("path/to/awesome-name-you-picked", from_pt=True) ``` Then you can save your new TensorFlow model with its new checkpoint: ```py >>> tf_model.save_pretrained("path/to/awesome-name-you-picked") ``` </tf> <jax> If a model is available in Flax, you can also convert a checkpoint from PyTorch to Flax: ```py >>> flax_model = FlaxDistilBertForSequenceClassification.from_pretrained( ... "path/to/awesome-name-you-picked", from_pt=True ... ) ``` </jax> </frameworkcontent> ## Push a model during training <frameworkcontent> <pt> <Youtube id="Z1-XMy-GNLQ"/> Sharing a model to the Hub is as simple as adding an extra parameter or callback. Remember from the [fine-tuning tutorial](training), the [`TrainingArguments`] class is where you specify hyperparameters and additional training options. One of these training options includes the ability to push a model directly to the Hub. Set `push_to_hub=True` in your [`TrainingArguments`]: ```py >>> training_args = TrainingArguments(output_dir="my-awesome-model", push_to_hub=True) ``` Pass your training arguments as usual to [`Trainer`]: ```py >>> trainer = Trainer( ... model=model, ... args=training_args, ... train_dataset=small_train_dataset, ... eval_dataset=small_eval_dataset, ... compute_metrics=compute_metrics, ... ) ``` After you fine-tune your model, call [`~transformers.Trainer.push_to_hub`] on [`Trainer`] to push the trained model to the Hub. 🤗 Transformers will even automatically add training hyperparameters, training results and framework versions to your model card! ```py >>> trainer.push_to_hub() ``` </pt> <tf> Share a model to the Hub with [`PushToHubCallback`]. In the [`PushToHubCallback`] function, add: - An output directory for your model. - A tokenizer. - The `hub_model_id`, which is your Hub username and model name. ```py >>> from transformers import PushToHubCallback >>> push_to_hub_callback = PushToHubCallback( ... output_dir="./your_model_save_path", tokenizer=tokenizer, hub_model_id="your-username/my-awesome-model" ... ) ``` Add the callback to [`fit`](https://keras.io/api/models/model_training_apis/), and 🤗 Transformers will push the trained model to the Hub: ```py >>> model.fit(tf_train_dataset, validation_data=tf_validation_dataset, epochs=3, callbacks=push_to_hub_callback) ``` </tf> </frameworkcontent> ## Use the `push_to_hub` function You can also call `push_to_hub` directly on your model to upload it to the Hub. Specify your model name in `push_to_hub`: ```py >>> pt_model.push_to_hub("my-awesome-model") ``` This creates a repository under your username with the model name `my-awesome-model`. Users can now load your model with the `from_pretrained` function: ```py >>> from transformers import AutoModel >>> model = AutoModel.from_pretrained("your_username/my-awesome-model") ``` If you belong to an organization and want to push your model under the organization name instead, just add it to the `repo_id`: ```py >>> pt_model.push_to_hub("my-awesome-org/my-awesome-model") ``` The `push_to_hub` function can also be used to add other files to a model repository. For example, add a tokenizer to a model repository: ```py >>> tokenizer.push_to_hub("my-awesome-model") ``` Or perhaps you'd like to add the TensorFlow version of your fine-tuned PyTorch model: ```py >>> tf_model.push_to_hub("my-awesome-model") ``` Now when you navigate to your Hugging Face profile, you should see your newly created model repository. Clicking on the Files tab will display all the files you've uploaded to the repository. For more details on how to create and upload files to a repository, refer to the Hub documentation [here](https://huggingface.co/docs/hub/how-to-upstream). ## Upload with the web interface Users who prefer a no-code approach are able to upload a model through the Hub's web interface. Visit [huggingface.co/new](https://huggingface.co/new) to create a new repository: ![new_model_repo](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/new_model_repo.png) From here, add some information about your model: - Select the owner of the repository. This can be yourself or any of the organizations you belong to. - Pick a name for your model, which will also be the repository name. - Choose whether your model is public or private. - Specify the license usage for your model. Now click on the Files tab and click on the Add file button to upload a new file to your repository. Then drag-and-drop a file to upload and add a commit message. ![upload_file](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/upload_file.png) ## Add a model card To make sure users understand your model's capabilities, limitations, potential biases and ethical considerations, please add a model card to your repository. The model card is defined in the `README.md` file. You can add a model card by: * Manually creating and uploading a `README.md` file. * Clicking on the Edit model card button in your model repository. Take a look at the DistilBert [model card](https://huggingface.co/distilbert-base-uncased) for a good example of the type of information a model card should include. For more details about other options you can control in the `README.md` file such as a model's carbon footprint or widget examples, refer to the documentation [here](https://huggingface.co/docs/hub/models-cards).
huggingface/diffusers/blob/main/docs/source/en/training/lora.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # LoRA <Tip warning={true}> This is experimental and the API may change in the future. </Tip> [LoRA (Low-Rank Adaptation of Large Language Models)](https://hf.co/papers/2106.09685) is a popular and lightweight training technique that significantly reduces the number of trainable parameters. It works by inserting a smaller number of new weights into the model and only these are trained. This makes training with LoRA much faster, memory-efficient, and produces smaller model weights (a few hundred MBs), which are easier to store and share. LoRA can also be combined with other training techniques like DreamBooth to speedup training. <Tip> LoRA is very versatile and supported for [DreamBooth](https://github.com/huggingface/diffusers/blob/main/examples/dreambooth/train_dreambooth_lora.py), [Kandinsky 2.2](https://github.com/huggingface/diffusers/blob/main/examples/kandinsky2_2/text_to_image/train_text_to_image_lora_decoder.py), [Stable Diffusion XL](https://github.com/huggingface/diffusers/blob/main/examples/text_to_image/train_text_to_image_lora_sdxl.py), [text-to-image](https://github.com/huggingface/diffusers/blob/main/examples/text_to_image/train_text_to_image_lora.py), and [Wuerstchen](https://github.com/huggingface/diffusers/blob/main/examples/wuerstchen/text_to_image/train_text_to_image_lora_prior.py). </Tip> This guide will explore the [train_text_to_image_lora.py](https://github.com/huggingface/diffusers/blob/main/examples/text_to_image/train_text_to_image_lora.py) script to help you become more familiar with it, and how you can adapt it for your own use-case. Before running the script, make sure you install the library from source: ```bash git clone https://github.com/huggingface/diffusers cd diffusers pip install . ``` Navigate to the example folder with the training script and install the required dependencies for the script you're using: <hfoptions id="installation"> <hfoption id="PyTorch"> ```bash cd examples/text_to_image pip install -r requirements.txt ``` </hfoption> <hfoption id="Flax"> ```bash cd examples/text_to_image pip install -r requirements_flax.txt ``` </hfoption> </hfoptions> <Tip> 🤗 Accelerate is a library for helping you train on multiple GPUs/TPUs or with mixed-precision. It'll automatically configure your training setup based on your hardware and environment. Take a look at the 🤗 Accelerate [Quick tour](https://huggingface.co/docs/accelerate/quicktour) to learn more. </Tip> Initialize an 🤗 Accelerate environment: ```bash accelerate config ``` To setup a default 🤗 Accelerate environment without choosing any configurations: ```bash accelerate config default ``` Or if your environment doesn't support an interactive shell, like a notebook, you can use: ```bash from accelerate.utils import write_basic_config write_basic_config() ``` Lastly, if you want to train a model on your own dataset, take a look at the [Create a dataset for training](create_dataset) guide to learn how to create a dataset that works with the training script. <Tip> The following sections highlight parts of the training script that are important for understanding how to modify it, but it doesn't cover every aspect of the script in detail. If you're interested in learning more, feel free to read through the [script](https://github.com/huggingface/diffusers/blob/main/examples/text_to_image/text_to_image_lora.py) and let us know if you have any questions or concerns. </Tip> ## Script parameters The training script has many parameters to help you customize your training run. All of the parameters and their descriptions are found in the [`parse_args()`](https://github.com/huggingface/diffusers/blob/dd9a5caf61f04d11c0fa9f3947b69ab0010c9a0f/examples/text_to_image/train_text_to_image_lora.py#L85) function. Default values are provided for most parameters that work pretty well, but you can also set your own values in the training command if you'd like. For example, to increase the number of epochs to train: ```bash accelerate launch train_text_to_image_lora.py \ --num_train_epochs=150 \ ``` Many of the basic and important parameters are described in the [Text-to-image](text2image#script-parameters) training guide, so this guide just focuses on the LoRA relevant parameters: - `--rank`: the number of low-rank matrices to train - `--learning_rate`: the default learning rate is 1e-4, but with LoRA, you can use a higher learning rate ## Training script The dataset preprocessing code and training loop are found in the [`main()`](https://github.com/huggingface/diffusers/blob/dd9a5caf61f04d11c0fa9f3947b69ab0010c9a0f/examples/text_to_image/train_text_to_image_lora.py#L371) function, and if you need to adapt the training script, this is where you'll make your changes. As with the script parameters, a walkthrough of the training script is provided in the [Text-to-image](text2image#training-script) training guide. Instead, this guide takes a look at the LoRA relevant parts of the script. The script begins by adding the [new LoRA weights](https://github.com/huggingface/diffusers/blob/dd9a5caf61f04d11c0fa9f3947b69ab0010c9a0f/examples/text_to_image/train_text_to_image_lora.py#L447) to the attention layers. This involves correctly configuring the weight size for each block in the UNet. You'll see the `rank` parameter is used to create the [`~models.attention_processor.LoRAAttnProcessor`]: ```py lora_attn_procs = {} for name in unet.attn_processors.keys(): cross_attention_dim = None if name.endswith("attn1.processor") else unet.config.cross_attention_dim if name.startswith("mid_block"): hidden_size = unet.config.block_out_channels[-1] elif name.startswith("up_blocks"): block_id = int(name[len("up_blocks.")]) hidden_size = list(reversed(unet.config.block_out_channels))[block_id] elif name.startswith("down_blocks"): block_id = int(name[len("down_blocks.")]) hidden_size = unet.config.block_out_channels[block_id] lora_attn_procs[name] = LoRAAttnProcessor( hidden_size=hidden_size, cross_attention_dim=cross_attention_dim, rank=args.rank, ) unet.set_attn_processor(lora_attn_procs) lora_layers = AttnProcsLayers(unet.attn_processors) ``` The [optimizer](https://github.com/huggingface/diffusers/blob/dd9a5caf61f04d11c0fa9f3947b69ab0010c9a0f/examples/text_to_image/train_text_to_image_lora.py#L519) is initialized with the `lora_layers` because these are the only weights that'll be optimized: ```py optimizer = optimizer_cls( lora_layers.parameters(), lr=args.learning_rate, betas=(args.adam_beta1, args.adam_beta2), weight_decay=args.adam_weight_decay, eps=args.adam_epsilon, ) ``` Aside from setting up the LoRA layers, the training script is more or less the same as train_text_to_image.py! ## Launch the script Once you've made all your changes or you're okay with the default configuration, you're ready to launch the training script! 🚀 Let's train on the [Pokémon BLIP captions](https://huggingface.co/datasets/lambdalabs/pokemon-blip-captions) dataset to generate our yown Pokémon. Set the environment variables `MODEL_NAME` and `DATASET_NAME` to the model and dataset respectively. You should also specify where to save the model in `OUTPUT_DIR`, and the name of the model to save to on the Hub with `HUB_MODEL_ID`. The script creates and saves the following files to your repository: - saved model checkpoints - `pytorch_lora_weights.safetensors` (the trained LoRA weights) If you're training on more than one GPU, add the `--multi_gpu` parameter to the `accelerate launch` command. <Tip warning={true}> A full training run takes ~5 hours on a 2080 Ti GPU with 11GB of VRAM. </Tip> ```bash export MODEL_NAME="runwayml/stable-diffusion-v1-5" export OUTPUT_DIR="/sddata/finetune/lora/pokemon" export HUB_MODEL_ID="pokemon-lora" export DATASET_NAME="lambdalabs/pokemon-blip-captions" accelerate launch --mixed_precision="fp16" train_text_to_image_lora.py \ --pretrained_model_name_or_path=$MODEL_NAME \ --dataset_name=$DATASET_NAME \ --dataloader_num_workers=8 \ --resolution=512 \ --center_crop \ --random_flip \ --train_batch_size=1 \ --gradient_accumulation_steps=4 \ --max_train_steps=15000 \ --learning_rate=1e-04 \ --max_grad_norm=1 \ --lr_scheduler="cosine" \ --lr_warmup_steps=0 \ --output_dir=${OUTPUT_DIR} \ --push_to_hub \ --hub_model_id=${HUB_MODEL_ID} \ --report_to=wandb \ --checkpointing_steps=500 \ --validation_prompt="A pokemon with blue eyes." \ --seed=1337 ``` Once training has been completed, you can use your model for inference: ```py from diffusers import AutoPipelineForText2Image import torch pipeline = AutoPipelineForText2Image.from_pretrained("runwayml/stable-diffusion-v1-5", torch_dtype=torch.float16).to("cuda") pipeline.load_lora_weights("path/to/lora/model", weight_name="pytorch_lora_weights.safetensors") image = pipeline("A pokemon with blue eyes").images[0] ``` ## Next steps Congratulations on training a new model with LoRA! To learn more about how to use your new model, the following guides may be helpful: - Learn how to [load different LoRA formats](../using-diffusers/loading_adapters#LoRA) trained using community trainers like Kohya and TheLastBen. - Learn how to use and [combine multiple LoRA's](../tutorials/using_peft_for_inference) with PEFT for inference.
huggingface/evaluate/blob/main/metrics/mape/README.md	-- title: MAPE emoji: 🤗 colorFrom: blue colorTo: red sdk: gradio sdk_version: 3.19.1 app_file: app.py pinned: false tags: - evaluate - metric description: >- Mean Absolute Percentage Error (MAPE) is the mean percentage error difference between the predicted and actual values. --- # Metric Card for MAPE ## Metric Description Mean Absolute Error (MAPE) is the mean of the percentage error of difference between the predicted $x_i$ and actual $y_i$ numeric values: ![image](https://user-images.githubusercontent.com/8100/200005316-c3975d32-8978-40f3-b541-c2ef57ec7c5b.png) ## How to Use At minimum, this metric requires predictions and references as inputs. ```python >>> mape_metric = evaluate.load("mape") >>> predictions = [2.5, 0.0, 2, 8] >>> references = [3, -0.5, 2, 7] >>> results = mape_metric.compute(predictions=predictions, references=references) ``` ### Inputs Mandatory inputs: - `predictions`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the estimated target values. - `references`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the ground truth (correct) target values. Optional arguments: - `sample_weight`: numeric array-like of shape (`n_samples,`) representing sample weights. The default is `None`. - `multioutput`: `raw_values`, `uniform_average` or numeric array-like of shape (`n_outputs,`), which defines the aggregation of multiple output values. The default value is `uniform_average`. - `raw_values` returns a full set of errors in case of multioutput input. - `uniform_average` means that the errors of all outputs are averaged with uniform weight. - the array-like value defines weights used to average errors. ### Output Values This metric outputs a dictionary, containing the mean absolute error score, which is of type: - `float`: if multioutput is `uniform_average` or an ndarray of weights, then the weighted average of all output errors is returned. - numeric array-like of shape (`n_outputs,`): if multioutput is `raw_values`, then the score is returned for each output separately. Each MAPE `float` value is postive with the best value being 0.0. Output Example(s): ```python {'mape': 0.5} ``` If `multioutput="raw_values"`: ```python {'mape': array([0.5, 1. ])} ``` #### Values from Popular Papers ### Examples Example with the `uniform_average` config: ```python >>> mape_metric = evaluate.load("mape") >>> predictions = [2.5, 0.0, 2, 8] >>> references = [3, -0.5, 2, 7] >>> results = mape_metric.compute(predictions=predictions, references=references) >>> print(results) {'mape': 0.3273...} ``` Example with multi-dimensional lists, and the `raw_values` config: ```python >>> mape_metric = evaluate.load("mape", "multilist") >>> predictions = [[0.5, 1], [-1, 1], [7, -6]] >>> references = [[0.1, 2], [-1, 2], [8, -5]] >>> results = mape_metric.compute(predictions=predictions, references=references) >>> print(results) {'mape': 0.8874...} >>> results = mape_metric.compute(predictions=predictions, references=references, multioutput='raw_values') >>> print(results) {'mape': array([1.3749..., 0.4])} ``` ## Limitations and Bias One limitation of MAPE is that it cannot be used if the ground truth is zero or close to zero. This metric is also asymmetric in that it puts a heavier penalty on predictions less than the ground truth and a smaller penalty on predictions bigger than the ground truth and thus can lead to a bias of methods being select which under-predict if selected via this metric. ## Citation(s) ```bibtex @article{scikit-learn, title={Scikit-learn: Machine Learning in {P}ython}, author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.}, journal={Journal of Machine Learning Research}, volume={12}, pages={2825--2830}, year={2011} } ``` ```bibtex @article{DEMYTTENAERE201638, title = {Mean Absolute Percentage Error for regression models}, journal = {Neurocomputing}, volume = {192}, pages = {38--48}, year = {2016}, note = {Advances in artificial neural networks, machine learning and computational intelligence}, issn = {0925-2312}, doi = {https://doi.org/10.1016/j.neucom.2015.12.114}, url = {https://www.sciencedirect.com/science/article/pii/S0925231216003325}, author = {Arnaud {de Myttenaere} and Boris Golden and Bénédicte {Le Grand} and Fabrice Rossi}, } ``` ## Further References - [Mean absolute percentage error - Wikipedia](https://en.wikipedia.org/wiki/Mean_absolute_percentage_error)
huggingface/pytorch-image-models/blob/main/docs/models/ensemble-adversarial.md	# Ensemble Adversarial Inception ResNet v2 Inception-ResNet-v2 is a convolutional neural architecture that builds on the Inception family of architectures but incorporates [residual connections](https://paperswithcode.com/method/residual-connection) (replacing the filter concatenation stage of the Inception architecture). This particular model was trained for study of adversarial examples (adversarial training). The weights from this model were ported from [Tensorflow/Models](https://github.com/tensorflow/models). ## How do I use this model on an image? To load a pretrained model: ```python import timm model = timm.create_model('ens_adv_inception_resnet_v2', pretrained=True) model.eval() ``` To load and preprocess the image: ```python import urllib from PIL import Image from timm.data import resolve_data_config from timm.data.transforms_factory import create_transform config = resolve_data_config({}, model=model) transform = create_transform(**config) url, filename = ("https://github.com/pytorch/hub/raw/master/images/dog.jpg", "dog.jpg") urllib.request.urlretrieve(url, filename) img = Image.open(filename).convert('RGB') tensor = transform(img).unsqueeze(0) # transform and add batch dimension ``` To get the model predictions: ```python import torch with torch.no_grad(): out = model(tensor) probabilities = torch.nn.functional.softmax(out[0], dim=0) print(probabilities.shape) # prints: torch.Size([1000]) ``` To get the top-5 predictions class names: ```python # Get imagenet class mappings url, filename = ("https://raw.githubusercontent.com/pytorch/hub/master/imagenet_classes.txt", "imagenet_classes.txt") urllib.request.urlretrieve(url, filename) with open("imagenet_classes.txt", "r") as f: categories = [s.strip() for s in f.readlines()] # Print top categories per image top5_prob, top5_catid = torch.topk(probabilities, 5) for i in range(top5_prob.size(0)): print(categories[top5_catid[i]], top5_prob[i].item()) # prints class names and probabilities like: # [('Samoyed', 0.6425196528434753), ('Pomeranian', 0.04062102362513542), ('keeshond', 0.03186424449086189), ('white wolf', 0.01739676296710968), ('Eskimo dog', 0.011717947199940681)] ``` Replace the model name with the variant you want to use, e.g. `ens_adv_inception_resnet_v2`. You can find the IDs in the model summaries at the top of this page. To extract image features with this model, follow the [timm feature extraction examples](https://rwightman.github.io/pytorch-image-models/feature_extraction/), just change the name of the model you want to use. ## How do I finetune this model? You can finetune any of the pre-trained models just by changing the classifier (the last layer). ```python model = timm.create_model('ens_adv_inception_resnet_v2', pretrained=True, num_classes=NUM_FINETUNE_CLASSES) ``` To finetune on your own dataset, you have to write a training loop or adapt [timm's training script](https://github.com/rwightman/pytorch-image-models/blob/master/train.py) to use your dataset. ## How do I train this model? You can follow the [timm recipe scripts](https://rwightman.github.io/pytorch-image-models/scripts/) for training a new model afresh. ## Citation ```BibTeX @article{DBLP:journals/corr/abs-1804-00097, author = {Alexey Kurakin and Ian J. Goodfellow and Samy Bengio and Yinpeng Dong and Fangzhou Liao and Ming Liang and Tianyu Pang and Jun Zhu and Xiaolin Hu and Cihang Xie and Jianyu Wang and Zhishuai Zhang and Zhou Ren and Alan L. Yuille and Sangxia Huang and Yao Zhao and Yuzhe Zhao and Zhonglin Han and Junjiajia Long and Yerkebulan Berdibekov and Takuya Akiba and Seiya Tokui and Motoki Abe}, title = {Adversarial Attacks and Defences Competition}, journal = {CoRR}, volume = {abs/1804.00097}, year = {2018}, url = {http://arxiv.org/abs/1804.00097}, archivePrefix = {arXiv}, eprint = {1804.00097}, timestamp = {Thu, 31 Oct 2019 16:31:22 +0100}, biburl = {https://dblp.org/rec/journals/corr/abs-1804-00097.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } ``` <!-- Type: model-index Collections: - Name: Ensemble Adversarial Paper: Title: Adversarial Attacks and Defences Competition URL: https://paperswithcode.com/paper/adversarial-attacks-and-defences-competition Models: - Name: ens_adv_inception_resnet_v2 In Collection: Ensemble Adversarial Metadata: FLOPs: 16959133120 Parameters: 55850000 File Size: 223774238 Architecture: - 1x1 Convolution - Auxiliary Classifier - Average Pooling - Average Pooling - Batch Normalization - Convolution - Dense Connections - Dropout - Inception-v3 Module - Max Pooling - ReLU - Softmax Tasks: - Image Classification Training Data: - ImageNet ID: ens_adv_inception_resnet_v2 Crop Pct: '0.897' Image Size: '299' Interpolation: bicubic Code: https://github.com/rwightman/pytorch-image-models/blob/d8e69206be253892b2956341fea09fdebfaae4e3/timm/models/inception_resnet_v2.py#L351 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-weights/ens_adv_inception_resnet_v2-2592a550.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 1.0% Top 5 Accuracy: 17.32% -->
huggingface/hub-docs/blob/main/docs/hub/flair.md	Using Flair at Hugging Face [Flair](https://github.com/flairNLP/flair) is a very simple framework for state-of-the-art NLP. Developed by [Humboldt University of Berlin](https://www.informatik.hu-berlin.de/en/forschung-en/gebiete/ml-en/) and friends. ## Exploring Flair in the Hub You can find `flair` models by filtering at the left of the [models page](https://huggingface.co/models?library=flair). All models on the Hub come with these useful features: 1. An automatically generated model card with a brief description. 2. An interactive widget you can use to play with the model directly in the browser. 3. An Inference API that allows you to make inference requests. ## Installation To get started, you can follow the [Flair installation guide](https://github.com/flairNLP/flair?tab=readme-ov-file#requirements-and-installation). You can also use the following one-line install through pip: ``` $ pip install -U flair ``` ## Using existing models All `flair` models can easily be loaded from the Hub: ```py from flair.data import Sentence from flair.models import SequenceTagger # load tagger tagger = SequenceTagger.load("flair/ner-multi") ``` Once loaded, you can use `predict()` to perform inference: ```py sentence = Sentence("George Washington ging nach Washington.") tagger.predict(sentence) # print sentence print(sentence) ``` It outputs the following: ```text Sentence[6]: "George Washington ging nach Washington." → ["George Washington"/PER, "Washington"/LOC] ``` If you want to load a specific Flair model, you can click `Use in Flair` in the model card and you will be given a working snippet! <div class="flex justify-center"> <img class="block dark:hidden" src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/hub/libraries-flair_snippet1.png"/> <img class="hidden dark:block" src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/hub/libraries-flair_snippet1-dark.png"/> </div> <div class="flex justify-center"> <img class="block dark:hidden" src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/hub/libraries-flair_snippet2.png"/> <img class="hidden dark:block" src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/hub/libraries-flair_snippet2-dark.png"/> </div> ## Additional resources * Flair [repository](https://github.com/flairNLP/flair) * Flair [docs](https://flairnlp.github.io/docs/intro) * Official Flair [models](https://huggingface.co/flair) on the Hub (mainly trained by [@alanakbik](https://huggingface.co/alanakbik) and [@stefan-it](https://huggingface.co/stefan-it))
gradio-app/gradio/blob/main/js/accordion/README.md	`@gradio/button` ```html <script> import { Button } from "@gradio/button"; </script> <button type="primary\|secondary" href="string" on:click="{e.detail === href}"> content </button> ```
huggingface/course/blob/main/subtitles/en/raw/chapter3/02a_datasets-overview-pt.md	he Hugging Face Datasets library: A Quick overview. The Hugging Face Datasets library is a library that provides an API to quickly download many public datasets and preprocess them. In this video we will explore how to do that. The downloading part is easy: with the load_dataset function, you can directly download and cache a dataset from its identifier on the Dataset hub. Here we fetch the MRPC dataset from the GLUE benchmark, which is a dataset containing pairs of sentences where the task is to determine the paraphrases. The object returned by the load_dataset function is a DatasetDict, which is a sort of dictionary containing each split of our dataset. We can access each split by indexing with its name. This split is then an instance of the Dataset class, with columns (here sentence1, sentence2. label and idx) and rows. We can access a given element by its index. The amazing thing about the Hugging Face Datasets library is that everything is saved to disk using Apache Arrow, which means that even if your dataset is huge you won't get out of RAM: only the elements you request are loaded in memory. Accessing a slice of your dataset is as easy as one element. The result is then a dictionary with list of values for each keys (here the list of labels, the list of first sentences and the list of second sentences). The features attribute of a Dataset gives us more information about its columns. In particular, we can see here it gives us the correspondence between the integers and names for the labels. 0 stands for not equivalent and 1 for equivalent. To preprocess all the elements of our dataset, we need to tokenize them. Have a look at the video "Preprocess sentence pairs" for a refresher, but you just have to send the two sentences to the tokenizer with some additional keyword arguments. Here we indicate a maximum length of 128 and pad inputs shorter than this length, truncate inputs that are longer. We put all of this in a tokenize_function that we can directly apply to all the splits in our dataset with the map method. As long as the function returns a dictionary-like object, the map method will add new columns as needed or update existing ones. To speed up preprocessing and take advantage of the fact our tokenizer is backed by Rust thanks to the Hugging Face Tokenizers library, we can process several elements at the same time to our tokenize function, using the batched=True argument. Since the tokenizer can handle list of first/second sentences, the tokenize_function does not need to change for this. You can also use multiprocessing with the map method, check out its documentation! Once this is done, we are almost ready for training: we just remove the columns we don't need anymore with the remove_columns method, rename label to labels (since the models from Hugging Face Transformers expect that) and set the output format to our desired backend: torch, tensorflow or numpy. If needed, we can also generate a short sample of a dataset using the select method.
huggingface/blog/blob/main/mantis-case-study.md	-- title: "Why we’re switching to Hugging Face Inference Endpoints, and maybe you should too" thumbnail: /blog/assets/78_ml_director_insights/mantis1.png authors: - user: mattupson guest: true --- # Why we’re switching to Hugging Face Inference Endpoints, and maybe you should too Hugging Face recently launched [Inference Endpoints](https://huggingface.co/inference-endpoints); which as they put it: solves transformers in production. Inference Endpoints is a managed service that allows you to: - Deploy (almost) any model on Hugging Face Hub - To any cloud (AWS, and Azure, GCP on the way) - On a range of instance types (including GPU) - We’re switching some of our Machine Learning (ML) models that do inference on a CPU to this new service. This blog is about why, and why you might also want to consider it. ## What were we doing? The models that we have switched over to Inference Endpoints were previously managed internally and were running on AWS [Elastic Container Service](https://aws.amazon.com/ecs/) (ECS) backed by [AWS Fargate](https://aws.amazon.com/fargate/). This gives you a serverless cluster which can run container based tasks. Our process was as follows: - Train model on a GPU instance (provisioned by [CML](https://cml.dev/), trained with [transformers](https://huggingface.co/docs/transformers/main/)) - Upload to [Hugging Face Hub](https://huggingface.co/models) - Build API to serve model [(FastAPI)](https://fastapi.tiangolo.com/) - Wrap API in container [(Docker)](https://www.docker.com/) - Upload container to AWS [Elastic Container Repository](https://aws.amazon.com/ecr/) (ECR) - Deploy model to ECS Cluster Now, you can reasonably argue that ECS was not the best approach to serving ML models, but it served us up until now, and also allowed ML models to sit alongside other container based services, so it reduced cognitive load. ## What do we do now? With Inference Endpoints, our flow looks like this: - Train model on a GPU instance (provisioned by [CML](https://cml.dev/), trained with [transformers](https://huggingface.co/docs/transformers/main/)) - Upload to [Hugging Face Hub](https://huggingface.co/models) - Deploy using Hugging Face Inference Endpoints. So this is significantly easier. We could also use another managed service such as [SageMaker](https://aws.amazon.com/es/sagemaker/), [Seldon](https://www.seldon.io/), or [Bento ML](https://www.bentoml.com/), etc., but since we are already uploading our model to Hugging Face hub to act as a model registry, and we’re pretty invested in Hugging Face’s other tools (like transformers, and [AutoTrain](https://huggingface.co/autotrain)) using Inference Endpoints makes a lot of sense for us. ## What about Latency and Stability? Before switching to Inference Endpoints we tested different CPU endpoints types using [ab](https://httpd.apache.org/docs/2.4/programs/ab.html). For ECS we didn’t test so extensively, but we know that a large container had a latency of about ~200ms from an instance in the same region. The tests we did for Inference Endpoints we based on text classification model fine tuned on [RoBERTa](https://huggingface.co/roberta-base) with the following test parameters: - Requester region: eu-east-1 - Requester instance size: t3-medium - Inference endpoint region: eu-east-1 - Endpoint Replicas: 1 - Concurrent connections: 1 - Requests: 1000 (1000 requests in 1–2 minutes even from a single connection would represent very heavy use for this particular application) The following table shows latency (ms ± standard deviation and time to complete test in seconds) for four Intel Ice Lake equipped CPU endpoints. ```bash size \| vCPU (cores) \| Memory (GB) \| ECS (ms) \| 🤗 (ms) ---------------------------------------------------------------------- small \| 1 \| 2 \| _ \| ~ 296 medium \| 2 \| 4 \| _ \| 156 ± 51 (158s) large \| 4 \| 8 \| ~200 \| 80 ± 30 (80s) xlarge \| 8 \| 16 \| _ \| 43 ± 31 (43s) ``` What we see from these results is pretty encouraging. The application that will consume these endpoints serves requests in real time, so we need as low latency as possible. We can see that the vanilla Hugging Face container was more than twice as fast as our bespoke container run on ECS — the slowest response we received from the large Inference Endpoint was just 108ms. ## What about the cost? So how much does this all cost? The table below shows a price comparison for what we were doing previously (ECS + Fargate) and using Inference Endpoints. ```bash size \| vCPU \| Memory (GB) \| ECS \| 🤗 \| % diff ---------------------------------------------------------------------- small \| 1 \| 2 \| $ 33.18 \| $ 43.80 \| 0.24 medium \| 2 \| 4 \| $ 60.38 \| $ 87.61 \| 0.31 large \| 4 \| 8 \| $ 114.78 \| $ 175.22 \| 0.34 xlarge \| 8 \| 16 \| $ 223.59 \| $ 350.44 \| 0.5 ``` We can say a couple of things about this. Firstly, we want a managed solution to deployment, we don’t have a dedicated MLOPs team (yet), so we’re looking for a solution that helps us minimize the time we spend on deploying models, even if it costs a little more than handling the deployments ourselves. Inference Endpoints are more expensive that what we were doing before, there’s an increased cost of between 24% and 50%. At the scale we’re currently operating, this additional cost, a difference of ~$60 a month for a large CPU instance is nothing compared to the time and cognitive load we are saving by not having to worry about APIs, and containers. If we were deploying 100s of ML microservices we would probably want to think again, but that is probably true of many approaches to hosting. ## Some notes and caveats: - You can find pricing for Inference Endpoints [here](https://huggingface.co/pricing#endpoints), but a different number is displayed when you deploy a new endpoint from the [GUI](https://ui.endpoints.huggingface.co/new). I’ve used the latter, which is higher. - The values that I present in the table for ECS + Fargate are an underestimate, but probably not by much. I extracted them from the [fargate pricing page](https://aws.amazon.com/fargate/pricing/) and it includes just the cost of hosting the instance. I’m not including the data ingress/egress (probably the biggest thing is downloading the model from Hugging Face hub), nor have I included the costs related to ECR. ## Other considerations ### Deployment Options Currently you can deploy an Inference Endpoint from the [GUI](https://ui.endpoints.huggingface.co/new) or using a [RESTful API](https://huggingface.co/docs/inference-endpoints/api_reference). You can also make use of our command line tool [hugie](https://github.com/MantisAI/hfie) (which will be the subject of a future blog) to launch Inference Endpoints in one line of code by passing a configuration, it’s really this simple: ```bash hugie endpoint create example/development.json ``` For me, what’s lacking is a [custom terraform provider](https://www.hashicorp.com/blog/writing-custom-terraform-providers). It’s all well and good deploying an inference endpoint from a [GitHub action](https://github.com/features/actions) using hugie, as we do, but it would be better if we could use the awesome state machine that is terraform to keep track of these. I’m pretty sure that someone (if not Hugging Face) will write one soon enough — if not, we will. ### Hosting multiple models on a single endpoint Philipp Schmid posted a really nice blog about how to write a custom [Endpoint Handler](https://www.philschmid.de/multi-model-inference-endpoints) class to allow you to host multiple models on a single endpoint, potentially saving you quite a bit of money. His blog was about GPU inference, and the only real limitation is how many models you can fit into the GPU memory. I assume this will also work for CPU instances, though I’ve not tried yet. ## To conclude… We find Hugging Face Inference Endpoints to be a very simple and convenient way to deploy transformer (and [sklearn](https://huggingface.co/scikit-learn)) models into an endpoint so they can be consumed by an application. Whilst they cost a little more than the ECS approach we were using before, it’s well worth it because it saves us time on thinking about deployment, we can concentrate on the thing we want to: building NLP solutions for our clients to help solve their problems. _If you’re interested in Hugging Face Inference Endpoints for your company, please contact us [here](https://huggingface.co/inference-endpoints/enterprise) - our team will contact you to discuss your requirements!_ _This article was originally published on February 15, 2023 [in Medium](https://medium.com/mantisnlp/why-were-switching-to-hugging-face-inference-endpoints-and-maybe-you-should-too-829371dcd330)._
huggingface/evaluate/blob/main/metrics/rouge/README.md	-- title: ROUGE emoji: 🤗 colorFrom: blue colorTo: red sdk: gradio sdk_version: 3.19.1 app_file: app.py pinned: false tags: - evaluate - metric description: >- ROUGE, or Recall-Oriented Understudy for Gisting Evaluation, is a set of metrics and a software package used for evaluating automatic summarization and machine translation software in natural language processing. The metrics compare an automatically produced summary or translation against a reference or a set of references (human-produced) summary or translation. Note that ROUGE is case insensitive, meaning that upper case letters are treated the same way as lower case letters. This metrics is a wrapper around Google Research reimplementation of ROUGE: https://github.com/google-research/google-research/tree/master/rouge --- # Metric Card for ROUGE ## Metric Description ROUGE, or Recall-Oriented Understudy for Gisting Evaluation, is a set of metrics and a software package used for evaluating automatic summarization and machine translation software in natural language processing. The metrics compare an automatically produced summary or translation against a reference or a set of references (human-produced) summary or translation. Note that ROUGE is case insensitive, meaning that upper case letters are treated the same way as lower case letters. This metrics is a wrapper around the [Google Research reimplementation of ROUGE](https://github.com/google-research/google-research/tree/master/rouge) ## How to Use At minimum, this metric takes as input a list of predictions and a list of references: ```python >>> rouge = evaluate.load('rouge') >>> predictions = ["hello there", "general kenobi"] >>> references = ["hello there", "general kenobi"] >>> results = rouge.compute(predictions=predictions, ... references=references) >>> print(results) {'rouge1': 1.0, 'rouge2': 1.0, 'rougeL': 1.0, 'rougeLsum': 1.0} ``` One can also pass a custom tokenizer which is especially useful for non-latin languages. ```python >>> results = rouge.compute(predictions=predictions, ... references=references, tokenizer=lambda x: x.split()) >>> print(results) {'rouge1': 1.0, 'rouge2': 1.0, 'rougeL': 1.0, 'rougeLsum': 1.0} ``` It can also deal with lists of references for each predictions: ```python >>> rouge = evaluate.load('rouge') >>> predictions = ["hello there", "general kenobi"] >>> references = [["hello", "there"], ["general kenobi", "general yoda"]] >>> results = rouge.compute(predictions=predictions, ... references=references) >>> print(results) {'rouge1': 0.8333, 'rouge2': 0.5, 'rougeL': 0.8333, 'rougeLsum': 0.8333}``` ``` ### Inputs - predictions (`list`): list of predictions to score. Each prediction should be a string with tokens separated by spaces. - references (`list` or `list[list]`): list of reference for each prediction or a list of several references per prediction. Each reference should be a string with tokens separated by spaces. - rouge_types (`list`): A list of rouge types to calculate. Defaults to `['rouge1', 'rouge2', 'rougeL', 'rougeLsum']`. - Valid rouge types: - `"rouge1"`: unigram (1-gram) based scoring - `"rouge2"`: bigram (2-gram) based scoring - `"rougeL"`: Longest common subsequence based scoring. - `"rougeLSum"`: splits text using `"\n"` - See [here](https://github.com/huggingface/datasets/issues/617) for more information - use_aggregator (`boolean`): If True, returns aggregates. Defaults to `True`. - use_stemmer (`boolean`): If `True`, uses Porter stemmer to strip word suffixes. Defaults to `False`. ### Output Values The output is a dictionary with one entry for each rouge type in the input list `rouge_types`. If `use_aggregator=False`, each dictionary entry is a list of scores, with one score for each sentence. E.g. if `rouge_types=['rouge1', 'rouge2']` and `use_aggregator=False`, the output is: ```python {'rouge1': [0.6666666666666666, 1.0], 'rouge2': [0.0, 1.0]} ``` If `rouge_types=['rouge1', 'rouge2']` and `use_aggregator=True`, the output is of the following format: ```python {'rouge1': 1.0, 'rouge2': 1.0} ``` The ROUGE values are in the range of 0 to 1. #### Values from Popular Papers ### Examples An example without aggregation: ```python >>> rouge = evaluate.load('rouge') >>> predictions = ["hello goodbye", "ankh morpork"] >>> references = ["goodbye", "general kenobi"] >>> results = rouge.compute(predictions=predictions, ... references=references, ... use_aggregator=False) >>> print(list(results.keys())) ['rouge1', 'rouge2', 'rougeL', 'rougeLsum'] >>> print(results["rouge1"]) [0.5, 0.0] ``` The same example, but with aggregation: ```python >>> rouge = evaluate.load('rouge') >>> predictions = ["hello goodbye", "ankh morpork"] >>> references = ["goodbye", "general kenobi"] >>> results = rouge.compute(predictions=predictions, ... references=references, ... use_aggregator=True) >>> print(list(results.keys())) ['rouge1', 'rouge2', 'rougeL', 'rougeLsum'] >>> print(results["rouge1"]) 0.25 ``` The same example, but only calculating `rouge_1`: ```python >>> rouge = evaluate.load('rouge') >>> predictions = ["hello goodbye", "ankh morpork"] >>> references = ["goodbye", "general kenobi"] >>> results = rouge.compute(predictions=predictions, ... references=references, ... rouge_types=['rouge_1'], ... use_aggregator=True) >>> print(list(results.keys())) ['rouge1'] >>> print(results["rouge1"]) 0.25 ``` ## Limitations and Bias See [Schluter (2017)](https://aclanthology.org/E17-2007/) for an in-depth discussion of many of ROUGE's limits. ## Citation ```bibtex @inproceedings{lin-2004-rouge, title = "{ROUGE}: A Package for Automatic Evaluation of Summaries", author = "Lin, Chin-Yew", booktitle = "Text Summarization Branches Out", month = jul, year = "2004", address = "Barcelona, Spain", publisher = "Association for Computational Linguistics", url = "https://www.aclweb.org/anthology/W04-1013", pages = "74--81", } ``` ## Further References - This metrics is a wrapper around the [Google Research reimplementation of ROUGE](https://github.com/google-research/google-research/tree/master/rouge)
huggingface/diffusers/blob/main/docs/source/en/api/pipelines/audioldm.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # AudioLDM AudioLDM was proposed in [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://huggingface.co/papers/2301.12503) by Haohe Liu et al. Inspired by [Stable Diffusion](https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion/overview), AudioLDM is a text-to-audio _latent diffusion model (LDM)_ that learns continuous audio representations from [CLAP](https://huggingface.co/docs/transformers/main/model_doc/clap) latents. AudioLDM takes a text prompt as input and predicts the corresponding audio. It can generate text-conditional sound effects, human speech and music. The abstract from the paper is: Text-to-audio (TTA) system has recently gained attention for its ability to synthesize general audio based on text descriptions. However, previous studies in TTA have limited generation quality with high computational costs. In this study, we propose AudioLDM, a TTA system that is built on a latent space to learn the continuous audio representations from contrastive language-audio pretraining (CLAP) latents. The pretrained CLAP models enable us to train LDMs with audio embedding while providing text embedding as a condition during sampling. By learning the latent representations of audio signals and their compositions without modeling the cross-modal relationship, AudioLDM is advantageous in both generation quality and computational efficiency. Trained on AudioCaps with a single GPU, AudioLDM achieves state-of-the-art TTA performance measured by both objective and subjective metrics (e.g., frechet distance). Moreover, AudioLDM is the first TTA system that enables various text-guided audio manipulations (e.g., style transfer) in a zero-shot fashion. Our implementation and demos are available at [this https URL](https://audioldm.github.io/). The original codebase can be found at [haoheliu/AudioLDM](https://github.com/haoheliu/AudioLDM). ## Tips When constructing a prompt, keep in mind: * Descriptive prompt inputs work best; you can use adjectives to describe the sound (for example, "high quality" or "clear") and make the prompt context specific (for example, "water stream in a forest" instead of "stream"). * It's best to use general terms like "cat" or "dog" instead of specific names or abstract objects the model may not be familiar with. During inference: * The _quality_ of the predicted audio sample can be controlled by the `num_inference_steps` argument; higher steps give higher quality audio at the expense of slower inference. * The _length_ of the predicted audio sample can be controlled by varying the `audio_length_in_s` argument. <Tip> Make sure to check out the Schedulers [guide](../../using-diffusers/schedulers) to learn how to explore the tradeoff between scheduler speed and quality, and see the [reuse components across pipelines](../../using-diffusers/loading#reuse-components-across-pipelines) section to learn how to efficiently load the same components into multiple pipelines. </Tip> ## AudioLDMPipeline [[autodoc]] AudioLDMPipeline - all - __call__ ## AudioPipelineOutput [[autodoc]] pipelines.AudioPipelineOutput
huggingface/course/blob/main/subtitles/en/raw/chapter2/04c_character-based-tokenizers.md	efore diving in character-based tokenization, understanding why this kind of tokenization is interesting requires understanding the flaws of word-based tokenization. If you haven't seen the first video on word-based tokenization we recommend you check it out before looking at this video. Let's take a look at character-based tokenization. We now split our text into individual characters, rather than words. There are generally a lot of different words in languages, while the number of characters stays low. Here for example, for the English language that has an estimated 170,000 different words, we would need a very large vocabulary to encompass all words. With a character-based vocabulary, we can get by with only 256 characters! Even languages with a lot of different characters like the Chinese languages have dictionaries with ~20,000 different characters but more than 375,000 different words. Character-based vocabularies let us fewer different tokens than the word-based tokenization dictionaries we would otherwise use. These vocabularies are also more complete than their word-based vocabularies counterparts. As our vocabulary contains all characters used in a language, even words unseen during the tokenizer training can still be tokenized, so out-of-vocabulary tokens will be less frequent. This includes the ability to correctly tokenize misspelled words, rather than discarding them as unknown straight away. However, this algorithm isn't perfect either! Intuitively, characters do not hold as much information individually as a word would hold. For example, "Let's" holds more information than "l". Of course, this is not true for all languages, as some languages like ideogram-based languages have a lot of information held in single characters, but for others like roman-based languages, the model will have to make sense of multiple tokens at a time to get the information held in a single word. This leads to another issue with character-based tokenizers: their sequences are translated into very large amount of tokens to be processed by the model. This can have an impact on the size of the context the model will carry around, and will reduce the size of the text we can use as input for our model. This tokenization, while it has some issues, has seen some very good results in the past and should be considered when approaching a new problem as it solves some issues encountered in the word-based algorithm.
huggingface/deep-rl-class/blob/main/units/en/unit7/hands-on.mdx	Hands-on Now that you learned the basics of multi-agents, you're ready to train your first agents in a multi-agent system: a 2vs2 soccer team that needs to beat the opponent team. And you’re going to participate in AI vs. AI challenges where your trained agent will compete against other classmates’ agents every day and be ranked on a new leaderboard. To validate this hands-on for the certification process, you just need to push a trained model. There are no minimal results to attain to validate it. For more information about the certification process, check this section 👉 [https://huggingface.co/deep-rl-course/en/unit0/introduction#certification-process](https://huggingface.co/deep-rl-course/en/unit0/introduction#certification-process) This hands-on will be different since to get correct results you need to train your agents from 4 hours to 8 hours. And given the risk of timeout in Colab, we advise you to train on your computer. You don’t need a supercomputer: a simple laptop is good enough for this exercise. Let's get started! 🔥 ## What is AI vs. AI? AI vs. AI is an open-source tool we developed at Hugging Face to compete agents on the Hub against one another in a multi-agent setting. These models are then ranked in a leaderboard. The idea of this tool is to have a robust evaluation tool: by evaluating your agent with a lot of others, you’ll get a good idea of the quality of your policy. More precisely, AI vs. AI is three tools: - A matchmaking process defining the matches (which model against which) and running the model fights using a background task in the Space. - A leaderboard getting the match history results and displaying the models’ ELO ratings: [https://huggingface.co/spaces/huggingface-projects/AIvsAI-SoccerTwos](https://huggingface.co/spaces/huggingface-projects/AIvsAI-SoccerTwos) - A Space demo to visualize your agents playing against others: [https://huggingface.co/spaces/unity/ML-Agents-SoccerTwos](https://huggingface.co/spaces/unity/ML-Agents-SoccerTwos) In addition to these three tools, your classmate cyllum created a 🤗 SoccerTwos Challenge Analytics where you can check the detailed match results of a model: [https://huggingface.co/spaces/cyllum/soccertwos-analytics](https://huggingface.co/spaces/cyllum/soccertwos-analytics) We're [wrote a blog post to explain this AI vs. AI tool in detail](https://huggingface.co/blog/aivsai), but to give you the big picture it works this way: - Every four hours, our algorithm fetches all the available models for a given environment (in our case ML-Agents-SoccerTwos). - It creates a queue of matches with the matchmaking algorithm. - We simulate the match in a Unity headless process and gather the match result (1 if the first model won, 0.5 if it’s a draw, 0 if the second model won) in a Dataset. - Then, when all matches from the matches queue are done, we update the ELO score for each model and update the leaderboard. ### Competition Rules This first AI vs. AI competition is an experiment: the goal is to improve the tool in the future with your feedback. So some breakups can happen during the challenge. But don't worry all the results are saved in a dataset so we can always restart the calculation correctly without losing information. In order for your model to get correctly evaluated against others you need to follow these rules: 1. You can't change the observation space or action space of the agent. By doing that your model will not work during evaluation. 2. You can't use a custom trainer for now, you need to use the Unity MLAgents ones. 3. We provide executables to train your agents. You can also use the Unity Editor if you prefer , but to avoid bugs, we advise that you use our executables. What will make the difference during this challenge are the hyperparameters you choose. We're constantly trying to improve our tutorials, so if you find some issues in this notebook, please [open an issue on the GitHub Repo](https://github.com/huggingface/deep-rl-class/issues). ### Chat with your classmates, share advice and ask questions on Discord - We created a new channel called `ai-vs-ai-challenge` to exchange advice and ask questions. - If you didn’t join the discord server yet, you can [join here](https://discord.gg/ydHrjt3WP5) ## Step 0: Install MLAgents and download the correct executable We advise you to use [conda](https://docs.conda.io/en/latest/) as a package manager and create a new environment. With conda, we create a new environment called rl with Python 3.10.12: ```bash conda create --name rl python=3.10.12 conda activate rl ``` To be able to train our agents correctly and push to the Hub, we need to install ML-Agents ```bash git clone https://github.com/Unity-Technologies/ml-agents ``` When the cloning is done (it takes 2.63 GB), we go inside the repository and install the package ```bash cd ml-agents pip install -e ./ml-agents-envs pip install -e ./ml-agents ``` Finally, you need to install git-lfs: https://git-lfs.com/ Now that it’s installed, we need to add the environment training executable. Based on your operating system you need to download one of them, unzip it and place it in a new folder inside `ml-agents` that you call `training-envs-executables` At the end your executable should be in `ml-agents/training-envs-executables/SoccerTwos` Windows: Download [this executable](https://drive.google.com/file/d/1sqFxbEdTMubjVktnV4C6ICjp89wLhUcP/view?usp=sharing) Linux (Ubuntu): Download [this executable](https://drive.google.com/file/d/1KuqBKYiXiIcU4kNMqEzhgypuFP5_45CL/view?usp=sharing) Mac: Download [this executable](https://drive.google.com/drive/folders/1h7YB0qwjoxxghApQdEUQmk95ZwIDxrPG?usp=share_link) ⚠ For Mac you need also to call this `xattr -cr training-envs-executables/SoccerTwos/SoccerTwos.app` to be able to run SoccerTwos ## Step 1: Understand the environment The environment is called `SoccerTwos`. The Unity MLAgents Team made it. You can find its documentation [here](https://github.com/Unity-Technologies/ml-agents/blob/develop/docs/Learning-Environment-Examples.md#soccer-twos) The goal in this environment is to get the ball into the opponent's goal while preventing the ball from entering your own goal. <figure> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/soccertwos.gif" alt="SoccerTwos"/> <figcaption>This environment was made by the <a href="https://github.com/Unity-Technologies/ml-agents"> Unity MLAgents Team</a></figcaption> </figure> ### The reward function The reward function is: <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/soccerreward.png" alt="SoccerTwos Reward"/> ### The observation space The observation space is composed of vectors of size 336: - 11 ray-casts forward distributed over 120 degrees (264 state dimensions) - 3 ray-casts backward distributed over 90 degrees (72 state dimensions) - Both of these ray-casts can detect 6 objects: - Ball - Blue Goal - Purple Goal - Wall - Blue Agent - Purple Agent ### The action space The action space is three discrete branches: <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/socceraction.png" alt="SoccerTwos Action"/> ## Step 2: Understand MA-POCA We know how to train agents to play against others: we can use self-play. This is a perfect technique for a 1vs1. But in our case we’re 2vs2, and each team has 2 agents. How then can we train cooperative behavior for groups of agents? As explained in the [Unity Blog](https://blog.unity.com/technology/ml-agents-v20-release-now-supports-training-complex-cooperative-behaviors), agents typically receive a reward as a group (+1 - penalty) when the team scores a goal. This implies that every agent on the team is rewarded even if each agent didn’t contribute the same to the win, which makes it difficult to learn what to do independently. The Unity MLAgents team developed the solution in a new multi-agent trainer called MA-POCA (Multi-Agent POsthumous Credit Assignment). The idea is simple but powerful: a centralized critic processes the states of all agents in the team to estimate how well each agent is doing. Think of this critic as a coach. This allows each agent to make decisions based only on what it perceives locally, and simultaneously evaluate how good its behavior is in the context of the whole group. <figure> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/mapoca.png" alt="MA POCA"/> <figcaption>This illustrates MA-POCA’s centralized learning and decentralized execution. Source: <a href="https://blog.unity.com/technology/ml-agents-plays-dodgeball">MLAgents Plays Dodgeball</a> </figcaption> </figure> The solution then is to use Self-Play with an MA-POCA trainer (called poca). The poca trainer will help us to train cooperative behavior and self-play to win against an opponent team. If you want to dive deeper into this MA-POCA algorithm, you need to read the paper they published [here](https://arxiv.org/pdf/2111.05992.pdf) and the sources we put on the additional readings section. ## Step 3: Define the config file We already learned in [Unit 5](https://huggingface.co/deep-rl-course/unit5/introduction) that in ML-Agents, you define the training hyperparameters in `config.yaml` files. There are multiple hyperparameters. To understand them better, you should read the explanations for each of them in [the documentation](https://github.com/Unity-Technologies/ml-agents/blob/release_20_docs/docs/Training-Configuration-File.md) The config file we’re going to use here is in `./config/poca/SoccerTwos.yaml`. It looks like this: ```csharp behaviors: SoccerTwos: trainer_type: poca hyperparameters: batch_size: 2048 buffer_size: 20480 learning_rate: 0.0003 beta: 0.005 epsilon: 0.2 lambd: 0.95 num_epoch: 3 learning_rate_schedule: constant network_settings: normalize: false hidden_units: 512 num_layers: 2 vis_encode_type: simple reward_signals: extrinsic: gamma: 0.99 strength: 1.0 keep_checkpoints: 5 max_steps: 5000000 time_horizon: 1000 summary_freq: 10000 self_play: save_steps: 50000 team_change: 200000 swap_steps: 2000 window: 10 play_against_latest_model_ratio: 0.5 initial_elo: 1200.0 ``` Compared to Pyramids or SnowballTarget, we have new hyperparameters with a self-play part. How you modify them can be critical in getting good results. The advice I can give you here is to check the explanation and recommended value for each parameters (especially self-play ones) against [the documentation](https://github.com/Unity-Technologies/ml-agents/blob/release_20_docs/docs/Training-Configuration-File.md). Now that you’ve modified our config file, you’re ready to train your agents. ## Step 4: Start the training To train the agents, we need to launch mlagents-learn and select the executable containing the environment. We define four parameters: 1. `mlagents-learn <config>`: the path where the hyperparameter config file is. 2. `-env`: where the environment executable is. 3. `-run_id`: the name you want to give to your training run id. 4. `-no-graphics`: to not launch the visualization during the training. Depending on your hardware, 5M timesteps (the recommended value, but you can also try 10M) will take 5 to 8 hours of training. You can continue using your computer in the meantime, but I advise deactivating the computer standby mode to prevent the training from being stopped. Depending on the executable you use (windows, ubuntu, mac) the training command will look like this (your executable path can be different so don’t hesitate to check before running). ```bash mlagents-learn ./config/poca/SoccerTwos.yaml --env=./training-envs-executables/SoccerTwos.exe --run-id="SoccerTwos" --no-graphics ``` The executable contains 8 copies of SoccerTwos. ⚠️ It’s normal if you don’t see a big increase of ELO score (and even a decrease below 1200) before 2M timesteps, since your agents will spend most of their time moving randomly on the field before being able to goal. ⚠️ You can stop the training with Ctrl + C but beware of typing this command only once to stop the training since MLAgents needs to generate a final .onnx file before closing the run. ## Step 5: Push the agent to the Hugging Face Hub Now that we trained our agents, we’re ready to push them to the Hub to be able to participate in the AI vs. AI challenge and visualize them playing on your browser🔥. To be able to share your model with the community, there are three more steps to follow: 1️⃣ (If it’s not already done) create an account to HF ➡ [https://huggingface.co/join](https://huggingface.co/join) 2️⃣ Sign in and store your authentication token from the Hugging Face website. Create a new token (https://huggingface.co/settings/tokens) with write role <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/notebooks/create-token.jpg" alt="Create HF Token"> Copy the token, run this, and paste the token ```bash huggingface-cli login ``` Then, we need to run `mlagents-push-to-hf`. And we define four parameters: 1. `-run-id`: the name of the training run id. 2. `-local-dir`: where the agent was saved, it’s results/<run_id name>, so in my case results/First Training. 3. `-repo-id`: the name of the Hugging Face repo you want to create or update. It’s always <your huggingface username>/<the repo name> If the repo does not exist it will be created automatically 4. `--commit-message`: since HF repos are git repositories you need to give a commit message. In my case ```bash mlagents-push-to-hf --run-id="SoccerTwos" --local-dir="./results/SoccerTwos" --repo-id="ThomasSimonini/poca-SoccerTwos" --commit-message="First Push"` ``` ```bash mlagents-push-to-hf --run-id= # Add your run id --local-dir= # Your local dir --repo-id= # Your repo id --commit-message="First Push" ``` If everything worked you should see this at the end of the process (but with a different url 😆) : Your model is pushed to the Hub. You can view your model here: https://huggingface.co/ThomasSimonini/poca-SoccerTwos It's the link to your model. It contains a model card that explains how to use it, your Tensorboard, and your config file. What's awesome is that it's a git repository, which means you can have different commits, update your repository with a new push, etc. ## Step 6: Verify that your model is ready for AI vs AI Challenge Now that your model is pushed to the Hub, it’s going to be added automatically to the AI vs AI Challenge model pool. It can take a little bit of time before your model is added to the leaderboard given we do a run of matches every 4h. But to ensure that everything works perfectly you need to check: 1. That you have this tag in your model: ML-Agents-SoccerTwos. This is the tag we use to select models to be added to the challenge pool. To do that go to your model and check the tags <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/verify1.png" alt="Verify"/> If it’s not the case you just need to modify the readme and add it <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/verify2.png" alt="Verify"/> 2. That you have a `SoccerTwos.onnx` file <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit10/verify3.png" alt="Verify"/> We strongly suggest that you create a new model when you push to the Hub if you want to train it again or train a new version. ## Step 7: Visualize some match in our demo Now that your model is part of AI vs AI Challenge, you can visualize how good it is compared to others: https://huggingface.co/spaces/unity/ML-Agents-SoccerTwos In order to do that, you just need to go to this demo: - Select your model as team blue (or team purple if you prefer) and another model to compete against. The best opponents to compare your model to are either whoever is on top of the leaderboard or the [baseline model](https://huggingface.co/unity/MLAgents-SoccerTwos) The matches you see live are not used in the calculation of your result but they are a good way to visualize how good your agent is. And don't hesitate to share the best score your agent gets on discord in the #rl-i-made-this channel 🔥
gradio-app/gradio/blob/main/demo/sales_projections/run.ipynb	Gradio Demo: sales_projections ``` !pip install -q gradio pandas numpy matplotlib ``` ``` import matplotlib.pyplot as plt import numpy as np import gradio as gr def sales_projections(employee_data): sales_data = employee_data.iloc[:, 1:4].astype("int").to_numpy() regression_values = np.apply_along_axis( lambda row: np.array(np.poly1d(np.polyfit([0, 1, 2], row, 2))), 0, sales_data ) projected_months = np.repeat( np.expand_dims(np.arange(3, 12), 0), len(sales_data), axis=0 ) projected_values = np.array( [ month * month * regression[0] + month * regression[1] + regression[2] for month, regression in zip(projected_months, regression_values) ] ) plt.plot(projected_values.T) plt.legend(employee_data["Name"]) return employee_data, plt.gcf(), regression_values demo = gr.Interface( sales_projections, gr.Dataframe( headers=["Name", "Jan Sales", "Feb Sales", "Mar Sales"], value=[["Jon", 12, 14, 18], ["Alice", 14, 17, 2], ["Sana", 8, 9.5, 12]], ), ["dataframe", "plot", "numpy"], description="Enter sales figures for employees to predict sales trajectory over year.", ) if __name__ == "__main__": demo.launch() ```
huggingface/datasets/blob/main/metrics/f1/README.md	Metric Card for F1 ## Metric Description The F1 score is the harmonic mean of the precision and recall. It can be computed with the equation: F1 = 2 * (precision * recall) / (precision + recall) ## How to Use At minimum, this metric requires predictions and references as input ```python >>> f1_metric = datasets.load_metric("f1") >>> results = f1_metric.compute(predictions=[0, 1], references=[0, 1]) >>> print(results) ["{'f1': 1.0}"] ``` ### Inputs - predictions (`list` of `int`): Predicted labels. - references (`list` of `int`): Ground truth labels. - labels (`list` of `int`): The set of labels to include when `average` is not set to `'binary'`, and the order of the labels if `average` is `None`. Labels present in the data can be excluded, for example to calculate a multiclass average ignoring a majority negative class. Labels not present in the data will result in 0 components in a macro average. For multilabel targets, labels are column indices. By default, all labels in `predictions` and `references` are used in sorted order. Defaults to None. - pos_label (`int`): The class to be considered the positive class, in the case where `average` is set to `binary`. Defaults to 1. - average (`string`): This parameter is required for multiclass/multilabel targets. If set to `None`, the scores for each class are returned. Otherwise, this determines the type of averaging performed on the data. Defaults to `'binary'`. - 'binary': Only report results for the class specified by `pos_label`. This is applicable only if the classes found in `predictions` and `references` are binary. - 'micro': Calculate metrics globally by counting the total true positives, false negatives and false positives. - 'macro': Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account. - 'weighted': Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters `'macro'` to account for label imbalance. This option can result in an F-score that is not between precision and recall. - 'samples': Calculate metrics for each instance, and find their average (only meaningful for multilabel classification). - sample_weight (`list` of `float`): Sample weights Defaults to None. ### Output Values - f1(`float` or `array` of `float`): F1 score or list of f1 scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher f1 scores are better. Output Example(s): ```python {'f1': 0.26666666666666666} ``` ```python {'f1': array([0.8, 0.0, 0.0])} ``` This metric outputs a dictionary, with either a single f1 score, of type `float`, or an array of f1 scores, with entries of type `float`. #### Values from Popular Papers ### Examples Example 1-A simple binary example ```python >>> f1_metric = datasets.load_metric("f1") >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0]) >>> print(results) {'f1': 0.5} ``` Example 2-The same simple binary example as in Example 1, but with `pos_label` set to `0`. ```python >>> f1_metric = datasets.load_metric("f1") >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], pos_label=0) >>> print(round(results['f1'], 2)) 0.67 ``` Example 3-The same simple binary example as in Example 1, but with `sample_weight` included. ```python >>> f1_metric = datasets.load_metric("f1") >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], sample_weight=[0.9, 0.5, 3.9, 1.2, 0.3]) >>> print(round(results['f1'], 2)) 0.35 ``` Example 4-A multiclass example, with different values for the `average` input. ```python >>> predictions = [0, 2, 1, 0, 0, 1] >>> references = [0, 1, 2, 0, 1, 2] >>> results = f1_metric.compute(predictions=predictions, references=references, average="macro") >>> print(round(results['f1'], 2)) 0.27 >>> results = f1_metric.compute(predictions=predictions, references=references, average="micro") >>> print(round(results['f1'], 2)) 0.33 >>> results = f1_metric.compute(predictions=predictions, references=references, average="weighted") >>> print(round(results['f1'], 2)) 0.27 >>> results = f1_metric.compute(predictions=predictions, references=references, average=None) >>> print(results) {'f1': array([0.8, 0. , 0. ])} ``` ## Limitations and Bias ## Citation(s) ```bibtex @article{scikit-learn, title={Scikit-learn: Machine Learning in {P}ython}, author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.}, journal={Journal of Machine Learning Research}, volume={12}, pages={2825--2830}, year={2011} } ``` ## Further References
huggingface/transformers/blob/main/docs/source/en/model_doc/timesformer.md	!--Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # TimeSformer ## Overview The TimeSformer model was proposed in [TimeSformer: Is Space-Time Attention All You Need for Video Understanding?](https://arxiv.org/abs/2102.05095) by Facebook Research. This work is a milestone in action-recognition field being the first video transformer. It inspired many transformer based video understanding and classification papers. The abstract from the paper is the following: We present a convolution-free approach to video classification built exclusively on self-attention over space and time. Our method, named "TimeSformer," adapts the standard Transformer architecture to video by enabling spatiotemporal feature learning directly from a sequence of frame-level patches. Our experimental study compares different self-attention schemes and suggests that "divided attention," where temporal attention and spatial attention are separately applied within each block, leads to the best video classification accuracy among the design choices considered. Despite the radically new design, TimeSformer achieves state-of-the-art results on several action recognition benchmarks, including the best reported accuracy on Kinetics-400 and Kinetics-600. Finally, compared to 3D convolutional networks, our model is faster to train, it can achieve dramatically higher test efficiency (at a small drop in accuracy), and it can also be applied to much longer video clips (over one minute long). Code and models are available at: [this https URL](https://github.com/facebookresearch/TimeSformer). This model was contributed by [fcakyon](https://huggingface.co/fcakyon). The original code can be found [here](https://github.com/facebookresearch/TimeSformer). ## Usage tips There are many pretrained variants. Select your pretrained model based on the dataset it is trained on. Moreover, the number of input frames per clip changes based on the model size so you should consider this parameter while selecting your pretrained model. ## Resources - [Video classification task guide](../tasks/video_classification) ## TimesformerConfig [[autodoc]] TimesformerConfig ## TimesformerModel [[autodoc]] TimesformerModel - forward ## TimesformerForVideoClassification [[autodoc]] TimesformerForVideoClassification - forward
huggingface/transformers/blob/main/docs/source/en/model_doc/swinv2.md	!--Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Swin Transformer V2 ## Overview The Swin Transformer V2 model was proposed in [Swin Transformer V2: Scaling Up Capacity and Resolution](https://arxiv.org/abs/2111.09883) by Ze Liu, Han Hu, Yutong Lin, Zhuliang Yao, Zhenda Xie, Yixuan Wei, Jia Ning, Yue Cao, Zheng Zhang, Li Dong, Furu Wei, Baining Guo. The abstract from the paper is the following: Large-scale NLP models have been shown to significantly improve the performance on language tasks with no signs of saturation. They also demonstrate amazing few-shot capabilities like that of human beings. This paper aims to explore large-scale models in computer vision. We tackle three major issues in training and application of large vision models, including training instability, resolution gaps between pre-training and fine-tuning, and hunger on labelled data. Three main techniques are proposed: 1) a residual-post-norm method combined with cosine attention to improve training stability; 2) A log-spaced continuous position bias method to effectively transfer models pre-trained using low-resolution images to downstream tasks with high-resolution inputs; 3) A self-supervised pre-training method, SimMIM, to reduce the needs of vast labeled images. Through these techniques, this paper successfully trained a 3 billion-parameter Swin Transformer V2 model, which is the largest dense vision model to date, and makes it capable of training with images of up to 1,536×1,536 resolution. It set new performance records on 4 representative vision tasks, including ImageNet-V2 image classification, COCO object detection, ADE20K semantic segmentation, and Kinetics-400 video action classification. Also note our training is much more efficient than that in Google's billion-level visual models, which consumes 40 times less labelled data and 40 times less training time. This model was contributed by [nandwalritik](https://huggingface.co/nandwalritik). The original code can be found [here](https://github.com/microsoft/Swin-Transformer). ## Resources A list of official Hugging Face and community (indicated by 🌎) resources to help you get started with Swin Transformer v2. <PipelineTag pipeline="image-classification"/> - [`Swinv2ForImageClassification`] is supported by this [example script](https://github.com/huggingface/transformers/tree/main/examples/pytorch/image-classification) and [notebook](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_classification.ipynb). - See also: [Image classification task guide](../tasks/image_classification) Besides that: - [`Swinv2ForMaskedImageModeling`] is supported by this [example script](https://github.com/huggingface/transformers/tree/main/examples/pytorch/image-pretraining). If you're interested in submitting a resource to be included here, please feel free to open a Pull Request and we'll review it! The resource should ideally demonstrate something new instead of duplicating an existing resource. ## Swinv2Config [[autodoc]] Swinv2Config ## Swinv2Model [[autodoc]] Swinv2Model - forward ## Swinv2ForMaskedImageModeling [[autodoc]] Swinv2ForMaskedImageModeling - forward ## Swinv2ForImageClassification [[autodoc]] transformers.Swinv2ForImageClassification - forward
huggingface/transformers/blob/main/docs/source/en/model_doc/rembert.md	!--Copyright 2020 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # RemBERT ## Overview The RemBERT model was proposed in [Rethinking Embedding Coupling in Pre-trained Language Models](https://arxiv.org/abs/2010.12821) by Hyung Won Chung, Thibault Févry, Henry Tsai, Melvin Johnson, Sebastian Ruder. The abstract from the paper is the following: We re-evaluate the standard practice of sharing weights between input and output embeddings in state-of-the-art pre-trained language models. We show that decoupled embeddings provide increased modeling flexibility, allowing us to significantly improve the efficiency of parameter allocation in the input embedding of multilingual models. By reallocating the input embedding parameters in the Transformer layers, we achieve dramatically better performance on standard natural language understanding tasks with the same number of parameters during fine-tuning. We also show that allocating additional capacity to the output embedding provides benefits to the model that persist through the fine-tuning stage even though the output embedding is discarded after pre-training. Our analysis shows that larger output embeddings prevent the model's last layers from overspecializing to the pre-training task and encourage Transformer representations to be more general and more transferable to other tasks and languages. Harnessing these findings, we are able to train models that achieve strong performance on the XTREME benchmark without increasing the number of parameters at the fine-tuning stage. ## Usage tips For fine-tuning, RemBERT can be thought of as a bigger version of mBERT with an ALBERT-like factorization of the embedding layer. The embeddings are not tied in pre-training, in contrast with BERT, which enables smaller input embeddings (preserved during fine-tuning) and bigger output embeddings (discarded at fine-tuning). The tokenizer is also similar to the Albert one rather than the BERT one. ## Resources - [Text classification task guide](../tasks/sequence_classification) - [Token classification task guide](../tasks/token_classification) - [Question answering task guide](../tasks/question_answering) - [Causal language modeling task guide](../tasks/language_modeling) - [Masked language modeling task guide](../tasks/masked_language_modeling) - [Multiple choice task guide](../tasks/multiple_choice) ## RemBertConfig [[autodoc]] RemBertConfig ## RemBertTokenizer [[autodoc]] RemBertTokenizer - build_inputs_with_special_tokens - get_special_tokens_mask - create_token_type_ids_from_sequences - save_vocabulary ## RemBertTokenizerFast [[autodoc]] RemBertTokenizerFast - build_inputs_with_special_tokens - get_special_tokens_mask - create_token_type_ids_from_sequences - save_vocabulary <frameworkcontent> <pt> ## RemBertModel [[autodoc]] RemBertModel - forward ## RemBertForCausalLM [[autodoc]] RemBertForCausalLM - forward ## RemBertForMaskedLM [[autodoc]] RemBertForMaskedLM - forward ## RemBertForSequenceClassification [[autodoc]] RemBertForSequenceClassification - forward ## RemBertForMultipleChoice [[autodoc]] RemBertForMultipleChoice - forward ## RemBertForTokenClassification [[autodoc]] RemBertForTokenClassification - forward ## RemBertForQuestionAnswering [[autodoc]] RemBertForQuestionAnswering - forward </pt> <tf> ## TFRemBertModel [[autodoc]] TFRemBertModel - call ## TFRemBertForMaskedLM [[autodoc]] TFRemBertForMaskedLM - call ## TFRemBertForCausalLM [[autodoc]] TFRemBertForCausalLM - call ## TFRemBertForSequenceClassification [[autodoc]] TFRemBertForSequenceClassification - call ## TFRemBertForMultipleChoice [[autodoc]] TFRemBertForMultipleChoice - call ## TFRemBertForTokenClassification [[autodoc]] TFRemBertForTokenClassification - call ## TFRemBertForQuestionAnswering [[autodoc]] TFRemBertForQuestionAnswering - call </tf> </frameworkcontent>
huggingface/diffusers/blob/main/docs/source/en/using-diffusers/inference_with_lcm_lora.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> [[open-in-colab]] # Performing inference with LCM-LoRA Latent Consistency Models (LCM) enable quality image generation in typically 2-4 steps making it possible to use diffusion models in almost real-time settings. From the [official website](https://latent-consistency-models.github.io/): > LCMs can be distilled from any pre-trained Stable Diffusion (SD) in only 4,000 training steps (~32 A100 GPU Hours) for generating high quality 768 x 768 resolution images in 2~4 steps or even one step, significantly accelerating text-to-image generation. We employ LCM to distill the Dreamshaper-V7 version of SD in just 4,000 training iterations. For a more technical overview of LCMs, refer to [the paper](https://huggingface.co/papers/2310.04378). However, each model needs to be distilled separately for latent consistency distillation. The core idea with LCM-LoRA is to train just a few adapter layers, the adapter being LoRA in this case. This way, we don't have to train the full model and keep the number of trainable parameters manageable. The resulting LoRAs can then be applied to any fine-tuned version of the model without distilling them separately. Additionally, the LoRAs can be applied to image-to-image, ControlNet/T2I-Adapter, inpainting, AnimateDiff etc. The LCM-LoRA can also be combined with other LoRAs to generate styled images in very few steps (4-8). LCM-LoRAs are available for [stable-diffusion-v1-5](https://huggingface.co/runwayml/stable-diffusion-v1-5), [stable-diffusion-xl-base-1.0](https://huggingface.co/stabilityai/stable-diffusion-xl-base-1.0), and the [SSD-1B](https://huggingface.co/segmind/SSD-1B) model. All the checkpoints can be found in this [collection](https://huggingface.co/collections/latent-consistency/latent-consistency-models-loras-654cdd24e111e16f0865fba6). For more details about LCM-LoRA, refer to [the technical report](https://huggingface.co/papers/2311.05556). This guide shows how to perform inference with LCM-LoRAs for - text-to-image - image-to-image - combined with styled LoRAs - ControlNet/T2I-Adapter - inpainting - AnimateDiff Before going through this guide, we'll take a look at the general workflow for performing inference with LCM-LoRAs. LCM-LoRAs are similar to other Stable Diffusion LoRAs so they can be used with any [`DiffusionPipeline`] that supports LoRAs. - Load the task specific pipeline and model. - Set the scheduler to [`LCMScheduler`]. - Load the LCM-LoRA weights for the model. - Reduce the `guidance_scale` between `[1.0, 2.0]` and set the `num_inference_steps` between [4, 8]. - Perform inference with the pipeline with the usual parameters. Let's look at how we can perform inference with LCM-LoRAs for different tasks. First, make sure you have [peft](https://github.com/huggingface/peft) installed, for better LoRA support. ```bash pip install -U peft ``` ## Text-to-image You'll use the [`StableDiffusionXLPipeline`] with the scheduler: [`LCMScheduler`] and then load the LCM-LoRA. Together with the LCM-LoRA and the scheduler, the pipeline enables a fast inference workflow overcoming the slow iterative nature of diffusion models. ```python import torch from diffusers import DiffusionPipeline, LCMScheduler pipe = DiffusionPipeline.from_pretrained( "stabilityai/stable-diffusion-xl-base-1.0", variant="fp16", torch_dtype=torch.float16 ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdxl") prompt = "Self-portrait oil painting, a beautiful cyborg with golden hair, 8k" generator = torch.manual_seed(42) image = pipe( prompt=prompt, num_inference_steps=4, generator=generator, guidance_scale=1.0 ).images[0] ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdxl_t2i.png) Notice that we use only 4 steps for generation which is way less than what's typically used for standard SDXL. <Tip> You may have noticed that we set `guidance_scale=1.0`, which disables classifer-free-guidance. This is because the LCM-LoRA is trained with guidance, so the batch size does not have to be doubled in this case. This leads to a faster inference time, with the drawback that negative prompts don't have any effect on the denoising process. You can also use guidance with LCM-LoRA, but due to the nature of training the model is very sensitve to the `guidance_scale` values, high values can lead to artifacts in the generated images. In our experiments, we found that the best values are in the range of [1.0, 2.0]. </Tip> ### Inference with a fine-tuned model As mentioned above, the LCM-LoRA can be applied to any fine-tuned version of the model without having to distill them separately. Let's look at how we can perform inference with a fine-tuned model. In this example, we'll use the [animagine-xl](https://huggingface.co/Linaqruf/animagine-xl) model, which is a fine-tuned version of the SDXL model for generating anime. ```python from diffusers import DiffusionPipeline, LCMScheduler pipe = DiffusionPipeline.from_pretrained( "Linaqruf/animagine-xl", variant="fp16", torch_dtype=torch.float16 ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdxl") prompt = "face focus, cute, masterpiece, best quality, 1girl, green hair, sweater, looking at viewer, upper body, beanie, outdoors, night, turtleneck" generator = torch.manual_seed(0) image = pipe( prompt=prompt, num_inference_steps=4, generator=generator, guidance_scale=1.0 ).images[0] ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdxl_t2i_finetuned.png) ## Image-to-image LCM-LoRA can be applied to image-to-image tasks too. Let's look at how we can perform image-to-image generation with LCMs. For this example we'll use the [dreamshaper-7](https://huggingface.co/Lykon/dreamshaper-7) model and the LCM-LoRA for `stable-diffusion-v1-5 `. ```python import torch from diffusers import AutoPipelineForImage2Image, LCMScheduler from diffusers.utils import make_image_grid, load_image pipe = AutoPipelineForImage2Image.from_pretrained( "Lykon/dreamshaper-7", torch_dtype=torch.float16, variant="fp16", ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdv1-5") # prepare image url = "https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/img2img-init.png" init_image = load_image(url) prompt = "Astronauts in a jungle, cold color palette, muted colors, detailed, 8k" # pass prompt and image to pipeline generator = torch.manual_seed(0) image = pipe( prompt, image=init_image, num_inference_steps=4, guidance_scale=1, strength=0.6, generator=generator ).images[0] make_image_grid([init_image, image], rows=1, cols=2) ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdv1-5_i2i.png) <Tip> You can get different results based on your prompt and the image you provide. To get the best results, we recommend trying different values for `num_inference_steps`, `strength`, and `guidance_scale` parameters and choose the best one. </Tip> ## Combine with styled LoRAs LCM-LoRA can be combined with other LoRAs to generate styled-images in very few steps (4-8). In the following example, we'll use the LCM-LoRA with the [papercut LoRA](TheLastBen/Papercut_SDXL). To learn more about how to combine LoRAs, refer to [this guide](https://huggingface.co/docs/diffusers/tutorials/using_peft_for_inference#combine-multiple-adapters). ```python import torch from diffusers import DiffusionPipeline, LCMScheduler pipe = DiffusionPipeline.from_pretrained( "stabilityai/stable-diffusion-xl-base-1.0", variant="fp16", torch_dtype=torch.float16 ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LoRAs pipe.load_lora_weights("latent-consistency/lcm-lora-sdxl", adapter_name="lcm") pipe.load_lora_weights("TheLastBen/Papercut_SDXL", weight_name="papercut.safetensors", adapter_name="papercut") # Combine LoRAs pipe.set_adapters(["lcm", "papercut"], adapter_weights=[1.0, 0.8]) prompt = "papercut, a cute fox" generator = torch.manual_seed(0) image = pipe(prompt, num_inference_steps=4, guidance_scale=1, generator=generator).images[0] image ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdx_lora_mix.png) ## ControlNet/T2I-Adapter Let's look at how we can perform inference with ControlNet/T2I-Adapter and LCM-LoRA. ### ControlNet For this example, we'll use the SD-v1-5 model and the LCM-LoRA for SD-v1-5 with canny ControlNet. ```python import torch import cv2 import numpy as np from PIL import Image from diffusers import StableDiffusionControlNetPipeline, ControlNetModel, LCMScheduler from diffusers.utils import load_image image = load_image( "https://hf.co/datasets/huggingface/documentation-images/resolve/main/diffusers/input_image_vermeer.png" ).resize((512, 512)) image = np.array(image) low_threshold = 100 high_threshold = 200 image = cv2.Canny(image, low_threshold, high_threshold) image = image[:, :, None] image = np.concatenate([image, image, image], axis=2) canny_image = Image.fromarray(image) controlnet = ControlNetModel.from_pretrained("lllyasviel/sd-controlnet-canny", torch_dtype=torch.float16) pipe = StableDiffusionControlNetPipeline.from_pretrained( "runwayml/stable-diffusion-v1-5", controlnet=controlnet, torch_dtype=torch.float16, safety_checker=None, variant="fp16" ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdv1-5") generator = torch.manual_seed(0) image = pipe( "the mona lisa", image=canny_image, num_inference_steps=4, guidance_scale=1.5, controlnet_conditioning_scale=0.8, cross_attention_kwargs={"scale": 1}, generator=generator, ).images[0] make_image_grid([canny_image, image], rows=1, cols=2) ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdv1-5_controlnet.png) <Tip> The inference parameters in this example might not work for all examples, so we recommend you to try different values for `num_inference_steps`, `guidance_scale`, `controlnet_conditioning_scale` and `cross_attention_kwargs` parameters and choose the best one. </Tip> ### T2I-Adapter This example shows how to use the LCM-LoRA with the [Canny T2I-Adapter](TencentARC/t2i-adapter-canny-sdxl-1.0) and SDXL. ```python import torch import cv2 import numpy as np from PIL import Image from diffusers import StableDiffusionXLAdapterPipeline, T2IAdapter, LCMScheduler from diffusers.utils import load_image, make_image_grid # Prepare image # Detect the canny map in low resolution to avoid high-frequency details image = load_image( "https://huggingface.co/Adapter/t2iadapter/resolve/main/figs_SDXLV1.0/org_canny.jpg" ).resize((384, 384)) image = np.array(image) low_threshold = 100 high_threshold = 200 image = cv2.Canny(image, low_threshold, high_threshold) image = image[:, :, None] image = np.concatenate([image, image, image], axis=2) canny_image = Image.fromarray(image).resize((1024, 1024)) # load adapter adapter = T2IAdapter.from_pretrained("TencentARC/t2i-adapter-canny-sdxl-1.0", torch_dtype=torch.float16, varient="fp16").to("cuda") pipe = StableDiffusionXLAdapterPipeline.from_pretrained( "stabilityai/stable-diffusion-xl-base-1.0", adapter=adapter, torch_dtype=torch.float16, variant="fp16", ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdxl") prompt = "Mystical fairy in real, magic, 4k picture, high quality" negative_prompt = "extra digit, fewer digits, cropped, worst quality, low quality, glitch, deformed, mutated, ugly, disfigured" generator = torch.manual_seed(0) image = pipe( prompt=prompt, negative_prompt=negative_prompt, image=canny_image, num_inference_steps=4, guidance_scale=1.5, adapter_conditioning_scale=0.8, adapter_conditioning_factor=1, generator=generator, ).images[0] make_image_grid([canny_image, image], rows=1, cols=2) ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdxl_t2iadapter.png) ## Inpainting LCM-LoRA can be used for inpainting as well. ```python import torch from diffusers import AutoPipelineForInpainting, LCMScheduler from diffusers.utils import load_image, make_image_grid pipe = AutoPipelineForInpainting.from_pretrained( "runwayml/stable-diffusion-inpainting", torch_dtype=torch.float16, variant="fp16", ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdv1-5") # load base and mask image init_image = load_image("https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/inpaint.png") mask_image = load_image("https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/inpaint_mask.png") # generator = torch.Generator("cuda").manual_seed(92) prompt = "concept art digital painting of an elven castle, inspired by lord of the rings, highly detailed, 8k" generator = torch.manual_seed(0) image = pipe( prompt=prompt, image=init_image, mask_image=mask_image, generator=generator, num_inference_steps=4, guidance_scale=4, ).images[0] make_image_grid([init_image, mask_image, image], rows=1, cols=3) ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdv1-5_inpainting.png) ## AnimateDiff [`AnimateDiff`] allows you to animate images using Stable Diffusion models. To get good results, we need to generate multiple frames (16-24), and doing this with standard SD models can be very slow. LCM-LoRA can be used to speed up the process significantly, as you just need to do 4-8 steps for each frame. Let's look at how we can perform animation with LCM-LoRA and AnimateDiff. ```python import torch from diffusers import MotionAdapter, AnimateDiffPipeline, DDIMScheduler, LCMScheduler from diffusers.utils import export_to_gif adapter = MotionAdapter.from_pretrained("diffusers/animatediff-motion-adapter-v1-5") pipe = AnimateDiffPipeline.from_pretrained( "frankjoshua/toonyou_beta6", motion_adapter=adapter, ).to("cuda") # set scheduler pipe.scheduler = LCMScheduler.from_config(pipe.scheduler.config) # load LCM-LoRA pipe.load_lora_weights("latent-consistency/lcm-lora-sdv1-5", adapter_name="lcm") pipe.load_lora_weights("guoyww/animatediff-motion-lora-zoom-in", weight_name="diffusion_pytorch_model.safetensors", adapter_name="motion-lora") pipe.set_adapters(["lcm", "motion-lora"], adapter_weights=[0.55, 1.2]) prompt = "best quality, masterpiece, 1girl, looking at viewer, blurry background, upper body, contemporary, dress" generator = torch.manual_seed(0) frames = pipe( prompt=prompt, num_inference_steps=5, guidance_scale=1.25, cross_attention_kwargs={"scale": 1}, num_frames=24, generator=generator ).frames[0] export_to_gif(frames, "animation.gif") ``` ![](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/diffusers/lcm/lcm_sdv1-5_animatediff.gif)
huggingface/diffusers/blob/main/examples/consistency_distillation/README_sdxl.md	Latent Consistency Distillation Example: [Latent Consistency Models (LCMs)](https://arxiv.org/abs/2310.04378) is a method to distill a latent diffusion model to enable swift inference with minimal steps. This example demonstrates how to use latent consistency distillation to distill SDXL for inference with few timesteps. ## Full model distillation ### Running locally with PyTorch #### Installing the dependencies Before running the scripts, make sure to install the library's training dependencies: Important To make sure you can successfully run the latest versions of the example scripts, we highly recommend installing from source and keeping the install up to date as we update the example scripts frequently and install some example-specific requirements. To do this, execute the following steps in a new virtual environment: ```bash git clone https://github.com/huggingface/diffusers cd diffusers pip install -e . ``` Then cd in the example folder and run ```bash pip install -r requirements.txt ``` And initialize an [🤗 Accelerate](https://github.com/huggingface/accelerate/) environment with: ```bash accelerate config ``` Or for a default accelerate configuration without answering questions about your environment ```bash accelerate config default ``` Or if your environment doesn't support an interactive shell e.g. a notebook ```python from accelerate.utils import write_basic_config write_basic_config() ``` When running `accelerate config`, if we specify torch compile mode to True there can be dramatic speedups. #### Example The following uses the [Conceptual Captions 12M (CC12M) dataset](https://github.com/google-research-datasets/conceptual-12m) as an example, and for illustrative purposes only. For best results you may consider large and high-quality text-image datasets such as [LAION](https://laion.ai/blog/laion-400-open-dataset/). You may also need to search the hyperparameter space according to the dataset you use. ```bash export MODEL_NAME="stabilityai/stable-diffusion-xl-base-1.0" export OUTPUT_DIR="path/to/saved/model" accelerate launch train_lcm_distill_sdxl_wds.py \ --pretrained_teacher_model=$MODEL_NAME \ --pretrained_vae_model_name_or_path=madebyollin/sdxl-vae-fp16-fix \ --output_dir=$OUTPUT_DIR \ --mixed_precision=fp16 \ --resolution=1024 \ --learning_rate=1e-6 --loss_type="huber" --use_fix_crop_and_size --ema_decay=0.95 --adam_weight_decay=0.0 \ --max_train_steps=1000 \ --max_train_samples=4000000 \ --dataloader_num_workers=8 \ --train_shards_path_or_url="pipe:curl -L -s https://huggingface.co/datasets/laion/conceptual-captions-12m-webdataset/resolve/main/data/{00000..01099}.tar?download=true" \ --validation_steps=200 \ --checkpointing_steps=200 --checkpoints_total_limit=10 \ --train_batch_size=12 \ --gradient_checkpointing --enable_xformers_memory_efficient_attention \ --gradient_accumulation_steps=1 \ --use_8bit_adam \ --resume_from_checkpoint=latest \ --report_to=wandb \ --seed=453645634 \ --push_to_hub \ ``` ## LCM-LoRA Instead of fine-tuning the full model, we can also just train a LoRA that can be injected into any SDXL model. ### Example The following uses the [Conceptual Captions 12M (CC12M) dataset](https://github.com/google-research-datasets/conceptual-12m) as an example. For best results you may consider large and high-quality text-image datasets such as [LAION](https://laion.ai/blog/laion-400-open-dataset/). ```bash export MODEL_NAME="stabilityai/stable-diffusion-xl-base-1.0" export OUTPUT_DIR="path/to/saved/model" accelerate launch train_lcm_distill_lora_sdxl_wds.py \ --pretrained_teacher_model=$MODEL_DIR \ --pretrained_vae_model_name_or_path=madebyollin/sdxl-vae-fp16-fix \ --output_dir=$OUTPUT_DIR \ --mixed_precision=fp16 \ --resolution=1024 \ --lora_rank=64 \ --learning_rate=1e-6 --loss_type="huber" --use_fix_crop_and_size --adam_weight_decay=0.0 \ --max_train_steps=1000 \ --max_train_samples=4000000 \ --dataloader_num_workers=8 \ --train_shards_path_or_url="pipe:curl -L -s https://huggingface.co/datasets/laion/conceptual-captions-12m-webdataset/resolve/main/data/{00000..01099}.tar?download=true" \ --validation_steps=200 \ --checkpointing_steps=200 --checkpoints_total_limit=10 \ --train_batch_size=12 \ --gradient_checkpointing --enable_xformers_memory_efficient_attention \ --gradient_accumulation_steps=1 \ --use_8bit_adam \ --resume_from_checkpoint=latest \ --report_to=wandb \ --seed=453645634 \ --push_to_hub \ ```
huggingface/transformers/blob/main/docs/source/en/model_doc/autoformer.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Autoformer ## Overview The Autoformer model was proposed in [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://arxiv.org/abs/2106.13008) by Haixu Wu, Jiehui Xu, Jianmin Wang, Mingsheng Long. This model augments the Transformer as a deep decomposition architecture, which can progressively decompose the trend and seasonal components during the forecasting process. The abstract from the paper is the following: Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. This model was contributed by [elisim](https://huggingface.co/elisim) and [kashif](https://huggingface.co/kashif). The original code can be found [here](https://github.com/thuml/Autoformer). ## Resources A list of official Hugging Face and community (indicated by 🌎) resources to help you get started. If you're interested in submitting a resource to be included here, please feel free to open a Pull Request and we'll review it! The resource should ideally demonstrate something new instead of duplicating an existing resource. - Check out the Autoformer blog-post in HuggingFace blog: [Yes, Transformers are Effective for Time Series Forecasting (+ Autoformer)](https://huggingface.co/blog/autoformer) ## AutoformerConfig [[autodoc]] AutoformerConfig ## AutoformerModel [[autodoc]] AutoformerModel - forward ## AutoformerForPrediction [[autodoc]] AutoformerForPrediction - forward
huggingface/blog/blob/main/hub-duckdb.md	-- title: "DuckDB: analyze 50,000+ datasets stored on the Hugging Face Hub" thumbnail: /blog/assets/hub_duckdb/hub_duckdb.png authors: - user: stevhliu - user: lhoestq - user: severo --- # DuckDB: run SQL queries on 50,000+ datasets on the Hugging Face Hub The Hugging Face Hub is dedicated to providing open access to datasets for everyone and giving users the tools to explore and understand them. You can find many of the datasets used to train popular large language models (LLMs) like [Falcon](https://huggingface.co/datasets/tiiuae/falcon-refinedweb), [Dolly](https://huggingface.co/datasets/databricks/databricks-dolly-15k), [MPT](https://huggingface.co/datasets/mosaicml/dolly_hhrlhf), and [StarCoder](https://huggingface.co/datasets/bigcode/the-stack). There are tools for addressing fairness and bias in datasets like [Disaggregators](https://huggingface.co/spaces/society-ethics/disaggregators), and tools for previewing examples inside a dataset like the Dataset Viewer. <div class="flex justify-center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/datasets-server/oasst1_light.png"/> </div> <small>A preview of the OpenAssistant dataset with the Dataset Viewer.</small> We are happy to share that we recently added another feature to help you analyze datasets on the Hub; you can run SQL queries with DuckDB on any dataset stored on the Hub! According to the 2022 [StackOverflow Developer Survey](https://survey.stackoverflow.co/2022/#section-most-popular-technologies-programming-scripting-and-markup-languages), SQL is the 3rd most popular programming language. We also wanted a fast database management system (DBMS) designed for running analytical queries, which is why we’re excited about integrating with [DuckDB](https://duckdb.org/). We hope this allows even more users to access and analyze datasets on the Hub! ## TLDR [Datasets Server](https://huggingface.co/docs/datasets-server/index) automatically converts all public datasets on the Hub to Parquet files, that you can see by clicking on the "Auto-converted to Parquet" button at the top of a dataset page. You can also access the list of the Parquet files URLs with a simple HTTP call. ```py r = requests.get("https://datasets-server.huggingface.co/parquet?dataset=blog_authorship_corpus") j = r.json() urls = [f['url'] for f in j['parquet_files'] if f['split'] == 'train'] urls ['https://huggingface.co/datasets/blog_authorship_corpus/resolve/refs%2Fconvert%2Fparquet/blog_authorship_corpus/blog_authorship_corpus-train-00000-of-00002.parquet', 'https://huggingface.co/datasets/blog_authorship_corpus/resolve/refs%2Fconvert%2Fparquet/blog_authorship_corpus/blog_authorship_corpus-train-00001-of-00002.parquet'] ``` Create a connection to DuckDB and install and load the `httpfs` extension to allow reading and writing remote files: ```py import duckdb url = "https://huggingface.co/datasets/blog_authorship_corpus/resolve/refs%2Fconvert%2Fparquet/blog_authorship_corpus/blog_authorship_corpus-train-00000-of-00002.parquet" con = duckdb.connect() con.execute("INSTALL httpfs;") con.execute("LOAD httpfs;") ``` Once you’re connected, you can start writing SQL queries! ```sql con.sql(f"""SELECT horoscope, count(*), AVG(LENGTH(text)) AS avg_blog_length FROM '{url}' GROUP BY horoscope ORDER BY avg_blog_length DESC LIMIT(5)""" ) ``` To learn more, check out the [documentation](https://huggingface.co/docs/datasets-server/parquet_process). ## From dataset to Parquet [Parquet](https://parquet.apache.org/docs/) files are columnar, making them more efficient to store, load and analyze. This is especially important when you're working with large datasets, which we’re seeing more and more of in the LLM era. To support this, Datasets Server automatically converts and publishes any public dataset on the Hub as Parquet files. The URL to the Parquet files can be retrieved with the [`/parquet`](https://huggingface.co/docs/datasets-server/quick_start#access-parquet-files) endpoint. ## Analyze with DuckDB DuckDB offers super impressive performance for running complex analytical queries. It is able to execute a SQL query directly on a remote Parquet file without any overhead. With the [`httpfs`](https://duckdb.org/docs/extensions/httpfs) extension, DuckDB is able to query remote files such as datasets stored on the Hub using the URL provided from the `/parquet` endpoint. DuckDB also supports querying multiple Parquet files which is really convenient because Datasets Server shards big datasets into smaller 500MB chunks. ## Looking forward Knowing what’s inside a dataset is important for developing models because it can impact model quality in all sorts of ways! By allowing users to write and execute any SQL query on Hub datasets, this is another way for us to enable open access to datasets and help users be more aware of the datasets contents. We are excited for you to try this out, and we’re looking forward to what kind of insights your analysis uncovers!
gradio-app/gradio/blob/main/guides/06_integrating-other-frameworks/Gradio-and-Wandb-Integration.md	Gradio and W&B Integration Related spaces: https://huggingface.co/spaces/akhaliq/JoJoGAN Tags: WANDB, SPACES Contributed by Gradio team ## Introduction In this Guide, we'll walk you through: - Introduction of Gradio, and Hugging Face Spaces, and Wandb - How to setup a Gradio demo using the Wandb integration for JoJoGAN - How to contribute your own Gradio demos after tracking your experiments on wandb to the Wandb organization on Hugging Face ## What is Wandb? Weights and Biases (W&B) allows data scientists and machine learning scientists to track their machine learning experiments at every stage, from training to production. Any metric can be aggregated over samples and shown in panels in a customizable and searchable dashboard, like below: <img alt="Screen Shot 2022-08-01 at 5 54 59 PM" src="https://user-images.githubusercontent.com/81195143/182252755-4a0e1ca8-fd25-40ff-8c91-c9da38aaa9ec.png"> ## What are Hugging Face Spaces & Gradio? ### Gradio Gradio lets users demo their machine learning models as a web app, all in a few lines of Python. Gradio wraps any Python function (such as a machine learning model's inference function) into a user interface and the demos can be launched inside jupyter notebooks, colab notebooks, as well as embedded in your own website and hosted on Hugging Face Spaces for free. Get started [here](https://gradio.app/getting_started) ### Hugging Face Spaces Hugging Face Spaces is a free hosting option for Gradio demos. Spaces comes with 3 SDK options: Gradio, Streamlit and Static HTML demos. Spaces can be public or private and the workflow is similar to github repos. There are over 2000+ spaces currently on Hugging Face. Learn more about spaces [here](https://huggingface.co/spaces/launch). ## Setting up a Gradio Demo for JoJoGAN Now, let's walk you through how to do this on your own. We'll make the assumption that you're new to W&B and Gradio for the purposes of this tutorial. Let's get started! 1. Create a W&B account Follow [these quick instructions](https://app.wandb.ai/login) to create your free account if you don’t have one already. It shouldn't take more than a couple minutes. Once you're done (or if you've already got an account), next, we'll run a quick colab. 2. Open Colab Install Gradio and W&B We'll be following along with the colab provided in the JoJoGAN repo with some minor modifications to use Wandb and Gradio more effectively. [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mchong6/JoJoGAN/blob/main/stylize.ipynb) Install Gradio and Wandb at the top: ```sh pip install gradio wandb ``` 3. Finetune StyleGAN and W&B experiment tracking This next step will open a W&B dashboard to track your experiments and a gradio panel showing pretrained models to choose from a drop down menu from a Gradio Demo hosted on Huggingface Spaces. Here's the code you need for that: ```python alpha = 1.0 alpha = 1-alpha preserve_color = True num_iter = 100 log_interval = 50 samples = [] column_names = ["Reference (y)", "Style Code(w)", "Real Face Image(x)"] wandb.init(project="JoJoGAN") config = wandb.config config.num_iter = num_iter config.preserve_color = preserve_color wandb.log( {"Style reference": [wandb.Image(transforms.ToPILImage()(target_im))]}, step=0) # load discriminator for perceptual loss discriminator = Discriminator(1024, 2).eval().to(device) ckpt = torch.load('models/stylegan2-ffhq-config-f.pt', map_location=lambda storage, loc: storage) discriminator.load_state_dict(ckpt["d"], strict=False) # reset generator del generator generator = deepcopy(original_generator) g_optim = optim.Adam(generator.parameters(), lr=2e-3, betas=(0, 0.99)) # Which layers to swap for generating a family of plausible real images -> fake image if preserve_color: id_swap = [9,11,15,16,17] else: id_swap = list(range(7, generator.n_latent)) for idx in tqdm(range(num_iter)): mean_w = generator.get_latent(torch.randn([latents.size(0), latent_dim]).to(device)).unsqueeze(1).repeat(1, generator.n_latent, 1) in_latent = latents.clone() in_latent[:, id_swap] = alphalatents[:, id_swap] + (1-alpha)mean_w[:, id_swap] img = generator(in_latent, input_is_latent=True) with torch.no_grad(): real_feat = discriminator(targets) fake_feat = discriminator(img) loss = sum([F.l1_loss(a, b) for a, b in zip(fake_feat, real_feat)])/len(fake_feat) wandb.log({"loss": loss}, step=idx) if idx % log_interval == 0: generator.eval() my_sample = generator(my_w, input_is_latent=True) generator.train() my_sample = transforms.ToPILImage()(utils.make_grid(my_sample, normalize=True, range=(-1, 1))) wandb.log( {"Current stylization": [wandb.Image(my_sample)]}, step=idx) table_data = [ wandb.Image(transforms.ToPILImage()(target_im)), wandb.Image(img), wandb.Image(my_sample), ] samples.append(table_data) g_optim.zero_grad() loss.backward() g_optim.step() out_table = wandb.Table(data=samples, columns=column_names) wandb.log({"Current Samples": out_table}) ``` alpha = 1.0 alpha = 1-alpha preserve_color = True num_iter = 100 log_interval = 50 samples = [] column_names = ["Referece (y)", "Style Code(w)", "Real Face Image(x)"] wandb.init(project="JoJoGAN") config = wandb.config config.num_iter = num_iter config.preserve_color = preserve_color wandb.log( {"Style reference": [wandb.Image(transforms.ToPILImage()(target_im))]}, step=0) # load discriminator for perceptual loss discriminator = Discriminator(1024, 2).eval().to(device) ckpt = torch.load('models/stylegan2-ffhq-config-f.pt', map_location=lambda storage, loc: storage) discriminator.load_state_dict(ckpt["d"], strict=False) # reset generator del generator generator = deepcopy(original_generator) g_optim = optim.Adam(generator.parameters(), lr=2e-3, betas=(0, 0.99)) # Which layers to swap for generating a family of plausible real images -> fake image if preserve_color: id_swap = [9,11,15,16,17] else: id_swap = list(range(7, generator.n_latent)) for idx in tqdm(range(num_iter)): mean_w = generator.get_latent(torch.randn([latents.size(0), latent_dim]).to(device)).unsqueeze(1).repeat(1, generator.n_latent, 1) in_latent = latents.clone() in_latent[:, id_swap] = alphalatents[:, id_swap] + (1-alpha)mean_w[:, id_swap] img = generator(in_latent, input_is_latent=True) with torch.no_grad(): real_feat = discriminator(targets) fake_feat = discriminator(img) loss = sum([F.l1_loss(a, b) for a, b in zip(fake_feat, real_feat)])/len(fake_feat) wandb.log({"loss": loss}, step=idx) if idx % log_interval == 0: generator.eval() my_sample = generator(my_w, input_is_latent=True) generator.train() my_sample = transforms.ToPILImage()(utils.make_grid(my_sample, normalize=True, range=(-1, 1))) wandb.log( {"Current stylization": [wandb.Image(my_sample)]}, step=idx) table_data = [ wandb.Image(transforms.ToPILImage()(target_im)), wandb.Image(img), wandb.Image(my_sample), ] samples.append(table_data) g_optim.zero_grad() loss.backward() g_optim.step() out_table = wandb.Table(data=samples, columns=column_names) wandb.log({"Current Samples": out_table}) ```` 4. Save, Download, and Load Model Here's how to save and download your model. ```python from PIL import Image import torch torch.backends.cudnn.benchmark = True from torchvision import transforms, utils from util import * import math import random import numpy as np from torch import nn, autograd, optim from torch.nn import functional as F from tqdm import tqdm import lpips from model import * from e4e_projection import projection as e4e_projection from copy import deepcopy import imageio import os import sys import torchvision.transforms as transforms from argparse import Namespace from e4e.models.psp import pSp from util import * from huggingface_hub import hf_hub_download from google.colab import files torch.save({"g": generator.state_dict()}, "your-model-name.pt") files.download('your-model-name.pt') latent_dim = 512 device="cuda" model_path_s = hf_hub_download(repo_id="akhaliq/jojogan-stylegan2-ffhq-config-f", filename="stylegan2-ffhq-config-f.pt") original_generator = Generator(1024, latent_dim, 8, 2).to(device) ckpt = torch.load(model_path_s, map_location=lambda storage, loc: storage) original_generator.load_state_dict(ckpt["g_ema"], strict=False) mean_latent = original_generator.mean_latent(10000) generator = deepcopy(original_generator) ckpt = torch.load("/content/JoJoGAN/your-model-name.pt", map_location=lambda storage, loc: storage) generator.load_state_dict(ckpt["g"], strict=False) generator.eval() plt.rcParams['figure.dpi'] = 150 transform = transforms.Compose( [ transforms.Resize((1024, 1024)), transforms.ToTensor(), transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5)), ] ) def inference(img): img.save('out.jpg') aligned_face = align_face('out.jpg') my_w = e4e_projection(aligned_face, "out.pt", device).unsqueeze(0) with torch.no_grad(): my_sample = generator(my_w, input_is_latent=True) npimage = my_sample[0].cpu().permute(1, 2, 0).detach().numpy() imageio.imwrite('filename.jpeg', npimage) return 'filename.jpeg' ```` 5. Build a Gradio Demo ```python import gradio as gr title = "JoJoGAN" description = "Gradio Demo for JoJoGAN: One Shot Face Stylization. To use it, simply upload your image, or click one of the examples to load them. Read more at the links below." demo = gr.Interface( inference, gr.Image(type="pil"), gr.Image(type="file"), title=title, description=description ) demo.launch(share=True) ``` 6. Integrate Gradio into your W&B Dashboard The last step—integrating your Gradio demo with your W&B dashboard—is just one extra line: ```python demo.integrate(wandb=wandb) ``` Once you call integrate, a demo will be created and you can integrate it into your dashboard or report Outside of W&B with Web components, using the gradio-app tags allows anyone can embed Gradio demos on HF spaces directly into their blogs, websites, documentation, etc.: ```html <gradio-app space="akhaliq/JoJoGAN"> </gradio-app> ``` 7. (Optional) Embed W&B plots in your Gradio App It's also possible to embed W&B plots within Gradio apps. To do so, you can create a W&B Report of your plots and embed them within your Gradio app within a `gr.HTML` block. The Report will need to be public and you will need to wrap the URL within an iFrame like this: ```python import gradio as gr def wandb_report(url): iframe = f'<iframe src={url} style="border:none;height:1024px;width:100%">' return gr.HTML(iframe) with gr.Blocks() as demo: report_url = 'https://wandb.ai/_scott/pytorch-sweeps-demo/reports/loss-22-10-07-16-00-17---VmlldzoyNzU2NzAx' report = wandb_report(report_url) demo.launch(share=True) ``` ## Conclusion We hope you enjoyed this brief demo of embedding a Gradio demo to a W&B report! Thanks for making it to the end. To recap: - Only one single reference image is needed for fine-tuning JoJoGAN which usually takes about 1 minute on a GPU in colab. After training, style can be applied to any input image. Read more in the paper. - W&B tracks experiments with just a few lines of code added to a colab and you can visualize, sort, and understand your experiments in a single, centralized dashboard. - Gradio, meanwhile, demos the model in a user friendly interface to share anywhere on the web. ## How to contribute Gradio demos on HF spaces on the Wandb organization - Create an account on Hugging Face [here](https://huggingface.co/join). - Add Gradio Demo under your username, see this [course](https://huggingface.co/course/chapter9/4?fw=pt) for setting up Gradio Demo on Hugging Face. - Request to join wandb organization [here](https://huggingface.co/wandb). - Once approved transfer model from your username to Wandb organization
gradio-app/gradio/blob/main/demo/duplicatebutton_component/run.ipynb	Gradio Demo: duplicatebutton_component ``` !pip install -q gradio ``` ``` import gradio as gr with gr.Blocks() as demo: gr.DuplicateButton() demo.launch() ```
huggingface/hub-docs/blob/main/docs/hub/models-widgets-examples.md	Widget Examples Note that each widget example can also optionally describe the corresponding model output, directly in the `output` property. See [the spec](./models-widgets#example-outputs) for more details. ## Natural Language Processing ### Fill-Mask ```yaml widget: - text: "Paris is the <mask> of France." example_title: "Capital" - text: "The goal of life is <mask>." example_title: "Philosophy" ``` ### Question Answering ```yaml widget: - text: "What's my name?" context: "My name is Clara and I live in Berkeley." example_title: "Name" - text: "Where do I live?" context: "My name is Sarah and I live in London" example_title: "Location" ``` ### Summarization ```yaml widget: - text: "The tower is 324 metres (1,063 ft) tall, about the same height as an 81-storey building, and the tallest structure in Paris. Its base is square, measuring 125 metres (410 ft) on each side. During its construction, the Eiffel Tower surpassed the Washington Monument to become the tallest man-made structure in the world, a title it held for 41 years until the Chrysler Building in New York City was finished in 1930. It was the first structure to reach a height of 300 metres. Due to the addition of a broadcasting aerial at the top of the tower in 1957, it is now taller than the Chrysler Building by 5.2 metres (17 ft). Excluding transmitters, the Eiffel Tower is the second tallest free-standing structure in France after the Millau Viaduct." example_title: "Eiffel Tower" - text: "Laika, a dog that was the first living creature to be launched into Earth orbit, on board the Soviet artificial satellite Sputnik 2, on November 3, 1957. It was always understood that Laika would not survive the mission, but her actual fate was misrepresented for decades. Laika was a small (13 pounds [6 kg]), even-tempered, mixed-breed dog about two years of age. She was one of a number of stray dogs that were taken into the Soviet spaceflight program after being rescued from the streets. Only female dogs were used because they were considered to be anatomically better suited than males for close confinement." example_title: "First in Space" ``` ### Table Question Answering ```yaml widget: - text: "How many stars does the transformers repository have?" table: Repository: - "Transformers" - "Datasets" - "Tokenizers" Stars: - 36542 - 4512 - 3934 Contributors: - 651 - 77 - 34 Programming language: - "Python" - "Python" - "Rust, Python and NodeJS" example_title: "Github stars" ``` ### Text Classification ```yaml widget: - text: "I love football so much" example_title: "Positive" - text: "I don't really like this type of food" example_title: "Negative" ``` ### Text Generation ```yaml widget: - text: "My name is Julien and I like to" example_title: "Julien" - text: "My name is Merve and my favorite" example_title: "Merve" ``` ### Text2Text Generation ```yaml widget: - text: "My name is Julien and I like to" example_title: "Julien" - text: "My name is Merve and my favorite" example_title: "Merve" ``` ### Token Classification ```yaml widget: - text: "My name is Sylvain and I live in Paris" example_title: "Parisian" - text: "My name is Sarah and I live in London" example_title: "Londoner" ``` ### Translation ```yaml widget: - text: "My name is Sylvain and I live in Paris" example_title: "Parisian" - text: "My name is Sarah and I live in London" example_title: "Londoner" ``` ### Zero-Shot Classification ```yaml widget: - text: "I have a problem with my car that needs to be resolved asap!!" candidate_labels: "urgent, not urgent, phone, tablet, computer" multi_class: true example_title: "Car problem" - text: "Last week I upgraded my iOS version and ever since then my phone has been overheating whenever I use your app." candidate_labels: "mobile, website, billing, account access" multi_class: false example_title: "Phone issue" ``` ### Sentence Similarity ```yaml widget: - source_sentence: "That is a happy person" sentences: - "That is a happy dog" - "That is a very happy person" - "Today is a sunny day" example_title: "Happy" ``` ### Conversational ```yaml widget: - text: "Hey my name is Julien! How are you?" example_title: "Julien" - text: "Hey my name is Clara! How are you?" example_title: "Clara" ``` ### Feature Extraction ```yaml widget: - text: "My name is Sylvain and I live in Paris" example_title: "Parisian" - text: "My name is Sarah and I live in London" example_title: "Londoner" ``` ## Audio ### Text-to-Speech ```yaml widget: - text: "My name is Sylvain and I live in Paris" example_title: "Parisian" - text: "My name is Sarah and I live in London" example_title: "Londoner" ``` ### Automatic Speech Recognition ```yaml widget: - src: https://cdn-media.huggingface.co/speech_samples/sample1.flac example_title: Librispeech sample 1 - src: https://cdn-media.huggingface.co/speech_samples/sample2.flac example_title: Librispeech sample 2 ``` ### Audio-to-Audio ```yaml widget: - src: https://cdn-media.huggingface.co/speech_samples/sample1.flac example_title: Librispeech sample 1 - src: https://cdn-media.huggingface.co/speech_samples/sample2.flac example_title: Librispeech sample 2 ``` ### Audio Classification ```yaml widget: - src: https://cdn-media.huggingface.co/speech_samples/sample1.flac example_title: Librispeech sample 1 - src: https://cdn-media.huggingface.co/speech_samples/sample2.flac example_title: Librispeech sample 2 ``` ### Voice Activity Detection ```yaml widget: - src: https://cdn-media.huggingface.co/speech_samples/sample1.flac example_title: Librispeech sample 1 - src: https://cdn-media.huggingface.co/speech_samples/sample2.flac example_title: Librispeech sample 2 ``` ## Computer Vision ### Image Classification ```yaml widget: - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/tiger.jpg example_title: Tiger - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/teapot.jpg example_title: Teapot ``` ### Object Detection ```yaml widget: - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/football-match.jpg example_title: Football Match - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/airport.jpg example_title: Airport ``` ### Image Segmentation ```yaml widget: - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/football-match.jpg example_title: Football Match - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/airport.jpg example_title: Airport ``` ### Image-to-Image ```yaml widget: - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/canny-edge.jpg prompt: Girl with Pearl Earring # `prompt` field is optional in case the underlying model supports text guidance ``` ### Text-to-Image ```yaml widget: - text: "A cat playing with a ball" example_title: "Cat" - text: "A dog jumping over a fence" example_title: "Dog" ``` ### Document Question Answering ```yaml widget: - text: "What is the invoice number?" src: "https://huggingface.co/spaces/impira/docquery/resolve/2359223c1837a7587402bda0f2643382a6eefeab/invoice.png" - text: "What is the purchase amount?" src: "https://huggingface.co/spaces/impira/docquery/resolve/2359223c1837a7587402bda0f2643382a6eefeab/contract.jpeg" ``` ### Visual Question Answering ```yaml widget: - text: "What animal is it?" src: "https://huggingface.co/datasets/mishig/sample_images/resolve/main/tiger.jpg" - text: "Where is it?" src: "https://huggingface.co/datasets/mishig/sample_images/resolve/main/palace.jpg" ``` ### Zero-Shot Image Classification ```yaml widget: - src: https://huggingface.co/datasets/mishig/sample_images/resolve/main/cat-dog-music.png candidate_labels: playing music, playing sports example_title: Cat & Dog ``` ## Other ### Structured Data Classification ```yaml widget: - structured_data: fixed_acidity: - 7.4 - 7.8 - 10.3 volatile_acidity: - 0.7 - 0.88 - 0.32 citric_acid: - 0 - 0 - 0.45 residual_sugar: - 1.9 - 2.6 - 6.4 chlorides: - 0.076 - 0.098 - 0.073 free_sulfur_dioxide: - 11 - 25 - 5 total_sulfur_dioxide: - 34 - 67 - 13 density: - 0.9978 - 0.9968 - 0.9976 pH: - 3.51 - 3.2 - 3.23 sulphates: - 0.56 - 0.68 - 0.82 alcohol: - 9.4 - 9.8 - 12.6 example_title: "Wine" ```
huggingface/diffusers/blob/main/docs/source/en/api/models/unet.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # UNet1DModel The [UNet](https://huggingface.co/papers/1505.04597) model was originally introduced by Ronneberger et al. for biomedical image segmentation, but it is also commonly used in 🤗 Diffusers because it outputs images that are the same size as the input. It is one of the most important components of a diffusion system because it facilitates the actual diffusion process. There are several variants of the UNet model in 🤗 Diffusers, depending on it's number of dimensions and whether it is a conditional model or not. This is a 1D UNet model. The abstract from the paper is: There is large consent that successful training of deep networks requires many thousand annotated training samples. In this paper, we present a network and training strategy that relies on the strong use of data augmentation to use the available annotated samples more efficiently. The architecture consists of a contracting path to capture context and a symmetric expanding path that enables precise localization. We show that such a network can be trained end-to-end from very few images and outperforms the prior best method (a sliding-window convolutional network) on the ISBI challenge for segmentation of neuronal structures in electron microscopic stacks. Using the same network trained on transmitted light microscopy images (phase contrast and DIC) we won the ISBI cell tracking challenge 2015 in these categories by a large margin. Moreover, the network is fast. Segmentation of a 512x512 image takes less than a second on a recent GPU. The full implementation (based on Caffe) and the trained networks are available at http://lmb.informatik.uni-freiburg.de/people/ronneber/u-net. ## UNet1DModel [[autodoc]] UNet1DModel ## UNet1DOutput [[autodoc]] models.unet_1d.UNet1DOutput
huggingface/blog/blob/main/ai-webtv.md	-- title: "Building an AI WebTV" thumbnail: /blog/assets/156_ai_webtv/thumbnail.gif authors: - user: jbilcke-hf --- # Building an AI WebTV The AI WebTV is an experimental demo to showcase the latest advancements in automatic video and music synthesis. 👉 Watch the stream now by going to the [AI WebTV Space](https://huggingface.co/spaces/jbilcke-hf/AI-WebTV). If you are using a mobile device, you can view the stream from the [Twitch mirror](https://www.twitch.tv/ai_webtv). ![thumbnail.gif](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/thumbnail.gif) # Concept The motivation for the AI WebTV is to demo videos generated with open-source [text-to-video models](https://huggingface.co/tasks/text-to-video) such as Zeroscope and MusicGen, in an entertaining and accessible way. You can find those open-source models on the Hugging Face hub: - For video: [zeroscope_v2_576](https://huggingface.co/cerspense/zeroscope_v2_576w) and [zeroscope_v2_XL](https://huggingface.co/cerspense/zeroscope_v2_XL) - For music: [musicgen-melody](https://huggingface.co/facebook/musicgen-melody) The individual video sequences are purposely made to be short, meaning the WebTV should be seen as a tech demo/showreel rather than an actual show (with an art direction or programming). # Architecture The AI WebTV works by taking a sequence of [video shot](https://en.wikipedia.org/wiki/Shot_(filmmaking)) prompts and passing them to a [text-to-video model](https://huggingface.co/tasks/text-to-video) to generate a sequence of [takes](https://en.wikipedia.org/wiki/Take). Additionally, a base theme and idea (written by a human) are passed through a LLM (in this case, ChatGPT), in order to generate a variety of individual prompts for each video clip. Here's a diagram of the current architecture of the AI WebTV: ![diagram.jpg](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/diagram.jpg) # Implementing the pipeline The WebTV is implemented in NodeJS and TypeScript, and uses various services hosted on Hugging Face. ## The text-to-video model The central video model is Zeroscope V2, a model based on [ModelScope](https://huggingface.co/damo-vilab/modelscope-damo-text-to-video-synthesis). Zeroscope is comprised of two parts that can be chained together: - A first pass with [zeroscope_v2_576](https://huggingface.co/cerspense/zeroscope_v2_576w), to generate a 576x320 video clip - An optional second pass with [zeroscope_v2_XL](https://huggingface.co/cerspense/zeroscope_v2_XL) to upscale the video to 1024x576 👉 You will need to use the same prompt for both the generation and upscaling. ## Calling the video chain To make a quick prototype, the WebTV runs Zeroscope from two duplicated Hugging Face Spaces running [Gradio](https://github.com/gradio-app/gradio/), which are called using the [@gradio/client](https://www.npmjs.com/package/@gradio/client) NPM package. You can find the original spaces here: - [zeroscope-v2](https://huggingface.co/spaces/hysts/zeroscope-v2/tree/main) by @hysts - [Zeroscope XL](https://huggingface.co/spaces/fffiloni/zeroscope-XL) by @fffiloni Other spaces deployed by the community can also be found if you [search for Zeroscope on the Hub](https://huggingface.co/spaces?search=zeroscope). 👉 Public Spaces may become overcrowded and paused at any time. If you intend to deploy your own system, please duplicate those Spaces and run them under your own account. ## Using a model hosted on a Space Spaces using Gradio have the ability to [expose a REST API](https://www.gradio.app/guides/sharing-your-app#api-page), which can then be called from Node using the [@gradio/client](https://www.npmjs.com/package/@gradio/client) module. Here is an example: ```typescript import { client } from "@gradio/client" export const generateVideo = async (prompt: string) => { const api = await client("* URL OF THE SPACE ") // call the "run()" function with an array of parameters const { data } = await api.predict("/run", [ prompt, 42, // seed 24, // nbFrames 35 // nbSteps ]) const { orig_name } = data[0][0] const remoteUrl = `${instance}/file=${orig_name}` // the file can then be downloaded and stored locally } ``` ## Post-processing Once an individual take (a video clip) is upscaled, it is then passed to FILM (Frame Interpolation for Large Motion), a frame interpolation algorithm: - Original links: [website](https://film-net.github.io/), [source code](https://github.com/google-research/frame-interpolation) - Model on Hugging Face: [/frame-interpolation-film-style](https://huggingface.co/akhaliq/frame-interpolation-film-style) - A Hugging Face Space you can duplicate: [video_frame_interpolation](https://huggingface.co/spaces/fffiloni/video_frame_interpolation/blob/main/app.py) by @fffiloni During post-processing, we also add music generated with MusicGen: - Original links: [website](https://ai.honu.io/papers/musicgen/), [source code](https://github.com/facebookresearch/audiocraft) - Hugging Face Space you can duplicate: [MusicGen](https://huggingface.co/spaces/facebook/MusicGen) ## Broadcasting the stream Note: there are multiple tools you can use to create a video stream. The AI WebTV currently uses [FFmpeg](https://ffmpeg.org/documentation.html) to read a playlist made of mp4 videos files and m4a audio files. Here is an example of creating such a playlist: ```typescript import { promises as fs } from "fs" import path from "path" const allFiles = await fs.readdir("* PATH TO VIDEO FOLDER ") const allVideos = allFiles .map(file => path.join(dir, file)) .filter(filePath => filePath.endsWith('.mp4')) let playlist = 'ffconcat version 1.0\n' allFilePaths.forEach(filePath => { playlist += `file '${filePath}'\n` }) await fs.promises.writeFile("playlist.txt", playlist) ``` This will generate the following playlist content: ```bash ffconcat version 1.0 file 'video1.mp4' file 'video2.mp4' ... ``` FFmpeg is then used again to read this playlist and send a [FLV stream](https://en.wikipedia.org/wiki/Flash_Video) to a [RTMP server](https://en.wikipedia.org/wiki/Real-Time_Messaging_Protocol). FLV is an old format but still popular in the world of real-time streaming due to its low latency. ```bash ffmpeg -y -nostdin \ -re \ -f concat \ -safe 0 -i channel_random.txt -stream_loop -1 \ -loglevel error \ -c:v libx264 -preset veryfast -tune zerolatency \ -shortest \ -f flv rtmp://<SERVER> ``` There are many different configuration options for FFmpeg, for more information in the [official documentation](http://trac.ffmpeg.org/wiki/StreamingGuide). For the RTMP server, you can find [open-source implementations on GitHub](https://github.com/topics/rtmp-server), such as the [NGINX-RTMP module](https://github.com/arut/nginx-rtmp-module). The AI WebTV itself uses [node-media-server](https://github.com/illuspas/Node-Media-Server). 💡 You can also directly stream to [one of the Twitch RTMP entrypoints](https://help.twitch.tv/s/twitch-ingest-recommendation?language=en_US). Check out the Twitch documentation for more details. # Observations and examples Here are some examples of the generated content. The first thing we notice is that applying the second pass of Zeroscope XL significantly improves the quality of the image. The impact of frame interpolation is also clearly visible. ## Characters and scene composition <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo4.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo4.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Photorealistic movie of a <strong>llama acting as a programmer, wearing glasses and a hoodie</strong>, intensely <strong>staring at a screen</strong> with lines of code, in a cozy, <strong>dimly lit room</strong>, Canon EOS, ambient lighting, high details, cinematic, trending on artstation</i></figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo5.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo5.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>3D rendered animation showing a group of food characters <strong>forming a pyramid</strong>, with a <strong>banana</strong> standing triumphantly on top. In a city with <strong>cotton candy clouds</strong> and <strong>chocolate road</strong>, Pixar's style, CGI, ambient lighting, direct sunlight, rich color scheme, ultra realistic, cinematic, photorealistic.</i></figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo7.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo7.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Intimate <strong>close-up of a red fox, gazing into the camera with sharp eyes</strong>, ambient lighting creating a high contrast silhouette, IMAX camera, <strong>high detail</strong>, <strong>cinematic effect</strong>, golden hour, film grain.</i></figcaption> </figure> ## Simulation of dynamic scenes Something truly fascinating about text-to-video models is their ability to emulate real-life phenomena they have been trained on. We've seen it with large language models and their ability to synthesize convincing content that mimics human responses, but this takes things to a whole new dimension when applied to video. A video model predicts the next frames of a scene, which might include objects in motion such as fluids, people, animals, or vehicles. Today, this emulation isn't perfect, but it will be interesting to evaluate future models (trained on larger or specialized datasets, such as animal locomotion) for their accuracy when reproducing physical phenomena, and also their ability to simulate the behavior of agents. <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo17.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo17.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Cinematic movie shot of <strong>bees energetically buzzing around a flower</strong>, sun rays illuminating the scene, captured in 4k IMAX with a soft bokeh background.</i></figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo8.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo8.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i><strong>Dynamic footage of a grizzly bear catching a salmon in a rushing river</strong>, ambient lighting highlighting the splashing water, low angle, IMAX camera, 4K movie quality, golden hour, film grain.</i></figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo18.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo18.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Aerial footage of a quiet morning at the coast of California, with <strong>waves gently crashing against the rocky shore</strong>. A startling sunrise illuminates the coast with vibrant colors, captured beautifully with a DJI Phantom 4 Pro. Colors and textures of the landscape come alive under the soft morning light. Film grain, cinematic, imax, movie</i></figcaption> </figure> 💡 It will be interesting to see these capabilities explored more in the future, for instance by training video models on larger video datasets covering more phenomena. ## Styling and effects <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo0.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo0.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i> <strong>3D rendered video</strong> of a friendly broccoli character wearing a hat, walking in a candy-filled city street with gingerbread houses, under a <strong>bright sun and blue skies</strong>, <strong>Pixar's style</strong>, cinematic, photorealistic, movie, <strong>ambient lighting</strong>, natural lighting, <strong>CGI</strong>, wide-angle view, daytime, ultra realistic.</i> </figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo2.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo2.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i><strong>Cinematic movie</strong>, shot of an astronaut and a llama at dawn, the mountain landscape bathed in <strong>soft muted colors</strong>, early morning fog, dew glistening on fur, craggy peaks, vintage NASA suit, Canon EOS, high detailed skin, epic composition, high quality, 4K, trending on artstation, beautiful</i> </figcaption> </figure> <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="demo1.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/demo1.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Panda and black cat <strong>navigating down the flowing river</strong> in a small boat, Studio Ghibli style > Cinematic, beautiful composition > IMAX <strong>camera panning following the boat</strong> > High quality, cinematic, movie, mist effect, film grain, trending on Artstation</i> </figcaption> </figure> ## Failure cases Wrong direction: the model sometimes has trouble with movement and direction. For instance, here the clip seems to be played in reverse. Also the modifier keyword green was not taken into account. <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="fail1.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/fail1.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Movie showing a <strong>green pumpkin</strong> falling into a bed of nails, slow-mo explosion with chunks flying all over, ambient fog adding to the dramatic lighting, filmed with IMAX camera, 8k ultra high definition, high quality, trending on artstation.</i> </figcaption> </figure> Rendering errors on realistic scenes: sometimes we can see artifacts such as moving vertical lines or waves. It is unclear what causes this, but it may be due to the combination of keywords used. <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="fail2.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/fail2.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Film shot of a captivating flight above the Grand Canyon, ledges and plateaus etched in orange and red. <strong>Deep shadows contrast</strong> with the fiery landscape under the midday sun, shot with DJI Phantom 4 Pro. The camera rotates to capture the vastness, <strong>textures</strong> and colors, in imax quality. Film <strong>grain</strong>, cinematic, movie.</i> </figcaption> </figure> Text or objects inserted into the image:** the model sometimes injects words from the prompt into the scene, such as "IMAX". Mentioning "Canon EOS" or "Drone footage" in the prompt can also make those objects appear in the video. In the following example, we notice the word "llama" inserts a llama but also two occurrences of the word llama in flames. <figure class="image flex flex-col items-center text-center m-0 w-full"> <video alt="fail3.mp4" autoplay loop autobuffer muted playsinline > <source src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/156_ai_webtv/fail3.mp4" type="video/mp4"> </video> <figcaption>Prompt: <i>Movie scene of a <strong>llama</strong> acting as a firefighter, in firefighter uniform, dramatically spraying water at <strong>roaring flames</strong>, amidst a chaotic urban scene, Canon EOS, ambient lighting, high quality, award winning, highly detailed fur, cinematic, trending on artstation.</i> </figcaption> </figure> # Recommendations Here are some early recommendations that can be made from the previous observations: ## Using video-specific prompt keywords You may already know that if you don’t prompt a specific aspect of the image with Stable Diffusion, things like the color of clothes or the time of the day might become random, or be assigned a generic value such as a neutral mid-day light. The same is true for video models: you will want to be specific about things. Examples include camera and character movement, their orientation, speed and direction. You can leave it unspecified for creative purposes (idea generation), but this might not always give you the results you want (e.g., entities animated in reverse). ## Maintaining consistency between scenes If you plan to create sequences of multiple videos, you will want to make sure you add as many details as possible in each prompt, otherwise you may lose important details from one sequence to another, such as the color. 💡 This will also improve the quality of the image since the prompt is used for the upscaling part with Zeroscope XL. ## Leverage frame interpolation Frame interpolation is a powerful tool which can repair small rendering errors and turn many defects into features, especially in scenes with a lot of animation, or where a cartoon effect is acceptable. The [FILM algorithm](https://film-net.github.io/) will smoothen out elements of a frame with previous and following events in the video clip. This works great to displace the background when the camera is panning or rotating, and will also give you creative freedom, such as control over the number of frames after the generation, to make slow-motion effects. # Future work We hope you enjoyed watching the AI WebTV stream and that it will inspire you to build more in this space. As this was a first trial, a lot of things were not the focus of the tech demo: generating longer and more varied sequences, adding audio (sound effects, dialogue), generating and orchestrating complex scenarios, or letting a language model agent have more control over the pipeline. Some of these ideas may make their way into future updates to the AI WebTV, but we also can’t wait to see what the community of researchers, engineers and builders will come up with!
huggingface/diffusers/blob/main/src/diffusers/pipelines/stable_diffusion/README.md	Stable Diffusion ## Overview Stable Diffusion was proposed in [Stable Diffusion Announcement](https://stability.ai/blog/stable-diffusion-announcement) by Patrick Esser and Robin Rombach and the Stability AI team. The summary of the model is the following: Stable Diffusion is a text-to-image model that will empower billions of people to create stunning art within seconds. It is a breakthrough in speed and quality meaning that it can run on consumer GPUs. You can see some of the amazing output that has been created by this model without pre or post-processing on this page. The model itself builds upon the work of the team at CompVis and Runway in their widely used latent diffusion model combined with insights from the conditional diffusion models by our lead generative AI developer Katherine Crowson, Dall-E 2 by Open AI, Imagen by Google Brain and many others. We are delighted that AI media generation is a cooperative field and hope it can continue this way to bring the gift of creativity to all. ## Tips: - Stable Diffusion has the same architecture as [Latent Diffusion](https://arxiv.org/abs/2112.10752) but uses a frozen CLIP Text Encoder instead of training the text encoder jointly with the diffusion model. - An in-detail explanation of the Stable Diffusion model can be found under [Stable Diffusion with 🧨 Diffusers](https://huggingface.co/blog/stable_diffusion). - If you don't want to rely on the Hugging Face Hub and having to pass a authentication token, you can download the weights with `git lfs install; git clone https://huggingface.co/runwayml/stable-diffusion-v1-5` and instead pass the local path to the cloned folder to `from_pretrained` as shown below. - Stable Diffusion can work with a variety of different samplers as is shown below. ## Available Pipelines: \| Pipeline \| Tasks \| Colab \|---\|---\|:---:\| \| [pipeline_stable_diffusion.py](https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py) \| Text-to-Image Generation \| [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/diffusers/training_example.ipynb) \| [pipeline_stable_diffusion_img2img](https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py) \| Image-to-Image Text-Guided Generation \| [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/diffusers/image_2_image_using_diffusers.ipynb) \| [pipeline_stable_diffusion_inpaint](https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py) \| Text-Guided Image Inpainting \| [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/diffusers/in_painting_with_stable_diffusion_using_diffusers.ipynb) ## Examples: ### Using Stable Diffusion without being logged into the Hub. If you want to download the model weights using a single Python line, you need to be logged in via `huggingface-cli login`. ```python from diffusers import DiffusionPipeline pipeline = DiffusionPipeline.from_pretrained("runwayml/stable-diffusion-v1-5") ``` This however can make it difficult to build applications on top of `diffusers` as you will always have to pass the token around. A potential way to solve this issue is by downloading the weights to a local path `"./stable-diffusion-v1-5"`: ``` git lfs install git clone https://huggingface.co/runwayml/stable-diffusion-v1-5 ``` and simply passing the local path to `from_pretrained`: ```python from diffusers import StableDiffusionPipeline pipe = StableDiffusionPipeline.from_pretrained("./stable-diffusion-v1-5") ``` ### Text-to-Image with default PLMS scheduler ```python # make sure you're logged in with `huggingface-cli login` from diffusers import StableDiffusionPipeline pipe = StableDiffusionPipeline.from_pretrained("runwayml/stable-diffusion-v1-5") pipe = pipe.to("cuda") prompt = "a photo of an astronaut riding a horse on mars" image = pipe(prompt).images[0] image.save("astronaut_rides_horse.png") ``` ### Text-to-Image with DDIM scheduler ```python # make sure you're logged in with `huggingface-cli login` from diffusers import StableDiffusionPipeline, DDIMScheduler scheduler = DDIMScheduler.from_pretrained("CompVis/stable-diffusion-v1-4", subfolder="scheduler") pipe = StableDiffusionPipeline.from_pretrained( "runwayml/stable-diffusion-v1-5", scheduler=scheduler, ).to("cuda") prompt = "a photo of an astronaut riding a horse on mars" image = pipe(prompt).images[0] image.save("astronaut_rides_horse.png") ``` ### Text-to-Image with K-LMS scheduler ```python # make sure you're logged in with `huggingface-cli login` from diffusers import StableDiffusionPipeline, LMSDiscreteScheduler lms = LMSDiscreteScheduler.from_pretrained("CompVis/stable-diffusion-v1-4", subfolder="scheduler") pipe = StableDiffusionPipeline.from_pretrained( "runwayml/stable-diffusion-v1-5", scheduler=lms, ).to("cuda") prompt = "a photo of an astronaut riding a horse on mars" image = pipe(prompt).images[0] image.save("astronaut_rides_horse.png") ``` ### CycleDiffusion using Stable Diffusion and DDIM scheduler ```python import requests import torch from PIL import Image from io import BytesIO from diffusers import CycleDiffusionPipeline, DDIMScheduler # load the scheduler. CycleDiffusion only supports stochastic schedulers. # load the pipeline # make sure you're logged in with `huggingface-cli login` model_id_or_path = "CompVis/stable-diffusion-v1-4" scheduler = DDIMScheduler.from_pretrained(model_id_or_path, subfolder="scheduler") pipe = CycleDiffusionPipeline.from_pretrained(model_id_or_path, scheduler=scheduler).to("cuda") # let's download an initial image url = "https://raw.githubusercontent.com/ChenWu98/cycle-diffusion/main/data/dalle2/An%20astronaut%20riding%20a%20horse.png" response = requests.get(url) init_image = Image.open(BytesIO(response.content)).convert("RGB") init_image = init_image.resize((512, 512)) init_image.save("horse.png") # let's specify a prompt source_prompt = "An astronaut riding a horse" prompt = "An astronaut riding an elephant" # call the pipeline image = pipe( prompt=prompt, source_prompt=source_prompt, image=init_image, num_inference_steps=100, eta=0.1, strength=0.8, guidance_scale=2, source_guidance_scale=1, ).images[0] image.save("horse_to_elephant.png") # let's try another example # See more samples at the original repo: https://github.com/ChenWu98/cycle-diffusion url = "https://raw.githubusercontent.com/ChenWu98/cycle-diffusion/main/data/dalle2/A%20black%20colored%20car.png" response = requests.get(url) init_image = Image.open(BytesIO(response.content)).convert("RGB") init_image = init_image.resize((512, 512)) init_image.save("black.png") source_prompt = "A black colored car" prompt = "A blue colored car" # call the pipeline torch.manual_seed(0) image = pipe( prompt=prompt, source_prompt=source_prompt, image=init_image, num_inference_steps=100, eta=0.1, strength=0.85, guidance_scale=3, source_guidance_scale=1, ).images[0] image.save("black_to_blue.png") ```
huggingface/huggingface_hub/blob/main/README_hi.md	p align="center"> <br/> <img alt="huggingface_hub library logo" src="https://huggingface.co/datasets/huggingface/documentation-images/raw/main/huggingface_hub.svg" width="376" height="59" style="max-width: 100%;"> <br/> </p> <p align="center"> <i>Huggingface Hub के लिए आधिकारिक पायथन क्लाइंट।</i> </p> <p align="center"> <a href="https://huggingface.co/docs/huggingface_hub/ko/index"><img alt="Documentation" src="https://img.shields.io/website/http/huggingface.co/docs/huggingface_hub/index.svg?down_color=red&down_message=offline&up_message=online&label=doc"></a> <a href="https://github.com/huggingface/huggingface_hub/releases"><img alt="GitHub release" src="https://img.shields.io/github/release/huggingface/huggingface_hub.svg"></a> <a href="https://github.com/huggingface/huggingface_hub"><img alt="PyPi version" src="https://img.shields.io/pypi/pyversions/huggingface_hub.svg"></a> <a href="https://pypi.org/project/huggingface-hub"><img alt="downloads" src="https://static.pepy.tech/badge/huggingface_hub/month"></a> <a href="https://codecov.io/gh/huggingface/huggingface_hub"><img alt="Code coverage" src="https://codecov.io/gh/huggingface/huggingface_hub/branch/main/graph/badge.svg?token=RXP95LE2XL"></a> </p> <h4 align="center"> <p> <a href="https://github.com/huggingface/huggingface_hub/blob/main/README.md">English</a> \| <a href="https://github.com/huggingface/huggingface_hub/blob/main/README_de.md">Deutsch</a> \| <b>हिंदी</b> \| <a href="https://github.com/huggingface/huggingface_hub/blob/main/README_ko.md">한국어</a> \| <a href="https://github.com/huggingface/huggingface_hub/blob/main/README_cn.md">中文（简体）</a> <p> </h4> --- दस्तावेज़ीकरण: <a href="https://hf.co/docs/huggingface_hub" target="_blank">https://hf.co/docs/huggingface_hub</a> सोर्स कोड: <a href="https://github.com/huggingface/huggingface_hub" target="_blank">https://github.com/huggingface/huggingface_hub</a> --- ## huggingface_hub लाइब्रेरी में आपका स्वागत है `huggingface_hub` लाइब्रेरी आपको [हगिंग फेस हब](https://huggingface.co/) के साथ बातचीत करने की अनुमति देती है, जो रचनाकारों और सहयोगियों के लिए ओपन-सोर्स मशीन लर्निंग का लोकतंत्रीकरण करने वाला एक मंच है। अपनी परियोजनाओं के लिए पूर्व-प्रशिक्षित मॉडल और डेटासेट खोजें या हब पर होस्ट किए गए हजारों मशीन लर्निंग ऐप्स के साथ खेलें। आप समुदाय के साथ अपने स्वयं के मॉडल, डेटासेट और डेमो भी बना और साझा कर सकते हैं। `huggingface_hub` लाइब्रेरी पायथन के साथ इन सभी चीजों को करने का एक आसान तरीका प्रदान करती है। ## प्रमुख विशेषताऐं - [फ़ाइलें डाउनलोड करें](https://huggingface.co/docs/huggingface_hub/en/guides/download) हब से। - [फ़ाइलें अपलोड करें](https://huggingface.co/docs/huggingface_hub/en/guides/upload) हब पर। - [अपनी रिपॉजिटरी प्रबंधित करें](https://huggingface.co/docs/huggingface_hub/en/guides/repository)। - तैनात मॉडलों पर [अनुमान चलाएँ](https://huggingface.co/docs/huggingface_hub/en/guides/inference)। - मॉडल, डेटासेट और स्पेस के लिए [खोज](https://huggingface.co/docs/huggingface_hub/en/guides/search)। - [मॉडल कार्ड साझा करें](https://huggingface.co/docs/huggingface_hub/en/guides/model-cards) अपने मॉडलों का दस्तावेजीकरण करने के लिए। - [समुदाय के साथ जुड़ें](https://huggingface.co/docs/huggingface_hub/en/guides/community) पीआर और टिप्पणियों के माध्यम से। ## स्थापना [pip](https://pypi.org/project/huggingface-hub/) के साथ `huggingface_hub` पैकेज इंस्टॉल करें: ```bash pip install huggingface_hub ``` यदि आप चाहें, तो आप इसे [conda](https://huggingface.co/docs/huggingface_hub/en/installation#install-with-conda) से भी इंस्टॉल कर सकते हैं। पैकेज को डिफ़ॉल्ट रूप से न्यूनतम रखने के लिए, `huggingface_hub` कुछ उपयोग मामलों के लिए उपयोगी वैकल्पिक निर्भरता के साथ आता है। उदाहरण के लिए, यदि आप अनुमान के लिए संपूर्ण अनुभव चाहते हैं, तो चलाएँ: ```bash pip install huggingface_hub[inference] ``` अधिक इंस्टॉलेशन और वैकल्पिक निर्भरता जानने के लिए, [इंस्टॉलेशन गाइड](https://huggingface.co/docs/huggingface_hub/en/installation) देखें। ## जल्दी शुरू ### फ़ाइलें डाउनलोड करें एकल फ़ाइल डाउनलोड करें ```py from huggingface_hub import hf_hub_download hf_hub_download(repo_id="tiiuae/falcon-7b-instruct", filename="config.json") ``` या एक संपूर्ण भंडार ```py from huggingface_hub import snapshot_download snapshot_download("stabilityai/stable-diffusion-2-1") ``` फ़ाइलें स्थानीय कैश फ़ोल्डर में डाउनलोड की जाएंगी. [this_guide] में अधिक विवरण (https://huggingface.co/docs/huggingface_hub/en/guides/manage-cache)। ### लॉग इन करें Hugging Face Hub एप्लिकेशन को प्रमाणित करने के लिए टोकन का उपयोग करता है (देखें [docs](https://huggingface.co/docs/hub/security-tokens))। अपनी मशीन में लॉगिन करने के लिए, निम्नलिखित सीएलआई चलाएँ: ```bash huggingface-cli login # या कृपया इसे एक पर्यावरण चर के रूप में निर्दिष्ट करें। huggingface-cli login --token $HUGGINGFACE_TOKEN ``` ### एक रिपॉजिटरी बनाएं ```py from huggingface_hub import create_repo create_repo(repo_id="super-cool-model") ``` ### फाइलें अपलोड करें एकल फ़ाइल अपलोड करें ```py from huggingface_hub import upload_file upload_file( path_or_fileobj="/home/lysandre/dummy-test/README.md", path_in_repo="README.md", repo_id="lysandre/test-model", ) ``` या एक संपूर्ण फ़ोल्डर ```py from huggingface_hub import upload_folder upload_folder( folder_path="/path/to/local/space", repo_id="username/my-cool-space", repo_type="space", ) ``` [अपलोड गाइड](https://huggingface.co/docs/huggingface_hub/en/guides/upload) में विवरण के लिए। ## हब से एकीकरण। हम मुफ्त मॉडल होस्टिंग और वर्जनिंग प्रदान करने के लिए शानदार ओपन सोर्स एमएल लाइब्रेरीज़ के साथ साझेदारी कर रहे हैं। आप मौजूदा एकीकरण [यहां](https://huggingface.co/docs/hub/libraries) पा सकते हैं। फायदे ये हैं: - पुस्तकालयों और उनके उपयोगकर्ताओं के लिए निःशुल्क मॉडल या डेटासेट होस्टिंग। - गिट-आधारित दृष्टिकोण के कारण, बहुत बड़ी फ़ाइलों के साथ भी अंतर्निहित फ़ाइल संस्करणिंग। - सभी मॉडलों के लिए होस्टेड अनुमान एपीआई सार्वजनिक रूप से उपलब्ध है। - अपलोड किए गए मॉडलों के साथ खेलने के लिए इन-ब्राउज़र विजेट। - कोई भी आपकी लाइब्रेरी के लिए एक नया मॉडल अपलोड कर सकता है, उन्हें मॉडल को खोजने योग्य बनाने के लिए बस संबंधित टैग जोड़ना होगा। - तेज़ डाउनलोड! हम डाउनलोड को जियो-रेप्लिकेट करने के लिए क्लाउडफ्रंट (एक सीडीएन) का उपयोग करते हैं ताकि वे दुनिया में कहीं से भी तेजी से चमक सकें। - उपयोग आँकड़े और अधिक सुविधाएँ आने वाली हैं। यदि आप अपनी लाइब्रेरी को एकीकृत करना चाहते हैं, तो चर्चा शुरू करने के लिए बेझिझक एक मुद्दा खोलें। हमने ❤️ के साथ एक [चरण-दर-चरण मार्गदर्शिका](https://huggingface.co/docs/hub/adding-a-library) लिखी, जिसमें दिखाया गया कि यह एकीकरण कैसे करना है। ## योगदान (सुविधा अनुरोध, बग, आदि) का अति स्वागत है 💙💚💛💜🧡❤️ योगदान के लिए हर किसी का स्वागत है और हम हर किसी के योगदान को महत्व देते हैं। कोड समुदाय की मदद करने का एकमात्र तरीका नहीं है। प्रश्नों का उत्तर देना, दूसरों की मदद करना, उन तक पहुंचना और दस्तावेज़ों में सुधार करना समुदाय के लिए बेहद मूल्यवान है। हमने संक्षेप में बताने के लिए एक [योगदान मार्गदर्शिका](https://github.com/huggingface/huggingface_hub/blob/main/CONTRIBUTING.md) लिखी है इस भंडार में योगदान करने की शुरुआत कैसे करें।
huggingface/transformers/blob/main/docs/source/en/model_doc/lxmert.md	!--Copyright 2020 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # LXMERT ## Overview The LXMERT model was proposed in [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://arxiv.org/abs/1908.07490) by Hao Tan & Mohit Bansal. It is a series of bidirectional transformer encoders (one for the vision modality, one for the language modality, and then one to fuse both modalities) pretrained using a combination of masked language modeling, visual-language text alignment, ROI-feature regression, masked visual-attribute modeling, masked visual-object modeling, and visual-question answering objectives. The pretraining consists of multiple multi-modal datasets: MSCOCO, Visual-Genome + Visual-Genome Question Answering, VQA 2.0, and GQA. The abstract from the paper is the following: Vision-and-language reasoning requires an understanding of visual concepts, language semantics, and, most importantly, the alignment and relationships between these two modalities. We thus propose the LXMERT (Learning Cross-Modality Encoder Representations from Transformers) framework to learn these vision-and-language connections. In LXMERT, we build a large-scale Transformer model that consists of three encoders: an object relationship encoder, a language encoder, and a cross-modality encoder. Next, to endow our model with the capability of connecting vision and language semantics, we pre-train the model with large amounts of image-and-sentence pairs, via five diverse representative pretraining tasks: masked language modeling, masked object prediction (feature regression and label classification), cross-modality matching, and image question answering. These tasks help in learning both intra-modality and cross-modality relationships. After fine-tuning from our pretrained parameters, our model achieves the state-of-the-art results on two visual question answering datasets (i.e., VQA and GQA). We also show the generalizability of our pretrained cross-modality model by adapting it to a challenging visual-reasoning task, NLVR, and improve the previous best result by 22% absolute (54% to 76%). Lastly, we demonstrate detailed ablation studies to prove that both our novel model components and pretraining strategies significantly contribute to our strong results; and also present several attention visualizations for the different encoders This model was contributed by [eltoto1219](https://huggingface.co/eltoto1219). The original code can be found [here](https://github.com/airsplay/lxmert). ## Usage tips - Bounding boxes are not necessary to be used in the visual feature embeddings, any kind of visual-spacial features will work. - Both the language hidden states and the visual hidden states that LXMERT outputs are passed through the cross-modality layer, so they contain information from both modalities. To access a modality that only attends to itself, select the vision/language hidden states from the first input in the tuple. - The bidirectional cross-modality encoder attention only returns attention values when the language modality is used as the input and the vision modality is used as the context vector. Further, while the cross-modality encoder contains self-attention for each respective modality and cross-attention, only the cross attention is returned and both self attention outputs are disregarded. ## Resources - [Question answering task guide](../tasks/question_answering) ## LxmertConfig [[autodoc]] LxmertConfig ## LxmertTokenizer [[autodoc]] LxmertTokenizer ## LxmertTokenizerFast [[autodoc]] LxmertTokenizerFast ## Lxmert specific outputs [[autodoc]] models.lxmert.modeling_lxmert.LxmertModelOutput [[autodoc]] models.lxmert.modeling_lxmert.LxmertForPreTrainingOutput [[autodoc]] models.lxmert.modeling_lxmert.LxmertForQuestionAnsweringOutput [[autodoc]] models.lxmert.modeling_tf_lxmert.TFLxmertModelOutput [[autodoc]] models.lxmert.modeling_tf_lxmert.TFLxmertForPreTrainingOutput <frameworkcontent> <pt> ## LxmertModel [[autodoc]] LxmertModel - forward ## LxmertForPreTraining [[autodoc]] LxmertForPreTraining - forward ## LxmertForQuestionAnswering [[autodoc]] LxmertForQuestionAnswering - forward </pt> <tf> ## TFLxmertModel [[autodoc]] TFLxmertModel - call ## TFLxmertForPreTraining [[autodoc]] TFLxmertForPreTraining - call </tf> </frameworkcontent>
huggingface/tokenizers/blob/main/docs/source-doc-builder/pipeline.mdx	The tokenization pipeline When calling `Tokenizer.encode` or `Tokenizer.encode_batch`, the input text(s) go through the following pipeline: - `normalization` - `pre-tokenization` - `model` - `post-processing` We'll see in details what happens during each of those steps in detail, as well as when you want to `decode <decoding>` some token ids, and how the 🤗 Tokenizers library allows you to customize each of those steps to your needs. If you're already familiar with those steps and want to learn by seeing some code, jump to `our BERT from scratch example <example>`. For the examples that require a `Tokenizer` we will use the tokenizer we trained in the `quicktour`, which you can load with: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START reload_tokenizer", "end-before": "END reload_tokenizer", "dedent": 12} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_reload_tokenizer", "end-before": "END pipeline_reload_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START reload_tokenizer", "end-before": "END reload_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> ## Normalization Normalization is, in a nutshell, a set of operations you apply to a raw string to make it less random or "cleaner". Common operations include stripping whitespace, removing accented characters or lowercasing all text. If you're familiar with [Unicode normalization](https://unicode.org/reports/tr15), it is also a very common normalization operation applied in most tokenizers. Each normalization operation is represented in the 🤗 Tokenizers library by a `Normalizer`, and you can combine several of those by using a `normalizers.Sequence`. Here is a normalizer applying NFD Unicode normalization and removing accents as an example: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START setup_normalizer", "end-before": "END setup_normalizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_setup_normalizer", "end-before": "END pipeline_setup_normalizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START setup_normalizer", "end-before": "END setup_normalizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> You can manually test that normalizer by applying it to any string: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START test_normalizer", "end-before": "END test_normalizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_test_normalizer", "end-before": "END pipeline_test_normalizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START test_normalizer", "end-before": "END test_normalizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> When building a `Tokenizer`, you can customize its normalizer by just changing the corresponding attribute: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START replace_normalizer", "end-before": "END replace_normalizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_replace_normalizer", "end-before": "END pipeline_replace_normalizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START replace_normalizer", "end-before": "END replace_normalizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> Of course, if you change the way a tokenizer applies normalization, you should probably retrain it from scratch afterward. ## Pre-Tokenization Pre-tokenization is the act of splitting a text into smaller objects that give an upper bound to what your tokens will be at the end of training. A good way to think of this is that the pre-tokenizer will split your text into "words" and then, your final tokens will be parts of those words. An easy way to pre-tokenize inputs is to split on spaces and punctuations, which is done by the `pre_tokenizers.Whitespace` pre-tokenizer: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START setup_pre_tokenizer", "end-before": "END setup_pre_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_setup_pre_tokenizer", "end-before": "END pipeline_setup_pre_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START setup_pre_tokenizer", "end-before": "END setup_pre_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> The output is a list of tuples, with each tuple containing one word and its span in the original sentence (which is used to determine the final `offsets` of our `Encoding`). Note that splitting on punctuation will split contractions like `"I'm"` in this example. You can combine together any `PreTokenizer` together. For instance, here is a pre-tokenizer that will split on space, punctuation and digits, separating numbers in their individual digits: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START combine_pre_tokenizer", "end-before": "END combine_pre_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_combine_pre_tokenizer", "end-before": "END pipeline_combine_pre_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START combine_pre_tokenizer", "end-before": "END combine_pre_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> As we saw in the `quicktour`, you can customize the pre-tokenizer of a `Tokenizer` by just changing the corresponding attribute: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START replace_pre_tokenizer", "end-before": "END replace_pre_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_replace_pre_tokenizer", "end-before": "END pipeline_replace_pre_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START replace_pre_tokenizer", "end-before": "END replace_pre_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> Of course, if you change the way the pre-tokenizer, you should probably retrain your tokenizer from scratch afterward. ## Model Once the input texts are normalized and pre-tokenized, the `Tokenizer` applies the model on the pre-tokens. This is the part of the pipeline that needs training on your corpus (or that has been trained if you are using a pretrained tokenizer). The role of the model is to split your "words" into tokens, using the rules it has learned. It's also responsible for mapping those tokens to their corresponding IDs in the vocabulary of the model. This model is passed along when intializing the `Tokenizer` so you already know how to customize this part. Currently, the 🤗 Tokenizers library supports: - `models.BPE` - `models.Unigram` - `models.WordLevel` - `models.WordPiece` For more details about each model and its behavior, you can check [here](components#models) ## Post-Processing Post-processing is the last step of the tokenization pipeline, to perform any additional transformation to the `Encoding` before it's returned, like adding potential special tokens. As we saw in the quick tour, we can customize the post processor of a `Tokenizer` by setting the corresponding attribute. For instance, here is how we can post-process to make the inputs suitable for the BERT model: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START setup_processor", "end-before": "END setup_processor", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_setup_processor", "end-before": "END pipeline_setup_processor", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START setup_processor", "end-before": "END setup_processor", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> Note that contrarily to the pre-tokenizer or the normalizer, you don't need to retrain a tokenizer after changing its post-processor. ## All together: a BERT tokenizer from scratch Let's put all those pieces together to build a BERT tokenizer. First, BERT relies on WordPiece, so we instantiate a new `Tokenizer` with this model: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_setup_tokenizer", "end-before": "END bert_setup_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_setup_tokenizer", "end-before": "END bert_setup_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_setup_tokenizer", "end-before": "END bert_setup_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> Then we know that BERT preprocesses texts by removing accents and lowercasing. We also use a unicode normalizer: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_setup_normalizer", "end-before": "END bert_setup_normalizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_setup_normalizer", "end-before": "END bert_setup_normalizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_setup_normalizer", "end-before": "END bert_setup_normalizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> The pre-tokenizer is just splitting on whitespace and punctuation: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_setup_pre_tokenizer", "end-before": "END bert_setup_pre_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_setup_pre_tokenizer", "end-before": "END bert_setup_pre_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_setup_pre_tokenizer", "end-before": "END bert_setup_pre_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> And the post-processing uses the template we saw in the previous section: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_setup_processor", "end-before": "END bert_setup_processor", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_setup_processor", "end-before": "END bert_setup_processor", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_setup_processor", "end-before": "END bert_setup_processor", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> We can use this tokenizer and train on it on wikitext like in the `quicktour`: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_train_tokenizer", "end-before": "END bert_train_tokenizer", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_train_tokenizer", "end-before": "END bert_train_tokenizer", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_train_tokenizer", "end-before": "END bert_train_tokenizer", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> ## Decoding On top of encoding the input texts, a `Tokenizer` also has an API for decoding, that is converting IDs generated by your model back to a text. This is done by the methods `Tokenizer.decode` (for one predicted text) and `Tokenizer.decode_batch` (for a batch of predictions). The `decoder` will first convert the IDs back to tokens (using the tokenizer's vocabulary) and remove all special tokens, then join those tokens with spaces: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START test_decoding", "end-before": "END test_decoding", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START pipeline_test_decoding", "end-before": "END pipeline_test_decoding", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START test_decoding", "end-before": "END test_decoding", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> If you used a model that added special characters to represent subtokens of a given "word" (like the `"##"` in WordPiece) you will need to customize the `decoder` to treat them properly. If we take our previous `bert_tokenizer` for instance the default decoding will give: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_test_decoding", "end-before": "END bert_test_decoding", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_test_decoding", "end-before": "END bert_test_decoding", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_test_decoding", "end-before": "END bert_test_decoding", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent> But by changing it to a proper decoder, we get: <tokenizerslangcontent> <python> <literalinclude> {"path": "../../bindings/python/tests/documentation/test_pipeline.py", "language": "python", "start-after": "START bert_proper_decoding", "end-before": "END bert_proper_decoding", "dedent": 8} </literalinclude> </python> <rust> <literalinclude> {"path": "../../tokenizers/tests/documentation.rs", "language": "rust", "start-after": "START bert_proper_decoding", "end-before": "END bert_proper_decoding", "dedent": 4} </literalinclude> </rust> <node> <literalinclude> {"path": "../../bindings/node/examples/documentation/pipeline.test.ts", "language": "js", "start-after": "START bert_proper_decoding", "end-before": "END bert_proper_decoding", "dedent": 8} </literalinclude> </node> </tokenizerslangcontent>
huggingface/pytorch-image-models/blob/main/docs/models/tresnet.md	TResNet A TResNet is a variant on a [ResNet](https://paperswithcode.com/method/resnet) that aim to boost accuracy while maintaining GPU training and inference efficiency. They contain several design tricks including a SpaceToDepth stem, [Anti-Alias downsampling](https://paperswithcode.com/method/anti-alias-downsampling), In-Place Activated BatchNorm, Blocks selection and [squeeze-and-excitation layers](https://paperswithcode.com/method/squeeze-and-excitation-block). ## How do I use this model on an image? To load a pretrained model: ```python import timm model = timm.create_model('tresnet_l', pretrained=True) model.eval() ``` To load and preprocess the image: ```python import urllib from PIL import Image from timm.data import resolve_data_config from timm.data.transforms_factory import create_transform config = resolve_data_config({}, model=model) transform = create_transform(**config) url, filename = ("https://github.com/pytorch/hub/raw/master/images/dog.jpg", "dog.jpg") urllib.request.urlretrieve(url, filename) img = Image.open(filename).convert('RGB') tensor = transform(img).unsqueeze(0) # transform and add batch dimension ``` To get the model predictions: ```python import torch with torch.no_grad(): out = model(tensor) probabilities = torch.nn.functional.softmax(out[0], dim=0) print(probabilities.shape) # prints: torch.Size([1000]) ``` To get the top-5 predictions class names: ```python # Get imagenet class mappings url, filename = ("https://raw.githubusercontent.com/pytorch/hub/master/imagenet_classes.txt", "imagenet_classes.txt") urllib.request.urlretrieve(url, filename) with open("imagenet_classes.txt", "r") as f: categories = [s.strip() for s in f.readlines()] # Print top categories per image top5_prob, top5_catid = torch.topk(probabilities, 5) for i in range(top5_prob.size(0)): print(categories[top5_catid[i]], top5_prob[i].item()) # prints class names and probabilities like: # [('Samoyed', 0.6425196528434753), ('Pomeranian', 0.04062102362513542), ('keeshond', 0.03186424449086189), ('white wolf', 0.01739676296710968), ('Eskimo dog', 0.011717947199940681)] ``` Replace the model name with the variant you want to use, e.g. `tresnet_l`. You can find the IDs in the model summaries at the top of this page. To extract image features with this model, follow the [timm feature extraction examples](https://rwightman.github.io/pytorch-image-models/feature_extraction/), just change the name of the model you want to use. ## How do I finetune this model? You can finetune any of the pre-trained models just by changing the classifier (the last layer). ```python model = timm.create_model('tresnet_l', pretrained=True, num_classes=NUM_FINETUNE_CLASSES) ``` To finetune on your own dataset, you have to write a training loop or adapt [timm's training script](https://github.com/rwightman/pytorch-image-models/blob/master/train.py) to use your dataset. ## How do I train this model? You can follow the [timm recipe scripts](https://rwightman.github.io/pytorch-image-models/scripts/) for training a new model afresh. ## Citation ```BibTeX @misc{ridnik2020tresnet, title={TResNet: High Performance GPU-Dedicated Architecture}, author={Tal Ridnik and Hussam Lawen and Asaf Noy and Emanuel Ben Baruch and Gilad Sharir and Itamar Friedman}, year={2020}, eprint={2003.13630}, archivePrefix={arXiv}, primaryClass={cs.CV} } ``` <!-- Type: model-index Collections: - Name: TResNet Paper: Title: 'TResNet: High Performance GPU-Dedicated Architecture' URL: https://paperswithcode.com/paper/tresnet-high-performance-gpu-dedicated Models: - Name: tresnet_l In Collection: TResNet Metadata: FLOPs: 10873416792 Parameters: 53456696 File Size: 224440219 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs ID: tresnet_l LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L267 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_l_81_5-235b486c.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 81.49% Top 5 Accuracy: 95.62% - Name: tresnet_l_448 In Collection: TResNet Metadata: FLOPs: 43488238584 Parameters: 53456696 File Size: 224440219 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs ID: tresnet_l_448 LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '448' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L285 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_l_448-940d0cd1.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 82.26% Top 5 Accuracy: 95.98% - Name: tresnet_m In Collection: TResNet Metadata: FLOPs: 5733048064 Parameters: 41282200 File Size: 125861314 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs Training Time: < 24 hours ID: tresnet_m LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L261 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_m_80_8-dbc13962.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 80.8% Top 5 Accuracy: 94.86% - Name: tresnet_m_448 In Collection: TResNet Metadata: FLOPs: 22929743104 Parameters: 29278464 File Size: 125861314 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs ID: tresnet_m_448 LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '448' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L279 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_m_448-bc359d10.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 81.72% Top 5 Accuracy: 95.57% - Name: tresnet_xl In Collection: TResNet Metadata: FLOPs: 15162534034 Parameters: 75646610 File Size: 314378965 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs ID: tresnet_xl LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '224' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L273 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_xl_82_0-a2d51b00.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 82.05% Top 5 Accuracy: 95.93% - Name: tresnet_xl_448 In Collection: TResNet Metadata: FLOPs: 60641712730 Parameters: 75646610 File Size: 224440219 Architecture: - 1x1 Convolution - Anti-Alias Downsampling - Convolution - Global Average Pooling - InPlace-ABN - Leaky ReLU - ReLU - Residual Connection - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - AutoAugment - Cutout - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA 100 GPUs ID: tresnet_xl_448 LR: 0.01 Epochs: 300 Crop Pct: '0.875' Momentum: 0.9 Image Size: '448' Weight Decay: 0.0001 Interpolation: bilinear Code: https://github.com/rwightman/pytorch-image-models/blob/9a25fdf3ad0414b4d66da443fe60ae0aa14edc84/timm/models/tresnet.py#L291 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-tresnet/tresnet_l_448-940d0cd1.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 83.06% Top 5 Accuracy: 96.19% -->
huggingface/hub-docs/blob/main/docs/hub/datasets-viewer-configure.md	Configure the Dataset Viewer The Dataset Viewer supports many [data files formats](./datasets-adding#file-formats), from text to tabular and from image to audio formats. It also separates the train/validation/test splits based on file and folder names. To configure the Dataset Viewer for your dataset, first make sure your dataset is in a [supported data format](./datasets-adding#files-formats). ## Configure dropdowns for splits or subsets In the Dataset Viewer you can view the [train/validation/test](https://en.wikipedia.org/wiki/Training,_validation,_and_test_data_sets) splits of datasets, and sometimes additionally choose between multiple subsets (e.g. one per language). To define those dropdowns, you can name the data files or their folder after their split names (train/validation/test). It is also possible to customize your splits manually using YAML. For more information, feel free to check out the documentation on [Data files Configuration](./datasets-data-files-configuration). ## Disable the viewer The dataset viewer can be disabled. To do this, add a YAML section to the dataset's `README.md` file (create one if it does not already exist) and add a `viewer` property with the value `false`. ``` --- viewer: false --- ``` Note that the viewer is always disabled on the private datasets.
huggingface/transformers/blob/main/examples/research_projects/jax-projects/big_bird/README.md	Author: [@vasudevgupta7](https://github.com/thevasudevgupta/) ## Intro In this project, we fine-tuned [BigBird](https://arxiv.org/abs/2007.14062) on [natural-questions](https://huggingface.co/datasets/natural_questions) dataset for question-answering task on long documents. BigBird, is a sparse-attention based transformer which extends Transformer based models, such as BERT to much longer sequences. Read more about BigBird at https://huggingface.co/blog/big-bird ## Fine-tuning Setup You need to install jax yourself by following the official docs ([refer this](https://github.com/google/jax#installation)). Other requirements for this project can be installed by running following command: ```shell pip3 install -qr requirements.txt ``` Download & prepare dataset The Natural Questions corpus contains questions from real users, and it requires QA systems to read and comprehend an entire Wikipedia article that may or may not contain the answer to the question. This corpus takes ~100 GB on disk. We have used HuggingFace datasets to download & process the dataset. ```shell # just run following CMD python3 prepare_natural_questions.py # this will download the whole dataset from HuggingFace Hub & will make it ready for training # this script takes ~3 hours to process the dataset ``` Launch Training We have trained on Cloud's TPU v3-8. Each epoch took around 4.5 hours and the model got converged in just 2 epochs. You can see complete training args in [this script](bigbird_flax.py). ```shell # just run following CMD python3 train.py # In case, you want to try hparams tuning, you can run wandb sweep wandb sweep --project=bigbird sweep_flax.yaml wandb agent <agent-id-obtained-by-above-CMD> ``` ## Evaluation Our evaluation script is different from the original script and we are evaluating sequences with length up to 4096 for simplicity. We managed to get the EM score of ~55.2 using our evaluation script. ```shell # download validation-dataset first mkdir natural-questions-validation wget https://huggingface.co/datasets/vasudevgupta/natural-questions-validation/resolve/main/natural_questions-validation.arrow -P natural-questions-validation wget https://huggingface.co/datasets/vasudevgupta/natural-questions-validation/resolve/main/dataset_info.json -P natural-questions-validation wget https://huggingface.co/datasets/vasudevgupta/natural-questions-validation/resolve/main/state.json -P natural-questions-validation # simply run following command python3 evaluate.py ``` You can find our checkpoint on HuggingFace Hub ([see this](https://huggingface.co/vasudevgupta/flax-bigbird-natural-questions)). In case you are interested in PyTorch BigBird fine-tuning, you can refer to [this repositary](https://github.com/thevasudevgupta/bigbird).
huggingface/blog/blob/main/fine-tune-clip-rsicd.md	-- title: Fine tuning CLIP with Remote Sensing (Satellite) images and captions thumbnail: /blog/assets/30_clip_rsicd/clip_schematic.png authors: - user: arampacha guest: true - user: devv guest: true - user: goutham794 guest: true - user: cataluna84 guest: true - user: ghosh-r guest: true - user: sujitpal guest: true --- # Fine tuning CLIP with Remote Sensing (Satellite) images and captions ## Fine tuning CLIP with Remote Sensing (Satellite) images and captions <img src="/blog/assets/30_clip_rsicd/clip-rsicd-header-image.png"/> In July this year, [Hugging Face](https://huggingface.co/) organized a [Flax/JAX Community Week](https://github.com/huggingface/transformers/blob/master/examples/research_projects/jax-projects/README.md), and invited the community to submit projects to train Hugging Face [transformers](https://github.com/huggingface/transformers) models in the areas of Natural Language Processing (NLP) and Computer Vision (CV). Participants used Tensor Processing Units (TPUs) with [Flax](https://github.com/google/flax) and [JAX](https://github.com/google/jax). JAX is a linear algebra library (like `numpy`) that can do automatic differentiation ([Autograd](https://github.com/hips/autograd)) and compile down to [XLA](https://www.tensorflow.org/xla), and Flax is a neural network library and ecosystem for JAX. TPU compute time was provided free by [Google Cloud](https://cloud.google.com/), who co-sponsored the event. Over the next two weeks, teams participated in lectures from Hugging Face and Google, trained one or more models using JAX/Flax, shared them with the community, and provided a [Hugging Face Spaces](https://huggingface.co/spaces) demo showcasing the capabilities of their model. Approximately 100 teams participated in the event, and it resulted in 170 models and 36 demos. Our team, like probably many others, is a distributed one, spanning 12 time zones. Our common thread is that we all belong to the [TWIML Slack Channel](https://twimlai.slack.com/), where we came together based on a shared interest in Artificial Intelligence (AI) and Machine Learning (ML) topics. We fine-tuned the [CLIP Network from OpenAI](https://openai.comclip/) with satellite images and captions from the [RSICD dataset](https://github.com/201528014227051/RSICD_optimal). The CLIP network learns visual concepts by being trained with image and caption pairs in a self-supervised manner, by using text paired with images found across the Internet. During inference, the model can predict the most relevant image given a text description or the most relevant text description given an image. CLIP is powerful enough to be used in zero-shot manner on everyday images. However, we felt that satellite images were sufficiently different from everyday images that it would be useful to fine-tune CLIP with them. Our intuition turned out to be correct, as the evaluation results (described below) shows. In this post, we describe details of our training and evaluation process, and our plans for future work on this project. The goal of our project was to provide a useful service and demonstrate how to use CLIP for practical use cases. Our model can be used by applications to search through large collections of satellite images using textual queries. Such queries could describe the image in totality (for example, beach, mountain, airport, baseball field, etc) or search or mention specific geographic or man-made features within these images. CLIP can similarly be fine-tuned for other domains as well, as shown by the [medclip-demo team](https://huggingface.co/spaces/flax-community/medclip-demo) for medical images. The ability to search through large collections of images using text queries is an immensely powerful feature, and can be used as much for social good as for malign purposes. Possible applications include national defense and anti-terrorism activities, the ability to spot and address effects of climate change before they become unmanageable, etc. Unfortunately, this power can also be misused, such as for military and police surveillance by authoritarian nation-states, so it does raise some ethical questions as well. You can read about the project on our [project page](https://github.com/arampacha/CLIP-rsicd), download our [trained model](https://huggingface.co/flax-community/clip-rsicd-v2) to use for inference on your own data, or see it in action on our [demo](https://huggingface.co/spaces/sujitpal/clip-rsicd-demo). ### Training #### Dataset We fine-tuned the CLIP model primarily with the [RSICD dataset](https://github.com/201528014227051/RSICD_optimal). This dataset consists of about 10,000 images collected from Google Earth, Baidu Map, MapABC, and Tianditu. It is provided freely to the research community to advance remote sensing captioning via [Exploring Models and Data for Remote Sensing Image Caption Generation](https://arxiv.org/abs/1712.0783) (Lu et al, 2017). The images are (224, 224) RGB images at various resolutions, and each image has up to 5 captions associated with it. <img src="/blog/assets/30_clip_rsicd/rsicd-images-sampling.png"/> <center><i>Some examples of images from the RSICD dataset</i></center> In addition, we used the [UCM Dataset](https://mega.nz/folder/wCpSzSoS#RXzIlrv--TDt3ENZdKN8JA) and the [Sydney dataset](https://mega.nz/folder/pG4yTYYA#4c4buNFLibryZnlujsrwEQ) for training, The UCM dataset is based on the UC Merced Land Use dataset. It consists of 2100 images belonging to 21 classes (100 images per class), and each image has 5 captions. The Sydney dataset contains images of Sydney, Australia from Google Earth. It contains 613 images belonging to 7 classes. Images are (500, 500) RGB and provides 5 captions for each image. We used these additional datasets because we were not sure if the RSICD dataset would be large enough to fine-tune CLIP. #### Model Our model is just the fine-tuned version of the original CLIP model shown below. Inputs to the model are a batch of captions and a batch of images passed through the CLIP text encoder and image encoder respectively. The training process uses [contrastive learning](https://towardsdatascience.com/understanding-contrastive-learning-d5b19fd96607) to learn a joint embedding representation of image and captions. In this embedding space, images and their respective captions are pushed close together, as are similar images and similar captions. Conversely, images and captions for different images, or dissimilar images and captions, are likely to be pushed further apart. <img src="/blog/assets/30_clip_rsicd/clip_schematic.png"/> <center><i>CLIP Training and Inference (Image Credit: CLIP: Connecting Text and Images (https://openai.comclip/))</i></center> #### Data Augmentation In order to regularize our dataset and prevent overfitting due to the size of the dataset, we used both image and text augmentation. Image augmentation was done inline using built-in transforms from Pytorch's [Torchvision](https://pytorch.org/vision/stable/index.html) package. The transformations used were Random Cropping, Random Resizing and Cropping, Color Jitter, and Random Horizontal and Vertical flipping. We augmented the text with backtranslation to generate captions for images with less than 5 unique captions per image. The [Marian MT]((https://huggingface.co/transformers/model_doc/marian.html)) family of models from Hugging Face was used to translate the existing captions into French, Spanish, Italian, and Portuguese and back to English to fill out the captions for these images. As shown in these loss plots below, image augmentation reduced overfitting significantly, and text and image augmentation reduced overfitting even further. <img src="/blog/assets/30_clip_rsicd/image-augment-loss.png"/> <img src="/blog/assets/30_clip_rsicd/image-text-aug-loss.png"/> <center><i>Evaluation and Training loss plots comparing (top) no augmentation vs image augmentation, and (bottom) image augmentation vs text+image augmentation</i></center> ### Evaluation #### Metrics A subset of the RSICD test set was used for evaluation. We found 30 categories of images in this subset. The evaluation was done by comparing each image with a set of 30 caption sentences of the form `"An aerial photograph of {category}"`. The model produced a ranked list of the 30 captions, from most relevant to least relevant. Categories corresponding to captions with the top k scores (for k=1, 3, 5, and 10) were compared with the category provided via the image file name. The scores are averaged over the entire set of images used for evaluation and reported for various values of k, as shown below. The `baseline` model represents the pre-trained `openai/clip-vit-base-path32` CLIP model. This model was fine-tuned with captions and images from the RSICD dataset, which resulted in a significant performance boost, as shown below. Our best model was trained with image and text augmentation, with batch size 1024 (128 on each of the 8 TPU cores), and the Adam optimizer with learning rate 5e-6. We trained our second base model with the same hyperparameters, except that we used the Adafactor optimizer with learning rate 1e-4. You can download either model from their model repos linked to in the table below. \| Model-name \| k=1 \| k=3 \| k=5 \| k=10 \| \| ---------------------------------------- \| ----- \| ----- \| ----- \| ----- \| \| baseline \| 0.572 \| 0.745 \| 0.837 \| 0.939 \| \| bs128x8-lr1e-4-augs/ckpt-2 \| 0.819 \| 0.950 \| 0.974 \| 0.994 \| \| bs128x8-lr1e-4-imgaugs/ckpt-2 \| 0.812 \| 0.942 \| 0.970 \| 0.991 \| \| [bs128x8-lr1e-4-imgaugs-textaugs/ckpt-4](https://huggingface.co/flax-community/clip-rsicd)<sup>2</sup> \| 0.843 \| 0.958 \| 0.977 \| 0.993 \| \| bs128x8-lr5e-5-imgaugs-textaugs/ckpt-8 \| 0.831 \| 0.959 \| 0.977 \| 0.994 \| \| bs128x8-lr5e-5-imgaugs/ckpt-4 \| 0.746 \| 0.906 \| 0.956 \| 0.989 \| \| bs128x8-lr5e-5-imgaugs-textaugs-2/ckpt-4 \| 0.811 \| 0.945 \| 0.972 \| 0.993 \| \| bs128x8-lr5e-5-imgaugs-textaugs-3/ckpt-5 \| 0.823 \| 0.946 \| 0.971 \| 0.992 \| \| bs128x8-lr5e-5-wd02/ckpt-4 \| 0.820 \| 0.946 \| 0.965 \| 0.990 \| \| [bs128x8-lr5e-6-adam/ckpt-1](https://huggingface.co/flax-community/clip-rsicd-v2)<sup>1</sup> \| 0.883 \| 0.968 \| 0.982 \| 0.998 \| _1 - our best model, 2 - our second best model_ #### Demo You can access the [CLIP-RSICD Demo](https://huggingface.co/spaces/sujitpal/clip-rsicd-demo) here. It uses our fine-tuned CLIP model to provide the following functionality: * Text to Image search * Image to Image search * Find text feature in image The first two functionalities use the RSICD test set as its image corpus. They are encoded using our best fine-tuned CLIP model and stored in a [NMSLib](https://github.com/nmslib/nmslib) index which allows Approximate Nearest Neighbor based retrieval. For text-to-image and image-to-image search respectively, the query text or image are encoded with our model and matched against the image vectors in the corpus. For the third functionality, we divide the incoming image into patches and encode them, encode the queried text feature, match the text vector with each image patch vector, and return the probability of finding the feature in each patch. ### Future Work We are grateful that we have been given an opportunity to further refine our model. Some ideas we have for future work are as follows: 1. Construct a sequence to sequence model using a CLIP encoder and a GPT-3 decoder and train it for image captioning. 2. Fine-tune the model on more image caption pairs from other datasets and investigate if we can improve its performance. 3. Investigate how fine-tuning affects the performance of model on non-RSICD image caption pairs. 4. Investigate the capability of the fine-tuned model to classify outside the categories it has been fine-tuned on. 5. Evaluate the model using other criteria such as image classification.
huggingface/transformers/blob/main/notebooks/README.md	!--- Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # 🤗 Transformers Notebooks You can find here a list of the official notebooks provided by Hugging Face. Also, we would like to list here interesting content created by the community. If you wrote some notebook(s) leveraging 🤗 Transformers and would like to be listed here, please open a Pull Request so it can be included under the Community notebooks. ## Hugging Face's notebooks 🤗 ### Documentation notebooks You can open any page of the documentation as a notebook in Colab (there is a button directly on said pages) but they are also listed here if you need them: \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [Quicktour of the library](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/quicktour.ipynb) \| A presentation of the various APIs in Transformers \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/quicktour.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/en/transformers_doc/quicktour.ipynb)\| \| [Summary of the tasks](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/task_summary.ipynb) \| How to run the models of the Transformers library task by task \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/task_summary.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/task_summary.ipynb)\| \| [Preprocessing data](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/preprocessing.ipynb) \| How to use a tokenizer to preprocess your data \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/preprocessing.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/preprocessing.ipynb)\| \| [Fine-tuning a pretrained model](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/training.ipynb) \| How to use the Trainer to fine-tune a pretrained model \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/training.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/training.ipynb)\| \| [Summary of the tokenizers](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/tokenizer_summary.ipynb) \| The differences between the tokenizers algorithm \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/tokenizer_summary.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/tokenizer_summary.ipynb)\| \| [Multilingual models](https://github.com/huggingface/notebooks/blob/main/transformers_doc/en/multilingual.ipynb) \| How to use the multilingual models of the library \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/transformers_doc/en/multilingual.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/transformers_doc/en/multilingual.ipynb)\| ### PyTorch Examples #### Natural Language Processing[[pytorch-nlp]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [Train your tokenizer](https://github.com/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb) \| How to train and use your very own tokenizer \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb)\| \| [Train your language model](https://github.com/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch.ipynb) \| How to easily start using transformers \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch.ipynb)\| \| [How to fine-tune a model on text classification](https://github.com/huggingface/notebooks/blob/main/examples/text_classification.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on any GLUE task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/text_classification.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/text_classification.ipynb)\| \| [How to fine-tune a model on language modeling](https://github.com/huggingface/notebooks/blob/main/examples/language_modeling.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on a causal or masked LM task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/language_modeling.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/language_modeling.ipynb)\| \| [How to fine-tune a model on token classification](https://github.com/huggingface/notebooks/blob/main/examples/token_classification.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on a token classification task (NER, PoS). \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/token_classification.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/token_classification.ipynb)\| \| [How to fine-tune a model on question answering](https://github.com/huggingface/notebooks/blob/main/examples/question_answering.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on SQUAD. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/question_answering.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/question_answering.ipynb)\| \| [How to fine-tune a model on multiple choice](https://github.com/huggingface/notebooks/blob/main/examples/multiple_choice.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on SWAG. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/multiple_choice.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/multiple_choice.ipynb)\| \| [How to fine-tune a model on translation](https://github.com/huggingface/notebooks/blob/main/examples/translation.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on WMT. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/translation.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/translation.ipynb)\| \| [How to fine-tune a model on summarization](https://github.com/huggingface/notebooks/blob/main/examples/summarization.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on XSUM. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/summarization.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/summarization.ipynb)\| \| [How to train a language model from scratch](https://github.com/huggingface/blog/blob/main/notebooks/01_how_to_train.ipynb)\| Highlight all the steps to effectively train Transformer model on custom data \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/blog/blob/main/notebooks/01_how_to_train.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/blog/blob/main/notebooks/01_how_to_train.ipynb)\| \| [How to generate text](https://github.com/huggingface/blog/blob/main/notebooks/02_how_to_generate.ipynb)\| How to use different decoding methods for language generation with transformers \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/blog/blob/main/notebooks/02_how_to_generate.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/blog/blob/main/notebooks/02_how_to_generate.ipynb)\| \| [How to generate text (with constraints)](https://github.com/huggingface/blog/blob/main/notebooks/53_constrained_beam_search.ipynb)\| How to guide language generation with user-provided constraints \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/blog/blob/main/notebooks/53_constrained_beam_search.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/blog/blob/main/notebooks/53_constrained_beam_search.ipynb)\| \| [Reformer](https://github.com/huggingface/blog/blob/main/notebooks/03_reformer.ipynb)\| How Reformer pushes the limits of language modeling \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/patrickvonplaten/blog/blob/main/notebooks/03_reformer.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/patrickvonplaten/blog/blob/main/notebooks/03_reformer.ipynb)\| #### Computer Vision[[pytorch-cv]] \| Notebook \| Description \| \| \| \|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------\|:-----------------------------------------------------------------------------------------------------------------------\|:-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\|------:\| \| [How to fine-tune a model on image classification (Torchvision)](https://github.com/huggingface/notebooks/blob/main/examples/image_classification.ipynb) \| Show how to preprocess the data using Torchvision and fine-tune any pretrained Vision model on Image Classification \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_classification.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_classification.ipynb)\| \| [How to fine-tune a model on image classification (Albumentations)](https://github.com/huggingface/notebooks/blob/main/examples/image_classification_albumentations.ipynb) \| Show how to preprocess the data using Albumentations and fine-tune any pretrained Vision model on Image Classification \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_classification_albumentations.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_classification_albumentations.ipynb)\| \| [How to fine-tune a model on image classification (Kornia)](https://github.com/huggingface/notebooks/blob/main/examples/image_classification_kornia.ipynb) \| Show how to preprocess the data using Kornia and fine-tune any pretrained Vision model on Image Classification \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_classification_kornia.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_classification_kornia.ipynb)\| \| [How to perform zero-shot object detection with OWL-ViT](https://github.com/huggingface/notebooks/blob/main/examples/zeroshot_object_detection_with_owlvit.ipynb) \| Show how to perform zero-shot object detection on images with text queries \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/zeroshot_object_detection_with_owlvit.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/zeroshot_object_detection_with_owlvit.ipynb)\| \| [How to fine-tune an image captioning model](https://github.com/huggingface/notebooks/blob/main/examples/image_captioning_blip.ipynb) \| Show how to fine-tune BLIP for image captioning on a custom dataset \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_captioning_blip.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_captioning_blip.ipynb)\| \| [How to build an image similarity system with Transformers](https://github.com/huggingface/notebooks/blob/main/examples/image_similarity.ipynb) \| Show how to build an image similarity system \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_similarity.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_similarity.ipynb)\| \| [How to fine-tune a SegFormer model on semantic segmentation](https://github.com/huggingface/notebooks/blob/main/examples/semantic_segmentation.ipynb) \| Show how to preprocess the data and fine-tune a pretrained SegFormer model on Semantic Segmentation \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/semantic_segmentation.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/semantic_segmentation.ipynb)\| \| [How to fine-tune a VideoMAE model on video classification](https://github.com/huggingface/notebooks/blob/main/examples/video_classification.ipynb) \| Show how to preprocess the data and fine-tune a pretrained VideoMAE model on Video Classification \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/video_classification.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/video_classification.ipynb)\| #### Audio[[pytorch-audio]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [How to fine-tune a speech recognition model in English](https://github.com/huggingface/notebooks/blob/main/examples/speech_recognition.ipynb)\| Show how to preprocess the data and fine-tune a pretrained Speech model on TIMIT \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/speech_recognition.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/speech_recognition.ipynb)\| \| [How to fine-tune a speech recognition model in any language](https://github.com/huggingface/notebooks/blob/main/examples/multi_lingual_speech_recognition.ipynb)\| Show how to preprocess the data and fine-tune a multi-lingually pretrained speech model on Common Voice \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/multi_lingual_speech_recognition.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/multi_lingual_speech_recognition.ipynb)\| \| [How to fine-tune a model on audio classification](https://github.com/huggingface/notebooks/blob/main/examples/audio_classification.ipynb)\| Show how to preprocess the data and fine-tune a pretrained Speech model on Keyword Spotting \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/audio_classification.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/audio_classification.ipynb)\| #### Biological Sequences[[pytorch-bio]] \| Notebook \| Description \| \| \| \|:----------\|:----------------------------------------------------------------------------------------\|:-------------\|------:\| \| [How to fine-tune a pre-trained protein model](https://github.com/huggingface/notebooks/blob/main/examples/protein_language_modeling.ipynb) \| See how to tokenize proteins and fine-tune a large pre-trained protein "language" model \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/protein_language_modeling.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/protein_language_modeling.ipynb) \| \| [How to generate protein folds](https://github.com/huggingface/notebooks/blob/main/examples/protein_folding.ipynb) \| See how to go from protein sequence to a full protein model and PDB file \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/protein_folding.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/protein_folding.ipynb) \| \| [How to fine-tune a Nucleotide Transformer model](https://github.com/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling.ipynb) \| See how to tokenize DNA and fine-tune a large pre-trained DNA "language" model \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling.ipynb) \| \| [Fine-tune a Nucleotide Transformer model with LoRA](https://github.com/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling_with_peft.ipynb) \| Train even larger DNA models in a memory-efficient way \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling_with_peft.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/nucleotide_transformer_dna_sequence_modelling_with_peft.ipynb) \| #### Other modalities[[pytorch-other]] \| Notebook \| Description \| \| \| \|:----------\|:----------------------------------------------------------------------------------------\|:-------------\|------:\| \| [Probabilistic Time Series Forecasting](https://github.com/huggingface/notebooks/blob/main/examples/time-series-transformers.ipynb) \| See how to train Time Series Transformer on a custom dataset \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/time-series-transformers.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/time-series-transformers.ipynb) \| #### Utility notebooks[[pytorch-utility]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [How to export model to ONNX](https://github.com/huggingface/notebooks/blob/main/examples/onnx-export.ipynb)\| Highlight how to export and run inference workloads through ONNX \| \| [How to use Benchmarks](https://github.com/huggingface/notebooks/blob/main/examples/benchmark.ipynb)\| How to benchmark models with transformers \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/benchmark.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/benchmark.ipynb)\| ### TensorFlow Examples #### Natural Language Processing[[tensorflow-nlp]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [Train your tokenizer](https://github.com/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb) \| How to train and use your very own tokenizer \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/tokenizer_training.ipynb)\| \| [Train your language model](https://github.com/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch-tf.ipynb) \| How to easily start using transformers \|[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/language_modeling_from_scratch-tf.ipynb)\| \| [How to fine-tune a model on text classification](https://github.com/huggingface/notebooks/blob/main/examples/text_classification-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on any GLUE task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/text_classification-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/text_classification-tf.ipynb)\| \| [How to fine-tune a model on language modeling](https://github.com/huggingface/notebooks/blob/main/examples/language_modeling-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on a causal or masked LM task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/language_modeling-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/language_modeling-tf.ipynb)\| \| [How to fine-tune a model on token classification](https://github.com/huggingface/notebooks/blob/main/examples/token_classification-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on a token classification task (NER, PoS). \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/token_classification-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/token_classification-tf.ipynb)\| \| [How to fine-tune a model on question answering](https://github.com/huggingface/notebooks/blob/main/examples/question_answering-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on SQUAD. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/question_answering-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/question_answering-tf.ipynb)\| \| [How to fine-tune a model on multiple choice](https://github.com/huggingface/notebooks/blob/main/examples/multiple_choice-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on SWAG. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/multiple_choice-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/multiple_choice-tf.ipynb)\| \| [How to fine-tune a model on translation](https://github.com/huggingface/notebooks/blob/main/examples/translation-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on WMT. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/translation-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/translation-tf.ipynb)\| \| [How to fine-tune a model on summarization](https://github.com/huggingface/notebooks/blob/main/examples/summarization-tf.ipynb)\| Show how to preprocess the data and fine-tune a pretrained model on XSUM. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/summarization-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/summarization-tf.ipynb)\| #### Computer Vision[[tensorflow-cv]] \| Notebook \| Description \| \| \| \|:---------------------------------------------------------------------------------------------------------------------------------------------------------\|:----------------------------------------------------------------------------------------------------\|:-------------\|------:\| \| [How to fine-tune a model on image classification](https://github.com/huggingface/notebooks/blob/main/examples/image_classification-tf.ipynb) \| Show how to preprocess the data and fine-tune any pretrained Vision model on Image Classification \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/image_classification-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/image_classification-tf.ipynb)\| \| [How to fine-tune a SegFormer model on semantic segmentation](https://github.com/huggingface/notebooks/blob/main/examples/semantic_segmentation-tf.ipynb) \| Show how to preprocess the data and fine-tune a pretrained SegFormer model on Semantic Segmentation \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/semantic_segmentation-tf.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/semantic_segmentation-tf.ipynb)\| #### Biological Sequences[[tensorflow-bio]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [How to fine-tune a pre-trained protein model](https://github.com/huggingface/notebooks/blob/main/examples/protein_language_modeling-tf.ipynb) \| See how to tokenize proteins and fine-tune a large pre-trained protein "language" model \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/protein_language_modeling-tf.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/protein_language_modeling-tf.ipynb) \| #### Utility notebooks[[tensorflow-utility]] \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [How to train TF/Keras models on TPU](https://github.com/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) \| See how to train at high speed on Google's TPU hardware \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) \| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/tpu_training-tf.ipynb) \| ### Optimum notebooks 🤗 [Optimum](https://github.com/huggingface/optimum) is an extension of 🤗 Transformers, providing a set of performance optimization tools enabling maximum efficiency to train and run models on targeted hardwares. \| Notebook \| Description \| \| \| \|:----------\|:-------------\|:-------------\|------:\| \| [How to quantize a model with ONNX Runtime for text classification](https://github.com/huggingface/notebooks/blob/main/examples/text_classification_quantization_ort.ipynb)\| Show how to apply static and dynamic quantization on a model using [ONNX Runtime](https://github.com/microsoft/onnxruntime) for any GLUE task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/text_classification_quantization_ort.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/text_classification_quantization_ort.ipynb)\| \| [How to quantize a model with Intel Neural Compressor for text classification](https://github.com/huggingface/notebooks/blob/main/examples/text_classification_quantization_inc.ipynb)\| Show how to apply static, dynamic and aware training quantization on a model using [Intel Neural Compressor (INC)](https://github.com/intel/neural-compressor) for any GLUE task. \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/text_classification_quantization_inc.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/text_classification_quantization_inc.ipynb)\| \| [How to fine-tune a model on text classification with ONNX Runtime](https://github.com/huggingface/notebooks/blob/main/examples/text_classification_ort.ipynb)\| Show how to preprocess the data and fine-tune a model on any GLUE task using [ONNX Runtime](https://github.com/microsoft/onnxruntime). \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/text_classification_ort.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/text_classification_ort.ipynb)\| \| [How to fine-tune a model on summarization with ONNX Runtime](https://github.com/huggingface/notebooks/blob/main/examples/summarization_ort.ipynb)\| Show how to preprocess the data and fine-tune a model on XSUM using [ONNX Runtime](https://github.com/microsoft/onnxruntime). \| [![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/summarization_ort.ipynb)\| [![Open in AWS Studio](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/main/examples/summarization_ort.ipynb)\| ## Community notebooks: More notebooks developed by the community are available [here](https://hf.co/docs/transformers/community#community-notebooks).
huggingface/blog/blob/main/informer.md	-- title: "Multivariate Probabilistic Time Series Forecasting with Informer" thumbnail: /blog/assets/134_informer/thumbnail.png authors: - user: elisim guest: true - user: nielsr - user: kashif --- # Multivariate Probabilistic Time Series Forecasting with Informer <script async defer src="https://unpkg.com/medium-zoom-element@0/dist/medium-zoom-element.min.js"></script> <a target="_blank" href="https://colab.research.google.com/github/huggingface/notebooks/blob/main/examples/multivariate_informer.ipynb"> <img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/> </a> ## Introduction A few months ago we introduced the [Time Series Transformer](https://huggingface.co/blog/time-series-transformers), which is the vanilla Transformer ([Vaswani et al., 2017](https://arxiv.org/abs/1706.03762)) applied to forecasting, and showed an example for the univariate probabilistic forecasting task (i.e. predicting each time series' 1-d distribution individually). In this post we introduce the _Informer_ model ([Zhou, Haoyi, et al., 2021](https://arxiv.org/abs/2012.07436)), AAAI21 best paper which is [now available](https://huggingface.co/docs/transformers/main/en/model_doc/informer) in 🤗 Transformers. We will show how to use the Informer model for the multivariate probabilistic forecasting task, i.e., predicting the distribution of a future vector of time-series target values. Note that this will also work for the vanilla Time Series Transformer model. ## Multivariate Probabilistic Time Series Forecasting As far as the modeling aspect of probabilistic forecasting is concerned, the Transformer/Informer will require no change when dealing with multivariate time series. In both the univariate and multivariate setting, the model will receive a sequence of vectors and thus the only change is on the output or emission side. Modeling the full joint conditional distribution of high dimensional data can get computationally expensive and thus methods resort to some approximation of the distribution, the easiest being to model the data as an independent distribution from the same family, or some low-rank approximation to the full covariance, etc. Here we will just resort to the independent (or diagonal) emissions which are supported for the families of distributions we have implemented [here](https://huggingface.co/docs/transformers/main/en/internal/time_series_utils). ## Informer - Under The Hood Based on the vanilla Transformer ([Vaswani et al., 2017](https://arxiv.org/abs/1706.03762)), Informer employs two major improvements. To understand these improvements, let's recall the drawbacks of the vanilla Transformer: 1. Quadratic computation of canonical self-attention: The vanilla Transformer has a computational complexity of \$O(T^2 D)\$ where \$T\$ is the time series length and \$D\$ is the dimension of the hidden states. For long sequence time-series forecasting (also known as the _LSTF problem_), this might be really computationally expensive. To solve this problem, Informer employs a new self-attention mechanism called _ProbSparse_ attention, which has \$O(T \log T)\$ time and space complexity. 1. Memory bottleneck when stacking layers: When stacking \$N\$ encoder/decoder layers, the vanilla Transformer has a memory usage of \$O(N T^2)\$, which limits the model's capacity for long sequences. Informer uses a _Distilling_ operation, for reducing the input size between layers into its half slice. By doing so, it reduces the whole memory usage to be \$O(N\cdot T \log T)\$. As you can see, the motivation for the Informer model is similar to Longformer ([Beltagy et el., 2020](https://arxiv.org/abs/2004.05150)), Sparse Transformer ([Child et al., 2019](https://arxiv.org/abs/1904.10509)) and other NLP papers for reducing the quadratic complexity of the self-attention mechanism when the input sequence is long. Now, let's dive into _ProbSparse_ attention and the _Distilling_ operation with code examples. ### ProbSparse Attention The main idea of ProbSparse is that the canonical self-attention scores form a long-tail distribution, where the "active" queries lie in the "head" scores and "lazy" queries lie in the "tail" area. By "active" query we mean a query \$q_i\$ such that the dot-product \$\langle q_i,k_i \rangle\$ contributes to the major attention, whereas a "lazy" query forms a dot-product which generates trivial attention. Here, \$q_i\$ and \$k_i\$ are the \$i\$-th rows in \$Q\$ and \$K\$ attention matrices respectively. \| ![informer_full_vs_sparse_attention](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/informer_full_vs_sparse_attention.png) \| \|:--:\| \| Vanilla self attention vs ProbSparse attention from [Autoformer (Wu, Haixu, et al., 2021)](https://wuhaixu2016.github.io/pdf/NeurIPS2021_Autoformer.pdf) \| Given the idea of "active" and "lazy" queries, the ProbSparse attention selects the "active" queries, and creates a reduced query matrix \$Q_{reduced}\$ which is used to calculate the attention weights in \$O(T \log T)\$. Let's see this more in detail with a code example. Recall the canonical self-attention formula: $$ \textrm{Attention}(Q, K, V) = \textrm{softmax}(\frac{QK^T}{\sqrt{d_k}} )V $$ Where \$Q\in \mathbb{R}^{L_Q \times d}\$, \$K\in \mathbb{R}^{L_K \times d}\$ and \$V\in \mathbb{R}^{L_V \times d}\$. Note that in practice, the input length of queries and keys are typically equivalent in the self-attention computation, i.e. \$L_Q = L_K = T\$ where \$T\$ is the time series length. Therefore, the \$QK^T\$ multiplication takes \$O(T^2 \cdot d)\$ computational complexity. In ProbSparse attention, our goal is to create a new \$Q_{reduce}\$ matrix and define: $$ \textrm{ProbSparseAttention}(Q, K, V) = \textrm{softmax}(\frac{Q_{reduce}K^T}{\sqrt{d_k}} )V $$ where the \$Q_{reduce}\$ matrix only selects the Top \$u\$ "active" queries. Here, \$u = c \cdot \log L_Q\$ and \$c\$ called the _sampling factor_ hyperparameter for the ProbSparse attention. Since \$Q_{reduce}\$ selects only the Top \$u\$ queries, its size is \$c\cdot \log L_Q \times d\$, so the multiplication \$Q_{reduce}K^T\$ takes only \$O(L_K \log L_Q) = O(T \log T)\$. This is good! But how can we select the \$u\$ "active" queries to create \$Q_{reduce}\$? Let's define the _Query Sparsity Measurement_. #### Query Sparsity Measurement Query Sparsity Measurement \$M(q_i, K)\$ is used for selecting the \$u\$ "active" queries \$q_i\$ in \$Q\$ to create \$Q_{reduce}\$. In theory, the dominant \$\langle q_i,k_i \rangle\$ pairs encourage the "active" \$q_i\$'s probability distribution away from the uniform distribution as can be seen in the figure below. Hence, the [KL divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) between the actual queries distribution and the uniform distribution is used to define the sparsity measurement. \| ![informer_probsparse](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/informer_probsparse.png) \| \|:--:\| \| The illustration of ProbSparse Attention from official [repository](https://github.com/zhouhaoyi/Informer2020)\| In practice, the measurement is defined as: $$ M(q_i, K) = \max_j \frac{q_ik_j^T}{\sqrt{d}}-\frac{1}{L_k} \sum_{j=1}^{L_k}\frac{q_ik_j^T}{\sqrt{d}} $$ The important thing to understand here is when \$M(q_i, K)\$ is larger, the query \$q_i\$ should be in \$Q_{reduce}\$ and vice versa. But how can we calculate the term \$q_ik_j^T\$ in non-quadratic time? Recall that most of the dot-product \$\langle q_i,k_i \rangle\$ generate either way the trivial attention (i.e. long-tail distribution property), so it is enough to randomly sample a subset of keys from \$K\$, which will be called `K_sample` in the code. Now, we are ready to see the code of `probsparse_attention`: ```python from torch import nn import math def probsparse_attention(query_states, key_states, value_states, sampling_factor=5): """ Compute the probsparse self-attention. Input shape: Batch x Time x Channel Note the additional `sampling_factor` input. """ # get input sizes with logs L_K = key_states.size(1) L_Q = query_states.size(1) log_L_K = np.ceil(np.log1p(L_K)).astype("int").item() log_L_Q = np.ceil(np.log1p(L_Q)).astype("int").item() # calculate a subset of samples to slice from K and create Q_K_sample U_part = min(sampling_factor * L_Q * log_L_K, L_K) # create Q_K_sample (the q_i * k_j^T term in the sparsity measurement) index_sample = torch.randint(0, L_K, (U_part,)) K_sample = key_states[:, index_sample, :] Q_K_sample = torch.bmm(query_states, K_sample.transpose(1, 2)) # calculate the query sparsity measurement with Q_K_sample M = Q_K_sample.max(dim=-1)[0] - torch.div(Q_K_sample.sum(dim=-1), L_K) # calculate u to find the Top-u queries under the sparsity measurement u = min(sampling_factor * log_L_Q, L_Q) M_top = M.topk(u, sorted=False)[1] # calculate Q_reduce as query_states[:, M_top] dim_for_slice = torch.arange(query_states.size(0)).unsqueeze(-1) Q_reduce = query_states[dim_for_slice, M_top] # size: clog_L_Q x channel # and now, same as the canonical d_k = query_states.size(-1) attn_scores = torch.bmm(Q_reduce, key_states.transpose(-2, -1)) # Q_reduce x K^T attn_scores = attn_scores / math.sqrt(d_k) attn_probs = nn.functional.softmax(attn_scores, dim=-1) attn_output = torch.bmm(attn_probs, value_states) return attn_output, attn_scores ``` Note that in the implementation, \$U_{part}\$ contain \$L_Q\$ in the calculation, for stability issues (see [this disccusion](https://discuss.huggingface.co/t/probsparse-attention-in-informer/34428) for more information). We did it! Please be aware that this is only a partial implementation of the `probsparse_attention`, and the full implementation can be found in 🤗 Transformers. ### Distilling Because of the ProbSparse self-attention, the encoder’s feature map has some redundancy that can be removed. Therefore, the distilling operation is used to reduce the input size between encoder layers into its half slice, thus in theory removing this redundancy. In practice, Informer's "distilling" operation just adds 1D convolution layers with max pooling between each of the encoder layers. Let \$X_n\$ be the output of the \$n\$-th encoder layer, the distilling operation is then defined as: $$ X_{n+1} = \textrm{MaxPool} ( \textrm{ELU}(\textrm{Conv1d}(X_n)) $$ Let's see this in code: ```python from torch import nn # ConvLayer is a class with forward pass applying ELU and MaxPool1d def informer_encoder_forward(x_input, num_encoder_layers=3, distil=True): # Initialize the convolution layers if distil: conv_layers = nn.ModuleList([ConvLayer() for _ in range(num_encoder_layers - 1)]) conv_layers.append(None) else: conv_layers = [None] num_encoder_layers # Apply conv_layer between each encoder_layer for encoder_layer, conv_layer in zip(encoder_layers, conv_layers): output = encoder_layer(x_input) if conv_layer is not None: output = conv_layer(loutput) return output ``` By reducing the input of each layer by two, we get a memory usage of \$O(N\cdot T \log T)\$ instead of \$O(N\cdot T^2)\$ where \$N\$ is the number of encoder/decoder layers. This is what we wanted! The Informer model in [now available](https://huggingface.co/docs/transformers/main/en/model_doc/informer) in the 🤗 Transformers library, and simply called `InformerModel`. In the sections below, we will show how to train this model on a custom multivariate time-series dataset. ## Set-up Environment First, let's install the necessary libraries: 🤗 Transformers, 🤗 Datasets, 🤗 Evaluate, 🤗 Accelerate and [GluonTS](https://github.com/awslabs/gluonts). As we will show, GluonTS will be used for transforming the data to create features as well as for creating appropriate training, validation and test batches. ```python !pip install -q transformers datasets evaluate accelerate gluonts ujson ``` ## Load Dataset In this blog post, we'll use the `traffic_hourly` dataset, which is available on the [Hugging Face Hub](https://huggingface.co/datasets/monash_tsf). This dataset contains the San Francisco Traffic dataset used by [Lai et al. (2017)](https://arxiv.org/abs/1703.07015). It contains 862 hourly time series showing the road occupancy rates in the range \$[0, 1]\$ on the San Francisco Bay area freeways from 2015 to 2016. This dataset is part of the [Monash Time Series Forecasting](https://forecastingdata.org/) repository, a collection of time series datasets from a number of domains. It can be viewed as the [GLUE benchmark](https://gluebenchmark.com/) of time series forecasting. ```python from datasets import load_dataset dataset = load_dataset("monash_tsf", "traffic_hourly") ``` As can be seen, the dataset contains 3 splits: train, validation and test. ```python dataset >>> DatasetDict({ train: Dataset({ features: ['start', 'target', 'feat_static_cat', 'feat_dynamic_real', 'item_id'], num_rows: 862 }) test: Dataset({ features: ['start', 'target', 'feat_static_cat', 'feat_dynamic_real', 'item_id'], num_rows: 862 }) validation: Dataset({ features: ['start', 'target', 'feat_static_cat', 'feat_dynamic_real', 'item_id'], num_rows: 862 }) }) ``` Each example contains a few keys, of which `start` and `target` are the most important ones. Let us have a look at the first time series in the dataset: ```python train_example = dataset["train"][0] train_example.keys() >>> dict_keys(['start', 'target', 'feat_static_cat', 'feat_dynamic_real', 'item_id']) ``` The `start` simply indicates the start of the time series (as a datetime), and the `target` contains the actual values of the time series. The `start` will be useful to add time related features to the time series values, as extra input to the model (such as "month of year"). Since we know the frequency of the data is `hourly`, we know for instance that the second value has the timestamp `2015-01-01 01:00:01`, `2015-01-01 02:00:01`, etc. ```python print(train_example["start"]) print(len(train_example["target"])) >>> 2015-01-01 00:00:01 17448 ``` The validation set contains the same data as the training set, just for a `prediction_length` longer amount of time. This allows us to validate the model's predictions against the ground truth. The test set is again one `prediction_length` longer data compared to the validation set (or some multiple of `prediction_length` longer data compared to the training set for testing on multiple rolling windows). ```python validation_example = dataset["validation"][0] validation_example.keys() >>> dict_keys(['start', 'target', 'feat_static_cat', 'feat_dynamic_real', 'item_id']) ``` The initial values are exactly the same as the corresponding training example. However, this example has `prediction_length=48` (48 hours, or 2 days) additional values compared to the training example. Let us verify it. ```python freq = "1H" prediction_length = 48 assert len(train_example["target"]) + prediction_length == len( dataset["validation"][0]["target"] ) ``` Let's visualize this: ```python import matplotlib.pyplot as plt num_of_samples = 150 figure, axes = plt.subplots() axes.plot(train_example["target"][-num_of_samples:], color="blue") axes.plot( validation_example["target"][-num_of_samples - prediction_length :], color="red", alpha=0.5, ) plt.show() ``` ![png](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/output_22_0.png) Let's split up the data: ```python train_dataset = dataset["train"] test_dataset = dataset["test"] ``` ## Update `start` to `pd.Period` The first thing we'll do is convert the `start` feature of each time series to a pandas `Period` index using the data's `freq`: ```python from functools import lru_cache import pandas as pd import numpy as np @lru_cache(10_000) def convert_to_pandas_period(date, freq): return pd.Period(date, freq) def transform_start_field(batch, freq): batch["start"] = [convert_to_pandas_period(date, freq) for date in batch["start"]] return batch ``` We now use `datasets`' [`set_transform`](https://huggingface.co/docs/datasets/v2.7.0/en/package_reference/main_classes#datasets.Dataset.set_transform) functionality to do this on-the-fly in place: ```python from functools import partial train_dataset.set_transform(partial(transform_start_field, freq=freq)) test_dataset.set_transform(partial(transform_start_field, freq=freq)) ``` Now, let's convert the dataset into a multivariate time series using the `MultivariateGrouper` from GluonTS. This grouper will convert the individual 1-dimensional time series into a single 2D matrix. ```python from gluonts.dataset.multivariate_grouper import MultivariateGrouper num_of_variates = len(train_dataset) train_grouper = MultivariateGrouper(max_target_dim=num_of_variates) test_grouper = MultivariateGrouper( max_target_dim=num_of_variates, num_test_dates=len(test_dataset) // num_of_variates, # number of rolling test windows ) multi_variate_train_dataset = train_grouper(train_dataset) multi_variate_test_dataset = test_grouper(test_dataset) ``` Note that the target is now 2-dimensional, where the first dimension is the number of variates (number of time series) and the second is the time series values (time dimension): ```python multi_variate_train_example = multi_variate_train_dataset[0] print("multi_variate_train_example["target"].shape =", multi_variate_train_example["target"].shape) >>> multi_variate_train_example["target"].shape = (862, 17448) ``` ## Define the Model Next, let's instantiate a model. The model will be trained from scratch, hence we won't use the `from_pretrained` method here, but rather randomly initialize the model from a [`config`](https://huggingface.co/docs/transformers/main/en/model_doc/informer#transformers.InformerConfig). We specify a couple of additional parameters to the model: - `prediction_length` (in our case, `48` hours): this is the horizon that the decoder of the Informer will learn to predict for; - `context_length`: the model will set the `context_length` (input of the encoder) equal to the `prediction_length`, if no `context_length` is specified; - `lags` for a given frequency: these specify an efficient "look back" mechanism, where we concatenate values from the past to the current values as additional features, e.g. for a `Daily` frequency we might consider a look back of `[1, 7, 30, ...]` or for `Minute` data we might consider `[1, 30, 60, 6024, ...]` etc.; - the number of time features: in our case, this will be `5` as we'll add `HourOfDay`, `DayOfWeek`, ..., and `Age` features (see below). Let us check the default lags provided by GluonTS for the given frequency ("hourly"): ```python from gluonts.time_feature import get_lags_for_frequency lags_sequence = get_lags_for_frequency(freq) print(lags_sequence) >>> [1, 2, 3, 4, 5, 6, 7, 23, 24, 25, 47, 48, 49, 71, 72, 73, 95, 96, 97, 119, 120, 121, 143, 144, 145, 167, 168, 169, 335, 336, 337, 503, 504, 505, 671, 672, 673, 719, 720, 721] ``` This means that this would look back up to 721 hours (~30 days) for each time step, as additional features. However, the resulting feature vector would end up being of size `len(lags_sequence)num_of_variates` which for our case will be 34480! This is not going to work so we will use our own sensible lags. Let us also check the default time features which GluonTS provides us: ```python from gluonts.time_feature import time_features_from_frequency_str time_features = time_features_from_frequency_str(freq) print(time_features) >>> [<function hour_of_day at 0x7f3809539240>, <function day_of_week at 0x7f3809539360>, <function day_of_month at 0x7f3809539480>, <function day_of_year at 0x7f38095395a0>] ``` In this case, there are four additional features, namely "hour of day", "day of week", "day of month" and "day of year". This means that for each time step, we'll add these features as a scalar values. For example, consider the timestamp `2015-01-01 01:00:01`. The four additional features will be: ```python from pandas.core.arrays.period import period_array timestamp = pd.Period("2015-01-01 01:00:01", freq=freq) timestamp_as_index = pd.PeriodIndex(data=period_array([timestamp])) additional_features = [ (time_feature.__name__, time_feature(timestamp_as_index)) for time_feature in time_features ] print(dict(additional_features)) >>> {'hour_of_day': array([-0.45652174]), 'day_of_week': array([0.]), 'day_of_month': array([-0.5]), 'day_of_year': array([-0.5])} ``` Note that hours and days are encoded as values between `[-0.5, 0.5]` from GluonTS. For more information about `time_features`, please see [this](https://github.com/awslabs/gluonts/blob/dev/src/gluonts/time_feature/_base.py). Besides those 4 features, we'll also add an "age" feature as we'll see later on in the data transformations. We now have everything to define the model: ```python from transformers import InformerConfig, InformerForPrediction config = InformerConfig( # in the multivariate setting, input_size is the number of variates in the time series per time step input_size=num_of_variates, # prediction length: prediction_length=prediction_length, # context length: context_length=prediction_length * 2, # lags value copied from 1 week before: lags_sequence=[1, 24 * 7], # we'll add 5 time features ("hour_of_day", ..., and "age"): num_time_features=len(time_features) + 1, # informer params: dropout=0.1, encoder_layers=6, decoder_layers=4, # project input from num_of_variateslen(lags_sequence)+num_time_features to: d_model=64, ) model = InformerForPrediction(config) ``` By default, the model uses a diagonal Student-t distribution (but this is [configurable](https://huggingface.co/docs/transformers/main/en/internal/time_series_utils)): ```python model.config.distribution_output >>> 'student_t' ``` ## Define Transformations Next, we define the transformations for the data, in particular for the creation of the time features (based on the dataset or universal ones). Again, we'll use the GluonTS library for this. We define a `Chain` of transformations (which is a bit comparable to `torchvision.transforms.Compose` for images). It allows us to combine several transformations into a single pipeline. ```python from gluonts.time_feature import TimeFeature from gluonts.dataset.field_names import FieldName from gluonts.transform import ( AddAgeFeature, AddObservedValuesIndicator, AddTimeFeatures, AsNumpyArray, Chain, ExpectedNumInstanceSampler, InstanceSplitter, RemoveFields, SelectFields, SetField, TestSplitSampler, Transformation, ValidationSplitSampler, VstackFeatures, RenameFields, ) ``` The transformations below are annotated with comments, to explain what they do. At a high level, we will iterate over the individual time series of our dataset and add/remove fields or features: ```python from transformers import PretrainedConfig def create_transformation(freq: str, config: PretrainedConfig) -> Transformation: # create list of fields to remove later remove_field_names = [] if config.num_static_real_features == 0: remove_field_names.append(FieldName.FEAT_STATIC_REAL) if config.num_dynamic_real_features == 0: remove_field_names.append(FieldName.FEAT_DYNAMIC_REAL) if config.num_static_categorical_features == 0: remove_field_names.append(FieldName.FEAT_STATIC_CAT) return Chain( # step 1: remove static/dynamic fields if not specified [RemoveFields(field_names=remove_field_names)] # step 2: convert the data to NumPy (potentially not needed) + ( [ AsNumpyArray( field=FieldName.FEAT_STATIC_CAT, expected_ndim=1, dtype=int, ) ] if config.num_static_categorical_features > 0 else [] ) + ( [ AsNumpyArray( field=FieldName.FEAT_STATIC_REAL, expected_ndim=1, ) ] if config.num_static_real_features > 0 else [] ) + [ AsNumpyArray( field=FieldName.TARGET, # we expect an extra dim for the multivariate case: expected_ndim=1 if config.input_size == 1 else 2, ), # step 3: handle the NaN's by filling in the target with zero # and return the mask (which is in the observed values) # true for observed values, false for nan's # the decoder uses this mask (no loss is incurred for unobserved values) # see loss_weights inside the xxxForPrediction model AddObservedValuesIndicator( target_field=FieldName.TARGET, output_field=FieldName.OBSERVED_VALUES, ), # step 4: add temporal features based on freq of the dataset # these serve as positional encodings AddTimeFeatures( start_field=FieldName.START, target_field=FieldName.TARGET, output_field=FieldName.FEAT_TIME, time_features=time_features_from_frequency_str(freq), pred_length=config.prediction_length, ), # step 5: add another temporal feature (just a single number) # tells the model where in the life the value of the time series is # sort of running counter AddAgeFeature( target_field=FieldName.TARGET, output_field=FieldName.FEAT_AGE, pred_length=config.prediction_length, log_scale=True, ), # step 6: vertically stack all the temporal features into the key FEAT_TIME VstackFeatures( output_field=FieldName.FEAT_TIME, input_fields=[FieldName.FEAT_TIME, FieldName.FEAT_AGE] + ( [FieldName.FEAT_DYNAMIC_REAL] if config.num_dynamic_real_features > 0 else [] ), ), # step 7: rename to match HuggingFace names RenameFields( mapping={ FieldName.FEAT_STATIC_CAT: "static_categorical_features", FieldName.FEAT_STATIC_REAL: "static_real_features", FieldName.FEAT_TIME: "time_features", FieldName.TARGET: "values", FieldName.OBSERVED_VALUES: "observed_mask", } ), ] ) ``` ## Define `InstanceSplitter` For training/validation/testing we next create an `InstanceSplitter` which is used to sample windows from the dataset (as, remember, we can't pass the entire history of values to the model due to time- and memory constraints). The instance splitter samples random `context_length` sized and subsequent `prediction_length` sized windows from the data, and appends a `past_` or `future_` key to any temporal keys in `time_series_fields` for the respective windows. The instance splitter can be configured into three different modes: 1. `mode="train"`: Here we sample the context and prediction length windows randomly from the dataset given to it (the training dataset) 2. `mode="validation"`: Here we sample the very last context length window and prediction window from the dataset given to it (for the back-testing or validation likelihood calculations) 3. `mode="test"`: Here we sample the very last context length window only (for the prediction use case) ```python from gluonts.transform.sampler import InstanceSampler from typing import Optional def create_instance_splitter( config: PretrainedConfig, mode: str, train_sampler: Optional[InstanceSampler] = None, validation_sampler: Optional[InstanceSampler] = None, ) -> Transformation: assert mode in ["train", "validation", "test"] instance_sampler = { "train": train_sampler or ExpectedNumInstanceSampler( num_instances=1.0, min_future=config.prediction_length ), "validation": validation_sampler or ValidationSplitSampler(min_future=config.prediction_length), "test": TestSplitSampler(), }[mode] return InstanceSplitter( target_field="values", is_pad_field=FieldName.IS_PAD, start_field=FieldName.START, forecast_start_field=FieldName.FORECAST_START, instance_sampler=instance_sampler, past_length=config.context_length + max(config.lags_sequence), future_length=config.prediction_length, time_series_fields=["time_features", "observed_mask"], ) ``` ## Create DataLoaders Next, it's time to create the DataLoaders, which allow us to have batches of (input, output) pairs - or in other words (`past_values`, `future_values`). ```python from typing import Iterable import torch from gluonts.itertools import Cached, Cyclic from gluonts.dataset.loader import as_stacked_batches def create_train_dataloader( config: PretrainedConfig, freq, data, batch_size: int, num_batches_per_epoch: int, shuffle_buffer_length: Optional[int] = None, cache_data: bool = True, kwargs, ) -> Iterable: PREDICTION_INPUT_NAMES = [ "past_time_features", "past_values", "past_observed_mask", "future_time_features", ] if config.num_static_categorical_features > 0: PREDICTION_INPUT_NAMES.append("static_categorical_features") if config.num_static_real_features > 0: PREDICTION_INPUT_NAMES.append("static_real_features") TRAINING_INPUT_NAMES = PREDICTION_INPUT_NAMES + [ "future_values", "future_observed_mask", ] transformation = create_transformation(freq, config) transformed_data = transformation.apply(data, is_train=True) if cache_data: transformed_data = Cached(transformed_data) # we initialize a Training instance instance_splitter = create_instance_splitter(config, "train") # the instance splitter will sample a window of # context length + lags + prediction length (from all the possible transformed time series, 1 in our case) # randomly from within the target time series and return an iterator. stream = Cyclic(transformed_data).stream() training_instances = instance_splitter.apply(stream) return as_stacked_batches( training_instances, batch_size=batch_size, shuffle_buffer_length=shuffle_buffer_length, field_names=TRAINING_INPUT_NAMES, output_type=torch.tensor, num_batches_per_epoch=num_batches_per_epoch, ) ``` ```python def create_backtest_dataloader( config: PretrainedConfig, freq, data, batch_size: int, kwargs, ): PREDICTION_INPUT_NAMES = [ "past_time_features", "past_values", "past_observed_mask", "future_time_features", ] if config.num_static_categorical_features > 0: PREDICTION_INPUT_NAMES.append("static_categorical_features") if config.num_static_real_features > 0: PREDICTION_INPUT_NAMES.append("static_real_features") transformation = create_transformation(freq, config) transformed_data = transformation.apply(data) # we create a Validation Instance splitter which will sample the very last # context window seen during training only for the encoder. instance_sampler = create_instance_splitter(config, "validation") # we apply the transformations in train mode testing_instances = instance_sampler.apply(transformed_data, is_train=True) return as_stacked_batches( testing_instances, batch_size=batch_size, output_type=torch.tensor, field_names=PREDICTION_INPUT_NAMES, ) def create_test_dataloader( config: PretrainedConfig, freq, data, batch_size: int, kwargs, ): PREDICTION_INPUT_NAMES = [ "past_time_features", "past_values", "past_observed_mask", "future_time_features", ] if config.num_static_categorical_features > 0: PREDICTION_INPUT_NAMES.append("static_categorical_features") if config.num_static_real_features > 0: PREDICTION_INPUT_NAMES.append("static_real_features") transformation = create_transformation(freq, config) transformed_data = transformation.apply(data, is_train=False) # We create a test Instance splitter to sample the very last # context window from the dataset provided. instance_sampler = create_instance_splitter(config, "test") # We apply the transformations in test mode testing_instances = instance_sampler.apply(transformed_data, is_train=False) return as_stacked_batches( testing_instances, batch_size=batch_size, output_type=torch.tensor, field_names=PREDICTION_INPUT_NAMES, ) ``` ```python train_dataloader = create_train_dataloader( config=config, freq=freq, data=multi_variate_train_dataset, batch_size=256, num_batches_per_epoch=100, num_workers=2, ) test_dataloader = create_backtest_dataloader( config=config, freq=freq, data=multi_variate_test_dataset, batch_size=32, ) ``` Let's check the first batch: ```python batch = next(iter(train_dataloader)) for k, v in batch.items(): print(k, v.shape, v.type()) >>> past_time_features torch.Size([256, 264, 5]) torch.FloatTensor past_values torch.Size([256, 264, 862]) torch.FloatTensor past_observed_mask torch.Size([256, 264, 862]) torch.FloatTensor future_time_features torch.Size([256, 48, 5]) torch.FloatTensor future_values torch.Size([256, 48, 862]) torch.FloatTensor future_observed_mask torch.Size([256, 48, 862]) torch.FloatTensor ``` As can be seen, we don't feed `input_ids` and `attention_mask` to the encoder (as would be the case for NLP models), but rather `past_values`, along with `past_observed_mask`, `past_time_features` and `static_real_features`. The decoder inputs consist of `future_values`, `future_observed_mask` and `future_time_features`. The `future_values` can be seen as the equivalent of `decoder_input_ids` in NLP. We refer to the [docs](https://huggingface.co/docs/transformers/main/en/model_doc/informer#transformers.InformerModel.forward.past_values) for a detailed explanation for each of them. ## Forward Pass Let's perform a single forward pass with the batch we just created: ```python # perform forward pass outputs = model( past_values=batch["past_values"], past_time_features=batch["past_time_features"], past_observed_mask=batch["past_observed_mask"], static_categorical_features=batch["static_categorical_features"] if config.num_static_categorical_features > 0 else None, static_real_features=batch["static_real_features"] if config.num_static_real_features > 0 else None, future_values=batch["future_values"], future_time_features=batch["future_time_features"], future_observed_mask=batch["future_observed_mask"], output_hidden_states=True, ) ``` ```python print("Loss:", outputs.loss.item()) >>> Loss: -1071.5718994140625 ``` Note that the model is returning a loss. This is possible as the decoder automatically shifts the `future_values` one position to the right in order to have the labels. This allows computing a loss between the predicted values and the labels. The loss is the negative log-likelihood of the predicted distribution with respect to the ground truth values and tends to negative infinity. Also note that the decoder uses a causal mask to not look into the future as the values it needs to predict are in the `future_values` tensor. ## Train the Model It's time to train the model! We'll use a standard PyTorch training loop. We will use the 🤗 [Accelerate](https://huggingface.co/docs/accelerate/index) library here, which automatically places the model, optimizer and dataloader on the appropriate `device`. ```python from accelerate import Accelerator from torch.optim import AdamW epochs = 25 loss_history = [] accelerator = Accelerator() device = accelerator.device model.to(device) optimizer = AdamW(model.parameters(), lr=6e-4, betas=(0.9, 0.95), weight_decay=1e-1) model, optimizer, train_dataloader = accelerator.prepare( model, optimizer, train_dataloader, ) model.train() for epoch in range(epochs): for idx, batch in enumerate(train_dataloader): optimizer.zero_grad() outputs = model( static_categorical_features=batch["static_categorical_features"].to(device) if config.num_static_categorical_features > 0 else None, static_real_features=batch["static_real_features"].to(device) if config.num_static_real_features > 0 else None, past_time_features=batch["past_time_features"].to(device), past_values=batch["past_values"].to(device), future_time_features=batch["future_time_features"].to(device), future_values=batch["future_values"].to(device), past_observed_mask=batch["past_observed_mask"].to(device), future_observed_mask=batch["future_observed_mask"].to(device), ) loss = outputs.loss # Backpropagation accelerator.backward(loss) optimizer.step() loss_history.append(loss.item()) if idx % 100 == 0: print(loss.item()) >>> -1081.978515625 ... -2877.723876953125 ``` ```python # view training loss_history = np.array(loss_history).reshape(-1) x = range(loss_history.shape[0]) plt.figure(figsize=(10, 5)) plt.plot(x, loss_history, label="train") plt.title("Loss", fontsize=15) plt.legend(loc="upper right") plt.xlabel("iteration") plt.ylabel("nll") plt.show() ``` ![png](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/output_62_0.png) ## Inference At inference time, it's recommended to use the `generate()` method for autoregressive generation, similar to NLP models. Forecasting involves getting data from the test instance sampler, which will sample the very last `context_length` sized window of values from each time series in the dataset, and pass it to the model. Note that we pass `future_time_features`, which are known ahead of time, to the decoder. The model will autoregressively sample a certain number of values from the predicted distribution and pass them back to the decoder to return the prediction outputs: ```python model.eval() forecasts_ = [] for batch in test_dataloader: outputs = model.generate( static_categorical_features=batch["static_categorical_features"].to(device) if config.num_static_categorical_features > 0 else None, static_real_features=batch["static_real_features"].to(device) if config.num_static_real_features > 0 else None, past_time_features=batch["past_time_features"].to(device), past_values=batch["past_values"].to(device), future_time_features=batch["future_time_features"].to(device), past_observed_mask=batch["past_observed_mask"].to(device), ) forecasts_.append(outputs.sequences.cpu().numpy()) ``` The model outputs a tensor of shape (`batch_size`, `number of samples`, `prediction length`, `input_size`). In this case, we get `100` possible values for the next `48` hours for each of the `862` time series (for each example in the batch which is of size `1` since we only have a single multivariate time series): ```python forecasts_[0].shape >>> (1, 100, 48, 862) ``` We'll stack them vertically, to get forecasts for all time-series in the test dataset (just in case there are more time series in the test set): ```python forecasts = np.vstack(forecasts_) print(forecasts.shape) >>> (1, 100, 48, 862) ``` We can evaluate the resulting forecast with respect to the ground truth out of sample values present in the test set. For that, we'll use the 🤗 [Evaluate](https://huggingface.co/docs/evaluate/index) library, which includes the [MASE](https://huggingface.co/spaces/evaluate-metric/mase) and [sMAPE](https://huggingface.co/spaces/evaluate-metric/smape) metrics. We calculate both metrics for each time series variate in the dataset: ```python from evaluate import load from gluonts.time_feature import get_seasonality mase_metric = load("evaluate-metric/mase") smape_metric = load("evaluate-metric/smape") forecast_median = np.median(forecasts, 1).squeeze(0).T mase_metrics = [] smape_metrics = [] for item_id, ts in enumerate(test_dataset): training_data = ts["target"][:-prediction_length] ground_truth = ts["target"][-prediction_length:] mase = mase_metric.compute( predictions=forecast_median[item_id], references=np.array(ground_truth), training=np.array(training_data), periodicity=get_seasonality(freq), ) mase_metrics.append(mase["mase"]) smape = smape_metric.compute( predictions=forecast_median[item_id], references=np.array(ground_truth), ) smape_metrics.append(smape["smape"]) ``` ```python print(f"MASE: {np.mean(mase_metrics)}") >>> MASE: 1.1913437728068093 print(f"sMAPE: {np.mean(smape_metrics)}") >>> sMAPE: 0.5322665081607634 ``` ```python plt.scatter(mase_metrics, smape_metrics, alpha=0.2) plt.xlabel("MASE") plt.ylabel("sMAPE") plt.show() ``` ![png](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/output_73_0.png) To plot the prediction for any time series variate with respect the ground truth test data we define the following helper: ```python import matplotlib.dates as mdates def plot(ts_index, mv_index): fig, ax = plt.subplots() index = pd.period_range( start=multi_variate_test_dataset[ts_index][FieldName.START], periods=len(multi_variate_test_dataset[ts_index][FieldName.TARGET]), freq=multi_variate_test_dataset[ts_index][FieldName.START].freq, ).to_timestamp() ax.xaxis.set_minor_locator(mdates.HourLocator()) ax.plot( index[-2 prediction_length :], multi_variate_test_dataset[ts_index]["target"][mv_index, -2 * prediction_length :], label="actual", ) ax.plot( index[-prediction_length:], forecasts[ts_index, ..., mv_index].mean(axis=0), label="mean", ) ax.fill_between( index[-prediction_length:], forecasts[ts_index, ..., mv_index].mean(0) - forecasts[ts_index, ..., mv_index].std(axis=0), forecasts[ts_index, ..., mv_index].mean(0) + forecasts[ts_index, ..., mv_index].std(axis=0), alpha=0.2, interpolate=True, label="+/- 1-std", ) ax.legend() fig.autofmt_xdate() ``` For example: ```python plot(0, 344) ``` ![png](https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/informer/output_77_0.png) ## Conclusion How do we compare against other models? The [Monash Time Series Repository](https://forecastingdata.org/#results) has a comparison table of test set MASE metrics which we can add to: \|Dataset \| SES\| Theta \| TBATS\| ETS \| (DHR-)ARIMA\| PR\| CatBoost \| FFNN \| DeepAR \| N-BEATS \| WaveNet\| Transformer (uni.) \| Informer (mv. our)\| \|:------------------:\|:-----------------:\|:--:\|:--:\|:--:\|:--:\|:--:\|:--:\|:---:\|:---:\|:--:\|:--:\|:--:\|:--:\| \|Traffic Hourly \| 1.922 \| 1.922 \| 2.482 \| 2.294\| 2.535\| 1.281\| 1.571 \|0.892\| 0.825 \|1.100\| 1.066 \| 0.821 \| 1.191 \| As can be seen, and perhaps surprising to some, the multivariate forecasts are typically _worse_ than the univariate ones, the reason being the difficulty in estimating the cross-series correlations/relationships. The additional variance added by the estimates often harms the resulting forecasts or the model learns spurious correlations. We refer to [this paper](https://openreview.net/forum?id=GpW327gxLTF) for further reading. Multivariate models tend to work well when trained on a lot of data. So the vanilla Transformer still performs best here! In the future, we hope to better benchmark these models in a central place to ease reproducing the results of several papers. Stay tuned for more! ## Resources We recommend to check out the [Informer docs](https://huggingface.co/docs/transformers/main/en/model_doc/informer) and the [example notebook](https://github.com/huggingface/notebooks/blob/main/examples/multivariate_informer.ipynb) linked at the top of this blog post.
huggingface/pytorch-image-models/blob/main/docs/models/se-resnet.md	SE-ResNet SE ResNet is a variant of a [ResNet](https://www.paperswithcode.com/method/resnet) that employs [squeeze-and-excitation blocks](https://paperswithcode.com/method/squeeze-and-excitation-block) to enable the network to perform dynamic channel-wise feature recalibration. ## How do I use this model on an image? To load a pretrained model: ```python import timm model = timm.create_model('seresnet152d', pretrained=True) model.eval() ``` To load and preprocess the image: ```python import urllib from PIL import Image from timm.data import resolve_data_config from timm.data.transforms_factory import create_transform config = resolve_data_config({}, model=model) transform = create_transform(**config) url, filename = ("https://github.com/pytorch/hub/raw/master/images/dog.jpg", "dog.jpg") urllib.request.urlretrieve(url, filename) img = Image.open(filename).convert('RGB') tensor = transform(img).unsqueeze(0) # transform and add batch dimension ``` To get the model predictions: ```python import torch with torch.no_grad(): out = model(tensor) probabilities = torch.nn.functional.softmax(out[0], dim=0) print(probabilities.shape) # prints: torch.Size([1000]) ``` To get the top-5 predictions class names: ```python # Get imagenet class mappings url, filename = ("https://raw.githubusercontent.com/pytorch/hub/master/imagenet_classes.txt", "imagenet_classes.txt") urllib.request.urlretrieve(url, filename) with open("imagenet_classes.txt", "r") as f: categories = [s.strip() for s in f.readlines()] # Print top categories per image top5_prob, top5_catid = torch.topk(probabilities, 5) for i in range(top5_prob.size(0)): print(categories[top5_catid[i]], top5_prob[i].item()) # prints class names and probabilities like: # [('Samoyed', 0.6425196528434753), ('Pomeranian', 0.04062102362513542), ('keeshond', 0.03186424449086189), ('white wolf', 0.01739676296710968), ('Eskimo dog', 0.011717947199940681)] ``` Replace the model name with the variant you want to use, e.g. `seresnet152d`. You can find the IDs in the model summaries at the top of this page. To extract image features with this model, follow the [timm feature extraction examples](https://rwightman.github.io/pytorch-image-models/feature_extraction/), just change the name of the model you want to use. ## How do I finetune this model? You can finetune any of the pre-trained models just by changing the classifier (the last layer). ```python model = timm.create_model('seresnet152d', pretrained=True, num_classes=NUM_FINETUNE_CLASSES) ``` To finetune on your own dataset, you have to write a training loop or adapt [timm's training script](https://github.com/rwightman/pytorch-image-models/blob/master/train.py) to use your dataset. ## How do I train this model? You can follow the [timm recipe scripts](https://rwightman.github.io/pytorch-image-models/scripts/) for training a new model afresh. ## Citation ```BibTeX @misc{hu2019squeezeandexcitation, title={Squeeze-and-Excitation Networks}, author={Jie Hu and Li Shen and Samuel Albanie and Gang Sun and Enhua Wu}, year={2019}, eprint={1709.01507}, archivePrefix={arXiv}, primaryClass={cs.CV} } ``` <!-- Type: model-index Collections: - Name: SE ResNet Paper: Title: Squeeze-and-Excitation Networks URL: https://paperswithcode.com/paper/squeeze-and-excitation-networks Models: - Name: seresnet152d In Collection: SE ResNet Metadata: FLOPs: 20161904304 Parameters: 66840000 File Size: 268144497 Architecture: - 1x1 Convolution - Batch Normalization - Bottleneck Residual Block - Convolution - Global Average Pooling - Max Pooling - ReLU - Residual Block - Residual Connection - Softmax - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA Titan X GPUs ID: seresnet152d LR: 0.6 Epochs: 100 Layers: 152 Dropout: 0.2 Crop Pct: '0.94' Momentum: 0.9 Batch Size: 1024 Image Size: '256' Interpolation: bicubic Code: https://github.com/rwightman/pytorch-image-models/blob/a7f95818e44b281137503bcf4b3e3e94d8ffa52f/timm/models/resnet.py#L1206 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-weights/seresnet152d_ra2-04464dd2.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 83.74% Top 5 Accuracy: 96.77% - Name: seresnet50 In Collection: SE ResNet Metadata: FLOPs: 5285062320 Parameters: 28090000 File Size: 112621903 Architecture: - 1x1 Convolution - Batch Normalization - Bottleneck Residual Block - Convolution - Global Average Pooling - Max Pooling - ReLU - Residual Block - Residual Connection - Softmax - Squeeze-and-Excitation Block Tasks: - Image Classification Training Techniques: - Label Smoothing - SGD with Momentum - Weight Decay Training Data: - ImageNet Training Resources: 8x NVIDIA Titan X GPUs ID: seresnet50 LR: 0.6 Epochs: 100 Layers: 50 Dropout: 0.2 Crop Pct: '0.875' Momentum: 0.9 Batch Size: 1024 Image Size: '224' Interpolation: bicubic Code: https://github.com/rwightman/pytorch-image-models/blob/a7f95818e44b281137503bcf4b3e3e94d8ffa52f/timm/models/resnet.py#L1180 Weights: https://github.com/rwightman/pytorch-image-models/releases/download/v0.1-weights/seresnet50_ra_224-8efdb4bb.pth Results: - Task: Image Classification Dataset: ImageNet Metrics: Top 1 Accuracy: 80.26% Top 5 Accuracy: 95.07% -->
huggingface/diffusers/blob/main/docs/source/en/api/pipelines/kandinsky_v22.md	!--Copyright 2023 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # Kandinsky 2.2 Kandinsky 2.2 is created by [Arseniy Shakhmatov](https://github.com/cene555), [Anton Razzhigaev](https://github.com/razzant), [Aleksandr Nikolich](https://github.com/AlexWortega), [Vladimir Arkhipkin](https://github.com/oriBetelgeuse), [Igor Pavlov](https://github.com/boomb0om), [Andrey Kuznetsov](https://github.com/kuznetsoffandrey), and [Denis Dimitrov](https://github.com/denndimitrov). The description from it's GitHub page is: Kandinsky 2.2 brings substantial improvements upon its predecessor, Kandinsky 2.1, by introducing a new, more powerful image encoder - CLIP-ViT-G and the ControlNet support. The switch to CLIP-ViT-G as the image encoder significantly increases the model's capability to generate more aesthetic pictures and better understand text, thus enhancing the model's overall performance. The addition of the ControlNet mechanism allows the model to effectively control the process of generating images. This leads to more accurate and visually appealing outputs and opens new possibilities for text-guided image manipulation. The original codebase can be found at [ai-forever/Kandinsky-2](https://github.com/ai-forever/Kandinsky-2). <Tip> Check out the [Kandinsky Community](https://huggingface.co/kandinsky-community) organization on the Hub for the official model checkpoints for tasks like text-to-image, image-to-image, and inpainting. </Tip> <Tip> Make sure to check out the schedulers [guide](../../using-diffusers/schedulers) to learn how to explore the tradeoff between scheduler speed and quality, and see the [reuse components across pipelines](../../using-diffusers/loading#reuse-components-across-pipelines) section to learn how to efficiently load the same components into multiple pipelines. </Tip> ## KandinskyV22PriorPipeline [[autodoc]] KandinskyV22PriorPipeline - all - __call__ - interpolate ## KandinskyV22Pipeline [[autodoc]] KandinskyV22Pipeline - all - __call__ ## KandinskyV22CombinedPipeline [[autodoc]] KandinskyV22CombinedPipeline - all - __call__ ## KandinskyV22ControlnetPipeline [[autodoc]] KandinskyV22ControlnetPipeline - all - __call__ ## KandinskyV22PriorEmb2EmbPipeline [[autodoc]] KandinskyV22PriorEmb2EmbPipeline - all - __call__ - interpolate ## KandinskyV22Img2ImgPipeline [[autodoc]] KandinskyV22Img2ImgPipeline - all - __call__ ## KandinskyV22Img2ImgCombinedPipeline [[autodoc]] KandinskyV22Img2ImgCombinedPipeline - all - __call__ ## KandinskyV22ControlnetImg2ImgPipeline [[autodoc]] KandinskyV22ControlnetImg2ImgPipeline - all - __call__ ## KandinskyV22InpaintPipeline [[autodoc]] KandinskyV22InpaintPipeline - all - __call__ ## KandinskyV22InpaintCombinedPipeline [[autodoc]] KandinskyV22InpaintCombinedPipeline - all - __call__
huggingface/blog/blob/main/huggy-lingo.md	-- title: "Huggy Lingo: Using Machine Learning to Improve Language Metadata on the Hugging Face Hub" thumbnail: blog/assets/156_huggylingo/Huggy_Lingo.png authors: - user: davanstrien --- ## Huggy Lingo: Using Machine Learning to Improve Language Metadata on the Hugging Face Hub tl;dr: We're using machine learning to detect the language of Hub datasets with no language metadata, and [librarian-bots](https://huggingface.co/librarian-bots) to make pull requests to add this metadata. The Hugging Face Hub has become the repository where the community shares machine learning models, datasets, and applications. As the number of datasets grows, metadata becomes increasingly important as a tool for finding the right resource for your use case. In this blog post, I'm excited to share some early experiments which seek to use machine learning to improve the metadata for datasets hosted on the Hugging Face Hub. ### Language Metadata for Datasets on the Hub There are currently ~50K public datasets on the Hugging Face Hub. Metadata about the language used in a dataset can be specified using a [YAML](https://en.wikipedia.org/wiki/YAML) field at the top of the [dataset card](https://huggingface.co/docs/datasets/upload_dataset#create-a-dataset-card). All public datasets specify 1,716 unique languages via a language tag in their metadata. Note that some of them will be the result of languages being specified in different ways i.e. `en` vs `eng` vs `english` vs `English`. For example, the [IMDB dataset](https://huggingface.co/datasets/imdb) specifies `en` in the YAML metadata (indicating English): <p align="center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/huggy_lingo/lang_metadata.png" alt="Screenshot of YAML metadata"><br> <em>Section of the YAML metadata for the IMDB dataset</em> </p> It is perhaps unsurprising that English is by far the most common language for datasets on the Hub, with around 19% of datasets on the Hub listing their language as `en` (not including any variations of `en`, so the actual percentage is likely much higher). <p align="center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/huggy_lingo/lang_freq.png" alt="Distribution of language tags"><br> <em>The frequency and percentage frequency for datasets on the Hugging Face Hub</em> </p> What does the distribution of languages look like if we exclude English? We can see that there is a grouping of a few dominant languages and after that there is a pretty smooth fall in the frequencies at which languages appear. <p align="center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/huggy_lingo/lang_freq_distribution.png" alt="Distribution of language tags"><br> <em>Distribution of language tags for datasets on the hub excluding English.</em> </p> However, there is a major caveat to this. Most datasets (around 87%) do not specify the language used; only approximately 13% of datasets include language information in their metadata. <p align="center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/huggy_lingo/has_lang_info_bar.png" alt="Barchart"><br> <em>The percent of datasets which have language metadata. True indicates language metadata is specified, False means no language data is listed. No card data means that there isn't any metadata or it couldn't be loaded by the `huggingface_hub` Python library.</em> </p> #### Why is Language Metadata Important? Language metadata can be a vital tool for finding relevant datasets. The Hugging Face Hub allows you to filter datasets by language. For example, if we want to find datasets with Dutch language we can use [a filter](https://huggingface.co/datasets?language=language:nl&sort=trending) on the Hub to include only datasets with Dutch data. Currently this filter returns 184 datasets. However, there are datasets on the Hub which include Dutch but don't specify this in the metadata. These datasets become more difficult to find, particularly as the number of datasets on the Hub grows. Many people want to be able to find datasets for a particular language. One of the major barriers to training good open source LLMs for a particular language is a lack of high quality training data. If we switch to the task of finding relevant machine learning models, knowing what languages were included in the training data for a model can help us find models for the language we are interested in. This relies on the dataset specifying this information. Finally, knowing what languages are represented on the Hub (and which are not), helps us understand the language biases of the Hub and helps inform community efforts to address gaps in particular languages. ### Predicting the Languages of Datasets Using Machine Learning We’ve already seen that many of the datasets on the Hugging Face Hub haven’t included metadata for the language used. However, since these datasets are already shared openly, perhaps we can look at the dataset and try to identify the language using machine learning. #### Getting the Data One way we could access some examples from a dataset is by using the datasets library to download the datasets i.e. ```python from datasets import load_dataset dataset = load_dataset("biglam/on_the_books") ``` However, for some of the datasets on the Hub, we might be keen not to download the whole dataset. We could instead try to load a sample of the dataset. However, depending on how the dataset was created, we might still end up downloading more data than we’d need onto the machine we’re working on. Luckily, many datasets on the Hub are available via the [datasets server](https://huggingface.co/docs/datasets-server/index). The datasets server is an API that allows us to access datasets hosted on the Hub without downloading the dataset locally. The Datasets Server powers the Datasets Viewer preview you will see for many datasets hosted on the Hub. For this first experiment with predicting language for datasets, we define a list of column names and data types likely to contain textual content i.e. `text` or `prompt` column names and `string` features are likely to be relevant `image` is not. This means we can avoid predicting the language for datasets where language information is less relevant, for example, image classification datasets. We use the Datasets Server to get 20 rows of text data to pass to a machine learning model (we could modify this to take more or fewer examples from the dataset). This approach means that for the majority of datasets on the Hub we can quickly request the contents of likely text columns for the first 20 rows in a dataset. #### Predicting the Language of a Dataset Once we have some examples of text from a dataset, we need to predict the language. There are various options here, but for this work, we used the [facebook/fasttext-language-identification](https://huggingface.co/facebook/fasttext-language-identification) fastText model created by [Meta](https://huggingface.co/facebook) as part of the [No Language Left Behind](https://ai.facebook.com/research/no-language-left-behind/) work. This model can detect 217 languages which will likely represent the majority of languages for datasets hosted on the Hub. We pass 20 examples to the model representing rows from a dataset. This results in 20 individual language predictions (one per row) for each dataset. Once we have these predictions, we do some additional filtering to determine if we will accept the predictions as a metadata suggestion. This roughly consists of: - Grouping the predictions for each dataset by language: some datasets return predictions for multiple languages. We group these predictions by the language predicted i.e. if a dataset returns predictions for English and Dutch, we group the English and Dutch predictions together. - For datasets with multiple languages predicted, we count how many predictions we have for each language. If a language is predicted less than 20% of the time, we discard this prediction. i.e. if we have 18 predictions for English and only 2 for Dutch we discard the Dutch predictions. - We calculate the mean score for all predictions for a language. If the mean score associated with a languages prediction is below 80% we discard this prediction. <p align="center"> <img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/huggy_lingo/prediction-flow.png" alt="Prediction workflow"><br> <em>Diagram showing how predictions are handled.</em> </p> Once we’ve done this filtering, we have a further step of deciding how to use these predictions. The fastText language prediction model returns predictions as an [ISO 639-3](https://en.wikipedia.org/wiki/ISO_639-3) code (an international standard for language codes) along with a script type. i.e. `kor_Hang` is the ISO 693-3 language code for Korean (kor) + Hangul script (Hang) a [ISO 15924](https://en.wikipedia.org/wiki/ISO_15924) code representing the script of a language. We discard the script information since this isn't currently captured consistently as metadata on the Hub and, where possible, we convert the language prediction returned by the model from [ISO 639-3](https://en.wikipedia.org/wiki/ISO_639-3) to [ISO 639-1](https://en.wikipedia.org/wiki/ISO_639-1) language codes. This is largely done because these language codes have better support in the Hub UI for navigating datasets. For some ISO 639-3 codes, there is no ISO 639-1 equivalent. For these cases we manually specify a mapping if we deem it to make sense, for example Standard Arabic (`arb`) is mapped to Arabic (`ar`). Where an obvious mapping is not possible, we currently don't suggest metadata for this dataset. In future iterations of this work we may take a different approach. It is important to recognise this approach does come with downsides, since it reduces the diversity of languages which might be suggested and also relies on subjective judgments about what languages can be mapped to others. But the process doesn't stop here. After all, what use is predicting the language of the datasets if we can't share that information with the rest of the community? ### Using Librarian-Bot to Update Metadata To ensure this valuable language metadata is incorporated back into the Hub, we turn to Librarian-Bot! Librarian-Bot takes the language predictions generated by Meta's [facebook/fasttext-language-identification](https://huggingface.co/facebook/fasttext-language-identification) fastText model and opens pull requests to add this information to the metadata of each respective dataset. This system not only updates the datasets with language information, but also does it swiftly and efficiently, without requiring manual work from humans. If the owner of a repo decided to approve and merge the pull request, then the language metadata becomes available for all users, significantly enhancing the usability of the Hugging Face Hub. You can keep track of what the librarian-bot is doing [here](https://huggingface.co/librarian-bot/activity/community)! #### Next Steps As the number of datasets on the Hub grows, metadata becomes increasingly important. Language metadata, in particular, can be incredibly valuable for identifying the correct dataset for your use case. With the assistance of the Datasets Server and the [Librarian-Bots](https://huggingface.co/librarian-bots), we can update our dataset metadata at a scale that wouldn't be possible manually. As a result, we're enriching the Hub and making it an even more powerful tool for data scientists, linguists, and AI enthusiasts around the world. As the machine learning librarian at Hugging Face, I continue exploring opportunities for automatic metadata enrichment for machine learning artefacts hosted on the Hub. Feel free to reach out (daniel at thiswebsite dot co) if you have ideas or want to collaborate on this effort!
huggingface/transformers/blob/main/docs/source/en/main_classes/trainer.md	!--Copyright 2020 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ⚠️ Note that this file is in Markdown but contain specific syntax for our doc-builder (similar to MDX) that may not be rendered properly in your Markdown viewer. --> # Trainer The [`Trainer`] class provides an API for feature-complete training in PyTorch, and it supports distributed training on multiple GPUs/TPUs, mixed precision for [NVIDIA GPUs](https://nvidia.github.io/apex/), [AMD GPUs](https://rocm.docs.amd.com/en/latest/rocm.html), and [`torch.amp`](https://pytorch.org/docs/stable/amp.html) for PyTorch. [`Trainer`] goes hand-in-hand with the [`TrainingArguments`] class, which offers a wide range of options to customize how a model is trained. Together, these two classes provide a complete training API. [`Seq2SeqTrainer`] and [`Seq2SeqTrainingArguments`] inherit from the [`Trainer`] and [`TrainingArgument`] classes and they're adapted for training models for sequence-to-sequence tasks such as summarization or translation. <Tip warning={true}> The [`Trainer`] class is optimized for 🤗 Transformers models and can have surprising behaviors when used with other models. When using it with your own model, make sure: - your model always return tuples or subclasses of [`~utils.ModelOutput`] - your model can compute the loss if a `labels` argument is provided and that loss is returned as the first element of the tuple (if your model returns tuples) - your model can accept multiple label arguments (use `label_names` in [`TrainingArguments`] to indicate their name to the [`Trainer`]) but none of them should be named `"label"` </Tip> ## Trainer[[api-reference]] [[autodoc]] Trainer - all ## Seq2SeqTrainer [[autodoc]] Seq2SeqTrainer - evaluate - predict ## TrainingArguments [[autodoc]] TrainingArguments - all ## Seq2SeqTrainingArguments [[autodoc]] Seq2SeqTrainingArguments - all
gradio-app/gradio/blob/main/demo/upload_button_component_events/run.ipynb	Gradio Demo: upload_button_component_events ``` !pip install -q gradio ``` ``` import gradio as gr with gr.Blocks() as demo: with gr.Row(): with gr.Column(): upload_btn = gr.UploadButton(label="Upload Single File", file_count="single") with gr.Column(): output_file_1 = gr.File(label="Upload Single File Output", file_count="single") num_load_btn_1 = gr.Number(label="# Load Upload Single File", value=0) output_click_1 = gr.Number(label="# Click Upload Single File Output", value=0) upload_btn.upload(lambda s,n: (s, n + 1), [upload_btn, num_load_btn_1], [output_file_1, num_load_btn_1]) upload_btn.click(lambda n: (n + 1), output_click_1, [output_click_1]) with gr.Row(): with gr.Column(): upload_btn_multiple = gr.UploadButton(label="Upload Multiple Files", file_count="multiple") with gr.Column(): output_file_2 = gr.File(label="Upload Multiple Files Output", file_count="multiple") num_load_btn_2 = gr.Number(label="# Load Upload Multiple Files", value=0) output_click_2 = gr.Number(label="# Click Upload Multiple Files Output", value=0) upload_btn_multiple.upload(lambda s,n: (s, n + 1), [upload_btn_multiple, num_load_btn_2], [output_file_2, num_load_btn_2]) upload_btn_multiple.click(lambda n: (n + 1), output_click_2, [output_click_2]) if __name__ == "__main__": demo.launch() ```
huggingface/course/blob/main/chapters/en/chapter6/4.mdx	Normalization and pre-tokenization[[normalization-and-pre-tokenization]] <CourseFloatingBanner chapter={6} classNames="absolute z-10 right-0 top-0" notebooks={[ {label: "Google Colab", value: "https://colab.research.google.com/github/huggingface/notebooks/blob/master/course/en/chapter6/section4.ipynb"}, {label: "Aws Studio", value: "https://studiolab.sagemaker.aws/import/github/huggingface/notebooks/blob/master/course/en/chapter6/section4.ipynb"}, ]} /> Before we dive more deeply into the three most common subword tokenization algorithms used with Transformer models (Byte-Pair Encoding [BPE], WordPiece, and Unigram), we'll first take a look at the preprocessing that each tokenizer applies to text. Here's a high-level overview of the steps in the tokenization pipeline: <div class="flex justify-center"> <img class="block dark:hidden" src="https://huggingface.co/datasets/huggingface-course/documentation-images/resolve/main/en/chapter6/tokenization_pipeline.svg" alt="The tokenization pipeline."> <img class="hidden dark:block" src="https://huggingface.co/datasets/huggingface-course/documentation-images/resolve/main/en/chapter6/tokenization_pipeline-dark.svg" alt="The tokenization pipeline."> </div> Before splitting a text into subtokens (according to its model), the tokenizer performs two steps: _normalization_ and _pre-tokenization_. ## Normalization[[normalization]] <Youtube id="4IIC2jI9CaU"/> The normalization step involves some general cleanup, such as removing needless whitespace, lowercasing, and/or removing accents. If you're familiar with [Unicode normalization](http://www.unicode.org/reports/tr15/) (such as NFC or NFKC), this is also something the tokenizer may apply. The 🤗 Transformers `tokenizer` has an attribute called `backend_tokenizer` that provides access to the underlying tokenizer from the 🤗 Tokenizers library: ```py from transformers import AutoTokenizer tokenizer = AutoTokenizer.from_pretrained("bert-base-uncased") print(type(tokenizer.backend_tokenizer)) ``` ```python out <class 'tokenizers.Tokenizer'> ``` The `normalizer` attribute of the `tokenizer` object has a `normalize_str()` method that we can use to see how the normalization is performed: ```py print(tokenizer.backend_tokenizer.normalizer.normalize_str("Héllò hôw are ü?")) ``` ```python out 'hello how are u?' ``` In this example, since we picked the `bert-base-uncased` checkpoint, the normalization applied lowercasing and removed the accents. <Tip> ✏️ Try it out! Load a tokenizer from the `bert-base-cased` checkpoint and pass the same example to it. What are the main differences you can see between the cased and uncased versions of the tokenizer? </Tip> ## Pre-tokenization[[pre-tokenization]] <Youtube id="grlLV8AIXug"/> As we will see in the next sections, a tokenizer cannot be trained on raw text alone. Instead, we first need to split the texts into small entities, like words. That's where the pre-tokenization step comes in. As we saw in [Chapter 2](/course/chapter2), a word-based tokenizer can simply split a raw text into words on whitespace and punctuation. Those words will be the boundaries of the subtokens the tokenizer can learn during its training. To see how a fast tokenizer performs pre-tokenization, we can use the `pre_tokenize_str()` method of the `pre_tokenizer` attribute of the `tokenizer` object: ```py tokenizer.backend_tokenizer.pre_tokenizer.pre_tokenize_str("Hello, how are you?") ``` ```python out [('Hello', (0, 5)), (',', (5, 6)), ('how', (7, 10)), ('are', (11, 14)), ('you', (16, 19)), ('?', (19, 20))] ``` Notice how the tokenizer is already keeping track of the offsets, which is how it can give us the offset mapping we used in the previous section. Here the tokenizer ignores the two spaces and replaces them with just one, but the offset jumps between `are` and `you` to account for that. Since we're using a BERT tokenizer, the pre-tokenization involves splitting on whitespace and punctuation. Other tokenizers can have different rules for this step. For example, if we use the GPT-2 tokenizer: ```py tokenizer = AutoTokenizer.from_pretrained("gpt2") tokenizer.backend_tokenizer.pre_tokenizer.pre_tokenize_str("Hello, how are you?") ``` it will split on whitespace and punctuation as well, but it will keep the spaces and replace them with a `Ġ` symbol, enabling it to recover the original spaces if we decode the tokens: ```python out [('Hello', (0, 5)), (',', (5, 6)), ('Ġhow', (6, 10)), ('Ġare', (10, 14)), ('Ġ', (14, 15)), ('Ġyou', (15, 19)), ('?', (19, 20))] ``` Also note that unlike the BERT tokenizer, this tokenizer does not ignore the double space. For a last example, let's have a look at the T5 tokenizer, which is based on the SentencePiece algorithm: ```py tokenizer = AutoTokenizer.from_pretrained("t5-small") tokenizer.backend_tokenizer.pre_tokenizer.pre_tokenize_str("Hello, how are you?") ``` ```python out [('▁Hello,', (0, 6)), ('▁how', (7, 10)), ('▁are', (11, 14)), ('▁you?', (16, 20))] ``` Like the GPT-2 tokenizer, this one keeps spaces and replaces them with a specific token (`_`), but the T5 tokenizer only splits on whitespace, not punctuation. Also note that it added a space by default at the beginning of the sentence (before `Hello`) and ignored the double space between `are` and `you`. Now that we've seen a little of how some different tokenizers process text, we can start to explore the underlying algorithms themselves. We'll begin with a quick look at the broadly widely applicable SentencePiece; then, over the next three sections, we'll examine how the three main algorithms used for subword tokenization work. ## SentencePiece[[sentencepiece]] [SentencePiece](https://github.com/google/sentencepiece) is a tokenization algorithm for the preprocessing of text that you can use with any of the models we will see in the next three sections. It considers the text as a sequence of Unicode characters, and replaces spaces with a special character, `▁`. Used in conjunction with the Unigram algorithm (see [section 7](/course/chapter7/7)), it doesn't even require a pre-tokenization step, which is very useful for languages where the space character is not used (like Chinese or Japanese). The other main feature of SentencePiece is reversible tokenization: since there is no special treatment of spaces, decoding the tokens is done simply by concatenating them and replacing the `_`s with spaces -- this results in the normalized text. As we saw earlier, the BERT tokenizer removes repeating spaces, so its tokenization is not reversible. ## Algorithm overview[[algorithm-overview]] In the following sections, we'll dive into the three main subword tokenization algorithms: BPE (used by GPT-2 and others), WordPiece (used for example by BERT), and Unigram (used by T5 and others). Before we get started, here's a quick overview of how they each work. Don't hesitate to come back to this table after reading each of the next sections if it doesn't make sense to you yet. Model \| BPE \| WordPiece \| Unigram :----:\|:---:\|:---------:\|:------: Training \| Starts from a small vocabulary and learns rules to merge tokens \| Starts from a small vocabulary and learns rules to merge tokens \| Starts from a large vocabulary and learns rules to remove tokens Training step \| Merges the tokens corresponding to the most common pair \| Merges the tokens corresponding to the pair with the best score based on the frequency of the pair, privileging pairs where each individual token is less frequent \| Removes all the tokens in the vocabulary that will minimize the loss computed on the whole corpus Learns \| Merge rules and a vocabulary \| Just a vocabulary \| A vocabulary with a score for each token Encoding \| Splits a word into characters and applies the merges learned during training \| Finds the longest subword starting from the beginning that is in the vocabulary, then does the same for the rest of the word \| Finds the most likely split into tokens, using the scores learned during training Now let's dive into BPE!
huggingface/simulate/blob/main/docs/source/howto/map_pools.mdx	!--Copyright 2022 The HuggingFace Team. All rights reserved. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # Map pools Map pools allow you to instantiate multiple versions of your environment on the backend, the enables higher throughput with parallelization of interaction in simulations and embodied environments. Using map pools is simple with 🤗 Simulate. First define a function that will generate your environment, we call each environment instance a "map". ``` def generate_map(index): root = sm.Asset(name=f"root_{index}") root += sm.Box( name=f"floor_{index}", position=[0, -0.05, 0], scaling=[10, 0.1, 10], material=sm.Material.BLUE, with_collider=True, ) root += sm.Box( name=f"wall1_{index}", position=[-1, 0.5, 0], scaling=[0.1, 1, 5.1], material=sm.Material.GRAY75, with_collider=True, ) root += sm.Box( name=f"wall2_{index}", position=[1, 0.5, 0], scaling=[0.1, 1, 5.1], material=sm.Material.GRAY75, with_collider=True, ) root += sm.Box( name=f"wall3_{index}", position=[0, 0.5, 4.5], scaling=[5.9, 1, 0.1], material=sm.Material.GRAY75, with_collider=True, ) # add actors, sensors, reward functions etc ... return root ``` You can then provide the `generate_map` method as an argument to the `sm.ParallelRLEnv` class, which will instantiate `n_maps`. Training with a subset of the maps is possible using the `n_show` option. At each environment reset, it cycles through to the next map. [[autodoc]] ParallelRLEnv

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